Dennis J. Diestler

On the Thermodynamic Stability of Confined Thin Films Under Shear

Thin films of monatomic fluid constrained between two plane-parallel structured solid walls have been modeled by Monte Carlo simulation under conditions (fixed temperature, chemical potential, and normal stress or load) prevailing in high-precision measurements of surface forces. Several states of the film, corresponding to different numbers of layers of fluid parallel with the walls, are generally consistent with these conditions, but only one is thermodynamically stable; the others are metastable. When the walls are properly aligned, epitaxial solid phases are stable. These melt under shear, eventually becoming metastable, whereupon a drainage (or imbibition) transition occurs, leading to a stable phase with fewer (or more) layers.

Analytical treatment of a simple fluid adsorbed in a slit-pore

A model for a simple fluid confined to a slit-pore (fluid sandwiched between two plane-parallel substrates with infinitesimally smooth surfaces) is presented. The analysis is based on thermodynamic perturbation theory, in which the free energy is split into a zero-order (unperturbed) contribution from a hard-sphere fluid reference system and a correction accounting for both fluid-fluid and fluid-substrate attractions. The correction is evaluated in the mean-field approximation and the (unperturbed) local density is assumed uniform in order to obtain a closed expression for the correction. The resulting equation of state has the same temperature and density dependence as the van der Waals equation of state for the bulk fluid, although it differs from the latter in that the a parameter (ap) is a function of the separation sz of the substrate surfaces. The inequality ap(sz)⩽ab holds, from which it follows that the critical temperature of the pore fluid is lower than that of the bulk fluid. For mesoscopic por...

Thermodynamics of a fluid confined to a slit pore with structured walls

In this article we extend our previous thermodynamic analysis of films confined to slit pores with smooth walls (i.e., plane–parallel solid surfaces without molecular structure) to the situation in which the walls themselves possess structure. Structured‐wall models are frequently employed to interpret experiments performed with the surface forces apparatus (SFA), in which thin films (1–10 molecular diameters thick) are subjected to shear stress by moving the walls laterally over one another at constant temperature, chemical potential, and normal stress or load. The periodic structure of the walls is reflected in a periodic variation of the shear stress with the lateral alignment (i.e., shear strain) of the walls. We demonstrate by means of a solvable two‐dimensional model that the molecular length scale imposed by the structure of the walls precludes the derivation of a simple mechanical expression for the grand potential analogous to that which holds in the smooth‐wall case. This conclusion is borne out...

Fluids in micropores. IV. The behavior of molecularly thin confined films in the grand isostress ensemble

The behavior of molecularly thin prototypical confined films [Lennard‐Jones (12,6) fluid constrained between two plane‐parallel walls consisting of like atoms fixed in the fcc (100) configuration] is studied by Monte Carlo in a new (grand isostress) ensemble whose parameters are the thermodynamic state variables [temperature T, chemical potential μ, and normal stress (load) applied to the walls Tzz] controlled in the surface forces apparatus used to study lubrication experimentally on a molecular scale. Additional parameters of the ensemble not generally controlled in this experiment are the film–wall interfacial area A and the crystallographic alignment (registry, or shear strain α) of the walls. A multiplicity of phases is found to comport with a given choice of the parameters. The thermodynamically stable one minimizes the grand isostress potential (free energy). By means of thermodynamic integration the stable phase of the film is determined as a function of α at fixed T, μ, Tzz, and A. Solid films co...

Transient coexisting nanophases in ultrathin films confined between corrugated walls

Grand‐canonical Monte Carlo and microcanonical molecular dynamics methods have been used to simulate an ultrathin monatomic film confined to a slit‐pore [i.e., between solid surfaces (walls)]. Both walls comprise atoms rigidly fixed in the face centered cubic (100) configuration; one wall is smooth on a nanoscale and the other is corrugated (i.e., scored with regularly spaced rectilinear grooves one to several nanometers wide). Properties of the film have been computed as a function of the lateral alignment (registry), with the temperature, chemical potential, and distance between the walls kept constant. Changing the registry carries the film through a succession of equilibrium states, ranging from all solid at one extreme to all fluid at the other. Over a range of intermediate registries the film consists of fluid and solid portions in equilibrium, that is fluid‐filled nanocapillaries separated by solid strips. The range of registries over which such fluid–solid equilibria exist depends upon the width of the grooves and the frequency of the corrugation. For grooves of width comparable to the range of the interatomic potential, fluid and solid phases cease to coexist. In the limit of very wide grooves the character of the film is similar to that of the film confined by strictly smooth walls. The rich phase behavior of the confined film due to the coupling between molecular (registry) and nano (corrugation) scales has obvious implications for boundary lubrication.

Solvation forces in thin films confined between macroscopically curved substrates

The microscopic structure of molecularly thin fluid films confined between solid substrates with macroscopically curved surfaces is investigated by means of grand canonical ensemble Monte Carlo (GCEMC) simulations, in which the thermodynamic state of the film is determined by its chemical potential μ and temperature T. This situation is akin to experiments involving the surface forces apparatus (SFA) in which the film is confined between two crossed cylinders of macroscopic radius R. The key quantity measured directly in SFA experiments is the “force per radius R,” F(h)/R, exerted by the film on the curved surfaces. This “solvation force” can be related to the local stress Tzz(h) normal to the locally planar surfaces, where h is the shortest distance between them. Because Tzz(h) and the microscopic structure of the confined film can be computed by GCEMC, the relation between Tzz and the macroscopically defined quantity F/R can be employed to interpret the dependence of the latter in terms of variations of...

Stratification-induced order--disorder phase transitions in molecularly thin confined films

By means of grand canonical ensemble Monte Carlo simulations of a monatomic film confined between unstructured (i.e., molecularly smooth) rigidly fixed solid surfaces (i.e., walls), we investigate the mechanism of molecular stratification, i.e., the tendency of atoms to arrange themselves in layers parallel with the walls. Stratification is accompanied by a heretofore unnoticed order–disorder phase transition manifested as a maximum in density fluctuations at the transition point. The transition involves phases with different transverse packing characteristics, although the number of layers accommodated between the walls remains unchanged during the transition, which occurs periodically as the film thickens. However, with increasing thickness, an increasingly smaller proportion of the film is structurally affected by the transition. Thus, the associated maximum in density fluctuations diminishes rapidly with film thickness.

Coarse-graining description of solid systems at nonzero temperature

The quasicontinuum (QC) technique, in which the atomic lattice of a solid is coarse-grained by overlaying it with a finite-element mesh, has been employed previously to treat the quasistatic evolution of defects in materials at zero temperature. It is extended here to nonzero temperature. A coarse-grained Hamiltonian is derived for the nodes of the mesh, which behave as quasiparticles whose interactions are mediated by the underlying (non-nodal) atoms constrained to move in unison with the nodes. Coarse-grained thermophysical properties are computed by means of the Monte Carlo (MC) method. This dynamically constrained QC MC procedure is applied to a simple model: A pure single crystal of two-dimensional Lennard-Jonesium. The coarse-grained isotropic stress (τc) is compared with the “exact” τ computed by the usual atomistic MC procedure for several thermodynamic states. The observed linear dependence of the error in τc on the degree of coarse-graining is rationalized by an analytical treatment of the model within the local harmonic approximation.The quasicontinuum (QC) technique, in which the atomic lattice of a solid is coarse-grained by overlaying it with a finite-element mesh, has been employed previously to treat the quasistatic evolution of defects in materials at zero temperature. It is extended here to nonzero temperature. A coarse-grained Hamiltonian is derived for the nodes of the mesh, which behave as quasiparticles whose interactions are mediated by the underlying (non-nodal) atoms constrained to move in unison with the nodes. Coarse-grained thermophysical properties are computed by means of the Monte Carlo (MC) method. This dynamically constrained QC MC procedure is applied to a simple model: A pure single crystal of two-dimensional Lennard-Jonesium. The coarse-grained isotropic stress (τc) is compared with the “exact” τ computed by the usual atomistic MC procedure for several thermodynamic states. The observed linear dependence of the error in τc on the degree of coarse-graining is rationalized by an analytical treatment of the model...

Liquid-vapor coexistence in a chemically heterogeneous slit-nanopore

Abstract A Lennard-Jonesium film confined between planar walls made of alternating strips of strongly and weakly adsorbing solid substrate was simulated by the grand canonical Monte Carlo method. When the walls are molecularly close, they serve as a nanoscale template, on which liquid bridging the gaps between the “strong” strips coexists with gas over the “weak” ones. The structure of the nanoscopic liquid-gas interface has the same form as that of the planar interface. When the walls become too far apart, the bridges give way to “nanodroplets” adhering to the strong strips coexisting with dilute gas.

Anomalous diffusion in confined monolayer films

A monolayer, solid, epitaxial film confined to a prototypal slit-pore (a monatomic substance constrained between two parallel planar walls of like atoms) and subjected to a shear strain (created by altering the transverse lateral alignment of the walls) begins to melt if a critical strain (shear melting point) is exceeded. The resulting ‘molten’ phase exhibits structural disorder characteristic of a liquid yet supports a shear stress. Molecular dynamics and Monte Carlo calculations are used to study self-diffusion in this molten phase as a function of the excess shear strain above the critical value. Three distinct self-diffusion time scales are manifest through plots of the mean-square displacement (MSD). Over the shortest time scale the MSD can be represented by a power-law, ∼td , where t is time and d is a function of the excess shear strain, varying from 0 for the solid just below the shear melting point to its Brownian-limit value of 1 for a completely liquefied film, having the disorder of a bulk fl...