Martin B. Sweatman

Cluster formation in fluids with competing short-range and long-range interactions

We investigate the low density behaviour of fluids that interact through a short-ranged attraction together with a long-ranged repulsion (SALR potential) by developing a molecular thermodynamic model. The SALR potential is a model of effective solute interactions where the solvent degrees of freedom are integrated-out. For this system, we find that clusters form for a range of interaction parameters where attractive and repulsive interactions nearly balance, similar to micelle formation in aqueous surfactant solutions. We focus on systems for which equilibrium behaviour and liquid-like clusters (i.e., droplets) are expected, and find in addition a novel coexistence between a low density cluster phase and a high density cluster phase within a very narrow range of parameters. Moreover, a simple formula for the average cluster size is developed. Based on this formula, we propose a non-classical crystal nucleation pathway whereby macroscopic crystals are formed via crystal nucleation within microscopic precursor droplets. We also perform large-scale Monte Carlo simulations, which demonstrate that the cluster fluid phase is thermodynamically stable for this system.

Modelling gas adsorption in slit-pores using Monte-Carlo simulation

Abstract We discuss the use of Monte Carlo simulation to model the equilibrium adsorption of gases in slit pores. Databases of adsorption isotherms have been calculated for nitrogen, carbon-monoxide, methane and carbon-dioxide for a range of pressures, pore widths and temperatures. We discuss the implications of these results for materials characterisation procedures based on gas adsorption data.

Simulating fluid-solid equilibrium with the Gibbs ensemble

The Gibbs ensemble is employed to simulate fluid–solid equilibrium for a shifted-force Lennard-Jones system. This is achieved by generating an accurate canonical Helmholtz free-energy model of the (defect-free) solid phase. This free-energy model is easily generated, with accuracy limited only by finite-size effects, by a single isothermal–isobaric simulation at a pressure not too far from coexistence for which the chemical potential is known. We choose to illustrate this method at the known triple-point because the chemical potential is easily calculated from the coexisting gas. Alternatively, our methods can be used to locate fluid–solid coexistence and the triple-point of pure systems if the chemical potential of the solid phase can be efficiently calculated at a pressure not too far from the actual coexistence pressure. Efficient calculation of the chemical potential of solids would also enable the Gibbs ensemble simulation of bulk solid–solid equilibrium and the grand-canonical ensemble simulation of bulk solids.

Molecular dynamics simulations for the prediction of the dielectric spectra of alcohols, glycols and monoethanolamine

The response of molecular systems to electromagnetic radiation in the microwave region (0.3–300 GHz) has been principally studied experimentally, using broadband dielectric spectroscopy. However, relaxation times corresponding to reorganisation of molecular dipoles due to their interaction with electromagnetic radiation at microwave frequencies are within the scope of modern molecular simulations. In this work, fluctuations of the total dipole moment of a molecular system, obtained through molecular dynamics simulations, are used to determine the dielectric spectra of water, a series of alcohols and glycols, and monoethanolamine. Although the force fields employed in this study have principally been developed to describe thermodynamic properties, most them give fairly good predictions of this dynamical property for these systems. However, the inaccuracy of some models and the long simulation times required for the accurate estimation of the static dielectric constant can sometimes be problematic. We show that the use of the experimental value for the static dielectric constant in the calculations, instead of the one predicted by the different models, yields satisfactory results for the dielectric spectra, and hence the heat absorbed from microwaves, avoiding the need for extraordinarily long simulations or re-calibration of molecular models.

Analysis of free energy functional density expansion theories

Density expansion theories are often used, within the density functional formalism, to approximate the Helmholtz free-energy functional of simple classical fluids. An overview of the theoretical framework of density expansion theories is presented. Several density functional theories that employ truncated density expansions are then analysed with attention focused on their thermodynamic properties. It is found that, of these theories, only the commonly used mean-field theory satisfies the Gibbs adsorption equation; the inconsistencies within the other theories arise from truncation of the density expansion without appropriate modification of the expansion coefficients. Other repercussions of truncating the density expansion are discussed.

Modelling gas mixture adsorption in active carbons

We review recent progress made concerning the modelling of equilibrium gas mixture adsorption in activated carbons. Much of the discussion focuses on modern statistical mechanical methods, such as classical density functional theory and Monte-Carlo simulation, as well as the surface models employed, i.e. the surface characterisation, and we confine our attention to work that has been compared quantitatively with experiment. We will see that for less demanding scenarios, i.e. relatively simple gas mixtures adsorbed at supercritical temperatures, current methods are satisfactory. But further developments in our models and theories are probably needed to describe the adsorption of more complex adsorbates such as those involving water at room temperature.

Analysis of gas adsorption in Kureha active carbon based on the slit–pore model and Monte-Carlo simulations

We analyse the adsorption of carbon dioxide and several light alkenes and alkanes on Kureha active carbon at a range of temperatures. We find generally good agreement between the alkene and alkane isotherms at moderate to high pressure, but find that at the lowest relative pressures for each gas there are significant discrepancies that seem to be correlated with the strength of gas–surface interactions. This pattern is similar to that observed in our previous work on the adsorption of light alkenes and alkanes on active carbon, except the errors here are much smaller. One possible explanation for this error is poor diffusion in the experiments at the lowest relative pressures, leading to measurements of non-equilibrium states. We suggest that this poor diffusion might be caused by potential barriers (i.e. it is activated diffusion) in the narrowest pores. We also find that our analysis of the adsorption of carbon dioxide at 273 K is inconsistent with all the alkene and alkane data. We suggest this discrepancy arises because our model of gas–surface interactions does not take contributions from polar surface sites into account. Although this study is specific to Kureha active carbon, we expect that our conclusions are relevant to other studies of gas adsorption on active carbon; they highlight the need for great care when taking measurements at low pressures, and motivate improvements in molecular models for gas adsorption in active carbons.

Monte Carlo calculations of the free energy of ice-like structures using the self-referential method

The self-referential method is a recently developed technique to compute the free energy of molecular crystals. In this paper, the method is extended to systems composed of nonlinear rigid molecules and applied to obtain the Helmholtz free energy of ice VII, hexagonal ice, cubic ice, and the Gibbs free energy of the empty structure I (sI) clathrate hydrate and fully occupied methane sI. It is shown that the method provides a viable alternative to other techniques to determine the free energy of solids. Good agreement with available reference literature data is found. We expect that the technique can be applied to a wide range of molecular crystals.

Comparison of absolute free energy calculation methods for fluids and solids

Several established and very general methods for calculating the absolute Helmholtz free energy from Monte Carlo simulations are compared, namely the method of Schilling and Schmid, Speedys method and the self-referential method of Sweatman et al., and an approach inspired by the phase-switch method of Wilding et al.. It is shown how they are all closely related, in that they all calculate the free energy difference between a pinned configuration, for which the free energy can be calculated analytically, and the state of interest. A novel scheme is devised based on analysis of the advantages and problems with each method. Performance tests with hard sphere fluid and face-centred-cubic crystalline states demonstrate that the novel scheme described here is the most straightforward, efficient and robust method of those tested. The method of Schilling and Schmid requires sampling of rare events and cannot be recommended for high density states. Speedys method is less efficient than the novel scheme proposed here, while a path sampling approach inspired by the phase-switch method is more complex and less efficient in general. However, for free energy difference calculations involving states that are structurally very similar, a phase-switch method might still be the most efficient method of those tested.

New techniques for simulating crystals

Methods for simulating solid crystalline phases are generally not as straightforward as those for fluids. This work discusses the reason for this and reviews some recently developed Monte-Carlo techniques for simulating crystalline phases. The self-referential (SR) method for calculating crystal free energies is described first. This technique is particularly straightforward and it is expected to be very versatile. Next, a novel kind of Gibbs ensemble method adapted to treat crystalline solid–fluid coexistence is described. This technique requires free energy calculations of the crystalline phase as input, and of course, these can be provided by the SR method.