Chemical model for positively charged dust particles

A chemical model of electron-dust plasmas consisting of electrons and dust particles is systematically developed. An insight is exploited that a single dust particle forms a potential well for electrons, whose depth is determined by the work function of the dust material. The whole electron fluid, initially concentrated inside the dust particles, is somehow reallocated between the bulk of the dust matter and the ambient space available, which is then interpreted as thermionic emission. An expression is employed for the Helmholtz free energy of the system, which includes the ideal and excess parts to thoroughly deal with interactions between the dusty plasma constituents. Numerical calculations of dust particle charge are performed in quite a broad domain of plasma parameters, and a straightforward comparison is made with the orbital motion limited (OML) approximation to demonstrate that the proposed calculation scheme predicts higher positive charge values of dust grains. It is also proved that the OML approximation exactly corresponds to the ideal-gas model when interactions between plasma particles are entirely neglected.