Long-time behavior of the angular velocity autocorrelation function

Abstract

In this Communication we present a hydrodynamic analysis to show that the asymptotic long-time tail of the angular velocity autocorrelation function of a Brownian particle is independent of the particle’s size or shape—a result in agreement with simulation and in accord with previous predictions from microscopic theories. The reason that earlier hydrodynamic treatments had predicted a shape dependent tail is because they implicitly assumed the particle to have a fixed orientation. Reorientation of the particle must be included to obtain the true long-time behavior.

Comment on “Long-time behavior of the angular velocity autocorrelation function” [J. Chem. Phys. 105, 9695 (1996)]

“…7 In our opinion, in the light of the above remarks on Ref. 4, a revision of the theory of the nonlinear effect would be desirable.…”

“…Finally, we note that the computer simulation 6 and the calculation by Masters 4 are for a lattice Boltzmann fluid for which the linearized hydrodynamic equations apply. The nonlinear effects for this system are due only to the kinematics of rigid body motion.…”

Response to “Comment on ‘Long time behavior of the angular velocity autocorrelation function’ ” [J. Chem. Phys. 107, 291 (1997)]

“…According to simulation results, 1,2 microscopic theory, 3,4 and the hydrodynamic analysis 5 now under discussion, the asymptotic long-time tail of the angular velocity autocorrelation function ͑AVACF͒ of a nonspherical Brownian particle is independent of particle shape. Only in the artificial case of a Brownian particle with zero rotational diffusion constant does one find a shape-dependent tail.…”

“…We argue, on the contrary, that particle reorientation plays a crucial role in the linear regime. To see this, we must first recall that the angular velocity that appears in the kind of hydrodynamic analysis under discussion [5][6][7] is really the expectation value of angular velocities taken from a nonequilibrium distribution ͑though close to equilibrium so that linear response holds true͒. We now consider a Brownian particle in thermal equilibrium with the fluid and thus with a Maxwellian distribution of angular velocities.…”

“…The first contribution is indeed nonlinear in angular velocity and thus was not included in the hydrodynamic analysis. 5 The second contribution, however, which is present even for zero initial angular momentum, must be included in a linear theory of the AVACF or, equivalently, in a theory of the relaxation function in the linear regime. This is precisely the analysis performed in Ref.…”