Theoretical analysis of the pseudo-second order kinetic model of adsorption. Application to the adsorption of Ag(I) to mesoporous silica microspheres functionalized with thiol groups

There is no universally accepted theoretical interpretation of the rate constant of the pseudo-second order kinetic model of adsorption. This study proposes a relationship for the rate constant of the pseudo-second order adsorption model based on the diffusion mass transfer of the adsorbate within spherical homogeneous adsorbent microspheres. This relationship provides a new interpretation of the physical meaning of the rate constant mentioned above.A detailed study of the adsorption of Ag(I) onto and within isolated mesoporous silica microspheres functionalized with thiol groups has been conducted. The experimental data were fitted successfully by the pseudo-second order model resulting in the determination of the values of the corresponding apparent diffusion coefficient (DAg) and the adsorbate adsorbed on the surface of the particles (qs). The latter value was found to be almost equal to the corresponding equilibrium value (qe). The logarithm of the value of DAg increased linearly from 2.5 × 10−17 m2/s to 6 × 10−16 m2/s with the decrease in the saturation ratio (qs/qmax where qmax is the maximum amount of Ag adsorbed).

• Equation for the rate constant in the pseudo-second order kinetic model is proposed.
• This rate constant is correlated to the diffusion coefficient in spherical particles.
• The adsorption of Ag(I) within mesoporous spherical particles is studied.
• The adsorption data are fitted by the spherical diffusion model.
• The diffusion coefficient value depends on the saturation ratio for adsorption.