Thermodynamics of mixtures of patchy and spherical colloids of different sizes: A multi-body association theory with complete reference fluid information.

We present a theory to predict the structure and thermodynamics of mixtures of colloids of different diameters, building on our earlier work [A. Bansal et al., J. Chem. Phys. 145, 074904 (2016)] that considered mixtures with all particles constrained to have the same size. The patchy, solvent particles have short-range directional interactions, while the solute particles have short-range isotropic interactions. The hard-sphere mixture without any association site forms the reference fluid. An important ingredient within the multi-body association theory is the description of clustering of the reference solvent around the reference solute. Here we account for the physical, multi-body clusters of the reference solvent around the reference solute in terms of occupancy statistics in a defined observation volume. These occupancy probabilities are obtained from enhanced sampling simulations, but we also present statistical mechanical models to estimate these probabilities with limited simulation data. Relative to an approach that describes only up to three-body correlations in the reference, incorporating the complete reference information better predicts the bonding state and thermodynamics of the physical solute for a wide range of system conditions. Importantly, analysis of the residual chemical potential of the infinitely dilute solute from molecular simulation and theory shows that whereas the chemical potential is somewhat insensitive to the description of the structure of the reference fluid, the energetic and entropic contributions are not, with the results from the complete reference approach being in better agreement with particle simulations.

Structure and thermodynamics of a mixture of patchy and spherical colloids: A multi-body association theory with complete reference fluid information.

A mixture of solvent particles with short-range, directional interactions and solute particles with short-range, isotropic interactions that can bond multiple times is of fundamental interest in understanding liquids and colloidal mixtures. Because of multi-body correlations, predicting the structure and thermodynamics of such systems remains a challenge. Earlier Marshall and Chapman [J. Chem. Phys. 139, 104904 (2013)] developed a theory wherein association effects due to interactions multiply the partition function for clustering of particles in a reference hard-sphere system. The multi-body effects are incorporated in the clustering process, which in their work was obtained in the absence of the bulk medium. The bulk solvent effects were then modeled approximately within a second order perturbation approach. However, their approach is inadequate at high densities and for large association strengths. Based on the idea that the clustering of solvent in a defined coordination volume around the solute is related to occupancy statistics in that defined coordination volume, we develop an approach to incorporate the complete information about hard-sphere clustering in a bulk solvent at the density of interest. The occupancy probabilities are obtained from enhanced sampling simulations but we also develop a concise parametric form to model these probabilities using the quasichemical theory of solutions. We show that incorporating the complete reference information results in an approach that can predict the bonding state and thermodynamics of the colloidal solute for a wide range of system conditions.

Isolating the non-polar contributions to the intermolecular potential for water-alkane interactions.

Intermolecular potential models for water and alkanes describe pure component properties fairly well, but fail to reproduce properties of water-alkane mixtures. Understanding interactions between water and non-polar molecules like alkanes is important not only for the hydrocarbon industry but has implications to biological processes as well. Although non-polar solutes in water have been widely studied, much less work has focused on water in non-polar solvents. In this study we calculate the solubility of water in different alkanes (methane to dodecane) at ambient conditions where the water content in alkanes is very low so that the non-polar water-alkane interactions determine solubility. Only the alkane-rich phase is simulated since the fugacity of water in the water rich phase is calculated from an accurate equation of state. Using the SPC/E model for water and TraPPE model for alkanes along with Lorentz-Berthelot mixing rules for the cross parameters produces a water solubility that is an order of magnitude lower than the experimental value. It is found that an effective water Lennard-Jones energy ε(W)/k = 220 K is required to match the experimental water solubility in TraPPE alkanes. This number is much higher than used in most simulation water models (SPC/E-ε(W)/k = 78.2 K). It is surprising that the interaction energy obtained here is also higher than the water-alkane interaction energy predicted by studies on solubility of alkanes in water. The reason for this high water-alkane interaction energy is not completely understood. Some factors that might contribute to the large interaction energy, such as polarizability of alkanes, octupole moment of methane, and clustering of water at low concentrations in alkanes, are examined. It is found that, though important, these factors do not completely explain the anomalously strong attraction between alkanes and water observed experimentally.

Exploring parameter space effects on structure-property relationships of surfactants at liquid-liquid interfaces.

The ubiquitous use of surfactants in commercial and industrial applications has led to many experimental, theoretical, and simulation based studies. These efforts seek to provide a molecular level understanding of the effects on structuring behavior and the corresponding impacts on observable properties (e.g., interfacial tension). With such physical detail, targeted system design can be improved over typical techniques of observational trends and phenomenological correlations by taking advantage of predictive system response. This research provides a systematic study of part of the broad parameter space effects on equilibrium microstructure and interfacial properties of amphiphiles at a liquid-liquid interface using the interfacial statistical associating fluid theory density functional theory as a molecular model for the system from the bulk to the interface. Insights into the molecular level physics and thermodynamics governing the system behavior are discussed as they relate to both predictions qualitatively consistent with experimental observations and extensions beyond currently available studies.