A stochastic description of pH within nanoscopic water pools

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.