BETTER THAN SEC’s

Paul S. RussoLouisiana State University

Texas Polymer CenterFreeport, TX

October 31, 2001

Obligatory Equation

SEC = GPC = GFCSize Exclusion Chromatography

Gel Permeation ChromatographyGel Filtration Chromatography

GPC

•Solvent flow carries molecules from left to right; big ones come out first while small ones get caught in the pores.

•It is thought that particle volume controls the order of elution.

•But what about shape?

Simple SEC

degas

pump

injector

DRIVe

log 10

M

c

c

log 10

M

c

log10M

Osmometry: Real Science

Semipermeable membrane: stops polymers, passes solvent.

h V = n R T

n = g/M

c = g/V

= c R T ...)1

( 2 cAM

Light Scattering: Osmometer without the membrane100,000

x

c

...)21

( 2,

1

cAM

cRTc

IpT

s

q

2

)2/sin(π4 o

nq

LS adds optical effects Size

q = 0 in phase Is maximum

q > 0 out of phase, Is goes down 3

122g

s

RqI

SEC/MALLS

degas

pump

injector

DRI

DRI

MALLS

SEC/MALLS

3D Plot - PBLG

4 5

6 7

8 9

10 11

12 13

14 15

16 Scatterin

g angle

Ve

Scattered intensity

Scattering Envelope for a Single Slice

0.0 0.2 0.4 0.6 0.8 1.00

20000

40000

60000

80000

100000

120000

140000

c = 0.044 mg/mLM = 130000 g/mol

R/K

c

sin2( /2)

SEC/RALS/VIS

degas

pump

injector

DRI

LS90o

P viscometer

Universal Calibration

Grubisic, Rempp & Benoit,

JPS Pt. B, 5, 753 (1967)

One of of the most importantPapers in polymer science.Imagine the work involved!6 pages long w/ 2 figures.Selected for JPS 50th Anniv. Issue.

Universal Calibration Equations

[] = KM a

 

[]AMA = []SMS= f

(Ve)

11 SA aSS

aAA MKMK

Mark-Houwink Relation

Universal Calibration A = analyte; S = standard

Combine to get these two equations, useful only if universal calibration works!1

11

AS

S

a

A

aS

A K

MKM

Objectives

• Use -helical rodlike homopolypeptides to test validity of universal calibration in GPC.

• Can GPC/Multi-angle Light Scattering arbitrate between disparate estimates of stiffness from dozens of previous attempts by other methods?

Severe test of universal calibration: compare rods & coils

Combine M’s from GPC/MALLS with []’s from literature Mark-Houwink relations.

Strategy

Ld

Hydrodynamic volume

Polymers Used

[NH-CHR-C]x

O

R = (CH2)2COCH2

[CH-CH]x

R = (CH2)2CO(CH2)CH3

Polystyrene (expanded random coil)Solvent: THF = tetrahydrofuran

Homopolypeptides (semiflexible rods)

PBLG = poly(benzylglutamate)Solvent: DMF=dimethylformamide

PBLG = poly(stearylglutamate)Solvent: THF = tetrahydrofuran

Mark-Houwink Relations

[] = 0.011·Mw0.725 for PS

 [] = 1.26·10-5·Mw

1.29 for PSLG

 [] = 1.58 10-5·Mw

1.35 for PBLG

Polystyrene Standards: the UsualTable 1. GPC/LS Parameters for PS in THF

Mw Mw/Mn

Vendor

Specified This Worka This Workb

3105 N/A 1.14 6207 N/A 1.03 10300 10250 1.03 43900 45900 1.01

102000 105800 1.02 212000 240900 1.01 170000 174700 1.01 422000 483900 1.02 929000 935900 1.01 1600000 1639000 1.16 1971000 2226000 1.03 2145000 2171000 1.1

a GPC/LS bSensitive to baseline and peak selection.

Polypeptide Samples Were Reasonably Monodisperse

Table 2. PSLG Molecular Weights

Mw Mw/Mn

13370 2.044 17570 2.044 51080 1.04 67700 1.022 93090 1.256 138400 1.019 150800 1.24 176000 1.125 249000 1.03

Table 3. PBLG Molecular Weights

Mw

Mw/Mn

10670 1.233 13690 1.267 18520 1.233 29980 1.07 45990 1.046 70870 1.119 86000 1.018 95920 1.05

265000 1.176 327500 1.04

NCA-ring opening was used to make these samples. Most were just isolated and used; a few were fractionated.

Universal Calibration Works for These Rods and Coils

12 14 16 18 20 22

4

6

8

10lo

g([

]M /

ml-

mol

-1)

Ve /ml

PS PSLG PBLG PBLG Mixture

2nd Virial Coefficient Equations

A2, = M 2A2 /Na

= kT(1 + A2, + …)

A2, = dL2/4

12

/

12,

ocalcg

MMLR

Osmotic pressure in numberdensity concentration () units

Relationship to the “normal” 2nd virial coefficient for conc.in mass per volume units.

Onsager 2nd virial coefficient for rods (L= length, d = dia.)

Rg for rods

2nd Virial Coefficient (Excluded Volume Limit) is Another Universal Descriptor

12 13 14 15 16 17 18 19 20 21 22104

105

106

107

108

109

PS PSLG PBLG PBLG Mixture

A2, /

10-2

4 cm

3

Ve /ml

Persistence Length ap from Rg

)]1(1[2

3/

3

22 paLppp

pg e

L

a

L

aa

LaR

Persistence length is the projection of an infinitely long chain on a tangent line drawn from one end. ap = for true rod.

Persistence Length of Helical Polypeptides is “Very High”

0 100000 200000 300000 400000 5000000

20

40

60

80

100

ap = 70 nm

ap = 120 nm

ap = 240 nm

Rod

Rg /

nm

M

What the biggest polymers in our sample would look like at this ap

SEC/MALLS in the Hands of a Real Expert

ap 15 nm

Much less than PBLG

Macromolecules, 29, 7323-7328 (1996)

ConclusionsThe new power of SEC/Something Else experiments is very real.

SEC is now a method that even the most jaded physical chemist should embrace. For example, our results favor higher rather than lower values for PBLG persistence length. This helps to settle about 30 years of uncertainty.

Universal calibration works well for semiflexible rods spanning the usual size range, even when the rods are quite rigid.

So, SEC is good enough for physical measurements, but is it still good enough for polymer analysis?

They were young when GPC was.

Small Subset of GPC Spare Parts

To say nothing of unions, adapters, ferrules, tubing (low pressure and high pressure), filters and their internal parts, frits, degassers, injector spare parts, solvent inlet manifold parts, columns, pre-columns, pressure transducers, sapphire plunger, and on it goes…

Other SEC Deficiencies

• 0.05 M salt at 10 am, 0.1 M salt at 2 pm?

• 45oC at 8 am and 50oC at noon?

• Non-size exclusion mechanisms: binding.

• Big, bulky and slow (typically 30 minutes/sample).

• Temperature/harsh solvents no fun.

• You learn nothing by calibrating.

Must we separate ‘em to size ‘em?Your local constabulary probably

doesn’t think so.

I-85N at Shallowford Rd.Sat. 1/27/01 4 pm

Sizing by Dynamic Light Scattering—a 1970’s advance in measuring motion, driven by need to measure sizes, esp. for small particles.

D

kTRh

oπη6

t

Is

It’s fluctuations again, but now fluctuations over time!DLS diffusion coefficient, inversely proportional to size.

Large, slow moleculesSmall, fast molecules

Molecular Weight Distribution byDLS/Inverse Laplace Transform--B.Chu, C. Wu, &c.

Where: G() ~ cMP(qRg)

= q2D

q2kT/(6Rh)

Rh = XRgg(t)

log10t

ILT

q2

D

G()

CALIBRATE MAP

M

c

log10M

log10D

Hot Ben Chu / Chi Wu Example

MWD of PTFESpecial solvents at ~330oC

Macromolecules, 21, 397-402 (1988)

This only “works” because of that wide, wide M distribution.Main problem with DLS/Laplace inversion is poor resolution.Things kinda go to pot at low M, too. Some assumptions have to be made to do this.

Reptation: inspired enormous advances in measuring polymer speed…and predicts More favorable results for polymers in a matrix.

There once was a theorist from FranceWho wondered how molecules dance."They're like snakes," he observed,"as they follow a curve,the large ones can hardly advance."*

D ~ M-2deGennes

More generally, we could write D ~ M- where increases as entanglements strengthen

*With apologies to Walter Stockmayer

Matrix Diffusion/Inverse Laplace TransformationGoal: Increase magnitude of

Difficult in DLS because matrix scatters, except special cases.Difficult anyway: dust-free matrix not fun!Still nothing you can do about visibility of small scatterersDOSY not much betterReplace DLS with FPR.Selectivity supplied by dye.Matrix = same polymer as analyzed, except no label.No compatibility problems.G() ~ c (sidechain labeling)G() ~ n (end-labeling)log10M

log10D

Stretching

Solution:

Matrix:

Painting Molecules* Makes Life Easier*R. S. Stein

Small Angle Neutron ScatteringForcedRayleighScattering

Fluorescence Photobleaching Recovery

Index-matched DLSmatch solvent & polymer refractive

indexcan't do in aqueous systems

Depolarized DLSworks for optically anisotropic probesworks for most matrix polymers

Fluorescence Photobleaching RecoveryFluorescence Photobleaching Recovery

0 50 100 150 2000

1

2

3

4

5

6

7

8

9

10

C(t

)

t / s

0.0 0.5 1.0 1.5 2.0 2.5 3.00.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

Dapp

< Dapp

Dapp

/ s

-1

K2 / 105 cm-2

2DK

1. An intense laser pulse photobleaches a striped pattern in the fluorescently tagged sample.

2. A decaying sine wave is produced by moving the illumination pattern over the pattern written into the solution.

3. An exponential decay is produced by monitoring the amplitude of the decaying sine wave. Fitting this curve produces from which D can be calculated.

BeCtC t )0(

FPR for Pullulan (a polysaccharide)FPR for Pullulan (a polysaccharide)

104 105

0.01

0.1

1

10

NaN3(aq) solution ( = 0.537 ± 0.035)

5% Matrix solution ( = 0.822 ± 0.018) 10% Matrix solution ( = 0.907 ± 0.038) 15% Matrix solution ( = 0.922 ± 0.037)

Dap

p / 1

0-7 c

m2 s

-1

M

0.1 1 1010

4

105

MD

app / 10

-7 cm

2 s

-1

Probe Diffusion: Polymer physics Calibration: polymer analysis

FPR ChromatogramFPR Chromatogram

1000 10000 100000 10000000

5

10

15

20

25

30

35

40

45 CONTIN Analysis Exponential Analysis Exponential Analysis

Pullulan, 5%w/w Dextran Matrix, 50/50 mix of 380K and 11.8K

FA

rbit

rary

Uni

ts

M Indicates targeted M.

Sure this is easy. Also easy for GPC.But not for DLS or DOSY!

Separation ResultsSeparation ResultsPullulan M = 50/50 mix of 11,800 and 380,000

Two ExponentialMatrix M1 / 1000 M2 / 1000

NaN3 (aq) 14.0 ± 1.0 (56.8%) 374.0 ± 37.2 (43.2%)5% w/w 12.2 ± 0.8 (52.3%) 313.9 ± 17.4 (47.7%)10% w/w 11.6 ± 0.6 (52.3%) 269.1 ± 20.9 (47.7%)15% w/w 12.0 ± 0.8 (51.1%) 261.4 ± 40.7 (48.9%)

CONTINMatrix M1 / 1000 M2 / 1000

NaN3 (aq) 14.1 ± 1.0 (54.5%) 393.1 ± 49.6 (42.1%)5% w/w 10.2 ± 1.3 (53.0%) 292.3 ± 23.4 (47.0%)10% w/w 10.0 ± 1.0 (50.3%) 221.4 ± 20.1 (47.5%)15% w/w 10.3 ± 1.1 (48.5%) 205.3 ± 38.3 (48.1%)

Better Resolution “Soon”?

Indicates targeted M.

1000 10000 100000 10000000.0

0.2

0.4

0.6

0.8

1.0

Pullulan, 8% HPC Solution, M=12,200 and 48,000

CONTIN Exponential Exponential

F Arb

itra

ry U

nits

M

Improvement in resolution is observed at lower concentrations due to a more viscous characteristic. A compatibility problem is seen though at higher concentrations.

Simulation of FPR ResultsSimulation of FPR Results(Most Desirable Situation)(Most Desirable Situation)

y = -0.4998x + 1.1518

0

1

2

3

4

5

6

-10 -8 -6 -4 -2 0

log D

log M

y = -2.0009x + 2.3045

-12

-10

-8

-6

-4

-2

0

2

4

0 2 4 6 8

log M

log

D

1000 10000 1000000.0

0.5

1.0

1.5

2.0

M = 10,000 and 20,000

CONTIN 2 Exponential

F Arb

itrar

y U

nits

M

1000 10000 100000 10000000.0

0.5

1.0

1.5

2.0

M = 10,000 and 160,000

CONTIN 2 Exponential

F Arb

itra

ry U

nits

M

1000 10000 1000000.0

0.5

1.0

1.5

2.0

M = 10,000 and 57,000

CONTIN 2 Exponential

F Arb

itrar

y U

nits

M

Examples of Examples of Separation Results Separation Results

from Simulation Datafrom Simulation Data

Indicates targeted M.

Ultimate Goal: A Black Box for MWDUltimate Goal: A Black Box for MWD

Matrix FPREasily Maintained

AccuratePrecise

Simple ConceptExpedient

Easy System SwitchBasic Info Obtained

MiniaturizableDetect Large MassesLabeling Required

GPCAccurate

Simple ConceptMiniaturizable

No Labeling RequiredBroad Distributions

PumpsParts

Press for MWD

DLSForm Factor

Index MatchingLong Acquisition for

Multiangle ExperimentsPrecise

Accurate

DOSYEasy System Switch

PreciseAccurate

Obtain Basic InfoLabeling Required

ConclusionsConclusionsFor a limited number of cases, this could really work.

We may not always need leaking pumps and large parts bins for polymer characterization.

What is good about GPC (straight GPC) is the simple concept; Matrix FPR keeps that—just replaces Ve with D.

Thank you!

LSU

Better than SEC’sMonday, January 29, 2001

Physical Info from SEC

Elena TemyankoHolly Ricks

N$F

Replacing SEC

Garrett Doucet

David Neau

Wieslaw Stryjewski

History of this Talk

• Used first at Georgia Tech, mods made after

• Same modifications to the USC talk, which is designed to be a little shorter & simpler

• The changes affect mostly the early parts of the diffusion part, near deGennes and Chu

• Used at Dow--Freeport