10 Size-Exclusion Chromatography with Light-Scattering Detection Downloaded by UNIV OF CALIFORNIA SAN DIEGO on March 16, 2017 | http://pubs.acs.org Publication Date: May 5, 1995 | doi: 10.1021/ba-1995-0247.ch010
at Two Angles Polystyrene in Tetrahydrofuran T h o m a s H. M o u r e y a n d H a n s
Coll
A n a l y t i c a l T e c h n o l o g y D i v i s i o n , Research Laboratories B-82, E a s t m a n K o d a k C o m p a n y , Rochester, NY 1 4 6 5 0 - 2 1 3 6
A method for the analysis of data from a size-exclusion chromatography (SEC) detector that measures elastic light-scattering intensities at two angles (15° and 90°) is evaluated for linear polystyrenes in tetrahydrofuran (THF). Over certain size ranges a single detector can be used to calculate molecular weights by assuming the particle-scattering function to be unity. The 90° scattering is useful for isotropic scatterers less than ~70,000 MW and the 15° scattering for polystyrenes less than ~500,000 MW. For anisotropic scatterers, the ratio of scattering intensities at the two angles is used to calculate the particle scattering function and root-mean-square radius, assuming a specific polymer shape (e.g., random coil). Scattering at the low angle and the particle-scattering function are then used to calculate weight-average molecular weights. It is shown that the assumption of shape has only a minor effect on the calculation of polymer sizes in the size range fractionated by common SEC columns. Accuracy and precison of measured radii are greatly affected by detector noise on the ratioing method, insensitivity of the light-scattering detector to small molecules in broad polymer distributions, interdetector volume, and data fitting. However, one method that uses the ratio of areas of the light-scattering signals alone calculates with high precision and accuracy an average radius that corresponds most closely to a z-average.
^ELASTIC L I G H T - S C A T T E R I N G D E T E C T I O N for size-exclusion chromatography (SEC) has evolved in two directions: low-angle laser light scattering 0065-2393/95/0247-0123$12.00/0 © 1995 American Chemical Society
Provder et al.; Chromatographic Characterization of Polymers Advances in Chemistry; American Chemical Society: Washington, DC, 1995.
124
CHROMATOGRAPHIC CHARACTERIZATIONOF POLYMERS
( L A L L S ) i n w h i c h measurements are made at a single angle, typically less than 7° (1,2); and multiangle laser light scattering ( M A L L S ) , w h i c h measures scattered light at angles typically between ~ 1 5 ° and 160° (3,4). T h e low angle of L A L L S approximates the zero-angle scattering intensity^Jthus simplifying calculation of the weight-average molecular weight, M . M A L L S relies on graphical methods to obtain intercepts and limiting (zero-angle) slopes of D e b y e (or related) plots, resulting i n M and, for large polymers, the z-average of the root-mean-square radius of gyration, r . B o t h methods have strengths and weaknesses. S i m u l taneous measurement of light-scattering intensities at two angles (in this case 15° and 90°) is a compromise between the two techniques. It does require, however, a different approach to data analysis than is currently used for L A L L S and M A L L S detectors. A n appreciation for the differ ences can be gained from an overview of conventional light-scattering data analysis methods for S E C light-scattering detectors. w
w
Downloaded by UNIV OF CALIFORNIA SAN DIEGO on March 16, 2017 | http://pubs.acs.org Publication Date: May 5, 1995 | doi: 10.1021/ba-1995-0247.ch010
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Theory L o c a l P r o p e r t i e s . " L o c a l p r o p e r t i e s " are values such as detector response, molecular weight, or polymer size at a particular retention volume of a size-exclusion chromatogram. T h e y are denoted by the sub script i. T h e excess Rayleigh scattering, R^, at each retention volume v of an S E C is related to the concentration at each retention volume, c and angle, 0, by {
i9
Kci
1
/ 1 X
P(B)i is the particle scattering function and A » is the second virial coef ficient at each retention volume. M is molecular weight at each reten tion volume and is a weight average i f molecules of more than one mo lecular weight elute at the same retention volume. R is measured by the light-scattering detector and c is obtained from an independent concentration detector such as a differential refractive index (DRI) de tector. Κ is the optical constant for light-scattering intensity perpendic ular to the plane of polarized incident light, 2
WI
E I
{
where η is the refractive index of the solvent, dn/dc is the polymer specific refractive index increment, λ is the wavelength of light i n vac u u m , and N is Avogadro's number. F o r the collection of scattered light 0
A
Provder et al.; Chromatographic Characterization of Polymers Advances in Chemistry; American Chemical Society: Washington, DC, 1995.
10.
125
SEC with LS Detection
MOUREY & C O L L
through an annular opening, such as i n L A L L S instruments, the optical constant for plane-polarized incident light is
Downloaded by UNIV OF CALIFORNIA SAN DIEGO on March 16, 2017 | http://pubs.acs.org Publication Date: May 5, 1995 | doi: 10.1021/ba-1995-0247.ch010
y
2 7 r B ( d n / d e ) ( l + cos β) 2
2
2
2
/ 0
,
Κ is the same as for unpolarized incident light w i t h a fixed-point detector. T h e second and higher concentration terms of equation 1 are usually negligible at the low concentrations used i n S E C . In this case, M
·»
(4)
R(H
A t low angles, the particle-scattering function approaches unity even for relatively large particle (polymer) sizes, further simplifying the cal culation of molecular weights using equation 4. A t higher angles, Ρ(θ) is commonly given i n the form of a power series i n s i n 0/2, w h i c h for ^ = 0 leads to the familiar result used i n the reciprocal scattering plots of Z i m m (5). 2
