Quasichemical theory and the description of associating fluids relative to a reference: Multiple bonding of a single site solute

We derive an expression for the chemical potential of an associating solute in a solvent relative to the value in a reference fluid using the quasichemical organization of the potential distribution theorem. The fraction of times the solute is not associated with the solvent, the monomer fraction, is expressed in terms of (a) the statistics of occupancy of the solvent around the solute in the reference fluid and (b) the Widom factors that arise because of turning on solute-solvent association. Assuming pair-additivity, we expand the Widom factor into a product of Mayer f-functions and the resulting expression is rearranged to reveal a form of the monomer fraction that is analogous to that used within the statistical associating fluid theory (SAFT). The present formulation avoids all graph-theoretic arguments and provides a fresh, more intuitive, perspective on Wertheim's theory and SAFT. Importantly, multi-body effects are transparently incorporated into the very foundations of the theory. We illustrate the generality of the present approach by considering examples of multiple solvent association to a colloid solute with bonding domains that range from a small patch on the sphere, a Janus particle, and a solute whose entire surface is available for association

Resummed thermodynamic perturbation theory for bond cooperativity in associating fluids with small bond angles: Effects of steric hindrance and ring formation

In this paper we develop a thermodynamic perturbation theory for two site associating fluids which exhibit bond cooperativity. We include both steric hindrance and ring formation such that the equation of state is bond angle dependent. Here the bond angle is the angle separating the centers of the two association sites. As a test, new Monte Carlo simulations are performed, and the theory is found to accurately predict the internal energy as well as the distribution of associated clusters as a function of bond angle and bond cooperativity.Comment: To appear in The Journal of Chemical Physic

Mini-grand canonical ensemble: chemical potential in the solvation shell

Quantifying the statistics of occupancy of solvent molecules in the vicinity of solutes is central to our understanding of solvation phenomena. Number fluctuations in small `solvation shells' around solutes cannot be described within the macroscopic grand canonical framework using a single chemical potential that represents the solvent `bath'. In this communication, we hypothesize that molecular-sized observation volumes such as solvation shells are best described by coupling the solvation shell with a mixture of particle baths each with its own chemical potential. We confirm our hypotheses by studying the enhanced fluctuations in the occupancy statistics of hard sphere solvent particles around a distinguished hard sphere solute particle. Connections with established theories of solvation are also discussed

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 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.Comment: arXiv admin note: text overlap with arXiv:1601.0438

A perturbation density functional theory for the competition between inter and intramolecular association

Using the framework of Wertheim's thermodynamic perturbation theory we develop the first density functional theory which accounts for intramolecular association in chain molecules. To test the theory new Monte Carlo simulations are performed at a fluid solid interface for a 4 segment chain which can both intra and intermolecularly associate. The theory and simulation results are found to be in excellent agreement. It is shown that the inclusion of intramolecular association can have profound effects on interfacial properties such as interfacial tension and the partition coefficient

A density functional theory for patchy colloids based on Wertheim's association theory: Beyond the single bonding condition

In the framework of Wertheimﾒs theory, we develop the first classical density functional theory for patchy colloids where the patch can bond more than once. To test the theory we perform new Monte Carlo simulations for the model system of patchy colloids in a planar slit pore. The theory is shown to be in excellent agreement with simulation for the density profiles and bonding fractions. It is also shown that the theory obeys the wall contact rule by accurately predicting bulk pressures from the wall contact density

Molecular theory for self assembling mixtures of patchy colloids and colloids with spherically symmetric attractions: The single patch case

In this work we develop a new theory to model self assembling mixtures of single patch colloids and colloids with spherically symmetric attractions. In the development of the theory we restrict the interactions such that there are short ranged attractions between patchy and spherically symmetric colloids, but patchy colloids do not attract patchy colloids and spherically symmetric colloids do not attract spherically symmetric colloids. This results in the temperature, density, and composition dependent reversible self assembly of the mixture into colloidal star molecules. This type of mixture has been recently synthesized by grafting of complimentary single stranded DNA [L. Feng, R. Dreyfus, R. Sha, N. C. Seeman, and P. M. Chaikin, Adv. Mater. 25(20), 2779–2783 (2013)]10.1002/adma.201204864. As a quantitative test of the theory, we perform new monte carlo simulations to study the self assembly of these mixtures; theory and simulation are found to be in excellent agreement

Role of Internal Motions and Molecular Geometry on the NMR Relaxation of Hydrocarbons

The role of internal motions and molecular geometry on $^1$H NMR relaxation times $T_{1,2}$ in hydrocarbons is investigated using MD (molecular dynamics) simulations of the autocorrelation functions for in{\it tra}molecular $G_R(t)$ and in{\it ter}molecular $G_T(t)$ $^1$H-$^1$H dipole-dipole interactions arising from rotational ($R$) and translational ($T$) diffusion, respectively. We show that molecules with increased molecular symmetry such as neopentane, benzene, and isooctane show better agreement with traditional hard-sphere models than their corresponding straight-chain $n$-alkane, and furthermore that spherically-symmetric neopentane agrees well with the Stokes-Einstein theory. The influence of internal motions on the dynamics and $T_{1,2}$ relaxation of $n$-alkanes are investigated by simulating rigid $n$-alkanes and comparing with flexible (i.e. non-rigid) $n$-alkanes. Internal motions cause the rotational and translational correlation-times $\tau_{R,T}$ to get significantly shorter and the relaxation times $T_{1,2}$ to get significantly longer, especially for longer-chain $n$-alkanes. Site-by-site simulations of $^1$H's along the chains indicate significant variations in $\tau_{R,T}$ and $T_{1,2}$ across the chain, especially for longer-chain $n$-alkanes. The extent of the stretched (i.e. multi-exponential) decay in the autocorrelation functions $G_{R,T}(t)$ are quantified using inverse Laplace transforms, for both rigid and flexible molecules, and on a site-by-site bases. Comparison of $T_{1,2}$ measurements with the site-by-site simulations indicate that cross-relaxation (partially) averages-out the variations in $\tau_{R,T}$ and $T_{1,2}$ across the chain of long-chain $n$-alkanes. This work also has implications on the role of nano-pore confinement on the NMR relaxation of fluids in the organic-matter pores of kerogen and bitumen

Hydrophobic and hydrophilic interactions in aqueous mixtures of alcohols at a hydrophobic surface

Aqueous solutions of alcohols are interesting because of their anomalous behavior that is believed to be due to the molecular structuring of water and alcohol around each other in solution. The interfacial structuring and properties are significant for application in alcohol purification processes and biomolecular structure. Here we study aqueous mixtures of short alcohols (methanol, ethanol, 1-propanol, and 2-propanol) at a hydrophobic surface using interfacial statistical associating fluid theory which is a perturbation density functional theory. The addition of a small amount of alcohol decreases the interfacial tension of water drastically. This trend in interfacial tension can be explained by the structure of water and alcohol next to the surface. The hydrophobic group of an added alcohol preferentially goes to the surface preserving the structure of water in the bulk. For a given bulk alcohol concentration, water mixed with the different alcohols has different interfacial tensions with propanol having a lower interfacial tension than methanol and ethanol. 2-propanol is not as effective in decreasing the interfacial tension as 1-propanol because it partitions poorly to the surface due to its larger excluded volume. But for a given surface alcohol mole fraction, all the alcohol mixtures give similar values for interfacial tension. For separation of alcohol from water, methods that take advantage of the high surface mole fraction of alcohol have advantages compared to separation using the vapor in equilibrium with a water-alcohol liquid