Effect of Surface Diffusion on Adsorption–Desorption and Catalytic Kinetics in Irregular Pores. II. Macro-Kinetics

4 years ago

Effect of Surface Diffusion on Adsorption–Desorption and Catalytic Kinetics in Irregular Pores. II. Macro-Kinetics

Saúl Iván Hernández, Iván Santamaría-Holek, Aldo Ledesma-Durán

In this work we show how the effective diffusion coefficient of a membrane, in which heterogeneous reaction-diffusion processes are present, is related to the geometric irregularity of the pores and how it is affected by the surface diffusion of an adsorbed phase. A theoretical expression for this effective membrane diffusion coefficient is deduced starting from a recent generalization of the so-called Fick–Jacobs approximation. Our analysis comprises the interrelation of bulk and surface diffusion with the heterogeneous catalysis and adsorption/desorption interchange of matter between the bulk and the walls of the pore. Therefore, our theoretical framework is a very useful tool in modeling the process of heterogeneous catalysis inside porous materials when the shape of the pores is known. Through some illustrative examples involving the classical Langmuir processes as a reference, we provide a useful methodology correlating the local properties of transport inside a pore of irregular shape with the effective diffusion coefficient of a membrane. This coefficient can be measured experimentally by fitting the spatio-temporal concentration profiles in adsorption experiments. We show the different dependencies of this coefficient with the surface diffusion, the shape of the pore, and the average loading of adsorbed particles. A reverse methodology is also sketched, in which we suggest how to use the data emerging from experiments in order to determine the intensity of the surface diffusivity.

Publisher URL: http://dx.doi.org/10.1021/acs.jpcc.7b03653

DOI: 10.1021/acs.jpcc.7b03653