Memory function moment analysis of dynamic light scattering data

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Abstract
The author considers the problem of obtaining long-time diffusivities DL(k) from dynamic light scattering data for suspensions of spherical particles. Starting from the integro-differential memory equation for the intermediate scattering function F(k,t), the author derives an infinite-order linear differential equation for F(k,t) with coefficients mu n(t) expressed as finite-time moments of the memory function. The author obtains an exact analytic representation of these moments for a model suspension of flow-density hard spheres; numerical results for the moments in this model suspension are presented for a range of values of wavenumber and time. The numerical study shows that at short or intermediate times t one may neglect all but the low-order moments leading to a simplified differential equation for F(k,t). At intermediate times this differential equation may be inverted to obtain the lowest moment mu 0(t) in terms of the experimentally measured slope of ln F(k,t). The numerical study of the moments for the hard-sphere system indicates that even at quite short times mu 0(t) gives an accurate estimate of mu 0( infinity ) from which the diffusivities DL(k) can be obtained.

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