Approximate analytical modeling of nonlinear CO₂ adsorption kinetics

Heterogeneous CO₂ adsorption kinetics on solid amine sorbents are analyzed using a Toth-type isotherm to describe equilibrium behavior, leading to a nonlinear ordinary differential equation governing the temporal evolution of surface coverage. The nonlinear adsorption rate, formulated in terms of the driving force between equilibrium and instantaneous coverages, is solved analytically using the Rajendran–Joy method (RJM), yielding closed-form expressions for transient adsorption uptake over a wide time domain. The analytical solutions are validated against numerical simulations and quantitatively benchmarked against established Toth-based kinetic models, demonstrating comparable predictive accuracy with significantly reduced computational cost and enhanced parametric transparency. Sensitivity analysis elucidates the influence of kinetic and isotherm parameters on adsorption dynamics and identifies limiting regimes where the model reduces to linear or pseudo-order kinetics. The model limitations, including its validity range under strongly nonlinear adsorption conditions, are discussed. Beyond gas–solid capture systems, the developed kinetic framework is also applicable to electrochemical interfaces where CO₂ adsorption on amine-functionalized electrodes or catalytic surfaces governs interfacial reaction rates, such as in electrochemical CO₂ reduction processes.