Length-Scale Dependent Hydration and Crossover at Solid-Liquid Interfaces of Diverse Chemistries

The free energy of hydration of a hydrophobic solute as a function of its size displays a crossover at nanometer length scales. To solvate small solutes, the hydrogen bond network of water is stretched, leading to solvation free energies that are super-extensive in volume and entropies that are negative. Beyond a certain solute size, water can no longer hydrogen bond around the solute, resulting in broken hydrogen bonds and the concomitant formation of a soft liquid-vapor-like interface with free energies that are proportional to the surface area and entropies that are positive. We explore the length-scale dependence of solvation at the interface between a self assembled monolayer (SAM) and water. The hydrophobicity (as measured by the contact angle), of the SAM surface can be tuned by choosing the appropriate head-group. Using molecular dynamics simulations, we quantify the free energies and entropies of cavity formation near various SAM surfaces. We show that near a hydrophilic surface, the free energy to solvate a hydrophobe displays the same cross-over behavior as in bulk water. In contrast, there is no such cross-over near a hydrophobic surface and the free energies are proportional to the surface area at all length scales. These results have implications on thermodynamics of binding and association for macromolecular solutes.