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The van Hove distribution function for Brownian hard spheres: Dynamical test particle theory and computer simulations for bulk dynamics.
journal contributionposted on 2017-08-14, 13:57 authored by Paul Hopkins, Andrea Fortini, Andrew ArcherAndrew Archer, Matthias Schmidt
We describe a test particle approach based on dynamical density functional theory (DDFT) for studying the correlated time evolution of the particles that constitute a fluid. Our theory provides a means of calculating the van Hove distribution function by treating its self and distinct parts as the two components of a binary fluid mixture, with the “self ” component having only one particle, the “distinct” component consisting of all the other particles, and using DDFT to calculate the time evolution of the density profiles for the two components.We apply this approach to a bulk fluid of Brownian hard spheres and compare to results for the van Hove function and the intermediate scattering function from Brownian dynamics computer simulations. We find good agreement at low and intermediate densities using the very simple Ramakrishnan–Yussouff [Phys. Rev. B 19, 2775 (1979)] approximation for the excess free energy functional. Since the DDFT is based on the equilibrium Helmholtz free energy functional, we can probe a free energy landscape that underlies the dynamics. Within the mean-field approximation we find that as the particle density increases, this landscape develops a minimum, while an exact treatment of a model confined situation shows that for an ergodic fluid this landscape should be monotonic. We discuss possible implications for slow, glassy, and arrested dynamics at high densities.
P.H. thanks the EPSRC for funding under Grant EP/E065619/1 and A.J.A. gratefully acknowledges financial support from RCUK M.S. and A.F. thank the DFG for support via SFB840/A3.
- Mathematical Sciences
Published inJ. Chem. Phys.
PagesArt.No. 224505 - ?
CitationHOPKINS, P. ...et al., 2010. The van Hove distribution function for Brownian hard spheres: Dynamical test particle theory and computer simulations for bulk dynamics. Journal of Chemical Physics , 133: 224505.
Publisher© the Authors. Published by AIP
- VoR (Version of Record)
Publisher statementThis work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/
NotesThis article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. The following article appeared in HOPKINS, P. ...et al., 2010. The van Hove distribution function for Brownian hard spheres: Dynamical test particle theory and computer simulations for bulk dynamics. Journal of Chemical Physics , 133: 224505. and may be found at http://dx.doi.org/10.1063/1.3511719