No abstract

No abstract

For practical applications of solid/solution adsorption processes, the kinetics of these processes is at least as much essential as their features at equilibrium. Meanwhile, the general understanding of this kinetics and its corresponding theoretical description are far behind the understanding and the level of theoretical interpretation of adsorption equilibria in these systems. The Lagergren empirical equation proposed at the end of 19th century to describe the kinetics of solute sorption at the solid/solution interfaces has been the most widely used kinetic equation until now. This equation has also been called the pseudo-first order kinetic equation because it was intuitively associated with the model of one-site occupancy adsorption kinetics governed by the rate of surface reaction. More recently, its generalization for the two-sites-occupancy adsorption was proposed and called the pseudo-second-order kinetic equation. However, the general use and the wide applicability of these empirical equations during more than one century have not resulted in a corresponding fundamental search for their theoretical origin. Here the first theoretical development of these equations is proposed, based on applying the new fundamental approach to kinetics of interfacial transport called the Statistical Rate Theory. It is shown that these empirical equations are simplified forms of a more general equation developed here, for the case when the adsorption kinetics is governed by the rate of surface reactions. The features of that general equation are shown by presenting exhaustive model investigations, and the applicability of that equation is tested by presenting a quantitative analysis of some experimental data reported in the literature.

It is shown that the popular pseudo-first-order Lagergren equation can be applied to correlate kinetic adsorption data only in the adsorption systems that are not far from equilibrium. Also, it is shown that the Lagergren equation is then the limiting form of the kinetic equations developed by assuming both diffusional and surface reaction kinetic models. However, the theoretical interpretation of the coefficients in the Lagergren equation is then different for the two different kinetic models. The comparison of the theoretically predicted values of these coefficients with their experimentally determined values creates a chance to conclude whether the diffusional or the surface reaction model should be assumed to represent the kinetics of adsorption in an investigated adsorption system.

Due to their crystallochemical properties, clay minerals feature different types of structural surfaces which have their own adsorption energy distribution. To study that type of surface heterogeneity, the DIS (derivative isotherm summation) method has been developed by us. Now, a modified version of the DIS method is derived by using the Jagiełło-Rudziński approach and assuming that the local energy distributions are represented by the Dubinin−Asthakov distributions. Two different types of isotherms equations are used, one to describe adsorption in micropores and another one for describing adsorption on external surfaces. The derivatives of experimental adsorption isotherms with regard to ln(p/p s) are simulated by combinations of the derivatives of corresponding local adsorption isotherms. This best fit provides information on adsorption capacity of the local existing domains, on the symmetry of their energy distribution function, and on the parameters characterizing the lateral interactions in each adsorption domain. Using the new equations for the local isotherm derivatives allows now to simulate very accurately derivatives of experimental adsorption isotherms, obtained by using our high-resolution quasi-equilibrium volumetric technique. This was proven in the case for three different well characterized clay minerals:  a structural microporous one (palygorskite) and two nonporous lamellar ones (kaolinites). The obtained parameters allow a description of the adsorption energy distribution of their different surfaces, their textural parameters, as well as the energy distrubution in micropores for the microporous samples. In addition to the experimental adsorption isotherms, the related experimental heats of adsorption were employed as a second independent source of information about the energetic heterogeneity of the studied clay minerals. Using the parameters determined from adsorption isotherms, the corresponding isosteric heats of adsorption were calculated and compared with experimental values. The simultaneous good fit of the experimental isotherm derivatives and of the experimental heats of adsorption was a solid check for the correctness of the determined parameters characterizing the adsorption energy distributions and the lateral interactions between the adsorbed molecules.

No abstract

The applicability of the pseudo-second order equation (PSOE) has been explained on the ground of the model assuming that the overall sorption rate is limited by the rate of sorbate diffusion in the pores of sorbent (intraparticle diffusion model). Mathematical expressions have been proposed in order to describe the dependence of the pseudo-second order constant on such parameters as the initial sorbate concentration, the progress of the sorption process and the solid/solution ratio. Further, it has been shown that equilibrium sorption capacities estimated by using PSOE may be much lower than the actual ones: it depends mainly on how the sorption system is close to equilibrium. The values of parameters applied in calculations were taken from the literature and correspond to the biosorption systems designed to remove the heavy metals from the aqueous solution.

A quantitative theoretical analysis of the enthaplic effects accompanying ion adsorption at the oxide/electrolyte interface, based on a model of energetically heterogeneous surface oxygens, is presented. The triple layer complexation model is accepted, along with the 2-pK charging mechanism. For the purpose of illustration a set of experimental data is subjected to that quantitative analysis including titration curves, radiometrically measured individual iostherms of ions, and calorimetric titration data for the alumina/NaCl electrolyte system. Two models of energetic heterogeneity were taken into consideration. One of them assumes that the binding-to-oxygen energies of the surface complexes vary but are highly correlated when going from one to another surface oxygen. The other model of surface heterogeneity assumes that these correlations are very small. Our numerical simultaneous analysis of the titration data, of the individual isotherms of Na+ and Cl- adsorption, and of the accompanying heat effects advocates strongly for the model of surface heterogeneity assuming small correlations to exist. A good simultaneous fit of all three kinds of experimental data is obtained, with a small uncertainty as for the values of the estimated adsorption parameters. A simultaneous fit of the measured enthalpic effects appears to be an especially strong criterion for a proper choice of adsorption parameters.