Charged particles on surfaces: Coexistence of dilute phases and periodic structures at interfaces

We consider a mixture of two immiscible oppositely charged molecules strongly adsorbed to an interface, with a neutral nonselective molecular background. We determine the coexistence between a high density ionic periodic phase and a dilute isotropic ionic phase. We use a strong segregation approach for the periodic phase and determine the one-loop free energy for the dilute phase. Lamellar and hexagonal patterns are calculated for different charge stoichiometries of the mixture. Molecular dynamics simulations exhibit the predicted phase behavior. The periodic length scale of the solid phase is found to scale as ε/(lBψ3/2), where ψ is the effective charge density, lB is the Bjerrum length, and ε is the cohesive energy.