Application of the General Theory of Gradient Elution to CharacterizationGradient Elution to Characterization of Functionalized Polymers

Christopher J. Rasmussen and Yefim BrunDuPont Central R&D, Corporate Center for

Analytical Science, Wilmington, DE

International Symposium on GPC/SEC and Related TechniquesOctober 22, 2015

Introduction

Separation & characterization of Exclusion dominatedSeparation & characterization of polymer and their property distribution

Time of retention depends on ht

SECLCCC

Enthalpy gain = Entropy lossTime of retention depends on

enthalpic (adsorption) and entropic (exclusion) interactions

Three primary modes: cula

r wei

g Entropy loss

p y1. Size Exclusion Chromatography

(SEC)2. Liquid Adsorption Chromatography

Mol

ec

LACAdsorption dominated

(LAC)3. Liquid Chromatography at Critical

Conditions (LCCC)

Retention time

Almost all real polymers distributed by molecular weight MGOAL: Suppress or eliminate dependence on M, separate by

2October 22, 2015 2

chemical or structural differences

Gradient ChromatographyMETHOD: Gradient Elution at the Critical Point of Adsorption (GE-CPA)

ΔS ↓, ΔH ↑1. Inject in ‘poor’ solvent, polymer retains2 Adjust solvent quality by solvent gradient

ΔF D

Free chain Confined chain

)exp( BTkFK

2. Adjust solvent quality by solvent gradient3. Polymer elutes at CPA, independent of MW

100 PS%

Polystyrene / styrene-acrylonitrile copolymer / styrene-butadiene copolymer blend

)p( B

5060708090

St-AcSBR

Eluent Gradient

ompo

sitio

n,

Separation by size

1020304050 St Ac

Sol

vent

Co

Separation by chemistry

3October 22, 2015 3SEC GE-CPAMinutes

14 15 16 17 18 19 20 21 22 23 24 25 26 270

Minutes0 2 4 6 8 10 12 14 16 18 20

Complex Polymers

Mono-, Di-functionized Star-shaped polymers Diblock copolymers

Functionalized star-h d l

Star-shaped block copolymers

Statistical copolymers

Capturing additional details in an expression for K results in

shaped polymerscopolymers

4October 22, 2015 4

Capturing additional details in an expression for K results in complicated expressions; analytical solutions not always possible

Modeling Gradient Chromatography

Ldx

Rs t

Ldtdxv 1. Balance equation

2. Solvent gradient Selected for given task

4 E i f titi ffi i t K f h i

3. Solvent model Linear near critical point approximation, introduces adjustable parameter

4. Expression for partition coefficient K of chain

Ideal chain (Flory, 1969): • Monomers distributed randomly• Describes chains with no excluded volume (Φ condition)Confined in non-adsorbing pore (Casassa, 1967)• Describes SEC elutionAdsorbing wall (de Gennes 1969)Adsorbing wall (de Gennes, 1969)• Monomers close to wall experience adsorption force• de Gennes boundary conditionIdeal chain in slit pore (Gorbunov, Skvortsov, 1986)

A l ti l l ti

5October 22, 2015 5

• Analytical solution• Form of Heat Equation

The General Case for K

Solution for ideal chain in adsorbing slit

222 exp2 g

Solution for ideal chain in adsorbing slit pore given by Gorbunov and Skvortsov(1986): SEC

LAC

)odd(1

22 1exp2

mm mm

m gK

2)1(arctan mmm r siz

e, g

coef

f., K

)(mm

Dimensionless size parameter: Pol

ymer

Par

titio

n c

g = 2RG/DP

Dimensionless adsorption parameter: LCC

C

Interaction param., λ

6October 22, 2015 6

Comparison to Asymptotic Solutions

2K 2exp gK NearCrit

3/exp 222 ggK Narrow

7October 22, 2015 7

Theory Prediction: Homopolymer Elution

Solution to integrated balance equation:Solution to integrated balance equation:

Only oneOnly one adjustable parameter:

sitio

n of

@

elu

tion dλ/dΦ

(Selectivity for

Φ, C

ompo

sgr

adie

nt @ given polymer /

substrate / solvent combination)

g = 2RG/DP

8October 22, 2015 8

Length of Polymer Chain

Fit to experimental data

Time of gradient, (0-100% THF)Only 1 adjustable parameter for all points here!

30

2

Only 1 adjustable parameter for all points here!

25

20

on

15

10me

of e

lutio

10

5

Ti

9October 22, 2015 9PS standards, Waters NovaPak® Silica 60Å column, linear gradient of n-hexane/THFPoints represent:

Extension to functionalized polymers

Many analytical extensions to complex polymers available in literature1:Many analytical extensions to complex polymers available in literature1:

)0()1(

Single terminal functional group

Di f ti l

aa pqKK )0()1(

Terminal functional groups at each endMono-functional

Di-functional

abbabbaa pqqpqpqKK )0()2(

qi > 0: The functional group adsorbs more strongly the repeat unit of the polymer chain

qi < 0: The functional group adsorbs less strongly the repeat unit of the polymer chain

Numerical Integrator allows for “drop in” expressions.

[1] A A G b d A V V kh h “Th f h t h f li d li

10October 22, 2015 10

[1] A. A. Gorbunov and A. V. Vakhrushev, “Theory of chromatography of linear and cyclic polymers with functional groups,” Polymer, vol. 45, no. 21, pp. 7303–7315, Sep. 2004.

Modelled Elution of Functionalized Polymer

Monofunctional polymers Difunctional polymers

Complete reversalIncreasing strengthof functional group

Complete reversal of elution behavior

qa =qa = qb =

Theoretical predictions; Parameters for polystyrene on silica, gradient rate 10 min.

11October 22, 2015 11

Comparison to experiment: Brominated PEG

Δt = 0.13q = 0.13

KLCCC = 1 + q Brominated PEG

PEG Standard

Δt = 0 2Δt = 0.2ΔΦ = 2%

Polyethylene gylcols (M=2000) on Symmetry® C4 column. Solvent: 50%

Minutes1.80 1.90 2.00 2.10 2.20 2.30 2.40 2.50 2.6

Polyethylene gylcols (M=2000) on Symmetry® C4 column

Minutes11.00 11.50 12.00 12.50 13.00

12October 22, 2015 12

ACN/H2O Solvent gradient: 100% H2O at 7 min to 100% ACN at 17min

Comparison: Experiment to theory

ΔΦ = 2%

Δt = 0.2q = 0.13

M = 2000

11 00 11 50 12 00 12 50 13 00 13 50

Δt 0.2ΔΦ = 2%

M 2000

Polyethylene gylcols on Symmetry® C4 columnSolvent gradient: 100% H2O at 7 min to 100%

ACN at 17min

Model recovers correct elution with functional

Minutes11.00 11.50 12.00 12.50 13.00 13.50

13October 22, 2015 13

ACN at 17min group

CPA separation of functionalized star-shaped polymers

Separation of 4-arm PEOs with -OH and -Cl ends on Xterra® C18Separation of 4 arm PEOs with OH and Cl ends on Xterra® C18

700 0350

0

500

600

250

3002 4

number of chloride ends:

mV

300

400

12 4

number of chloride ends:

150

200

3

100

200 13

50

100 1

Minutes3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0

Minutes21 22 23 24 25 26 27 28

Isocratic elution at CPA: Linear gradient:

14October 22, 2015 14

ACN/water (60.1/39.9, v/v)g

20% ACN/H2O → 100% ACN/H2O

Comparing gradient results and theory

300

3500

4number of chloride ends:

4 attractive groups

mV

200

250

3002 4

2 attractive, 2 repulsive

100

150

200

13 4 repulsive groups

50

Minutes21 22 23 24 25 26 27 28

Linear gradient: 20% ACN/H2O → 100%

ACN/H2O

Theoretical prediction; Parameters fit from exp.,

gradient rate 10 min.

15October 22, 2015 15

ACN/H2O gradient rate 10 min.

On-Line LC/MS w/LTQ_Orbitrap of 4-arm PEG Sample #2

IPC-MS of functionalized PEG star

Peak#5

Peak#3Peak#1Peak#4

Peak#2

N L :1 . 5 5 E 8T I C M S 0 5 2 7 1 1 _ P EG 1 0 2 2 i n

Peak#3Peak#20 Cl1 Cl 2 ClTIC

G _ 1 0 2 _ 2 _ i n_ w a t e r _ 0 7

Peak#1 Peak#4

Peak#2

Peak#5

0 Cl3 Cl

4 Cl

16October 22, 2015 163 0 3 2 3 4 3 6 3 8 4 0 4 2 4 4 4 6 4 8 5 0 5 2

T i m e ( m i n )

PDMS – Reverse Phase vs Normal Phase

Reverse phaseNormal phase

CH3 CHCH

nSi

CH3

CH3

O Si

CH3

CH3

CH3OSi

CH3

CH3

CH3

Minutes2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00 20.00 22.00

17October 22, 2015 17

Non‐functionalized PDMS has weak critical point in Normal Phase separation

Si

CH3

O Si

CH3

OSi

CH3

CH3 OOH Normal Phase IPC = More polar, late elution

Interaction chromatography of functionalized PDMS

nSi

CH3

CH3

O Si

CH

CH3

OSi

CH3

CH3

O

O

OH

nCH3 CH3CH3

O

Mw ~ 4700

Si

CH3CH3OHCH3

OH

CH3 CH3CH3 OOH

O

OH

CH3

OSi

CH3

n

M 500 nSiH

O

O

Si

CH3

CH3

Si CH3

CH3

Mw ~ 5600Mw ~ 900

Mw ~ 500

Mw ~ 700

12.00 13.00 14.00 15.00 16.00 17.00 18.00 19.00 20.00 21.00 22.00

CH3

18October 22, 2015 18

Minutes Aldrich Mono OH PDMSAldrich PDMS DiolSilsurf A008-UP DMS-EO-DMSSilsurf A004 DMS-EO-DMSSilmer OH Di-10 DMS-diol

TICRT: 11.66 - 17.29 SM: 7B

80

10013.27 NL: 6.98E8

TIC F: FTMS + p ESI Full ms [600.00-4000.00] MS

IPC-MS: PDMS Mono-OH (Mw ~ 4700)

80

100

20

40

60

14.28 14.62

13.59

[ ]040914_PDMS_mono_OH_5_mgmLTHF_01

NL: 8.85E5m/z= 2332.5916-2332.7828 F: FTMS + p ESI Full ms [600 00 4000 00] MS

Si

CH3

O Si

CH3

OSi

CH3

CH3 OOH

XIC li 28

60

80

1000

20

40

60

13.87 14.4213.07

13.50

[600.00-4000.00] MS 040914_PDMS_mono_OH_5_mgmLTHF_01

NL: 1.54E6m/z= 2777.3549-2778.1489 F: FTMS + p ESI Full ms [600.00-4000.00] MS 34

Si

CH3

O Si

CH3

OSi

CH3

CH3 OOH

XIC: oligomer n=34

28CH3 CH3CH3

Molecular Formula = C66H194O31Si30Monoisotopic Mass = 2322.668189 Da

XIC: oligomer n=28

60

80

1000

20

40

60

13.39

[ ]040914_PDMS_mono_OH_5_mgmLTHF_01

NL: 1.98E6m/z= 3370.7546-3371.1781 F: FTMS + p ESI Full ms [600.00-4000.00] MS 040914 PDMS mono OH 542

Si

CH

CH3

O Si

CH

CH3

OSi

CH3

CH

CH3 OOH

XIC: oligomer n=42

34CH3 CH3CH3

Molecular Formula = C78H230O37Si36

Monoisotopic Mass = 2766.780934 Da

XIC: oligomer n=34

60

80

1000

20

40

13.30

040914_PDMS_mono_OH_5_mgmLTHF_01

NL: 2.95E6m/z= 3963.8587-3965.3673 F: FTMS + p ESI Full ms [600.00-4000.00] MS 040914_PDMS_mono_OH_5_

50Si

CH3

CH3

O Si

CH3

CH3

OSi

CH3

CH3

CH3 OOHXIC: oligomer n=50

CH3 CH3CH3

Molecular Formula = C94H278O45Si44

Monoisotopic Mass = 3358.931261 Da

XIC: oligomer n 42

40

60

80

1000

20

40

13.13

_ _ _ _ _mgmLTHF_01

NL: 1.07E6m/z= 2801.1357-2801.3547 F: FTMS + p ESI Full ms [600.00-4000.00] MS 040914_PDMS_mono_OH_5_mgmLTHF 01

72Si

CH3

CH3

O Si

CH3

CH3

OSi

CH3

CH3

CH3 OOH

3Molecular Formula = C110H326O53Si52

Monoisotopic Mass = 3951.081587 Da

XIC: oligomer n=72

19October 22, 2015

12.0 12.5 13.0 13.5 14.0 14.5 15.0 15.5 16.0 16.5 17.0Time (min)

0

20

4013.53 13.84

mgmLTHF_01Molecular Formula = C154H458O75Si74

Monoisotopic Mass = 5579.494985 Da

RT: 9.31 - 18.54

10014.6614.03 NL: 6.53E8

TIC F: FTMS + p ESI Full ms CH3 CH3CH3OOH TIC

IPC-MS: PDMS Diol (Mw ~ 5600)

80

100

20

40

60

80 13.52

15.18 15.41 15.73

15.90

15 44

p[600.00-4000.00] MS 040914_PDMS_diol_6_mgmLTHF_02

NL: 1.44E7m/z= 1011.3370-1011.4187 F: FTMS + p ESI Full msSi

CH3

O Si

CH3

OSi

CH3OOH

nSi

CH3

O Si

CH3

OSi

CH3 OOH

XIC: oligomer n=9

80

1000

20

40

60

80 15.44

14.66 15.04

F: FTMS + p ESI Full ms [600.00-4000.00] MS 040914_PDMS_diol_6_mgmLTHF_02

NL: 5.26E6m/z= 991.2658-991.4223 F: FTMS + p ESI Full ms 22

Si

CH3

O Si

CH3

OSi

CH3

CH

OOH

9CH3 CH3CH3 OOH

Molecular Formula = C32H88O14Si11

Monoisotopic Mass = 1004.363593 Da

XIC: oligomer n=9

XIC: oligomer n=22

60

80

1000

20

40

60

14.26

[600.00-4000.00] MS 040914_PDMS_diol_6_mgmLTHF_02

NL: 2.13E6m/z= 2400.5526-2400.7860 F: FTMS + p ESI Full ms [600.00-4000.00] MS60

Si

CH

CH3

O Si

CH

CH3

OSi

CH3

CH

O

O

OH

22CH3 CH3CH3 OOH

Molecular Formula = C58H166O27Si24

Monoisotopic Mass = 1966.607874 Da

XIC: oligomer n=60

60

80

1000

20

40

60

13.92

[600.00 4000.00] MS 040914_PDMS_diol_6_mgmLTHF_02

NL: 9.98E5m/z= 2393.5301-2393.7422 F: FTMS + p ESI Full ms [600.00-4000.00] MS 040914 PDMS diol 6 mgm

92Si

CH3

CH3

O Si

CH3

CH3

OSi

CH3

CH3

O

OOH

OH

60CH3 CH3CH3 O

OHMolecular Formula = C134H394O65Si62

Monoisotopic Mass = 4779.321925 Da

XIC: oligomer n=92

60

80

1000

20

40

13.6613.61

040914_PDMS_diol_6_mgmLTHF_02

NL: 7.93E5m/z= 2408.5511-2408.9754 F: FTMS + p ESI Full ms [600.00-4000.00] MS 040914_PDMS_diol_6_mgm125

Si

CH3

CH3

O Si

CH3

CH3

OSi

CH3

CH3

O

OOH

OH

3 OH

Molecular Formula = C198H586O97Si94

Monoisotopic Mass = 7147.923231 Da

XIC: oligomer n=125

20October 22, 2015

9.5 10.0 10.5 11.0 11.5 12.0 12.5 13.0 13.5 14.0 14.5 15.0 15.5 16.0 16.5 17.0 17.5 18.0 18.5Time (min)

0

20

4013.92

LTHF_02OHMolecular Formula = C264H784O130Si127

Monoisotopic Mass = 9590.543328 Da

Conclusions

Solvent gradient chromatography at the critical point Solvent gradient chromatography at the critical point of adsorption offers the ability to separate polymers by chemical or structural distributions, while suppressing molecule weight

Developed flexible ODE model of gradient elution at critical point of adsorptioncritical point of adsorption

Experimentally validated for homopolymers, linear functionalized and functionalized star polymersfunctionalized, and functionalized star polymers

Offers insight to more complex separation problems, such as strongly adsorbing functional p , g y ggroups and separation by microstructure of linear copolymers

21October 22, 2015 21

Acknowledgments

• Brian McCauley (PEG chromatography)• Brian McCauley (PEG chromatography)• Wei Li (PDMS IPC)• Bogdan Szostek (Mass Spectrometry)• Deb Liczwek, Alex Neimark (Supervisorial support)Funding:

GOALI A d N b 1064170 M lti l M d li f• GOALI Award Number 1064170, Multiscale Modeling of Adsorption Equilibrium and Dynamics in Polymer Chromatography

• Rutgers University Department of Chemical & Biochemical Engineering Venkatarama Fellowship

22October 22, 2015 22