Fractional Kinetic Strategy toward the Adsorption of Organic Dyes: Finding a Way Out of the Dilemma Relating to Pseudo-First- and Pseudo-Second-Order Rate Laws

Abstract

Recently, there has been debate about using a pseudo-second-order model in adsorption kinetics and its ability to fit experimental data, especially at the initial stages. This paper introduces a generalized fractional kinetic model obtained via a fractional reaction–diffusion equation with a time-dependent reaction rate. This model is presented as a dependable approach to understanding chemical adsorption kinetics. It offers insights into the adsorbate history and extends classical kinetic models, such as pseudo-first-order and pseudo-second-order models. The generalized fractional kinetic model accounts for memory effects with long-range interactions, heterogeneity, and nonequilibrium dynamics, leading to more accurate predictions of adsorption rates, capacities, and equilibrium values. As an applied context, we use the fractional kinetic model to analyze experimental data on the adsorption of anionic acid yellow-17 and cationic brilliant green dyes in single and binary systems. The fractional kinetic model is employed to fit the data by incorporating waiting times into the adsorption process and correlating macroscopic properties, such as the pH, with adsorption dynamics.