Molecular Theory and the Effects of Solute Attractive Forces on Hydrophobic Interactions

How do water-mediated interactions and osmotic second virial coefficients vary with particle size?

We examine quantitatively the solute-size dependences of the effective interactions between nonpolar solutes in water and in a simple liquid. The potential w(r) of mean force and the osmotic second virial coefficients B are calculated with high accuracy from molecular dynamics simulations. As the solute diameter increases from methane's to C60's with the solute-solute and solute-solvent attractive interaction parameters fixed to those for the methane-methane and methane-water interactions, the first minimum of w(r) lowers from -1.1 to -4.7 in units of the thermal energy kT. Correspondingly, the magnitude of B (<0) increases proportional to σα with some power close to 6 or 7, which reinforces the solute-size dependence of B found earlier for a smaller range of σ [H. Naito, R. Okamoto, T. Sumi and K. Koga, J. Chem. Phys., 2022, 156, 221104]. We also demonstrate that the strength of the attractive interactions between solute and solvent molecules can qualitatively change the characteristics of the effective pair interaction between solute particles, both in water and in a simple liquid. If the solute-solvent attractive force is set to be weaker (stronger) than a threshold, the effective interaction becomes increasingly attractive (repulsive) with increasing solute size.

Thermodynamics of Hydration from the Perspective of the Molecular Quasichemical Theory of Solutions

The quasichemical organization of the potential distribution theorem, molecular quasichemical theory (QCT), enables practical calculations and also provides a conceptual framework for molecular hydration phenomena. QCT can be viewed from multiple perspectives: (a) as a way to regularize an ill-conditioned statistical thermodynamic problem; (b) as an introduction of and emphasis on the neighborship characteristics of a solute of interest; or (c) as a way to include accurate electronic structure descriptions of near-neighbor interactions in defensible statistical thermodynamics by clearly defining neighborship clusters. The theory has been applied to solutes of a wide range of chemical complexity, ranging from ions that interact with water with both long-ranged and chemically intricate short-ranged interactions, to solutes that interact with water solely through traditional van der Waals interations, and including water itself. The solutes range in variety from monatomic ions to chemically heterogeneous macromolecules. A notable feature of QCT is that, in applying the theory to this range of solutes, the theory itself provides guidance on the necessary approximations and simplifications that can facilitate the calculations. In this Perspective, we develop these ideas and document them with examples that reveal the insights that can be extracted using the QCT formulation.

A modeling approach for quantitative assessment of interfacial interaction between two rough particles in colloidal systems

HYPOTHESIS AND BACKGROUND

The simulation of rough particle surface is important to understand and control the interface behavior of particles in colloidal systems. Literature analysis suggested a lack of information for an accurate model simulating the interfacial interaction between two rough particles. It is hypothesized that the total interfacial energy developed between two rough particles would depend on the surface morphologies of particles, and it could be predicted if a mathematical model to represent the interaction of two rough particles were created accurately.

EXPERIMENTS

In this study, mathematical models were developed to determine the interfacial energy created between two particles according to the XDLVO theory by considering the rippled particle theory and surface element integral (SEI) method. Three different scenarios of particle interactions were assumed in the simulation. The present study provides deep insights into particle interactions via considering aspect ratio, size, and surface roughness of two particles in colloidal systems.

FINDINGS

The assessment of the interfacial interaction revealed that an increase in the aspect ratio, surface roughness, and relative surface roughness of particles would weaken the total interaction energy generated between particles and promote particle aggregation. Increased interaction energy was predicted for the interaction of particles by increasing the particle size. The asperity ratio was more effective than the asperity number in controlling the interfacial energy between two particles. The results of this study could be used for foreseeing the interaction of rough particles, which has a significant application in particle coagulation or dispersion in colloidal systems.

Short solvent model for ion correlations and hydrophobic association

Coulomb interactions play a major role in determining the thermodynamics, structure, and dynamics of condensed-phase systems, but often present significant challenges. Computer simulations usually use periodic boundary conditions to minimize corrections from finite cell boundaries but the long range of the Coulomb interactions generates significant contributions from distant periodic images of the simulation cell, usually calculated by Ewald sum techniques. This can add significant overhead to computer simulations and hampers the development of intuitive local pictures and simple analytic theory. In this paper, we present a general framework based on local molecular field theory to accurately determine the contributions from long-ranged Coulomb interactions to the potential of mean force between ionic or apolar hydrophobic solutes in dilute aqueous solutions described by standard classical point charge water models. The simplest approximation leads to a short solvent (SS) model, with truncated solvent-solvent and solute-solvent Coulomb interactions and long-ranged but screened Coulomb interactions only between charged solutes. The SS model accurately describes the interplay between strong short-ranged solute core interactions, local hydrogen-bond configurations, and long-ranged dielectric screening of distant charges, competing effects that are difficult to capture in standard implicit solvent models.

Hydration-Shell Vibrational Spectroscopy

Hydration-shell vibrational spectroscopy provides an experimental window into solute-induced water structure changes that mediate aqueous folding, binding, and self-assembly. Decomposition of measured Raman and infrared (IR) spectra of aqueous solutions using multivariate curve resolution (MCR) and related methods may be used to obtain solute-correlated spectra revealing solute-induced perturbations of water structure, such as changes in water hydrogen-bond strength, tetrahedral order, and the presence of dangling (non-hydrogen-bonded) OH groups. More generally, vibrational-MCR may be applied to both aqueous and nonaqueous solutions, including multicomponent mixtures, to quantify solvent-mediated interactions between oily, polar, and ionic solutes, in both dilute and crowded fluids. Combining vibrational-MCR with emerging theoretical modeling strategies promises synergetic advances in the predictive understanding of multiscale self-assembly processes of both biological and technological interest.

Methane Hydration-Shell Structure and Fragility

The influence of oily molecules on the structure of liquid water is a question of importance to biology and geology and many other fields. Previous experimental, theoretical, and simulation studies of methane in liquid water have reached widely conflicting conclusions regarding the structure of hydrophobic hydration-shells. Herein we address this question by performing Raman hydration-shell vibrational spectroscopic measurements of methane in liquid water from -10 °C to 300 °C (at 30 MPa, along a path that parallels the liquid-vapor coexistence curve). We show that, near ambient temperatures, methane's hydration-shell is slightly more tetrahedral than pure water. Moreover, the hydration-shell undergoes a crossover to a more disordered structure above ca. 85 °C. Comparisons with the crossover temperature of aqueous methanol (and other alcohols) reveal the stabilizing influence of an alcohol OH head-group on hydrophobic hydration-shell fragility.

Intramolecular Interactions Overcome Hydration to Drive the Collapse Transition of Gly15

Simulations and experiments show oligo-glycines, polypeptides lacking any side chains, can collapse in water. We assess the hydration thermodynamics of this collapse by calculating the hydration free energy at each of the end points of the reaction coordinate, here taken as the end-to-end distance (r) in the chain. To examine the role of the various conformations for a given r, we study the conditional distribution, P(R_g|r), of the radius of gyration for a given value of r. The free energy change versus R_g, -k_BT ln P(R_g|r), is found to vary more gently compared to the corresponding variation in the excess hydration free energy. Using this observation within a multistate generalization of the potential distribution theorem, we calculate a tight upper bound for the hydration free energy of the peptide for a given r. On this basis, we find that peptide hydration greatly favors the expanded state of the chain, despite primitive hydrophobic effects favoring chain collapse. The net free energy of collapse is seen to be a delicate balance between opposing intrapeptide and hydration effects, with intrapeptide contributions favoring collapse.

What are the key factors governing the nucleation of CO2 hydrate?

Microsecond molecular dynamics simulations were performed to provide molecular insights into the nucleation of CO₂ hydrate. The adsorption of sufficient CO₂ molecules around CO₂ hydration shells is revealed to be crucial to effectively stabilize the hydrogen bonds formed therein, catalyzing the hydration shells into hydrate cages and inducing the nucleation. Moreover, a high aqueous CO₂ concentration is found to be another key factor governing the nucleation of CO₂ hydrate, and only above a critical concentration can the nucleation of CO₂ hydrate occur. The 4¹5¹⁰6² cages, with size similar to the CO₂ hydration shell and an elliptical space closely matching a linear CO₂ molecule, play a dominant role in initiating the nucleation and remain the most abundant. The incipient CO₂ hydrate is rather amorphous due to the abundance of metastable cages (mostly 4¹5¹⁰6²).

Hydration thermodynamics beyond the linear response approximation

The solvation energetics associated with the transformation of a solute molecule at infinite dilution in water from an initial state A to a final state B is reconsidered. The two solute states have different potentials energies of interaction, [Formula: see text] and [Formula: see text], with the solvent environment. Throughout the A [Formula: see text] B transformation of the solute, the solvation system is described by a Hamiltonian [Formula: see text] that changes linearly with the coupling parameter ξ. By focusing on the characterization of the probability density [Formula: see text] that the dimensionless perturbational solute-solvent interaction energy [Formula: see text] has numerical value y when the coupling parameter is ξ, we derive a hierarchy of differential equation relations between the ξ-dependent cumulant functions of various orders in the expansion of the appropriate cumulant generating function. On the basis of this theoretical framework we then introduce an inherently nonlinear solvation model for which we are able to find analytical results for both [Formula: see text] and for the solvation thermodynamic functions. The solvation model is based on the premise that there is an upper or a lower bound (depending on the nature of the interactions considered) to the amplitude of the fluctuations of Y in the solution system at equilibrium. The results reveal essential differences in behavior for the model when compared with the linear response approximation to solvation, particularly with regards to the probability density [Formula: see text]. The analytical expressions for the solvation properties show, however, that the linear response behavior is recovered from the new model when the room for the thermal fluctuations in Y is not restricted by the existence of a nearby bound. We compare the predictions of the model with the results from molecular dynamics computer simulations for aqueous solvation, in which either (1) the solute-solvent electrostatic interactions, or (2) the shorter-range attractive interactions are switched-on in the A [Formula: see text] B process.

Statistical Analyses of Hydrophobic Interactions: A Mini-Review

This review focuses on the striking recent progress in solving for hydrophobic interactions between small inert molecules. We discuss several new understandings. First, the inverse temperature phenomenology of hydrophobic interactions, i.e., strengthening of hydrophobic bonds with increasing temperature, is decisively exhibited by hydrophobic interactions between atomic-scale hard sphere solutes in water. Second, inclusion of attractive interactions associated with atomic-size hydrophobic reference cases leads to substantial, nontrivial corrections to reference results for purely repulsive solutes. Hydrophobic bonds are weakened by adding solute dispersion forces to treatment of reference cases. The classic statistical mechanical theory for those corrections is not accurate in this application, but molecular quasi-chemical theory shows promise. Finally, because of the masking roles of excluded volume and attractive interactions, comparisons that do not discriminate the different possibilities face an interpretive danger.