Parameters Affecting the Accuracy of Molar Mass Distribution Determined

by SEC with a MALS Detector

Stepan Podzimek 1SYNPO

2University of Pardubice 3Wyatt Technology Europe stepan.podzimek@synpo.cz

Outline

o Multi-angle light scattering (MALS) as an absolute method of molar mass determination

o Principle of SEC-MALS o Parameters affecting the MMD by SEC-MALS

• Quantities of the light scattering equation • Performance of separation • Sample preparation

Basic Light Scattering Equation

( ) ( )θθθ 222* 2 PcMAMP

cKR

−=

Rθ Excess Rayleigh ratio (light scattering intensity related to the intensity of incident light, scattering volume and its distance from the detector) at angle θ

n0 refractive index of the solvent NA Avogadro’s number λ0 vacuum wavelength of the incident light dn/dc specific refractive index increment (constant for given polymer and solvent) c concentration of the polymer molecules (g/mL) M molar mass, weight-average (Mw) in case of polydisperse polymers A2 second virial coefficient (polymer‒solvent interactions) P(θ) particle scattering function, P(0) = 1

Alternative light scattering formalisms:

2

40

20

2* 4

=

dcdn

NnK

Aλπ

( ) cAMPR

cK2

*

21+=

θθ ( ) ( )θθθ

MPcAMPR

cK2

*

21+=

Determination of M and R by SEC-MALS

Extrapolation of light scattering intensities at elution volume of 33.9 mL for broad polyethylene NIST 1475a PE standard.

0.0 0.2 0.4 0.6 0.8 1.04.5x10-6

4.8x10-6

5.1x10-6

5.4x10-6

5.7x10-6

sin2(θ/2)

K* c/R(θ)

M = 218,000 g/molR = 30.8 nm

25 30 35 40 45 50 55

0.0

0.2

0.4

0.6

0.8

1.0

Rela

tive

Scal

e

Volume (mL)

m0 slope at zero θ R0 intensity at zero θ M molar mass R radius of gyration

( ) cAMPR

cK2

*

21+=

θθ

21

2

20

1

20

*

1632

=

−=

−

πλ MmR cA

RcKM

Light scattering is an absolute method of molar mass determination

Rayleigh ratio ≈ Molar mass …but it does not mean it is necessarily correct

Light Scattering Equation

Light Scattering Equation

( ) ( )θθθ 222* 2 PcMAMP

cKR

−=

2

40

20

2* 4

=

dcdn

NnK

Aλπ

Parameters to consider o Rayleigh ratio o Specific refractive index increment dn/dc o Concentration c o The second virial coefficient A2 (in SEC mode neglecting the A2

mostly results in negligible errors)

Rayleigh Ratio: MALS Detector Calibration

Calibration of MALS ≈ determination of instrumental constant that allows conversion of voltage to Rayleigh ratio:

Rayleigh ratio ≈ calibration constant × voltage

1. Liquid of known Rayleigh ratio established by a fundamental physical procedure 2. Polymer standard of know molar mass:

2

40

20

2* 4

=

dcdn

NnK

Aλπ

( )

1

2* 21

−

+= cA

MPcKR

θθ

Specific Refractive Index Increment (dn/dc)

2

40

20

2* 4

=

dcdn

NnK

Aλπ( ) ( )θθθ 22

2* 2 PcMAMPcK

R−=

dcdnsignalsignalc baselinei

i−

=α

o N % error of dn/dc ≈ 2 N % error of molar mass in batch MALS

o N % error of dn/dc ≈ N % error of molar mass in SEC-MALS

Determination of dn/dc

0.0 4.0x10-4 8.0x10-40.0

5.0x10-5

1.0x10-4

1.5x10-4

2.0x10-4

Diffr

entia

l RI

Concentration (mg/mL)

Determination of dn/dc by direct injection of solutions of various concentration in the differential refractive index detector.

Concentration: RI Detector Calibration

dcdnsignalsignalc baselinei

i−

=α

α calibration constant of refractive index (RI) detector, RIU/V alternative concentration sensitive detectors are UV or infrared dn/dc specific refractive index increment

N % error of α ≈ N % error of molar mass

RI Detector Constant Verification

1. Crosscheck with UV detector: Polymer with reliably known extinction coefficient (PS, proteins)

2. Crosscheck with batch measurement (Zimm plot)

sin²(ϴ/2) + kc-0.5 0.0 0.5

K*c/

R(ϴ

)

-63.4x10

-63.6x10

-63.8x10

-64.0x10

Mw = (303 ± 3) × 103 g/mol

15 20 25 30 35 40104

105

106

Time (min)M

olar

Mas

s (g

/mol

)

Mw = (296 ± 3) × 103 g/mol

Performance of SEC Separation Important for MM distribution

Poor SEC Separation

Molar mass versus retention time plots of branched polystyrene determined by SEC-MALS and AF4-MALS. RI signals are overlaid here.

20 30 40 50104

105

106

107

Time (min)M

olar

Mas

s (g

/mol

)

AF4

8 10 12 14 16 18

105

106

107

Time (min)

Mol

ar M

ass

(g/m

ol)

SEC

Impact of Abnormal SEC Elution on MMD

Cumulative molar mass distribution of branched polystyrene determined by SEC-MALS and AF4-MALS.

104 105 106 1070.0

0.2

0.4

0.6

0.8

1.0

SEC-MALS AF4-MALSMn = 149,000 / 124,000 g/mol

Mw = 475,000 g/mol / 631,000 g/mol

Mz = 2.1 x 106 g/mol / 6.8 x 106 g/mol

Cum

ulat

ive W

eigh

t Fra

ctio

n

Molar Mass (g/mol)

8 10 12 14 16 18

105

106

107

Time (min)

Mol

ar M

ass

(g/m

ol)

SEC

Shearing Degradation Makes Polymers Alike

Rubber Mw (103 g/mol)

SEC-MALS AF4-MALS

1 320 320

2 340 460

3 370 720

4 340 1140

o SEC packing particle size (3, 5, 10, 20, 30 µm; shearing degradation versus performance); sub-3 µm APC columns

o Asymmetric flow field flow fractionation (AF4) as more gentle separation technique

Sample Preparation Solubility, filtration, dissolution method

Partial Solubility Rubber A Rubber C

Partial Solubility

Dissolution of 0.5 g of natural rubber in Soxhlet. Sample solubility ≈ 45 %.

Sample Filtration

Distribution curves of PBD determined by AF4-MALS: sample filtration with 1 µm filter versus 5 µm filter.

Filter (µm) Mn (103 g/mol) Mw (103 g/mol) Mz (103 g/mol)

1 130 610 3620

5 130 860 7310

104 105 106 1070.0

0.2

0.4

0.6

0.8

1.0

Cum

ulat

ive W

eigh

t Fra

ctio

n

Molar Mass (g/mol)

Sample Dissolution

105 106 1070.0

0.2

0.4

0.6

0.8

1.0

Cum

ulat

ive W

eigh

t Fra

ctio

n

Molar Mass (g/mol)Solid acrylics: ten minutes sonication in THF drastically decreases molar mass due to shear degradation. Mw (no sonication) = 4.9 × 106 g/mol (sample dissolved overnight) Mw (10 min sonication) = 2.2 × 106 g/mol

Conclusions / Final Remarks

MALS detector provides absolute molar mass … that is as absolute as …

1. MALS calibration: liquid versus polymer standard

2. Molar mass is as absolute as absolute is the concentration, i.e.., as the RI detector calibration constant is accurate

3. Molar mass is as absolute as absolute is dn/dc

4. Molar mass distribution is affected by poor SEC separation (anchoring of branched polymers, interaction with column packing) and shearing degradation; alternative separation by FFF

5. Sample solubility

6. Sample preparation (avoid vortex, ultrasonic bath, intensive stirring)

7. Sample filtration