Adsorption kinetics model stages

It is surprising that complicated dynamic behaviour proved to be characteristic of the simplest and quite ordinary kinetic models of catalytic reactions, namely of the Langmuir Hinshelwood adsorption mechanism. We are possibly at the initial stage of interpreting the kinetics of complex reactions and the "Sturm und Drang period has not yet been completed. 

Table 1 presents several examples of unsteady-state kinetics models. These models are presented in the form of rate dependencies for catalytic reaction stages and side processes. The parameters of the models, such as reaction rate constants and activation energies, are given in references (Table 1) and were determined mainly from experimental data using transient response techniques. For the reaction of CO oxidation over a supported platinum catalyst, the kinetic gas theory was applied for estimating the adsorption constants. 

Kinetic regime. The first mechanism corresponds to the so-called kinetic regime (Popel 1994, Grigorenko et al. 1998) which is similar to the adsorption/desorption model (Blake 1993). Contrary to macroscopic hydrodynamic models, the adsorption/desorption model is based on the hypothesis that the motion of the triple line is ultimately determined by the statistical kinetics of atomic or molecular events occurring within the three-phase zone (Samsonov and Muravyev 1998). Such processes may be limiting at the very early stages of spreading of low... 

The mechanism of sulphate formation is still under debate. Recently, a kinetic model has been proposed for alumina sulphation [13]. Two different types of alumina surface sites could be involved in the elementary stages. The first one would be an oxygen atom on the surface that would favor SO2 adsorption and then sulphation. The second one would allow the dissociation of oxygen. After the formation of superficial sulphates on the surface of the alumina, a nucleation of core sulphates, via a slow process, causes formation of irreversible chemical species. 

This process may be a rate limiting stage at high concentration of reactant in the gas phase. Its influence on the adsorption kinetics has been considered in detail by Unger [6] and Jaroniec and Madey [29]. The following simultaneous diffusion-adsorption model may be applied to the experimental kinetic data in order to derive effective diffusion coefficients [66] ... 

Validation of our proposed kinetic model is illustrated by the solid and dashed curves shown by the C vs time results shown in Figs. 6-8 and 6-9 for C0 of 50 and 100 mg L-1. Here all model parameters for both the multireaction and second-order models were based on adsorption data only. With the exception of p and 0, initial conditions for this initial-value problem were the only input required. Based on these predictions, we can conclude that both models predicted Cu desorption or release behavior satisfactorily. However, predictions of desorption isotherms were not considered adequate at the initial stages of desorption following adsorption. In addition, the model underpredicted amount sorbed that directly influences subsequent predictions for the desorption isotherms. Discrepancies between experimental and predicted are expected if the amounts of Cu in the various phases (C, Se, Sh and S2) at each desorption step were significantly different. These underpredictions also may be due to the inherent assumptions of the model. Specifically, the models may... 

Adsorption capacities of different adsorbent was compared by Choi et al. (2009) modeling using Langmuir adsorption isothermal model (Eq. 2.1) and three stage kinetic model as shown in Eqs. (2.2) and (2.3) below. 

A kinetic model involving the rate of interface reaction, pore-diffusion and gas-film diffusion has been formulated for the core-and-shell reduction [115]. The enthalpy of adsorption of water on the reaction interface is 163.2 45.2 kJ/mole in this model [115]. The core-and-shell model is invalid in the final stages of reduction for samples containing high (27%) concentrations of wustite [26, 27, 80] in the presence of small amounts of water [97,131]. 

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... 

A variety of models have been derived to describe the kinetics of semiconductor photocatalysis, but the most commonly used model is the Langmuir-Hinshel-wood (LH) model [77-79]. The LH model relates the rate of surface-catalyzed reactions to the surface covered by the substrate. The simplest representation of the LH model [Eq. (7)] assumes no competition with reaction by-products and is normally applied to the initial stages of photocatalysis under air- or oxygen-saturated conditions. Assuming that the surface coverage is related to initial concentration of the substrate and to the adsorption equilibrium constant, K, tire initial... 

Calorimetric data indicate that in the case of oxygen adsorption on oxygenated silver (the surface sites of which we denote as Z) [i.e., in the case of the process corresponding to stage 4 of scheme (220)], the surface behaves in such a way as if it were uniform, in accordance with Assumption 3 formulated in Section IX. Thus the model of an ideal surface layer may be used to obtain the kinetic equations. Applying the stage steady-state conditions... 

Chapter 8 provides a unified view of the different kinetic problems in condensed phases on the basis of the lattice-gas model. This approach extends the famous Eyring s theory of absolute reaction rates to a wide range of elementary stages including adsorption, desorption, catalytic reactions, diffusion, surface and bulk reconstruction, etc., taking into consideration the non-ideal behavior of the medium. The Master equation is used to generate the kinetic equations for local concentrations and pair correlation functions. The many-particle problem and closing procedure for kinetic equations are discussed. Application to various surface and gas-solid interface processes is also considered. 

Jantti s approach was originally developed enabling short adsorption measurements when a simple molecular adsorption model is applicable and the number of sites available for adsorption is infinite. In the present paper we show that with also in the case of a restricted number of sites combined with the possibility of more than one layer of adsorbed molecules Jantti s approach can lead to the saving of time. An estimate of the equilibrium value of the adsorbed mass as well as of other kinetic parameters in an early stage of the measurements is... 

The present paper reports measurements of the rate of uptake of oxygen in both the adsorption (premonolayer) and incorporation stages, and from an analysis of the kinetics it is shown that the tentative model outlined above can be implemented and elaborated. 

The values for the exudation rate F, interaction coefficient (A), buffer power of exudate in soil b and the decomposition rate constant for the exudate k were adopted from Kirk (1999). The value of the forward rate constant was estimated from Scheckel and Sparks (2001), who evaluated kinetic adsorption data of Ni to different minerals where ranged from 2.5 x 10 to 9.78 X 10 s For the simulation, an average value of 5.00 x 10 was used. This value also coincides with the values that Kirk and Staunton (1989) suggested for the kinetic adsorption of Q to soil, where the values ranged from lO" to 10 2 s f This same value was assumed for the rate constant for the two-stage sorption model, a2- The fraction of type 1 sites (F ) was assumed to be 0.3. Table 7 summarizes all input parameter values. 

Uptake experiments were carried out on cultures of a planctonic alga, Scenedesmus obliquus, exposed to i Ag at different stages of development . The accumulation of the radionuclide was rapid and intense, and equilibrium was reached in an exposure time of less than 24 hours. The uptake kinetics showed the algal concentration level to be dependent only on the medium concentration and on the cell development at the time of 0 Ag addition. Passive uptake was described by Freundlich adsorption isotherms. During the depuration phase the Ag retention by S. obliquus developed in accordance with an exponential model based on the existence of two biological half-hves i.e. a very short one of a few seconds and a longer one of 115 h. In a similar study the radioactivity of sea water was determined by studying the concentration of metals in squid livers and the distribution of Ag in them. 

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