application of the general theory of gradient elution to ......gradient chromatography method:...
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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