Interpretation of Quasielastic Scattering Spectra of Probe Species in Complex Fluids

The objective of this paper is to correct an error in analyses of quasielastic scattering spectra. The error invokes a valid calculation under conditions in which its primary assumptions are incorrect, resulting in misleading interpretations of spectra. Quasielastic scattering from dilute probes yields the incoherent structure factor g^(1s)(q,t) = <exp(i q Dx(t))>, with q being the magnitude of the scattering vector q and Dx(t) being the probe displacement parallel to q during a time interval t. The error is a claim that g^(1s)(q,t) ~ exp(- q^2 <(Dx(t))^2> /2) for probes in an arbitrary solution, leading to the incorrect belief that <(Dx(t))^2 > of probes in complex fluids can be inferred from quasielastic scattering. The actual theoretical result refers only to monodisperse probes in simple Newtonian liquids. In general, g^(1s)(q,t) is determined by all even moments <(Dx(t))^(2n) >, n = 1, 2, 3,… of the displacement distribution function P(Dx,t). Correspondingly, <(Dx(t))^2

cannot in general be inferred from g^(1s)(q,t). The theoretical model that ties g^(1s)(q,t) to <(Dx(t))^2 > also quantitatively determines exactly how <(Dx(t))^2> /2 must behave, namely <(Dx(t))^2 > must increase linearly with t. If the spectrum is not a single exponential in time, g^(1s)(q,t) does not determine <(Dx(t))^2>.