Chemical potential, Helmholtz free energy and entropy of argon with kinetic Monte Carlo simulation

Thermodynamics of liquid and fluid mixtures from the kinetic Monte Carlo viewpoint

In this study a binary mixture is modelled in a uniform simulation cell at various temperatures using an extended version of the grand canonical kinetic Monte Carlo (GC-kMC) method. The main goal of this study is to consider the thermodynamic properties of binary liquids, gases, and gas-liquid mixtures from a more general point of view than that applied to the particular case of vapour-liquid equilibrium when the pressure and partial chemical potentials in coexisting phases are the same. Particular attention is paid to thermodynamic functions such as chemical potentials, Gibbs free energy and entropy. For the pair potential of unlike molecules a more universal scheme is proposed in comparison with the Lorentz-Berthelot combining rule. The approach is tested on an Ar-Kr mixture in a wide range of temperatures. In all cases, the obtained values of chemical potentials, pressure and internal energy for the entire set of component densities and temperature fully satisfy the Gibbs-Duhem equation with a high degree of accuracy. For the case of vapour-liquid equilibrium, the developed approach made it possible to reproduce the experimental pressure-composition diagrams with the highest accuracy ever achieved in the literature. Despite the fact that the Ar-Kr mixture, according to Raoult's law, is close to an ideal system, it was found that the partial pressures in the liquid phase or in a dense supercritical gas mixture are non-linear functions of the composition, and the partial pressure of the heavier component (Kr) can even be negative.

Superionic Colloidal Crystals: Ionic to Metallic Bonding Transitions

Size-asymmetric binary charged colloidal solutions can assemble into ionic colloidal crystals. These are often stabilized by ionic-type bonding, where the components with smaller size and charge sit at fixed points within the lattice of large particles. Here, we study the transition termed ionic to metallic bonding transition, by which the lattice of the smaller component melts while the crystal of the large particles is preserved, as in metallic bonding. We simulate a charged colloidal crystal in equilibrium with a solution containing small colloidal particles and counterions using the Coulomb interaction between the finite-size components. We find ionic to metallic first-order transitions by increasing either the temperature or the concentration of the small particles in the solution. The transition is accompanied by a lattice expansion and increased absorption of small particles into the crystal. We compute the free energies of the ionic and metallic states using the Madelung constant and Wigner-Seitz cell approaches, respectively, combined with the quasi-harmonic lattice model. The calculation reproduces the simulated transition and reveals that the enthalpic gain is more pronounced than the entropic gain in the transition from ionic to metallic bonding when material is exchanged with the solution.

Computational Simulations of Nanoconfined Argon Film through Adsorption–Desorption in a Uniform Slit Pore

We performed hybrid grand canonical Monte Carlo/molecular dynamics (GCMC/MD) simulations to investigate the adsorption-desorption isotherms of argon molecules confined between commensurate and incommensurate contacts in nanoscale thickness. The recently proposed mid-density scheme was applied to the obtained hysteresis loops to produce a realistic equilibrium phase of nanoconfined fluids. The appropriate chemical potentials can be determined if the equilibrium structures predicted by GCMC/MD simulations are consistent with those observed in previously developed liquid-vapor molecular dynamics (LVMD) simulations. With the chemical potential as input, the equilibrium structures obtained by GCMC/MD simulations can be used as reasonable initial configurations for future metadynamics free energy calculations.

On the canonical isotherms for bulk fluid, surface adsorption and adsorption in pores: A common thread

Kinetic Monte Carlo simulated isotherms calculated in the canonical ensemble, at temperatures below the critical temperature, for bulk fluid, surface adsorption and adsorption in a confined space, show a van der Waals (vdW) loop with a vertical phase transition between the rarefied and dense spinodal points at the co-existence chemical potential, µ_co. Microscopic examination of the state points on this loop reveals features that are common to these systems. At state points with chemical potentials greater than μ_co the microscopic configurations show clusters, which coalesce to form two co-existing phases along the vertical section of the loop (the coexistence line). As more molecules are added, the dense region expands at the expense of the rarefied region, to the point where the rarefied region becomes spherical (cylindrical for 2D-systems) with a curvature greater than that of the coexisting phases. This results in a decrease of chemical potential from µ_co to the liquid spinodal point where the rarefied region disappears. With a further increase in loading, the chemical potential and the density increase. The existence of a vdW loop is the microscopic reason for the hysteresis observed in the grand canonical isotherm, where the adsorption and desorption boundaries of the hysteresis loop are first-order transitions, enclosing the vertical section of the vdW loop of the canonical isotherm. However, a first-order transition is rarely observed in experiments where transitions are usually steep, but not vertical. From our extensive simulations, we provide two possible reasons: (1) the finite extent of the system and (2) the existence of high energy sites that localize the clusters. In the first case, the desorption branch, and in the second case the adsorption branch, either comes close to, or collapses onto the coexistence line. When both occur, the hysteresis loop disappears and the isotherm is reversible, as often observed experimentally.

Nonwetting/Prewetting/Wetting Transition of Ammonia on Graphite

Simulations of ammonia adsorption on graphite were carried out over a range of temperatures to investigate the transition from nonwetting to wetting. The process is governed by a subtle interplay between the various interactions in the system and the temperature. At temperatures below the bulk triple point, the system is nonwetting; above the triple point, we observed continuous wetting, preceded by a prewetting region in which the so-called thin-to-thick film transition occurs. This system serves as an excellent example of wetting/nonwetting behavior in an associating fluid as a function of temperature because the heat of sublimation (or condensation) is greater than the isosteric heat of adsorption at zero loading. The nonwetting-to-wetting transition (NW/W) is also strongly affected by the adsorbate-adsorbate interaction, which becomes important when this contribution to the isosteric heat is of a similar magnitude to the heat of condensation. An appropriate indicator of a NW/W transition at a given loading is therefore the difference between the isosteric heat and the heat of sublimation (or condensation). Our simulation results show the "thin-to-thick" film transition in the temperature range between 195 and 240 K, which has not been previously explained. Above 240 K, continuous wetting occurs. This study provides a basis for a better understanding of adsorption in a range of systems because ammonia is an intermediate between simple molecules, such as argon, and strongly associating fluids, such as water.

Water Sites, Networks, And Free Energies with Grand Canonical Monte Carlo

Water molecules play integral roles in the formation of many protein-ligand complexes, and recent computational efforts have been focused on predicting the thermodynamic properties of individual waters and how they may be exploited in rational drug design. However, when water molecules form highly coupled hydrogen-bonding networks, there is, as yet, no method that can rigorously calculate the free energy to bind the entire network or assess the degree of cooperativity between waters. In this work, we report theoretical and methodological developments to the grand canonical Monte Carlo simulation technique. Central to our results is a rigorous equation that can be used to calculate efficiently the binding free energies of water networks of arbitrary size and complexity. Using a single set of simulations, our methods can locate waters, estimate their binding affinities, capture the cooperativity of the water network, and evaluate the hydration free energy of entire protein binding sites. Our techniques have been applied to multiple test systems and compare favorably to thermodynamic integration simulations and experimental data. The implications of these methods in drug design are discussed.

Phase equilibrium in argon films stabilized by homogeneous surfaces and thermodynamics of two-stage melting transition

Freezing of gases adsorbed on open surfaces (e.g., graphite) and in narrow pores is a widespread phenomenon which is a subject of a large number of publications. Modeling of the gas/liquid-solid transition is usually accomplished with a molecular simulation technique. However, quantitative analysis of the gas/liquid-solid coexistence and thermodynamic properties of the solid layer still encounters serious difficulties. This is mainly due to the effect of simulation box size on the lattice constant. Since the lattice constant is a function of loading and temperature, once the ordering transition has occurred, the simulation box size must be corrected in the course of simulation according to the Gibbs-Duhem equation. A significant problem is also associated with accurate prediction of the two-dimensional liquid-solid coexistence because of a small difference in densities of coexisting phases. The aim of this study is thermodynamic analysis of the two-dimensional phase coexistence in systems involving crystal-like free of defects layers in narrow slit pores. A special attention was paid to the determination of triple point temperatures. It is shown that intrinsic properties of argon monolayer adsorbed on the graphite surface are similar to those of isolated monolayer accommodated in the slit pore having width of two argon collision diameters. Analysis of the latter system is shown to be clearer and less time-consuming than the former one, which has allowed for explanation of the experimentally observed two-stage melting transition of argon monolayer on graphite without invoking the periodic surface potential modulation and orientational transition.