A modification of the Langmuir rate equation for diffusion-controlled adsorption kinetics

It is widely agreed that the classical Langmuir rate equation cannot be applied for describing the kinetics of adsorption processes whose rate is controlled by diffusive transport phenomena. To overcome this limit, we propose a modification of the Langmuir rate equation, referred to as Diffusion-Controlled Langmuir Kinetics (DCLK), assuming that the macroscopic forward rate of adsorption is inversely related to the square root of time. We tested the DCLK model on experimental adsorption kinetic data. The results indicate that the DCLK model describes the kinetic data better than the traditional pseudo-second order model. Consistently with the intraparticle adsorption/diffusion theory, the adsorption amount predicted by the DCLK model proportionally increases with the square root of time at the beginning of the process. The effect of temperature on the adsorption rate and the relative role played by kinetics and thermodynamics are discussed.