Ion fluctuations within an aqueous microdroplet in an apolar medium

The density fluctuation of counterions within an aqueous droplet is investigated. In terms of mean-square dipole moment, the fluctuation grows and becomes saturated as the counterion concentration is increased. Using fluctuation-dissipation theorem, the mean-square dipole moment is found to be proportional to the polarizability of the microdroplet. This relation is confirmed by simulations and indicates that the nature of ion fluctuations is possible to be captured by the simple mean-field theory. With the Debye-Hückel approximation, an analytical expression for the mean-square dipole moment is obtained by the Poisson-Boltzmann theory. It agrees reasonably well with the results by simulations.