Light scattering from dilute macromolecular solutions

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Abstract
The polarized light scattering spectrum from a dilute solution of spherical macromolecules is customarily interpreted on the basis of independent particle diffusion. However, it is known that diffusion in such a system is governed by a many particle diffusion equation with cross-diffusion coefficients Dij that depend on the inverse distance between all pairs of particles (i, j). Here we prove that the spectrum from the system described by the N-particle diffusion equation is identical to the spectrum obtained from the simple, but incorrect, independent particle diffusion model. The physical reason for this suprising simplication is that the Dij are proportional to Oseen's tensor which holds for an incompressible fluid and hence has no longitudinal part. When short-range forces are taken into account as well as the long-range hydrodynamic interaction present in Dij, it is possible to obtain simple approximate expression for a k-dependent effective diffusion constant Deff(k). This expression is evaluated for the case where the macromolecules are treated as hard spheres and one obtains Deff(k) = D0[1 + 2.0φ] for low k where φ is the volume fraction of macromolecules in solution.

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