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The role of available sites in the activity of lattice gases with geometric constraints.

The activity in lattice-gas systems with geometric constraints is shown to be the ratio of the number of particles to the number of available sites. The key role of sites available for occupation is emphasized. Available sites may be different for different species and are not necessarily just unoccupied sites. Location-specific or non-local constraints are allowed. An analytical expression for the number of available sites is given for the hard-hexagon model. The utility of an expression for available sites is illustrated for the non-trivial case of a mixed Langmuir/hard-hexagon adsorption system, where the influence of the Langmuir adsorbates on the hard-hexagon phase transition is investigated. The dependence on available sites indicates how to extend these results to the kinetic regime and simulations of kinetic voltammograms for the hard-hexagon model are given as an example.