Lattice theory of competitive binding: Influence of van der Waals interactions on molecular binding and adsorption to...

The reversible binding of molecules to surfaces is one of the most fundamental processes in condensed fluids, with obvious applications in the molecular separation of materials, chromatographic characterization, and material processing. Motivated in particular by the ubiquitous occurrence of binding processes in molecular biology and self-assembly, we have developed a lattice type theory of competitive molecular binding to solid substrates from binary mixtures of two small molecule liquids that interact between themselves by van der Waals forces in addition to exhibiting binding interactions with the solid surface. The derived theory, in contrast to previously existing theoretical frameworks, enables us to investigate the influence of van der Waals interactions on interfacial binding and selective molecular adsorption. For reference, the classic Langmuir theory of adsorption is recovered when all van der Waals interaction energies between the molecules in the bulk liquid phase and those on the surface are formally set to zero. Illustrative calculations are performed for the binding of molecules to a solid surface from pure liquids and from their binary mixtures. The properties analyzed include the surface coverage θ, the binding transition temperature T_bind, the individual surface coverages, θ_A and θ_C, and the relative surface coverages, σ_AC≡θ_A/θ_C or σ_CA≡θ_C/θ_A. The latter two quantities coincide with the degrees of adsorption directly determined from experimental adsorption measurements. The Langmuir theory is shown to apply formally under a wide range of conditions where the original enthalpies (Δh or Δh_A and Δh_C) and entropies (Δs or Δs_A and Δs_C) of the binding reactions are simply replaced by their respective "effective" counterparts (Δh_eff or Δh_A^eff and Δh_C^eff and Δs_eff or Δs_A^eff and Δs_C^eff), whose values depend on the strength of der Waals interactions and of the "bare" free energy parameters (Δh or Δh_A and Δh_C, and Δs or Δs_A and Δs_C). Numerous instances of entropy-enthalpy compensation between these effective free energy parameters follow from our calculations, confirming previous reports on this phenomenon obtained from experimental studies of molecular binding processes in solution.