Quantification of the water-mediated interaction varying with solute size Hidefumi Naito, Tomonari Sumi and Kenichiro Koga Okayama University, Japan Water-mediated interactions, i.e., effective interactions between solute molecules in aqueous solutions, are qualitatively different from those in a vacuum. They are the driving force for molecular assemblies of amphiphiles, play significant roles in the stability of proteins and protein complexes in vivo, and are responsible for rich phase behaviors of colloidal systems. There are two important factors that determine the strength of a water-mediated interaction at a given thermodynamic condition: geometric factor (size and shape of a solute molecule) and chemical factor (solute-water interaction). The main purpose of the present study is to quantify the solute size dependence of the strength of water-mediated interactions. One way to quantify the strength of effective interactions is the measurement of the osmotic second virial coefficient B as it is related to the potential of mean force between solutes in an infinitely dilute solution. Experimental data and computer-simulation results of B for different solute species are still sparse, and so we know very little about the effect of solute size on B . Using molecular dynamics (MD) simulation, we evaluated B for spherical nonpolar solutes with diameters σ in the range corresponding to methane to C 60 diameters. In this diameter range, B is negative and rapidly decreases with increasing σ . The numerical data of B vs. σ is the best fit by the power law σ α with α = 7. We reported earlier that the power is close to 6 for a slightly narrower range of σ 1 . Since the second virial coefficient B gas of a gas (e.g., Lennard-Jones particles) is proportional to σ 3 , the size dependence of the osmotic second virial coefficient is by far stronger than that of B gas . The thermodynamic relation between B and B′′ (the analog of B but for the expansion of the osmotic pressure at fixed density of the solvent instead of fixed chemical potential of the solvent) suggests the 6th-power dependence but does not exclude other dependences, including the 7th power 2 . To explore the σ dependence of B over a wide range of σ , we calculated B for two-component hard-sphere mixtures using integral equation theory. The results are partly consistent with the MD simulation results and may explain why B seems not to follow a single power law. References
1. H. Naito, R. Okamoto, T. Sumi, and K. Koga, J. Chem. Phys. , 2022, 156 , 221104. 2. K. Koga, V. Holten, and B. Widom, J. Phys. Chem. B , 2015, 119 , 13391-13397.
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