Penetration of an Ion Through a Monolayer of Similar Ions Adsorbed on a Metal

A fractional monolayer film of ions is formed by the adsorption of a gas onto a metal substrate. These ions form a discrete dipole layer, the potential across it being the change in electron work function of the surface. As additional ions are brought to the surface, they penetrate only a fraction f of the potential across the dipole layer. In this work the penetration coefficient f valid for the entire range of coverages is derived for two limiting types of films, immobile and mobile. By considering thermal effects, a penetration coefficient for partially mobile films is also derived. The values obtained for the penetration coefficient are applicable to any substrate-adsorbate system. The theoretical expressions for the penetration coefficient are evaluated for cesium on tungsten and compared with the data of Taylor and Langmuir.