Polimer KarakterizasyonTeknikleri – GPC/SEC

Evren Depren, Aplikasyon Uzmanı

Atomika Teknik Cihazlar

Temmuz 2018

1

The Triple DetectionTechnique

2

3

› Hardware Schematic

› Mechanism of separation: size exclusion chromatography

› Overview of the detectors

� Concentration

� Light scattering

� Viscometer

› Equations governing the response of the detectors

OVERVIEW

› Involves passing a mixture dissolved in a "mobile phase" through astationary phase,

� Separates the analyte to be measured from other molecules in themixture and allows it to be isolated.

› Separation takes place on size not molecular weight

› After the column, the separated molecules can be analysed by oneor more detectors.

› GPC is a solution-based technique. The polymer sample must bedissolved in a suitable solvent for the analysis.

› Molecular weight, Size and Structure of our macromolecule

GPC – Gel Permeation Chromatography

SEC – Size Exclusion Chromatography

GFC – Gel Filtration Chromatography

What is GPC/SEC?

4

SE

PA

RA

TIO

ND

ET

EC

TIO

N

5

SEC Instrument Schematic

Tetra Detection

ViscometerLight Scattering

Refractive Index

UltraViolet -PDA

GPC SYSTEMS

Triple/Tetra detection

Conventional detection Advanced Triple/Tetra detection

RImax

OMNISEC

TDAmaxHT-GPC

Tetra detection at high temperatures

6

SEPARATION

7

SEPARATION: SEC

A

Sample loaded on column.

B

Sample components separated by hydrodynamic size.

C and D

Components elute from column and pass through detectors.

› Solution based technique.

› Purely physical separation.

Larger molecules elute first

› No interaction with column.

SAMPLE MIXTUREA B C D

DETECTORS

SOLVENT

FLOW

CHROMATOGRAM

RETENTION

VOLUMEA B C D

POROUS

PACKING

SIZE EXCLUSION CHROMATOGRAPHY

8

THE SEPARATION PROCESS

Lo

gM

W

Retention Volume

V0

Vt

Exclusion Total Permeation

Mobile Phase Flow

Stationary Phase

Gel Particle

Vo = Void volume

Vt = Total column volume

9

THINK!

A B

20 nm 5 nm

WHICH MOLECULE WOULD ELUTE FIRST IN GPC?

Hydrodynamic

size

10

THINK!

WHAT WOULD THE CHROMATOGRAM LOOK LIKE?

Retention Time or Volume

De

tecto

r In

ten

sity

A

20 nm

B

5 nm

11

THINK!

A B

20 nm 19 nm

WHICH MOLECULE WOULD ELUTE FIRST IN GPC?

Hydrodynamic

size

12

13

THINK!

WHAT WOULD THE CHROMATOGRAM LOOK LIKE?

Retention Time or Volume

De

tecto

r In

ten

sity

A B

20 nm 19 nm

14

THINK!

A B

20 nm 20 nm

B

HYDRODYNAMIC VOLUMESIZE & STRUCTURE!

WHICH MOLECULE WOULD ELUTE FIRST IN GPC?

Hydrodynamic

volume

15

THINK!

WHAT WOULD THE CHROMATOGRAM LOOK LIKE?

Retention Time or Volume

De

tecto

r In

ten

sity

A

20 nm

B

16

QUIZ!

200 KDa100 KDa

BBA

10 nm6 nm

6 nm10 nm

WHICH MOLECULE WOULD ELUTE FIRST IN GPC?

Molecular weight

Hydrodynamic size

17

DETECTION

18

DETECTOR OUTPUT

SSIZEIZE

IINTRINSICNTRINSIC

VVISCOSITYISCOSITYCCONCENTRATIONONCENTRATION

MMOLECULAR OLECULAR

WWEIGHTEIGHT

SECSEC--TDATDA

SSIZEIZE

IINTRINSICNTRINSIC

VVISCOSITYISCOSITYCCONCENTRATIONONCENTRATION

MMOLECULAR OLECULAR

WWEIGHTEIGHT

SECSEC--TDATDA

RI & UVVISCOMETER

VISCOMETER+LIGHT SCATTERING

LIGHT SCATTERINGRALS & LALS

19

Concentration Detectors

Sample

cell

Reference

cell

Incident Beam

Flow Cell

› Deflection of beam corresponds to

sample concentration

20

› Principle: Light travels at different

speeds in different media.

› This causes bending or refraction of the

light.

Differential Refractometer

No sample

Low conc.

High conc.

21

Ultraviolet Spectroscopy

› Principle: The molecule absorbs light

at a specific wavelength.

› The detector measures the difference

between the intensity of light passed

through the reference and sample.

ItI0Reference

Sample

22

HOW DO RI & UV DETECTORS GIVE CONCENTRATION?

Concentration profile

UVRI

2 4 6 8 10

Concentration

De

tecto

r re

sp

onse

2 4 6 8 10

Concentration

De

tecto

r re

sp

onse

Classical concentration determination:• The UV or RI responses of standards would be plotted against concentration.

Response = k • C

Slope

Unknown C = Response

k

In triple detection:

Refractive index k ~ dn/dc

Ultraviolet k = dA/dc

These values allow us to determine the concentration of polymer at every point in the chromatogram

23

EQUATIONS GOVERNING THE DETECTORS

RI Output (mV) = KRI • dn/dc • Concentration

UV Output (mV) = KUV • dA/dc • Concentration

24

Light Scattering Detectors

25

› Photons from an incident beam is absorbed by a macromolecule and re-emitted in all directions

LIGHT SCATTERING DETECTOR

LIGHT SCATTERING THEORY

› The relationship between light scattering and molecular weight is defined by the Rayleigh equation:

› Where:

� C = the sample concentration

� θ is the measurement angle

� Rθ = the Rayleigh ratio (the ratio of scattered light intensity to incident light intensity) at the measurement angle θ

� Mw = molecular weight

� A2 = the second virial coefficient

� Pθ = a term that defines angular dependence

� K = a constant (which is expanded on the next slide…)

��

��

= �

��+ 22�

�

�

26

LIGHT SCATTERING THEORY

› K is an constant dependent on the system, solvent and the sample being measured

› Where:

� λ = the wavelength of the laser in a vacuum

� NA = Avogadro’s number

� n0 = is the refractive index of the solvent

› This term contains the value of dn/dc which is a measure of the difference in refractive index between the sample and the solvent

› dn/dc is squared in the equation meaning it is very important to have an accurate value

� = ���

����

�

�0��

��2

27

LIGHT SCATTERING THEORY

› The Rayleigh equation can be used to measure molecular weight by measuring the intensity of the light scattered by the sample if all the other parameters are known

28

ANGULAR DISSYMMETRY

› The consequence of the 1/Pθ term is that different molecules scatter

light in different directions with different intensity

� Smaller molecules scatter light evenly in all directions (isotropic scattering)

� Larger molecules scatter light in different directions with different intensities (anisotropic scattering)

› This is dependent on:

� The molecule’s size

� The measurement angle

� The laser wavelength

› Only the light scattered at zero degrees does not suffer interference

29

LIGHT SCATTERING THEORY

› 1/Pθ is a term that defines the angular dependence of

the scattered light

› Where

� n0 = the refractive index of the solvent

� Rg = the sample’s radius of gyration

� λ0 = the wavelength of the laser in a vacuum

� θ = the measurement angle

› The result of this is that light scattered by larger

molecules at higher angles has a different intensity

› If we are going to measure the Mw, we must account

for this effect

�

�

= 1+�����

���

��

���� sin2 �

�

30

ISOTROPIC SCATTERERS

› Molecules that are small with respect to the laser wavelength scatter light isotropically (i.e. evenly in all directions)

� ‘small’ means < 1/20th of the laser wavelength

› Any measurement of the light scattering intensity should be sufficient to determine the molecular weight

� 1/Pθ is very close to 1 so has no effect on the result

Sin2 θ/2 (essentially – angle)K

C/R

θ

Mw measured

31

RIGHT-ANGLE LIGHT SCATTERING (RALS)

› RALS measures the intensity of scattered light at 90°

› RALS is limited to ‘small’ molecules (<15nm radius)� Isotropic scatterers

› This level of scattering is assumed to be the same as 0°

› RALS has excellent signal-to-noise

32

ANISOTROPIC SCATTERERS

› Larger molecules scatter light in different directions with different intensities

� ‘large’ means >1/20th of the laser wavelength

› In large molecules, the light is scattered by the different mass cores within the molecule

› Individual scattered photons interfere with each other to change the overall light scattering intensity

› Pθ ≠ 1 and so affects the calculated molecular weight

33

ACCOUNTING FOR ANISOTROPIC SCATTERING

› By plotting KC/Rθ as a function of sin2(θ/2) we can see the change in scattering intensity with angle

› Mw can be calculated from the KC/Rθ at the intercept

34

ACCOUNTING FOR ANISOTROPIC SCATTERING

› We must account for the anisotropic scattering in some way in order to calculate the correct molecular weight

› The Rayleigh equation tells us that if θ = 0 then the scattered light intensity relates directly to the sample’s molecular weight

› We can’t measure at θ = 0 because the incident light is too bright

35

LOW-ANGLE LIGHT SCATTERING

› LALS measure the scattered light intensity at an angle as close to 0° as possible

› This level of scattering is assumed to the be the same as 0° as 1/Pθ will be very close to 1

› LALS has good signal-to-noise

› LALS works for all molecules, large and small

36

RALS/LALS

› A RALS/LALS detector has the sensitivity of RALS

for small molecules AND can account for anisotropy

for large moleculesSmall molecules

Large molecules

37

38

LIGHT SCATTERING PROPERTIES OF DIFFERENT

MOLECULES

Hyaluronic Acid (1 MDa) ~ 60nm

LALS (7 deg)

RALS (90 deg)

12,0 15,0 18,0 21,0 24,0 27,0

-1,0

14,3

29,5

44,8

60,0

Retention Volume (mL)

PEO (23 kDa ~ 5nm)

LALS (7 deg)

RALS (90 deg)

17,0 20,0 23,0 26,0 29,0 32,0

-0,5

2,8

6,0

9,3

12,5

Re

sp

on

se

(m

V)

Isotropic scatterersEither RALS or LALS provides correct Mw

Non -isotropic scatterersLALS provides correct Mw

2

0 '

×∝

dc

dnCKMR w

The OmniSEC software automatically detects the transition

between RALS and LALS

› For small molecules (e.g. polymers < 200kDa) there is no

angular dependence of the LS signal

� Molecular weight can be measured directly and accurately using RALS

� RALS always give highest signal-to-noise

› For larger molecules (e.g. polymers >200kDa) you need

to:

� Molecular weight is measured directly at low angle (7º) using LALS

� LALS minimises angular dependence

SUMMARY OF ANGULAR DEPENDENCE

39

40

The Viscometer

› Invented by Max Haney in 1983

› Based on the Wheatstone bridge principle

› Used to determine the Intrinsic Viscosity of sample

THE 4 CAPILLARY DIFFERENTIAL VISCOMETER

+ -

-+

41

Viscosity is an inherent property of the solvent and specific!!

Imagine that these solvent molecules are arranged in sheets that are

trying to flow over one another.

42

WHAT IS VISCOSITY?

Solvent

e.g: water

The resistance to this flow is

the solvent’s viscosity.

VISCOMETERY

Which is more resistant to flow:

Milk

Or

Honey?

43

WHAT IS INTRINSIC VISCOSITY?

Solute (polymer) dissolved in Solvent

When a solute is dissolved in the solvent, the ability of these sheets to

flow over one another is changed.

This contribution of the solute to the overall viscosity of the solution is

known as the intrinsic viscosity of the solute.

VISCOMETERY

Traditional Solution Viscosity Measurements

c

relinh

)ln(ηη =1−= relsp ηη

Set Volume

Capillary

Reservoir

00 t

trel ==

η

ηη

Solution Drop Time

Solvent Drop Time

Derived from relative viscosity

Ubbelohde Tube

44

45

Intrinsic viscosity is the concentration normalized ‘specific’ viscosity of the polymer in solution at infinite dilution.

η sp is called the specific viscosity of the solution whose concentration is C.

η o is the Solvent Viscosity.

η is the Solution Viscosity.

[ ]0→

==c

sp

cIV

ηη

0

0

η

ηηη

−=sp

In GPC, concentrations of solutions are

sufficiently dilute that the extrapolation

to zero concentration is negligible.

HOW DO WE DEFINE IV?

46

HOW CAN WE RELATE IV TO STRUCTURE?

Intrinsic viscosity has the units:

dL/g

We can look at structure in these terms:

IV ∝ volumemass

Intrinsic viscosity is inversely proportional to molecular density:

Which of these two molecules with the same mass occupies the largest volume of space?

IV ∝ 1 Cdensity

IP+ -

DP-+GPC IN OUT

Solvent

Sample

HOW DO WE MEASURE IV?4-capiliary viscometer bridge - The Wheatstone Bridge Concept

The viscometer detects changes in pressure when the sample travels though the viscometer.

Relationship of the output from the pressure transducers and specific viscosity

Relationship of the specific viscosity and intrinsic viscosity

DPIP

DPsp 2

4

−=η IVC ×=

47

0

0

η

ηηη

−=sp

WHAT DOES THE IV TELL US ABOUT OUR SAMPLE?

CONFORMATION

Molecule folded on itself ⇒ high density – low IV

In general: IV rod > IV coil > IV sphere

› Since the hydrodynamic volume is smaller, with the same mass enclosed

with the same total chain length, the density must be higher, producing a

lower Intrinsic Viscosity

48

WHAT DOES THE IV TELL US ABOUT OUR SAMPLE?

LENGTH OF CHAIN

Increasing length ⇒ density decrease – IV increase

BRANCHINGS (INCLUDING DENDRIMERS)

Branchings ⇒ more compact structure

⇒ higher density, lower IV

M

log [η]

log M

Mark-Houwink equation relates Mw to IV :

[η] = kMa

log [η] = log k + a logM

M – H a = Related to the way chains are added to the backbone of a polymer

M – H K = Density of the backbone

Average over whole or part of the molecular weight range

49

50

Triple Detection

Multi Detector SEC

› Addition of advanced detectors enhances GPC/SEC

greatly

� Light Scattering – Molecular Weight

� Viscometer – Molecular Structure

› Triple Detection – Light Scattering and Viscometer

› Tetra Detection – Addition of 2nd Concentration Det.

� Copolymers, Blends

� Conjugates, PEGylation, PDCs

51

52

TRIPLE DETECTION DATA: OUTPUT FROM ALL

DETECTORS

50

75

100

125

150

175

200

225

250

275

Re

fra

ctive

In

de

x (

mv)

80

100

120

140

160

180

200R

igh

t A

ng

le L

igh

t S

ca

tte

rin

g (

mv)

90

100

110

120

130

140

150

160

Lo

w A

ng

le L

igh

t S

ca

tte

rin

g (

mv)

-360

-340

-320

-300

-280

-260

-240

-220

Vis

co

me

ter

- D

P (

mv)

0 5 10 15 20 25 30 35 40 45 50Retention Volume (mL)

RI

LS

IV

Detectors respond to different properties of a macromolecule

EQUATIONS GOVERNING THE DETECTORS

› Concentration Detectors

› Absolute Molecular Weight Measurement� Static light scattering

› Hydrodynamic Size and Intrinsic Viscosity� Four-capillary viscometer

ii Cdc

dn

n

KRI ⋅⋅=

0

ii Cdc

dAKA ⋅⋅=

CPP

P

i

sp ⋅=∆−

∆=

−= ][

2

4

0

0 ηη

ηηη

Differential Refractive Index UV-Vis

Right Angle (90°) and Low Angle (7°) Light Scattering

Intrinsic Viscosity

53

54

EQUATIONS GOVERNING THE DETECTORS

RI Output (mV) = KRI • dn/dc • Concentration

UV Output (mV) = KUV • dA/dc • Concentration

Visc. Output (mV) = KVisc • IV • Concentration

LS Output (mV) = KLS • Mw • (dn/dc)2 • Concentration

� Absolute molecular weight� Molecular weight distribution� Intrinsic viscosity� Molecular size� Long-chain branching� Mark-Houwink coefficients� % Polymer

-1.0

210.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0

90.0

100.0

110.0

120.0

130.0

140.0

150.0

160.0

170.0

180.0

190.0

200.0

Re

fra

ctive

In

de

x R

esp

on

se

(m

V)

3.000

7.000

3.200

3.400

3.600

3.800

4.000

4.200

4.400

4.600

4.800

5.000

5.200

5.400

5.600

5.800

6.000

6.200

6.400

6.600

6.800

Lo

g M

ole

cu

lar

Weig

ht

-1.0

175.0

8.0

16.0

24.0

32.0

40.0

48.0

56.0

64.0

72.0

80.0

88.0

96.0

104.0

112.0

120.0

128.0

136.0

144.0

152.0

160.0

168.0

Ultra

Vio

let @

26

0.0

nm

Re

sp

on

se

(m

V)

-1.0

90.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

40.0

45.0

50.0

55.0

60.0

65.0

70.0

75.0

80.0

85.0

Vis

co

me

ter

- D

P R

esp

on

se

(m

V)

-1.0

95.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

40.0

45.0

50.0

55.0

60.0

65.0

70.0

75.0

80.0

85.0

90.0

Lo

w A

ng

le L

igh

t S

ca

tte

rin

g R

esp

on

se

(m

V)

-1.0

145.0

7.0

14.0

21.0

28.0

35.0

42.0

49.0

56.0

63.0

70.0

77.0

84.0

91.0

98.0

105.0

112.0

119.0

126.0

133.0

140.0

Rig

ht A

ng

le L

igh

t S

ca

tte

rin

g R

esp

on

se

(m

V)

12.00 20.20

Retention Volume (mL)

12.6 12.9 13.2 13.5 13.8 14.1 14.4 14.7 15.0 15.3 15.6 15.9 16.2 16.5 16.8 17.1 17.4 17.7 18.0 18.3 18.6 18.9 19.2 19.5 19.8

Data File: 2008-07-18_17;03;55_PS_273K_01.vdt Method: PDACopoly3-0000.vcm

SEC Chromatogram Using OmniSECTM Software

DRI

UV-Vis

[η]

RALS

LALS

Mn - (Da) 142,344Mw - (Da) 273,337Mz - (Da) 419,713Mp - (Da) 239,145Mw / Mn 1.92[η] - (dL/g) 0.92Rh - (nm) 15.1Rg - (nm) 21.4Wt Fr (Peak) 1.0a 0.74logK -4.04Branches 0.00Branch Freq. 0.00dn/dc - (mL/g) -0.104

Results Table

Triple/Tetra Detection GPC/SEC by Malvern

55

Molecular size by Triple Detection (random coil

polymers)

Pe x

x

x

( )( )θ =

− −−

212

Rh Rg

2

)2/sin(n

Rg3

8x

θλ

π=Where:

Rg from LS (only above ~10-15nm)

Rh from LS and Visc. (no limits)

Rh3

•3

10= π]M[η •ΝΑ

IV Mw Constants

56

Size Measurements - Rg and Rh

› Radius of Gyration (Rg)

� Rg is the root-mean-square of the radii from the centre of the mass to the different mass cores within the molecule.

� Direct measurement by changes in scattered light intensities with observation angle

� Limitations:

• Requires good S/N light scattering signal

• Lower size detection limit = 10-15 nm

• Large structures require non-linear curve fitting

� A good estimate can be made using viscometry and the Flory-Fox equation

› Hydrodynamic Radius (Rh)

� RH is the radius of an equivalent sphere that diffuses with the same speed as the molecule of interest.

� Measured two ways

• Dynamic Light Scattering

• Triple Detection SEC/GPC – IV and Mw

� Triple Detection

• Analyze hydrodynamic size from < 1 nm to the exclusion limit of the SEC

column (~200 nm)

• No extrapolation or fitting parameters57

58

› Triple detection technique uses 3 detectors:

RI + Light Scattering + Viscometer

› The signals are processed together at each data slice

� 5 Hz

› Specific equations govern each detector which allow concentration, Mw, intrinsic viscosity and molecular size to be determined across the entire distribution.

› Adding a fourth detector – UV – allows for compositional analysis in copolymer samples.

SUMMARY

Conventional GPC

59 59

Hardware Schematic Conventional GPC

GPC PumpVacuum

Degasser

Solvent

Autosampler

Injection Loop

Column Oven and Columns

Waste

RI Detector

1.00

LOW PRESSURE

HIGH PRESSURE 60

Separation Mechanism

Columns

Detection

Calibration

Summary

Conventional GPC

61

(A) (B) (C) (D) RETENTIONTIME

(A) (B) (C) (D)

POROUS

PACKING

SAMPLE MIXTURE

+

CONCENTRATION

DETECTOR

CHROMATOGRAM

SOLVENT

FLOW

unlike HPLC,

NO chemical

interaction

with the GPC

column is

permitted.

GPC relies on a

pure physical

separation

principle.

Separation Mechanism

RETENTION

VOLUME

62

Example data output – Broad distribution polystyrene sample

8.53

18.88

29.23

39.58

49.93

60.28

70.63

Re

fra

ctiv

e In

de

x (

mV

)

Retention Volume (mL)

5.00 10.00 15.00 20.00 25.00

0.00

0.19

0.39

0.58

0.77

0.97

1.16W

F /

dL

og

MW

Log Molecular Weight

3.00 4.00 5.00 6.00 7.00

Raw

Chromatogram

Calculated

Molecular Weight

Distribution

Data reversed!

63

Gel Permeation Chromatography

SEC - Size Exclusion Chromatography

GFC - Gel Filtration Chromatography (LP)

HPSEC - High Pressure/Performance SEC

GPC/SEC retention is an equilibrium, entropy-controlled size exclusion process

Separation takes place on size not molecular weight

64

Temp.=65 0CTemp.=65 0C

Temp.=10 0CTemp.=10 0C

Effect of Temperature on SEC Mechanism

Sharper peaks at higher temperature

due to improved diffusion.

Sharper peaks at higher temperature

due to improved diffusion.

Retention volume is not strongly dependent on temperature

Retention volume is not strongly dependent on temperature

65

Effect of flow rate on SEC mechanism

Flow Rate

Increase

Flow Rate

Increase

Increasing flow rate will reduce resolution but not change elution volumeIncreasing flow rate will reduce resolution but not change elution volume

66

Conventional GPC

Separation Mechanism

Columns

Detection

Calibration

Summary

67

GPC Column Selection

Need to match sample/solvent combination to

column selected.

Two broad categories:� Organic - Dominated by Styrene Divinyl Benzene

� Aqueous - More variety

68

GPC Column Selection

Columns available either:

� Packed with gel (packing) having pores all of the same size. - Single Porosity columns. These are generally used as a ‘set’ of different pore sizes to cover the required range for the application.

� Packed with a mixture of gels with different pore sizes. -Linear or Mixed-Bed columns. These can be used as a single column for ‘screening’ but are often combined in sets of 2 or 3 to give additional resolution.

Typical column dimensions 8mm x 300mm.

69

GPC Column Selection

70

Conventional GPC

Separation Mechanism

Columns

Detection

Calibration

Summary

71

Types of Concentration Detectors for GPC

Diode Array or UV/Vis. - Probably second most commonDiode Array or UV/Vis. - Probably second most common

Infrared Spectrometer - Probably least commonInfrared Spectrometer - Probably least common

Evaporative Mass - Linearity problemsEvaporative Mass - Linearity problems

Refractive Index - Almost universalRefractive Index - Almost universal

72

RI Detectors - Schematic

Beam Splitter

Zero Glass

Diverting Mirror

Flow Cell Concave

Mirror

Photodiode

Photodiode LED

nsnr

Beam

Splitter

73

Separation Mechanism

Columns

Detection

Calibration

Summary

Conventional GPC

74

To use the technique quantitatively the column retention volume must be calibrated in some way.

Use polymer standards of known molecular weight.� (Remember though, the columns separate by size not

molecular weight so the calibration is only relative.)

Flow rate must be controlled carefully.

Conventional Calibration

75

Refr

active I

ndex

Response (

mV

)

Retention Volume (mL )

12,50 15,00 17,50 20 ,00 22,50 25,00 27,50 30,00 32,50

150 ,55

138 ,97

127 ,40

115 ,82

104 ,24

92,66

81,08

69,51

57,93

162 ,13

46,35

10,00 35,00

Size Exclusion Chromatography

RI Detector

170.000

46.500

5.450

Exclusion Limit

Total Permeation

76

Narrow Standards Calibration

77

Weight Average (Mw)

∑∑

=ii

i

Mc

cMn

/

∑∑

=i

ii

c

McMw

Number Average (Mn)

Z-Average (Mz)

Retention Volume

RI

Hei

gh

t (W

eig

ht

Fra

ctio

n)

Mi

ci

Lo

g (

Mo

lecu

lar

Wei

gh

t)

∑∑

=ii

ii

Mc

McMz

2

MWD’s using Conventional Calibration.

78

1) Simple Setup.

(Only one detector required - RI or UV)

2) Solution concentration not a variable.

(Approximate concentrations are good enough)

3) Excellent precision (repeatability)

(Related to column and pump performance)

Advantages of Conventional Calibration

79

2.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

6.5

18 20 22 24 26 28 30Retention Volume (ml)

Lo

g (

Mo

lecu

lar

Weig

ht)

PSPAMSPMM

API

PPBDPP

G

Overlay of Conventional Calibration Curves

Each Polymer has its own size to

Molecular weight relationship:Vh ≈ [η]xM

80

Effect of molecular shape on GPC

retention volume

Structural changes will affect

results

Columns separate on

size not MWt.

Sphere

Coil

Rod

Retention volume

81

1) Each polymer has its own calibration line,

so the Molecular Weight values are only

accurate for the same sample type:

only relative MW obtained

2) Any structural change such as branching

will affect the accuracy of this value:

gives incorrect relative MW!

3) Does not give any structural information.

Disadvantages of Conventional Calibration

82

Conventional Calibration GPC - Summary

Simple technique to give whole polymer distribution

� Need to take care with sample/solvent/column

compatibility

� Comparison of samples is easy

Calibration is main difficulty

� Data is therefore only relative

No structural information

� Not useful for branched polymers

83

Universal GPC

84 84

Hardware Schematic Universal Calibration

GPC PumpVacuum

Degasser

Solvent

Autosampler

Injection Loop

Column Oven and Columns

Waste

Viscometer Detector

RI Detector

1.001.00

85

Universal Calibration

•Why Universal Calibration

•Theory

•Viscosity Detector

•Examples

86

Why Universal Calibration?Size Exclusion Chromatography (SEC)

(A) (B) (C) (D) RETENTIONTIME

(A) (B) (C) (D)

POROUS

PACKING

SAMPLE MIXTURE

+

CONCENTRATION

DETECTOR

CHROMATOGRAM

SOLVENT

FLOW

unlike HPLC,

NO chemical

interaction

with the GPC

column is

permitted.

GPC relies on

a pure

physical

separation

principle.

(A) Injection

(B) Separation

(C) Elution of

large

molecules

(D) Elution of

small

molecules

Polymer separation

based on SIZE

(hydrodynamic volume)

87

2.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

6.5

18 20 22 24 26 28 30Retention Volume (ml)

Lo

g (

Mo

lecu

lar

Weig

ht)

PSPAMSPMMAPIPPBDPPG

Overlay of Conventional Calibration Curves

Each Polymer has its own size to

Molecular weight relationship:Vh ≈ [η]xM

88

Universal CalibrationUniversal Calibration was first demonstrated

and proven by Benoit in 1967, who showed

that a wide range of polymer structures

eluted on the same calibration curve when

the intrinsic viscosity is included.

It does not matter whether the polymer is

linear, branched, block copolymer,

heterogeneous copolymer, or whatever...

105

106

107

108

109

Lo

g [

η]

M

18 20 22 24 26 28 30

ELUTION VOLUME

PS “Comb”PS

PS “Star”

Hetero-Graft CopolymerPolyMethylMethacrylatePolyVinylChlorideGraft Copolymer: PS/PMMAPolyPhenylSiloxane

Polybutadiene

89

Universal CalibrationIntrinsic Viscosity

Intrinsic viscosity is the concentration normalized

viscosity of the polymer in solution at infinite dilution.

ηsp is called the specific viscosity of the solution whose concentration is C.

ηo is the Solvent Viscosity.

η is the Solution Viscosity.

[ ]0→

==c

sp

cIV

ηη

0

0

η

ηηη

−=sp

In GPC, concentrations of solutions are

sufficiently dilute that the extrapolation

to zero concentration is negligible.

90

Universal Calibration

91

Universal Calibration4- capillary Differential Viscosity Detector

IP

+ -

DP-+GPC IN OUT

Solvent

Wheatstone bridge concept - M. Haney, 1984Wheatstone bridge concept - M. Haney, 1984

Sample

92

Universal CalibrationCalculation of Viscosity

Intrinsic Viscosity is Determined by the Viscometer Detector Signal.

[ ]ηη

= =IVC

sp

IVCDPIP

DP

o

o

sp×=

−=

−=

24

ηηη

η

93

ViscometerDelay

Volume

IP (-)IP (+)

DP (-)

DP (+)

Inlet Outlet

Pump pulsation noise cancels

At DP transducer:

This is a direct pneumatic cancellation

The bridge doesn’t see solvent differences

It only sees actual polymer differences

Four Capillary Viscometer

5.0 7.0 9.0 11.0 13.0 15.0

Retention Volume (mL)

Det

ecto

r R

esp

on

se

Pump Noise

is cancelled out

94

Universal CalibrationDual Detector Response

Detector Responses VISC ∝ IV x C

RI ∝ dn/dc x C

Polystyrene

850,000

15.0 17.0 19.0 21.0 23.0 25.0

0

50

100

150

200

250

Retention Volume (mL)

Det

ecto

r R

esp

on

se (

mV

)

Refractomete

rPolystyrene

30,000

Viscometer

95

Universal Calibration – RI response

RI ChromatogramPS10-1 RIps1-1 RIps11-1 RIps12-1 RIps2-1 RIps3-1 RIps4-1 RIps5-1 RIps6-1 RIps7-1 RIps8-1 RIps9-1 RI

8,0 10,2 12,4 14,7 16,9 19,1 21,3 23,6 25,8 28,0-20

-2

15

33

50

68

86

103

121

138

Retention Volume (mL)

Res

ponse

(m

V)

Date of Run: Tue May 04 199909:26:17

Viscotek Corporation

Viscotek PolyCal standards

96

Viscosity ChromatogramPS10-1 DPps1-1 DPps11-1 DPps12-1 DPps2-1 DPps3-1 DPps4-1 DPps5-1 DPps6-1 DPps7-1 DPps8-1 DPps9-1 DP

8,0 10,2 12,4 14,7 16,9 19,1 21,3 23,6 25,8 28,0-70

-29

12

52

93

134

175

216

257

298

Retention Volume (mL)

Res

ponse

(m

V)

Date of Run: Tue May 04 199909:26:17Viscotek PolyCal standards

Universal Calibration – Viscometer Response

97

Universal Calibration Line

1,000

8,000

2,100

2,800

3,500

4,200

4,900

5,600

6,300

7,000

Log

( M

p x

IV

)

17,000 28,000

Retention Volume (mL)

19,000 20,000 21,000 22,000 23,000 24,000 25,000 26,000

1,870 e 6

940,000

400,000

170,000

94,400

46,500

18,000

5,450

2,560

98

Retention

Volume

Log MxIV

IV MW IVxMW

Polymer A (Standard)

1.0 250,000 250,000

Polymer B (Sample)

0.83 300,000 250,000

MWAIVA = MWBIVB

Universal CalibrationCalculation

99

Universal CalibrationResults

Differential MWD

3,81 4,21 4,61 5,02 5,42 5,82 6,230,00

0,27

0,53

0,79

1,06

Log(Molecular Weight)

d(W

f) /

d(L

og

M)

Differential IVD

3,81 4,29 4,78 5,26 5,74 6,230,00

0,30

0,60

0,89

1,19

1,49

Log(Molecular Weight)

d(W

f)/d

(Log

IV)

Size Distribution

3,81 4,29 4,78 5,26 5,74 6,230,00

0,37

0,74

1,11

1,49

1,86

Log(Molecular Weight)

d(W

f)/d

(Log

Rg

)

Mark-HouwinkPS250K-1 IV LS

3,81 4,29 4,78 5,26 5,74 6,23-1,21

-0,86

-0,52

-0,17

0,17

0,52

Log(Molecular Weight)

Lo

g (

IV)

100

Universal CalibrationStructure Analysis Mark-Houwink Plot

PS250K-1 IV LSpsrr1-1 IV LSnbs706-1 IV LS

3,80 4,23 4,66 5,08 5,51 5,94 6,36-1,22

-0,76

-0,30

0,16

0,62

Log(Molecular Weight)

Log[I

ntr

isic

Vis

cosi

ty]

101

Universal CalibrationSummary

Advantages:

•True molecular weight/intrinsic viscosity

•MH a and K values (broad distributions)

•Structure/branching information

•Sensitive from high to low Mw (< 1000)

•No dn/dc needed

Disadvantages:

•True size exclusion separation necessary

•Standards in the same Mw(Vh) range as unknown

•Need to know concentration

102

Branching

103

Types of Polymer Branching

1. Short Chain 2. Long Chain - Star

4. Long Chain - Comb3. Long Chain Random

104

The Kuhn–Mark–Houwink–Sakurada equation

αη MwK ×= ][

› [η] is the Intrinsic Viscosity (IV)

› K and α are the MH parameters which depend on the nature of the polymer & solvent

› Mw is the weight average molar mass (molecular weight)

› a describes the relationship between molecular weight and IV, K is the intercept, describing the flexibility of the backbone.

The equation describes the dependence of the intrinsic

viscosity of a polymer to molecular weight

6TH INTERNATIONAL CONFERENCE ON THE HISTORY OF CHEMISTRY Staudinger - Mark - Kuhn: Historical Notes from the Development of Macromolecular Chemistry105

Branching AnalysisMark-Houwink Plots

Log M

Lo

g I

V

Log M

Lo

g I

V

Non-Uniform Branching

Typical for

random long chain branching

Uniform Branching

Typical for

short chain branching

106

Effect of Branching on Molecular Size

› Difference in volume between a linear chain and a

branched chain with the same total chain length

› Since the hydrodynamic volume is smaller, with the

same mass enclosed, the density must be higher,

producing a lower Intrinsic Viscosity

107

Star Branched PS

Decrease in

Viscosity

Area

Equivalent Molecular Weight Star Branched PS vs. Linear PS

Star Viscosity

Linear Viscosity

Retention Volume (mL)

Dete

ctor

Resp

onse

Equivalent

Molecular Weight

Areas

Decrease in Retention Volume (Rg)

Star LS

Linear LS

Mw IV star IV linear IV ratio Bn

340,000 0.805 1.162 0.693 4

100,000 0.318 0.497 0.639 5

+2,500,000 1.308 4.632 0.282 10

IV linear equivalent measured from MH-Coefficients of linear polystyrene. Star branch viscosities

measured directly with the differential viscometer detector.

Three Star Branched PS

108

The Zimm-Stockmayer theory defines the g factor as the ratio of the radius of gyration of

the branched polymer to the radius of gyration of the linear polymer, at the same

molecular weight.

The radius of gyration can be measured by light scattering from the initial slope of the

Zimm plot.

The practical difficulty here is that Rg measured by light scattering does not extend to

molecules below Rg = 15 nm.

M

=

(lin) R

(br) R g

2

g

2

g

Long Chain Branching - Zimm-Stockmayer

109

Long Chain Branching - Zimm-Stockmayer

The Zimm-Stockmayer theory also defines the g factor in terms of the intrinsic viscosity

ratio

.

Where ε is a shape factor, generally taken as ~0.75.

This formulation is not as rigorous as that using the RG, considering that ε is ill-defined

by the theory. However, it is more practical in the sense that intrinsic viscosity can be

measured over nearly the entire distribution of the polymer.

[ ][ ]

ε

η

η1/

Ml,

Mb,

g

=

110

Equations of Zimm-Stockmayer for g

111

Values of Epsilon in the g Equation

112

Calculation of branching – Zimm Stockmayer

› Branching ratio (g) defined in terms of Rg (radius of gyration)• Not an easy parameter to measure

accurately – initial slope of Zimm plotat Θ = 0° not overall slope!

• Impossible to measure below ~15nm

› Branching ratio can also be defined in terms of Intrinsic Viscosity (g’)• More practical solution• Easier to measure across entire size

range 1nm to >100nm• Better sensitivity (density, not size)• More reproducible

› ….but need to use shape factor (ε)• Typically 0.75 used for PE• Results are only relative, unless ε

can be determined absolutely• Can check from Rg estimate if large

enough

linM

brM

Rg

Rgg

,2

,2

=

[ ][ ]

ε

η

η1/

Ml,

Mb,

g

=

[ ][ ] linM

brM

Mg,

,'

η

η=

113

Long-Chain Branching Parameters

› Star Branching

• For regular distribution of arms, Number of Arms ‘f’ (or Bn)

• For random distribution of arms:

2/)23( ffg −=

( )( )21

6

++=

ff

fg

f (or Bn) = 2f (or Bn) = 2

f (or Bn) = 3

114

› The number of branches per molecule (Bn) is

determined for random tri-functional branching using:

Long-Chain Branching Parameters

( )

( )g

B

B

B

B B

B Bn

n

n

n n

n n

=+

+ +

+ −

−

6 1

2

2 2

2

1

1

2

1

2

1

2

1

2

1

2

ln

115

Branching Frequency

Constant Number of Branches per Molecule

(not likely)Constant Branching Frequency (Density)

e.g. For polyethylene we set

R=14,000 to give ‘branches per

1000 C atomsM

BR nM

⋅=λ

Branching frequency (f or λ) can also be determined

(How many branches are there as you go along backbone)

116

Example

› Branching in polyethylene

› NIST standards

• NBS 1475 – Linear

• NBS 1476 – Branched

117

0.1

0.2

0.3

1

2

3

10

Intr

insic

Vis

co

sity (

dL

/g)

410

42x10

43x10

510

52x10

53x10

610

Molecular Weight (Da)

Comparison of NBS 1475 (Linear) and 1476 (Branched) using M-H plot

300

350

400

450

500

550

600

650

700

750

Vis

com

ete

r -

DP

(m

v)

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

Retent ion Volume (mL)

300

350

400

450

500

550

600

650

700

750

Vis

com

ete

r -

DP

(m

v)

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

Retention Volume (mL)

Refractive IndexViscosityLow Angle LS

160°C TCB2.5 mg/ml, 200ul

118

Branching Module in OmniSEC™

119

Reproducibility determined by Mark Houwink plot

120

1. What is the minimum length of long chain branches in this method?

Ans: 6-12 carbons in length.

1. What is the minimum length of long chain branches in this method?

Ans: 6-12 carbons in length.

2. What can I use for a linear reference if I do not know whether any of my polymers are linear?

Ans: Use the Mark-Houwink constants of a close relative polymer.

Or : Use the least branched polymer that you have as a reference.

Then the values will be useful on a relative basis.

2. What can I use for a linear reference if I do not know whether any of my polymers are linear?

Ans: Use the Mark-Houwink constants of a close relative polymer.

Or : Use the least branched polymer that you have as a reference.

Then the values will be useful on a relative basis.

3.What if I see apparent differences in branching in my samples but other information suggests that they are not branched?

Ans: May be some copolymer, blending or other chemical

heterogeneity present in the samples.

Or: There is some other variable that affects the density of the

molecule.

3.What if I see apparent differences in branching in my samples but other information suggests that they are not branched?

Ans: May be some copolymer, blending or other chemical

heterogeneity present in the samples.

Or: There is some other variable that affects the density of the

molecule.

Common Questions regarding Branching

121

Branching Summary

› Triple detection can be used to measure branching

› Comparison of Mark-Houwink plots is often enough

› Quantitative analysis requires a linear reference, either

• Linear polymer sample, or

• Mark-Houwink ‘a’ and ‘log k’ values

› Branching number (Bn) gives branches per molecule

• Most useful for star branching

• Less useful for random branching

› Branching frequency (λ) more useful

• Gives branches per selected repeat unit

122

Copolymer Analysis

123

Sample Types

PROTEIN POLYMER

DNA

Homogenous, mono-constituent molecules

Homopolymer Copolymer – Conjugate Analysis

PROTEIN/

POLYMER

Heterogeneous, multi-constituent complexes

PROTEIN/

PROTEIN

PROTEIN/

DNAPOLYMER/

POLYMER

PROTEIN/

DETERGENT

DNA/

DETERGENT

124

Copolymers: What are they?

› Homo-polymer� chemical homogeneity in the distribution independent

of molecular weight.

› Copolymer� chemical composition can change with respect to

molecular weight.

Homo-polymer Co-polymers

Alternating

Block

Random

Grafted

125

Multi Detector SEC

› Addition of advanced detectors enhances GPC/SEC

greatly

� Light Scattering – Molecular Weight

� Viscometer – Molecular Structure

› Triple Detection – Light Scattering and Viscometer

› Tetra Detection – Addition of 2nd Concentration Det.

� Copolymers, Blends

� Conjugates, PEGylation, PDCs

126

Copolymers - Introduction› Some types of copolymers can be treated like

homopolymers:

� Copolymers with alternating sequence

� (A-B-A-B, or A-A-B-A-A-B-, ......)

� Copolymers with MW independent composition

� Copolymers with negligible dn/dc difference of the different monomeric units e.g. Polylactide/glycolide

› For some block-copolymers, blends, copolymers with MW

dependent composition dn/dc is not a constant. Therefore:

� RI chromatogram is not a concentration chromatogram

› The MWD’s of co-polymers derived from LS and a

concentration detector (RI or UV ) are incorrect, because

the dn/dc of the polymer is different for each elution

volume.

127

Why do we need an accurate concentration profile?

› Concentration for each slice is needed to calculate Molecular weight.

-1,0

43,0

5,0

10,0

15,0

20,0

25,0

30,0

35,0

Lo

w A

ng

le L

igh

t S

ca

tte

rin

g R

esp

on

se

(m

V)

0,0

22,0

3,0

6,0

9,0

12,0

15,0

18,0

Re

fra

ctive

In

de

x R

esp

on

se

(m

V)

0,0

64,0

7,0

14,0

21,0

28,0

35,0

42,0

49,0

56,0

Ultra

Vio

let R

esp

on

se

(m

V)

11,50 20,80

Retention Volume (mL)

13,0 14,0 15,0 16,0 17,0 18,0 19,0

MwM c

c

i i

i

=∑∑

2)/(.

ResponseLS

dcdnconcKMi

××=

128

129

EQUATIONS GOVERNING THE DETECTORS

RI Output (mV) = KRI • dn/dc • Concentration

UV Output (mV) = KUV • dA/dc • Concentration

Visc. Output (mV) = KVisc • IV • Concentration

LS Output (mV) = KLS • Mw • (dn/dc)2 • Concentration

Why Can’t We Use The Homopolymer Method?

DE

TE

CT

OR

RE

SP

ON

SE

RI LS

Direct relationship

between the molecule

and detector response

Both constituents of the

complex contribute to the

response of the signals

RI LS

130

Why Can’t We Use The Homopolymer Method?

dn/dc = RI Output (mV)

KRI • Conc.

Mw = LS Output (mV)

KLS • (dn/dc)2 • Concentration

Not usually known for

copolymers

Cannot determine

concentration of

copolymer

We need to find dn/dc copolymer

131

Describing dn/dc and dA/dc In Copolymers

B

A

dn

dc copolymer

=dn

dc A

dn

dc B

+11 + δ

δ

1 + δ

We don’t know δ

dA

dc copolymer

=dA

dc A

dA

dc B

+11 + δ

δ

1 + δ

Copolymer = 1 + δ

Equation A

Equation B

A = Homopolymer A

B = Homopolymer B

132

Describing dn/dc In Terms Of Detector Responses

dn

dc copolymer

= RI

?

Change in RI response

Concentration of copolymer=

dA

dc copolymer

= UVccopolymer

Substitute for ccopolymer

Equation C

133

Describing dn/dc In Terms Of Detector Responses

dn

dc copolymer

= RI • (dA/dc) copolymer

UV=

RI

UVdA

dc A

dA

dc B

+11 + δ

δ

1 + δ

Derived in Equation B

Equation D

134

Solve For δ

Combining Equations A and D gives

dn

dc A

dn

dc B

+11 + δ

δ

1 + δRI

UVdA

dc A

dA

dc B

+11 + δ

δ

1 + δ=

dn/dcA, dA/dcA, dn/dcB, dA/dcB, RI and UV output all known….

Solve for δ and determine the dn/dccopolymer using equation A.

dn

dc copolymer

=RI

UVdA

dc A

dA

dc B

+11 + δ

δ

1 + δ

Equation D

135

Determination of Mwcopolymer & MwA

Conccopolymer = RI Output (mV)

KRI • dn/dc copolymer

Mwcopolymer = LS Output (mV)

KLS • (dn/dc)copolymer2 • Conccopolymer

Mwcopolymer = (1 + δ) • MwA

136

Example: PS/PMMA Copolymer Blend: 50:50

› PMMA 122K broad distribution

› PS 250K broad distribution

- 1 ,0

48 ,0

5 ,0

10 ,0

15 ,0

20 ,0

25 ,0

30 ,0

35 ,0

40 ,0

Response (

mV

)

11 ,50 20 ,80

Retention Volume ( mL )

12 ,6 13 ,3 14 ,0 14 ,7 15 ,4 16 ,1 16 ,8 17 ,5 18 ,2 18 ,9 19 ,6

Refractive Index

Ultra Violet

Low Angle Light Scattering

Viscometer DP

137

PS/PMMA Copolymer Blend :Total of Responses

RIHT = Height of RI Chromatogram

UVHT = Height of UV Chromatogram

ARI = RI Response Factor for Polymer A

BRI = RI Response Factor for Polymer B

AUV = UV Response Factor for Polymer A

BUV = UV Response Factor for Polymer B

HT A UV B UV

RIHT = CA ARI + CB BRI (1)

UVHT = CA AUV + CB BUV (2)

For each slice of data

138

PS/PMMA Copolymer Blend Calculation of true concentration profile

0,0

6,9 e-5

1,0 e-5

2,0 e-5

3,0 e-5

4,0 e-5

5,0 e-5

6,0 e-5

Conc P

S

0,0

6,9 e-5

1,0 e-5

2,0 e-5

3,0 e-5

4,0 e-5

5,0 e-5

6,0 e-5

Conc (

PS

+P

MM

A)

0 ,0

6,9 e-5

1,0 e-5

2,0 e-5

3,0 e-5

4,0 e-5

5,0 e-5

6,0 e-5

Conc P

MM

A

0 ,0

22 ,0

3,0

6,0

9,0

12 ,0

15 ,0

18 ,0

Refr

active Index R

esponse (

mV

)

11 ,50 20 ,80

Retention Volume (mL )

12 ,8 13 ,6 14 ,4 15 ,2 16 ,0 16 ,8 17 ,6 18 ,4 19 ,2

Conc PS

Conc (PS +PMMA)

Conc PMMA

Refractive Index

139

PS/PMMA Copolymer Blend dn/dc distribution

0,100

0,200

0,110

0,120

0,130

0,140

0,150

0,160

0,170

0,180

0,190

dn

/dc o

f C

op

oly

me

r

0,0

22,0

2,0

4,0

6,0

8,0

10,0

12,0

14,0

16,0

18,0

20,0

Re

fra

ctive

In

de

x R

esp

on

se

(m

V)

11,50 20,80

Retention Volume (mL)

12,6 13,2 13,8 14,4 15,0 15,6 16,2 16,8 17,4 18,0 18,6 19,2 19,8

dn/dc PS = 0.185

dn/dc PMMA = 0.084

][][B

BA

B

ABA

A

i dcdn

CC

C

dcdn

CC

C

dcdn ×

++×

+=

140

Copolymer Analysis - Summary of Results

› True RI concentration profile� difference in UV and RI response needed (UV1/UV2 or

RI/IR)

› dn/dc for each slice

› Co-polymer Mw

› % co-monomers (% A and B)

141

Some Selected Application Examples

Synthetic Polymers

� Polystyrene

� Polycarbonate

� HT-GPC - Polyolefins

Natural Polymers

� DNA

� Polysaccharides

� Maltodextrins (Polysaccharide)

142

Some Selected Application Examples

Synthetic Polymers

� Polystyrene

� Polycarbonate

� HT-GPC - Polyolefins

Natural Polymers

� DNA

� Polysaccharides

� Maltodextrins (Polysaccharide)

143

Comparison of calculated Mw values for Polystyrene

2005-10-08_19;37;32_AT_comb-ps_BPS_B108-1_01.vdt: Refractive Index

-43.03

-6.10

30.82

67.75

104.67

141.59

Re

fra

ctiv

e In

de

x (

mV

)

Retention Volume (mL)

0.10 3.59 7.08 10.57 14.06 17.55 21.04 24.53 28.02 31.51 35.00

Conventional Calibration (RI only)

720,000 140,000

910,000 144,000Triple Detection

144

Decrease in

Viscosity

Area

Star Viscosity

Star LS

Linear Viscosity

Linear LS

12.5 13.5 14.5 15.50

20

40

60

80

100

Retention Volume (mL)

Det

ecto

r R

espon

se

Equivalent

Molecular Weight

Areas

Decrease in Retention Volume (Rg)

Star Branched PolymersAt the same molecular weight,

a star branched polymer has a

much lower intrinsic viscosity.

The addition of the viscometer

provides a direct measurement

of size. The number of branches

(Bn) can then be determined.

PS PS-Star

Mw 100,000 100,000

IV(dL/g) 0.495 0.318

Rg(nm) 14 10

Equivalent Molecular WeightStar Branched PS Vs. Linear PS

145

Polycarbonates

Polycarbonates are used in many applications including CD/DVDs, automotive and electronics.

Polycarbonates can exhibit branching which will affect the material properties.

Two samples are analysed - one linear, one has a very small level of branching.

Can we quantify the branching?

146

Polycarbonates -Molecular weight comparison

Molecular Weight Distribution

PC 1 PC 2

3,00 3,40 3,80 4,20 4,60 5,00 5,40 5,80 0,00

0,20

0,40

0,60

0,80

1,00

1,20

1,40

Log(Molecular Weight)

Wf

/ [d

log

MW

]

147

Polycarbonates - Structural comparison

Mark-Houwink-Plot

PC 1 PC 2 Polystyrene

3,20 3,60 4,00 4,40 4,80 5,20 5,60 6,00 6,40 6,80-1,70

-1,40

-1,10

-0,80

-0,50

-0,20

0,10

0,40

0,70

Log(Molecular Weight)

Log(I

ntr

insi

c V

isco

sity

)

Log I

VLog MW

Linear

Branched

Expanded scale

148

Polycarbonates - Branching quantification

Number of Branches

4,20 4,40 4,60 4,80 5,00 5,20 5,40 5,60 0,00

0,40

0,80

1,20

1,60

2,00

2,40

2,80

Log(Molecular Weight)

Bn

Branching Frequency

4,20 4,40 4,60 4,80 5,00 5,20 5,40 5,60 0,50

0,70

0,90

1,10

1,30

1,50

1,70

1,90

2,10

2,30

2,50

Log(Molecular Weight)

Lam

bda

λ( )MRB

M

n=

R = 1000 D

149

The Light Scattering Clearly Shows a

High Molecular Weight Species

at 2 Hours Dissolution.

Dissolved 2 Hours 24 Hours

Mz 13,000,000 3,000,000

Mw 155,000 154,000

Mn 38,000 38,000

IV(dL/g) 0.283 0.483

Rg(nm) 10 12

Analysis of GelsThe RI Chromatogram does not

Show any Differences Between

Samples Dissolved for 2 Hours

Versus 24 Hours.

Viscometer Chromatogram

10.0 12.0 14.0 16.0 18.0 20.0

0.0

2.0

4.0

6.0

8.0

10.0

Retention Volume (mL)

Res

pon

se (

mV

)

Refractometer Chromatogram

0.0

2.0

4.0

6.0

8.0

10.0

Res

pon

se (

mV

)

Light Scattering Chromatogram

0.00

1.00

2.00

3.00

4.00

5.00

Res

pon

se (

mV

)

2 Hours

24 Hours

Dissolution Time

2 Hours

24 Hours

Dissolution Time

2 Hours

24 Hours

Dissolution Time

The Large Increase in Viscosity

From 2 to 24 Hours Suggests that

the Molecules Were Not Fully

Solvated at 2 Hours.

150

Polysaccharide Modification

Triple Chromatogramch2 RIch2 DPch2 LS

7.0 10.6 14.2 17.8 21.4 25.0-50

-10

30

70

110

150

Retention Volume (mL)

Rel

ativ

e R

esponse

GMPWxl x2

0.1M NaNO3+5%ACN

0.7ml/min

Mw = 32,500

IVw = 0.38

151

Polysaccharide Modification

Triple Chromatogramch3 RIch3 DPch3 LS

7.0 10.6 14.2 17.8 21.4 25.0-50

-10

30

70

110

150

Retention Volume (mL)

Rel

ativ

e R

esp

on

se

GMPWxl x2

0.1M NaNO3+5%ACN

0.7ml/min

Mw = 139,000

IVw = 0.74

152

Mark-Houwink Plot

CH2 IV LSCH3 IV LS

3.50 4.00 4.50 5.00 5.50 6.00 6.50-1.50

-0.88

-0.25

0.38

1.00

Log(Molecular Weight)

Log[I

ntr

isic

Vis

cosi

ty]

a = 0.699

a = 0.927

Polysaccharide Modification

153

Triple Chromatogramch2 RIch2 DPch2 LS

7.0 10.6 14.2 17.8 21.4 25.0-50

-10

30

70

110

150

Retention Volume (mL)

Rel

ativ

e R

esp

on

se

Triple Chromatogramch3 RIch3 DPch3 LS

7.0 10.6 14.2 17.8 21.4 25.0-50

-10

30

70

110

150

Retention Volume (mL)

Rel

ativ

e R

esp

on

se

Polysaccharide

The difference in chain

stiffness can be clearly

seen in both the raw

chromatograms and

the M-H plot

Mark-Houwink Plot

3.50 4.00 4.50 5.00 5.50 6.00-2.00

-1.25

-0.50

0.25

1.00

Log(Molecular Weight)

Lo

g[I

ntr

isic

Vis

cosi

ty]

154

Any questions?

155