Persistent Anti-Correlations in Brownian Dynamics Simulations of Dense Colloidal Suspensions Revealed by Noise Suppression

Transport properties of a hard-sphere colloidal fluid are investigated by Brownian dynamics simulations. We implement a novel algorithm for the time-dependent velocity-autocorrelation function (VACF) essentially eliminating the noise of the bare random motion. The measured VACF reveals persistent anti-correlations manifested by a negative algebraic power-law tail $t^{-5/2}$ at all densities. At small packing fractions the simulations fully agree with the analytic low-density prediction, yet the amplitude of the tail becomes dramatically suppressed as the packing fraction is increased. The mode-coupling theory of the glass transition provides a qualitative explanation for the strong variation in terms of the static compressibility as well as the slowing down of the structural relaxation.

Figure 1

(a) Mean-square displacement $⟨\mathrm{\Delta }\mathbf{R}(t{)}^2⟩$ of monodisperse Brownian hard spheres for various packing fractions $\phi$. Inset: Long-time diffusion coefficients $D^{(s)}$ vs packing fraction. (b) Each term in Eq. (3) for packing fractions $\phi =0.005$ (solid lines) and $\phi =0.25$ (dashed lines).

Figure 2

Log-log plot of the reduced VACF of monodisperse Brownian hard spheres for increasing packing fraction $\phi$. Symbols represent simulation data. The black solid line is the exact low-density expansion, Eq. (5). The colored dashed lines are fits to the power-law tails. The dashed black line labeled $t^{-5/2}$ is added as guide to the eye. Inset: Prefactor of the tail vs packing fraction.

Figure 3

Mode-coupling-theory results for the reduced VACF $Z(t)/\phi$ for packing fraction $\phi$ with Percus-Yevick closure such that the diffusion coefficients match the simulation results. The short-dashed line indicates a power law $t^{-5/2}$ and serves as a guide to the eye. The long-dashed line corresponds to the weak-coupling approximation (w.c.a.) and is virtually on top of the MCT result for the lowest packing fraction. Inset: Prefactor of the tail vs packing fraction.