Martin Schoen

Shear forces in molecularly thin films

Monte Carlo and molecular dynamics methods have been used to study the shearing behavior of an atomic fluid between two plane-parallel solid surfaces having the face-centered cubic (100) structure. A distorted, face-centered cubic solid can form epitaxially between surfaces that are separated by distances of one to five atomic diameters. Under these conditions a critical stress must be overcome to initiate sliding of the surfaces over one another at fixed separation, temperature, and chemical potential. As sliding begins, a layer of solid exits the space between the surfaces and the remaining layers become fluid.

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.

SUBSTRATE-INDUCED ORDER IN CONFINED NEMATIC LIQUID-CRYSTAL FILMS

In orientationally biased grand canonical ensemble Monte Carlo (GCEMC) simulations we investigated the microscopic structure of liquid-crystalline films confined between two plane parallel solid surfaces (i.e., walls) consisting of Ns discrete, rigidly fixed atoms. These wall atoms are distributed across the plane of a wall according to the (100) structure of the face-centered cubic lattice. Parameters of the film–wall interaction potential are chosen such that a homeotropic alignment of film molecules is favored. In the simulations the thermodynamic state of the film is determined by the temperature T, the chemical potential μ, the distance between the walls sz, and the film–wall interfacial area A. Thermodynamic states of the film are chosen such that a corresponding bulk liquid crystal is nematic. To simulate nematic phases in the GCEMC we modified the classic Gay–Berne potential for the interaction between a pair of film molecules so that the isotropic–nematic phase transition in the bulk occurs at su...

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...

Slit-pore sorption isotherms by the grand-canonical Monte Carlo method

The grand-canonical ensemble Monte Carlo method has been used to study sorption isotherms (plots of density versus chemical potential) for a rare-gas fluid in a slit-pore whose plane-parallel walls comprise rigidly fixed rare-gas atoms. Hysteresis in the vicinity of the capillary-condensation transition is evinced by fluctuations between liquid and vapour phases as the length of the Markov chain increases (at fixed chemical potential). The degree of hysteresis, which reflects the non-ergodic behaviour of the Markov chain, can be diminished by increasing the surface area of the pore wall and by extending the Markov chain. It is concluded that hysteresis is a non-equilibrium phenomenon that cannot be properly treated by equilibrium statistical-mechanical methods.

Mesoscale modeling of complex binary fluid mixtures: towards an atomistic foundation of effective potentials.

This paper is devoted to equilibrium molecular-dynamics (MD) simulations of a fully atomistic model of binary mixtures of water (component 1) and ethanol (component 2). We investigate ways to extract from these simulations effective, pairwise additive potentials suitable to describe the interactions between coarse-grained molecules (i.e., beads) in corresponding mesoscale dissipative particle-dynamics simulations. The fully atomistic model employed in MD simulations is mapped onto an implicit water model, where the internal degrees of freedom of ethanol and all the degrees of freedom of water are integrated out. This gives us an effective one-component system consisting only of ethanol beads. The effective interaction potential between a pair of ethanol beads, Phi(R), is approximated at three levels of sophistication. At the lowest one, we approximate Phi(R) by the potential of mean force between the centers of mass of two ethanol beads calculated in the fully atomistic MD simulations; at the second level, we take Phi(R) to be the potential linked to total and direct correlation functions in the hypernetted-chain closure of the Ornstein-Zernike equation. At the third level we approximate Phi(R) numerically by improving it iteratively through the Boltzmann inversion scheme. Our results indicate that the level-one approach works only at the lowest (8 wt %) concentration; the level-two approach works only up to intermediate ethanol concentrations (ca. 50 wt %). Only the Boltzmann inversion scheme works for all, up to the highest concentration considered (70 wt %).

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...

Monte Carlo simulation of a complex fluid confined to a pore with nanoscopically rough walls

Understanding the properties of fluid films of nanometer scale thickness confined between two solid substrates is of fundamental interest as well as of practical importance for engineering applications such as lubrication, adhesion, and friction. We address here the question of the effect of the wall corrugation on the confined fluid structure. We report configurational bias grand canonical Monte Carlo simulations for model butane confined between planar and nonplanar walls. Furrowed walls have been used to model surface roughness effects on the nanometer length scale, while the confining walls remain smooth on the atomic scale. It is shown that the fluid confined between planar walls exhibits a damped oscillatory solvation pressure profile. A transition from an oscillatory to a nonoscillatory behavior is observed when the characteristic length of the furrow reaches the typical dimensions of a butane molecule. It is inferred from these simulations that disrupted oscillatory forces observed in the experime...

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.