Light Scattering: Solutions of polymers
The solute no longer acts as a point source when it a polymer.
Light scattering from different parts of the same molecule is no longer in phase.
The scattering envelope, PC Fig. 10.8, becomes asymmetric, because destructive interference is more important for backward than for forward scattering, PC Fig. 10.9.
The particle scattering factor, P(theta), takes account of the influence of the size and shape of the solute,
K(1 + cos2 theta)c/Rtheta = (1/MwP(theta)) (1 + 2 gamma2c + ....)
K = (2 pi2n02/L lambda4) (d n/d c)2
with L denoting Avogadro's number.
Truncating the expression for P(theta) after the first term yields
2Kc/Rtheta = (1/MwP(theta)) (1 + S sin2(theta / 2))
where S is related to the mean square radius of gyration.
Two types of applications are common in polymer science.
- The measurement can be performed at a single very low angle, so that one can tolerate the errors made in assuming cos theta = 1 and sin2 (theta/2) = 0.
This approach is frequently used for estimation of Mw.
- Measurements over a series of angles, for solutions with a series of concentration.
- For a solution of given concentration, an intercept of 1/Mw at sin2 (theta/2) = 0 is obtained in a plot of K(1 + cos2 theta)c/Rtheta vs. sin2 (theta/2).
The slope provides information about the mean square radius of gyration.
- For measurements at a given angle, an extrapolation to c = 0 yields 1/Mw, and the slope provides information about the second virial coefficient.
- In practice the total data set is used, permitting a double extrapolation using a Zimm plot, PC Fig. 10.10.
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July 2, 1999
Wayne L. Mattice: wlm@polymer.uakron.edu