Multi-detector GPC Characterization

Drew Poche’

Outline

• Basics-On the mechanism of GPC

• Detection– Light Scattering– Viscometry

• Putting it together- multi-detector GPC

• Lots of numbers-What’s it good for?

How big is big?

Drew Poche’Materials CharacterizationDow Chemical, Plaquemine

Alphabet SoupSEC-Size Exclusion Chromatography• Includes rigid stationary phases

GPC-Gel Permeation Chromatography• “Soft” gel stationary phases

GFC-Gel Filtration Chromatography• Separation of biological molecules (nature’s polymers)

in an aqueous environment

HPLC? You bet.

Mobile phase pump auto-injector column(s) detector(s) data acquisition

Temperature control

Putting it in perspective

• Typical organic molecule vs typical polymer molecule

•Mass spec•GC-MS, LC-MS•NMR•Modeling, quantum mechanics•Other colligative property based measurements

EASY

TOUGH

Measuring size and molar mass

Polymer standards--Column Calibration

Rtn Vol Peak Mw15.739 750000015.728 750000016.878 256000016.879 256000017.92 841700

17.935 84170018.95 320000

18.953 32000019.605 14800019.62 148000

20.387 5950020.386 5950020.581 5000020.583 5000020.583 5000021.073 2850021.087 2850022.008 1085022.005 1085023.359 293023.378 293024.832 58024.838 580

GPC Calibration

log(Mw ) = 0.0009Ve3 - 0.0534Ve

2 + 0.6303Ve + 6.8161

R2 = 0.9996

0

20

40

60

80

100

120

14 16 18 20 22 24 26 28

Ve [mL]

Det

ecto

r R

espo

nse

0

1

2

3

4

5

6

7

8

log(

Mw)

Can it get worse?•Typical synthetic organic molecules in a pure sample are all the same molar mass

•Typical synthetic polymer molecules in a pure sample may differ not only in molar mass but also in molecular shape

Ordinary small molecule sample

Ordinary synthetic polymer sample

GPC Mechanism

Wiggling (chain conformations)determines average dimensionsand pore permeation

Eliminate enthalpic interactions

Entropic effects alone govern

Getting it right

Problems, Problems

•Polymer chains are not created equal

Ma MbMc= =

Va VbVc<>

Solutions

•Absolute molecular weight detectors (light scattering, viscometry)•Universal calibration

Bent out of Shape

First, let’s select a couple of chain conformations...

Then, stuff them into a confined space and see what happens

Forbiddenconformation

Allowedconformation

Loss of conformational entropy dictates partitioningbetween pore and non-pore space

Center of mass tooclose to wall

Let’s clarifyGibbs Free energy change of a process,

op

op

op STHG

Gibbs free energy change of permeation ofthe pores at equilibrium conditions (suffi cienttime for diff usion into and out of pores)

GPC

op KlnRTG

KGPC is the fraction of internal pore volumepenetrated (equilibrium constant)

With non-enthalphic interactions squelched,

op

op STG so, R/S

GPC

opeK

Also, 2L

RAS sop

where, As is surface area/pore volume

L is the mean molecular projection ofthe chain in solution

Bottom line:

)Llog(KGPC

)Llog(Ve

or

Who wants to be a millionaire?

If the polymer chains are restricted to one configuration (e.g. rods), what drives the partitioning between pore space and non-pore space?

a) rotational orientation b) pore gremlins

c) there’s no such thing as rod d) Huh? shaped chains

If GPC really separates by SIZE, which chain dimension correlates with elution order?

•I don’t know

•It’s a rather complicated question because pore characteristics and chain geometry influence the magnitude of the equilibrium constant, KGPC

• Leading candidates: •radius of gyration, Rg

•hydrodynamic volume, Rh3 or Vh (universal calibration)

For the million dollars….

Column selection

FIPA

Making sense of the chromatogram

• Synthetic polymers are composed of a distribution of chain sizes

• We use statistics to get average dimensions to describe the bulk sample

• Commonly computed from GPC: Mn the arithmetic mean

Mw weight average

• Computing Mw and Mn is sensible since these averages “fall out” naturally from experiments used to measure molar mass

– Mn from colligative or counting methods (NMR, osmometry, and those boring experiments you did in freshman chem)

– Mw from methods sensitive to molecular size (LS, centrifugation)

Time to count

i

iiiin n

MnMxM

x i i s t h e i t h m o l e f r a c t i o nn i i s t h e n u m b e r o f c h a i n s i n t h e i t h f r a c t i o n

ii

2ii

iiw Mn

MnMwM

w i i s t h e i t h w e i g h t f r a c t i o n

Where do ni and Mi come from?

i

i

i

i

iiiin

M

h

h

n

MnMxM

i

ii

ii

2ii

iiw h

Mh

Mn

MnMwM

h i i s t h e c o n c e n t r a t i o n o f t h e i t h f r a c t i o n

Multiple numbers of standards Column Calibration

• That’s one source of Mi

Problem: only equivalent Mi is obtained

E pluribus unum

• Universal Calibration• Gives molar mass without

regard to chain architecture

• Valid? Nearly always.

• Suggests: L Vh

Wait a minute!

• If I don’t know how M and [] are related for my polymer, how do I use universal calibration?

YOU DON’T

• Mark-Houwink (empirical power law)

stdastdstdstd MK][ and unka

unkunkunk MK][

since unkunkstdstd M][M][

unka1/1

unk

stdstdunk K

M][M

“…too much dancing and not nearly enough prancing...”

C. Montgomery Burns, commenting on GPC prior to molar mass sensitive detectors

• Visible light scattering used for polymer characterization has been around almost as

long as chemists have believed in polymers

• However, GPC detectors based upon the technique are relatively new (1970s)

• Light scattering, by its nature, returns the weight average molar mass

Visible Light vs. polymer chain

Particle view: Incident light“pushes” electrons, producingtransient dipoles

Thermo view: Incident lightcouples to concentrationgradient found in real solutions

How to get Mw from the measurement

1 cA2M1

RKc

2 as q approaches 0

2M3

Rq

M1

RKc

2g

2

as c approaches 0

MALLS uses Eq 1 and 2 and returns Mw and Rg

LALLS and RALLS use Eq 3 and return Mw

caveat: RALLS requires a shape correction when Rg approaches (/50)n

Scattering

contains dn/dc

Particle form factor

3 cA2)q(MP

1RKc

2

How LS returns other molar mass averages

• Simple assumption….monodisperse fractions

from the GPC columns. Therefore,

Mw,i = Mi

• This assumption may lead to an over-estimation of Mn

“I’m going to describe the apparatus first before I set it motion. Then you’ll be able to follow the proceedings better.”

Franz Kafka

• Advantages– MALLS gives molecular architecture information

without assumptions IF there is a measurable angular dependence on the scattered light intensity

– RALLS is more forgiving of dusty samples and returns essentially the same information as

LALLS IF the polymer is small compared to

– LALLS is more sensitive, requires no correction over a huge range of molar mass

“Do you suppose,” the Walrus said, “that they could get it clear?”

“I doubt it,” said the Carpenter, and shed a bitter tear. Lewis Carroll

DUST, GELS, or assorted particulate vs. Light Scattering

"...died a dusty death!"00713T-2 LS

11.1 16.3 21.5 26.6 31.8 37.0 0

20

40

60

80

100

Retention Volume (mL)

Rela

tiv

e R

esp

on

se

Column Calibration? Not!

PS 50K vs. 100K DRI detection00628X-2 RI00628y-2 RI

4.9 9.8 14.6 19.5 24.4 29.2 85

142

200

258

315

373

Retention Volume (mL)

Res

pons

e (m

V)

PS 50K vs. 100K LALLS Detection00628X-2 LS00628y-2 LS

4.9 9.8 14.6 19.5 24.4 29.2-0.10

0.23

0.56

0.88

1.21

1.54

Retention Volume (mL)

3R

espo

nse

(mV

) x10

Specific refractive index increment

T,0 c

limdcd

nn

c

If polymer solvent combo is isorefractive, no scattering will be observed

•The bigger the better•Depends on:

•solvent•temperature•light wavelength

n = n - no

Why dn/dc matters

FIPA LS data (similar concentration)

PS 50 KSBS 50K

0.19 0.87 1.56 2.25 2.94 3.63 192

218

245

271

297

324

Retention Volume (mL)

Res

pons

e (m

V)

The plot thickens-Viscosity

• Viscometers as GPC detectors are based upon the measurement of a differential pressure between pure solvent and polymer solution

sp

How to get []i

• Software computes both sp,i and rel,i

• Solomon-Gottesman

[]i = 21/2(sp,i-ln(rel,i)1/2/c

Important point: sp and rel are concentration dependent

[] is, by definition, a “zero” concentration property

Like LS, the viscometer is sensitive to bigger chains

PS 50K vs. 100K VIS Detection00628X-2 DP00628y-2 DP

4.9 9.8 14.6 19.5 24.4 29.2 37

53

69

85

101

117

Retention Volume (mL)

Resp

onse

(mV

)

PS 50K vs. 100K DRI detection00628X-2 RI00628y-2 RI

4.9 9.8 14.6 19.5 24.4 29.2 85

142

200

258

315

373

Retention Volume (mL)

Res

pons

e (m

V)

All that work for two numbers?

• Re-visit universal calibration…units analysis

Mw x [] (Rh)3

gmol-1 x cm3g-1 = cm3mol-1

From two simple measurements we can estimate size or volume!

Implication: chain architecture elucidation

Let the fun begin

• Getting Mi and [n]i from GPC fractionation mean:

– Rapid M-H relationships– Molecular architecture determinations– Calculation of other polymer dimensions– Correlation to physical properties– Identification of tiny fractions of high molar mass

material

From a few months to a few minutes!

PS 168300828C-2 RI00828C-2 DP00828C-2 LS

7.8 10.0 12.2 14.5 16.7 18.9-0

20

40

60

80

100

Retention Volume (mL)

Relat

ive R

espo

nse

M-H Plot from single run PS 1683

3.86 4.42 4.98 5.55 6.11 6.67-1.17

-0.78

-0.40

-0.01

0.37

0.75

Log(Molecular Weight)

Log[

Intri

nsic

Vis

cosi

ty]

Behold the Power of M-H[] = KMa

• a parameter: approaching 0 ; spheres0.5 ;theta condition for linear chains0.7-0.8 ; expanded coils1.8 ; ideally rigid rod

a may or may not change with branching

• K parameter: shifts with comonomer composition or branching density

What happens when branches are present

Star branched

Had enough?

Linear vs. Random LCB

LinearBranched

4.49 4.90 5.31 5.72 6.13 6.54-6.38

-3.62

-0.86

1.90

4.66

7.42

Log(Molecular Weight)

-1L

og[I

ntri

nsic

Vis

cosi

ty]

x10

More commonly encounteredlong chain branching

Have you noticed that the hydrodynamic dimensions of a branchedpolymer are “shrunken” compared to its linear counterpart?

Branching? YIKES!

• Triple detection GPC measurements (LS,VIS, DRI)

• Determine []-Mw relationship (M-H values)

• Compare []-Mw relationship to that of a linear sample

• Apply appropriate branching model to calculate branching density Possibilities: star, off-center star, comb, random long

chain branching, H, super-H, Pom-Pom

Dependence of Performance Properties on Molar Mass

+ property increase

- property decreaseo little change

Ten

sile

Str

engt

h

Elo

ngat

ion

Yie

ld S

tren

gth

Tou

ghne

ss

Bri

ttle

ness

Har

dne

ss

Abra

sion

Res

ista

nce

Sof

teni

ng T

emp

Mel

t V

isco

sity

Adhes

ion

Che

mic

al R

esis

tanc

e

Sol

ubili

ty

I ncrease molar mass + + + + + + + + + - + -

Narrow the MWD + - - + - - + + + - + o