Orbital motion limited theory for porous dust grains: Charging of mesoporous nanoparticles in dusty plasmas

Orbital motion limited (OML) theory has described dust grain charging in plasmas for nearly four decades under the assumption that grains are solid and impenetrable. We relax this assumption by recognizing that ions incident on a porous grain can enter surface pores and be diverted from the outer-shell collection current. The resulting porous OML equation modifies the standard current balance by a single factor (1−ε) on the ion current, where ε is the effective fraction of the ion current diverted through pore channels. Perturbation analysis yields the floating potential shift ΔVf=−Te α ε, where the porosity response coefficient α depends only on the plasma environment; no grain radius, pore diameter, shell thickness, or porosity enters α at any point in the derivation. All geometric information resides in ε alone. We develop a transmission pipeline that computes ε from measurable grain parameters and validate the framework across five hollow mesoporous silica geometries. Stochastic charging analysis via master equation and Gillespie simulation confirms the mean-field predictions at the discrete-charge level. All reported shifts are upper bounds in the transparent-shell limit, where the ion-escape probability Pescape=1 (every ion entering a pore exits the grain without depositing charge); the optimized geometry produces an upper-bound shift of 65.9 mV (6.6× the Langmuir probe detection threshold) in this limit.