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Comprehensive characterization of branched polymers
Edam, R.
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Download date: 27 Jun 2020
Comprehensive Characterizationof Branched Polymers
Rob EdamC
omprehensive C
haracterization of Branched Polymers Rob Edam
edam_omslag_FINAL.indd 1 26-12-2012 12:50:08
Comprehensive Characterization of Branched Polymers
Comprehensive Characterization of Branched Polymers
ACADEMISCH PROEFSCHRIFT
ter verkrijging van de graad van doctor
aan de Universiteit van Amsterdam
op gezag van de Rector Magnificus
prof. dr. D.C. van den Boom
ten overstaan van een door het college voor promoties ingestelde
commissie, in het openbaar te verdedigen in de Agnietenkapel
op donderdag 21 februari 2013, te 14:00 uur
door
Rob Edam
geboren te Avenhorn
Promotor: Prof. Dr. Ir. P.J. Schoenmakers
Overige leden: Prof. Dr. Ir. J.G.M. Janssen
Prof. Dr. Sj. van der Wal
Prof. Dr. A.M. van Herk
Dr. W.Th. Kok
Dr. W. Radke
Dr. F.A. van Damme
Faculteit der Natuurwetenschappen, Wiskunde en Informatica
Comprehensive characterization of branched polymers; R. Edam
Printed by Universal Press, Veenendaal, The Netherlands
This research is part of the research program of the Dutch Polymer Institute (DPI), project #509.
ISBN 978-90-9027351-8
Contents
Chapter 1: General introduction ....................................................................................... 9
1.1 An introduction to polymers ......................................................................... 10 1.1.1 Macromolecules ........................................................................................ 11 1.1.2 Early characterization of polymers ........................................................... 11 1.1.3 Polymer structure ...................................................................................... 13 1.1.4 Branched polymers ................................................................................... 15
1.2 Characterization and separation of branched polymers ................................. 19 1.2.1 TREF, Crystaf and DSC ........................................................................... 19 1.2.2 Rheology ................................................................................................... 20 1.2.3 Spectroscopy ............................................................................................. 23
1.3 Size-exclusion chromatography with selective detection .............................. 25 1.3.1 SEC separation of branched polymers ...................................................... 25 1.3.2 SEC with on-line (micro-)viscometry ....................................................... 27 1.3.3 SEC with multi-angle laser-light-scattering detection .............................. 32 1.3.4 Application and challenges of existing methodology ............................... 33
1.4 Scope of the thesis......................................................................................... 36
Chapter 2: Hydrodynamic chromatography of macromolecules using polymer monolithic columns ........................................................................................................ 41
2.1 Introduction ................................................................................................... 42
2.2 Experimental ................................................................................................. 45 2.2.1 Chemicals and materials ........................................................................... 45 2.2.2 Instrumentation ......................................................................................... 46 2.2.3 Column preparation .................................................................................. 46
2.3 Results and discussion .................................................................................. 47 2.3.1 Preparation and characterization of monoliths for HDC........................... 47 2.3.2 HDC separation of polymers .................................................................... 51 2.3.3 Flow-rate dependence in polymer separations .......................................... 55
2.4 Conclusions ................................................................................................... 61
2.5 Appendix ....................................................................................................... 62 2.5.1 Mercury intrusion and extrusion ............................................................... 62 2.5.2 SEC separation of alkylbenzenes and solvents on monolith ..................... 64 2.5.3 Deborah numbers ...................................................................................... 66
Chapter 3: Branched-Polymer Separations using Comprehensive Two-Dimensional Molecular-Topology Fractionation × Size-Exclusion Chromatography......................... 69
3.1 Introduction ................................................................................................... 70
3.2 Experimental ................................................................................................. 73 3.2.1 Samples and materials .............................................................................. 73 3.2.2 Instrumentation and methods .................................................................... 74
3.3 Results and discussion .................................................................................. 75 3.3.1 Calibration curve for molecular-topology-fractionation column .............. 75 3.3.2 Branched-polymer separations ................................................................. 77
3.4 Conclusions ................................................................................................... 83
3.5 Appendix ....................................................................................................... 84
Chapter 4: Branched Polymers Characterized by Comprehensive Two-Dimensional Separations with fully Orthogonal Mechanisms ............................................................. 89
4.1 Introduction ................................................................................................... 90
4.2 Theory ........................................................................................................... 92 4.2.1 Separation techniques based on size ......................................................... 92 4.2.2 Deformation of polymers in solution ........................................................ 93 4.2.3 Reptation ................................................................................................... 96 4.2.4 Calibration curves and separation of deformed-polymers ........................ 98
4.3 Experimental ............................................................................................... 101 4.3.1 Chemicals and materials ......................................................................... 101 4.3.2 Instrumentation and operating conditions ............................................... 102 4.3.3 Columns and experimental conditions .................................................... 103
4.4 Results and discussion ................................................................................ 104 4.4.1 Flow-rate effect for columns with different pore size ............................. 104 4.4.2 Branched-polymer separations ............................................................... 108 4.4.3 Selectivity for branched polymers .......................................................... 110 4.4.4 Effect of flow rate on migration of branched polymers .......................... 113 4.4.5 Effect of temperature on migration of polymers in MTF ....................... 115
4.5 Conclusions ................................................................................................. 115
4.6 Appendix ..................................................................................................... 117 4.6.1 Comprehensive HDC×SEC experiment ................................................. 117 4.6.2 Second-dimension calibration for MTF×SEC ........................................ 118 4.6.3 Flow-rate effect in MTF×SEC ................................................................ 118 4.6.4 MTF×SEC at orthogonal conditions ....................................................... 121
4.6.5 MTF×SEC-UV/MALLS on long-chain-branched polystyrene .............. 123 4.6.6 Selectivity in MTF as a function of flow rate ......................................... 124 4.6.7 Effect of temperature on MTF×SEC separations .................................... 126
Chapter 5: Z-RAFT Star Polymerization of Styrene: Comprehensive Characterization using Size-Exclusion Chromatography ........................................................................ 131
5.1 Introduction ................................................................................................. 132
5.2 Experimental Section .................................................................................. 134 5.2.1 Chemicals ............................................................................................... 134 5.2.2 Instrumentation ....................................................................................... 134 5.2.3 RAFT agent synthesis ............................................................................. 137 5.2.4 Polymerizations ...................................................................................... 140
5.3 Results and Discussion ................................................................................ 141
5.4 Conclusion .................................................................................................. 159
Summary ...................................................................................................................... 163
Samenvatting ................................................................................................................ 167
Acknowledgements ...................................................................................................... 171
Publications .................................................................................................................. 175
9
Chapter 1: General introduction
Abstract
In this chapter the objective of the PhD study is introduced. Theory, concepts,
instruments and technologies for the analysis of branched polymers are presented. Also
different ways to achieve branching in the polymer structure and the impact on the
polymer properties are reviewed.
Chapter 1
10
1.1 An introduction to polymers
The ability to characterize polymers has been of critical importance for progress in the
field of macromolecular chemistry. It allows one to understand how a material behaves,
how it was made and how to make it better. Continuous development of polymers has
resulted in materials that are highly optimized and in the rapid proliferation of polymers
into everyday life of the 21st century. Polymers with a very wide range of physical
properties can now be produced, often at low cost. They cover an incredible application
space that continues to expand. The traditional applications, such as simple molded
items, fibers and disposable items, are still present today. More recent is the
introduction of functionalized and smart materials. Modification of the polymers can be
used to increase durability, conduct electricity or even provide self-healing properties.
These specialty materials provide higher added value and are, therefore, of great interest
for production in a commercial setting. An overview of common synthetic polymers and
their applications is presented in Table 1.
Table 1. Synthetic polymers and their application in traditional and functional materials
Material Application example
Polystyrene Coffee cups Envelope window film Insulation foam
Polyvinylchloride Piping Window lining Wire & cable insulation
Polyethylene Bags Garbage containers Artificial ice-skating floors Fishing lines Joint replacement
Polypropylene Automotive bumpers Heat-resistant food packaging
Polyester Soda bottles (polyethylene terephthalate) Clothing / fibers
Polyamide Nylon stockings
Introduction
11
1.1.1 Macromolecules
A landmark in history has been the discovery of covalent bonding between smaller
molecules (monomers) [1] to form polymers or ‘macromolecules’ of high molar mass
[2]. These concepts were introduced in the 1920’s by Hermann Staudinger, for which he
was awarded the Nobel Prize in 1953 [3].The term ‘polymerization’ was introduced
already in 1863 by Berthelot, who recognized the ability of unsaturated compounds to
react with themselves and yield high-boiling oligomers [4]. His work did not comprise
the formation of higher polymers. The idea of higher polymers was opposed by the
ruling misconception from crystallography that molecules had to fit in a single unit cell.
It was not until the late 1920’s that the concept of higher polymers became accepted.
Before this time the mechanism of polymerization was not well understood and was
attributed to self-assembly of small molecules by colloidal interactions [5]. Poor
understanding of molecular structure did not withhold Baekeland from producing the
first fully synthetic polymer already in 1907 [6,7].
1.1.2 Early characterization of polymers
The difficulty in obtaining experimental proof for higher polymers was one of the
reasons that it took a long time for macromolecules to become accepted. Many methods
for determining the molar mass of macromolecules were published in the years
following the introduction of the macromolecular concept [8]. This is not strange,
considering that the interpretation of most measurement techniques depends on
(assumptions about) the structure of the analyte.
Colligative properties of polymers in dilute solution can be used to determine molar
mass. The response of such properties corresponds to the mole fraction in solution as
pointed by Johannes van ‘t Hoff (Nobel Prize in Chemistry, 1901) and may be used to
obtain number-averaged molar-mass (Mn) data. Membrane osmometry has historically
been favored over other techniques, such as freezing-point-depression and vapor-
pressure measurements, because it is more practical to measure and offers better
accuracy. End-group determination may also yield Mn, provided that a selective
detection of terminal groups is possible and the polymer molecules are known to be
linear. Other techniques available for molar-mass determination are light scattering and
Chapter 1
12
ultracentrifugation [9]. Both techniques may be used to provide accurate (“absolute”)
molar masses, as is the case for the colligative properties described before.
Viscosity of polymer solutions has been recognized as a readily accessible and sensitive
property for molar-mass determination by so-called viscometry. It is due to the
expanded nature of the molecules in solution that viscosity is increased by most
polymers. The empirical relation between intrinsic viscosity ([η]) and relative molar
mass (Mr) was introduced by Staudinger [10] (Eq. 1).
[𝜂] = 𝐾𝑀𝑟𝑎 (1)
This equation has become known as the Mark-Houwink relation after their efforts to
improve the theory of this relation and their documentation of constants K and a for
different polymer-solvent systems at given temperatures [11,12,13]. The simplicity of
capillary viscometry for determining molar mass resulted in a high popularity of this
method and documentation of Mark-Houwink constants for many polymer-solvent
systems [14]. Viscometric methods are relative measurements, because the relation
between molar mass and viscosity needs to be determined for each different polymer at
each set of conditions (solvent and temperature). Relations between polymer melt
viscosity and molar mass were also investigated. Determination of molar mass with
much better precision was possible due to the higher viscosity of the pure polymer than
of a polymer-containing solution, but the empirical relations were found only to hold for
relatively low molar masses [15,16,17].
The macromolecular structure of polymers was supported by published work on the
application of these techniques for polymers. Polymer science and related analytical
capabilities expanded rapidly once the scientific community accepted the existence of
macromolecules. Research into polymerization reactions and mechanisms thereof
increased throughout the 1930’s. This revolutionized polymer synthesis and quickly
resulted in the first commercial production of polystyrene, polyesters,
polyvinylchloride, polyethylene and polyamides. Development of polymer-
characterization techniques was driven by the need to support polymer production and
studies into new synthesis routes and application fields. In 1953 Flory wrote ‘Principles
of polymer chemistry’, an overview of both polymer chemistry, as well as
Introduction
13
characterization methods for polymers, which is still considered an important reference
work [8]. Flory’s contributions to the theory of polymers in solution (Flory-Huggins
solution theory and excluded volume) earned him the Nobel Prize in Chemistry in 1974.
According to IUPAC the modern definition for macromolecule or polymer is: "A
molecule of high relative molecular mass, the structure of which essentially comprises
the multiple repetition of units derived, actually or conceptually, from molecules of low
relative molecular mass” [18]. Different types of polymer may be identified depending
on their origin. Most common are synthetic polymers and natural- or biopolymers.
Examples of natural polymers include proteins, starch, cellulose and DNA. The
emphasis throughout the work presented in this thesis will be on synthetic polymers.
Table 2. Different levels of polymer structure
Polymer Additives
Micro- level
(molecular)
Relative molar mass (MMD) (Relative) Monomer content (CCD) Functionality (end groups) Branching / Topology
Structure and concentrations
Meso-level (morphology)
Crystallinity
Self-assembly Particle size distribution Mixing and compatibilization Orientation
Spatial distribution Migration behavior
Macro-level (polymer properties)
Density Glass transition temperature Melting point Optical properties
Solubility Strength Viscosity (melt)
Effects of additives, such as plasticizers, fillers, reinforcing agents, stabilizers, anti-static agents, colorants, on polymer properties
1.1.3 Polymer structure
The characteristics of polymeric materials are the results of many structural features
(Table 2). It is for this reason that characterization is not straightforward and that
understanding of the material properties requires information on more than a single
structural feature. The basic structure of a polymer is determined by the chemistry of the
repeat units and how they are linked together (micro-level). Structural features at the
Chapter 1
14
meso- and macro-level depend on the molecular features, but also on the processing
conditions of the material. Polymers are heterogeneous materials and so the distribution
of micro-structural features is important as well.
A very important parameter is the number of repeat units in a chain, which is also
known as the degree of polymerization. It has a large impact on polymer properties
(macro-level) and is typically expressed as the relative molar mass (Mr). A molar-mass
distribution (MMD) is invariably present in synthetic polymers due to the stochastic
nature of polymerization reactions. This does result in molecules with different Mr being
formed even when reaction conditions are kept identical. A common metric for the
MMD in polymers is the polydispersity index (Eq. 2), which is defined as the ratio of
weight averaged to number-averaged molar mass (Mw and Mn respectively).
𝑃𝐷𝐼 = 𝑀𝑤𝑀𝑛
(2)
Optimization of polymerization conditions makes it possible to control Mr and MMD
and obtain polymers with targeted properties. Reversely, measuring Mr and MMD may
provide information on the polymerization conditions, in particular the termination
reactions [19]. Details on various types of polymerization reactions can be found in
textbooks on polymer chemistry [e.g. 8,20].
Chemistry is the broadest variable in polymer structure. Polymers with different
monomer chemistries have vastly different properties and application areas. Co-
polymers can be created with monomers of different chemistry, which are appropriately
referred to as co-monomers. The chemical-composition distribution (CCD) may deal
with overall composition (inter-chain composition), as well as distribution within chains
(intra-chain distribution). Examples include randomness and block-length distribution.
Tacticity is an intra-molecular form of stereochemistry and may therefore also be
considered part of the CCD. When the chemistry of individual repeat units has affects
reactivity or structure this is classified as “functionality”. Typical examples are reactive
end groups and pendant groups on the backbone.
Introduction
15
Fig. 1. Schematic representation of various types of chain structures, including linear, long-chain-branched,
short-chain-branched, cyclic, network, comb, brush, dendritic and star polymers
1.1.4 Branched polymers
Branching and topology are other important aspects of the polymer structure. Polymers
with branching may be obtained through the addition of (multi-functional) co-
monomers, post-reaction processing or ‘back-biting’ side-reactions taking place during
polymerization [21]. There are many variations possible to the linear structure, resulting
in branched polymers with many different forms (Fig. 1). The most common
applications of branched polymers take advantage of the melt rheology and solid-state
material properties that are unique for these materials. These macro-level effects can be
explained by the characteristics at the meso- and micro-structural level. Especially the
level of (inter-molecular) chain entanglement and crystallinity are affected by branching
properties, which affects material properties related to stretching, deformation or flow
of the polymer.
Changes on the molecular level as a result of branching include a higher number of end
groups, shorter back-bone length and a more compact structure relative to linear
polymers. Branched polymer with chemically different or modified end groups can be
used as highly effective functional materials. The compact molecular structure of
branched molecules gives rise to the melt and material properties corresponding to a
Chapter 1
16
combination of shorter chain length but higher molar mass. It is also an important
handle in the characterization of branched polymers using dilute-solution techniques,
which will be explained later. The main classes of branched polymers are presented in
Table 3.
Table 3. Different types of branched polymers and the properties
Type Effects and applications Chemical pathways Examples
Long-chain branching
Melt rheology modification
Increased toughness
Back-biting in ethylene and acrylate polymerization
Co-polymerization
Light Cross-linking [22]
LDPE, polypropylene, polycarbonate [23], polystyrene, nylon, PMMA [24]
Short-chain branching
Reduction in crystallinity
Improved material properties
Back-biting in ethylene polymerization
Co-polymerization
Polyolefins, LLDPE
Star Model component in rheology research
Multi-functional macro-monomers
Functional materials
Core-first
Multi-functional initiator
Thermo-responsive polymer [25] Low-viscosity inkjet ink [26]
Light-switchable coatings [27]
Combs/brush Model component in rheology research Functional materials
Macro-monomer polymerization [28]
Polyelectrolites [29] Biomimetic materials [30]
Dendrimers / Hyperbranched polymers
Multi-functional macro-monomers Functional materials [31]
Drug delivery [32]
OLEDs [33]
Short-chain branching (SCB) is a property that is almost exclusively associated with
polyolefins. This is because in other polymers the functionality of pendant groups is
different from the backbone and it is reflected in the CCD. Unlike other forms of
branching, the impact of short-chain branches on polymer properties is mainly a result
of interference with crystallinity at the microscopic level (meso scale). The most
common application of SCB is in the modification of linear high-density polyethylene.
With Ziegler-Natta catalysts linear low-density polyethylene may be produced by co-
polymerization of ethylene with alpha-olefins, ranging from propylene to 1-hexadecene,
Introduction
17
to introduce SCB. With contemporary single-site and metallocene catalysts it is possible
to precisely control the degree and distribution of SCB in LLDPE polymers and, thus, to
produce materials with highly optimized properties. An increase in SCB density results
in lower crystallinity and lower density of the material. These are important
characteristics of linear low-density polyethylene, where ‘linear’ in the name refers
merely to the absence of long-chain branching (LCB). It is generally accepted that very
short branching introduces rubber-like behavior (e.g. ethylene-propylene rubbers),
whereas longer chains as obtained by copolymerizing 1-hexene or 1-octene provides
elasticity and other properties beneficial for LLDPE films [34]. Low-density
polyethylene (LDPE) is produced by free-radical polymerization at high pressure and
contains both SCB and LCB as a result of back-biting. This is a side-reaction where in a
propagation step the free radical at a terminal methylene group is transferred to a
methylene group somewhere in the chain by hydrogen abstraction. Branches of random
length and at random position are created in this way. LDPE combines the distinct
advantages of LCB polymers with a lower density than linear high-density polyethylene
(HDPE).
Advantages of LCB polymers are higher zero-shear viscosity, improved melt strength,
reduced melt fracture, reduced melt viscosity at high shear rates (i.e. shear thinning) and
extensional thickening. Polymers with LCB have superior processing properties and
they can be used for demanding applications such as blow molding, blown-film
formation and closed-cell foam production. Long-chain branching has an effect on
viscosity through entanglement of the polymer molecules. Above the critical molecular
weight Mc , which marks the onset of chain entanglement, the melt viscosity of
polymers increases no longer linearly with mass but with Mr3.4 [35,36]. The average
length of the chain segments between entanglements Me can be determined using
experimental techniques [37,38]. An overview of Me values for many polymers has
been established based on rheology and small-angle neutron scattering (SANS)
measurements on linear and short-chain-branched model compounds [39]. For
amorphous polymers the critical molecular weight Mc ≈ 2 Me. The chemical
composition of the polymer backbone has a large effect on the onset of entanglement.
Therefore, the effects of LCB may differ for polymers with different chemistries
through the effect on Me. Branches in LCB-polymers should be longer than Me to affect
Chapter 1
18
the rheology of the material. In practice long-chain branches will have a significant
chain length relative to the backbone of the polymer. Polyolefins with LCB are created
using free-radical polymerization, but may also be obtained in metallocene catalyzed
polymerization. Using constraint geometry catalysts (CGC) it is possible to produce and
incorporate chains with vinyl terminal groups into the final polymer [40,41,42]. The
typical branching frequency for CGC and other metallocene polyethylenes is less than 1
long chain branch per polymer [43], while in LDPE between 3 and 7 long chain
branches are common. LCB in CGC polyethylene will be longer (1300 – 1600 carbon
atoms) than LCB in LDPE, which has branches with 200 – 300 carbon atoms in the
backbone [44,45,46,47,48]. Other pathways for the introduction of LCB are the use of
multi-functional co-monomers [24] or multi-functional initiators. Cross-linking after
reaction can also be used to introduce LCB, for instance by addition of peroxides or
irradiation. Treatment of HDPE and LLDPE with gamma-irradiation has been
performed to induce LCB successfully [22]. A too high degree of cross-linking will
result in network or gel formation, which will compromise the melt behavior of the
material.
LCB is introduced in most commercially produced polymers by chemistry that adds
branches at random locations on the backbone. The polymerization processes for
polymers with controlled and regular LCB (star, comb and brush polymers) are usually
not cost effective for the production of commodity plastics, because of the need for
high-purity monomers or expensive reactants. These materials are typically produced
using multi-step reactions, in which macro-monomers or multi-functional cores are
coupled using anionic polymerization or controlled polymerization reactions, such as
atom-transfer radical-polymerization (ATRP) [49], nitroxide mediated polymerization
(NMP) [50] or reversible addition-fragmentation chain-transfer polymerization (RAFT)
[51]. Only the use for specialty applications or functional materials justifies the cost
involved in producing these materials (Table 3). The ability to create polymers with
well-defined branching topologies and branch lengths is important for studies into the
rheological behavior of polymers [37,38,52]. In this way the effect of increased
branching frequency and branch length on various rheological and material properties
can be determined. Results from this type of research are used to design new materials
with optimized properties.
Introduction
19
In dendrimers and hyperbranched polymers the branching functionality is included in
the main polymerization process, rather than a variation to linear polymerization. Most
often such polymers are produced using condensation polymerizations. The emphasis is
on chemical functionality of the material and most dendrimers are used as functional
materials [31].
1.2 Characterization and separation of branched polymers
Nowadays several techniques are available for the characterization of branched
polymers. The effectiveness generally depends on the type of branching, as well as the
impact on the measurement by other structural properties of the polymer and the
distribution thereof. In certain cases it is therefore desirable or even necessary to add a
separation step before measurements are performed on the polymer.
1.2.1 TREF, Crystaf and DSC
Measurements on crystallization behavior and rheological properties of polymers are
common in quality control, production and application-related testing. These tests are
highly sensitive towards the impact of branching on the macro level properties. The
impact of branching on crystallinity and melt-behavior was described in the section on
polymer structure above. Techniques that are often applied are differential scanning
calorimetry (DSC), temperature-rising elution fractionation (TREF) and crystallization
analysis fractionation (Crystaf). In TREF the polymer is first loaded on a stationary
phase and subsequently eluted as temperature is increased [53]. The loading step is
performed by having the polymer crystallize slowly out of solution. The polymer
eluting from the stationary phase upon temperature increase may either be fractionated
or subject to concentration detection for characterization of the redissolution behavior.
TREF was developed in the early 1980’s and has been widely applied to characterize
the short-chain-branching distribution (SCBD) and tacticity, but it may also be used to
fractionate by chemical composition for certain polyolefins. In more recent applications
the analysis of TREF fractions by, for instance, size-exclusion chromatography (SEC)
has been automated [54]. Crystaf was developed in the 1990’s and is used to monitor
the crystallization of polymer in solution when the temperature is decreased [55].
Crystaf is preferred over TREF, because the analysis can generally be performed at
higher cooling rates, provided the desired information on polymer composition can still
Chapter 1
20
be obtained. The suitability of either technique depends on specific crystallization
behavior. It is known that the crystallization and dissolution delays for ethylene and
propylene polymers are different, which implies that the separation of polyethylene and
polypropylene is only possible with TREF. Another complication is the “supercooling”
of crystallizable materials in solution when the solution is cooled down faster than
nucleation in solution occurs [56,57]. Crystallization steps should be performed at
sufficiently slow so as to prevent co-crystallization. These effects have been illustrated
in a comparison between TREF, Crystaf and DSC for the analysis of LLDPE and blends
with polypropylene [58].
Results for Crystaf analysis of an LDPE and an LLDPE resin are compared in Fig. 2
[59]. Crystaf and TREF results are typically presented in the same way with differential
polymer concentrations in solution on the y-axis and temperature on the x-axis. For
Crystaf analysis the results have been measured starting at 95°C down to 30°C in 1,2,4-
trichlorobenzene (TCB). For LLDPE a typical bi-modal distribution is observed. The
mode near 80°C corresponds to crystalline polyethylene segments in the polymer,
whereas the broad mode below 75°C represents the amorphous material. Only one
single mode is observed for LDPE in the amorphous region as a result of both SCB and
LCB. Crystallization behavior is influenced not only by the amount of co-monomer (i.e.
degree of branching), but also by the distribution and block-length of segments with
different crystalline properties. Therefore, crystallization techniques are the method of
choice for characterizing modern LLDPE polymers. These may be prepared using
multiple metallocene catalysts or in a multi-stage reactions, resulting in complex
distribution of SCB. Crystaf and related techniques are the first choice for monitoring
catalyst efficiency in production processes or for investigating unexpected changes in
polymer performance.
1.2.2 Rheology
Measurements of viscosity and the behavior of polymer melts are among the most
sensitive methods known for characterizing LCB in polymers. Rheological experiments
allow for direct characterization of macro-level properties. Different types of
measurements are performed, depending on the shear-rate regime of interest [60].
Introduction
21
Fig. 2. CRYSTAF results for typical LDPE (1) and LLDPE (2) materials [59]
Dynamic-mechanical analysis (DMA) can be performed to obtain detailed information
on stress-strain relations typically in the range between 0.1 and 100 s-1 using rotational
viscometers. Zero-shear viscosity is obtained from the viscosity value at an arbitrary
low shear value, typically 0.1 s-1. Elastic properties (e.g. shear storage- and loss
modulus) and dampening (tan δ) may be investigated by oscillatory viscometry in
frequency-sweep experiments. All these parameters have been compared against
structural properties for polyethylene and were found to be affected by SCB and LCB in
distinct ways [37,61]. Measurements with an extensional rheometer are used to test for
strain-hardening behavior, and uniaxial and biaxial elongation [62]. Branching often
improves strain-hardening and biaxial-elongational properties of polymers. Therefore,
extensional rheology can be used for quality control of LLDPE and other branched
polymers. DMA at shear rates < 0.1 s-1 is rarely used for purposes other than studies on
creep behavior of polymers. Capillary viscometers are used for measurement at shear
rates > 100 s-1. Applications include the measurement of polymer melt-flow-rate (MFR,
also referred to as melt flow index in case of polyethylenes) and determination of
intrinsic viscosity of polymers in dilute solution. Solution measurements using capillary
viscometry will be described in more detail later (see section Size-exclusion
chromatography with selective detection).
Chapter 1
22
Fig. 3. Trends in shear-dependence of melt viscosity for polyethylene polymers
with different degrees of branching by DMA [45]
The effect of long-chain branching on viscosity is demonstrated in a comparison of
rheology curves for polyethylenes with different LCB frequency (Fig. 3) [45]. These
materials were prepared using a constrained-geometry catalyst, which is a metallocene-
type catalyst that allows for accurate control of LCB in the polymer [61,63]. An
increased zero-shear viscosity and a shear-thinning effect at high shear rate are observed
for polymers with higher branching frequencies. A metric that is used to express shear-
rate sensitivity is the ratio of melt-flow indices obtained with two different loads. The
measurement of melt-flow indices is performed at standardized conditions (ASTM D-
1238), where the melt flow through a capillary is measured with either 2.18 or 10 kg of
load on the piston driving the polymer. For polyethylene this measurement is typically
performed at 190°C.
Investigation of LCB using rheology curves is complicated, because the viscosity and
the shear-rate dependence thereof are also influenced by other properties of the
polymer. Comparing polymers with different MMDs is difficult. An increase in the
molar mass will result in a higher viscosity, irrespective of the shear rate. Changes in
the polydispersity will affect shear-rate-dependent viscosity, with an increase in PDI
resulting in changes comparable to those observed for polymers with increased LCB
frequency. The presence of additives (Table 2) will also affect rheology curves. It is
known that additives can have an unexpected impact on rheology that interferes with the
Introduction
23
measurement. Rheological measurements, therefore, are most useful when performed on
pure polymers with comparable characteristics. Access to a number of comparable pure
reference materials with known architecture is highly desirable for interpretation of the
results in terms of relative differences. Comparison of molar-mass data and zero-shear
viscosity for such a set of data provides very sensitive detection of LCB in the polymer
[43].
1.2.3 Spectroscopy
Information obtained from spectroscopic techniques can be used to elucidate the micro-
level structure of polymers. Infrared detection is traditionally used for monitoring the
chemical composition and it can be used to discriminate between repeat units and
branch points. It was used already in 1940 by Fox and Martin to prove branching in
polyethylene polymers [64]. The only common application for branching-selective
detection with IR today, however, is for the determination of SCB in polyolefins by
selective detection of C-H bonds on secondary and primary carbon atoms [65]. Short-
chain-branching frequency is reported as the number of methyl groups per 1000 carbon
atoms. Most often information on the SCB distribution of a polymer rather than an
average SCB frequency is desired. Such information can be obtained by infrared
analysis of the fractionated polymer or by using a hyphenated technique, such as SEC-
FTIR. Deslauriers et al. demonstrated SEC-FTIR with a precision of ±0.5
Methyl/1000C under optimized conditions for ethylene 1-olefin copolymers with ethyl
and butyl branches [65]. Partial least squares regression was used to build a calibration
between a selected spectral region and reference data on SCB frequency. Precision of
FTIR detection depends on the training set used to build a model. Either levels of ethyl
en butyl branches beyond that of the training set or inclusion of different functionality
will reduce the accuracy of the model. On-line coupling with chromatographic
techniques reduces the sensitivity of FTIR, because of the dilute solutions inherent to
most forms of chromatography [66,67]. An alternative to dilute-solution detection in
flow cells is available in the form of on-line polymer deposition on a germanium disk
using an LC-transform interface [68]. Polymer composition may be detected more
sensitively in this way without interference by the solvent, but the precision and
accuracy of the method leave to be desired [69].
Chapter 1
24
Both SCB and LCB may be studied by NMR spectroscopy. In case of 13C NMR
quantitative results well below 1 in 104 carbon atoms have been reported for polyolefins
with good precision using modern techniques [61]. It is possible to distinguish between
branches of different length up to hexyl side-groups and report their frequency
independently [48,70]. Branching frequency may be reported per molecule or an
arbitrary number of carbon atoms, provided molar-mass information is available. Most
quantitative results have been obtained by measurement of polymer solutions, but melt
analysis by magic-angle spinning NMR has also been reported [66]. Unfortunately,
measurement of the backbone atoms near or at low-abundance branch points requires
very long measurement times in 13C NMR. Fractionation and even on-line coupling
with HPLC or SEC is possible, but this is only practical for 1H NMR for reasons of
sensitivity and speed [71]. LC-NMR is used more often for screening of chemical
composition [72] than for characterizing LCB.
Mass-spectrometric characterization of branched polymers is limited to a specific
number of applications, despite its proliferation for polymer characterization in general
[73]. Soft ionization techniques, such as matrix-assisted laser/desorption ionization
(MALDI) and electrospray ionization (ESI), in combination with high-resolution mass
spectrometry (e.g. time-of-flight mass spectrometry, ToF-MS) are most useful for the
analysis of dendrimers [74]. These techniques are not applicable for polyolefins and
traditional random LCB polymers, because their molar mass is too high and branching
does not induce distinct mass differences of fragments. Mass spectrometry can be
applied successfully for branched polymers with moderate molecular weight and
sufficient ionizability. Products of condensation polymerization, including dendrimers
and hyperbranched polymers, are often amenable for characterization using mass
spectrometry [75,76]. Most mass-spectrometry applications for polymers deal with the
analysis of chemical-composition distributions, which includes the use of
multifunctional initiators and repeat units ultimately resulting in branched polymers.
Hyphenation of various types of liquid chromatography with ESI-ToF-MS provides a
strong combination for these polymers [77].
Introduction
25
1.3 Size-exclusion chromatography with selective detection
Separations are important in many techniques for the characterization of polymer
microstructure and are essential when studying the distribution in polymer properties.
Size-exclusion chromatography (SEC) is one of the most-common techniques in the
characterization of polymers. Since its introduction the 1960’s [78,79] SEC has been
used for the characterization of molar mass and MMD of polymers. In combination with
selective-detection techniques, such as on-line laser-light scattering and viscometry, the
degree of branching may be studied as a function of molar mass. The sensitivity of these
techniques is highest for LCB polymers, but other types of branching may be
investigated as well. A general requirement is that the polymers under consideration are
well dissolved and do not significantly differ from random-coil behavior in solution.
Different configurations of SEC with selective detection may be applied to obtain
comparable information of branched polymers. Preference for any separation or detector
configuration depends on specific strengths and tolerances. Separation and different
forms of detection are presented in the following sections to introduce the
considerations for common configurations of SEC with selective detection.
1.3.1 SEC separation of branched polymers
Separation in SEC is achieved through size-selective migration of polymers in dilute
solution through a column packed with porous particles [80]. The separation is entropic
in nature and interactions between the polymer and the column packing should be
negligible. Large polymer molecules are selectively excluded from pore space in the
SEC column. Their reduced access to the stagnant mobile phase in the pores results in
elution before materials that can enter the pore volume driven by random diffusion. The
relevant size parameter is that of the free molecule in solution and is referred to as the
hydrodynamic size or volume of the polymer [81].
Separation in SEC is an indirect result of molar mass and branching through their
impact on hydrodynamic size. It is therefore important to understand how experimental
and molecular properties affect the relation between size and mass. The theory for
solution behavior of flexible-chain linear polymers has been described in detail by Flory
and Casassa [8, 82]. They found that random-coil statistics could be used to describe the
relation between molar mass and ‘coil dimensions in solution’ (simply referred to as
Chapter 1
26
polymer size from here on) for ideal polymers. Application of random-coil statistics can
be used to describe many other structure-property relations of real polymers
appropriately using scaling laws [83]. The relation between polymer size r and molar
mass may be described using the general scaling law shown as Eq. 3, with empirical
constants a and b correcting for polymer-solvent specific behavior (with b = 0.5 for a
random coil).
𝑟 = 𝑎 𝑀𝑏 (3)
Scaling laws can be used, for instance, to describe mass dependency of intrinsic
viscosity using the Mark-Houwink relation (Eq. 1) over a molar-mass range of several
orders in magnitude [84]. Branching in polymers will interfere with the scaling behavior
between hydrodynamic size rh and molar mass M (Fig. 4) [85,86].
Fig. 4. Schematic representation of polymer structure in solution
An increasing level of (long-chain) branching will result in a reduced freedom of the
chain and therefore a smaller size in solution. Another effect is the increase in segment
density, which generally results in a lower intrinsic viscosity. The differences in scaling
behavior between linear and branched polymers i.e. different relation between molar
mass and polymer size, may result in co-elution of polymers with different molar mass
when linear and branched molecules are present. Branched polymers will generally
elute from the SEC column together with linear polymers with lower molar mass (but
identical hydrodynamic size) due to their more compact coil structure. Local
polydispersity in SEC [87,88,89] as a result of branching has been studied by several
experts. Its presence was proven experimentally by careful consideration of the results
from on-line detection techniques that provide either number- or weight-average molar
mass at each elution increment. The calculation of local polydispersity is typically not
Identical M – different topology
Identical rh – different topology
Introduction
27
included in the workflow of multi-detector SEC techniques and only possible with the
additional effort of setting up a universal calibration. This highlights one of the
fundamental limitations of multi-detector SEC and supports the need for better
separation techniques that can resolve linear and branched materials.
1.3.2 SEC with on-line (micro-)viscometry
Capillary viscometry has been used for calculation of molar mass since the early
discovery of the Mark-Houwink relation for polymers. Before the advent of on-line
detectors in the 1980’s, Mark-Houwink relations had to be established by measurement
of solution viscosity using, for instance, Ubbelohde viscometers. With the introduction
of differential viscometry it became possible to hyphenate viscometers with separation
techniques [80]. Viscometers based on the Wheatstone-bridge design have been
commercialized and have become widely available for viscosity measurement in SEC
[90]. Most commercial detectors use a Wheatstone bridge constructed made with four
steel capillaries with matched restriction. For the work presented in the rest of this
section a novel micro-sized viscometer has been used. This detector was made available
by Polymer Laboratories and Micronit in an effort to address the challenges experienced
with traditional commercial viscometers [91]. The Wheatstone bridge of this detector
has a total volume of only 8 µL and has been created on a glass chip, which allows for
tight engineering specifications and a perfectly balanced bridge. At a flow rate of 100
µL/min the viscometer operates at a shear rate of 3000 s-1, which is the standard for
commercial capillary viscometers. With the reduced detector bridge volume this
detector can match cell volumes encountered in contemporary light scattering and
concentration detectors. A complete set of miniaturized detectors allows also for
“miniaturized” separations. Therefore, SEC columns with dimensions of 4.6 mm ID ×
250 mm were used.
With differential viscometry the specific viscosity can be measured on-line. In
combination with on-line concentration detection it will allow calculation of intrinsic
viscosity at each elution volume (Fig. 5). For polymers with known Mark-Houwink
constants the molar mass can also be calculated at each elution volume. This approach
is not practical for the analysis of branched polymers, because the Mark-Houwink
parameters change with branching properties and frequency. However, other approaches
Chapter 1
28
that do not require Mark-Houwink parameters may be used to characterize branched
polymers using SEC with viscometry.
Fig. 5. Instrument configuration for SEC with on-line viscometry as used for universal calibration.
1.3.2.1 Universal calibration
Regular molar-mass calibrations, prepared using narrow standards, have limited
applicability. Corrections for other polymer systems can only be made when Mark-
Houwink constants are known for both calibrant and analyte. A universal calibration
method was introduced by Grubistic [92]. Knowledge on Mark-Houwink parameters of
the analyte is no longer required for molar-mass calculation when an on-line viscometer
is used. Intrinsic viscosity may be used to calculate molar mass directly when a column
calibration is available in terms of hydrodynamic volume (Vh). This is possible because
of the direct proportionality between Vh and the product of intrinsic viscosity [η] and
molar mass (M) (Eq. 4).
𝑉ℎ ∝ [𝜂]𝑀 (4)
Validity of the universal calibration for polymers of different architecture and
composition has been demonstration by the good correlation for all polymers in a plot of
[η]M against elution volume [84,92]. Accuracy of the results obtained by universal
calibration is challenged by the sensitivity of this calibration principle to experimental
imperfections. For samples with narrow MMD the incomplete separation is incorrectly
interpreted, resulting in a higher PDI and “anomalies” in Mark-Houwink plots. Better
results are obtained using the concentration and viscometer signals from the setup in
Fig. 6. For samples with broad MMD acceptable results could be obtained. Also these
results were extremely sensitive to changes in absolute retention time (correction using
flow-marker possible) and inter-detector delay volume. Changes in the room
Introduction
29
temperature suffice to compromise the accuracy of universal calibration for systems that
are not fully thermostatted, such as the setup used in this study. Good results with
acceptable accuracy may be obtained using universal calibration performed under well-
controlled conditions.
Fig. 6. Instrument configuration for triple-detection SEC.
1.3.2.2 Triple detection SEC
With on-line light-scattering detection the molar mass of polymers can be measured
directly. For polymers in dilute solution the weight-average molar mass may be
calculated from the intensity of the scattered light using the Rayleigh-Gans-Debye
approximation [80,86]. A practical complication is the angular dependence of scattering
as a result of destructive interference of scattered light from molecules in solution larger
than roughly 1/20 times the wavelength of the light. The applicable size is the root-
mean-square radius of the polymer, also referred to as radius of gyration (rg). A
correction is generally applied to obtain corrected values for M and rg through iterative
calculations [93].
In triple-detection SEC both a light scattering and viscometer are added to the detector
array. In the original configuration of triple detection SEC a right-angle laser-light-
scattering detector is used [93]. With measurement of light scattering at 90° the
traditional problems with signal noise at low angles are avoided, but a correction for
angular dependence is required. This is achieved using an estimate of rg calculated using
the viscometer data, estimated M and the Flory-Fox equation. The detector
Chapter 1
30
configuration allows for calculation of both M and [η] at every elution volume without
the need for column calibration. This prevents issues and limitations inherent to the
universal calibration with respect to absolute elution-volume differences. The sensitivity
to errors in inter-detector delay or band broadening remains. In Fig. 7 the effect of inter-
detector band broadening in a non-optimized setup is demonstrated for the analysis of
six-arm star polystyrenes with narrow MMD [94]. Broadening in the detector signals for
the RALLS and viscochip was caused by splitting of the flow towards the differential
refractive index (dRI) detector before the RALLS detector (in contrast to the
configuration in Fig. 6). This resulted in an unrealistic increase in both M and [η] at
higher elution volumes. The RALLS signal was found to be broadened by 2 seconds for
a narrow-standard peak with a width at half height of 36 seconds on the dRI signal.
With the appropriate detector configuration as displayed in Fig. 6 good results have
been obtained without artifacts resulting from inter-detector band broadening. Z-RAFT
six-arm star polystyrenes were analyzed using triple-detection SEC with UV absorption
for concentration detection (Fig. 8 and Fig. 9). The extent of inter-detector band
broadening was minimal due to the small UV detector-cell volume of only 2.5 µL. Most
of the polystyrene polymers were found to have an extremely narrow MMD (i.e. PDI <
1.1), with the exception of polymerization products obtained at very high levels of
conversion. Absolute molar-mass results obtained using triple detection were used for
confirmation in studies into the molar-mass offset in conventionally calibrated SEC by
polymers with known branching topology [94,95]. The results of this work are treated in
more detail in Chapter 5.
The traditional strength of triple-detection SEC lies in the possibility of absolute molar-
mass detection for polymers with relatively low molar mass. A RALLS detector is
simpler by design (less expensive) and can be built with a smaller detector-cell volume
relative to the more complex forms of light-scattering detection. In modern applications
the uncertainties introduced by angular correction and estimation of rg using the Flory-
Fox equation may be alleviated by using a dual-angle detector. Above an arbitrary mass
or estimate of rg the low-angle signal is used, which is much less sensitive to angular
dependence.
Introduction
31
Fig. 7. Mark-Houwink plot; example of triple-detector data subject to inter-detector band broadening.
(a) linear PS1683, (b) 6-arm star polystyrene polymers with different molar mass but uniform arm length
Fig. 8. Chromatograms of narrow-MMD six-arm star polymers and a broad-MMD reference; (a) linear PS1683, (b) 6-arm star PS polymers, (c) 6-arm star PS polymer obtained at high monomer conversion
Fig. 9. Mark-Houwink plot for narrow-MMD six-arm star polymers and a broad-MMD reference
Chapter 1
32
1.3.3 SEC with multi-angle laser-light-scattering detection
The different relation between molar-mass and intrinsic viscosity of branched polymers
is clearly observable in the Mark-Houwink plot. Six-arm star polymers have higher
molar mass and lower intrinsic viscosity than linear polystyrene with an identical
hydrodynamic size. The difference in solution properties of branched polymers relative
to those of linear polymers can be detected using SEC with selective detectors. Multi-
angle laser-light scattering (MALLS) is another selective detector that was not
introduced yet, but is commonly used in the characterization of branched polymers. Due
to the added information of scattering at multiple angles relative to the incident light the
angular dependence may be solved to obtain rg directly at every elution volume,
provided that the particle is large enough to yield appreciable angular dependence.
Calculation of rg does not require any other detector signal and is therefore not affected
by the experimental imperfections of multi-detector arrays, such as inter-detector
volumes and inter-detector band-broadening.
Relative differences in solution behavior of polymers are often expressed as contraction
ratios based on either MALLS detection (Eq. 5) or viscometry (Eq. 6). The subscripts B
and L indicate data for branched and linear reference polymer respectively, comparing
data of identical molar mass as indicated as the subscript M.
𝑔 = ��𝑟𝑔�𝐵
2
�𝑟𝑔�𝐿2�𝑀
(5)
𝑔′ = �[𝜂]𝐵[𝜂]𝐿
�𝑀
(6)
Differences in rg and [η] between linear and branched polymers may be small and hard
to observe in log-plots in comparison with plots of contraction ratio vs. molar mass.
Theoretical models for long-chain-branching frequency based on the relative changes
compared to linear polymers were derived for random-coil polymers even before SEC
with on-line detection became available [96]. Nowadays contraction ratios have been
tabulated for many branched polymers under different solvent conditions [86]. Plots of
contraction factors, rg or [η] as a function of molar mass provide important information
on the branching distribution and are often indicative of the polymerization mechanism
Introduction
33
related to the inclusion of branching. The relation between the parameters g and g’ has
been of great interest, because the models for branching frequency are based on g. The
relation between both parameters is not straightforward and varies within polymers as a
function of molar mass. SEC-MALLS and triple-detection SEC with a MALLS detector
may be used to investigate this relation on-line [97,98].
1.3.4 Application and challenges of existing methodology
Measurement of differences in rg and intrinsic viscosity with SEC in combination with
selective detection techniques is particularly useful for polymers with a low degree of
long-chain branching. Branched polystyrenes that have been used throughout this thesis
were analysed using triple-detection SEC (Fig. 10 and Fig. 11) and SEC-MALLS-dRI
(Fig. 12). Both techniques demonstrate good signal quality for high-molar-mass
polymers, because of the high light-scattering intensity. Contraction is observed in rg
and intrinsic viscosity measurements of the branched materials and increases towards
increasing molar mass, which indicates an increase in long-chain branching. At the low
molar-mass end the data quality is not so good, in particular for the MALLS data. Data
for the low-LCB polymer is of similar quality as the linear reference and the scatter in rg
is caused by the small angular dependence of the light scattered by the smaller
molecules.
Anomalous results are observed for the polystyrene with high LCB. The material that is
eluting later from the SEC columns is responsible for the upward curvature in the
conformation plot (Fig. 12). A change of the curve for LCBps in the Mark-Houwink
plot towards higher molar mass is observed at the low-mass end, which is indicative of
SCB in case of a good SEC separation [99].This phenomenon is known as anomalous
late elution or late elution in SEC and occurs specifically for branched materials.
Detailed investigation of the experimental parameters in the SEC separation and
comparison with field-flow fractionation (FFF) was performed for polystyrenes and
acrylates [100] as well as for LDPE [101]. It was concluded that the high molar-mass
tail of branched polymers is retained in the SEC column and slowly elutes together with
the molecules of low molar mass.
Chapter 1
34
Fig. 10. Chromatograms of broad-MMD linear and branched polystyrene samples. (a) linear PS1683, (b) low-LCB PS1500-10, (c) LCB PS PA2258-123 / PSbranch
Fig. 11. Mark-Houwink plot for broad-MMD linear and branched polystyrene samples
Fig. 12. Conformation plot of linear and branched polystyrene samples
Introduction
35
The separation of this high-LCB polystyrene was performed using FFF, which separates
also the large molecules in solution very well [102] (Fig. 13). In the same figure an
overlay is provided of the SEC and asymmetrical flow field-flow fractionation (AF4)
results. It is clear that the material on the high molar-mass end is not separated by SEC.
As a result of the incomplete separation in SEC the eluent fractions will be
polydisperse. Overestimation of rg is promoted by the higher sensitivity of the MALLS
for larger polymers, as the calculated value over the average population is a z-average.
Polymers with very-high molar mass fractions that are not well separated using SEC are
preferably separated using FFF or another technique that does not suffer from problems
with late-elution of branched or high-molar-mass materials. Separation techniques that
do include light scattering will provide the end user with data that makes it possible to
recognize problems with late elution, whereas in universal calibration this is not
observed unless significant material is observed to elute after the column void volume
using the concentration detector. In practice the amount of late-eluting material is very
small and it is unlikely that this is detected using a concentration detector. A broader
overview of complications in SEC with on-line light scattering and viscometry has been
provided by Mourey [103].
Fig. 13. SEC-MALS and AF4-MALS of the same highly branched polystyrene
10
100
1000
1.0E+04 1.0E+05 1.0E+06 1.0E+07 1.0E+08 1.0E+09
Rg (n
m)
Molar Mass (g/mol)
LCBps SEC PS1683 AF4 LCBps AF4
Chapter 1
36
1.4 Scope of the thesis
The aim of this work is to explore new technology for the characterization of branched
polymers, not limited by the traditional boundaries of common applied analytical
techniques. Initial results on molecular topology fractionation [104] served as an
inspiration to explore this separation further. The mechanism behind this fractionation
was still open for multiple explanations, because separation conditions could often not
be defined or studied systematically. Monolithic columns were prepared specifically to
address this issue. Columns for MTF were applied in a two-dimensional separation with
a size-based separation to study and optimize a true separation by topological properties
of the polymer.
Chapter 2 deals with the preparation of monolithic columns and their optimization for
polymer separations. Monolithic stationary phases have received much attention as an
alternative for packed beds for interaction chromatography. The highly interconnected
network of channels in polymeric monoliths provides an excellent environment for
hydrodynamic separations. Monoliths with different macropore sizes were prepared and
the materials were studied in an effort to understand the porous structure. It was
concluded that hydrodynamic chromatography was the prevailing separation mechanism
based on the confirmation of a unimodal pore-size distribution and a continuous flow-
through nature of the pores.
Chapter 3 details the application of multi-dimensional separations with selectivity based
on topology. The idea to separate a polymer based on its hydrodynamic size and
topology in a comprehensive two-dimensional separation is demonstrated for the first
time. A star polymer was used for the branching-selective separation. This serves as a
model compound for LCB polymers.
In Chapter 4 the application of MTF is considered in more detail and the mechanism of
separation is discussed. A systematic study on the selectivity is conducted using
columns with different channel sizes. Knowledge obtained in Chapter 2 on the pore
structure and separation characteristics of the columns was taken into account. Columns
used in this study provided better efficiency compared to previously used MTF
columns, which were short in length and were packed with polydisperse silica. The
Introduction
37
flow-rate effect on migration has been investigated thoroughly for both linear and
branched polymers.
In Chapter 5 the synthesis and analysis of branched polymers with well-defined
topology is presented. It is demonstrated that for polymers prepared with well-defined
topology the molar mass can be calculated from conventional SEC experiments. The
application is compared with results from theoretical studies for correction factors and
experimental results from other researchers. Absolute molar-masses were calculated for
the star-branched polymers for validation of the predicted molar mass using both
correction factors and theoretical molar mass for specific monomer conversion in the
polymer synthesis.
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41
Chapter 2: Hydrodynamic chromatography of
macromolecules using polymer monolithic columns
Abstract
The selectivity window of size-based separations of macromolecules was tailored by
tuning the macropore size of polymer monolithic columns. Monolithic materials with
pore sizes ranging between 75 nm and 1.2 μm were prepared in-situ in large I.D.
columns. The dominant separation mechanism was hydrodynamic chromatography in
the flow-through pores. The calibration curves for synthetic polymers matched with the
elution behavior by HDC separations in packed columns with ‘analyte-to-pore’ aspect
ratios (λ) up to 0.2. For large-macropore monoliths, a deviation in retention behavior
was observed for small polystyrene polymers (Mr < 20 kDa), which may be explained
by a combined HDC-SEC mechanism for λ < 0.02. The availability of monoliths with
very narrow pore sizes allowed investigation of separations at high λ values. For high-
molecular weight polymers (Mr > 300,000 Da) confined in narrow channels, the
separation strongly depended on flow rate. Flow-rate dependent elution behavior was
evaluated by calculation of Deborah numbers and confirmed to be outside the scope of
classic shear deformation or slalom chromatography. Shear-induced forces acting on the
periphery of coiled polymers in solution may be responsible for flow-rate dependent
elution.
Chapter 2
42
2.1 Introduction
Liquid chromatography (LC) is an invaluable analytical separation technique for the
characterization of synthetic polymers and bio-macromolecules. Large molecules with
relative molecular weights up to several millions can be separated, provided that they
are well dissolved in the mobile phase [1,2]. Size-exclusion chromatography (SEC),
hydrodynamic chromatography (HDC) and flow field-flow fractionation (F4) are often
used in the analysis of macromolecules. The separation conditions are typically mild
(moderate temperatures and shear stress), leaving the molecules intact for further
characterization (e.g. light scattering, viscometry, spectroscopy), separation, or
collection of fractions. Each of these techniques separates the analytes by size in
solution and enthalpic interactions between analytes and stationary surfaces must be
negligible. When this is the case, the physical properties of the stationary phase, rather
than the surface chemistry, are of paramount importance in creating a suitable
hydrodynamic environment for separation.
As opposed to SEC, HDC separations are based on partitioning within the transient
mobile phase [3,4,5]. The separation is a result of partitioning induced by surface-
exclusion in flow-through pores and hydrodynamic forces on the polymer in laminar
flow. Small analyte molecules can sample the low-velocity flow regions near the
stationary-phase surface that cannot be sampled by larger analytes. The latter are
excluded from the channel surface, because of both steric and hydrodynamic effects. An
overview of conditions and requirements of separations techniques for macromolecule
characterization is provided in Table 1. Hydrodynamic separations are ideally
performed in very narrow open (tubular) channels, because of their well-described
geometry, which allows rigorous theoretical description and calibration [6], and the
absence of eddy diffusion. The selectivity in HDC depends on the aspect-ratio (λ = r /
R) that relates the size of the analyte molecule (radius r) to the size of the flow-through
channel (radius R). For solutes moving through open-tubular channels with laminar
(Poiseuille) flow (i.e. a parabolic flow profile), the migration rate can generally be
expressed as the residence time of an analyte polymer or particle (tp) relative to the
migration time of a small-molecule marker (tm) as defined in Eq. 1 where τ is the
relative retention (with τ = 1 for a flow marker). In the basic form with C = 1 Eq.1
Hydrodynamic chromatography of macromolecules using polymer monolithic columns
43
describes solute migration based on surface exclusion only. This is the dominant effect
for low values of λ. C is a variable used for including hydrodynamic effects. Its value
varies between 1 and 5.3 depending on solute type and model assumptions [7].
𝜏 = 𝑡𝑝𝑡𝑚
= 11+2𝜆−𝐶𝜆2
(1)
Table 1. Description and boundary conditions for selected size-based macromolecule separations.
SEC HDC MTF
Principal requirements
Stagnant pore volume. Transient mobile phase + inhomogeneous flow profile (e.g. Poiseuille flow).
Obstructed flow for analyte molecules.
Critical dimensions Stagnant-pore size related to size of analyte molecules in solution.
Channel diameter 5 to 50 times the diameter of analyte molecules in solution.
0.02 < λ < 0.2
Channel diameter less than 2.5 times the diameter of analyte molecules in solution.
λ > 0.4
Implementation Porous particles; monoliths with bimodal pore-size distributions.
Open-tubular columns (≤ 2 µm inner diameter); packed columns (non-porous particles; ≤ 2 µm particle diameter), monoliths ≤ 1 µm channel diameter).
Columns packed with sub-micron (non-porous) particles; monoliths (ca. 0.1 µm channel diameter).
Selectivity Molecular size (flow-rate independent).
Molecular size (largely flow-rate independent).
Molecular size, branching (flow-rate dependent).
Stationary-phase characterization
Particle-size measurement (Coulter counter, SEM, FFF); MIP; Inverse SEC
Particle-size measurement; MIP
MIP, permeability
Linear (interstitial) velocity
0.5 mm/s 1 to 2 mm/s 0.05 mm/s
Typical column dimensions
300 × 7.5 mma 150 × 4.6 mm (packed columns)b
150 × 4.6 mm
Volumetric flow rate 1 mL/min 1 mL/min (packed columns)b
10 µL/min
Typical analysis time
10 mina 4 min 180 min
a Often several columns are used in series. b Typical dimensions of open columns for HDC would be 500 mm × 1 µm I.D. and the flow rate would be of
the order of 10 nL/min. Such experiments are highly impractical.
Chapter 2
44
Separations of particles in open-tubular columns are extremely difficult to perform, due
to the exceptionally narrow column diameters needed (internal diameter of the order of
1 µm) and the resulting brutal requirements on injection, detection and other aspects of
the instrumentation [8]. HDC can more conveniently be performed on columns packed
with non-porous particles. In such columns, the inter-particle space serves as a network
of narrow channels where the hydrodynamic separation takes place [9]. For packed
beds, the dimensions of R scale with the particle size. Columns with narrow and
uniformly sized flow-through channels require homogeneous packing of very small
particles, which is notoriously difficult. Packing capabilities for small particles dictate
the lower limit of selectivity attainable in packed-column chromatography. HDC has
been demonstrated using 1-µm non-porous particles where a value of R = 213 nm was
obtained [10]. Alternative stationary phases that provide suitable flow-through
characteristics may be applied to perform HDC. As a result of advances in micro
fabrication, chips and pillar-structured micro channels have been used with increasing
success to perform hydrodynamic separations [11,12]. However, R values suitable for
the separation of synthetic polymers are difficult to realize even with the most-advanced
contemporary fabrication technologies.
Monolithic columns, which have become increasingly popular as separation media for
LC [13], can also be considered for HDC. Hydrodynamic separations can be performed
in the macropores, which offer a highly interconnected network of flow-through pores
in the monolith. In contrast to the well-defined structure of packed beds with uniform
particles, the structure and porous properties of monoliths may vary with the type of
material and the preparation conditions. Although many different formulations and
preparation techniques for monoliths have been presented in recent years [14], silica
monoliths [15] and organic-polymer monoliths [16,17] have become most wide-spread
in liquid chromatography. Separations of polystyrenes with low dispersity based on
SEC-type partitioning have been demonstrated using silica monoliths featuring a
bimodal pore-size distribution (PSD) [18]. However, the small volume of stagnant
mobile phase in mesopores in comparison with the much larger external volume in the
flow-through pores (εi/εe << 1) limits the resolution and sample capacity for SEC
separations on this type of monolith. The ratio εi/εe is even more unfavorable for
Hydrodynamic chromatography of macromolecules using polymer monolithic columns
45
polymeric monoliths due to the absence of mesopores (microglobules in the polymeric
material) and thus the absence of stagnant zones in the column [19].
Separations of synthetic polymers by HDC using organic-polymer monoliths have been
investigated in this work. Polystyrene-co-divinylbenzene (PS-DVB) was selected as the
material of the monoliths based on its mechanical strength, solvent compatibility and
low susceptibility for enthalpic interactions with synthetic polymers. Due to the low
degree of dimensional shrinkage during polymerization, PS-DVB columns can be
prepared successfully in-situ in wide-bore stainless steel columns [20], which allows
usage in a manner analogous to contemporary high-performance SEC. We will attempt
to elucidate the separation mechanism by relating the observed selectivity to the
morphology and the pore-size distribution.
2.2 Experimental
2.2.1 Chemicals and materials
Styrene (PS, >99.5%), divinylbenzene (DVB, ~80%), dodecanol (98%), and azodiiso-
butyrodinitrile (AIBN, 98%) were purchased from Sigma-Aldrich (Zwijndrecht, The
Netherlands). Tetrahydrofuran (THF, 99.8% unstabilized HPLC grade), diethyl ether
(99.5%), and toluene (99.7%) were obtained from Biosolve (Valkenswaard, The
Netherlands). Ethanol (99.7%) was obtained from BDH Chemicals (Poole, England).
2,6-di-tert-butyl-4-methylphenol (ionol, 99%) was acquired at Acros (Geel, Belgium).
Polystyrene and poly(methyl methacrylate) standards with low dispersity and relative
molecular weights (Mr) ranging between 580 Da and 3.7 MDa were obtained from
Polymer Laboratories (Church Stretton, UK).
The monomers were purified by passing them over activated basic alumina followed by
a distillation under reduced pressure. AIBN was refluxed in diethylether for 30 min, re-
crystallized, and dried under vacuum before use. Helium 5.0 (99,999% Praxair,
Vlaardingen, The Netherlands) was used to degas the HPLC mobile phase prior to use.
The polymer standards were dissolved in THF.
Chapter 2
46
Stainless-steel column hardware (100 mm × 4.6 mm I.D. and 250 × 4.6 mm I.D.; SS
grade 316), including end fittings, and 2-μm frits was purchased from Restek
(Bellefonte, PA, USA).
2.2.2 Instrumentation
HPLC experiments were performed on a Shimadzu LC system (‘s Hertogenbosch, The
Netherlands) consisting of a system-controller (SCL10a), a micro-pump (LC10Advp), a
column oven (CTO7), and a UV detector (SPD10AVvp). Data acquisition was
performed using ClassVP software. Separations were performed applying 5-μL
injections, with the column placed in the oven thermostatted at 50°C. The flow rate was
varied between 10 and 500 μL/min to record calibration curves on different monolithic
materials. UV detection was performed at 260 nm or 280 nm.
Porosity data were obtained by using Pascal 140 and 440 mercury-intrusion
porosimeters (CE Instruments, Milan, Italy) for low- and high-pressure analysis,
respectively. The pore-size distribution was calculated using Pascal software using a
model based on the Washburn equation [21] assuming cylindrical pores and a surface-
contact angle of 140° for mercury with the monolith. The samples for mercury-intrusion
porosimetry (MIP) were obtained by extruding the monolithic columns from their steel
cladding by removing one end fitting of the column and applying a flow. The monolith
was cut into coarse pieces and dried overnight under vacuum.
2.2.3 Column preparation
Monolithic columns were prepared in-situ in 4.6-mm I.D. stainless-steel columns. The
composition of the polymerization mixture was 20% styrene, 20% divinylbenzene
(w/w). The percentage of toluene was varied in between 10 and 24% (w/w) to control
the pore size; dodecanol was used to make up to the composition (60% w/w minus the
toluene content). After purging the polymerization mixture with Helium for 10 min. it
was transferred into the column, closed by stainless-steel disks in lieu of porous frits.
Polymerization was performed in a water bath (with Neslab RTE-140 water circulator,
Thermo, Waltham, MA, USA) for 24 hours at 80°C. After completion of the
polymerization reaction, the stainless-steel disks were replaced by porous frits and the
columns were flushed with at least 50 column volumes of THF at 50°C and 10 µL/min.
Hydrodynamic chromatography of macromolecules using polymer monolithic columns
47
2.3 Results and discussion
2.3.1 Preparation and characterization of monoliths for HDC
To make the polymer HDC separations compatible with conventional detectors for the
characterization of macromolecules, such as refractive-index detection, viscometry, and
static light-scattering, the monoliths were developed in wide-bore (4.6 mm I.D.)
columns. No covalent bonding of the monolith with the wall was required since the
cross-linked polymer was significantly more swollen in the SEC mobile phase (THF).
For a “small” molecule (ionol) symmetric peak shapes were observed, indicating the
absence of channeling effects.
To create monoliths with macropores that give inter-particle space of comparable
dimensions to columns packed with sub-3 μm particles [7], the porogen ratio in the
polymerization mixture was adjusted while the monomer composition was kept
constant. A detailed description of pore formation and the effect of porogen
composition on the phase separation and consequently on pore and globule size is
provided by Eeltink et al. [22]. Figure 1 shows the intrusion curves (A) and the volume
distributions (B) of the monolithic materials as determined with mercury-intrusion
porosimetry (MIP). The macropore size of the monolithic materials decreased with
increasing toluene content in the reaction mixture. Remarkably, the monoliths with the
smallest mode pore size (< 500 nm) appear to have a bimodal pore-size distribution.
This is probably an artifact of the MIP measurements, due to compression effects of the
semi-flexible monoliths during the intrusion process. In the MIP experiment dried
monolith (under vacuum) is immersed in mercury and subsequently pressurized. At
initial conditions mercury does not protrude the pores. During the intrusion process the
macropores are filled with mercury at the pressure required to overcome the surface
tension of mercury to enter the pores. For the material with the largest pores (sample 1
with a macropore diameter of 1200 nm) this occurs at approximately 1.2 MPa. For
monoliths with smaller pores higher pressures are required, because the intrusion
pressure is inversely related to the pore size. However, these materials are compressed
before the onset of pore intrusion, as shown in Fig. 1a, and this will result in an
increasing bias to smaller pore size and even an apparent bimodal pore size (Fig. 1b).
Chapter 2
48
Fig. 1. (a) Intrusion curves and (b) pore-size distributions of monoliths with different macropore size as determined with mercury-intrusion porosimetry. Numbers correspond to materials depicted in Table 2.
Hydrodynamic chromatography of macromolecules using polymer monolithic columns
49
In the Appendix (section 2.5) it is discussed how extrusion data obtained by MIP may
be used to confirm sample compression during intrusion measurements. Caution should
be exercised in interpretation of the PSD from Fig. 1b, because this may be influenced
by the extent of compression at the moment of mercury intrusion. This may result in the
apparent narrow distribution, particularly for pores larger than the mode of PSD, as
observed for materials 6 and 7.
Flow-restriction measurements with THF were used to compare macropore sizes for
monolithic columns without errors introduced by compression of the monolith. The
Hagen-Poiseuille equation (Eq. 2) can be used to relate changes in flow resistance to
macropore-size, under the assumption that the monoliths have narrow pore-size
distributions. It relates backpressure (∆P) and average linear mobile-phase velocity (u0)
in cylindrical channels to solvent viscosity (η), column length (L), and channel radius
(r). This relationship has been demonstrated to hold for the pores in acrylic and styrenic
monoliths [23].
∆𝑃𝑢0
= 8η𝐿𝑟2
(2)
The ∆P/u0 ratio was determined for material 4, which was selected as reference for its
balance between pore size and compression effects. Under the assumption that the
morphology remains the same, Eq. 2 was used to convert the changes in ∆P/u0 ratio to
macropore size (diameter DP) for the other materials with r = DP/2. Table 2 summarizes
mode pore sizes as determined with mercury-intrusion porosimetry (Dmip) and flow-
resistance measurements (DP). The deviation between Dmip and DP becomes larger for
monoliths with smaller pores. This is indicative for compression effects in MIP.
The microscopic images obtained with scanning electron microscopy (SEM; see Fig. 2)
show the typical globular structures of the monoliths prepared with different porogen
composition. It was observed that monoliths with sub-micron pores have the same
globular structure as their highly-permeable counterparts, but the domain size (i.e. the
length scale of both pore and globular support) is different. Surface roughness of the
fused globular structure for sample 1 provides some void space with dimensions
significantly smaller than the through pores of 1.2 µm. Exclusion from such pores may
Chapter 2
50
contribute to the separation (SEC mechanism), but because the void volume is
obviously low compared to εe this contribution will be small. For monoliths with sub-
micron pores no large through pores were observed. Therefore, the mobile phase must
be flowing through the sub-micron pores, thereby providing a suitable environment for
HDC of polymers.
Fig. 2. Scanning electron micrographs of polymer monoliths prepared with different porogen ratios. (a) material 1: 10% toluene, 50% dodecanol, 20% PS, 20% DVB, (b) material 6: 18% toluene, 42% dodecanol, 20% PS, 20% DVB.
Table 2. Porous properties of monolithic materials as obtained with mercury-intrusion porosimetry and pressure measurements.
Monolithic material Wt% toluene in polymerization mixture
Mode pore size (nm) MIP Dmip
Mode pore size correction using Poiseuille, DP
1 10 1170 1194
2 12 550 571
3 14 305 321
4 15 258 258*
5 16 216 241
6 18 127 162
7 20 93 126
8 22 50 104
9 24 28 75
*reference value in DP calculation
Hydrodynamic chromatography of macromolecules using polymer monolithic columns
51
2.3.2 HDC separation of polymers
Polystyrene (PS) and polymethylmethacrylate (PMMA) standards were used to study
the separation performance of PS-DVB monoliths with different pore sizes. Figure 3
shows overlaid chromatograms obtained for individual PS standards obtained on a 100
mm × 4.6 mm I.D. monolithic column with DP of 258 nm (material 4) operating at flow
rates of 300 μL/min and 100 µL/min. Good peak symmetry, As = b / a < 1.24 (with b =
the peak width of the tail at 10% of peak height and a = the peak width at the front at
10% of the peak height) was observed. The peak width at half height for 20 kDa PS was
6.1 s for the 300 µL/min separation, yielding a (minimum) plate height of 18 µm.
Backpressure over the monolith was 120 bar for THF at 50°C at 300 µL/min.
Fig. 3. Hydrodynamic chromatographic separation of polystyrene standards on a 100 mm × 4.6 mm I.D.
polymer monolithic column with 260 nm macropores. Peak identification: 1 = ionol, 2 = 20 kDa PS, 3 = 200 kDa PS, 4 = 1120 kDa PS. Flow rates: a = 300 μL/min, b = 100 µL/min. Mobile phase: 100% THF at 50°C.
Compared to the best plate-height values, about 6 µm for HDC separations reported on
columns packed with 2.7-µm particles at a linear velocity of 0.5 mm/s or higher, the
peaks are significantly broader [7]. Since the mass-transfer contribution to the total peak
width can be neglected in HDC, peak dispersion for polymers can be attributed to the
Chapter 2
52
large eddy-diffusion contribution induced by the column inhomogeneity. No significant
changes in polymer separation efficiency have been observed with changes in the
mobile-phase velocity (Fig. 3) or macropore size of the different monolithic materials.
Ionol is commonly used as a marker for the mobile-phase volume and its dimensionless
retention was defined as τ = 1. Different elution volumes were observed for other low-
molecular-weight flow markers, such as benzene, toluene, and alkylbenzenes.
Alkylbenzenes were found to elute earlier with increasing molecular weight, supporting
a separation based on size rather than a separation based on (adsorption) interactions.
Similar behaviour was observed for commercially available SEC columns with PS-DVB
cross-linked porous packings (Appendix, section 2.5.2). Low-molecular-weight non-
polar markers can adsorb onto or diffuse into the cross-linked PS-DVB phase. In case of
the ionol both processes are unfavourable, because of its polarity. Different behavior of
the flow marker may cause an offset, which should be taken into account when
comparing phases with different cross-link densities or permeabilities. Monolithic
columns compared in this work were all prepared with the same monomer-to-cross-
linker ratio and they all behaved comparably.
High flow-rates could not be used on all monolithic materials, because of the high
backpressures generated in the narrow macropores and the concomitant risk of phase
compression. Separations of polystyrene standards were obtained with flow rates
ranging from 300 µL/min (material 2 and 3) down to 20 µL/min for material 9. The
effect of macropore size on the retention behaviour and on the selectivity window is
demonstrated by the calibration curves depicted in Figure 4. Monoliths with different
macropore sizes show selectivity across different molecular-weight ranges. Columns
with narrower macropores (and thus lower permeabilities) separate smaller polymers.
This concurs with the expectation of HDC being the dominating retention mechanism as
postulated in the introduction. Selectivity for the different monolithic materials is very
similar between 0.75 < τ < 0.95, but the corresponding molecular-weight ranges differ
by more than one order of magnitude. For each monolith the effective range of
separation covers at least 2 orders of magnitude in polystyrene molecular weight. For
values of τ < 0.75 differences in the shapes of the calibration curves were observed. For
the materials with larger macropores (materials 3 through 6) the separation window
Hydrodynamic chromatography of macromolecules using polymer monolithic columns
53
extended down to τ = 0.65, which is extraordinary for HDC-type separations.
Separations at the upper end of the calibration curve have been observed to be flow-rate
dependent in previous studies in which packed columns were used [7,10]. Comparison
of the calibration curves in a universal format provides a better means to evaluate this
hypothesis using monolithic columns. In a universal calibration graph the aspect ratio λ
is displayed on the y-axis, which allows for a direct comparison of HDC-type
separations irrespective of macropore size or molecular weight of the analyte polymer.
Fig. 4. Effect of macropore size of monolithic columns on HDC selectivity for polymers with Mr ranging
between 990 Da and 3.7 MDa. Numbers correspond to materials depicted in Table 2. Monolith materials 2 and 3 were operated at 300 µL/min, materials 5 through 8 at 50 µL/min. and material 9 at 20 µL/min.
The size of the flow-through channel and that of the solute molecules in solution must
be known to calculate λ. Neither is obvious in the case of monolithic columns and
dissolved synthetic polymers. Irregular shapes of the macropores and uncertainties
about the morphology prevent a straightforward calculation of the hydraulic radius (i.e.
the surface-to-volume ratio), which has been successfully used to calculate the
equivalent capillary size for packed beds with non-porous particles [7]. The mode of
pore size from MIP is expected to be less accurate when either the pore-size distribution
in the monolith is broad or when compression occurs during MIP before the mode of
Chapter 2
54
pore size is reached. Therefore macropore size DP as determined from flow-restriction
measurements was used in calculation of λ (Table 2). This is appropriate, because
backpressure depends on the restriction in the flow-through pores where HDC takes
place by definition.
Polymers in solution do not behave as hard spheres, but as flexible chains following
random coil statistics. Excluded volume of the polymer chain contributes to the coil size
and varies with solvent and polymer chemistry [24]. The distance of exclusion near a
surface has been used successfully in modeling retention behavior. This size is
commonly referred to as the effective size and is conveniently defined relative to the
radius of gyration for linear random-coil polymers [25] as
𝑟𝑒𝑓𝑓 = √𝜋2𝑟𝑔 (3)
The relation between molecular weight (M) and radius of gyration (rg) in THF as
obtained using light scattering [26] was substituted in Eq. 3. The effective size (reff) of
PS and PMMA polymer standards was calculated using Eq. 4 and Eq. 5.
𝑟𝑒𝑓𝑓,𝑃𝑆 = √𝜋2
0.0118 𝑀0.600 (4)
𝑟𝑒𝑓𝑓,𝑃𝑀𝑀𝐴 = √𝜋2
0.0110 𝑀0.596 (5)
The same calibration curves for columns with various pore sizes in Fig. 4 are presented
in the form of a universal HDC calibration plot in Fig. 5a. A theoretical curve for HDC
on packed columns (calculated using Eq. 1 and C = 2.7) is provided for reference
purposes [9]. Experimental data match the theoretical curve for HDC separation best for
solutes in the center of the selectivity window of the columns (around λ = 0.1). The
slope in this central region is identical for all curves, which suggests that the balance
between size exclusion and hydrodynamic effects is identical to that encountered with
HDC in capillaries and packed beds.
The experimental curves do not coincide with the theoretical curve, with an offset
towards lower elution volumes that increases with macropore size. This offset is
Hydrodynamic chromatography of macromolecules using polymer monolithic columns
55
believed to result from additional size-exclusion effects. For λ < 0.1 size exclusion of
the polymer from the walls of flow-through channels is the main mechanism of
separation [6]. Modeled retention assumes surface exclusion in cylindrical channels.
Globular morphology and a distribution of the pore sizes (PSD) of the monolith,
however, provide an increased volume for SEC effects. For macropores with a large
average diameter this may result in increased selectivity at low λ. The broad PSD for
materials 1 and 2 (Fig. 1B) and increased selectivity of material 2 for λ < 0.02 (Fig. 5a)
illustrate this effect on monolithic columns. Size-exclusion effects other than wall
exclusion in flow-through pores observed for λ < 0.02 decrease with macropore size and
account for < 5% in elution volume for all monoliths. This effect is different from
exclusion in HDC using columns packed with non-porous particles, which is limited to
the geometric exclusion volume of spheres and scales with particle size [27]. It is
dependent on the morphology of the monolith and may, therefore, be reduced further by
optimization of the column-preparation process.
2.3.3 Flow-rate dependence in polymer separations
Flow-rate dependent elution behavior was observed for polymers separated at λ ~ 0.2
and above (Figs. 5 and 6). Hydrodynamic interactions (particle rotation, drag, flow-
induced radial force, etc.) become significant for solutes approaching the flow-through
channel size and depend on both flow rate and solute characteristics [9]. Only when
these contributions hold universally, retention will scale with λ and a single constant
can be used to account for hydrodynamic interactions in Eq. 1 (e.g. C = 2.7, assuming
rotating, non-draining behaviour of polymers in cylindrical channels according to
Dimarzio & Guttman [28]). However, this universality fails for λ > 0.4 and the
selectivity becomes dependent on either macropore or polymer size (Fig. 5a). For
materials 5 through 8 the calibration curve for monoliths with smaller macropores
demonstrates stronger reversal due to stronger retardation by hydrodynamic effects. The
same calibration curves acquired at 20 µL/min (Fig. 5b) closely resemble the theoretical
curve, which predicts strong retardation at λ > 0.2 after the assumption of non-draining
polymer coils. At λ = 0.4 reversal of the calibration curves towards higher τ values is
observed. Both PS and PMMA polymers are present as random coils under good-
solvent conditions and their flow-rate dependent elution behaviour is identical (Fig. 6).
Chapter 2
56
Fig. 5. Universal retention plot showing the calibration curves on monoliths with different macropore size. (a) Materials and LC condition similar as in Fig. 4. (b) Reversal of calibration curves for material 5 through 8
when operating at a flow rate of 20 μL/min.
Hydrodynamic chromatography of macromolecules using polymer monolithic columns
57
Fig. 6. Flow-rate dependent calibration curves of PS and PMMA polymers on monolith material 7 (a) and corresponding chromatograms for PS standards 1.1 MDa, 523 kDa, 200 kDa, 71 kDa, 20 kDa, 7 kDa and 2
kDa at a flow rate 50 μL/min (b). Column dimensions: 250 mm × 4.6 mm I.D. monolithic column.
Chapter 2
58
Flow-rate dependent elution of high-molecular weight polymers has been observed for
separations under wall-exclusion (HDC-like) conditions in other studies
[7,10,29,30,31]. It has been attributed to either deformation or elongation of the
polymer coil. The time-averaged coil size measured perpendicular to the flow direction
will decrease when the polymer molecules are subjected to shear stress. To describe
these effects the Deborah number (De) can be introduced [29]. De expresses the ratio of
hydrodynamic (elongation) forces to Brownian (relaxation) forces. For dilute polymer
migrating through packed beds it can be described as follows
𝐷𝑒 = 𝐾𝑑𝑒𝑏ν𝑑𝑝
6.12 Φ η 𝑟𝑔3
𝑅 𝑇 (6)
where Kdeb is a constant (with a typical value of 6 [29]), ν is the superficial solvent
velocity, dp the particle size of the packing, Φ the Flory-Fox parameter, η the solvent
viscosity, rg the radius of gyration of the polymer, R the gas constant and T the absolute
temperature.
Application of Eq. 6 for monoliths is complicated, because reference data only exist for
packed beds [29,32]. In the elongation factor in Eq. 6 (Kdeb ν /dp) the particle size can
be replaced by the hydrolic radius (i.e. the radius of a capillary with an identical
surface-to-volume ratio). For a packed bed of non-porous monodisperse particles Rh =
2/9 dp assuming a porosity of 0.4 [5,7]. This relation was used successfully in
comparing HDC selectivity between packed beds and capillary columns, but may be
used for monoliths as well. For monoliths Rh = DP / 2 was used. Kdeb is a constant that
accounts for the effect of pore structure on elongation. It is determined semi-empirically
by matching selectivity changes in HDC for well characterized systems with De = 0.5
[32]. Since Kdeb could not be established accurately for monoliths, the typical value for
particle-packed beds was used.
Random spherical coils prevail at low values of De. The onset of polymer deformation
is commonly assumed to occur around a value of De of 0.1. At still higher values (De >
0.5) the chains become completely elongated, resulting in a separation mechanism
termed “slalom chromatography” to picture the migration of flexible, stretched polymer
chains through the interstitial channels of the support [31]. Liu et al. describe a system
Hydrodynamic chromatography of macromolecules using polymer monolithic columns
59
with λ values on the order of 0.1 (dp = 15 µm, Rh = 3.3 µm, polystyrene rg = 125 to 450
nm). On the 4.6-mm I.D. column used the onset of slalom chromatography was
observed for flows in excess of 0.1 mL/min. The present separations on monoliths differ
significantly from those described by Liu on packed columns in terms of analyte
molecular weight (De ÷ rg3) and aspect ratio (λ). Uliyanchenko et al. reported on slalom
chromatography for polymers in the same molecular-weight range as used in the present
study. They used contemporary HPLC conditions (dp = 1.7 µm, Rh = 0.38 µm) [30] with
a flow rate of 1 mL/min on 4.6-mm I.D. columns, which corresponded to De = 0.6 for
the 2.0-MDa PS.
Deborah values were calculated for separations on monoliths with different macropore
sizes (see Appendix, section 2.5.3). At the point where the calibration curves in Fig. 5
show a reversal towards higher elution volumes the De values were almost always much
lower than 0.1. Thus, the present observations are not akin to the slalom
chromatography described elsewhere [31]. Conventionally, De numbers are calculated
for channels much larger than the diameter of the polymer coil (λ < 0.2). In that case the
elongation (Kdeb × ν /dp) can be assumed not to depend on the coil size. In the present
study we consider phenomena that occur for much higher λ values. Clearly, the
straightforward calculation of De values does not suffice to describe the observations in
such narrow channels, where the shear stress caused by the Poiseuille flow profile only
affect the periphery of the polymer coil and rotation of the coil is largely prohibited.
Very large polymers with λ ≈ 1 elute faster than the average fluid velocity (τ = 1; see
Fig. 5). This suggests that the polymer coils are “reptating” [33,34] through the
stationary-phase channels without significant restriction. Higher flow rates cause an
increase in the migration rate, which suggests that chain segments of the reptating coil
move towards the faster-moving central part of the Poiseuille flow profile (assuming
that the non-draining assumption holds). It appears that they no longer possess the
spherical coil geometry that prevails under equilibrium conditions at De < 0.1 in the
absence of constriction. The chromatographic selectivity arising from coil-reptation-
based elution is large and expected to cover the complete elution window of HDC. This
is supported by calibration curves obtained at different flow rates for materials 5
through 8 (cf. λ > 0.4 range in Fig. 5). It is not expected that a fully flexible polymer
such as polystyrene will uncoil at conditions of moderate constriction (λ ≈ 1), because
Chapter 2
60
of fast relaxation by Brownian motion under the conditions used here. In reptation or
translocation of charged polymers and biomaterials, however, complete elongation may
readily occur as a result of reduced flexibility in the polymers, highly constricted pores
or conditions featuring much slower relaxation due to Brownian motion [35, 36, 37, 38].
A different mechanistic explanation is therefore desired for flow-rate sensitive polymer
separation in monoliths.
A useful concept from the theory of flow-rate-dependent migration in HDC is “stress-
induced diffusion” (SID) [9,39]. This concept implies that polymers in Poiseuille flow
migrate away from the channel walls, driven by the lower entropy as a result of
elongation and reduced orientation by shear stress in this region. Migration towards the
channel center (and avoiding the elongating shear forces) leads to an increase in entropy
[40]. This effect is strongest at high shear rates and for high molecular weights. The
same arguments can be applied to reptating coiled polymers in confined channels.
Relaxation towards a spherical coil sampling the full channel diameter (natural trend to
increased entropy) will result in strong internal forces near the channel walls (induced
decrease in entropy). This effect is in agreement with the results for polymers eluted
from confined channels in monoliths in Fig. 5. Higher Mr polymers eluting at identical λ
from larger macropores get stronger deformed by SID due to their longer relaxation
times and the calibration curve demonstrates less reversal. The mechanism described
here is also in agreement with topology based separation by MTF [41,42]. Branched
polymers with identical hydrodynamic size but increased segment may exhibit stronger
resistance to SID compared to linear polymers under identical conditions. The
mechanism of an entropy-barrier was postulated before [41], but emphasized the role of
migration through orifices as compared to SID which takes place in continuous narrow
channels.
Hydrodynamic chromatography of macromolecules using polymer monolithic columns
61
2.4 Conclusions
Monolithic columns for separations of macromolecules were successfully prepared in-
situ in wide bore (4.6-mm I.D.) stainless-steel columns. The selectivity window
depended strongly on the size of the macropores tuned by the ratio of porogens. HDC is
the dominant mechanism of separation, since the mesoporous volume required for SEC
was too small. Also, calibration curves match with elution behavior as expected for
HDC separation up to λ = 0.2. Only for large-macropore monoliths, a deviation in
retention behavior is observed for small polymers (Mr < 20 kDa), which may be
explained by a combined HDC-SEC mechanism for λ < 0.02.
Macropores with much smaller hydrolic radii relative to packed columns were obtained
and therefore selectivity for lower-Mr macromolecules can be obtained. Our approach
allowed the preparation of monoliths with a pore size as small as 75 nm and a selectivity
window in HDC corresponding to a theoretical column packing with 0.17 µm particles
(DP = 4/9 dp). These monoliths have limited applicability for fast size-based separations
due to their low permeability. Monoliths with 258 nm macropores yielded polymer
separations in the molecular weight-range common for SEC separations. Selectivity
equivalent to 0.6 µm particles was demonstrated on this material with only 120 bar for
THF at 0.5 mm/s on a 100 mm column (Fig. 3). Size-based separations featuring
selectivity beyond what is possible with contemporary column-packing techniques are
readily obtained. The efficiency of polymers monoliths for HDC may be improved
further by optimization of the column heterogeneity.
For high-molecular weight polymers (Mr > 300,000 Da) the separation in monoliths
with confining channels strongly depended on flow rate. This situation differs from
other flow-rate dependent in that the shear rate is not identical throughout mobile phase
sampled by the coil. Response to the high shear rate experienced in the polymer-coil
periphery was suggested to result in departure from thermodynamic equilibrium
geometry and flow-rate dependent elution. This hydrodynamic-based explanation was
found to be in semi-quantitative agreement with experimental results for linear
polystyrene polymers.
Chapter 2
62
2.5 Appendix
In this supporting information extrusion data is provided from mercury intrusion
porosimetry. It is explained how this information may be helpful to confirm
compression of monolithic samples during porosimetry measurements.
Separation of alkylbenzenes on cross-linked polystyrene-co-divinylbenzene monoliths
and SEC-particles is presented to demonstrate the absence of adsorption effects and
diffusion of small molecules into the stationary phase compared to non-porous silica
columns.
The calculation of Deborah numbers is explained for polymer separations on monolithic
columns. Threshold values for molecular weight and λ are presented for the separation
conditions that were used in obtaining calibration curves for monolithic columns with
various macropore sizes.
2.5.1 Mercury intrusion and extrusion
Mercury extrusion data for two monoliths is presented in support of the discussion on
compression of monoliths. During the intrusion measurement the pressure was
increased up to 300 MPa. At this pressure porosity in pores with a diameter down to 5
nm can be measured. Porosity data for monolithic materials 7 and 8 (Table 2) was
obtained during both pressure increase and decrease and is presented in Fig. S-1.
Once the pressure is decreased, mercury will be extruded from pores again driven by its
surface tension. The pressure where extrusion will always be somewhat lower compared
to the intrusion pressure. Compression of the material during intrusion measurement
will result in a higher pressure required for mercury intrusion, because the pores become
smaller when the material is compressed. If the compression is a reversible process, the
sample will reassume its equilibrium dimensions once it has been intruded by the
mercury under high pressure. Little or no effect of compression is expected for the
extrusion pressure. The higher pressure difference between intrusion and extrusion
pressure for material 8 supports the assumption that this material suffers more
compression compared to material 7 at the moment of mercury intrusion.
The recovery may depend on actual pore geometry as well as the rate at which pressure
was reduced. For the results presented here pressure was decreased at a faster rate
Hydrodynamic chromatography of macromolecules using polymer monolithic columns
63
compared to the pressure increase. A study of mercury extrusion under well controlled
conditions can reveal useful information with respect to sample compression during the
intrusion measurement. Unfortunately, such data was not acquired for the work here,
because the hypothesis of compression was formed after most of the measurements
were completed.
Fig. S-1. Mercury intrusion during pressure increase and decrease
Chapter 2
64
2.5.2 SEC separation of alkylbenzenes and solvents on monolith
The elution for ionol, benzene, toluene and alkylbenzenes was measured to confirm that
absence of adsorption effects. Ionol, benzene, toluene, ethylbenzene, propylbenzene,
butylbenzene and hexylbenzene were diluted in THF before injection at a concentration
of about 1 mg/ml. Detection was performed by UV at 260 nm. All separations were
performed at room temperature to minimize axial diffusion. Column dimensions were
150 × 4.6 mm I.D. in each case.
(A) Monolithic material 4, DP 258 nm, 100 µL/min THF
(B) 106 Å PLgel, dp 10 µm, 200 µL/min THF
(C) Non-porous silica, dp 1.0 µm, 100 µL/min THF
The elution order in Fig. S-2 and S-3 was, from left to right, ionol, hexylbenzene,
butylbenzene, propylbenzene, ethylbenzene, toluene/benzene with the lowest peak
height for benzene. In Fig. S-4 all elute at the same volume, because the samples do not
diffuse into or adsorb onto the non-porous silica.
Fig. S-2. Separation of small molecules on cross-linked PS-DVB monolith (A)
Hydrodynamic chromatography of macromolecules using polymer monolithic columns
65
Fig. S-3. Separation of small molecules on cross-linked PS-DVB SEC particles (B)
Fig. S-4. Separation of small molecules on non-porous silica (C)
Chapter 2
66
2.5.3 Deborah numbers
The polystyrene molecular weight corresponding to a Deborah value of 0.1 was
calculated using Eq. 6. This specific value of De = 0.1 was used, because it provides the
lower limit where the effects of polymer deformation may be observed. For each
monolith the flow rate that was used to obtain its calibration curve in Fig. 5a was used.
Common variables used in calculating De were a viscosity of 0.356 Cp for THF at
50°C, a Flory-Fox parameter of 2.5⋅1023 mol-1 and fictive particle size of dp = 4/9 DP.
The results are presented in Table S-1 and Fig. S-5. The onset of deformation is reached
at increasingly lower molecular weight with smaller macropore size. However, it was
not reached within the classic HDC selectivity range for separations on monolithic
columns.
The mobile phase flow-rate directly impacts the expected onset of deformation.
Deborah scales linear with both particle size (channel size) and average linear mobile-
phase velocity u0. In practice the flow rate and thus u0 are a result from backpressure
limitations and permeability of the column. According to Hagen-Poiseuille (Eq. 2) u0
scales quadratic with increasing pore size at identical backpressure. Therefore,
deformation of analytes is more commonly observed for highly permeable stationary
phases with large interstitial pores. De > 0.1 is reached at much lower backpressure,
within the range of common separation conditions.
Table S-1. Lower-limits for polymer deformation according to Deborah-number calculation, expressed in PS molecular weight and λ.
Monolithic material
DP
(nm) Flow rate (µL/min)
De = 0.1 PS Mr (MDa)
De = 0.1 λ
1 1194
2 571 300 2.0 0.22
3 321 300 1.45 0.32
4 258
5 241 50 3.4 0.72
6 162 50 2.7 0.93
7 126 50 2.35 1.09
8 104 50 2.1 1.25
9 75 20 3.0 2.15
Hydrodynamic chromatography of macromolecules using polymer monolithic columns
67
Fig. S-5. Calibration curves on monoliths with different macropore size with diamonds indicating
De = 0.1 for conditions described in Table S-1.
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69
Chapter 3: Branched-Polymer Separations using
Comprehensive Two-Dimensional Molecular-Topology
Fractionation × Size-Exclusion Chromatography
Abstract
Branching has a strong influence on the processability and properties of polymers.
However, the accurate characterization of branched polymers is genuinely difficult.
Branched molecules of a certain molecular weight exhibit the same hydrodynamic
volumes as linear molecules of substantially lower weights. Therefore, separation by
size-exclusion chromatography (SEC), will result in the co-elution of molecules with
different molecular weights and branching characteristics. Chromatographic separation
of the polymer molecules in sub-micron channels, known as molecular-topology
fractionation (MTF), may provide a better separation based on topological differences
among sample molecules. MTF elution volumes depend on both the topology and molar
mass. Therefore co-elution of branched molecules with linear molecules of lower molar
mass may also occur in this separation. Because SEC and MTF exhibit significantly
different selectivity, the best and clearest separations can be achieved by combining the
two techniques in a comprehensive two-dimensional (MTF×SEC) separation system. In
this work such a system has been used to demonstrate branching-selective separations of
star branched polymers and of randomly long-chain branched polymers. Star-shaped
polymers were separated from linear polymers above a column-dependent molecular
weight or size.
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3.1 Introduction
Knowledge of the relationships between polymerization conditions and functional
properties of the polymers being formed enables polymer chemists to make materials
that are largely optimized for their application. High-performance polymers meet
specific needs in the market place. The desired properties of such polymers are typically
achieved by optimizing the parameters of the polymerization process. Such an
optimization can be performed much more efficiently when key structural parameters
affecting polymer properties are understood. Meaningful structure-property
relationships can only be developed if the key structural parameters can be measured. In
the case of branched polymers, a more detailed description of branching, beyond a basic
estimate of the average number of branch points per molecule, is required. Distributions
of the molecular properties must be revealed, which requires that the molecules with
different degrees of branching be separated, ideally in combination with selective
detection techniques. Knowledge of detailed molecular characteristics and their effect
on functional properties will ultimately allow the design of high-performance polymers.
Spectroscopic techniques (e.g. Fourier-transform infrared, FTIR, or nuclear magnetic
resonance, NMR) and physical measurements (e.g. light scattering or viscometry) are
used on a routine basis to characterize the overall (or average) molecular structure of
polymers. Using hyphenated techniques (typically combinations of a chromatographic
separation with one or more spectroscopic or physical methods) more information
concerning the distributed properties may be obtained. Size-exclusion chromatography
(SEC) with light scattering and/or viscometry detection is commonly used to
characterize long-chain branching (LCB) in high-molecular-weight polymers [1,2,3].
The characterization of LCB in polymers is of particular interest, because of the
influence of LCB on processing properties, such as zero-shear viscosity and melt
strength. Branching factors based on the Zimm-Stockmayer theory [4] may be
calculated when a linear-polymer (reference) sample with identical chemistry or its
Mark-Houwink parameters are available. These can subsequently be converted to
branching frequencies if assumptions are made regarding the functionality of the
branching points and the average branch length. SEC with selective detection is,
however, not able to fully characterize branched polymers. Separation by size of the
Branched-Polymer Separations using Comprehensive 2D MTF × SEC
71
unperturbed chain in solution yields fractions containing molecules with equal
hydrodynamic volumes, but with different topologies and molecular weights. This
distribution cannot be characterized by selective detection techniques. For example,
light scattering only provides the weight-average molecular weight for the ensemble of
chains eluting in each SEC fraction. Molecular-weight polydispersity at a given SEC
elution volume was recently confirmed by comparing selective-detection techniques
that yielded different types of molecular-weight averages (weight average from light
scattering and number average from viscometry, [5]). The authors demonstrated that the
so-called local polydispersity was affected by the distribution of the degree of branching
and the functionality. NMR is an alternative technique for determining the structure and
the frequency of branch points, but the technique has some limitations. A high-field
instrument is needed to detect and quantify low levels of LCB, but discrimination of
different branch lengths is still not possible when branches are longer than a few carbon
atoms [6]. Most importantly, NMR provides only an average number of branches per
molecule.
Multi-dimensional separations can be used to study complex polymers that feature more
than one distribution simultaneously. In a comprehensive two-dimensional separation
system, denoted by the “×” sign, every part of the sample is subjected to two
independent mechanisms and the separation obtained in the first dimension is
maintained in the final two-dimensional chromatogram) [7]. The peak capacity is
increased substantially by comprehensive operation of multi-dimensional separations.
However, the separation power is only used efficiently when different selectivity in
each separation dimension allows the sample to be separated among its distributions of
interest [8,9]. Only in orthogonal separations the retention times in the different
dimensions are by definition completely independent (uncorrelated). Although most
multi-dimensional separation systems are not orthogonal, confounded distributions that
remain unresolved in a single separation step can be separated using two independent
separations with different selectivity. Therefore, complex polymers with distributions in
distinct molecular properties can successfully be resolved using multi-dimensional
systems. Separations by functionality [10] and chemical composition [11] have, for
example, been combined with separations according to size using SEC to fully elucidate
two mutually dependent distributions.
Chapter 3
72
Branched polymers can also be separated using combinations of independent
separations, such as interactive liquid chromatography and SEC, in a comprehensive
two-dimensional setup. Selectivity for branched versus linear polymers has resulted
from differences in the number of repeat units, number of branch points or size in
solution. Star polymers prepared by coupling living polystyrene anions were separated
by an off-line combination of temperature-gradient interaction chromatography (TGIC)
and SEC [12]. The TGIC separation is thought to be based on molecular weight, while
SEC is based on the size of molecules in solution. The relationships between molecular
weight and hydrodynamic volume are different for branched and linear polymers
allowing separations of differently branched polymers by a combination of both
methods. Similar star polymers of lower molecular weights were separated on-line by
liquid chromatography at the critical composition in combination with either SEC or
TGIC (LCCC×SEC or TGIC×LCCC [13]). In the LCCC separation, branched polymers
were separated by interaction of the apolar side-groups at the coupling agent. The
techniques described here yielded good separations for branched homo-polymers with
numerous branches and chemically different branch points or end groups. High-
molecular-weight polymers, with very little long-chain branching (LCB), or without
functional groups at the branch points or chain ends of different polarity cannot be
separated using these techniques.
For LCB polymers, complete separation may be obtained when the polymer is also
separated based on branching parameters. Such a separation has previously been
demonstrated on monolithic columns containing sub-micron macro pores [14] and on
columns packed with sub-micron particles [15]. Both separation systems featured sub-
micron flow channels. Polymers above a stationary-phase dependent molecular weight
become retained at low flow rates. Branched polymers were found to elute much later
than linear ones of the same molecular weight. This separation method was termed
molecular-topology fractionation (MTF) and it was thought to result from the topology-
dependent relaxation-time spectrum of polymers in dilute solution [15]. The word
topology reflects the geometrical structure of the polymer molecules, more specifically
the branch length, frequency and functionality of the branch points. Separation of
branched polymers by MTF can only be applied to samples with very narrow
molecular-weight distributions, since the degree of polymerization also affects the
Branched-Polymer Separations using Comprehensive 2D MTF × SEC
73
retention. Off-line fractionation of LCB polymer by SEC and re-injection of the
fractions in MTF was used to demonstrate the differences in selectivity of the two
techniques for LCB polymers [15]. Similar to the comprehensive two-dimensional
separation systems (described in the previous paragraph) for separating star polymers,
samples featuring LCB could be resolved when the separation dimensions display
significantly different selectivity towards long-chain branching and hydrodynamic size.
In this paper, the separation of long-chain branched polymers using MTF×SEC will be
demonstrated. Knowledge of the relationship between molecular weight, hydrodynamic
size and branching will be used to interpret the selectivity in MTF separations. The
separation of polymers with similar hydrodynamic size, but different topologies is
demonstrated for star polymers with narrow molecular-weight distributions. Results on
the separation of randomly long-chain-branched polymers and star polymers will be
used to discuss the selectivity of MTF and the applicability MTF×SEC for the
separation of complex samples of branched polymers.
3.2 Experimental
3.2.1 Samples and materials
The eluent for MTF and SEC separations was non-stabilized HPLC-grade
tetrahydrofuran (THF; Biosolve, Valkenswaard, The Netherlands); it was continuously
degassed by purging with helium 5.0 (99,999% Praxair, Vlaardingen, The Netherlands).
Sample polymers were dissolved in HPLC-grade THF stabilized with 250 ppm butyl-
hydroxylated toluene to prevent degradation by radicals. Narrowly distributed linear
polystyrene standards (Polymer Laboratories, Church Stretton, UK) were used to study
retention behaviour. These standards were dissolved at concentrations of 0.5 mg/mL. A
nominal three-arm star polystyrene sample was obtained from Polymer Source (Dorval,
Canada) and used at a concentration of 1.0 mg/mL. This star polymer was synthesized
by coupling of anionically polymerized arms with a tri-functional agent (α,α’,α’’-
trichloromesitylene). The manufacturer specified a nominal molar mass of 1,480 kg/mol
for the precursor arms. However, thorough analysis using size-exclusion
chromatography with low-angle light scattering and differential viscometry revealed an
arm molar-mass closer to 1,250 kg/mol. The sample composition was determined from
Chapter 3
74
the same experiment. Integration of the concentration signal revealed ~5% to be
uncoupled precursor, ~45% linear polymer with double the precursor molecular weight
and a remainder of three-arm coupling product. A small amount of higher-coupling
products as a result of lithium-halide exchange [16,22] was evident from the overall
molecular weight of the star-polymer sample as estimated by SEC with light-scattering
detection. A four-arm coupling side-product by lithium-halide exchange is expected to
have all arms coupled in one functional centre. The concentration of this large-molecule
fraction could not be determined quantitatively by SEC. The reaction scheme of the
coupling and analysis results have been presented by Meunier et al. [15]. Polystyrene
with a high LCB frequency was obtained from the Dow Chemical Company (Midland,
MI, USA). The Mark-Houwink plot and information on the molecular-weight
distribution of this material can be found in the supplementary information of this
article. Details regarding the preparation of this high-LCB sample can be found
elsewhere [17].
A custom-made 150 mm × 4.6 mm I.D. column packed with 10-µm 106 Å PLgel
particles by Polymer Laboratories was used for fast SEC as the second dimension
separation at a flow rate of 750 µL/min. The MTF-column packing consisted of a
polydisperse mixture of particles in the range of 0.1 to 1 µm (Admatech, Aichi, Japan).
Particle-size-distribution data provided by the supplier revealed that the average particle
diameter was 0.5 µm and the half-width of the distribution was about 0.3 µm. The
particles were functionalized with C8 chains to facilitate the packing procedure. A 150
mm × 4.6 mm I.D. column was packed by Diazem (Midland, MI, USA) using an
identical procedure as that used previously for packing columns for MTF [15].
3.2.2 Instrumentation and methods
Comprehensive two-dimensional MTF×SEC was performed on a system assembled in-
house. Basic components of the system were two LC10ADvp pumps (Shimadzu, ‘s
Hertogenbosch, The Netherlands) to perform isocratic separations in the two
dimensions, along with an SCL10a system controller (Shimadzu) for interfacing with
the data-acquisition computer. Either 10 or 20 µL injections of the samples were
performed by a SIL9a autosampler and columns were kept at 50°C in a CTO7 column
oven (both from Shimadzu). Detection in MTF×SEC experiments was performed using
Branched-Polymer Separations using Comprehensive 2D MTF × SEC
75
a Spectroflow 757 (ABI, Ramsey, NJ, USA) UV-absorbance detector equipped with an
8-µl flow cell. Data acquisition was typically performed at 5 Hz, recording the signals
of both detectors. A capillary UV detector was used (Linear UVIS 200, Linear
Instruments, Reno, NV, USA) to record the data for the calibration curve in Fig. 1. The
detector wavelength of UV detectors was set to 260nm, close to the absorption
maximum of polystyrene in tetrahydrofuran.
Modulation in comprehensive two-dimensional separations was accomplished with an
air-actuated VICI two-position 10-port valve (Valco, Schenkon, Switzerland). This
valve was operated using a high-speed switching accessory. The digital valve interface
(DVI; Valco) was connected to the SCL10a system controller. The 10-port valve was
plumbed for symmetrical dual-loop modulation [11]. Two injection loops of equal
volume (43 or 92 µL) were used. From the moment of injection on the MTF column,
the 10-port valve was switched either every 2, 2.67 or 4 minutes in order to inject 40
µL from the first dimension (running at 20, 15 or 10 µL/min respectively) at the SEC
column. Instrument control and data acquisition were achieved with ClassVP v7.4
build15 software (Shimadzu). Exported data were processed in Matlab v7.3 (The
Mathworks, Natick, MA, USA) using in-house written software for data folding and
visualization of two-dimensional colour plots.
3.3 Results and discussion
3.3.1 Calibration curve for molecular-topology-fractionation column
Linear polystyrene standards with a well-defined molecular-weight distribution (MWD)
are readily available, in contrast to well-characterized branched polymers with high
molecular weights. Therefore, linear polystyrenes were used to determine retention
behaviour in MTF as a function of molecular weight. The elution volume at the peak
maximum is plotted against the logarithm of the peak molecular weight in Fig. 1.
Reversal of the curve is observed around 200 kg/mol. The molecular weight where such
a reversal occurs will be referred to as the critical molecular weight Mcrit for reversal.
The elution order for polymers below Mcrit was consistent with that observed for
polystyrenes separated on columns packed with 1-µm, non-porous particles and can be
explained as hydrodynamic chromatography [18]. The interest in MTF stems from the
Chapter 3
76
elution region above Mcrit, because in this range the selectivity for branching (molecular
topology) has been observed [14, 15]. Although branched molecules are more
effectively retained than linear ones (section 3.2), the flow-rate effect on retention of
linear molecules may be used as a benchmark for the MTF selectivity of the column.
Fig. 1. MTF calibration curve for linear polystyrenes; obtained at a flow rate of 20 µL/min, at 10 µL/min.
Retention times of linear polymers above Mcrit were measured at two different flow
rates. The influence of flow rate on retention volume is much larger for high molar
masses, i.e. above Mcrit. Elution-order reversal has also been observed for polystyrene
standards in hydrodynamic chromatography (HDC) on columns packed with 1-µm non-
porous particles [18], but in that case the effect is very much smaller than observed for
MTF. In HDC the reversal in the calibration curve has been explained by shear
deformation of the polymers in solution [18]. After such a deformation the radius of the
polymer molecules perpendicular to the direction of flow is effectively smaller
compared to its unperturbed state. As a result the deformed molecules can get closer to
the channel walls, where the linear velocity is lower, and elute later from HDC columns.
Reversal due to polymer deformation is expected to be observed most strongly at high
shear and thus high flow rates. This is indeed observed in HDC, but not in the present
MTF system, where the effect is strongest at the lowest flow rates (Fig. 1). Our
calibration curves (molecular weight vs. elution volume) are thus not in agreement with
HDC data. However, our results are in agreement with observations in previous MTF
studies [14]. Thus, the separation mechanisms in HDC and MTF are based on different
principles.
Branched-Polymer Separations using Comprehensive 2D MTF × SEC
77
One important difference between the more conventional chromatographic separation
techniques (SEC, HDC, or field-flow fractionation, FFF) and MTF is the aspect ratio
(λ), defined as the ratio of the effective radius of the polymer in solution and the radius
of the channel that it is migrating through. Hydrodynamic separation techniques (such
as HDC) are typically operated below λ = 0.2 [19], whereas branching selectivity in
MTF is obtained only at values of λ that exceed this value. HDC theory predicts that for
large values of λ the forces resulting from rotation and solvent lagging (inertia) will
reduce the migration rate of the polymer, ultimately resulting in elution volumes greater
than the column volume. Shear alignment or deformation at such high values of λ may
be responsible for decreasing retention with increasing flow rate for large polymers
(above Mcrit). However, this is unlikely in MTF considering that the linear velocity of
the mobile phase is several times lower for MTF than in HDC with 1-µm particles [18].
A quantitative comparison of λ values for the different separation systems cannot be
made, because absolute values of the average diameter of the flow-through channels are
hard to obtain for the column used in this study. The flow path in particle packed beds is
much more complex than that in open-tubular channels, for which HDC theory was
derived. Successful attempts to relate hydrodynamic retention in particle packed beds
with retention in capillaries were made by using the hydraulic radius to define the
interstitial channel diameter [18, 20, 21]. However, the polydisperse packing material of
the present MTF column complicates the use of the classical concepts. Stationary
phases with well-defined channel parameters will have to be used to for a robust
comparison of HDC and MTF in terms of the aspect ratio.
3.3.2 Branched-polymer separations
Because branched polymers and linear polymers of the same hydrodynamic size co-
elute in SEC, triple-detection SEC can only be used to obtain the average number of
branches per molecule at any given elution volume. Therefore, branching properties
cannot be fully characterized when polymers are separated by hydrodynamic size only.
Comprehensive two-dimensional separation by hydrodynamic size and by branching
properties will be used to demonstrate this point. MTF is used in the first dimension to
fractionate polymers that vary in molecular weight and/or branching properties. This
choice for MTF in the first dimension is dictated by the experimental conditions. MTF
Chapter 3
78
is operated at flow rates between 10 and 20 µL/min on a 150 mm × 4.6 mm I.D.
column, resulting in analysis times of one or several hours. Therefore, MTF is
convenient as a (slow) first-dimension separation, but it cannot be applied as a (fast)
second-dimension separation. In MTF×SEC, 120 fractions of 40 µL each were collected
using the two-way 10-port switching valve. These fractions were injected and analysed
in real time on a fast SEC column. The same number of fractions was collected,
irrespective of the first-dimension flow rate. The time used for collection and second-
dimension separation was adapted to the first-dimension flow rate. By keeping the
number of fractions and the second-dimension flow rate constant, we were able to
directly compare the resulting chromatograms in terms of (MTF) resolution in relation
to the hydrodynamic size (SEC retention volume) of the molecules.
A sample of a star polymer, prepared by coupling anionically polymerized linear
polystyrene [22], was used for our studies. Because the PS-precursors possess a very
narrow molecular-weight distribution, the sample exhibits a nearly discrete relationship
between molecular weight and topology (the number of branches connected to the
coupling point in the molecule). The molecular weight of the PS-precursor was
determined to be 1,250 kg/mol [15]. In the star synthesis of the star polymers, coupling
was performed by reaction of the living ends of the precursor polymers with a tri-
functional coupling agent. Besides a three-arm star molecule, some unreacted linear
polymer remains and linear two-arm polymers are formed, as well as some higher order
coupling products. The presence of a four-arm star was first demonstrated using one-
dimensional MTF with low-angle-light-scattering detection [15]. More details on the
synthesis and composition of the star polymer can be found in the experimental section.
Linear polymers with molar masses comparable to the coupling products of the
precursor polymer were injected for reference purposes.
Coupling of one, two or three precursor polymers (arms) used for the star-polymer
sample would result in the peaks as observed in figure 2a, b and c if the MTF separation
would be based solely on molecular weight. In the chromatogram of the star sample in
Fig. 3a, which was obtained using identical experimental conditions, two peaks (1.60
and 2.68 mL) are observed at MTF elution volumes higher than any of the peaks
observed in Fig. 2. The elution volumes corresponding to peak-maxima have been
Branched-Polymer Separations using Comprehensive 2D MTF × SEC
79
summarized in Table 1 for both dimensions. Because retention of branched molecules is
expected to be higher in MTF, it can be tentatively concluded that the peak in Fig. 3a at
VMTF = 1.6 mL is due to the three-arm star-shaped coupling product. Comparison of
VSEC values suggests that the hydrodynamic size of the three-arm star is close to that of
the linear polymer of 2,536 kg/mol. Both the increased retention in MTF and the
decreased elution volume in size-exclusion chromatography compared to linear polymer
of identical mass can be explained by branching. The last peak eluting in Fig. 3a is
consistent with a higher order star as the peak has nearly the same SEC retention
volume as the three-arm star, but is retained much longer in the MTF column. The
probability of such products being formed decreases with increasing functionality, but
the presence of a peak corresponding to the four-arm coupling product is clearly visible
in Fig. 3a.
At lower MTF flow rates the components of the star-polymer sample were better
separated. This is illustrated in Fig. 3b and 3c where flow rates of 15 and 10 µL/min
were used. At low flow rates the calibration curves in MTF become less steep (Fig.1 )
and branched components are retained much longer. Because of the very slow
molecular diffusion of high molecular-weight polymers we do not anticipate increased
band broadening at very low flow rates. Indeed, peak broadening is hardly affected by
the long residence time in the MTF column (Fig. 3). Comparison of the peak widths in
Fig. 3 with those of the linear polystyrene standards (with Mw/Mn 1.03 – 1.04) in Fig. 2
shows that the peak widths of branched polymers are not significantly greater than those
of narrowly distributed linear standards. The observed broadening may be due to the
limited efficiency of the column. Furthermore, it is known that overloading occurs
easily in HDC. Therefore, overloading may also be a threat when using MTF. The low
porosity (ε = 0.3) of the column may well aggravate the loadability issues.
To assess whether shear degradation was occurring in the system, polymer elution was
studied as MTF flow rate was varied. It was speculated that at relatively high flow rates
in MTF shear-induced degradation (i.e. chain scission) of the polymer could occur.
Because even partial degradation of the polymer is likely to have a significant effect on
the hydrodynamic-size distribution of the polymer, MTF×SEC provides information on
the likelihood of chain scission. Neither increase in SEC elution volume nor tailing in
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80
the SEC dimension towards lower molecular weights was observed as MTF flow rate
was increased. Thus, polymer molecules do not appear to be shear degraded as a result
of MTF separation. Shear degradation in the SEC separation has been addressed in the
supporting information of this article. No significant evidence for shear degradation that
might impair the integrity of MTF×SEC was found. It is much more difficult to
establish whether or not the polymer molecules are deformed during the MTF
separation. If they are, it is likely that the molecules relax to their unperturbed shapes
before they are analysed by SEC or characterized by light scattering.
Table 1. Peak maxima in MTF and SEC for different first-dimension flow rates.
MTF 20 µL/min MTF 15 µL/min MTF 10 µL/min
Vmax (mL) MTF SEC MTF SEC MTF SEC
1,373 kg/mol 1.08 1.43
2,536 kg/mol 1.24 1.35
3,742 kg/mol 1.24 1.31
1-arm linear polymer 1.00 1.47 1.12 1.46 1.20 1.47
2-arm linear polymer 1.16 1.37 1.40 1.36 1.72 1.37
1.60 1.34 2.12 1.34 3.28 1.34
4-arm star polymer 2.68 1.33 > 3.5 > 3.5
Another example of the separation of a branched polymer is presented by the separation
of a broadly distributed polystyrene (PDI = 3.3, see supplementary information) with
random long-chain branching (LCB) in Fig. 4a. For a sample with a considerable degree
of LCB (MTF flow rate 20 µL/min) a low-concentration tail towards higher MTF
elution volume is observed which is considerably different from that of the three-arm
star polymer sample. However, the star sample contained discrete populations of
branched species which could be separated into discrete peaks in the MTF separation.
On the other hand, the broadly distributed PS contains a nearly continuous distribution
of branched components varying in the number of branch points and branch lengths.
The fact that peaks in the MTF separation tail to larger elution volumes, while the SEC
separation becomes constants, suggests that this distribution of branching may result in
separation in the MTF direction. Elution of this material in the SEC dimension was
compared to that of the linear polymers shown in Fig. 2. The peak maximum of the
Branched-Polymer Separations using Comprehensive 2D MTF × SEC
81
branched PS in SEC for an MTF elution volume of 1.24 mL was 1.47 mL. This is
considerably different from the 1.35 mL and 1.31 mL that were found for linear
polymer (table 1).
Fig. 2. (left). Comprehensive two-dimensional MTF×SEC of linear polystyrene standards with MTF at 20 µL/min. Nominal molecular weights (a) Mp 1373 kg/mol, (b) 2536 kg/mol, (c) 3742 kg/mol,
(a)/(b)/(c) 126.7 kg/mol (internal-reference peak in top-left corner).
Fig. 3. (right). Comprehensive two-dimensional MTF×SEC of linear and star-branched polymers. (a) MTF at 20 µL/min, (b) MTF at 15 µL/min, (c) MTF at 10 µL/min.
Chapter 3
82
Fig. 4. Separations of a polystyrene sample with a broad MWD and a high degree of LCB
(a) MTF×SEC, (b) SEC×SEC
An important question is whether or not the samples are fully eluted from the MTF
column (featuring sub-µm flow-through channels). Recovery may be negatively
affected if the flow rate is decreased in order to increase resolution. At 15 µL/min the
four-arm star polymer is no longer observed to elute within about five column volumes
(Fig. 2b). The chromatograms in Fig. 2 were integrated over MTF volumes from 0.5 to
3.5 mL and SEC volumes from 1.15 to 1.7 mL. Compared to MTF performed at 20
µL/min, only 89% of the sample was eluted at 15 µL/min in the same retention window.
For 10 µL/min this relative recovery drops to 80%. The sample that is not recovered is
expected to elute after the elution window as a result of increased retention. The
separation was not extended long enough to observe all the branched polymers at flow
rates below 20 µL/min. Therefore, the run length was increased in subsequent
experiments for recovery studies (Fig. 5a). Furthermore, these experiments were all
performed at 20 µL/min.
Fig. 5. Separations of the star-polymer sample (a) MTF×SEC, (b) SEC×SEC
Branched-Polymer Separations using Comprehensive 2D MTF × SEC
83
To assess absolute sample recovery in the MTF×SEC system, the MTF column was
replaced by a SEC column (V0 = 1.2 mL; Fig. 4b and 5b). The experimental conditions
were equal to those for MTF×SEC, except that the first-dimension separation was run
until only 1.5 times the total permeation volume had passed through the first-dimension
SEC column. No polymer is expected to elute after this point. This showed that in the
MTF×SEC set-up linear polymers with high molecular weight (Fig. 2) and the LCB
polystyrene (Fig. 4) were all recovered quantitatively (> 95%). The star polymer sample
was recovered for 92% (average of triplicate MTF×SEC measurements) when
integrated over MTF volumes from 0.5 to 4.7 mL (Fig. 5a). When the integration was
extended to a volume of 7.2 mL the recovery was also found to be quantitative (>95%).
3.4 Conclusions
Molecular-topology fractionation (MTF) provides branching-selective separation. The
technique can be used to separate molecules according to their degree of long-chain
branching, but only for samples with extremely narrow molecular-weight distributions.
In all other cases, the effect of branching on retention in MTF is confounded with the
effect of molecular weight. A solution to this problem has been found by combining
MTF and size-exclusion chromatography into a comprehensive two-dimensional
separation system. This MTF×SEC technique was used to clearly demonstrate the
branching-selective separation obtained by MTF for a sample of (narrowly distributed)
star-shaped polystyrenes. MTF×SEC was also applied to a broadly distributed
polystyrene sample that featured a high degree of long-chain branching (LCB).
Although some selectivity was observed, the separation may need to be improved if we
are to obtain quantitative measures for LCB. However, even in the present, immature
state, the fractionation of LCB polymers may prove to be useful in predicting
rheological properties of polymers.
Only high-molecular-weight polymers were separated using MTF for this study. The
range of applicability of MTF is limited to the range above the reversal molecular
weight (Mcrit), which in turn depends on the diameter of the flow-through-channels.
Several improvements are foreseen in the near future. The presently used MTF column
was packed with polydisperse particles. It is difficult to obtain such columns, let alone
Chapter 3
84
pack them reproducibly. Even the repeatability of nominally identical columns is poor.
It is also difficult to use these columns to perform fundamental studies on MTF, because
accurate information regarding the size of the inter-particle (flow-through) channels is
cannot be obtained. Because it is difficult to accurately characterize the channel
dimensions in these packed columns, the relationship of the former with elution
behaviour is challenging to evaluate. Columns packed with mono-disperse particles are
needed to sensibly compare hydrodynamic chromatography (HDC) and MTF. However,
because the two techniques operate in different regimes of the aspect ratio (size of
molecules compared with that of the flow channels) and because the effects of changes
in the flow rate were found to be opposite, we believe that HDC and MTF are based on
different separation mechanisms. Columns that are well packed with uniform sub-
micron particles are also difficult to obtain. Monolithic stationary phases with well-
characterized sub-micron flow-through pores may be a viable alternative. The use of
such monolithic columns for MTF separations will be reported elsewhere.
3.5 Appendix
MTF column parameters
The column volume and efficiency were determined by injection of 5 µL of a 1000-ppm
solution of ethylbenzene. At a flow rate of 20 µL/min THF and a column-oven
temperature of 50°C ethylbenzene eluted at 38.1 minutes. Therefore, the MTF column
volume (V0) was 762 µL, the efficiency of the separation was 3400 plates per meter.
The porosity of the packing was calculated by dividing the ethylbenzene elution volume
by the theoretically calculated volume of the empty column (150 x 4.6 mm) and was ε =
0.30.
Characterization of long-chain-branched polystyrene sample
The long-chain-branched (LCB) polystyrene sample was characterized using size-
exclusion chromatography (SEC) with multi-angle light scattering (MALS) and on-line
viscometry detection. The SEC columns used were three mixed-B columns (300x7.5
mm each; 10-µm particles) from Polymer Labs (Church Stretton, UK). Stabilized THF
Branched-Polymer Separations using Comprehensive 2D MTF × SEC
85
(J.T. Baker, Deventer, The Netherlands) was used as the mobile phase at a flow rate of 1
mL/min.
The weight-average molecular weight of the LCB polymer (measured by SEC-MALS)
was 810 kg/mol with a polydispersity of PDI = 3.3. The presence of long-chain
branching at high molecular weights is illustrated by the reduction in intrinsic viscosity
in the Mark-Houwink plot in Fig. 1.
Fig. S1. Mark-Houwink plot for the long-chain branched polystyrene used in this article
and a linear reference polystyrene polymer.
Verification of SEC at elevated flow rates
SEC was performed at two and a half times the recommended flow rate in the
MTF×SEC experiment. The impact of separation at elevated flow rates was validated by
performing SEC separations comparable to those in a two-dimensional experiment at
the recommended and elevated flow rates.
SEC was performed at 300 and 750 µL/min on a 150 mm x 4.6 mm I.D. column with
10-µm PLgel particles with a pore size of 106 Å. The porosity of the frits in this column
was 5 µm. The mobile phase was non-stabilized tetrahydrofuran (Biosolve,
Valkenswaard, The Netherlands) and separations were performed at 50°C. The injection
volume was 5 µL of polymer solution. Four samples and one blank were injected in
duplicate. Polystyrenes with peak molecular weights of 7,450, 3,742, 2,536 and 1,373
kg/mol (Polymer laboratories, Church Stretton, UK) were dissolved in tetrahydrofuran
individually at a concentration of 0.1 mg/mL. The samples with 3,742, 2,536 and 1,373
Chapter 3
86
kg/mol polystyrene were all used with an additional 0.2 mg/mL of 126.7 kg/mol
polystyrene (reference standard). All four samples and the blank contained
approximately 250 ppm butyl-hydroxylated toluene to prevent degradation by radicals.
Detection was performed using a Spectroflow 757 (ABI, Ramsey, NJ, USA) UV-
absorbance detector equipped with an 8-µl flow cell and set for detection at 260 nm.
The chromatograms have been overlaid in Fig. S2. An x-axis multiplier was chosen to
have this x-axis display the elution volume. Peak assignment for Fig. S2 from left to
right: 7,450, 3,742, 2,536, 1,373 and 126.7 kg/mol linear polystyrene, ionol, injection-
solvent related peak.
Fig. S2. UV absorbance of high molecular weight polystyrenes at 750 µL/min (offset 0 mAU) and 300
µL/min (offset 15 mAU). Retention times are annotated in red for 7,450 kg/mol PS, ionol and an injection-solvent related peak.
For all high-molecular-weight PS polymers a shift towards higher elution volume is
observed when separated at 750 µL/min. This shift is small compared to the separation
of the individual standards and therefore has a small effect on the separation. The shift
in elution volume may possibly be explained by the slow diffusion of high-molecular-
weight polymers, being responsible for incomplete inclusion of the polymer in the pores
of the packing material. If any shear degradation were to occur, this would be expected
to result in significant tailing and changes in the peak shape. Only the peak front of the
7,450 kg/mol appears to be deformed at 750 µL/min. Absolute molecular-weight
determination techniques, such as low-angle laser light scattering, can be used to
discriminate between poor chromatography or shear degradation. Because fast SEC is
not used for absolute-molecular-weight determination, this discussion is beyond the
Branched-Polymer Separations using Comprehensive 2D MTF × SEC
87
scope of the present article. Based on the results in Fig. S2 we conclude that peak
elution volumes for polystyrene polymers up to a molecular weight of 7,450 kg/mol
may be used to compare hydrodynamic size parameters at 750 µL/min. under the
conditions used for MTF×SEC.
References
[1] T.H. Mourey, Int. J. Polym. Anal. Charact. 9 (2004) 97.
[2] S. Pang, A. Rudin, in T. Provder (Editors), Chromatography of Polymers (ACS Symposium Series, No.
521), American Chemical Society, Washington, DC, 1993, p. 254.
[3] K.D. Caldwell, in H.G. Barth, J.W. Mays (Editors), Modern Methods of Polymer Characterization,
Wiley, New York, 1991, p. 113.
[4] B.H. Zimm, W.H. Stockmayer, J. Chem. Phys. 17 (1949) 1301.
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Chromatogr. A 1190 (2008), 215.
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[7] P.J. Schoenmakers, P. Marriott, J. Beens, LC-GC Eur. 16 (2003) 335.
[8] J.C. Giddings, J. Chromatogr. A 703 (1995) 3.
[9] P.J. Schoenmakers, G. Vivó-Truyols, W.M.C. Decrop, J. Chromatogr. A 1120 (2006) 282.
[10] X. Jiang, A. v.d. Horst, V. Lima, P.J. Schoenmakers, J. Chromatogr. A 1076 (2005) 51.
[11] A. v.d. Horst, P.J. Schoenmakers, J. Chrom. A 1000 (2003) 693.
[12] J. Gerber, W. Radke, Polymer 46 (2005) 9224.
[13] K. Im, Y. Kim, T. Chang, K. Lee, N. Choi, J. Chromatogr. A 1103 (2006) 235.
[14] D.M. Meunier, S.A. Baker, P.B. Smith, Macromolecules 38 (2005) 5313.
[15] D.M. Meunier, T.M. Stokich Jr., D. Gillespie, P.B. Smith, Macromol. Symp. 257 (2007) 56.
[16] R. Matmour, A. Lebreton, C. Tsitsilianis, I. Kallitsis, V. Héroguez, Y. Gnanou, Angew. Chem. Int. Ed.
44 (2005) 284.
[17] J.L. Hahnfeld, W.C. Pike, D.E. Kirkpatrick, T.G. Bee, in R. Quirk (Editor), Applications of Anionic
Polymerization Research (ACS Symposium Series, No. 696), American Chemical Society, Washinton,
DC, 1996, p. 167.
[18] E. Venema, J.C. Kraak, H. Poppe, R. Tijssen, J. Chromatogr. A 740 (1996) 159.
[19] R. Tijssen, J. Bos, in F. Dondi, G. Guiochon (Editors), Theoretical Advancement in Chromatography
and Related Separation Techniques, Kluwer, Dordrecht, 1992, p. 424.
[20] G. Stegeman, R. Oostervink, J.C. Kraak, H. Poppe, K.K. Unger, J. Chromatogr. 506 (1990) 547.
[21] G. Stegeman, J.C. Kraak, H. Poppe, R. Tijssen, J. Chromatogr. A 657 (1993) 283.
[22] T. Altares Jr., D. P. Wyman, V. R. Allen, K. Meyersen, J. Polym. Sci., Part A : Polym. Chem. 3 (1965)
4131.
89
Chapter 4: Branched Polymers Characterized by
Comprehensive Two-Dimensional Separations with Fully
Orthogonal Mechanisms
Abstract
Polymer separations under non-conventional conditions have been explored to obtain a
separation of long-chain branched polymers from linear polymers with identical
hydrodynamic size. In separation media with very narrow flow-through channels (of the
same order as the size of the analyte molecules in solution) the separation and the
elution order of polymers are strongly affected by the flow rate. At low flow rates the
largest polymers are eluted last. At high flow rates they are eluted first. By tuning the
channel size and flow rate, conditions can be found were separation becomes
independent of molar mass or size. Other differences between polymer molecules are
revealed, such as the extent of long-chain branching. This type of separation is referred
to as molecular-topology fractionation (MTF) at critical conditions. MTF involves
partial deformation of polymer coils in solution. The increased coil density and
resistance to deformation can explain the different retention behavior of branched
molecules. Much higher efficiency and selectivity were obtained by MTF in columns
than with traditional membrane fractionations. MTF in combination with size-exclusion
chromatography (SEC) was applied for the separation of branched polymers. Branching
selectivity was demonstrated for three- and four-arm “star” polystyrenes of 3 to 5 × 106
g/mol molar mass. Baseline separation could be obtained between linear polymer, Y-
shaped molecules, and X-shaped molecules in a single experiment at constant flow rate.
For randomly branched polymers the branching selectivity inevitably results in an
envelope of peaks, because it is not possible to fully resolve the huge numbers of
different branched and linear polymers of varying molar mass. Separations performed
by comprehensive two-dimensional MTF×SEC revealed the presence of branched
polymers that could not be discerned with one-dimensional SEC in combination with
mass-selective detectors, such as light scattering or viscometry.
Chapter 4
90
4.1 Introduction
Branching that is accidentally or purposefully introduced in (high-molar-mass)
polymers may be advantageous. Long chain branching in thermoplastics improves melt
strength and flow, which allows for faster processing and unique applications [1].
Through the introduction of branching a favorable balance may be obtained between
modulus (i.e. stress-strain relation), viscosity, and elongation behavior [2,3,4]. A major
challenge up to this day remains the analysis of long-chain-branched (LCB) polymers,
because a distribution of different topologies (or “qualitative geometries”) [5,6] is
confounded with a molar-mass distribution (MMD). In many polymer samples both
linear molecules and molecules with various degrees of branching are present,
depending on the polymerization conditions. Unequivocally demonstrating the
properties of branched-polymeric materials can only be achieved by synthesis and
physical testing of model compounds with well-described branching topologies [7].
Branching may also be introduced by post-synthesis blending of linear polymers with
LCB molecules. Although the positive effects of branched polymers remain after
blending with other polymers, no existing techniques can specifically characterize the
properties of branched molecules. Recent theories on structure-property relationships
for branched polymers emphasize the role of the intra-molecular structure [8]. For
material characterization it is, therefore, important that polymers can be separated
according to their structure and that molecules can be discriminated based on their
topology. However, conventional polymer-analysis techniques cannot be used to
perform such separations for LCB polymers. Separations by either branches or end
groups based on interaction chromatography [9,10] may be possible for polymers of low
to moderate molecular weight with chemically different end groups [11]. High-
molecular-weight short-chain-branched (SCB) polyolefins may also be analyzed with
gradient liquid chromatography [12]. While spectroscopic techniques offer the best
possibility to identify functional groups, they only provide information on population
averages of the sample. Hyphenation of size-exclusion chromatography (SEC) with
NMR or FTIR spectroscopy has been applied successfully to investigate distributions in
terms of functionality [13] or SCB frequency [14]. Studying the extent of LCB using
this approach is extremely difficult, because the low frequency of functional groups (i.e.
branch points) would require an exceptional sensitivity and dynamic range [15].
Branched-Polymers Characterized by Comprehensive 2D Separations with Fully Orthogonal Mechanisms
91
Polymers of high molar mass and moderate to low degree of branching are typically
separated based on their hydrodynamic size using SEC or field-flow fractionation
(FFF), often followed by selective detection using on-line viscometry and/or light
scattering [16,17]. Results for branched polymers are commonly reported as so-called
contraction ratios based on radius of gyration (rg, Eq. 1, [18]) or intrinsic viscosity ([η],
Eq. 2, [19]).
𝑔 = ��𝑟𝑔�𝐵
2
�𝑟𝑔�𝐿2�𝑀
(1)
𝑔′ = �[𝜂]𝐵[𝜂]𝐿
�𝑀
(2)
where B refers to branched polymers and L to the linear-equivalent reference polymer
and the subscript M indicates molecules of equal mass. LCB has a strong impact on the
solution properties of macromolecules, such as the relation between hydrodynamic size,
molar mass and intrinsic viscosity. Contraction ratios can be used to estimate the
branching frequency and to obtain information on the topology [20] when information
on polymer chemistry and linear reference polymers are available. This methodology
has developed over the years into the most popular method for LCB analysis [21].
Nevertheless, the separation by SEC is based on the hydrodynamic size of the analyte
molecules and is only indirectly related to branching and topology. This is a limitation
and a source of errors inherent to this method. As in conventional SEC analysis, a
significant bias may be accepted in practice, especially when comparing similar
polymers (prepared by identical chemistries). Algorithms exist to estimate the branching
frequency for tri- and tetra-functional branching based on the Zimm-Stockmayer theory
[18], but failure to separate by topology prevents such an approach from successfully
discriminating between branching functionality and frequency. The relationship
between molar mass and size in solution is affected by the topology and this implies that
a fraction of given size will be polydisperse when a branching distribution is present
[22,23].
The ability to separate polymers according to their topology and degree of LCB would
clearly benefit the characterization of branched polymers. Potentially interesting for this
Chapter 4
92
purpose are separations that exploit differences in what has been referred to [24] as
polymer dynamics in solution. In this study the application of molecular-topology
fractionation (MTF) [25,26] has been explored for the separation of branched polymers.
This technique is based on the migration of polymers in dilute solution through
chromatographic columns with very narrow flow channels. Unlike fractionation under
conditions of strong confinement that require the coil to unwind (e.g. reptation), the
separation is based on continuous migration of the coiled polymers. This renders MTF
less sensitive to clogging of the pores. The size of the polymer in solution has an effect
on MTF as well and, therefore, the separation by branching properties will be
confounded with the molar-mass distribution. Therefore, comprehensive two-
dimensional MTF×SEC (after nomenclature in [27]) separations were used to
independently study the selectivities due to branching and due to hydrodynamic size
[28]. In the present study key variables, such as the pore size and the flow rate, have
been optimized in an attempt to obtain orthogonal separation mechanisms. Accurate
information on the pore size will be used to provide a better definition of the MTF
separation and predict its application range. Flow-rate gradients have been explored to
enhance the applicability of the technique.
4.2 Theory
4.2.1 Separation techniques based on size
Polymers in dilute solution are present as coils. For ideal polymers behaving as perfect
random-flight chains the time-averaged coil size scales with the square root of the molar
mass. Deviations from this scaling law for real polymers are implied by limited
flexibility in the backbone, excluded volume by the chain itself and solvent adsorbed by
the coil due to enthalpic interactions [29,30]. A relation where size follows a power law
of mass is often still valid across broad molar-mass ranges, provided that composition
and structure of the polymer remain constant.
The equilibrium size of polymers in solution provides a robust basis for SEC and HDC
separations. Wall exclusion from the stationary-phase surface based on coil-size of
dissolved polymers is the driving force in both separations (steric exclusion). In SEC
smaller polymers selectively populate the stagnant volume in narrow pores by diffusion
Branched-Polymers Characterized by Comprehensive 2D Separations with Fully Orthogonal Mechanisms
93
from adjacent convective channels [31,32]. In packed beds with porous particles the
porous properties can be optimized to provide selective exclusion and convective
transport takes place in the interstitial space between the particles. In HDC large
polymers are excluded from the slow-moving solvent layers near the walls in convective
pores [33,34,35]. Selectivity scales with the aspect-ratio (λ) that relates the size of the
solute molecules (radius r) to the size of the flow-through channel (radius rc) as λ = r /
rc. Besides steric exclusion, which increases the migration rate for larger polymers,
hydrodynamic interactions in convective flow will affect the polymer migration rate.
For most flexible-chain polymers with M > 10 kg/mol the polymer coil behaves as if
impermeable to flow (i.e. non-draining behavior) under the mild conditions of SEC or
viscometry [16,36,37]. Friction in shear flow due to non-draining behavior of the
analyte will generally result in retardation and counteract the exclusion effect at higher
λ values [38,39,40]. Hydrodynamic interaction is specific to the conditions used and
depends on both λ and absolute size. A detailed breakdown of hydrodynamic effects for
polymers in shear flow has been provided by Tijssen et al. [41] and Stegeman et al.
[42]. Migration in HDC can be described using Eq. 3 where migration rate (τ) is defined
as residence time of the polymer (tp) relative to the residence time of a flow marker (tm)
and expressed as a function of λ and a constant C describing hydrodynamic interaction.
𝜏 = 𝑡𝑝𝑡𝑚
= 11+2𝜆−𝐶𝜆2
(3)
4.2.2 Deformation of polymers in solution
Under HDC conditions shear stress on the solute may become significant and result in
flow-rate-dependent elution behavior [42]. The effective size (r) may decrease when the
molecules are subjected to shear stress above a certain threshold that may be related to
the Deborah number (De) [24,43]. De is defined as the product of effective elongation
(𝜀̇) and the longest relaxation time of the polymer (τrel) . The effect of elongation may
become detectable in HDC for Deborah numbers exceeding 0.1, while for De > 0.5
severe elongation may occur. Separation in this latter domain does result in elution
behavior that differs significantly from that of HDC and is referred to as slalom
chromatography (SC) [44]. Deborah numbers can be calculated using either molar mass
Chapter 4
94
(Eq. 4) or radius of gyration (Eq. 5), depending on the experimental conditions and
available data on the polymer [24,45].
𝐷𝑒 = 𝜀̇𝜏𝑟𝑒𝑙 = 𝐾𝑑𝑒𝑏ν𝑑𝑝
0.42 η𝑠 [η] 𝑀𝑅 𝑇
(4)
𝐷𝑒 = 𝜀̇𝜏𝑟𝑒𝑙 = 𝐾𝑑𝑒𝑏ν𝑑𝑝
6.12 Φ η𝑠 𝑟𝑔3
𝑅 𝑇 (5)
Kdeb is a constant related to the geometry of the pores (with a typical value of 6), ν is the
superficial solvent velocity, dp the particle size of the packing, Φ the Flory-Fox
parameter, ηs the solvent viscosity, [η] the polymer intrinsic viscosity, rg the polymer
radius of gyration, R the gas constant and T the absolute temperature. The Flory-Fox
equation (Eq. 6) is used to transform Eq. 4 into Eq. 5.
[𝜂]𝑀 = 63/2Φ𝑟𝑔3 (6)
It is important to note that the Flory-Fox parameter is a measure of hydrodynamic
interaction and depends on solvent conditions, molar mass and branching of the
polymer. For example, values ranging from Φ = 1.8 × 1023 mol-1 for linear polymers to
Φ = 3.5 × 1023 mol-1 for branched polymers have been observed, while at θ-conditions
(indicated by the subscript 0) a value of Φ0 = 2.8 × 1023 mol-1 is common [46,47]. When
studying molecules of varying topology in good solvents we prefer to use Eq. 4,
avoiding the assumptions inherent to Eq. 5.
A problem with the application of Deborah numbers for branched polymers is in the
treatment of polymer relaxation. The polymer relaxation τrel (Eq. 7) is based on a model
by Zimm for a chain of beads connected by ideal springs [48,49].
𝜏𝑟𝑒𝑙 = 𝐶𝑍η𝑠 [η] 𝑀𝑅 𝑇
(7)
The constant CZ corrects for hydrodynamic interaction (e.g. draining behavior) of the
polymer. Branching and topology effects are not included in the model and correct
treatment should therefore not be assumed. Notice that according to Eq. 7 relaxation for
polymers with identical hydrodynamic volumes is identical. Linear and branched
Branched-Polymers Characterized by Comprehensive 2D Separations with Fully Orthogonal Mechanisms
95
polymers in dilute solution can be expected to respond differently to stress. It is known
that branching leads to increased segment density and reduced internal freedom of
motion for random-coil polymers in solution [50,51]. The entropy decrease resulting
from deformation of a branched molecule will be greater than that for the deformation
of a linear polymer. Therefore, branched polymers are expected to deform less than
linear polymers under identical stress. A size-dependent separation may then be applied
to achieve branching selectivity, dependent on the level of stress on the molecules (i.e.
on the flow rate).
The aspect ratio and Deborah number provide convenient metrics to compare separation
techniques based on size and dynamic properties of the polymers. In Fig. 1 techniques
are indicated at λ and De values corresponding to typical operating conditions. Arrows
in the insert indicate how λ and De values respond to changes in the separation
conditions, such as increasing the flow rate and decreasing the particle size (dp). Molar
mass has an indirect effect on both λ and De through its impact on the radius. Ultra-
high-pressure SEC separations are by definition operated at higher flow rates and with
smaller particles. Complex multi-mode separations result for samples with high molar
mass [52]. Some uncertainty is introduced in the assessment of elongation for λ > 0.3
(shaded region in Fig. 1), because shear stress experienced by the polymer is no longer
continuous and its elongation character is reduced. In Poiseuille flow shear stress will
mainly affect the periphery of the coiled polymer with λ > 0.3 and rotation is largely
prohibited. This situation no longer meets the assumptions in calculation of Deborah
numbers i.e. steady elongation against relaxation of the entire coil, but it is expected that
deformation as a result of shear forces will still occur. Hydrodynamic interaction of
polymers is significant for λ > 0.3 and MTF separations can be obtained under these
conditions. The upper limit of λ for MTF separations is not strictly defined. The dashed
line in Fig.1 puts an approximate limit at λ = 1, but MTF separations with linear
polymers up to λ = 2 have been performed.
Chapter 4
96
Fig. 1. Classification of separation techniques based on Deborah number and aspect ratio. Arrows in the insert
indicate changes implied by variation of experimental conditions.
4.2.3 Reptation
Separation techniques which are performed at conditions associated with MTF are
reviewed for similarities that can explain the topology sensitivity obtained at different
flow rates. Different mechanisms can be identified for polymer migration through
strongly confining media i.e. λ > 1. Sieving, entropic-barrier transport, and reptation can
be distinguished based on channel geometry and rigidity of the solute [53]. Random-coil
polymers in dilute solution with equilibrium sizes larger than the flow-through channels
through which they migrate will be continuously squeezed into a stretched
conformation. This condition is most similar to the tube-like diffusion path of molecules
as described in the theory of reptation [41,54]. This model finds its origin in the
description of the rheological behavior of melted polymers, where it is used to describe
motion, diffusion, and viscosity successfully [7,55]. Modifications to the theory have
been described for polymers in dilute solution, specifically for the case of separating
polymers by their degree of branching [56]. The barrier energy and critical flux required
to overcome the osmotic pressure under strong and weak confinement was derived for
ideal-star and randomly branched chains. Shortcomings of the theory impose serious
Branched-Polymers Characterized by Comprehensive 2D Separations with Fully Orthogonal Mechanisms
97
limitations on its applicability for real chains. For critical-flux calculations the flow
needed to overcome diffusion of a polymer segment is considered, while treating the
molecule as free-draining (i.e. interaction of each polymer segment with flow is not
affected by other segments in the molecule). Because non-draining conditions are more
likely for real chains, shear inside the coil domain will be low, resulting in smaller drag
forces on the chains in comparison with free-draining conditions. Thus, flow-induced
migration through strongly confining pores, resulting in unwinding of the polymer and
in molar-mass insensitivity for linear chains, will not take place for real polymers. It
was later pointed out that the critical flux for linear and branched chains under strong
confinement will be identical and cannot be used to achieve separation, because of the
progressive nature of the drag force once the first segments of a chain have entered the
pore [57].
In the weak-confinement case deformation and moderate stretching are considered for
polymers in solution. Most theoretical work takes into account constriction by the pore
walls alone, whereas for real polymers hydrodynamic interactions are present as well.
The forces induced by solvent shear on the polymer contribute to deformation and can
be controlled externally by adjusting the flow rate. Polycarbonate or mica filtration
membranes prepared by fast-atom bombardment and track-etching have been used to
study reptation of synthetic polymers. Flow-rate-dependent rejection of polymers with
equilibrium dimensions close to or larger than the membrane pores has been described
by Long and Anderson [58]. They confirmed that polymer migration through pores in a
mica membrane at higher flow rates was due to deformation rather than degradation for
the range 1 < λ < 2. Selective rejection of branched-polymers was considered in a
follow-up article [59]. A greater rejection of comb and star polymers relative to linear
polymers was attributed to deformability of the polymers. Unfortunately, the branched
samples used in this study had different molecular weights and high dispersities.
Challenges with membrane separations are the limited separation efficiency and low
sample capacity (concentrations of 160 ppm w/w had to be used). It was observed that
high concentrations (above the overlap limit) were needed for polymers with λ ≈ 1 to
diffuse through the membrane when using osmotic pressure only [60,61]. Therefore
concentration build-up on membranes in flow-driven separations may present a
problem, because this would alter the migration behavior of the polymer [62]. The
Chapter 4
98
results obtained for flow-rate dependent polymer rejection are most relevant to the
separations considered here, since the conditions and findings are in good agreement
with the observations for molecular-topology fractionation (MTF).
4.2.4 Calibration curves and separation of deformed-polymers
The impact of polymer deformation on migration can be very different depending on the
separation technique and corresponding conditions. Whether a useful separation may be
obtained for polymers with different deformability is assessed by comparing the
calibration curves as a function of polymer equilibrium size (Fig. 2). SEC (pore
exclusion) and HDC (wall exclusion) separate non-deformed macromolecules and result
in decreasing residence times for analyte molecules with increasing size. SEC by
definition takes place in pores that are not subject to convective transport. Pores in
stationary phases for SEC are typically smaller than the flow-through channels and may
be optimized independently from the flow-through-channel size. The channel size
(related to the particle diameter) may vary, but λ is generally below 0.1 for polymers
separated by SEC. Modern phases offer both high porosity, which ensures a broad
separation window (e.g. 0.5 < τ < 1), and a high mechanical strength, which allows
separation at higher flow rates. In case high-molar-mass polymers are separated using
small particles (i.e. small flow-through channels) λ may be high enough for a seamless
transition into HDC to occur [63,64]. A continuous SEC-HDC separation is the result,
with the largest polymers eluting first. However, if λ increases beyond about 0.35 a
strong reversal of the HDC calibration curve is observed (Fig. 2). Unlike rigid particles,
which will be significantly retarded for λ > 0.4, polymers will respond to shear stress
either through deformation or degradation. Deformation is broadly defined and may
comprise many effects, such as compression, elongation or increased flow draining of
the coil periphery. In the MTF region (above λ ≈ 0.35; see Fig.2) the behavior of non-
rigid polymers may be used to discriminate between different architectures.
Deformation of polymers results in departure from the HDC calibration curve, which
applies for rigid solutes, with λ corresponding to the non-deformed-polymer. All
molecules will be deformed, but linear molecules more so than branched ones. The
linear molecules, therefore, elute earlier (indicated by the gray horizontal arrows in Fig.
2).
Branched-Polymers Characterized by Comprehensive 2D Separations with Fully Orthogonal Mechanisms
99
Fig. 2. Schematic calibration curves for SEC, HDC, MTF and SC. Arrows indicate the effect of flow-induced polymer deformation.
Hydrodynamic interactions of polymers play an important role in flow-induced
deformation. This is supported by the observation that linear polymers with equilibrium
dimensions of the order of the channel size elute much faster at increased flow rates
[65]. In the absence of deformation the polymer lags the solvent in its surrounding due
to non-draining behavior (i.e. impermeability to flow). Especially in monoliths or
packed beds with highly interconnected flow-through channels this results in τ > 1 for
polymers with λ ≈ 1. At elevated flow rate τ = 0.7 was observed, which is possible only
by depletion of the slower-moving solvent layers near the stationary phase surface (Fig.
3). The effect does not occur for smaller polymers that do not have sufficient
hydrodynamic interaction relative to the fast internal relaxation, rotation and
translational diffusion. Only for large polymers will a higher shear strain near the
surface result in a higher internal stress, thereby making conformations that occupy this
region unfavorable. To think of this effect as stress-induced diffusion or stress-induced
deformation depends on whether or not migration of the entire coil perpendicular to the
direction of flow is achieved. Separation due to stress-induced deformation is a more-
accurate description for the aspect ratios considered in MTF.
Chapter 4
100
Fig. 3. Stress-induced deformation presented schematically. (a) Deformation absent at low flow rate;
(b) depletion of high-shear region near channel surface at high flow rate.
Higher entropic elasticity of branched polymers was suggested as a qualitative
explanation for topology selectivity. Different possible interpretations of polymer
deformation prevent a more accurate description at this moment. Deformation may be
explained as selective population of polymer conformations. After all, the spherical
equilibrium dimensions represent the average of many instantaneous aspherical
conformations at a time scale longer than the longest relaxation time of the polymer
[66,67]. This supports the entropic nature of (stress-induced) deformation. Differences
in flow permeability are reflected in the viscosity-shielding ratio [21], the Flory-Fox
parameter, and ratios of viscosity radius and radius of gyration [16] in Poiseuille flow
under traditional separation conditions. Most published work on deformation under flow
conditions focuses on the coil-stretch transition in elongational flow. The shear-rate
dependent coil-stretch transition for DNA was found to agree very well with predictions
based on Brownian dynamics for random coils [68]. Experiments on polystyrene,
however, demonstrated that the extended length under flow conditions did not exceed
twice the radius of gyration and was generally lower than predicted [69,70].
Experimental evidence from light scattering and birefringence measurements on the
absence of a coil-stretch transition for polystyrene were later suggested to be biased and
not selective [68,71]. Furthermore, it was suggested that shear levels were simply too
low for the polymers considered and the experiments therefore failed to provide
conclusive results.
Branched-Polymers Characterized by Comprehensive 2D Separations with Fully Orthogonal Mechanisms
101
In slalom chromatography (SC) coil-stretch transition interferes with the accelerated
migration by wall-exclusion of the polymer. Stretched molecules are retarded in the
tortuous interstitial space by frequent conformational changes and changes in flow
direction through the stationary phase packing. In the SC region, the extent of
deformation could potentially result in a different elution volume for linear and
branched molecules. Successful application of SC is unlikely, because it is expected that
the selectivity (length of the arrows in Fig. 2) is limited. Conditions where wall-
exclusion and slalom chromatography co-exist and their effects on migration cancel out
do not exist. Instead it was observed that flow rate could be used to obtain coil-stretch
transition for different molar masses in agreement with Deborah-number calculations.
Once this transition was reached elution volumes increased quickly [52].
4.3 Experimental
4.3.1 Chemicals and materials
The eluent for MTF and SEC separations was non-stabilized tetrahydrofuran (THF,
HPLC-grade, Biosolve, Valkenswaard, The Netherlands). The eluent was degassed by
purging with helium 5.0 (99.999% Praxair, Vlaardingen, The Netherlands). Sample
polymers were dissolved in THF stabilized with 250 mg/L butyl-hydroxylated toluene
to prevent degradation by radicals. Narrowly distributed linear polystyrene standards
(Polymer Laboratories, Church Stretton, UK) with molar masses (M) between 1,990 and
3.74 × 106 g/mol with polydispersity indices (PDI) no larger than 1.05 were used to
study retention behaviour. These standards were dissolved at concentrations between
0.1 and 1 mg/mL. A nominal “three-arm star” (or Y-shaped) polystyrene sample was
obtained from Polymer Source (Dorval, Canada) and used at a concentration of 1.0
mg/mL. Synthesis of the “star” polymer was by coupling of anionically polymerized
arms with a tri-functional agent (α,α’,α’’-trichloromesitylene). Analysis using SEC
with light scattering and viscometry revealed an arm molar-mass of 1,250 kg/mol and a
composition of 5% uncoupled precursor, 45% linear two-arm coupling product and a
remainder of three-arm coupling product [26]. Suspected side products were a four-arm
star polymer formed by lithium-halide exchange with all arms coupled in one functional
centre (X-shaped) [72,73]. The concentration of this large-molecule fraction could not
be determined quantitatively by SEC.
Chapter 4
102
Polystyrenes with broad molar-mass distributions were obtained from the Dow
Chemical Company (Midland, MI, USA). Dow polystyrene 1683 (weight-average molar
mass (Mw) 250 kg/mol, PDI 2.5) was used as a linear reference material. LCB
polystyrene (Mw 810 kg/mol, PDI 3.3, SEC-MALLS [28]) and low-LCB polystyrene
(Mw 310 kg/mol, PDI 5) were used for analysis of branched polymers. Long-chain
branching at high-molar mass is confirmed by the reduced intrinsic viscosity in the
Mark-Houwink plot (Fig. 7). The LCB polystyrenes were prepared by coupling of
polystyryl anions with di- and tri-functional benzyl chlorides as published elsewhere
[74]. Comb polystyrene (kindly donated by Dr. C. Fernyhough, University of Sheffield)
has a backbone molar mass of around 200 kg/mol and approximately 30 randomly
placed branches of 70 kg/mol. The synthesis technique of the comb polymer has been
described in [75].
4.3.2 Instrumentation and operating conditions
HPLC experiments were performed on a Shimadzu LC system (‘s Hertogenbosch, The
Netherlands) consisting of a system-controller (SCL10a), two micro-pumps
(LC10ADvp), a column oven (CTO7), autosampler (SIL9a), UV detector
(SPD10AVvp) and right-angle laser light scattering (RALLS) detector model LD600
(Viscotek, Houston, TX, USA). UV detection was performed simultaneously at 260 nm
and 214 nm. Modulation for comprehensive two-dimensional separation was performed
with a VICI two-position 10-port valve (Valco, Schenkon, Switzerland) with a high-
speed switching accessory and digital valve interface. The 10-port valve was plumbed
for symmetrical dual-loop modulation [76]. From the moment of injection on the 1D
column, the 10-port valve was switched at regular intervals between 1 and 3 minutes in
order to inject first-dimension effluent on the 2D SEC column. Instrument control and
data acquisition were achieved with ClassVP v7.4 build15 software (Shimadzu).
Exported data were processed in Matlab v7.3 (The Mathworks, Natick, MA, USA)
using in-house written software for data folding and visualization of two-dimensional
colour plots.
Triple-detection SEC was performed using the Shimadzu LC system plumbed for 1D
chromatography. The detection array consisted of a UV detector (SPD10AVvp),
RALLS detector (LD 600) and chip-based on-line viscometer (Polymer Laboratories /
Branched-Polymers Characterized by Comprehensive 2D Separations with Fully Orthogonal Mechanisms
103
Micronit, Enschede, The Netherlands). Data acquisition and processing was performed
with PLCirrus (Polymer Laboratories, v3.0) based on triple-detection SEC principles
[1].
4.3.3 Columns and experimental conditions
Wide-bore columns (4.6-mm I.D.) were used for all separations. The sample volume
injected on the 1D column was between 5 and 25 μL. Monolithic columns with narrow
macropore sizes were prepared in columns of 100, 150 and 250 mm length according to
the procedure published previously [65]. Custom-made columns (Polymer Laboratories)
were used for fast 2D SEC. A 150-mm long column packed with 10-µm 106 Å PLgel
particles (V0 = 1.9 mL) was used at 750 µL/min. Two 100-mm long columns packed
with 5-µm 105 Å PLgel particles were used in series only for the 2D separation in
HDC×SEC at 600 µL/min.
Chromatograms in the HDC×SEC mode (Fig. 5, Fig. S-1) were acquired with two 150
mm 1D monolithic column in series (V0 = 3.1 mL) at 10 µL/min. 160 2D chromatograms
were obtained during a runtime of 480 minutes at 50°C. Flow-rate studies in MTF×SEC
(Fig. 6) were performed on a 250 mm monolithic 1D column (V0 = 2.6 mL) with Dpore
126 nm and a 150 mm 106 Å 2D column, with both columns operated at 40°C. 200 2D
chromatograms were obtained by injection of 30 µL 1D effluent fractions at a
modulation interval matched to the 1D flow rate. MTF×SEC at conditions with minimal
molar mass selectivity (Fig. 7) was achieved using two 150 mm monolithic columns
(Dpore = 126 nm, 30 µL/min) and a 150 mm 106 Å 2D column. 80 2D chromatograms
were obtained during a runtime of 120 minutes at 50°C.
Light scattering was used in most 2D experiments. It allows for overlapped 2D
injections, because a solvent signal is not present. This is beneficial in experiments
where higher 1D flow rates are used and the time required to complete the 2D separation
is rate limiting. More second-dimension chromatograms can be obtained when using the
RALLS signal.
Triple-detection SEC was performed at room temperature with a flow rate of 0.3
mL/min. A set of two minimix B (10-µm particles) and one minimix C (5-µm particles)
columns (each 250 mm long) was used.
Chapter 4
104
4.4 Results and discussion
4.4.1 Flow-rate effect for columns with different pore size
Monolithic columns with well-controlled macropore sizes were prepared by in-situ
polymerization of polystyrene and divinylbenzene. In thermodynamically favorable or
‘good’ solvents, such as tetrahydrofuran for polystyrene, polymers readily dissolve and
can be separated free from enthalpic interaction with the column. The selectivity for
hydrodynamic separations on monolithic columns has been studied for linear polymers
[65]. A flow-rate effect on migration rate was observed and stress-induced diffusion
(SID) was presented as the mechanism responsible for this effect when separating
synthetic polymers in macropores close to unperturbed-polymer dimensions. The
hypothesis of SID playing an important role in MTF separations will be tested with the
results obtained in this work on branched-polymer separations. After presenting the
results we provide a detailed discussion on the mechanism.
Channel dimensions of the columns used in the present work have been optimized for
MTF separation. Separation by a HDC mechanism according to unperturbed-polymer
dimensions was obtained at low flow rates. This is demonstrated by the calibration
curves obtained with narrow-molar-mass polystyrenes for columns with pore sizes
(Dpore) ranging from 160 nm down to 75 nm (Fig. 4, Table 1). At 20 µL/min reversal of
the calibration curve is observed for high molar masses. This is in agreement with HDC
separation of rigid solutes (solid spheres) where hydrodynamic interaction at λ > 0.4
will reduce the migration rate. The retardation for high- molar-mass polymers is
generally reduced when the flow rate is increased to 50 µL/min. This was also observed
for micro-porous membranes where the rejection of large polymers decreased at higher
flow rates [58]. Calibration curves in Fig. 4 indicate that only the hydrodynamic effects
for λ approaching 1 are affected, because the selectivity for molecular weights below
the point of reversal is maintained. Wall exclusion-effects and coil dimensions that
induce these effects apparently have not changed for polymers below the reversal molar
mass. Under certain conditions the molar-mass selectivity diminishes above the reversal
point. Hydrodynamic interactions and calibration-curve reversal depend on the aspect
ratio λ, rather than on the molar mass. Thus, we should preferably speak of a reversal
(or critical) size. In practice, we may refer to a critical molar mass. In the present case
Branched-Polymers Characterized by Comprehensive 2D Separations with Fully Orthogonal Mechanisms
105
this is a linear-polystyrene-equivalent molar mass. The effective radius for wall-
exclusion separations [77] is used in calculating λ and is given in Eq. 8 for polystyrene
in THF [78].
𝑟𝑒𝑓𝑓 = √𝜋2𝑟𝑔 = √𝜋
20.0118 𝑀0.600 (8)
In MTF experiments it has been observed that branched polymers are ‘retained’ longer
than linear polymers for λ > 0.4 [41,28]. At optimized experimental conditions a
separation may then be performed where linear polymers above a critical molar mass
co-elute, while branched materials elute later from the column and co-elute with linear
polymers of lower molecular weight. In a comprehensive MTF×SEC separation the co-
eluting species can be separated and distributions in terms of hydrodynamic size and
branching will be obtained.
Monolithic columns with three different flow-through-pore sizes were considered for
MTF in MTF×SEC separations. Small pores are required to obtain λ values high
enough to allow MTF separations of polymers below 1000 kg/mol. A special test was
designed to establish the molecular weight at the point of reversal in the calibration
curve. Broad-MWD polystyrene was analyzed in a comprehensive two-dimensional
separation with the monolith in the first dimension (1D) and a regular SEC column in
the second dimension (2D). Separation in the ‘HDC×SEC-mode’ was obtained for
monolith 7 (see Table 3) with Dpore = 126 nm at a flow rate of 10 µL/min (Fig. 5). The
ionol peak originating from the sample solvent marks the void volume in both the 1st
and 2nd dimensions at τ = 1.00 and Vsec = 2.4 mL, respectively. The earliest eluting
polymeric material from the monolith (τ = 0.69) was used to determine the critical molar
mass of reversal. Mcrit, (Table 1) is the peak molar mass in the 2D SEC separation of the
first fraction containing polymer. Two-dimensional separations for monolith 8 and 9, as
well as the calibration curve for the 2D SEC separation are presented in section 4.6.1 of
the Appendix. Calibration-curve reversal for separation at 10 µL/min occurs at roughly
identical values of λ (Table 1), which are very close to the expected value of 0.37 based
on the Dimarzio-Guttman retention model for HDC of unperturbed polymers (Eq. 3
with C = 2.7).
Chapter 4
106
Fig. 4. Calibration curves for narrow polystyrene standards obtained on monoliths
at 20 µL/min (a) and 50µL/min (b).
Branched-Polymers Characterized by Comprehensive 2D Separations with Fully Orthogonal Mechanisms
107
Fig. 5. Calibration plot obtained by MTF×SEC for a broad standard 1F = 10 µL/min
(PS1683; Mw = 250 kg/mol, PDI = 2.5) using monolith 7 in the first dimension.
Table 1. Reversal molar masses for monoliths determined by HDC×SEC at 10 µL/min.
Monolithic ID Dpore (nm) Mcrit (kg/mol) λ
6 160 [700]* [0.4]*
7 126 355 0.36
8 104 260 0.36
9 75 207 0.39
*Approximate values obtained from calibration curve at 20 µl/min
Comprehensive-two-dimensional chromatography is highly useful for exploring the
migration behavior in MTF. Not only does it provide more information than a
calibration curve based on the injection of narrow-MWD standards, it also allows the
characterization of samples with a high polydispersity. The 2D chromatogram gives a
qualitative impression of the calibration curve in a single experiment (Fig. 5).
Therefore, the flow-rate effect was examined by MTF×SEC with 1D flow rates (1F)
between 10 and 75 µL/min. A shorter 2D column with packing optimized for separation
of large polymers was used (supplementary information, S2). Linear polymers with
molecular weights above Mcrit were separated on a monolith with Dpore = 126 nm at 10
µL/min (Fig. 6a) and at 30 µL/min (Fig. 6b). A sample of three polystyrene standards of
1.37⋅106, 2.56⋅106 and 3.74⋅106 g/mol was used, which for this monolith corresponds to
aspect ratios in the range 0.80 < λ < 1.46. Higher flow rates result in a transition from
Chapter 4
108
polymers separated under equilibrium conditions (HDC) to polymers separated in a
deformed state (MTF) (Fig. 6, Fig. S-4). The three peaks corresponding to the narrow
standards merge into a single peak in 1D and molecular-weight independence is
achieved for these high-molecular-weight materials. For the monolith with Dpore = 126
nm a flow rate of 1F = 30 µL/min was used in subsequent experiments to suppress the
molar-mass selectivity. A similar suppression of molar-mass selectivity above Mcrit was
obtained with a Dpore = 104 nm monolith, but at a higher flow rate. In 2D experiments
with this column (L = 100 mm) the lowest degree of molar-mass selectivity was
obtained for 1F = 50 µL/min (Fig. S-6). The calibration curves in Fig. 4b confirm this
trend, but do reveal little retention above Mcrit. The small 1D column volume is limiting
the number of 2D chromatograms and thus the resolution of the 2D experiment.
However, the use of long columns with narrow pores is experimentally challenging. The
pressure drop that is required for operating longer monolithic columns with Dpore = 104
nm or smaller is so high as to cause irreversible damage by compression of the
stationary phase. Additional results on MTF×SEC at various flow rates for both column
types are presented in the supplementary information, section S3.
Fig. 6. A mixture of three narrow-MMD polystyrenes separated on an MTF column with Dpore = 126 nm at
different flow rates. (a) 10 µL/min (b) 30 µL/min.
4.4.2 Branched-polymer separations
Conditions for MTF separation with minimal molar-mass selectivity for linear polymers
above Mcrit were established. Branched polymers with different topology were analyzed
at those conditions using MTF×SEC to assess branching-selectivity in MTF (Fig. 7). A
linear reference prepared by mixing Dow1683 with the narrow standards from Fig. 6
was used to cover a wide molar-mass range. Only little retardation for the highest
Branched-Polymers Characterized by Comprehensive 2D Separations with Fully Orthogonal Mechanisms
109
molar-mass polymers was observed in Fig. 7a. Such small difference may be the result
of inaccuracy of the flow or the porous properties of the column (similar columns were
used, see section 4.3.3). Star-branched polystyrene prepared by coupling of 1250
kg/mol linear ‘arms’ was mixed with the linear reference. Base-line separation of the 3-
arm (Y-shaped) and 4-arm (X-shaped) branched coupling products from the linear
materials is obtained (Fig.7b). The linear 2-arm coupling product and single arm
polystyrene elute together with the linear materials. The 4-arm star, which is a by-
product from the coupling reaction, is base-line separated from the 3-arm star. This
separation provides a dramatic demonstration of the separation of high molar-mass,
branched polymers with only a single branching point from linear polymers with a
broad range in molar mass and hydrodynamic size. An overview of the elution volumes
in both dimensions is given in Table 2. Calibration of the 2D separation with linear
polymers was used to calculate λ values for the branched material eluting from the MTF
column (supplementary information, S2).
Retardation of polymers with higher branching frequency was observed already at
smaller hydrodynamic size relative to long-chain branched (LCB) star polymer.
Random long-chain branched material (LCB PS, Fig. 7c) and a comb polymer with
controlled long-chain branching (Fig. 7d) were separated at the same conditions as those
used in Fig.7a and 7b. The results of analyses by SEC with triple detection are provided
in Fig. 8 for reference. For both the separations of LCB PS and Comb polymers by
MTF×SEC a tail is observed in the MTF direction. This is the expected result for the
LCB PS, because here the degree of branching increases with molecular weight. In case
of the comb the tail may reflect a cross-linking byproduct of the synthesis. The comb
itself (VMTF = 2.48 mL) is hardly retained, most likely because its aspect ratio (λ) is too
low for significant hydrodynamic interactions to occur. In the UV chromatogram a
small amount of polystyrene with a smaller hydrodynamic size than the bulk of the
sample can also be observed (Fig. S-7). This material is not separated from the bulk in
the 2D SEC separation or in the triple-detection analysis. Most likely this is a uncoupled
linear precursor that has remained in the comb sample as a side-product.
Chapter 4
110
The branched materials retarded in MTF have different hydrodynamic sizes depending
on their topology. In Fig. 9 an overlay with 2D-SEC peak maxima from Fig. 7 is
presented on top of the linear reference polymer. LCB and comb polymers start to be
retained at lower hydrodynamic sizes than the star polymers. This implies that stress-
induced deformation effects are less effective in counteracting the hydrodynamic effects
for polymers with higher degree of branching. A plausible explanation is that polymers
with higher segment density are less susceptible to deformation. Segment density in
solution is inversely related to intrinsic viscosity, which is given in Fig. 8. Lower
intrinsic viscosity for polymers above log M = 6 correlates well with the lower λ for
material retarded in MTF (Table 2).
4.4.3 Selectivity for branched polymers
A better look at the separation conditions is needed to understand the separation
selectivity for branched polymers. We will assume that polymers with higher segment
densities than linear polymer will deform to a lesser extent under stress and , therefore,
resemble HDC behaviour. Material eluting later than linear polymers above Mcrit at λ >
0.4 will have a higher segment density and/or a larger hydrodynamic size. In the case of
3- and 4-arm star polymers the elution is affected by segment density only, because
hydrodynamic size (e.g. λ) is identical. For the randomly branched LCB polymer
branching and hydrodynamic size both increase, indicating that molar mass increases
for material eluting later from the MTF column. However, when segment density is too
high to allow for deformation and hydrodynamic size is large then polymers may elute
very late or not at all. The tail for both LCB and comb polystyrene is indicative of very
dense polymer (possibly crosslinked) that is not completely eluting. Applicability of the
present separation conditions is limited to conditions that allow polymers to elute from
the MTF column within reasonable time. This may be achieved by using MTF columns
with pore size matched to polymers of interest or by changing the conditions to make
also more dense polymers at higher λ elute.
While material eluting slowly from the MTF column can be explained as material with
exceptional high coil density, it can also be argued that this is the result of polymer
degradation. The light-scattering signal from RALLS divided by a concentration signal
(UV) was used to estimate molar-mass changes for material eluting from the MTF
Branched-Polymers Characterized by Comprehensive 2D Separations with Fully Orthogonal Mechanisms
111
column. High angular dependence of the RALLS signal makes it impossible to
quantitatively compare LS/UV ratios without correction for angular dependence, which
strongly depends on polymer size. However, it is possible to use the LS/UV ratio for a
qualitative comparison when dealing with polymers of identical size (e.g. eluting at
identical 2tr). The LS/UV ratio for polymers in Fig. 7 is presented in Fig. S-7. In all
cases material eluting later from the MTF column was found to have a higher LS/UV
ratio, which is indicative of higher molar mass. MTF×SEC-MALLS was performed to
obtain accurate molar mass following the separation of LCB PS on the monolithic
column with Dpore = 104 nm (Supplementary Information, S5). The gradual increase in
molar mass was confirmed and material up to the highest mass present in this polymer
as measured in Fig. 8 was found back in fractions eluting later from the MTF column.
Fig. 7. 2D Chromatograms of polystyrene polymers separated by MTF×SEC with 1F 30 µL/min. (a) Linear polymers 20 – 3740 kg/mol; (b) linear and star polymers; (c) LCB PS; (d) comb PS.
Chapter 4
112
Table 2. Elution volume and aspect ratio for polymers of different topology in MTF×SEC (V0,MTF = 3.1 mL).
MTF SEC MTF linear reference
Vmax (mL) τ Vmax (mL) λ τ 3-arm star 3.02 0.97 1.28 0.88 0.78
4-arm star 4.41 1.42 1.28 0.87 0.78
LCB 3.02 0.97 1.38 0.53 0.78
3.38 1.09 1.37 0.55 0.78
3.60 1.16 1.37 0.56 0.77
4.37 1.41 1.36 0.58 0.77
5.09 1.64 1.35 0.60 0.77
Comb 2.48 0.80 1.42 0.43 0.77
3.38 1.09 1.41 0.47 0.77
5.04 1.63 1.38 0.54 0.77
Fig. 8. Mark-Houwink plot of linear and branched polystyrene samples. Dow PS1683 (1), star [26] (2), low-LCB PS (3), LCB PS (4), comb (5).
Branched-Polymers Characterized by Comprehensive 2D Separations with Fully Orthogonal Mechanisms
113
Fig. 9. Linear polymer separated by MTF×SEC;
overlay of peak maxima in 2D light-scattering signal for star (+), LCB (o) and comb (x) polymers.
4.4.4 Effect of flow rate on migration of branched polymers
The flow rate applied in MTF separation can be used to change migration behavior for
branched polymers in a similar way as it was used to obtain molecular-weight
independent elution for linear polymers. MTF×SEC experiments were performed with
MTF flow rates up to 75 µL/min on the star polymer and two LCB polymers with
different degrees of branching (Supplementary information, S6). At 75 µL/min the star
polymer and the polymer with a low degree of LCB could be completely eluted within a
single column volume. These results support that flow rate can be used to control
migration rates for both linear and branched polymers and influence their recovery.
Only polystyrene with material that is highly branched or even cross-linked did not
readily elute at these conditions.
Polymers with a low degree of branching are not well separated in the MTF separation
at higher flow rates. In order to obtain good separation for materials subject to much
different extent of retardation on the MTF column a flow-rate gradient may be applied.
It was observed in experiments at constant flow rate that little separation was obtained
for polymers eluting after the column void volume (V0). An MTF×SEC experiment was
performed in which the flow rate was increased gradually from 10 µL/min to 20 µL/min
between 150 and 250 minutes or once the elution volume approached V0 (Fig. 10). A
Chapter 4
114
complete separation resulted, in which well-resolved peaks were observed for the
single-arm precursor up to the 4-arm star. Even a high molar-mass coupling product can
be discerned, which has a slightly smaller hydrodynamic size. The elution of highly-
branched materials with a smaller hydrodynamic size than earlier eluting material was
also observed in constant flow rate experiments for three-arm star polymer (Fig. S-9)
and LCB polystyrene (Fig. S-10).
Fig. 10. MTF×SEC separation of star-polymer sample using a flow-rate gradient; (1) unreacted single-arm
polymer (2) two-arm linear coupling product (3) 3-arm star polymer (4) 4-arm star polymer (5) higher coupling product.
The star polymer separated in Fig. 10 could even be fractionated by topology in a 1D-
MTF experiment. Such a separation is unlikely for other branched polymers under the
conditions used for this separation, because linear and branched polymers may co-elute
as a result of the low flow rate. Operating at conditions with minimal selectivity for
linear polymers provides the most powerful application. The optimal experiment would
therefore start at conditions with minimal selectivity for linear chains. Once linear
materials have eluted the flow rate may be ramped up to elute branched material with
higher segment density from the column.
Branched-Polymers Characterized by Comprehensive 2D Separations with Fully Orthogonal Mechanisms
115
4.4.5 Effect of temperature on migration of polymers in MTF
The effect of flow rate on selectivity in MTF is very clear and can be understood. It
provides direct control over the levels of shear and stress that polymers in solution are
subjected to. Temperature as a parameter to control deformation was not considered in
detail, but it may certainly be used for this purpose considering the low speed of
separation. Higher temperatures induce faster polymer relaxation (τrel, eq. 7) through
faster Brownian motion and lower solvent viscosity. The migration of polymer above
Mcrit will be slower at higher temperatures because of less deformation. This trend was
confirmed in a comparison of linear and star polymers separated at both 50 °C and room
temperature. However, the effect of temperature on retention proved rather small, even
at low flow rates (Supplementary section S7). Great changes in polymer relaxation
times cannot be achieved within the limits of practical separation conditions. Flow rate
is a more effective parameter, exerting a greater effect on migration and selectivity.
4.5 Conclusions
Molecular-topology fractionation (MTF) is a term used to denote separations of
branched and linear polymers as a result of selective deformation. MTF separations
combine characteristics of HDC and reptation. Polymers were separated on monolithic
column with flow-through channels only slightly larger than the polymer itself. At such
conditions polymer molecules experience strong hydrodynamic interactions, resulting in
deformation and increased migration rates. MTF separations were used successfully to
fractionate polymers by their topology in a comprehensive two-dimensional separation
with size-exclusion chromatography (SEC) in the second dimension (MTF×SEC).
Selectivity based on topology is introduced through faster relaxation of branched
polymers subject to shear deformation. At optimized conditions the effects of
hydrodynamic interaction and deformation for linear polymers compensate for each
other. Such conditions allows for an orthogonal separation of polymers by their
hydrodynamic size and branching properties above Mcrit.
Branched polystyrenes with λ between 0.4 and 0.9 were separated from linear polymers
with identical hydrodynamic size. A relation was observed between the aspect ratio of
branched polymers retarded in MTF and coil density in solution. The absence of
migration effects resulting from polymer properties other than topology with an effect
Chapter 4
116
on coil density was not rigorously validated in this study. It would be interesting to
assess the impact of chemical composition and short-chain branching on migration for
application of MTF to polyolefins and polar synthetic polymers. Several results support
the hypothesis of molecular relaxation as the decisive property for selectivity in MTF,
such as increased retention above Mcrit at higher temperature or the higher flow rates
needed for molar-mass-independent elution from monoliths with narrower flow-through
channels.
MTF×SEC was used to investigate MTF separations preferably on long 1D columns for
better separation efficiency. Lengthy experiments were the result and comprehensive
on-line coupling with SEC proved impossible without a significant sacrifice in terms of
separation efficiency. For practical purposes off-line fractionation may be used once the
separation conditions are known [26]. A simple SEC-MTF experiment with MTF
performed at conditions with minimal molar mass selectivity above Mcrit can be used for
a fast and inexpensive screening for branched material. In another approach a short
MTF column may be used to obtain the fraction with branched material and linear
molecules below Mcrit. A high-resolution SEC experiment with selective detection may
than be used to characterize only the branched material free from co-eluting linear
material.
A challenge for the application of MTF is still the lack of commercially available
stationary phases with suitable flow-through-channel dimensions. High diffusion and
fast relaxation of synthetic polymers require an aspect ratio (λ) close to unity for
branched molecules. Extension of deformation-selective separation of branched
polymers towards either larger polymers or polymers with longer relaxation times may
be possible even when using commercially available HDC columns. Starches and bio-
polymers may satisfy this criterion and provide interesting cases [79].
Branched-Polymers Characterized by Comprehensive 2D Separations with Fully Orthogonal Mechanisms
117
4.6 Appendix
4.6.1 Comprehensive HDC×SEC experiment
Monolithic columns with different pore sizes were used to obtain chromatograms at
identical conditions (see Table 1). The chromatograms obtained using each monolith in
the first dimension for HDC×SEC are presented in Fig. S-1.
Fig. S-1. HDC×SEC performed with 1D monolithic phases 7 (a), 8 (b) and 9 (c).
The sample was 0.8 mg/mL PS1683 + 0.1 mg/mL 2MDa narrow-standard PS in THF.
Two 100 mm × 4.6 mm I.D. column packed with 5-µm 105 Å PLgel were used in the
second dimension. Accurate molar-mass calibration was performed by injection of four
mixtures, each with three narrow-MMD PS standards. Calibration samples were
injected at 30 min intervals with 1F = 10 µL/min. Elution volumes corresponding to
peak maxima were used to construct a third order polynomial fit (Fig. S-2). This
calibration data were used to calculate Mcrit for each monolithic phase (Table 1).
Fig. S-2. Narrow MMD PS standards separated using HDC×SEC (a)
and calibration of the second-dimension SEC separation (b).
y = -2.5x3 + 11.8x2 - 20.6x + 18.1
3
4
5
6
7
1 1.5 2 2.5
log
M
Elution volume (mL)
(b)
Chapter 4
118
4.6.2 Second-dimension calibration for MTF×SEC
For MTF×SEC experiments a 2D column with a high exclusion limit (10-µm 106 Å
PLgel particles, 150 × 4.6 mm I.D.) was used to prevent overloading and anomalous-
elution behavior in the 2D-SEC separation. Accurate molar-mass calibration was
performed by injection of four mixtures, each with three narrow-MMD PS standards.
Peak maxima from the UV signal were used to construct the calibration curve (Fig. S-
3). The polynomial equation fitted to the calibration curve was used to calculate
polymer size corresponding to each elution volume in order to calculate λ values (Eq. 8 /
Table 2).
Fig. S-3. Calibration experiment and calibration curve for second-dimension of MTF×SEC separations.
4.6.3 Flow-rate effect in MTF×SEC
The transition from an HDC to an MTF-type separation at critical conditions is
demonstrated in Fig. S-4 using a comprehensive two-dimensional experiment. Linear
and star-branched polymers were separated on a 250-mm long monolithic column with
Dpore = 126 nm at 10, 15, 20 and 30 µL/min (Fig. S-4). A sample containing three linear
polystyrene standards of 1.37⋅106, 2.56⋅106 and 3.74⋅106 g/mol was used, as well as a
nominal “three-arm star” (or Y-shaped) polystyrene sample obtained from Polymer
Source (Dorval, Canada; see section 4.3.1).
A particularly challenging aspect of studies into flow-rate effects is the transfer of all 1D
effluent to the 2D separation. The flow rate and injected amount in the 2D were kept
identical to maximize the comparability. 200 Injections of 30 µL each were transferred
to the 2D in all chromatograms, irrespective of the 1D flow.
y = -251x5 + 1,897x4 - 5,720x3 + 8,597x2 - 6,443x + 1,933
2
3
4
5
6
7
1 1.5 2
log
M
Elution volume (mL)
(b)
Branched-Polymers Characterized by Comprehensive 2D Separations with Fully Orthogonal Mechanisms
119
For the chromatogram with 1F = 30 µL/min only one minute is available for each 2D
chromatogram. An experimental problem is the overlap or wrap-around in the UV
signal for these short sampling intervals. Signals near the void volume of the 2D column
interfere with the high-molar-mass peaks in the subsequent 2D chromatogram.
Fig. S-4. Transition of the 1D separation mode from HDC to MTF.
Linear polymer at 10 (a), 15 (b), 20 (c) and 30 µl/min 1F (d); three-arm “star” polymer at 10 (e), 15 (f), 20 (g) and 30 µl/min 1F (h).
Experiments were performed with RALLS detection using 150 mm 1D columns to study
selectivity at higher flow rates for linear polymers. The sample was a mixture of nine
narrow-MMD linear PS standards in the range 200 – 3740 kg/mol. Separations on
monolithic material 7 were performed with 1F between 75 and 10 µL/min (Fig. S-5). A 1D flow rate higher than 33 µL/min does not significantly change the selectivity or bring
additional advantages other than analysis-time reduction. Such high flow rates are not
practical for comprehensive 2D separations, because adjustments to the second
dimension are required to deal with the larger 1D flow. These will result in either a
reduced separation efficiency or a lower sensitivity. For 1F of 50 and 75 µL/min part of
the 1D effluent is lost between 2D injections.
Chapter 4
120
Fig. S-5. Flow-rate effect for linear polystyrene on a 150 × 4.6 mm I.D. monolith with Dpore = 126 nm.
1F = 75 (a), 50 (b), 33 (c), 22 (d), 15(e) and 10 (f) µl/min.
Flow-rate effects were also investigated for a 100 mm monolith with smaller pores (Fig.
S-6). Molar-mass selectivity can be suppressed at comparable or slightly higher flow
rates relative to a Dp = 126 nm monolith. At a flow rate in between 33 and 50 µL/min a
separation can be obtained with minimal molar-mass selectivity. The narrow-pores of
this monolith induced higher operating pressures. A backpressure of 13 MPa was
measured for separation at 50 µL/min with THF at 50°C.
Branched-Polymers Characterized by Comprehensive 2D Separations with Fully Orthogonal Mechanisms
121
Fig. S-6. Flow-rate effect for linear polystyrene on a 100 × 4.6 mm I.D. monolith with Dpore = 104 nm.
1F = 50 (a), 33 (b), 22 (c), 15 (d), and 10 (e) µl/min.
4.6.4 MTF×SEC at orthogonal conditions
All detector signals for the separations shown in Fig. 7 (see section 4.4.3) are presented
in Fig. S-7. The detector array consisted of a Shimadzu dual-wavelength UV detector
and a Viscotek right-angle laser light scattering (RALLS) detector coupled in series. In
the bottom row the light-scattering signal divided by the UV absorption signal at 214
nm is presented to give an indication of changes in molar mass. The angular dependence
for 90° light scattering is significant for the polymers considered here. Regardless of the
reduced scattering intensity for large solutes, the signal is most sensitive for high molar-
mass polymers. A comparison of the LS/UV ratio at identical 2tr yields a qualitative
indication of molar-mass changes. The ratio is sensitive to inter-detector delay and
inter-detector band broadening.
Chapter 4
122
Fig. S-7. Polystyrene separated by MTF×SEC at 30 µL/min; consecutive detector signals from top to bottom: UV 260nm, UV 214nm, 90° light scattering and light scattering / UV 214nm ratio (indicated near color bar).
(a) linear polymers (b) linear and star polymers (c) LCB polymer Mw 810 kg/mol (d) comb polymer
Branched-Polymers Characterized by Comprehensive 2D Separations with Fully Orthogonal Mechanisms
123
4.6.5 MTF×SEC-UV/MALLS on long-chain-branched polystyrene
An experiment was performed where the RALLS detector in the MTF×SEC-
UV/RALLS setup was replaced by a MALLS detector. For the 1D a 150 mm × 4.6 mm
I.D. column with Dpore = 104 nm monolith (monolith 8) was used with 1F = 30µL/min.
The 2D was identical to other MTF×SEC experiments (150 mm × 4.6 mm I.D. 10 µm
106 PLgel with 2F = 750 µL/min). 25 µL of 1 mg/mL LCBps were injected. Fractions of
90 µL each were transferred to the 2D separation. Results of this experiment are
presented in Fig. S-8.
Fig. S-8. 2D plots for UV absorption (a) and the 90° light-scattering signal (b), as well as molar mass for MTF
fractions from the MTF×SEC-UV/MALLS experiment between 1.1 and 1.9 mL in the 1D (c).
41.0x10
51.0x10
61.0x10
71.0x10
1.2 1.4 1.6 1.8 2.0
Mol
ar M
ass
(g/m
ol)
Volume (mL)
Molar Mass vs. Volume LCBps_03LCBps_04LCBps_05LCBps_06LCBps_07LCBps_08LCBps_09LCBps_10
(c)
Chapter 4
124
The signal from the MALLS detector was sufficient to calculate molar-masses, but not
for calculating Rg. Therefore, a conformation plot with results of the different fractions
could not be created. The increase in molar mass for materials eluting at the same
hydrodynamic volume (in the 2D) supports the hypothesis that material eluting later
from the MTF column has an increasing degree of branching.
4.6.6 Selectivity in MTF as a function of flow rate
MTF×SEC Experiments were performed with linear (Fig. S-5) and branched polymers
(Fig. S-9 through Fig. S-11) at different 1D flow rates. A 150 mm × 4.6 mm I.D. column
with Dpore 126nm with V0 = 1.65 mL was used. Experimental conditions are presented
in Table S-1.
Red +++ was added as a marker for 2D-peak maxima to 2D chromatograms of branched
samples as a visual aid to help establish whether material is still eluting from the 1D
column.
Fig. S-9. “Star” polymer separated at different flow rates in 1D MTF.
75 (a), 50 (b), 33 (c), 22 (d), 15(e) and 10 µL/min (f)
Branched-Polymers Characterized by Comprehensive 2D Separations with Fully Orthogonal Mechanisms
125
Fig. S-10. LCB Polymer separated at different flow rates in 1D MTF.
75 (a), 50 (b), 33 (c), 22 (d), 15(e) and 10 µL/min (f).
Fig. S-11. Polymer with little LCB separated at different flow rates in 1D MTF.
75 (a), 50 (b), 33 (c), 22 (d), 15(e) and 10 µL/min (f). A problem with the 2D pump prevented completion of the experiment at 10 µl/min (f).
Chapter 4
126
Table S-1.: Experimental conditions for the separations in Fig. S-9, S-10 and S-11.
1D flowrate (µL/min)
2D time (min)
2D injection volume (µL)
Total time min.
(2D chromatograms)
Total volume 1D (mL)
75 1.33 100* 80 (60) 6
50 1.33 66.6* 120 (90) 6
33 1.33 34 180 (135) 6
22 1.33 30 266 (200) 6
15 2 30 400 (200) 6
10 3 30 600 (200) 6
* Incomplete sampling is expected due to the use of 45 µL transfer loops.
4.6.7 Effect of temperature on MTF×SEC separations
Separations of linear and star-branched polystyrene polymers by MTF×SEC were
performed under identical conditions, but at room temperature and 50°C different
temperatures. For the 1D a 100 mm × 4.6 mm I.D. column with Dpore = 104 nm
(monolith 8) was used with 1F = 10 µL/min. The 2D was a 250 mm × 4.6 mm I.D., 10
µm Mini-mixed B column with 2F = 600 µL/min. 25 µL of sample solution were
injected. 60 Consecutive fractions of 50 µL were transferred to the 2D.
2D Chromatograms of the separations are provided in Fig. 12 and Fig. 13.
Dimensionless elution volume (τ) is provided for a convenient comparison of elution
volumes in the first-dimension (table S-2) and the second-dimension (table S-3).
Table S-2.: First-dimension temperature dependence of polymer separations in Fig. S-12 and S-13
Elution volume MTF (mL) τMTF
Label Sample 25°C 50°C 25°C 50°C
1 ionol 1.1 1.1 1 1
2 9.9 kg/mol PS 1.05 1.05 0.95 0.95
3 197 kg/mol PS 0.8 0.8 0.73 0.73
4 3742 kg/mol PS 1.25 1.4 1.14 1.27
5 ionol 1.15 1.15 1 1
6 2-arm linear PS 1.2 1.3 1.09 1.18
7 3-arm “Star” PS 1.65 1.95 1.50 1.77
Branched-Polymers Characterized by Comprehensive 2D Separations with Fully Orthogonal Mechanisms
127
Table S-3.: Second-dimension temperature dependence of polymer separations in Fig. S-12 and S-13
Elution volume SEC (mL) τSEC
Label Sample 25°C 50°C 25°C 50°C
1 ionol 3.04 2.94 1 1
2 9.9 kg/mol PS 2.59 2.52 0.85 0.86
3 197 kg/mol PS 2.21 2.14 0.73 0.73
4 3742 kg/mol PS 1.81 1.76 0.60 0.60
5 ionol 3.18 3.09 1 1
6 2-arm linear PS 1.87 1.82 0.62 0.62
7 3-arm “Star” PS 1.84 1.79 0.61 0.61
Fig. S-12. Room-temperature separation of narrow-MMD linear standards (a)
and a three-arm “Star” Polymer (b).
. Fig. S-13. Separation of narrow-MMD PS standards (a) and a three-arm “Star” Polymer (b) at 50°C.
Chapter 4
128
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131
Chapter 5: Z-RAFT Star Polymerization of Styrene:
Comprehensive Characterization using Size-Exclusion
Chromatography
Abstract
Reversible Addition-Fragmentation Chain Transfer (RAFT) polymerizations of styrene
in bulk at 80°C using tri-, tetra-, and hexafunctional trithiocarbonates, in which the
active RAFT-groups are linked to the core via the stabilizing Z-group, were studied in
detail. These Z-RAFT star polymerizations of styrene showed excellent molecular
weight control up to very high monomer conversions and star sizes of more than 200
kDa. The application of high pressure up to 2600 bar was found to significantly increase
the relative amount of living star polymer. Not even at very high monomer conversions
and for large star molecules, a shielding effect of growing arms hampering the RAFT
process could be identified. Absolute molecular weights of star polymers using a
conventionally calibrated SEC setup were determined with high precision by using a
mixture of linear and star-shaped RAFT agents. When using phenylethyl as the leaving
R-group, well-defined star polymers that perfectly match the theoretical predictions
were formed. However, when using benzyl as the leaving group, a pronounced impact
of monomer conversion on the star polymer topology was observed and pure star
polymers with the expected number of arms could not be obtained.
Chapter 5
132
5.1 Introduction
The precise tailoring of macromolecules on a molecular level is a major key for
controlling the polymer properties. Within this context, the control of macromolecular
topology is an ongoing research theme [1]. Among these topologies, star polymers are
of special interest since years, because of their distinct rheological behavior arising from
their spatial shape both in solution and melt, which is exploited, e.g., in oils and
lubricants for automotives [2,3], in adhesives [4], and for flocculation [5]. In addition,
star polymers are becoming increasingly important for life sciences, where they e.g. find
applications in the field of drug release [6], serve as unimolecular polymeric micelles
[7,8], and are used as nucleic acid delivery vectors [9]. A lot of effort was put into the
investigation of properties of stars [10,11] as well as into the development of new
methods for their synthesis [12]. The rise of controlled radical polymerization ignited
enormous research activities in the field of topological polymer design, as these
methods allow the preparation of samples with narrowly distributed and controlled
molecular weights of a wide array of different monomers and under various reaction
conditions. Especially Reversible Addition-Fragmentation Chain Transfer (RAFT)
polymerization [13-17] has proven to be extremely versatile. In this method,
propagating macroradicals are in equilibrium with the dormant polymeric RAFT
compounds via reversible chain transfer and all chains have thus an equal probability to
grow which results in relatively narrow chain length distributions. Core-first star
polymers can easily be produced via RAFT polymerization when using multifunctional
RAFT agents that, in addition to controlling the process, predetermine the final polymer
topology [18,19]. When targeting very well defined star polymers, a RAFT agent design
has to be chosen, in which the stabilizing group (so called Z-group) constitutes the core
(see Scheme 1) [20-25]. This Z-RAFT star polymerization approach effectively
prevents extensive coupling reactions between star polymers as well as side-production
of linear material, which occur when connecting the RAFT-groups to the core via its
reinitiating leaving group (so called R-group) [18,19,23,26-29]. For a detailed
description of the mechanistic underpinnings of core-first RAFT star polymerizations,
the reader is referred to reference [25].
Z-RAFT Star Polymerization of Styrene: Comprehensive Characterization using SEC
133
Scheme 1. Main equilibrium of Z-RAFT star polymerization.
In Z-RAFT star polymerization, the growing radical center sits at the end of a linear
chain (i.e., the arm) and the equilibrating reaction occurs near the center of the star,
where the thiocarbonylthio-moieties are located throughout the entire reaction. As a
matter of fact, the controlling reaction is increasingly shielded by the surrounding
polymer segments. It was, however, experimentally found that Z-RAFT star
polymerization of acrylates is well controlled up to relatively high monomer
conversions and up to star molar masses of over one million Da [25]. We therefore
scrutinized earlier reported arguments about the detrimental steric shielding of growing
arms, which was accused to increasingly hamper the RAFT process [20,21,30-32]. In
order to quantify this shielding for the first time, we performed Monte Carlo simulations
of polymer chain pairs that mimic the steric situation occurring in Z-RAFT star
polymerization, showing that the shielding is not sufficiently large to impede the RAFT
process [33,34]. We also modeled the initial transfer reaction in Z-RAFT star
polymerization by pseudo-kinetic Monte Carlo simulations [35].
Our motivation for comprehensively study Z-RAFT star polymerization is driven by our
efforts in designing well-defined unimolecular nano-carriers, which base on star
polymers as templates [36]. We thus comprehensively studied 6-arm Z-RAFT star
polymerization of various acrylates [25], in which we identified intermolecular transfer
to polymer as side reaction that induces star-star coupling at high monomer conversions.
Based on a detailed kinetic analysis of this transfer-to-polymer reaction, we were able to
develop guidelines for poly(acrylate) stars of very uniform structure. The objective of
the present work is to in-depth characterize 3-arm, 4-arm, and 6-arm Z-RAFT star
polymerization of styrene in order to obtain very homogenous star polymers from this
important monomer. By exploiting the distinct mechanistic features of Z-RAFT star
Chapter 5
134
polymerization, we develop a novel and relatively easy method for characterizing
absolute molecular weights and true numbers of arms of the generated star polymers.
5.2 Experimental Section
5.2.1 Chemicals
Dipentaerythritol hexakis(3-mercaptopropionate) was obtained from Wako Chemicals
and used without further purification. The initiator 1,1′-azobis(cyanocyclohexane)
(ACCN, Aldrich) was used as received. Styrene (≥ 99.0 %, Fluka) was purified by
passing through a column filled with inhibitor remover for 4-tert-butylcatechol
(Aldrich). Column-chromatographic purification of the RAFT agent was performed
using silica gel (Merck, Kieselgel 60) and technical grade n-pentane, ethyl acetate and
CH2Cl2. Tetrahydrofuran was used as the eluent in size-exclusion chromatography
(THF, Carl Roth, Rotipuran, stabilized with 2,6-di-tert-butyl-4-methylphenol). It was
used as received for all experiments using refractive-index and UV detection. Non-
stabilized HPLC-grade THF from Biosolve (Valkenswaard, The Netherlands) was
filtered over a 20 nm ceramic filter (Anodisk 47 from Whatman, Maidstone, England)
and continuously purged with helium 5.0 (99,999 %, Praxair, Vlaardingen, The
Netherlands) for the triple-detection SEC measurements. All other chemicals were
purchased from Aldrich and used without further purification.
5.2.2 Instrumentation
Molecular weight distributions were determined by size-exclusion chromatography
(SEC) using a JASCO (Tokyo, Japan) AS-2055-plus autosampler, a Waters 515 HPLC
pump (Milford, MA, USA), three PSS-SDV columns (Mainz, Germany) with nominal 5
µm particle size and pore sizes of 105, 103 and 102 Å, a Waters 2410 refractive index-
detector, a Viskotek (Houston, TX, USA) VE3210 UV/VIS detector, and THF at 35°C
as the eluent at a flow rate of 1.0 mL·min–1. 50 µL of polymer solution with a
concentration of approximately 3 mg/mL were injected. The SEC setup was calibrated
with polystyrene standards of narrow polydispersity (Mp = 410 to 2 000 000 g mol–1)
from PSS.
The triple-detector SEC setup comprised a SIL9a autosampler, LC20Advp micropump
and SCL10a system controller all from Shimadzu (Kyoto, Japan). Various columns with
Z-RAFT Star Polymerization of Styrene: Comprehensive Characterization using SEC
135
mixed-bed particles were used (Resipore 3 µm, Minimix-C 5 µm and Minimix-B 10
µm, 250x4.6 mm each). All of these were obtained from Polymer Laboratories (Church
Stretton, UK). The separation was performed at a flow rate of 400 µL/min and 50 µL of
sample was injected. The sample solution was prepared by dissolving the polymer at a
concentration of approximately 1.5 mg/mL in THF with 250 ppm butyl-hydroxylated
toluene (Acros, 99 %) to prevent degradation by radicals. The triple-detection array was
assembled in-house (University of Amsterdam) and comprised an LC600 90° light
scattering detector (Viscotek), an on-line viscometry detector (Viscochip, Polymer
Laboratories) and a differential refractive-index detector (RID10a, Shimadzu). The data
were acquired using a PL-datastream A/D converter (Polymer Laboratories) and
processed using PL-Cirrus v3.0 software (Polymer Laboratories). Processing of the data
was performed in compliance with the triple-detection principle [37,38].
Electrospray-ionization mass spectrometry (ESI-MS) experiments were carried out
using a Finnigan LCQ ion trap mass spectrometer (Thermo Finnigan, San Jose, CA,
USA). For further details regarding the ESI-MS setup see ref. [39].
NMR spectroscopy was performed using a Varian Mercury 200 and a Varian Unity 300
NMR spectrometer.
Elemental analysis was carried out on a Heraeus CHN-O-Rapid Analyzer and on a
METROHM 662 photometer equipped with a 636 Tiroprocessor.
Chapter 5
136
S
S
SR
O
OO
O
O
O
S
S
S
SR
S
SR
S
SRS
O
OO
OO
O
O
OS
SS
SS
RS
SR
S
S RS
SR
S
1,2
3,4
5,6
O
O
O
O
OOO
O
SS
SR
O
S
S
SR
O
S
S SR
O S
SS
R
O S
S
SR
OS
S
SR
7,8
7: R = 8: R =
5: R = 6: R =
3: R = 4: R =
1: R = 2: R =
Chart 1. Mono-, tri-, tetra-, and hexafunctional RAFT agents used in this study.
Z-RAFT Star Polymerization of Styrene: Comprehensive Characterization using SEC
137
5.2.3 RAFT agent synthesis
Hexyl-benzyl-trithiocarbonate, 1. To a solution of 1-hexanethiol (1.00 g, 8.46 mmol)
in 50 mL chloroform triethylamine (1.41 mL, 1.03 g, 10.2 mmol, 1.2 eq) was added.
After stirring the reaction mixture for one hour at room temperature, 5 ml of CS2 and
benzyl bromide (1.21 mL, 1.74 g, 10.1 mmol, 1.2 eq) were added slowly. The mixture
was stirred for 15 h and the reaction was then quenched by adding 50 mL of 10 %
hydrochloric acid. The organic phase was separated and washed two times with 50 mL
of water and dried over Na2SO4. Solvent and traces of non-reacted starting materials
were removed in vacuum. 2.41 g (99 %) of 1 were received as a yellow liquid.
1H-NMR (300 MHz, CDCl3) δ (ppm): 0.89 (t, J = 7.1 Hz, 3 H, CH3-CH2), 1.35 (m, 6 H,
CH2), 1.71 (p, J = 7.2 Hz, 2 H, -S-CH2-CH2-CH2-), 3.37 (t, J = 7.4 Hz, 2 H, S-CH2),
4.62 (s, 1 H, CH2), 7.35 (m ,5 H, Har).
13C-NMR (300 MHz, CDCl3) δ (ppm): 13.96 (CH3-CH2), 22.45 (CH2), 27.90 (CH2),
28.56 (CH2), 31.25 (CH2), 37.03 (CH2), 41.31 (CH2), 127.69 (CarH), 128.65 (CarH),
129.22 (CarH), 135.07 (Car), 223.78 (C=S).
Mass spectrometry: m/z 285.1 (M + H+), 302.2 (M + NH4+), 319.2 (M + NH3 +NH4
+),
586.3 (2 M + NH4+).
Hexyl-1-phenylethyl-trithiocarbonate, 2. The synthesis was according to that of 1, but
using (1-bromoethyl)benzene (1.39 mL, 1.88 g, 10.1 mmol, 1.2 eq) instead of benzyl
bromide. 2.49 g (97 %) of 2 were received as a yellow liquid.
1H-NMR (300 MHz, CDCl3) δ (ppm): 0.89 (t, J = 6.7 Hz, 3 H, CH3-CH2), 1.35 (m, 6 H,
CH2), 1.68 (p, J = 7.2 Hz, 2 H, -S-CH2-CH2-CH2-), 1.76 (d, J = 7.1 Hz, 3H, CH3-CH),
3.34 (t, J = 7.4 Hz, 2 H, S-CH2), 5.38 (q, J = 7.1 Hz, 1 H, CH), 7.35 (m ,5 H, Har).
13C-NMR (300 MHz, CDCl3) δ (ppm): 13.96 (CH3-CH2), 21.34 (CH3-CH), 22.44 (CH2),
27.90 (CH2), 28.56 (CH2), 31.25 (CH2), 36.79 (CH2), 50.03 (CH), 127.63 (CarH), 127.67
(CarH), 128.60 (CarH), 141.16 (Car), 223.07 (C=S).
Mass spectrometry: m/z 299.1 (M + H+), 316.2 (M + NH4+), 614.3 (2M + NH4
+).
Chapter 5
138
Trimethylolpropane-tris-3-(S-benzyl-trithiocarbonyl)propanoate), 3. To a solution
of trimethylolpropane-tris-(3-mercaptopropionate) (1.00 mL, 1.21 g, 3.04 mmol) in 50
mL chloroform triethylamine (1.52 mL, 1.11 g, 10.9 mmol, 3.6 eq) was added. After
stirring the reaction mixture for one hour at room temperature 5 mL of CS2 and benzyl
bromide (1.30 mL, 1.87 g, 10.9 mmol, 3.6 eq) were added slowly. The mixture was
stirred for 15 h and the reaction was then quenched by adding 50 mL of 10%
hydrochloric acid. The organic phase was separated and washed two times with 50 mL
of water and dried over Na2SO4. Solvent and traces of non reacted starting materials
were removed in vacuum. 2.73 g (99%) of 3 were received as a yellow liquid.
1H-NMR (300 MHz, CDCl3) δ (ppm): 0.88 (t, J = 7.6 Hz, 3 H, CH3), 1.47 (q, J =
7.6 Hz, 2 H, CH2), 2.79 (t, J = 7.0 Hz, 6 H, CH2), 3.62 (t, J = 7.0 Hz, 6 H, CH2), 4.05 (s,
6 H, CH2), 4.61 (s, 6 H, CH), 7.32 (m, 15 H, Har).
13C-NMR (300 MHz, CDCl3) δ (ppm): 7.34 (CH3), 23.02 (CH3-CH), 31.23 (C(CH2)3),
33.07 (CH2), 33.13 (CH2), 40.73 (CH2), 64.12 (CH2), 127.79 (CarH), 128.69 (CarH),
129.24 (CarH), 134.79 (Car), 170.96 (C=O), 221.98 (C=S).
Mass spectrometry: m/z 897.07(M + H+), 914.10 (M + NH4+).
(An alternative pathway for the synthesis of 3 is given by Stenzel and co-workers [40].)
Trimethylolpropane-tris-(3-(S-phenylethyl-trithiocarbonyl)propanoate), 4. The
synthesis was according to that of 3, but using (1-bromoethyl)benzene (1.50 mL, 2.02 g,
10.9 mmol, 3.6 eq) instead of benzyl bromide. 2.86 g (99 %) of 4 were received as a
yellow liquid.
1H-NMR (300 MHz, CDCl3) δ (ppm): 0.87 (t, J = 7.6 Hz, 3 H, CH3), 1.45 (q, J =
7.6 Hz, 2 H, CH2) 1.75 (d, J = 7.1 Hz, 9 H, CH3-CH), 2.76 (t, J = 7.0 Hz, 6 H, CH2),
3.57 (t, J = 7.0 Hz, 6 H, CH2), 4.02 (s, 6 H, CH2), 5.32 (q, J = 7.1 Hz, 3 H, CH), 7.32
(m, 15 H, Har).
Z-RAFT Star Polymerization of Styrene: Comprehensive Characterization using SEC
139
13C-NMR (300 MHz, CDCl3) δ (ppm): 7.33 (CH3), 21.32 (CH3-CH), 26.79 (CH), 30.95
(C(CH2)3), 33.08 (CH2), 33.15 (CH2), 40.72 (CH2), 50.36 (CH3), 64.07 (CH2), 127.66
(CarH), 127.73 (CarH), 128.64 (CarH), 140.92 (Car), 221.98 (C=S).
Mass spectrometry: m/z 956.14 (M+NH4+).
Pentaerythritol-tetrakis-(3-(S-benzyl-trithiocarbonyl)propanoate), 5, was
synthesized according to Mayadunne et al. [19].
Pentaerythritol-tetrakis-(3-(S-1-phenylethyl-trithiocarbonyl)propanoate), 6. To a
solution of pentaerythritol tetrakis(3-mercaptopropionate) (0.71 mL, 1.44 g, 5.00 mmol)
in 100 mL chloroform triethylamine (5.53 mL, 4.04 g, 40.0 mmol, 8 eq) was added.
After stirring the reaction mixture for one hour at room temperature 10 mL of CS2 and
(1-bromoethyl)benzene (3.02 mL, 4.07 g, 22.0 mmol, 4.1 eq) were added slowly. The
mixture was stirred for 15 h and afterwards the reaction was quenched by adding 100
mL of 10 % hydrochloric acid. The organic phase was separated and washed two times
with 100 mL of water and dried over Na2SO4. Solvent was removed in vacuum and the
crude product was purified on silica with CH2Cl2 (Rf = 0.38) as eluent. 2.98 g (49 %) of
6 were received as yellow oil.
1H-NMR (200 MHz, CDCl3) δ (ppm): 1.75 (d, J = 7.1 Hz, 12 H, CH3-CH), 2.76 (t, J =
7.0 Hz, 8 H, CH2), 3.56 (t, J = 7.0 Hz, 8 H, CH2), 4.02 (s, 8 H, CH2), 5.32 (q, J = 7.1 Hz,
4 H, CH), 7.32 (m, 20 H, Har).
13C-NMR (300 MHz, CDCl3) δ (ppm): 21.32 (CH3-CH), 30.92 (C(CH2)3), 32.98 (CH2),
40.92 (CH2), 50.36 (CH3), 62.52 (CH2), 127.67 (CarH), 127.73 (CarH), 128.63 (CarH),
140.87 (Car), 170.76 (C=O), 221.89 (C=S).
Mass spectrometry: m/z 1226.13 (M+NH4+)
Dipentaerythritol-hexakis-(3-(S-benzyl-trithiocarbonyl)propanoate), 7, was
synthesized as recently reported by Johnston-Hall and Monteiro [41].
Dipentaerythritol-hexakis-(3-(S-1-phenylethyl-trithiocarbonyl)propanoate), 8. To a
solution of dipentaerythritol hexakis(3-mercaptopropionate) (3.915 g, 5.00 mmol) in
Chapter 5
140
200 mL chloroform triethylamine (6.32 mL, 6.07 g, 60.0 mmol, 12 eq) was added. After
stirring the reaction mixture for one hour at room temperature 50 mL of CS2 and (1-
bromoethyl)benzene (4.78 mL, 6.48 g, 60.0 mmol, 12 eq) were added slowly. The
mixture was stirred for 15 h and afterwards the reaction was quenched by adding 100
mL of 10 % hydrochloric acid. The organic phase was separated and washed two times
with 100 mL of water and dried over Na2SO4. The solvent was evaporated in vacuum.
The crude product was purified via column chromatography on silica gel using
pentane:ethyl acetate (3:1; Rf = 0.38) as eluent. 4.48 g (48 %) of 8 were received as
yellow oil.
1H-NMR (300 MHz, CDCl3) δ (ppm): 1.75 (d, J = 7.1 Hz, 12 H, CH3), 2.76 (t, J = 7.0
Hz, 12 H, CH2), 3.56 (t, J = 7.0 Hz, 12 H, CH2), 4.11 (s, 12 H, CH2), 5.32 (q, J = 7.1
Hz, 6 H, CH), 7.25 (m, 30 H, Har).
13C-NMR (200 MHz, CDCl3) δ (ppm): 21.33 (CH3), 30.79 (C(CH2), 30.93 (CH2), 32.99
(CH2), 42.92 (CH2), 50.37 (CH2), 62.53 (CH2), 127.68 (CarH), 127.74 (CarH), 128.64
(CarH), 140.88 (Car), 170.77 (C=O), 221.98 (C=S).
Elemental analysis: C, 52.81; H, 5.08; S, 30.95 (theor.). C, 53.32; H, 5.38; S, 29.95
(exp.)
5.2.4 Polymerizations
Styrene was degassed via three freeze-pump-thaw cycles, transferred along with RAFT
agent and initiator into an argon-filled glove box (oxygen content below 1.5 ppm),
where stock solutions of 10 mL monomer, initiator (ACCN), and RAFT agent or RAFT
agent mixtures were prepared. For the ambient pressure experiments, ten samples of
each stock solution were filled into individual glass vials and sealed with Teflon/rubber
septa. The vials were subsequently inserted into a block heater, thermostated at
80 ± 0.1 °C. The samples were removed after preset time intervals and the reactions
were stopped by cooling the solutions in an ice bath. The reaction times were up to 144
h. Polymerizations up to pressures of 2600 bar were performed in in-house-made
pressure cells. For details see ref. [42]. Monomer to polymer conversions was
determined gravimetrically.
Z-RAFT Star Polymerization of Styrene: Comprehensive Characterization using SEC
141
5.3 Results and Discussion
For our studies of Z-RAFT star polymerization of styrene, we chose multifunctional
trithiocarbonates as RAFT agents (see Chart 1). Trithiocarbonates become increasingly
popular as RAFT agents, due to their facile preparation and due to the absence of
potentially disturbing rate retardation effects, which are observed with more reactive
RAFT agents such as dithiobenzoates [43]. Mayadunne et al. [19] were the first who
introduced pentaerythritol-based multifunctional trithiocarbonates as Z-RAFT star
agents. Since then, the synthesis protocols for this class of star-shaped RAFT agents
were adapted by us [25] and others [41], providing access to bi-, tri-, tetra- and hexa-
functional mediating agents. Other trithiocarbonate-typed Z-RAFT star agents used in
styrene polymerization were based on β-cyclodextrin cores [20], on hyperbranched
polymer cores [30], and on dendrimers [24]. Multifunctional dithiobenzoates for usage
in styrene polymerization were constructed as dendrimers [21] and as 1,3,5-benzene-tri-
dithiocarboxylic-esters [32]. All these RAFT agents used for Z-RAFT star
polymerization of styrene were decorated with a benzyl-moiety as the reinitiating
leaving group. This is surprising, as it is well understood that benzyl as leaving group
results in a relatively low apparent chain transfer coefficient of the associated RAFT
agent in styrene polymerization, both with trithiocarbonates [44] and with
dithiobenzoate [45]. This is due to the relatively high energy of the benzyl radical,
which slows down the fragmentation rate of the initial intermediate radical and speeds
up the undesired back-transfer within the pre-equilibrium in comparison to monomer
addition. This scenario results in a pronounced so-called hybrid behavior [46], which
describes the formation of relatively high molecular weights of the resulting polymer
after only negligible monomer conversion, X, that is, experimental molecular weight vs.
X plots show a significant intercept instead of crossing the origin. The resulting
polydispersities are consequently significantly higher than in systems with more
effective pre-equilibriums [45]. The preference for benzyl as leaving group seen in
every study into Z-RAFT star polymerization of styrene performed so far is obviously
due to the easiness of the associated RAFT agent synthesis. In an effort to optimize this
polymerization system, we consequently implemented phenylethyl as leaving group,
which induces a more effective pre-equilibrium in styrene polymerization [44]. It should
be noted that benzyl as the leaving group may unfold sufficient transfer activity in other
Chapter 5
142
monomer systems, such as acrylates, due to a pronouncedly different fragmentation
selectivity of the RAFT intermediate of the pre-equilibrium.
When using RAFT agents 1, 3, 5, and 7 at, e.g., ca. 1 mmol∙L–1 of RAFT-group
concentration, intercepts of the experimental number average molecular weight, nM ,
vs. X traces of around 8000 g∙mol–1 were observed (not shown). This finding is in
agreement with literature reports about benzyltrithiocarbonate-mediated styrene
polymerizations, in which similar intercepts were found [20,32,47]. The Z-RAFT star
polymerization of styrene using RAFT agents 4, 6, and 8, which carry a phenylethyl
moiety revealed - as anticipated - that the hybrid-behavior is largely reduced in
comparison to benzyl as the leaving group. Nevertheless, a minor hybrid behavior could
still be observed, especially with low RAFT agent concentrations. In Figure 1a, the
intercept values 𝑀𝑛,0% are depicted on the example of 8-mediated 6-arm star
polymerization. The other RAFT agents showed very similar behavior. It can clearly be
seen that the intercept is below 4000 g∙mol–1, even for RAFT agent concentrations
below 1 mmol∙L−1, and approaches zero with increasing RAFT agent concentration. The
polymerizations were performed at 80 °C, which we identified as optimal. Since styrene
is a slowly propagating monomer [48] and usage of vast amounts of initiator is not
advisable, as it drastically increases the amount of terminated polymer, reaction times in
which full monomer conversion were reached lasted up to several days. It was hence
necessary to use the slowly decomposing initiator ACCN, which has about the same
fragmentation rate at 80 °C as has AIBN at 60 °C [49].
It is tempting to use the intercepts for obtaining average chain-transfer constants for the
initial RAFT step via plotting the inverse number average degree of polymerization at
zero monomer conversion, 1/𝑃𝑛,0% , against the RAFT agent concentration, as has been
demonstrated by Barner-Kowollik and co-workers [50,51]. However, this approach is
beset by problems in the case of star polymers, as the molecular weights obtained using
SEC calibrated with linear standards differ significantly from true molecular weights.
This needs to be addressed in the evaluation procedure, which will be presented below.
Z-RAFT Star Polymerization of Styrene: Comprehensive Characterization using SEC
143
0 1 2 3 4 5 6 70
1000
2000
3000
4000
5000
0.00 0.01 0.02 0.03 0.040.0
0.2
0.4
0.6
0.8
[RAFT] / mmol⋅L−1
Mn,
0% /
g⋅m
ol−1
(a) 1
/Pn,
0% (c
orr.)
[RAFT-groups] / mol⋅L−1
(b)
Fig. 1. (a) Intercepts of apparent number average molecular weight from conventional calibration using linear standards, 𝑀𝑛 vs. X traces in 8-mediated styrene bulk polymerization (6-arm star polymerization) vs. RAFT
agent concentrations at 80 °C using ACCN (cACCN = 3 mmol∙L–1) as the initiator. (b) Inverse degree of polymerization (corrected by K taken from Fig. 9 according to the procedure described in the text) at zero monomer conversion (extrapolated values) of star arm polymer vs. the concentration of trithiocarbonate
groups. The line indicates the best linear fit, forced through the origin.
The performed Z-RAFT star polymerizations using 3-, 4, and 6-armed RAFT
agents exhibited very well controlled behavior up to full monomer conversion, as is
exemplified on 8-mediated 6-arm star polymerization of styrene (see Fig. 2).
Polydispersities show minimal values of 1.07 at X = 20 % when using RAFT agent
Chapter 5
144
concentrations of 6.4 mmol∙L−1, which refers to 3.8×10–2 mol∙L−1 of trithiocarbonate
moieties. The slight curvature of the 𝑀𝑛 vs. X traces originates from continues
formation of dead chains (see below).
Fig. 2. Polydispersity index, PDI, and apparent number average molecular weight from conventional
calibration using linear standards, 𝑀𝑛, vs. monomer conversion in 8-mediated styrene bulk polymerization (6-arm star polymerization) at various RAFT agent concentrations at 80 °C using ACCN (cACCN = 3 mmol∙L–1) as
the initiator.
Full molecular weight distributions of the formed star polymers, as exemplified on 6-
mediated styrene polymerization (4-arm star polymerization) (see Fig. 3) are narrow and
unimodal, as expected for a well-controlled polymerization. This is in contrast to Z-
RAFT star polymerization of acrylates, in which star-star coupling side reactions were
observed after intermediate values of X [25]. The polymerization behaviors of 4-, 6, and
8-mediated polymerizations of styrene were very similar to each other, thus, only
demonstrating examples are presented.
Z-RAFT Star Polymerization of Styrene: Comprehensive Characterization using SEC
145
Fig. 3. SEC-distributions, wlogM, of polystyrene samples produced in 6-mediated (c6 = 9.6 mmol∙L−1) styrene bulk polymerization (4-arm star polymerization) at 80 °C using ACCN (cACCN = 3 mmol∙L–1) as the initiator,
after monomer conversion of 30 % (PDI = 1.06), 46 % (PDI = 1.08), 73 % (PDI = 1.11) and after full monomer conversion (PDI = 1. 17).
RAFT polymerization requires continuous delivery of initiating radicals, whereby dead
polymer is formed throughout the entire polymerization. Especially at low RAFT agent
concentrations and with slowly propagating monomers, such as styrene, the amount of
terminated polymer can become significant. In Z-RAFT star polymerization,
termination occurs between two growing arms (see Scheme 1), generating dead polymer
that at maximum, in the case of termination via combination, has double the chain
length of one arm polymer, which is lower than the degree of polymerization of the
complete star. Dead polymer consequently occurs completely at the low molecular
weight side of the living star polymer, as demonstrated in Fig. 4, in which 4-arm star
polymer is presented that has been formed in presence of relatively low RAFT agent
concentration. UV-detection set to 330 nm has been used to selectively detect the
trithiocarbonyl group, i.e., the living star polymer, which – after appropriate correction
[25] – can be related to the molecular weight distribution from RI-detection, which
includes both the living and the dead polymer.
It is clear, that the formation of dead polymer is an obstacle for obtaining pure and
narrowly dispersed star polymer. Terminated linear polymer can either be separated
Chapter 5
146
from the star polymer, e.g., via selective extraction [21], or its formation can be
minimized during the process via the following strategies: (i) The polymerizations can
be performed at high RAFT agent concentrations, which suppresses the relative
influence of terminated polymer. The maximum molecular weight, however, which can
be achieved thereby, is restricted. (ii) When performing the RAFT polymerization at
very low radical concentrations, the kinetic chain length becomes long, i.e., termination
is suppressed in comparison to propagation. This lowering of dead polymer, however, is
on the expense of polymerization rate, which can thus become considerable. The low
initiator concentrations used in the present study, for instance, yielded well-defined star
polymers with relatively low amounts of dead polymer; the reaction times, however,
were several days (e.g., see gaps in Fig. 2 which indicate overnight periods). (ii) The
kinetic chain length can also be stretched by applying high pressure, as we demonstrated
earlier for cumyldithiobenzoate-mediated polymerizations [42]. The impact of high
pressure becomes evident when quantifying the amount of dead polymer. Due to the
clear separation of dead and living polymer in Z-RAFT star polymerization (see Fig. 4),
these species can roughly be separated via multi-Gaussian fitting, yielding estimates for
the weight fraction of terminated polymer.
Inspection of Fig. 5 clearly shows that the fraction of dead polymer is largely reduced
when applying high pressure. Since samples are compared that were taken after
identical monomer conversions, they have almost identical molecular weights. As high
pressure increases the value of kp/kt, the rate of polymerization is increased as well, that
is, the reaction times for obtaining identical monomer conversion is significantly
reduced with increasing pressure. It goes without saying that the decreased amount of
terminated polymer is also reducing the polydispersity of the overall generated polymer;
the impact on the polydispersity of the living star polymer, which may be anticipated
due to the pressure dependence of the individual RAFT reactions, however, remains too
small to be detected unambiguously. For a detailed discussion of the pressure effect in
RAFT polymerization, the reader is referred to reference [42].
Z-RAFT Star Polymerization of Styrene: Comprehensive Characterization using SEC
147
Fig. 4. SEC-distribution, wlogM, of polystyrene samples produced in 6-mediated (c6 = 0.8 mmol∙L−1) styrene bulk polymerization (4-arm star polymerization) at 80°C using ACCN (cACCN = 3 mmol∙L–1) as the initiator, after 26% of monomer conversion. (---) RI detection (overall molecular-weight distribution); (–––) via UV
detection at 330 nm (trithiocarbonate end-groups, indicating living star polymer). The UV signal was corrected according to ref. [25] to allow comparison. The RI signal was subjected to multi-Gaussian fitting.
0 1000 2000 30000
10
20
30
w.-%
of d
ead
polym
er
p /bar
Fig. 5. Weight percent of dead polymer, w.-%, vs. applied pressure in 6-mediated (c6 = 1.2 mmol∙L−1) styrene bulk polymerization (4-arm star polymerization) at 80°C using ACCN (cACCN = 3 mmol∙L–1) as the initiator
after 25% of monomer conversion.
Chapter 5
148
In order to further characterize the Z-RAFT star polymerizations of styrene, we
compared molecular weights from SEC measurements to theoretical values, 𝑀𝑛𝑡ℎ𝑒𝑜
,
which were calculated using Eq. 1.
( )− ⋅
⋅ ⋅= +
+ ⋅ ⋅ ⋅ − d
0theo M monomern RAFT0 0
RAFT I 1 k t
X c MM Mc c d f e
(1)
with the monomer to polymer conversion, X, the initial monomer concentration, 0Mc ,
the initial RAFT agent concentration, 0RAFTc , the initial initiator concentration, 0
Ic , the
molecular weights of monomer, Mmonomer, and of RAFT agent, MRAFT, with d being the
number of chains that are generated in the termination process (d ≈ 1 for styrene), with
the initiator decomposition rate coefficient, kd (kd = 1.02×10–5 s–1 for ACCN [49]), and
the initiator efficiency f, which we recently determined to be around unity [52]. In many
reported studies, a simplified version of Eq. 1 is used, which does not account for the
continuous production of chains via initiation and yields straight lines for 𝑀𝑛𝑡ℎ𝑒𝑜
vs. X
traces. Such approach is, however, not advisable for slowly propagating monomers,
such as styrene, were significant amounts of additional chains are produced before
elevated monomer conversions are reached.
Inspection of Fig. 6 reveals that almost perfect agreement between molecular
weights from SEC and predicted values is found up to very high X values when using
the monofunctional trithiocarbonate 2 to obtain linear polymer. When using star-shaped
RAFT agents, however, a systematic deviation from theoretical values is observed; the
magnitude of the deviation increases with increasing numbers of arms. This effect is
well understood [53] and relates to the fact that star polymers exhibit a smaller
hydrodynamic volume in a good solvent than the linear polymers of identical molecular
weight that served as molecular-weight calibrants for the SEC setup. Star polymers are
consequently eluted later (corresponding to smaller hydrodynamic volumes). If
molecular weights were to be calculated using conventionally (linear) standards, the
obtained values would be too low. Since the studied Z-RAFT star polymerizations of
styrene exhibit well-controlled behavior, i.e. steadily increasing molecular weights and
low polydispersities up to very high monomer conversion (see Figs. 2 and 6), we
Z-RAFT Star Polymerization of Styrene: Comprehensive Characterization using SEC
149
conclude that the controlling reaction of macroradicals and RAFT groups near the
center of the core is fast enough to guarantee an efficient RAFT equilibrium,
independent of the number (if ≤6) and length of the growing arms. This finding is in
line with our recent simulation studies [33,34]. Apparent ceasing of star polymer
growth, reported by Stenzel and co-workers [20,24,30,31] and Gnanou and co-workers
[32], which was attributed to a loss of RAFT control due to shielding effects, was
possibly more likely due to large fractions of dead polymer because of high initiator
concentrations and high reaction temperatures, and due to arm cleavage via RAFT
reaction of small initiating radicals at elevated monomer conversions, which
counterbalance the star polymer growth.
Fig. 6. Number average molecular weight, 𝑀𝑛, by conventionally calibrated SEC vs. monomer conversion in styrene bulk polymerizations at 80°C using ACCN (cACCN = 3 mmol∙L–1) as the initiator and 2, 4, 6, and 8 (see
Chart 1) as the RAFT agents. The concentration of trithiocarbonate groups was 38 mmol∙L−1 in all cases. Lines indicate the theoretical molecular weights, calculated via Eq. 1.
The good agreement between experimental 𝑀𝑛 and theoretical 𝑀𝑛𝑡ℎ𝑒𝑜
vs. X plots for
monofunctional RAFT agent (see Fig. 6) indicates that Eq. 1 is valid and the curvature
of the plot is due to formation of dead chains. The deviations for the star polymers
therefore have to be attributed to a different effect, i.e. the reduced hydrodynamic
volume of star polymers. In order to prove this assumption, the absolute molecular
weights of the star polymers need to be known. This can either be done via light
scattering detection (see below), which is challenging for polymer of low and medium
Chapter 5
150
molecular weights and moreover may not be available in every laboratory, or via arm
cleavage yielding linear polymer that can be measured via conventionally calibrated
SEC [19,23,25]. We found that arm cleavage experiments, either via treatment with
amines or radical sources, give not well reproducible results and are prone to several
side reactions that alter the molecular weight distribution. For an approximate
characterization of star polymers, this might be sufficient; for a more detailed study,
however, methods with higher precision are required. We hence developed a very
straightforward method, which enables to measure absolute molecular weights of star
polymers from Z-RAFT star polymerization via conventionally calibrated SEC.
When performing a RAFT polymerization using a mixture of monofunctional
and star-shaped Z-RAFT agent, two RAFT equilibriums are established, which are
interlinked via the growing macroradicals, i.e. the individual arms (see Scheme 2).
Because of the controlled nature of RAFT polymerization, all macroradicals in the
system have approximately the same chain length and, during the polymerization, either
add to a linear polymeric RAFT agent (linear RAFT equilibrium) or to a living star
polymer (Z-RAFT star equilibrium). This situation implies that linear polymer and arm
polymer within the star at any time have identical average molecular weights, as they
are constantly exchanged via the RAFT equilibriums.
Scheme 2. The interdigitated equilibriums of simultaneously proceeding linear and Z-RAFT star polymerization. Thiocarbonylthio-moieties are indicated by circles.
Z-RAFT Star Polymerization of Styrene: Comprehensive Characterization using SEC
151
3.5 4.0 4.5 5.0(a)
(c)
(b)
star
star
star
linear
linear
linear
log (M / g⋅mol−1)
w logM
Fig. 7. Molecular weight (SEC) distributions, wlogM, of polystyrene (M are apparent molecular weights from conventional calibration using linear standards) generated in the presence of 19 mmol∙L−1 of linear RAFT
agent 2, 4.8 mmol∙L−1 of tetrafunctional RAFT agent 6, and 3.0 mmol∙L−1 ACCN as the initiatior at (a) 29 %, (b) 43 %, and (c) 81 % of monomer conversion.
It should be noted that this approach works best when all RAFT groups in the system
have similar chain transfer reactivity, independent whether they are in mono- or
multifunctional RAFT agents. This guarantees an even distribution of arms between the
free and the linked state and can generally be achieved by using identical RAFT agent
moieties both in mono- and multifunctional agents. Molecular-weight distributions of
polymer formed in the presence of a mixture of mono- and a multifunctional RAFT-
agent are distinctively bimodal, as shown in Fig. 7 on the example of a 4-arm star
polymerization. For such trithiocarbonate-mediated systems, the transfer activity was–
as required for this method – found as being independent on the RAFT agent
functionality [35]. Both the linear polymer (arms) and the star polymer increase steadily
in molecular weight with monomer conversion.
Chapter 5
152
Since the trithiocarbonate-group concentration was chosen to be identical for both
RAFT agents, the weight fraction of both types of polymer is identical, too. It can also
be seen that the polydispersity of the star polymer is smaller than that of the individual
arms, which is due to the arbitrary combination of dispersed arm polymer within one
star polymer molecule.
As the molecular weight of the linear arm polymer can accurately be determined via
conventionally calibrated SEC, the true number average molecular weight of the star
polymer can be calculated by multiplying the number average molecular weight of one
arm by the number of arms of the respective star. Both the arm and star polymers are
narrowly distributed due to the RAFT process. Thus, the number average molecular
weights are well represented by the peak molecular weight. This implies that by
dividing the peak molecular weight of the star polymer, Mp,star, by the peak molecular
weight of the linear arm polymer, Mp,arm, the apparent number of arms, as shown in Fig.
8 for 3-arm, 4-arm, and 6-arm stars, can be calculated.
It can clearly be seen that the apparent number of arms is always smaller than the
expected number, which reflects the contracted nature of the star polymers in
comparison to linear chains. 6-Arm stars appear to have only 3.94 arms, 4-arm stars
appear to have only 3.05 arms, and 3-arm stars seem to have only 2.58 arms. Further
important information drawn from Fig. 8 is that the apparent numbers of arms remain
constant throughout the polymerization. This means that the topology of the star
polymer remains unaltered, independent of monomer conversion, i.e., star-star coupling
or arm cleavage reactions at elevated X values are absent. From the apparent number of
arms, a correction factor K for the SEC setup was calculated by dividing the theoretical
number of arms (ftheory) by the apparent number of arms (fapp) (see Eq. 2). This factor
relates absolute molecular weight of a star polymer Mstar to that of a linear polymer Ml
eluting at the same hydrodynamic volume and is depicted in Fig. 9 as function of
number of arms, f. Comparison of polymers at identical molecular weight or
hydrodynamic volume is indicated by a subscript M or V respectively.
𝐾 = �𝑓𝑡ℎ𝑒𝑜𝑟𝑦𝑓𝑎𝑝𝑝
� = �𝑀𝑠𝑡𝑎𝑟𝑀𝑙
�𝑉
(2)
Z-RAFT Star Polymerization of Styrene: Comprehensive Characterization using SEC
153
0.0 0.2 0.4 0.6 0.8 1.02.0
2.5
3.0
3.5
4.0
4.5R =
3-arm star (4)
4-arm star (6)
Mp,
star /
Mp,
arm
monomer conversion
6-arm star (8)
Fig. 8. Ratio of peak molecular weights of star polymer and peak molecular weights of linear arm polymer
(Mp,star/Mp,arm), as obtained by conventionally calibrated SEC vs. monomer conversion for styrene bulk polymerizations at 80°C using ACCN (cACCN = 3 mmol∙L–1) as the initiator and mixtures of 2 and 4 (3-arm star
polymerization), 2 and 6 (4-arm star polymerization), and 2 and 8 (6-arm star polymerization). The overall trithiocarbonate-group concentration was around 38 mmol∙L−1 for all samples with approximately half the number of RAFT groups belonging to multifunctional RAFT agents. Horizontal lines indicate the average
value.
2 3 4 5 6 7
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8 this work Douglas' equation (semi-emp.) Radke et al. (exp.) Radke et al. (simul.)
corre
ctio
n fa
ctor
, K
number of arms, f
Fig. 9. Correction factor, K, for calculating absolute molecular weights of star polymers from values obtained using SEC with conventional calibration with linear standards. Closed circles: data from this work;
dashed line: semi-empirical equation by Douglas et al. [54]; open squares: mean values of experimental data collated by Radke et al. [55], error bars are standard deviations; dashed-dotted line: computer simulations by
Radke et al. [55,56].
Chapter 5
154
Branching ratios describing the reduction of the radius of gyration, rg, or of the
hydrodynamic radius, rH, of branched polymers have been subject of research for quite
some time. In order to compare our results, which were obtained via SEC separation
without on-line light scattering or viscosity detection, with branching ratios from
literature that are usually reported for identical molar mass, a calculation procedure,
e.g., starting from the viscosity branching ratio, is required. The viscosity branching
ratio g’ (see Eq. 3)
𝑔′ = �[𝜂]𝑏𝑟[𝜂]𝑙
�𝑀
(3)
is relating intrinsic viscosity [η] at identical mass of branched (index br) and linear
(index l) polymer and can be rewritten using the theory of universal calibration [57],
yielding Eq. 4, which related molecular weight of the linear and branched polymer of
identical hydrodynamic volume.
𝑔′ = � 𝑀𝑙𝑀𝑏𝑟
�𝑉
𝑎+1
(4)
The exponent a in Eq. 4 is the Mark-Houwink coefficient a of the linear polymer, i.e.,
0.700 for polystyrene in THF at 30 °C [58] as used in the present study. The correction
factor K can then be compared to branching-ratio data from other studies by combining
Eqs. 2 and 4, resulting in Eq. 5.
𝐾 = 𝑔′(−1𝑎+1) (5)
A prominent data set was reported by Douglas and co-workers [54], who calculated g’
for regular stars using the theoretical model by Stockmayer and Fixman [59]. They
found a semi-empirical relation (Eq. 6) which describes the viscosity branching ratio for
regular stars in good solvent best for ε = 0.58, which is an empirical form factor.
𝑔′ = �3𝑓−2𝑓2
�𝜀�1−0.276−0.015(𝑓−1)
1−0.276� (6)
Z-RAFT Star Polymerization of Styrene: Comprehensive Characterization using SEC
155
Based on this, Tsitsilianis et al. [60] described that the functionality of regular stars can
be calculated using SEC and Eqs. 4 and 6, that is, they used an approach that is similar
to the one described in this work. Inspection of Fig. 9 shows that the values obtained in
the present study are in relatively good agreement with semi-empirical g’ values
reported by Douglas et al. [54], calculated by via Eq. 6 and transformed to K values via
Eq. 5. Interestingly, the trend of our data is well matching that of Douglas’ data,
although the absolute values of our results are slightly higher.
Correction factors K for usage in conventionally calibrated SEC were also reported by
Radke et al. [55,56], who collated experimental contraction factors of star polymers that
were generated by various techniques and performed simulations of star polymer
shapes. These data are also plotted in Fig. 9. It can be seen that our results fit excellently
to the averaged experimental values by Radke et al. [55] for 3-arm stars (7 reported data
points) and 4-arm stars (6 reported data points) and that the simulated data by Radke et
al. [55,56] nicely matches Douglas’ Eq. 6. A somewhat higher discrepancy can be seen
for 6 arm stars: Our data are slightly higher than the simulated data by Radke et al. as
well as the semi-empirical data by Douglas et al., whereas the experimental values
reported by Radke et al. are significantly lower than these calculated values. This data
point originates from two samples only, which were generated via coupling of pre-
polymer and subsequent separation of grafted polymers having various arm numbers.
These laborious procedures might be a source of uncertainty. Since our method prepares
star and arm polymer simultaneously in a simple and straightforward fashion, the herein
reported data are possibly more precise. It is also gratifying to note that our data almost
perfectly follow the relative trend of the calculated data by Radke et al. and Douglas et
al.
In order to probe the precision, it seems rational to use our correction factors, K, to
estimate absolute molecular weight data by multiplying K with the molecular weights
from conventionally calibrated SEC. This approach is demonstrated in Fig. 10, in which
both the uncorrected and corrected data from conventional SEC calibration are plotted
together with the theoretically expected values. It can be clearly seen that the corrected
molecular weights almost perfectly match the 𝑀𝑛𝑡ℎ𝑒𝑜
values, suggesting that our
procedure is capable of yielding true molecular weights of star polymers. In order to
Chapter 5
156
finally prove that the perfect match between the corrected experimental values and the
predicted molecular weights is not a coincidence, we measured absolute molecular
weights of selected star polymer samples after SEC separation using a triple-detection
system that comprised an RI, a viscometry, and a light-scattering detector. Fig. 10
shows convincingly that the thus obtained absolute molecular weights perfectly blend
into the data obtained using the introduced correction method.
The concise picture that is obtained for Z-RAFT star polymerization of styrene up to 6
arms and using phenyl ethyl as the leaving group allows the following conclusions to be
drawn.
1. The number of arms of star polymer is constant above 30 % of monomer
conversion.
2. The number of arms is identical to the functionality of the star-shaped RAFT
agent, i.e., all RAFT groups have initiated arm growth.
3. Even at very high monomer conversions (thus yielding large star molecules),
there is no shielding effect observable that hampers the RAFT process.
Otherwise, deviations from theoretical predictions would occur.
Having now a method at hand to correctly determine molecular weights of star
polymers, we can evaluate the chain-transfer constant, CRAFT, of the initial RAFT step.
From a plot of the inverse number average degree of polymerization of one individual
arm against the concentration of trithiocarbonate groups, CRAFT can be evaluated via
linear fitting according to the procedure introduced by Barner-Kowollik and co-workers
[50,51]. Inspection of Fig. 1b shows that good linear behavior is observed in such a plot,
from which a CRAFT = 164 for phenylethyl-trithiocarbonate in styrene polymerization at
80°C can be estimated. This relatively large value is indicative of a very effective chain
transfer.
Z-RAFT Star Polymerization of Styrene: Comprehensive Characterization using SEC
157
0.0 0.2 0.4 0.6 0.80.0
2.0x104
4.0x104
6.0x104
8.0x104
1.0x105
conventional calibration corrected conventional calibration triple detection theoretical values
Mn /
g⋅m
ol−1
monomer conversion
Fig. 10. Number average molecular weight, 𝑀𝑛, of six-arm star polymer (data taken from Fig. 6) vs. monomer conversion, obtained via conventional SEC calibration (raw data and corrected by K given in Fig. 9) and via
triple-detection. The dashed line marks the theoretical molecular weight according to Eq. 1.
We also applied our method for obtaining apparent number of arms to Z-RAFT star
polymerizations having benzyl as the leaving group. This study was inspired by the fact
that all literature reports about Z-RAFT star polymerization of styrene used benzyl as
the leaving group. When applying exactly the same experimental conditions and
evaluation procedures as above, but using benzyl instead of phenylethyl as R-group, a
completely different picture is obtained, as can be seen in Fig. 11: The apparent arm
numbers are steadily increasing with monomer conversion and do reach the expected
and confirmed values for the anticipated arm numbers – indicated by the horizontal
dashed lines – only at very high X values, if at all. As the chemical nature of these stars
and that of the solvent are identical, the strong deviations from the star polymers
described above imply that the polymers from benzyl-typed star-shaped RAFT agents
have a distinct different topology. The data suggest that the real arm numbers are well
below the expected values and only slowly approach the expected numbers.
Chapter 5
158
0.0 0.2 0.4 0.6 0.8 1.0
1.5
2.0
2.5
3.0
3.5
4.0
R =
6-arm star (7) 4-arm star (5) 3-arm star (3)
Mpe
ak,s
tar /
M
peak
,linea
r
monomer conversion
Fig. 11. Ratio of peak molecular weights of star polymers and peak molecular weights of linear arm polymers (Mp,star/Mp,arm; representing the apparent number of arms in conventionally calibrated SEC) vs. monomer
conversion, from styrene bulk polymerizations at 80°C using ACCN (cACCN = 3 mmol∙L–1) as the initiator and mixtures of 1 and 3 (3-arm star polymerization), 1 and 5 (4-arm star polymerization), and 1 and 7 (6-arm star polymerization). The overall trithiocarbonate-group concentration was around 38 mmol∙L−1 for all samples
with approximately half the number of RAFT groups belonging to multifunctional RAFT agents. Horizontal lines indicate the average values from Fig. 8.
Stenzel and co-workers made similar observations in Z-RAFT star polymerizations with
benzyl-trithiocarbonates already in one of their early publications [20], in which they
found evidence for an increasing number of arms with proceeding reaction. However,
they did not quantify this effect, since they measured only apparent molecular weights
of star polymers. Surprisingly, this worrying effect was not considered since then and
benzyl-typed star-shaped RAFT agents were uncritically used by many research groups.
It may hence be that many observations, which were attributed to the mechanism of Z-
RAFT star polymerization, simply stem from an inefficient pre-equilibrium, which
apparently is highly relevant for the final topology.
It seems to be clear that the imperfect pre-equilibrium when using benzyl as the leaving
group hampers the rapid initiation of arm growth, which apparently not only affects
polydispersity, but more importantly, the topology of the final star polymer product.
This dramatic effect is due to the multifunctionality of the star-shaped RAFT agent,
which effectively needs to be initiated several times in a row before becoming a star.
Z-RAFT Star Polymerization of Styrene: Comprehensive Characterization using SEC
159
Unfortunately, our method for obtaining true molecular weights of star polymers is not
able to detect apparent arm numbers at very low monomer conversions, as linear and
star polymer species are not well separated in this regime. In order to fill this gap and to
study the topologically evolution of star growth also in more effective systems, detailed
theoretical and experimental studies of arm growth initiation at low monomer
conversions are underway in our laboratory.
5.4 Conclusion
Z-RAFT star polymerization of styrene leading to star polymers having 3, 4, and 6 arms
show very well controlled behavior up to very high monomer conversion. The
application of high pressure up to 2600 bar could suppress the amount of dead polymer
by more than a factor of 2.5, which is especially important for systems with low RAFT
agent concentrations, where the fraction of terminated linear polymer may become
substantial. No shielding effects were observed that would obstruct the RAFT process,
not even at very high monomer conversions (yielding large star molecules). By using a
mixture of linear and star-shaped RAFT agents, we were able to determine precise
absolute molecular weights of star polymers using a conventionally calibrated SEC
setup. When using trithiocarbonate-typed RAFT agents with phenylethyl as the leaving
group, a rapid chain-transfer of the initial RAFT step was found and well-defined star
polymers were formed, which perfectly match the theoretical predictions. However,
when using benzyl as the leaving group in the star-shaped RAFT agents, a pronounced
impact of monomer conversion on the number of arms was observed. It was found to be
impossible to synthesize pure star polymers with the expected number of arms, when
using benzyl as the leaving group.
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163
Summary
Branched polymers are different from other polymers in many different ways. Due to
their structure and properties branched polymers present a challenging class of materials
for structural analysis. The main goal of project CoBra (viz. ‘Comprehensive
characterization of Branched polymers’) has been the development of new analytical
technologies and methodology for branched polymers. Traditional characterization
techniques fail to separate long-chain-branched from linear polymers and do not
discriminate between the effects of degree of branching and topology. The approach
followed in the work described in this thesis has been the exploration and detailed study
of separations with unique selectivity towards branched polymers. The emphasis has
been on hydrodynamic separations and molecular-topology fractionation (MTF) for
high-molar-mass linear and long-chain-branching polymers. Comprehensive two-
dimensional separations have been used extensively with combinations of both new and
conventional separation modes. These experiments were used to improve understanding
of topology-sensitive separations, as well as experimental optimization ultimately
resulting in highly-selective separation of branched polymers.
The background of polymer structure and the importance of branching on material
properties are presented in chapter 1. A broad overview of different branched polymers
and their applications is provided. Classification of branched polymers is based on
molecular structure. Topology and branch length together determine the kind of
branching, as well as the impact on material properties. Common characterization
techniques for different kinds of branching are presented. The overview serves to
illustrate that the analytical needs for polymers with highly-abundant branching or low
molar masses can be properly addressed using the available characterization techniques.
Limitations with respect to conventional characterization of long-chain-branched
polymers and the distinct impact of even low levels of branching on rheology provide
the main drivers for the work presented in this thesis.
164
In chapter 2 the preparation of monolithic columns and their application for polymer
separations is described. It was verified that columns could be obtained with well-
defined and uniform flow-through pores. The application of such stationary phases was
of high interest for the studies of topology-selective separations, because these
separations require flow-through channels with dimensions comparable to the size of
analyte molecules. Flow-resistance measurements and mercury-intrusion porosimetry
were performed to obtain accurate pore-size information. Based on these results and the
observed polymer separations it was concluded that the prevailing separation
mechanism was hydrodynamic chromatography (HDC).
The first demonstration of a comprehensive two-dimensional separation for high-molar-
mass polymers with identical size, but different topology is presented in chapter 3.
Branching-selective separation was performed on an MTF column with polydisperse
sub-1-µm particles. The calibration curve for this column (established using one-
dimensional separations) showed reversal of the calibration curve analogous to HDC. In
an MTF×SEC experiment (comprehensive two-dimensional liquid chromatography with
MTF in the first and size-exclusion chromatography in the second dimension) the
branching selectivity in MTF was confirmed, although the effects of size and topology
remained confounded. Another important step forward in branching-selective separation
demonstrated in this chapter is the separation of a long-chain-branched polymer with a
broad molar-mass distribution. The need for MTF columns with well-defined porous
properties is highlighted by this work, because accurate statements on the separation
mechanism were hindered by the ill-defined nature of the interstitial-channels in a bed
with polydisperse particles.
State-of-the-art separations of branched polymers in chapter 4 are the result of progress
made in terms of both column technology and understanding of polymer separations in
monoliths with extremely narrow flow-through channels. Monoliths described in
chapter 2 were used in a systematic study of experimental conditions, such as pore size,
flow rate, and hydrodynamic size and topology of analyte polymers. An overview is
presented of different separation modes for random-coil polymers in terms of the aspect
ratio (λ) and Deborah numbers. The analogy between HDC to MTF at low flow rates
and deviations at higher flows are studied using comprehensive MTF×SEC. The
165
occurrence of ‘critical conditions’, where the non-equilibrium deformation of polymers
and retardation effects at high λ cancel out, is recognized as a means to enhance the
applicability of MTF separations. Within the relatively narrow window of 0.4 < λ < 0.9
the separation of linear from branched polymers is demonstrated for materials with
different branching topology.
In chapter 5 the preparation and characterization of well-defined star polymers is
described. Reversible addition-fragmentation chain transfer (RAFT) polymerization is a
living polymerization. Star polymers can be created with a pre-defined number of arms
using multi-functional RAFT agents, provided that suitable leaving groups are used.
Mixtures of linear and star polymers were prepared with the linear segments or ‘arms’
all having the same degree of polymerization. The bi-modal molar-mass distribution of
the product served as a well-defined star polymer with an internal linear reference. The
viscosity contraction ratio was indirectly used to calculate correction factors for SEC
separations calibrated with linear polymers. Results of the study were validated against
externally published work and against accurate molar masses determined using triple-
detection SEC.
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Samenvatting
Vertakte polymeren verschillen van andere polymeren in veel opzichten. Vertakte
polymeren vertegenwoordigen een bijzonder uitdagende klasse van materialen vanwege
hun structuur en eigenschappen. Het voornaamstel doel van project CoBra (acroniem
voor ‘comprehensive characterization of branched polymers’ ofwel de alomvattende
analyse van vertakte polymeren) is de ontwikkeling van nieuwe analytische technologie
en methodologie voor vertakte polymeren. Traditionele analytischetechnieken voldoen
niet om hoogmoleculair materiaal met lange vertakkingen (zogenaamde ‘long-chain-
branched polymeren’) te onderscheiden van lineair materiaal, dan wel onderscheid te
maken tussen de mate en soort van de vertakkingen. De aanpak van deze uitdaging,
zoals beschreven in dit proefschrift, is gericht op de verkenning en verdieping in
scheidingmethoden met een unieke selectiviteit voor vertakte polymeren. De nadruk
binnen dit werk ligt op de toepassing van hydrodynamische scheiding en fractionering
op basis van moleculaire topologie (MTF) voor hoogmoleculair lineair en vertakt
materiaal met lange vertakkingen. Alomvattende twee-dimensionale scheidingen zijn
uitvoerig gebruikt, met zowel nieuwe als bestaande analytische scheidingsmethoden.
Deze experimenten dienen zowel voor het verdiepen van inzicht in scheidingen met
selectiviteit voor topologie, als voor experimentele optimalisering om een effectieve
scheiding van vertakte polymeren te verkrijgen.
De achtergrond van vertakte polymeren, de moleculaire structuur en de
materiaaleigenschappen worden behandeld in hoofdstuk 1. Een brede achtergrond wordt
geschetst voor vertakte polymeren en de toepassingsgebieden hiervan. De classificering
van vertakte polymeren vindt plaats op basis van de moleculaire structuur. Topologie en
de lengte van de vertakkingen bepalen samen tot welke klasse het polymeer behoort en
wat de gevolgen zijn voor materiaaleigenschappen. Een overzicht van gangbare
analytische technieken voor verschillende klassen van vertakte polymeren wordt
gepresenteerd. Hieruit blijkt dat met de gangbare technieken in voldoende mate kan
worden voorzien in de analytische behoefte voor polymeren met een hoge mate van
vertakking of een laag moleculair gewicht. De beperkingen van deze technieken doen
168
zich met name gelden voor polymeren met lange vertakkingen, die reeds bij zeer
beperkte aanwezigheid de materiaaleigenschappen beïnvloeden. Dit vormt de
belangrijkste drijfveer voor het werk dat wordt gepresenteerd in dit proefschrift.
In hoofdstuk 2 worden de bereiding van monolithische kolommen en toepassing daarvan
voor de scheiding van polymeren beschreven. De mogelijkheid om kolommen te maken
met goed gedefinieerde en uniforme doorstroomkanaaltjes wordt hierin geverifieerd.
Toepassing van dit soort stationaire fasen is van bijzondere interesse voor studies met
betrekking tot topologie-gevoelige scheidingen, omdat hiervoor een stationaire fase
gewenst is met doorstroomkanaaltjes van vergelijkbare grootte als de
polymeermoleculen in oplossing. Metingen van de stromingsweerstand en
kwikverzadigingsporosimetrie werden uitgevoerd om een nauwkeurig beeld te krijgen
van de poriegrootte. De resultaten hiervan, in combinatie met observaties voor
polymeerscheidingen op deze materialen, leidden tot de conclusie dat een
hydrodynamisch mechanisme verantwoordelijk was voor chromatografische scheiding.
Een eerste demonstratie van een alomvattende twee-dimensionale scheiding van
hoogmoleculaire polymeren met identieke hydrodynamische omvang, maar
verschillende topologie, wordt gepresenteerd in hoofdstuk 3. Vertakkingsgevoelige
scheiding werd uitgevoerd op een kolom met polydisperse deeltjes kleiner dan 1 µm. De
kalibratie van deze kolom (op basis van één-dimensionale experimenten) bevestigde de
omslag van de kalibratiecurve vergelijkbaar met hydrodynamische scheidingen. In een
MTF×SEC experiment (alomvattende twee-dimensionale scheiding met MTF in de
eeerste en “size-exclusion” chromatografie in de tweede dimensie) werd de
vertakkingsgevoeligheid voor fractionering op basis van moleculair topologie bevestigd,
ondanks dat de scheiding tevens beïnvloed werd door de hydrodynamische omvang van
de moleculen. Een belangrijke stap vooruit in de vertakkingsgevoelige scheiding wordt
ge zet met de scheiding van een polymeer met lange vertakking in combinatie met een
brede moleculaire gewichtsverdeling. De behoefte aan MTF kolommen met goed
gedefinieerde doorstroomkanaaltjes werd wederom bevestigd in dit werk, omdat een
nauwkeurige analyse van het scheidingsmechanisme niet mogelijk was bij gebrek aan
goed gedefinieerde poriën in de stationaire fase.
169
De best mogelijke analytische scheidingen van vertakte polymeren in hoofdstuk 4 zijn
het resultaat van de vooruitgang die geboekt in kolomtechnologie en verbeterd inzicht in
polymeerscheidingen in monolithische kolommen met zeer nauwe
doorstroomkanaaltjes. De monolithische kolommen zoals beschreven in hoofdstuk 2
werden toegepast in een systematisch onderzoek naar de invloed van experimentele
condities, zoals de grootte van doorstroomkanaaltjes, het debiet en de hydrodynamische
straal en de topologie van de polymeermoleculen. Een overzicht van verschillende
scheidingsmechanismen die van toepassing zijn voor polymeren met een flexibele
ketenstructuur is opgesteld op basis van de relatieve polymeergrootte (λ) en
Deborahgetallen. De overeenkomst tussen hydrodynamische scheiding en MTF,
alsmede de verschillen bij hogere debieten, werden bestudeerd met MTF×SEC. Het
verschijnsel van ‘kritische condities’, waarbij de effecten van de verstoring van de
polymeeromvang onder evenwichtscondities worden opgeheven door de trage relaxatie
van relatief grote polymeermoleculen wordt aangemerkt als een mogelijkheid om de
toepasbaarheid van MTF te verruimen. Binnen een relatief klein toepassingsgebied (0.4
< λ < 0.9) wordt de analytische scheiding van lineaire en vertakte polymeren
gedemonstreerd voor materialen met verschillende topologie.
In hoofdstuk 5 word de bereiding en analyse van goed gedefinieerde sterpolymeren
beschreven. Reversibele additie-fragmentatie ketenoverdrachtspolymerisatie (RAFT) is
een vorm van levende polymerisatie. Sterpolymeren kunnen worden bereid met een
vooraf gekozen aantal armen met behulp van multifunctionele RAFT start
verbindingen, op voorwaarde dat een geschikte vertrekkende groep wordt gebruikt.
Mengsels van lineaire en stervormige polymeren kunnen worden gemaakt met een
vergelijkbare polymerisatiegraad voor alle lineaire ‘arm’ segmenten. De bimodale
molaire-massa verdeling van het product reflecteert zowel een goed gedefinieerd
sterpolymeer als een lineaire interne standaard. De relatieve viscositeitscontractie
verhouding kan indirect worden gebruikt voor een correctie op een massa’s verkregen
uit SEC op basis van een kalibratie met lineaire polymeren. De resultaten van het
gebruik van deze correctie werden gevalideerd door middel van een vergelijking met
extern gepubliceerd werk, alsmede met een zeer nauwkeurige moleculaire-massa meting
met behulp van “triple” detectie SEC.
170
171
Acknowledgements
The time has finally come to finish this thesis, but before I do so I would like to say
thank you to everyone who contributed to the result that lies before you. Over the time
of my thesis research I came to meet and work together with many people. I owe them
my gratitude for the great collaboration and the good times in Amsterdam during my
PhD research.
First of all I would like to thank Peter, my promotor, for his trust and support that have
made it possible to perform and complete this work. The way that you convey your
enthusiasm and engage people with analytical chemistry got me interested to continue in
this field (starting back in the first year at university for both of us, 1999, Algemene
Chemie). After various projects and courses in the analytical-chemistry group and Shell
both of us were convinced that a PhD-project was the way to move forward. Jan
Blomberg deserves a fair share in the credit here as well! I would like to mention the
many possibilities people get in the group to visit meetings, conferences and even help
organize them. They have been the best times and created a wealth of personal
development opportunities. Thank you for always being ready to join singing good-old
Dutch songs on Friday evenings. You once accused me in York of comprehensive waste
of time, but this wasn’t one of them.
Special thanks go out to members of the thesis committee: Sjoerd van der Wal, Hans-
Gerd Janssen, Alex van Herk, Wim Kok, Wolfgang Radke and Freddy van Damme. I
appreciate our discussions and the critical question with respect to the various subjects
of this thesis. Without your challenging this thesis could not have reached the level it
has now. I also appreciate the possibilities of visiting the DKI in Darmstadt (Wolfgang
Radke, Harald Pasch, Tibor Macko, Mubasher Bashir, Yonggang Liu and others, thank
you for your hospitality), DSM in Geleen, and Unilever in Vlaardingen (ice cream!).
Colleagues and friends of the analytical-chemistry group at University of Amsterdam –
the list has grown long after being around for almost seven years! Fiona Fitzpatrick and
Aschwin van der Horst, thank you for giving me the chance to work with liquid
chromatography and SEC for the first times during the bachelor internships. Simona
Popovici, I’m happy that we meet again in our new roles now you’re teaching at
172
Hogeschool Zeeland. I like the student visits to Dow, you’re welcome. Xulin, Maya
Ziari, Wybren Frankema (I still don’t say RMS-radius, though you are right), thank you
for sharing the office space at the fourth floor of Roeterseiland when I just joined the
group. Many other colleagues there I would like to thank for the work we did and good
times we had. Yuli, Filippo (I will remember you surrounded by a canteen full of girls
only in Groningen), Mauro (you should have been there), Erwin (has similar problems
with English women when dressed in purple), Sonja (outclasses all of them together),
Peter Pruim & Stella (I’d better make sure the fridge is full when you are there, I
appreciate your attendance on Friday afternoons), Linda, Elena (thank you for the royal
banquet upon your arrival), Aleksandra and Daniela. Sebastiaan Eeltink, thank you not
only for teaching me how to make monoliths and guiding me in doing PhD research
when I just started, but also for being a good friend (especially when you let me win
with squash…). HPLC2006 San Francisco was one of the best symposium visits,
because of the associated holidays. Gabriel (thank you for supporting the group with
chemometrics expertise), Sonja and Frederique; thank you for joining the road trips
around SF and being part of this adventure. Wim Decrop, I’ve learned a great deal from
you with respect to two-dimensional liquid chromatography and data processing in
Matlab. Other things that come to mind are the tree W’s: waffles, Westvleteren and DJs
Wipneus & Pim. Dominique and Korneel (he can open a beer with anything, included a
printed version of J Chromatogr A.), I’m grateful for the work you did on making
monolithic and particle-packed columns. Apart from that there were the barbeques,
wok-frituren; we had a lot of fun as well. When their project was finished Siri took over
making monoliths. No wonder you are doing a PhD now in Switzerland, within a few
weeks we did some of the best experiments ever with monoliths. Then there are Petra
(jij regelde de hulptroepen bij symposia en activiteiten, ook als de Jenever op moest),
Tom and Peter Verschuren. Thank you for making the group successful as it is. Marjo,
your help with the porosimetry has been most valuable to this work, thank you! To all
of you, it has been my pleasure to run the FBI for so long. I enjoyed many Friday-
afternoon events with you of the Friday beer initiative. After the department had fallen
short of a crazy woman to serve coffee I was happy to jump in and set something up for
that as well. It’s less flattering than the previous initiative, but having access to descent
coffee at work is priceless.
173
I’ve met many great people that I would like to mention that are active on the subject of
polymers through collaboration in the European Graduate School (Thank you Wibke
Dempwolf and Alex for your efforts to make EGS possible). Ellen Donkers, Patricia
Geelen, Joris Salari, Marie-Claire Hermant, Roxana Abu, Joost Leswin, Bas Staal,
Maarten Staal, thank you for the nice times (EGS and not to forget Lunteren) and
collaboration. Thanks to Phillip Vana and Daniel Boschmann (Göttingen) for
collaboration on synthesis and analysis of star polymers as part of EGS as well.
Eindhoven is home also to the Dutch Polymer Institute that has made project CoBra
possible. Through the update meetings I’ve met great collaborators within the Dutch
Polymer Institute. Joachim Loos and Kangbo Lu, thank you for providing the cryo-TEM
results and 3D mapping of monolith structure. Rob Duchateau, Wouter Gerritsen, I
appreciate the knowledge we shared on the high-temperature SEC for high-throughput
polymer synthesis.
Also I would like to acknowledge my colleagues and friends at Dow that I’ve interacted
with during and after my time at University. Freddy, Edwin and David, thank you for
making this possible, as well as for the regular contact on results and progress of this
project. I am most grateful for the possibilities you offered me to visit Dow in
Terneuzen and Midland where we worked on high-temperature 2D-LC. David Meunier,
I really appreciate the time you made available for me during the longer visit to Midland
– not only at work, but also for visiting the Loons games, traveling for football through
most of Michigan. Ted Stokich, thank you for the work on 2D-LC we did. I appreciated
the confrontation with my own culture (the Holland visit) and having shooting classes
as well. Credit for visiting Holland goes to Pat Smith as well. Pat is a great person, he
helped me with the essentials: a bicycle, good coffee (we grind beans) and a trip to a
microbrewery once in a while. Most of all thank you for your contribution to great
science in making new analytical techniques possible. Dave Walter, I appreciate the
concept lunch meeting as well as moose-burger. I remember you as an engaged project
leader and great people leader. The return favor of showing you the analytical
department and the rest of Amsterdam was therefore more than deserved. In the post-
university time I’ve learned from a number of people about how we do characterization
of (branched) polymers: Jaap den Doelder, Sjoerd de Vries, Marc Mangnus, Hans de
Jonge; I would like to thank you for your time and the contributions to this thesis.
174
Albena Lederer, Marion Gaborieu, Patrice Castignolles, Bob Gilbert, Walther Burchard
and Wolfgang Radke; thank you for organizing the stimulating workshop on
characterization of branched polymers in Dresden. I have learned a lot at this meeting
about things I did not know. Thanks Anna, Susanne and Michael for your contributions
as well, I will try and get you a version of this thesis.
Various others have contributed to project Cobra. Christine Fernyhough from the
University of Sheffield. Thank you for making comb polymers available early in my
project! Another contact established at the ISPAC 2005 meeting was with Polymer
Laboratories. Adrian Williams, Steve O’Donohue and Greg Saunders. Thank you for
providing us with the second-dimension SEC columns. Many thousands of second-
dimension chromatograms have been analyzed on rock-solid columns that lasted the
entire project! Through collaboration between PL and Micronit it was possible to work
with a chip-sized viscometer. Marco Blom is gratefully acknowledged for the support
with this apparatus. We got it to work properly pretty soon as you can see in the
introduction. Small things can have huge impact, as proven again by Ben Klein
Meulekamp from our mechanical workshop. Thanks to the disks provided by you we
were able to make monoliths in wide-bore steel columns successfully.
Acknowledgements also to Johan Scholtens (Shimadzu, LC-equipment) and Jeroen de
Jong (Interscience, empty column hardware) for their engagement with this work and
going the extra mile to get us the tools to make this work possible.
It’s time to finish. I would like to thank my parents, Ton en Ria, for their support. After
you pushed me to finish up the last corrections of the manuscript I can go on a nice
holiday with the writing finished. Khanh, you’ve permitted me the time to complete this
work. Good life balance is important and you helped me to relax from time to time.
When you were not around I was able to work twice as hard and fill my micro-pauses
with improving my Gangnam-style dance. Time to show you the result, the plane is here
now for my flight to Hanoi.
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Publications
1. Fiona Fitzpatrick, Rob Edam, Peter J. Schoenmakers, “Application of the
reversed-phase liquid chromatographic model to describe the retention
behavior of polydisperse macromolecules in gradient and isocratic liquid
chromatography”, J. Chromatogr. A, 988 (2003) 53.
2. R. Edam, J. Blomberg, H.-G. Janssen, P.J. Schoenmakers, “Comprehensive
multi-dimensional chromatographic studies on the separation of saturated
hydrocarbon ring structures in petrochemical samples”, J. Chromatogr. A,
1086 (2005) 12.
3. R. Edam, D.M. Meunier, E.P.C. Mes, F.A. Van Damme, P.J. Schoenmakers,
“Branched-polymer separations using comprehensive two-dimensional
molecular-topology fractionation × size-exclusion chromatography”, J.
Chromatogr. A, 1201 (2008) 208.
Chapter 3 of this thesis
4. Daniel Boschmann, Rob Edam, Peter J. Schoenmakers, Philipp Vana, “Z-
RAFT star polymerization of styrene: Comprehensive characterization using
size-exclusion chromatography”, Polymer, 49 (2008) 5199.
5. Daniel Boschmann, Rob Edam, Peter J. Schoenmakers, Philipp Vana,
“Characterization of Z-RAFT star polymerization of butyl acrylate by size-
exclusion chromatography”, Macromol. Symp., Vol. 275-276 Issue 1 (2009)
184.
Chapter 5 of this thesis
6. R. Edam, Sebastiaan Eeltink, Dominique J.D. Vanhoutte, Wim Th. Kok, Peter
J. Schoenmakers, “Hydrodynamic chromatography of macromolecules using
polymer monolithic columns”, J. Chromatogr. A, 1218 (2011) 8638.
Chapter 2 of this thesis
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7. James F. Griffith, William L. Winniford, Kefu Sun, Rob Edam, Jim C. Luong,
“A reversed-flow differential flow modulator for comprehensive two-
dimensional gas chromatography”, J. Chromatogr. A, 1226 (2012) 116.
8. Rob Edam, Edwin P.C. Mes, David M. Meunier, Freddy A. Van Damme, Peter
J. Schoenmakers, “Branched polymers characterized by comprehensive two-
dimensional separations with fully orthogonal mechanisms: molecular-
topology fractionation × size-exclusion chromatography”, submitted for
publication in J. Chromatogr. A, 2013.
Chapter 4 of this thesis