Theoretical description of the kinetics of solute adsorption at heterogeneous solid/solution interfaces: On the possibility of distinguishing between the diffusional and the surface reaction kinetics models

Abstract

The kinetics of adsorption at solid/liquid interfaces is of crucial importance for life on our planet and a variety of technological processes. Let us remark, for instance, that the oxide/electrolyte interface is the largest natural interface existing on the earth. It is very impressive to observe the growing number of the papers reporting on application of adsorption processes in the technologies of environmental protection. The purification of wastewaters, for instance, has become one of the largest industries now. To optimize the cost and performance of the adsorption technology, one has to consider both the costs of sorbents, and the efficiency of the adsorption process. That efficiency is related not only to the equilibrium features of an adsorption system but also to the kinetics of the adsorption process. In technological processes a sorbent and a solution are brought into contact for a limited period of time, so, the rate of the transport of solute molecules from the bulk to the adsorbed phase is here of a primary importance. According to some generally expressed views a sorption process can be described by four consecutive kinetic steps: 1. transport in the bulk solution; 2. diffusion across the film surrounding the sorbent particles; 3. diffusion in the pores of the sorbent; 4. sorption and desorption on the solid surface viewed as a kind of chemical reaction. One of these steps is the slowest and controls the rate of sorption. Depending on the assumption which of these steps is the rate-controlling one, a variety of equations have been proposed in literature to describe that kinetic step. The knowledge of the nature of that kinetic and its theoretical description are very crucial for practical applications, as a key to design the adsorption equipment and conditions for an optimum efficiency to be achieved. So, first some laboratory experimental tests and next their subsequent theoretical analyses are carried out to elucidate the nature of the rate-controlling kinetic process. Such studies may involve a variety of experiments whose time dependence of adsorption is the most fundamental information. Sometimes accompanying studies of the corresponding adsorption equilibria are also carried out, but it seems that the importance of these studies has not been sufficiently recognized. Only such combined study creates a chance to distinguish correctly between one and another kinetic model to be assumed. However, the most essential condition is using proper theoretical expressions to represent the features of some kind of kinetics. Here we will show how the above-mentioned conditions may affect distinguishing between the kinetics which is governed by the intraparticle diffusion, and that in which surface reactions control the rate of sorption in an adsorption system. This is because these two kinetic models are most frequently assumed in the theoretical interpretation of experimental kinetic data.