The Importance of Online Viscometer in the Age of Multi ......• Conventional calibration (left) versus universal calibration (right). • Once the universal calibration is established

CONFIDENTIAL © Wyatt Technology Corporation – All Rights Reserved 1

The Importance of Online Viscometer in the Age of Multi-Angle Light Scattering

Stepan Podzimek1,2,3 1Wyatt Technology Europe GmbH

2SYNPO, Pardubice, Czech Republic 3University of Pardubice, Republic


Outline

• What is (and what is not) the intrinsic viscosity

• Applications of online viscometer

– Universal calibration

– Mark-Houwink equation

– Mark-Houwink plot

– Flory-Fox equation

– Hydrodynamic radius

• Online viscometer for the structural studies

• Online viscometer for fluorescent polymers

• Final remarks


Intrinsic Viscosity

• Intrinsic viscosity is not viscosity!!!

• Viscosity is the proportionality constant in the Newton´s law for fluids

• Newton´s law for fluids

𝜏 = 𝜂𝑑𝑣

𝑑𝑦

– τ = shear stress (N/m2)

– η = viscosity (Pa.s)

– dv/dy = velocity gradient (s-1)

Velocity profile in liquid placed between moving and stationary plate.


Temperature Dependence of Viscosity

RT

E

e

viscosity E activation energy of flow T temperature R universal gas constant


Temperature Dependence of Intrinsic Viscosity

From T. S. Rushing and R. D. Hester, J. Appl. Polym. Sci., 89, 2831 (2003).


Intrinsic Viscosity

• Intrinsic Viscosity

– Fundamental property characterizing polymer chain conformation and thermodynamic quality of the solvent = volume fraction of polymer in solution c = concentration in mg/mL

• Specific viscosity

η = viscosity of polymer solution η0 = viscosity of pure solvent t = time needed for solution or solvent to flow from one mark to the other

lim0 c

sp

c

5.2sp

10

0

0

0

relativespt

tt


Classical Determination of Intrinsic Viscosity

• Determination of intrinsic viscosity of polystyrene NIST 706 in THF, 25 °C.

• Data obtained by Ubbelohde capillary viscometer.

0.0 2.0x10-3

4.0x10-3

6.0x10-3

8.0x10-3

1.0x10-2

80

85

90

95

100

105

110

115

sp/c

(m

L/g

)

c (g/mL)

Equation y = a + b*x

Weight No Weighting

Residual Sum of Squares

4.00547

Adj. R-Square 0.98755

Value Standard Error

BIntercept 85.3 0.8

Slope 2764.3 138.6


Online Determination of Intrinsic Viscosity

IPDP

PIP

Psp

2

4

c

sp

c

0lim

P imbalance pressure across the bridge

IP pressure drop from inlet to outlet

sp specific viscosity

14 16 18 20 22 24

10

100

Volume (mL)

Intr

insic

Vis

co

sity (

mL

/g)

400


Applications of Intrinsic Viscosity in Polymer Science

• Molar mass from Mark-Houwink equation

• Hydrodynamic radius from [η] and molar mass

• Root mean square (RMS) radius (radius of gyration) from [η] and molar mass

• SEC with universal calibration for the determination of molar mass distribution

• Polymer structure from Mark-Houwink plot: log [] vs. log M


Mark-Houwink Equation

Traditional way of molar mass determination


Mark-Houwink Equation

• K, a = constants of Mark-Houwink equation for given polymer, solvent and temperature; M = molar mass

• Traditional method of the determination of molar mass

• Viscosity average (Mv) close to weight-average (Mw)

– NIST 706, [η] = 85.3 mL/g: Mv = 244,000 g/mol; Mw ≈ 270,000 g/mol

– K = 0.0117 mL/g, a = 0.717 (THF, 25 °C, M. Kolinsky and J. Janca, J. Polym. Sci., Polym. Chem. Ed., 12, 1181 (1974).

aKM


Molar Mass from Mark-Houwink Equation

Molar mass versus elution volume plots of linear polystyrene by MALS and calculated from Mark-Houwink equation.

cK

RM

*

0

16 18 20 22 24

104

105

106

Volume (mL)

Mo

lar

Ma

ss (

g/m

ol)

MALS vs. Mark-Houwink

a

KM

1


Hydrodynamic Radius


Hydrodynamic Radius

Vh = hydrodynamic volume M = molar mass NA = Avogadro´s number

• Hydrodynamic radius (Rh)

– Rh is radius of hydrodynamically equivalent sphere, i.e., a hypothetical sphere having the product of intrinsic viscosity and molar mass the same as the polymer molecule.

– It can be used as an alternative size parameter to RMS radius.

– Viscometry is often more sensitive than a golden standard dynamic light scattering.

3

1

5.2 4

3

A

hN

MR

A

hN

MV

5.2

3

3

4RVsphere


Hydrodynamic Radius: DLS versus Viscometry

Conformation plots of polystyrene based on hydrodynamic radius determined by online viscometer and dynamic light scattering.

105

106

10

Hyd

rod

yn

am

ic R

ad

ius (

nm

) V

isco

sity /

DL

S

Molar Mass (g/mol)

3

80


Flory-Fox Equation


Flory-Fox: RMS Radius by Viscometry … or [η] by MALS

• T. G. Fox and P. J. Flory, J. Am. Chem. Soc., 73, 1904 (1951)

• O. B. Ptitsyn and Yu. E. Eizner, Sov. Phys. Tech. Phys., 4, 1020 (1960)

3

12

)86.263.21(1086.2 221

a

3

1

6

1

MR

= Flory-Fox constant

a = exponent of Mark-Houwink equation

[η] in dL/g, R in cm


RMS Radius by MALS vs. Viscometry

20 40 60 80 100

20

40

60

80

100R

MS

Ra

diu

s (

nm

) b

y F

lory

-Fo

x

RMS Radius (nm) by MALS

Intercept = 1.1

Slope = 0.95

Correlation of RMS radius by Flory-Fox with MALS (Polystyrene, THF, 25 °C).


Intrinsic Viscosity by MALS

From S. Podzimek, J. Appl. Polym. Sci., 54, 91 (1994). PMMA, THF, 25 °C, a = 0.72.

𝜂 =632 𝑅3Φ

𝑀


Universal Calibration


Universal Calibration Z. Grubisic, P. Rempp, H. Benoit, Polymer Letters, 5, 753 (1967)

... log bVaM

[] intrinsic viscosity M molar mass

20 22 24 26

106

107

108

109

[]M

Elution Volume (5 mL counts, THF)


Universal Calibration

• Conventional calibration (left) versus universal calibration (right).

• Once the universal calibration is established typically by narrow standards, the molar mass of polymer is calculated from the intrinsic viscosity determined by viscometer and universal calibration curve.

14 16 18 20 22 24

4

5

6

7

8

9

log

([

]M)

Volume (mL)

Linear PS

Branched PIBMA

PBZMA

Branched PBZMA

Branched PS

Phenoxy resin

14 16 18 20 22 2410

3

104

105

106

107

Mo

lar

Ma

ss (

g/m

ol)

Volume (mL)

Linear PS

Branched PIBMA

PBZMA

Branched PBZMA

Branched PS

Phenoxy resin


Universal Calibration vs. MALS: Band Broadening in SEC

Ideal and experimental broadened chromatogram and polydispersity within elution volume slice.

10 12 14 16 18

0.0

0.1

0.2

0.3

0.4

Re

sp

on

se

Elution Volume

13.6 13.8 14.0 14.2 14.4

0.0

0.1

0.2

0.3oooo

oooo

oooo

oooo

oooo

oooo

oooo

oooo

oooo

oooo

oooo

oooo

oooo

oooo

oooo

oooo

oooo

oooo

oooo

oooo

oooo

oooo

oooo

oooo

oooooooo

oooo

oooo

oooo

Response

Elution Volume

14/2

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oooo

oooo

oooo

oooo

oooo

oooo

oooo

oooo

oooo

oooo

oooo

oooo


Universal Calibration vs. MALS

Polydisperse slice

– Slice polydispersity is always larger in case of branched polymers compared to

linear polymers

– Molar masses are not Mi

– MALS measures weight-average Mw,i

– SEC-VIS-UC measures number-average Mn,i (Balke, S. T., Mourey, T. H., and

Harrison, C. A. J. Appl. Polym. Sci. 1994, 51, 2087)

– Molar mass versus elution volume plots from MALS and UC should be parallel

and the difference should indicate the slice polydispersity


Universal Calibration vs. MALS: Number-Average Mn

103

104

105

106

103

104

105

106

103

104

105

106

0

20

40

60

80

100

120

140

Mn(g

/mol)

, U

C

Mn(g/mol), MALS

Mn(%

), U

C v

s M

AL

S

Mn(g/mol), MALS


Universal Calibration vs. MALS: Weight-Average Mw

103

104

105

106

107

103

104

105

106

107

103

104

105

106

107

60

80

100

120

140

Mw (

g/m

ol)

, U

C

Mw (g/mol), MALS

Mw (

%),

UC

vs

MA

LS

Mw (g/mol), MALS


Universal Calibration vs. MALS: Molar Mass Plots

10 12 14 1610

3

104

105

106

Elution Volume (mL)

Mo

lar

Ma

ss (

g/m

ol)

10 12 14 1610

2

103

104

105

106

107

Elution Volume (mL)

Mola

r M

ass (

g/m

ol)

Molar mass versus elution volume plots from MALS and universal calibration for linear polystyrene (left) and branched polystyrene (right).


Universal Calibration vs. MALS: Molar Mass Distribution

Cumulative molar mass distributions from MALS and universal calibration for linear polystyrene (left) and branched polystyrene (right).

104

105

106

0.0

0.2

0.4

0.6

0.8

1.0

Cu

mu

lative

We

igh

t F

ractio

n

Molar Mass (g/mol)

Mn = 110,000 g/mol

Mw = 270,000 g/mol

Mn = 73,000 g/mol

Mw = 244,000 g/mol

Mn (MO) = 137,000 g/mol

104

105

106

107

0.0

0.2

0.4

0.6

0.8

1.0

Cu

mu

lative

We

igh

t F

ractio

n

Molar Mass (g/mol)

Mn = 240,000 g/mol

Mw = 938,000 g/mol

Mn = 35,000 g/mol

Mw = 548,000 g/mol


Universal Calibration vs. MALS: Molar Mass Plots

Molar mass versus elution volume plots from MALS and universal calibration for fluorescent polymer (lignin). RI chromatogram is shown here.

12 14 16 18

102

103

104

105

106

Elution Volume (mL)

Mola

r M

ass (

g/m

ol)

Mn = 850,000

Mn = 1800

Mw = 1,650,000

Mn = 13,000


Mark-Houwink Plot Characterization of Polymer Structure

log─log [η] versus molar mass


Molecular Structure from Mark-Houwink Plot

Exponent of Mark-Houwink equation

– Linear macromolecules in thermodynamically good solvents: a ≈ 0.7

– Linear macromolecules in thermodynamically poor solvents: a ≈ 0.5

– Oligomers: a ≈ 0.5

– Hard spheres: a ≈ 0

– Extended chains: a ≈ 0.8 to ≈1.5

– Linear polymers have linear MH plots

– Curved plots indicates branching


Chain Stiffness from VIS/MALS Chromatograms

SEC- MALS-VIS-RI chromatograms of PS (left) and cellulose tricarbanilate (right) in THF.

9 10 11 12 13 14 15 16

0.0

0.5

1.0

Re

lative

Sca

le

Volume (mL)

MALS

VIS

RI

9 10 11 12 13 14 15 16

0.0

0.5

1.0

MALS

VIS

RI

Re

lative

Sca

leVolume (mL)

a < 1 a > 1

cS

McS

McS

RI

a

VIS

MALS


High-Molar-Mass Highly Branched Fractions

• Chromatograms from MALS, viscometer and infrared detector for NIST 1476 branched PE. • Mark-Houwink exponent a → 0 makes response of viscometer proportional to concentration.

14 16 18 20 22 24

0.0

0.2

0.4

0.6

0.8

1.0R

ela

tive

Sca

le

Volume (mL)



• Mark-Houwink plots of epoxy resin, linear polystyrene, linear poly(methyl methacrylate, linear poly(benzyl methacrylate), linear poly(iBuPOSSMA) and star-branched poly(isobutyl methacrylate).

103

104

105

106

107

[]

(mL

/g)

Molar Mass (g/mol)

a ≈ 0.71

a ≈ 0.69

a ≈ 0.50

a ≈ 0.70

a ≈ 0.69

a ≈ 0



Mark-Houwink plots of alginate, xanthan, pullulan, and dextran in aqueous NaNO3.

104

105

106

10

100

1000

slope = 0.62

slope = 1.49

[]

(mL

/g)

Molar Mass (g/mol)

slope = 1.09


Branching from Mark-Houwink Plot

Mark-Houwink plots of linear polystyrene and branched polystyrene prepared by copolymerization of styrene with various amounts of divinylbenzene. The degree of branching growths in the order of blue, magenta and green.

105

106

10

100

Intr

insic

Vis

co

sity (

mL

/g)

Molar Mass (g/mol)

400

a = 0.7


Branching from Mark-Houwink Plot

Mark-Houwink plots of linear PLGA 50/50 and branched PLGA containing 0.5 %; 3 % and 5 % dipentaerythritol.

103

104

105

10

20

[]

(mL

/g)

Molar Mass (g/mol)

2

a ≈ 0.56


Micro-Viscometer

Advanced Polymer Chromatography, APC

μ-SEC

μ-DAWN, UT-rEX, μ-ViscoStar


SEC-MALS versus APC-μMALS: Molar Mass Distribution

104

105

106

0.0

0.2

0.4

0.6

0.8

1.0C

um

ula

tive W

eig

ht F

raction

Molar Mass (g/mol)

APC @ 0.5 mL/min

APC @ 0.9 mL/min

SEC @ 1 mL/min

Cumulative molar mass distribution of NIST 706 polystyrene.


APC-μMALS- μVIS: Molar Mass and Intrinsic Viscosity Averages

Set-up Mn

(103 g/mol) Mw

(103 g/mol) Mz

(103 g/mol) [η]

(mL/g)

SEC-MALS-VIS* 1 mL/min

110 ± 1 269 ± 1 424 ± 4 87.8 ± 0.1

SEC-μMALS-μVIS** 0.9 mL/min

127 ± 7 259 ± 3 410 ± 3 89.4 ± 0.5

SEC-μMALS-μVIS** 0.5 mL/min

116 ± 4 263 ± 1 426 ± 2 91.1 ± 0.3

*Agilent 1100 HPLC; PLgel Mixed-C 300 × 7.5 mm 5 μm columns; HELEOS, T-rEX, ViscoStar III

**Waters Acquity APC; 900 Å, 4.6 × 150 mm, 2.5 µm; 450 Å, 4.6 × 75 mm, 2.5 µm; 125 Å, 4.6 × 150 mm, 2.5 µm; and 45 Å, 4.6 × 150 mm, 1.7 µm; μDAWN, UT-rEX, μViscoStar


SEC-MALS versus APC-μMALS: Mark-Houwink Plot

104

105

106

10

100

APC @ 0.5 mL/min

SEC @ 1 mL/min

Intr

insic

Vis

cosity (

mL/g

)

Molar Mass (g/mol)


Summary

• Universal calibration is valid, but less accurate and robust than MALS.

• UC for highly branched polymers (Mn) and fluorescent polymers.

• The major application of online viscometer is in the area of structural studies.

• Mark-Houwink plot provides information about polymer chain conformation and branching.

• Intrinsic viscosity allows calculation of hydrodynamic radius with higher sensitivity than DLS.

• Wyatt Technology ViscoStar® III is a successor of the previous two generations of the instrument with several advanced features.

– Bridge balance autotune

– Faster pressure sensors (less peak broadening)

• Wyatt Technology μ-ViscoStar is compatible with APC

Documents

The Importance of Online Viscometer in the Age of Multi ......• Conventional calibration (left) versus universal calibration (right). • Once the universal calibration is established