1302.7009 (George D. J. Phillies)

Interpretation of Quasielastic Scattering Spectra of Probe Species in
Complex Fluids    [PDF]

George D. J. Phillies

The objective of this paper is to correct a substantial, widespread error in parts of the quasielastic scattering literature. This error leads to entirely erroneous interpretations of quasielastic scattering spectra. The error, which is most prominent for interpreting spectra of dilute probe particles diffusing in complex fluids, arises from a valid calculation that is being invoked under circumstances in which its primary assumptions are incorrect. Quasielastic scattering from dilute probes yields the incoherent structure factor g^(1s)(q,t) = < \exp(i q \Delta x(t)) >, with q being the magnitude of the scattering vector {\bf q} and \Delta x(t) being the probe displacement parallel to {\bf q} during a time interval t. The error is the claim that g^(1s)(q,t) for dilute probe particles uniformly reduces to \exp(- q^2 <(\Delta x(t))^2 >/2), regardless of the nature of the surrounding medium. If true, this claim would allow one to use quasielastic scattering to determine the time-dependent mean-square probe displacements in complex fluids. In reality, g^(1s)(q,t) is determined by all even moments <(\Delta x(t))^(2n) > for n = 1, 2, 3, ..., of the displacement distribution function P(\Delta x,t). Only in the very special case of monodisperse probes in a simple Newtonian solvent is g^(1s)(q,t) entirely determined by <(\Delta x(t))^{2}>. Furthermore, the Langevin equation approach that ties g^(1s)(q,t) to <(\Delta x(t))^2 > also requires with equal certainty that g^(1s)(q,t) relaxes as a simple exponential \exp(- \Gamma t), \Gamma being a time-independent constant. Contrariwise, if the spectrum is not a simple exponential in time, g^(1s)(q,t) is not determined by <(\Delta x(t))^{2}>. Several related subsidiary errors are discussed.

View original: http://arxiv.org/abs/1302.7009