Pseudosecondorder

Pseudosecondorder, or pseudo-second-order kinetics, is a commonly used kinetic model in adsorption science and related fields. It describes processes in which the rate of adsorption depends on the square of the number of unoccupied sites, yielding an apparent second-order dependence when expressed in terms of the adsorbate uptake. The model is frequently written as dq_t/dt = k2 (q_e - q_t)^2, where q_t is the amount adsorbed at time t, q_e is the equilibrium adsorption capacity, and k2 is the rate constant of pseudo-second-order adsorption.

Integration of the rate equation yields forms used to fit experimental data. The linear form most often employed is t/q_t = 1/(k2 q_e^2) + t/q_e, from which q_e and k2 can be estimated by linear regression. The nonlinear form expresses the time dependence directly as q_t = q_e - 1/(k2 t + 1/q_e). These forms allow researchers to extract kinetic parameters and compare different adsorbents or conditions.

Applications and interpretation vary. Pseudosecondorder behavior is widely observed for chemisorption processes, such as dye molecules or metal ions binding to activated carbon and other sorbents, and is often interpreted as the rate-limiting step involving chemical bonding rather than diffusion. However, the model is empirical and a good fit does not prove a particular mechanism. Alternative kinetics models (for example, pseudo-first-order, Elovich, or intraparticle diffusion) may better describe some systems.

Origin and usage. The pseudo-second-order model was popularized in adsorption studies by Ho and McKay in the late 1990s and has since become a standard tool for analyzing adsorption kinetics.