Interpretation of Quasielastic Scattering Spectra of Probe Species in Complex Fluids

TL;DR

This paper corrects a common misconception in quasielastic scattering analysis, emphasizing that the incoherent structure factor relates to all even moments of probe displacement, not just the mean square displacement, especially in complex fluids.

Contribution

It clarifies the theoretical relationship between the structure factor and displacement moments, correcting prior assumptions and providing a more accurate framework for interpreting scattering spectra in complex fluids.

Findings

g^(1s)(q,t) depends on all even moments of displacement

<Dx(t)^2> cannot be directly inferred from spectra in complex fluids

g^(1s)(q,t) is a single exponential only in simple Newtonian liquids

Abstract

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>.