Classical dynamical density functional theory: from fundamentals to applications

Abstract

Classical dynamical density functional theory (DDFT) is one of the cornerstones of modern statistical mechanics. It is an extension of the highly successful method of classical density functional theory (DFT) to nonequilibrium systems. Originally developed for the treatment of simple and complex fluids, DDFT is now applied in fields as diverse as hydrodynamics, materials science, chemistry, biology, and plasma physics. In this review, we give a broad overview over classical DDFT. We explain its theoretical foundations and the ways in which it can be derived. The relations between the different forms of deterministic and stochastic DDFT as well as between DDFT and related theories, such as quantum-mechanical time-dependent DFT, mode coupling theory, and phase field crystal models, are clarified. Moreover, we discuss the wide spectrum of extensions of DDFT, which covers methods with additional order parameters (like extended DDFT), exact approaches (like power functional theory), and systems with more complex dynamics (like active matter). Finally, the large variety of applications, ranging from fluid mechanics and polymer physics to solidification, pattern formation, biophysics, and electrochemistry, is presented.

Dynamical coupling of ion adsorption with fluid flow in nanopores

“…Secondly, in the temporal evolution of density profile, the flow effect is introduced by involving a tensor composed of local momentum, which means the flow velocity brings certain influence on the structure of local density. This feature is significantly different with other recent extensions of DDFT equation to fluid flow systems 40,41 . For instance, by introducing the flow velocity into the DDFT equation, the advected‐DDFT is proposed, 40 in which, however, the applied shear flow along the surface has no influence on the density profile in the normal direction.…”

Active binary switching of soft colloids: stability and structural properties

“…In the absence of switching activity, the time-dependent density profiles of the colloids affected by these external fields, {r i (r,t)}, can be predicted by the dynamical density functional theory (DDFT), which represents an adaptation of the classical equilibrium density functional theory for fluids of Brownian particles to non-equilibrium conditions. 38,39 According to DDFT, the time evolution of the ensemble average density profiles obeys the following continuity equation 40,41 @r i ðr; tÞ…”

Non-hyperuniform metastable states around a disordered hyperuniform state of densely packed spheres: stochastic density functional theory at strong coupling

“…This section is intended to provide a brief overview of theoretical approaches to jammed structures for explaining the relevance of stochastic DFT [44][45][46][47][48][49][50][51][52][53][54][55][56] to the degradation of hyperuniformity.…”

“…For assessing the applicability of density functional approaches to the free-energy landscape in glassy systems, let us compare stochastic DFT [44][45][46][47][48][49][50][51][52][53][54][55][56] and equilibrium DFT, or classical DFT conventionally used. [57][58][59][60][61][62][63][64][65][66][67][68][69][70][71][72][73][74] Equilibrium DFT, [57][58][59][60][61][62][63][64][65][66][67][68][69][70][71][72][73][74] one of the ensemble approaches, has been found relevant to investigate the free-energy landscape.…”

“…To this end, we formulate an analytical form of the non-vanishing zero-wavevector structure factor that satisfies eqn (2) under the condition of eqn (7). A key ingredient of our formulation is the strongcoupling approximation of stochastic density functional theory (DFT) [44][45][46][47][48][49][50][51][52][53][54][55][56] which can consider intermittent fluctuations while fixing the density field at a given distribution of dense packings near and at jamming.…”