Temperature and Pressure Dependence of Methane Correlations and Osmotic Second Virial Coefficients in Water

The Dependence of Hydrophobic Interactions on the Shape of Solute Surface

According to our recent studies on hydrophobicity, this work is aimed at understanding the dependence of hydrophobic interactions on the shape of a solute's surface. It has been observed that dissolved solutes primarily affect the structure of interfacial water, which refers to the top layer of water at the interface between the solute and water. As solutes aggregate in a solution, hydrophobic interactions become closely related to the transition of water molecules from the interfacial region to the bulk water. It is inferred that hydrophobic interactions may depend on the shape of the solute surface. To enhance the strength of hydrophobic interactions, the solutes tend to aggregate, thereby minimizing their surface area-to-volume ratio. This also suggests that hydrophobic interactions may exhibit directional characteristics. Moreover, this phenomenon can be supported by calculated potential mean forces (PMFs) using molecular dynamics (MD) simulations, where different surfaces, such as convex, flat, or concave, are associated with a sphere. Furthermore, this concept can be extended to comprehend the molecular packing parameter, commonly utilized in studying the self-assembly behavior of amphiphilic molecules in aqueous solutions.

Hydrophobic association: A facile approach to prepare physical cross-linked gelatin hydrogel with desirable thermal stability, flexibility and self-healing ability

Methacrylic anhydride was added to 20 % gelatin solution to prepare gelatin methacryloyl (GelMA) but an unexpected gelation process was observed within several minutes. The experimental data revealed that the methacryloyl substitution can increase the hydrophobicity of gelatin and the micellar diameter in solution. Therefore, we speculated that the methacryloyl substitution caused the formation of micellar cross-links based on the hydrophobic residues of gelatin and the methacryloyl groups, thus obtaining the hydrophobic association hydrogels. The thixotropic and tensile experiments confirmed that GelMA hydrogel possessed the features of hydrophobic association hydrogels like self-healing and stretchable abilities. The rheological experiments revealed that the gelation rate and the mechanical strength of the GelMA hydrogels were in direct proportion to the concentration of GelMA and the degree of methacryloyl substitution. GelMA hydrogels possessed desirable thermal stability that it didn't melt after being heated to 90 °C. Furthermore, the MTT assays and calcein AM/PI staining revealed that GelMA hydrogel was biocompatible. These results collectively confirm that the hydrophobic association is a prospective and facile approach to prepare gelatin hydrogel with desirable properties for further application.

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.

Osmotic Force Balance Evaluation of Aqueous Electrolyte Osmotic Pressures and Chemical Potentials

Concentrated aqueous salt solutions are ubiquitous in problems of biological and environmental relevance. The development of accurate force fields that capture the interactions between dissolved species in solution is crucial to simulating these systems to gain molecular insights into the underlying processes under saline conditions. The osmotic pressure is a relatively simple thermodynamic property connecting the experimental and simulation measurements of the associative properties of the ions in solution. Milner [C. Gillespie and S. T. Milner, Soft Matter, 16, 9816 (2020)] proposed a simulation approach to evaluate the osmotic pressures of salts in solution by applying a restraint potential to the ions alone in solution and determining the resulting pressure required to balance that potential, referred to here as the osmotic force balance. Here, we expand Milner's approach, demonstrating that the chemical potentials of the salts in solution as a function of concentration can be fitted to the concentration profiles determined from simulation, additionally providing an analytical expression for the osmotic pressure. This approach is used to determine the osmotic pressures of 15 alkali halide salts in water from simulations. The cross interactions between cations and anions in solution are subsequently optimized to capture their experimental osmotic pressures.

Osmotic second virial coefficients for hydrophobic interactions as a function of solute size

To gain quantitative insight into how the overall strength of the hydrophobic interaction varies with the molecular size, we calculate osmotic second virial coefficients B for hydrophobic spherical molecules of different diameters σ in water based on molecular simulation with corrections to the finite-size and finite-concentration effects. It is shown that B (<0) changes by two orders of magnitude greater as σ increases twofold and its solute-size dependence is best fit by a power law B ∝ σ^α with the exponent α ≃ 6, which contrasts with the cubic power law that the second virial coefficients of gases obey. It is also found that values of B for the solutes in a nonpolar solvent are positive but they obey the same power law as in water. A thermodynamic identity for B derived earlier [K. Koga, V. Holten, and B. Widom, J. Phys. Chem. B 119, 13391 (2015)] indicates that if B is asymptotically proportional to a power of σ, the exponent α must be equal to or greater than 6.

Simulation studies of polypeptoids using replica exchange with dynamical scaling and dihedral biasing

Polypeptoids differ from polypeptides in that the amide bond can more frequently adopt both cis and trans conformations. The transition between the two conformations requires overcoming a large energy barrier, making it difficult for conventional molecular simulations to adequately visit the cis and trans structures. A replica-exchange method is presented that allows for easy rotations of the amide bond and also an efficient linking to a high temperature replica. The method allows for just three replicas (one at the temperature and Hamiltonian of interest, a second high temperature replica with a biased dihedral potential, and a third connecting them) to overcome the amide bond sampling problem and also enhance sampling for other coordinates. The results indicate that for short peptoid oligomers, the conformations can range from all cis to all trans with an average cis/trans ratio that depends on side chain and potential model.

Insights into the Thermal Response of a Poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) Triblock Polymer in Water

A thermal responsive block copolymer made up of ethylene oxide (EO) and propylene oxide (PO) blocks was simulated with optimized atomistic potentials and enhanced sampling methods over a range of temperatures. The results for the L42 pluronic polymer (EO)₄(PO)₂₂(EO)₄, which is known to undergo a transition in this temperature range, and the similarly sized (EO)₃₀ polymer, which does not, are compared. The thermal responsive L42 polymers in a dilute solution tend to aggregate, and this tendency gets stronger as temperature increases. The poly(ethylene oxide) polymer shows no such tendency. The aggregation is stabilized by the hydrophobic contact of the propylene oxide methyl groups, which outweighs a small loss in hydrogen bonds between the ether oxygens and water.

Temperature, Pressure, and Concentration Derivatives of Nonpolar Gas Hydration: Impact on the Heat Capacity, Temperature of Maximum Density, and Speed of Sound of Aqueous Mixtures

The hydrophobic effect is an umbrella term encompassing a number of solvation phenomena associated with solutions of nonpolar species in water, including the following: a meager solubility opposed by entropy at room temperature; large positive hydration heat capacities; positive shifts in the temperature of maximum density of aqueous mixtures; increases in the speed of sound of dilute aqueous mixtures; and negative volumes of association between interacting solutes. Here we present a molecular simulation study of nonpolar gas hydration over the temperature range 273.15-373.15 K and a pressure range -500 to 1000 bar to investigate the interrelationships between distinct hydrophobic phenomena. We develop a new free energy correlation for the solute chemical potentials founded on the Tait equation description of the equation-of-state of liquid water. This analytical correlation is shown to provide a quantitatively accurate description of nonpolar gas hydration over the entire range of thermodynamic state points simulated, with an error of ∼0.02 k_BT or lower in the fitted chemical potentials. Our simulations and the correlation accurately reproduce many of the available experimental results for the hydration of the solutes examined here. Moreover, the correlation reproduces the characteristic entropies of hydration, temperature dependence of the hydration heat capacity, perturbations in the temperature of maximum density, and changes in the speed of sound. While negative volumes of association result from pairwise interactions in solution, beyond the limits of our simulations performed at infinite dilution, we discuss how our correlation could be supplemented with second virial coefficient information to expand to finite concentrations. In total, this work demonstrates that many distinct phenomena associated with the hydrophobic effect can be captured within a single thermodynamically consistent correlation for solute hydration free energies.

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.

Connections between the Anomalous Volumetric Properties of Alcohols in Aqueous Solution and the Volume of Hydrophobic Association

The partial molar volumes of alcohols in water exhibit a non-monotonic dependence on concentration at room temperature, initially decreasing with increasing concentration before passing through a minimum and rising to the pure liquid plateau. This anomalous behavior is associated with hydrophobic interactions. We report molecular simulations of short chain alcohols and alkanes in water to examine the volumetric properties of these mixtures at infinite dilution over a range of temperatures. Our simulations find this anomaly disappears at a crossover temperature, above which the solute volume only varies monotonically with concentration. A Voronoi volume analysis of solution configurations finds that solutes in clusters take up less space than individual solutes at low temperature and more space at elevated temperatures. These changes in cluster volumes are subsequently shown to correlate with the derivative of the solute partial molar volume with respect to solute concentration. The changes in solute volume upon nonpolar solute association impact the response of molecular-scale hydrophobic interactions for assembly with increasing pressure.

Hydrophobicity Varying with Temperature, Pressure, and Salt Concentration

Temperature-, pressure-, and salt-concentration-induced variations in the solubility of small nonpolar solutes in aqueous solution and the corresponding variations in the solvent-induced pair attraction between such solute molecules are investigated. The variations in the solvation free energy of a solute and those in the solvent-induced pair attraction are well reproduced by a mean-field approximation in which the repulsive cores of solute molecules are treated as hard spheres and the mean-field energy of a solute molecule is taken to be the average potential energy that the solute molecule feels in solution. The mechanisms of variation in the solvation free energy and those of variation in the solvent-induced pair potential, with increasing temperature, pressure, and salt concentration, are clarified. Correlations between the solvation free energy and the solvent-induced pair potential at a contact distance in temperature, pressure, and salt concentration variations are near linear in any mode of variation, but the slope of the linear relation is dependent on the mode of variation and is determined by a ratio of the solvation thermodynamic quantities characteristic of each mode of variation.

Cosolvent Effects on Polymer Hydration Drive Hydrophobic Collapse

Water-mediated hydrophobic interactions play an important role in self-assembly processes, aqueous polymer solubility, and protein folding, to name a few. Cosolvents affect these interactions; however, the implications for hydrophobic polymer collapse and protein folding equilibria are not well-understood. This study examines cosolvent effects on the hydrophobic collapse equilibrium of a generic 32-mer hydrophobic polymer in urea, trimethylamine- N-oxide (TMAO), and acetone aqueous solutions using molecular dynamics simulations. Our results unveil a remarkable cosolvent-concentration-dependent behavior. Urea, TMAO, and acetone all shift the equilibrium toward collapsed structures below 2 M cosolvent concentration and, in turn, to unfolded structures at higher cosolvent concentrations, irrespective of the differences in cosolvent chemistry and the nature of cosolvent-water interactions. We find that weakly attractive polymer-water van der Waals interactions oppose polymer collapse in pure water, corroborating related observations reviewed by Ben-Amotz ( Annu. Rev. Phys. Chem. 2016, 67, 617-638). The cosolvents studied in the present work adsorb at the polymer/water interface and expel water molecules into the bulk, thereby effectively removing the dehydration energy penalty that opposes polymer collapse in pure water. At low cosolvent concentrations, this leads to cosolvent-induced stabilization of collapsed polymer structures. Only at sufficiently high cosolvent concentrations, polymer-cosolvent interactions favor polymer unfolding.

Communication: Stiffening of dilute alcohol and alkane mixtures with water

We probe the anomalous compressibilities of dilute mixtures of alcohols and alkane gases in water using molecular simulations. The response to increasing solute concentration depends sensitively on temperature, with the compressibility decreasing upon solute addition at low temperatures and increasing at elevated temperatures. The thermodynamic origin of stiffening is directly tied to the solute's partial compressibility, which is negative at low temperatures and rises above water's compressibility with increasing temperature. Hydration shell waters concurrently tilt towards clathrate-like structures at low temperatures that fade with heating. Kirkwood-Buff theory traces the solute's partial compressibility to changes in the solute-water association volume upon heating and incongruous packing of waters at the boundary between the more structured hydration shell and bulk water.

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.

Cononsolvency behavior of hydrophobes in water + methanol mixtures

The molecular origin of cononsolvency behavior is explored using molecular dynamics simulations.

Driving forces for the pressure-induced aggregation of poly(N-isopropylacrylamide) in water

Driving forces for the pressure-induced aggregation of poly(N-isopropylacrylamide) in water are discussed.