Modeling the mass-action expression for bidentate adsorption

The number of bidentate binding sites on a pristine surface (i.e., sites comprising two adjacent monodentate sites plus the space between them) can be substantially larger than the maximum number of bidentate molecules that can adsorb to the surface. When bidentate sorption occurs, the number of available bidentate sites decreases in response to direct occupation of some sites, but an even more significant loss results from the fact that several unoccupied sites immediately surrounding each adsorbed molecule can also become unavailable. Recognition of this phenomenon allows development of a model for the adsorption process that matches simulated data from Monte Carlo (MC) modeling extremely well. The model also explains the observation that, on a given surface with a given fractional occupation, the number of available bidentate sites depends on whether the occupied sites are populated by monodentate or bidentate adsorbed species. A model developed more than 60 years ago but not widely recognized by modern adsorption modelers also fits the MC simulations very well. The simulated data are also reasonably approximated by assuming that the number of available bidentate sites on a surface is proportional to the square of the number of available monodentate sites, although the fit is not as good as with the models mentioned above. By contrast, approximating the number of available sites as proportional to the number of monodentate sites to the first power yields predictions that do not match the simulations. The results have implications for modeling of both multidentate adsorption reactions and monovalent-divalent ion exchange.