Effect of electrostatic interaction on deposition of colloid on partially covered surfaces: Part I. Model formulation

We discuss the existing 2D and 3D random sequential adsorption (RSA) models and demonstrate that some of the assumptions used in these models can lead to incorrect results. Specifically, neglecting the particle–surface interaction at a distance from the adsorption surface in the 2D model can result in overestimating the surface blocking effect, while the assumption of the rectilinear particle trajectory in the model 3D can lead to inaccurate pair correlation functions. Next, we propose a new RSA approach that overcomes these shortcomings of the 2D and 3D models and allows modeling soft colloidal particle deposition (irreversible adsorption) on surfaces precovered with smaller particles. This approximate model allowing electrostatic interaction of colloid particles at a charged interface employs a many-body superposition approximation and considers adsorbing particle curvilinear trajectory in the thin electrolyte layer adjacent to the interface. Finally, we derive approximate analytical expressions for the available surface function of the adsorbing particle in the limit of low surface coverage, applying the 2D scaled-particle theory with a modification for the sphere geometry and electrostatic interaction.