Dynamic decay and superadiabatic forces in the van Hove dynamics of bulk hard sphere fluids

Abstract

We study the dynamical decay of the van Hove function of Brownian hard spheres using event-driven Brownian dynamics simulations and dynamic test particle theory. Relevant decays mechanisms include deconfinement of the self particle, decay of correlation shells, and shell drift. Comparison to results for the Lennard-Jones system indicates the generality of these mechanisms for dense overdamped liquids. We use dynamical density functional theory on the basis of the Rosenfeld functional with self interaction correction. Superadiabatic forces are analysed using a recent power functional approximation. The power functional yields a modified Einstein long-time self diffusion coefficient in good agreement with simulation data.

Perspective: How to overcome dynamical density functional theory

“…We have restricted our discussion to a single and relatively easily accessible type of nonequilibrium dynamics, that of stationary uniaxial compressional flow that represents a model steady (batch) sedimentation situation. The power functional approach allows to go much further, including the treatment of viscoelasticity [57], as arising from superadiabatic memory, deconfinement under shear [58], the dynamic decay of the van Hove pair correlation function as governed by drag, viscous and structural forces [69,70], and the complex forms of both flow and structural forces that arise under spatially complex forms of driving [60]. Time-dependent uniaxial flow is relevant in a variety of situations, including colloidal stratification [119,120] and sedimentation [121].…”

“…The concept was originally formulated as an approximation within DDFT [63,64] and formally exactly within power functional theory [67]. Two-body superadiabatic effects were shown via simulation work to be significant [68][69][70] and they arise naturally in an exact formulation of the test particle dynamics [67]. The test particle limit allowed for a rationalization of the dynamical pair structure as e.g.…”

“…Even simple mathematical model forms for the nonequilibrium contribution to the power functional, such as equations ( 16) and ( 17), already capture essential physics (as we demonstrate below) and dynamical two-body correlation functions are accessible via test particle dynamics [9,10,[62][63][64][65][66][67][68][69][70]. The power functional is thereby not to be confused with the often vague concept of a 'nonequilibrium free energy'.…”

“…Although setting f sup (r, t) = 0 yields the DDFT (1), the superadiabatic force field f sup (r, t) was demonstrated to exist [55][56][57][58][59][60][61] and in general to play a major role in the dynamics on the one-body level and, based on test-particle concepts [62][63][64][65][66][67], two-body correlation functions [68][69][70], and for active matter [71][72][73][74][75]. Both the flow properties as well as the spatial structure formation in the system are affected.…”

“…The relevance of superadiabatic contributions to the dynamics, i.e. of those effects that lie beyond equation ( 1), has been amply demonstrated in the literature [55][56][57][58][59][60][68][69][70]. Both adiabatic and superadiabatic effects arise from integrating out the dynamical degrees of freedom of the many-body problem.…”