Adsorption of patchy colloids on a patchy surface: A combined thermodynamic perturbation theory and Henderson–Abraham–Barker approach

Reversible binding of ligands to their substrates is a common refrain in physics, chemistry, and other disciplines that features prominently in problems as diverse as the binding of proteins to membranes or passivating ligands depositing onto quantum dots. Here, we introduce a theoretical formalism to describe this phenomenon analytically with the help of very basic physical concepts. We assume that the ligands can be modeled as spherical particles that interact with each other via an attractive patch placed rigidly on their surface. The ligands are located above an infinite impenetrable surface with which they also interact via attractive patches. Therefore, the proposed model captures excluded volume of ligands, confinement in space, and adsorption to planes mediated by attractive forces—the three basic properties common to all complexation processes near surfaces. The Wertheim thermodynamic perturbation theory for associating fluids is extended to the proposed model utilizing the Henderson–Abraham–Barker-type approach. Analytical expressions are derived for the surface coverage as a function of various parameters such as temperature, ligand density, and others. Computer simulations are performed to test and confirm the accuracy of the theoretical predictions. Increasing ligand density is seen to enhance the surface coverage, while ligand–ligand interactions always lead to surface destabilization. Similarly, sticky patches on a surface in close proximity to each other negatively affect its ligand coverage. Our findings add new insight to the basic understanding of ligand–surface interactions, suggesting that the proposed model can be used as a powerful tool with which to design and analyze new surface-based materials.