On the Gaussian approximation in colloidal hard sphere fluids.

Alice L Thorneywork,Dirk G A L Aarts,Roel P A Dullens,Jürgen Horbach

doi:10.1039/c5sm03049h

Alice L Thorneywork, Dirk G A L Aarts + Show 2 more

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https://doi.org/10.1039/c5sm03049h

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Abstract

We study the behaviour of the self-intermediate scattering function and self-van Hove correlation function for quasi-two-dimensional colloidal hard sphere fluids at a range of area fractions. We compute these functions first directly from the particle coordinates and secondly from the mean squared displacement via the Gaussian approximation. This allows us to test the validity of this approximation over a range of length and time scales, where we find that the Gaussian approximation holds if the hydrodynamic limits are appropriately probed. Surprisingly, only small deviations from Gaussian behaviour are seen at intermediate times, even for dense fluids. We next consider these deviations from Gaussian behaviour firstly via the non-Gaussian parameter and secondly by considering the relaxation times of the intermediate scattering function. From these measurements we develop a scaling relation in order to directly determine the combinations of wavevectors and times at which the non-Gaussian behavior is seen. This allows for the clear identification of the hydrodynamic regimes and thus provides new insight into the crossover between long- and short-time self-diffusion.

Highlights

Scattering techniques have long played an important role in the study of complex fluids, where they have been used to probe a wide range of phenomena related to the structure and dynamics of systems such as colloidal fluids, polymer solutions or proteins in membranes.[1,2,3,4,5,6,7,8] In scattering experiments, the central dynamic quantity is the intermediate scattering function (ISF), F(k,t) with k the wavevector, which is directly related to the fluctuations in the intensity of the scattered light as a function of time.[9]
The conversion between the self-ISF obtained from scattering measurements and the mean squared displacement (MSD) requires the use of the Gaussian approximation.[10,11]
For the system at f = 0.66, slower decay of Fs(k,t) at a particular value of k is seen when compared to the system at f = 0.08. This is consistent with the smaller particle displacements and slower particle motion seen at higher f in the MSDs

Summary

Introduction

Scattering techniques have long played an important role in the study of complex fluids, where they have been used to probe a wide range of phenomena related to the structure and dynamics of systems such as colloidal fluids, polymer solutions or proteins in membranes.[1,2,3,4,5,6,7,8] In scattering experiments, the central dynamic quantity is the intermediate scattering function (ISF), F(k,t) with k the wavevector, which is directly related to the fluctuations in the intensity of the scattered light as a function of time.[9]. The conversion between the self-ISF obtained from scattering measurements and the MSD requires the use of the Gaussian approximation.[10,11] This assumes that the self-ISF is Gaussian and related to the MSD as

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