Rethinking of the intraparticle diffusion adsorption kinetics model: Interpretation, solving methods and applications

Adsorption is a widely used unit process in various fields, such as chemical, environmental and pharmaceutical, etc. The intraparticle diffusion adsorption kinetics model is one of the most widely used adsorption kinetics models. However, the application and solving method of this model have yet to be discussed. This model has two forms (qt = kt1/2 and qt = kt1/2 + constant, where qt is the adsorption capacity at time t, k and constant are the model parameters), which have not been unified yet. Moreover, the interpretation of this kinetics model lacks a theoretical basis (if the line passes through the origin point (0, 0), the adsorption is dominated by the intra-particle diffusion; if not, it is a multiple adsorption process). In this study, we analyzed the proper equations of the intraparticle diffusion model and their applications, discussed the interpretation of the mass transfer steps revealed by this model, and provided the solving methods. The result indicated that the piecewise function qt = k1t1/2 (0 < t < t1); qt -qt = t1 = k2(t- t1)1/2 (t1 < t < t2) is the proper form of this model. The adsorbate diffusion in the pores inside the adsorbent is the mass transfer step revealed by this model. The statistical parameters should be used to evaluate the fitting results instead of judging whether the model lines pass through the origin point (0, 0). We provide the solving methods to use the Origin and Microsoft EXCEL software to solve the model. Our study established the method for application of the intraparticle diffusion model.