Evaporation Rate of Water in Hydrophobic Confinement

Abstract: The drying of hydrophobic cavities is believed to play an important role in biophysical phenomena such as the folding of globular proteins, the opening and closing of ligand-gated ion channels, and ligand binding to hydrophobic pockets. We use forward flux sampling, a molecular simulation technique, to compute the rate of capillary evaporation of water confined between two hydrophobic surfaces separated by nanoscopic gaps, as a function of gap, surface size and temperature. Over the range of conditions investigated (gaps between 9 and 14 {\AA} and surface areas between 1 and 9 nm^2) the free energy barrier to evaporation scales linearly with the gap between hydrophobic surfaces, suggesting that line tension makes the predominant contribution to the free energy barrier. The exponential dependence of the evaporation rate on the gap between confining surfaces causes a ten order-of-magnitude decrease in the rate when the gap increases from 9 to 14 {\AA}. The computed free energy barriers are of the order of 50kT, and are predominantly enthalpic. Evaporation rates per unit area are found to be two orders of magnitude faster in confinement by the larger (9 nm^2) than by the smaller (1nm^2) surfaces considered here, at otherwise identical conditions. We show that this is a direct consequence of the dependence of hydrophobic hydration on the size of solvated objects. For sufficiently large surfaces, the critical nucleus for the evaporation process is a gap-spanning cylindrical vapor tube.