Adsorption kinetics Elovich equation

In practice the kinetics are usually more complex than might be expected on this basis, siace the activation energy generally varies with surface coverage as a result of energetic heterogeneity and/or sorbate-sorbate iateraction. As a result, the adsorption rate is commonly given by the Elovich equation (15) ... 

Kinetics of Adsorption and Desorption and the Elovich Equation C. Aharoni and F. C. Tompkins... 

Reaction kinetics. The time-development of sorption processes often has been studied in connection with models of adsorption despite the well-known injunction that kinetics data, like thermodynamic data, cannot be used to infer molecular mechanisms (19). Experience with both cationic and anionic adsorptives has shown that sorption reactions typically are rapid initially, operating on time scales of minutes or hours, then diminish in rate gradually, on time scales of days or weeks (16,20-25). This decline in rate usually is not interpreted to be homogeneous The rapid stage of sorption kinetics is described by one rate law (e.g., the Elovich equation), whereas the slow stage is described by another (e.g., an expression of first order in the adsorptive concentration). There is, however, no profound significance to be attached to this observation, since a consensus does not exist as to which rate laws should be used to model either fast or slow sorption processes (16,21,22,24). If a sorption process is initiated from a state of supersaturation with respect to one or more possible solid phases involving an adsorptive, or if the... 

The Elovich equation was developed to determine the kinetics of heterogeneous chemisorption of gases on sohd surfaces. This equation assumes a heterogeneous distribution of adsorption energies, where the energy of activation E) increases linearly with surface coverage (Rao et al. 1989). A simplified Elovich equation used to study the rate of soil chemical processes is given by... 

In the cases of Cr203, NiO, and Fe2Ch it was possible (24) to follow the kinetics of the adsorption of 02 at constant pressures around 6 cm. It was found that the uptake q followed the Elovich equation ... 

Rudzinski W. and Panczyk T. Sur ce Heterogeneity Effects on Adsorption Equilibria and Kinetics Rationalisation of Elovich Equation. In SCHWARZ J. and CONTESCU C. (eds.) Surfaces of Nanoparticles and Porous Materials (Marcel Dekker, 1999), pp.355-390. 

Rather than trying to describe the sparse and occasional results hitherto reported, this work is devoted to the foundation of a general and comprehensive theory of adsorption-desorption kinetics. The emphasis, however, will not be concentrated on the formal mathematical aspects of the theory, but rather on its physical bases in particular, the validity of the methods developed will be checked by verifying how they are able to explain the observed experimental behaviours. Among them one plays a special role — the time-logarithm law known as Elovich equation. 

The kinetics of adsorption and desorption and the Elovich equation have been the matter of a comprehensive review by Aharoni and Tompkins in 1970 [14]. At that time, however, concepts now pervasive in physical chemistry of surfaces like fractality were not known, the mathematical theory of adsorption equilibrium on heterogeneous surfaces was at its beginning, and the notion of equilibrium surfaces had not demonstrated yet its usefulness in the understanding of adsorption phenomena on real surfaces. In view of these facts there is a space for another work, which however does not intend to be as comprehensive as that of Aharoni and Tompkins, but rather aims to study the Elovich behaviour met in new situations, to elucidate the theoretical origin of Eq. (3), and to relate the macroscopic empiric parameters te, and t and to microscopic quantities. 

Surface heterogeneity has ever been considered to play a major role on adsorption [desorption] kinetics on [from] real surfaces and on heterogeneous catalytic processes. In fact, the most frequently observed kinetics which deviate from the theoretical first- or second-order ones, i.e. the time-logarithm law commonly known as Elovich equation, have in most cases been interpreted as due to surface heterogeneity. 

As a fundamental method to monitor the adsorption efficiency, the adsorption kinetics are often used to predict the adsorption characteristics and mechanisms. The kinetic models involve pseudo-first-order, [17] pseudo-second-order, [18] Elovich, [19] and intraparticle [20] diffusion model, of which the pseudo-first and pseudo-second-order equations are listed as Equations (11.11) and (11.12), respectively ... 

Surface Heterogeneity Effects on Adsorption Equilibria and Kinetics Rationalizations of the Elovich Equation 355... 

That equation and its integral form soon gained enormous popularity among scientists investigating the kinetics of gas adsorption on solid surfaces. Correlations of experimental data usually started with the application of that equation, and the frequently noted deviations from "Elovich behavior" were the form of analysis in dozens of published papers. Even reviews followed that general trend, discussing the Elovich equations and "deviations" from it. 

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