Parameters Affecting the Accuracy of Molar Mass ......Parameters Affecting the Accuracy of Molar...
Transcript of Parameters Affecting the Accuracy of Molar Mass ......Parameters Affecting the Accuracy of Molar...
Parameters Affecting the Accuracy of Molar Mass Distribution Determined
by SEC with a MALS Detector
Stepan Podzimek 1SYNPO
2University of Pardubice 3Wyatt Technology Europe [email protected]
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
( ) ( )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
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 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