An Adsorption Isotherm That Includes the Interactions between Adsorbates

We have developed a new adsorption isotherm that includes repulsive interactions between the adsorbates. By regarding the adsorbate–surface system as a finite array of classical dipoles, we can theoretically derive that the repulsive electrostatic interactions lead to a quadratic coverage dependence in the adsorption energy. On a phenomenological level, density functional theory calculations for N atoms on an Fe{100} surface show that adsorbates interact by a combination of electronic and electrostatic interactions along with positional relaxations to minimize repulsive interactions. We observe that the combination of all these effects also leads to a quadratic coverage dependence in the adsorption energy (or cubic, if the adsorbates cannot relax positionally). The quadratic coverage dependence reflects that the electronic and electrostatic adsorbate interaction mechanisms are highly localized and therefore relatively more important at higher coverages where more adsorbates come into closer proximity. This quadratic coverage dependence is incorporated into the new isotherm. When evaluated against the dissociative adsorption of nitrogen on an industrial iron catalyst for ammonia synthesis, the new isotherm is superior to the classic Frumkin-Temkin isotherms and far superior to the Langmuir isotherm. These new measurements also show that the existing microkinetic models, which constitute the state of the art understanding of industrial ammonia synthesis, overestimate the critical N₂ dissociation rate by multiple orders of magnitude due to oversimplifications in the underlying Langmuir descriptions. This illustrates the value of the new isotherm for description of adsorption in connection with catalytic reactions. Additionally, the new isotherm provides a superior description of diverse cases such as nutrient adsorption on soil particles, chromatographic purification of proteins, and adsorption processes for CO₂ capture.