A classical density functional theory for solvation across length scales

TL;DR

This paper introduces a classical density functional theory approach that accurately models solvation of apolar solutes across multiple length scales, incorporating critical phenomena and temperature dependence, with improved simplicity over existing theories.

Contribution

It develops a new cDFT-based method building on LCW theory, enabling easier and more general modeling of solvation phenomena across length scales.

Findings

Captures critical drying physics in solvation.

Accounts for temperature dependence of solvation.

Simplifies numerical implementation compared to LCW theory.

Abstract

A central aim of multiscale modeling is to use results from the Schr\"odinger Equation to predict phenomenology on length scales that far exceed those of typical molecular correlations. In this work, we present a new approach rooted in classical density functional theory (cDFT) that allows us to accurately describe the solvation of apolar solutes across length scales. Our approach builds on the Lum-Chandler-Weeks (LCW) theory of hydrophobicity [K. Lum et al., J. Phys. Chem. B 103, 4570 (1999)] by constructing a free energy functional that uses a slowly-varying component of the density field as a reference. From a practical viewpoint, the theory we present is numerically simpler and generalizes to solutes with soft-core repulsion more easily than LCW theory. Furthermore, by assessing the local compressibility and its critical scaling behavior, we demonstrate that our LCW-style cDFT approach contains the physics of critical drying, which has been emphasized as an essential aspect of hydrophobicity by recent theories. As our approach is parameterized on the two-body direct correlation function of the uniform fluid and the liquid-vapor surface tension, it straightforwardly captures the temperature dependence of solvation. Moreover, we use our theory to describe solvation at a first-principles level, on length scales that vastly exceed what is accessible to molecular simulations.