A stochastic description of pH within nanoscopic water pools

Abstract

The nature of pH in a pure water pool that is too small to have a continuous population of ions formed by water dissociation is not settled. Here, we use stochastic kinetics simulations of the water dissociation reaction in pools ranging from 103 to 1016 waters to characterize water ion lifetimes and populations. An availability coefficient is defined to quantify the intermittent presence of ion pairs during an arbitrary observation period and used in a proposed definition for the effective pH of nanoscopic pools. The effective pH converges to the bulk value of 7 for water pools in the range of 1010 waters. The lifetimes of water ion pairs are found to increase with increasing water pool size due to the balance between their formation and recombination kinetics, with a maximum near the size where bulk-like characteristics begin to dominate and ion pairs are continuously present.