Umberto Marini Bettolo Marconi

Dynamic density functional theory of fluids

We present a new time-dependent density functional approach to study the relaxational dynamics of an assembly of interacting particles subject to thermal noise. Starting from the Langevin stochastic equations of motion for the velocities of the particles we are able by means of an approximated closure to derive a self-consistent deterministic equation for the temporal evolution of the average particle density. The closure is equivalent to assuming that the equal-time two-point correlation function out of equilibrium has the same properties as its equilibrium version. The changes in time of the density depend on the functional derivatives of the grand canonical free energy functional F[ρ] of the system. In particular the static solutions of the equation for the density correspond to the exact equilibrium profiles provided one is able to determine the exact form of F[ρ]. In order to assess the validity of our approach we performed a comparison between the Langevin dynamics and the dynamic density functional...

Fluctuation-Dissipation: Response Theory in Statistical Physics

Abstract General aspects of the Fluctuation–Dissipation Relation (FDR), and Response Theory are considered. After analyzing the conceptual and historical relevance of fluctuations in statistical mechanics, we illustrate the relation between the relaxation of spontaneous fluctuations, and the response to an external perturbation. These studies date back to Einstein’s work on Brownian Motion, were continued by Nyquist and Onsager and culminated in Kubo’s linear response theory. The FDR has been originally developed in the framework of statistical mechanics of Hamiltonian systems, nevertheless a generalized FDR holds under rather general hypotheses, regardless of the Hamiltonian, or equilibrium nature of the system. In the last decade, this subject was revived by the works on Fluctuation Relations (FR) concerning far from equilibrium systems. The connection of these works with large deviation theory is analyzed. Some examples, beyond the standard applications of statistical mechanics, where fluctuations play a major role are discussed: fluids, granular media, nanosystems and biological systems.

Lennard‐Jones fluids in cylindrical pores: Nonlocal theory and computer simulation

We present adsorption isotherms, phase diagrams, and density profiles for a Lennard‐Jones fluid confined to a cylindrical pore. In particular, we concentrate on the gas–liquid transition in the pore (capillary condensation). We compare simulations for a series of radii and different temperatures with mean field density functional theory (MFT). Two forms of MFT are considered, the simple local density approximation (LDA) and Tarazona’s nonlocal or smoothed density approximation (SDA). We find that the SDA provides a quite accurate description of fluid structure in the pore and that it produces phase diagrams in good agreement with the simulation data. For larger radii and temperatures T/Tc≳0.6 the SDA shows steep rises in adsorption close to the transition. This strongly affects the shape of the coexistence curve in the T, ρ plane. Here ρ is defined as the average density inside the pore. This behavior is confirmed by the simulation. In contrast, LDA gives a poor representation of the fluid structure and...

Capillary condensation and adsorption in cylindrical and slit-like pores

The nature of adsorption of simple fluids confined in model pores is investigated by means of a density functional approach. For temperatures T corresponding to a partial wetting situation a first-order phase transition (capillary condensation) from dilute ‘gas’ to dense ‘liquid’ occurs at relative pressures p/psat close to those predicted by the macroscopic Kelvin equation, even for radii Rc or wall separations H as small as 10 molecular diameters. In a complete wetting situation, where thick films develop, the Kelvin equation is, in general, not accurate. At fixed T the adsorption Γm(p) exhibits a loop; Γm jumps discontinuously at the first-order transition, but the accompanying metastable portions of the loop could produce hysteresis similar to that observed in adsorption measurements on mesoporous solids. Metastable thick films persist to larger p/psat in slits than in cylinders and this has repercussions for the shape of hysteresis loops. For a given pore size the loop in Γm shrinks with increasing T and disappears at a capillary critical temperature Tcapc( Tcapc condensation no longer occurs and hysteresis of Γm will not be observed. Such behaviour is found in experiments. A prewetting (thick–thin film) transition can occur for confined fluids. The transition is shifted to a smaller value of p/psat than that appropriate to prewetting at a single planar wall. Whereas the magnitude of the shift is very small for slits, it is substantial for cylinders and this leads to the possibility of finding a triple point, where ‘liquid’ and thick and thin films coexist, in cylindrical pores whose radii may not be too large for investigation by experiment or computer simulation. Adsorption of supercritical fluids (T > Tc, the bulk critical temperature) in cylinders is mentioned briefly.

Pore‐end effects on adsorption hysteresis in cylindrical and slitlike pores

We present grand canonical and canonical simulation results for the adsorption hysteresis in cylindrical and slitlike pores. Simulations for cylindrical symmetry were carried out for a continuous potential model, whereas the lattice gas was used to investigate the slitlike pores. In particular, we have studied the effects of pore ends on pore filling and pore emptying mechanism. We find that while the pore filling is unaffected, pore emptying is very sensitive to the presence of pore ends. Our findings confirm earlier lattice gas density functional theory results and indicate that fluctuations do not basically alter the mean field picture.

Hard-sphere Mixtures Near A Hard-wall

We report a study of hard‐sphere mixtures of different sizes near a hard wall using both the Monte Carlo method and density functional theory. The theory is based on a semiempirical free‐energy functional for an inhomogeneous hard‐sphere mixture and is similar to that developed by Tarazona for pure hard‐sphere fluids. Comparison between the theoretical results and the simulations for the density profiles of both species and the mole fraction profile shows that the present theory is capable of describing the structure of hard‐sphere mixtures against a hard wall up to a size ratio, R≡σ2/σ1, of about 3. For R values greater than 3 the theory gives some discrepancies for densities very close to the wall.

Multidimensional stationary probability distribution for interacting active particles

We derive the stationary probability distribution for a non-equilibrium system composed by an arbitrary number of degrees of freedom that are subject to Gaussian colored noise and a conservative potential. This is based on a multidimensional version of the Unified Colored Noise Approximation. By comparing theory with numerical simulations we demonstrate that the theoretical probability density quantitatively describes the accumulation of active particles around repulsive obstacles. In particular, for two particles with repulsive interactions, the probability of close contact decreases when one of the two particle is pinned. Moreover, in the case of isotropic confining potentials, the radial density profile shows a non trivial scaling with radius. Finally we show that the theory well approximates the “pressure” generated by the active particles allowing to derive an equation of state for a system of non-interacting colored noise-driven particles.

Lennard-Jones Mixtures In A Cylindrical Pore. A Comparison of Simulation and Density Functional Theory

Abstract We report simulation results for binary Lennard-Jones mixtures in narrow cylindrical pores. The parameters are chosen to model an Ar-Kr mixture in a carbon dioxide pore. We focus on capillary condensation and locate this transition directly via a molecular dynamics simulation of two-phase coexistence. The chemical potentials in the pore are obtained via the particle insertion method. The latter results are used in a subsequent grand canonical Monte Carlo simulation in order to determine the bulk pressure, density and composition. We report density profiles and phase diagrams and compare the results with the local version of mean field density functional theory predictions for the same model. The simulation results for a mixture in which we neglect the size difference between Ar and Kr are compared with the non-local theory.

Phase-space approach to dynamical density functional theory

The authors consider a system of interacting particles subjected to Langevin inertial dynamics and derive the governing time-dependent equation for the one-body density. They show that, after suitable truncations of the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy, and a multiple time scale analysis, they obtain a self-consistent equation involving only the one-body density. This study extends to arbitrary dimensions previous work on a one-dimensional fluid and highlights the subtleties of kinetic theory in the derivation of dynamical density functional theory.

Kinetic theory of correlated fluids: from dynamic density functional to Lattice Boltzmann methods.

Using methods of kinetic theory and liquid state theory we propose a description of the nonequilibrium behavior of molecular fluids, which takes into account their microscopic structure and thermodynamic properties. The present work represents an alternative to the recent dynamic density functional theory, which can only deal with colloidal fluids and is not apt to describe the hydrodynamic behavior of a molecular fluid. The method is based on a suitable modification of the Boltzmann transport equation for the phase space distribution and provides a detailed description of the local structure of the fluid and its transport coefficients. Finally, we propose a practical scheme to solve numerically and efficiently the resulting kinetic equation by employing a discretization procedure analogous to the one used in the Lattice Boltzmann method.