Response to “Rotational velocity autocorrelation function of interacting Brownian particles”

Abstract

In their paper, Cichocki and Felderhof re-analyse our numerical data for the angular velocity autocorrelation function (AVACF), CR(t), for colloidal hard spheres [1] in a concentrated suspension. They treat the normalized correlation function as a response function R(), where =t=M and M is the integral over all times of the normalized AVACF. For a single colloidal sphere, the Laplace transform of R() can be calculated analytically [2]. The denominator can be written in terms of the transform variable and the inverse of a polynomial involving the square root of the transform variable. In the time domain, the latter gives rise to the long time behaviour of the correlation function. Cichocki and Felderhof make the ad hoc approximation that, in a suspension, the Laplace transform of the AVACF takes a similar form. However, the inverse polynomial is replaced by the ratio of two polynomials whose coecients are treated as adjustable parameters. They determine these parameters by tting to our numerical data. At zero frequency their relaxation function is constructed to have a value of unity. In the time domain, this means that the integral over time of their t is constrained to be equal to M. Their tting procedure therefore requires a value for M as input. This value can nonetheless be calculated from the numerical data. Having carried out this procedure, Cichocki and Felderhof’s t appears rather poor at short times (t<20), but adequately describes our data over the remainder of the time interval we studied. However, their method suggests that, at longer times than those simulated, the decay of the correlation function is somewhat dierent to that postulated by ourselves. Before we address this substantive point, let us address the question of the integral of the normalized correlation function, M. This, as Cichocki and Felderhof point out, is related to the rotational diusion coecient DR. For this particular volume fraction (=0:2), we quoted a value ofDR=0:85D 0 , with an upper limit of 4% for the numerical error. Here D 0 R is the Debye{Einstein rotational diusion coecient, valid in the dilute