Non-invertibility of Multiple-Scattered QELSS Spectra

TL;DR

This paper demonstrates the fundamental impossibility of inverting multiple-scattering quasielastic light scattering spectra to retrieve single-scattering information in complex viscoelastic fluids, highlighting limitations in data interpretation.

Contribution

It establishes the non-invertibility of multiple-scattering spectra to single-scattering spectra in complex fluids, clarifying what information is lost and under what conditions inversion is possible.

Findings

Inversion of f_m(t) to f_1(q,t) is fundamentally impossible in complex viscoelastic fluids.

f_1(q,t) depends on all even moments of particle displacement, which are lost in multiple scattering.

In simple fluids with known f_1(q,t), inversion from f_m(t) is possible, but only due to prior knowledge.

Abstract

We consider the spectrum S(q,t) and field correlation function f(q,t) of light quasielastically scattered from diffusing optical probes in complex viscoelastic fluids. Relationships between the single-scattering f_1(q,t) and the multiple-scattering f_m(t) are examined. We show that it is fundamentally impossibly to invert f_m(t) to obtain f_1(q,t) or particle displacement moments <X^{2n}>, except with assumptions that are certainly not correct in complex, viscoelastic fluids. For diffusing dilute probes in viscoelastic fluids, f_1(q,t) is determined by all even moments <X^{2n}>, n > 0$, of the particle displacement X; this information is lost in f_m(t). In the special case of monodisperse probes in a true simple fluid, f_1(q,t) can be obtained from f_m(t), but only because the functional form of f_1(q,t) is already known.