where the summation is taken over all unique types of species, q α is the charge on species type α, and n (α) 0 is the bulk number density of species α. The exponential term asserts that the position-dependent concentration of species α is Boltzmann distributed according to the charge-potential interaction. For dilute solutions, and systems with V 0 lower than about 0.5mV, the exponent in Eq. 15 can be expanded to first order in φ to yield an interfacial potential profile that decays approximately exponentially with a specific form, 67