Diffusion Influenced Adsorption Kinetics

• Published in: The journal of physical chemistry. B Vol. 119; no. 34; pp. 10954 - 10961
• Main Authors: Miura, Toshiaki, Seki, Kazuhiko
• Format: Journal Article
• Language: English
• Published: United States American Chemical Society 27.08.2015
• Subjects: Adsorption; chemical elements; Diffusion; equations; Exact solutions; Lower bounds; Mathematical analysis; Mathematical models; Nonlinearity; solutes; Surface chemistry
• ISSN: 1520-6106; 1520-5207; 1520-5207
• DOI: 10.1021/acs.jpcb.5b00580

When the kinetics of adsorption is influenced by the diffusive flow of solutes, the solute concentration at the surface is influenced by the surface coverage of solutes, which is given by the Langmuir–Hinshelwood adsorption equation. The diffusion equation with the boundary condition given by the Langmuir–Hinshelwood adsorption equation leads to the nonlinear integro-differential equation for the surface coverage. In this paper, we solved the nonlinear integro-differential equation using the Grünwald–Letnikov formula developed to solve fractional kinetics. Guided by the numerical results, analytical expressions for the upper and lower bounds of the exact numerical results were obtained. The upper and lower bounds were close to the exact numerical results in the diffusion- and reaction-controlled limits, respectively. We examined the validity of the two simple analytical expressions obtained in the diffusion-controlled limit. The results were generalized to include the effect of dispersive diffusion. We also investigated the effect of molecular rearrangement of anisotropic molecules on surface coverage.