Theory of light scattering from a system of interacting Brownian particles

W. Hess and R. Klein

Physica A: Statistical Mechanics and its Applications, 1976, vol. 85, issue 3, 509-527

Abstract: Starting from a N-particle diffusion equation for a system of N interacting spherical Brownian particles, a non-linear transport equation for concentration fluctuations δc(r, t) of the particles is derived. This dynamic equation is transformed into a hierarchy of equations for retarded propagators of increasing numbers of concentration fluctuations. A cluster expansion to lowest order in the average concentration results in a set of two coupled equations. The spectrum of light scattered by the interacting particles is in general not a Lorentzian, due to the non-linear term in the transport equation. For small scattering wave vectors k the width is D(ω)k2, where ω is the transferred frequency. It is shown that D(0) = De, the effective diffusion coefficient. For a hardcore interaction potential the spectrum is Lorentzian and it is found that De = D0(1 + φ), where D0 is the diffusion constant for independent particles and φ the volume concentration of Brownian particles.

Date: 1976
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:85:y:1976:i:3:p:509-527

DOI: 10.1016/0378-4371(76)90022-4

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