Desorption/adsorption processes kinetics

The quantitative solution of the problem, i.e. simultaneous determination of both the sequence of surface chemical steps and the ratios of the rate constants of adsorption-desorption processes to the rate constants of surface reactions from experimental kinetic data, is extraordinarily difficult. The attempt made by Smith and Prater 82) in a study of cyclohexane-cyclohexene-benzene interconversion, using elegant mathematic procedures based on the previous theoretical treatment 28), has met with only partial success. Nevertheless, their work is an example of how a sophisticated approach to the quantitative solution of a coupled heterogeneous catalytic system should be employed if the system is studied as a whole. 

To interpret the kinetics experimental data of an organic pollutant(s) or leachate from complex organic mixtures, it is necessary to determine the adsorption/ desorption process steps in a given experimental system which govern the overall adsorption/desorption rate. For instance, the adsorption process of an organic compound by a porous adsorbent can be categorized as three consecutive steps ... 

Liu C, Zachara JM, Smith SC, McKinley JP, Ainsworth CC (2003) Desorption kinetics of radiocesium from subsurface sediments at Hanford Site USA. Geochim Cosmochim Acta 67 2893-2912 Loffredo E, Senesi N (2006) Eate of anthropogenic organic pollutants in soils with emphasis on adsorption/desorption processes of endocrine disruptor compounds. Pure App Chem 78 947-961... 

The reaction of ammonia with oxygen over V-based catalysts produces mainly nitrogen, according to the stoichiometry of R5 in Table V. Analogously to the case of the ammonia adsorption-desorption, specific runs were carried out in order to extract the intrinsic kinetics of ammonia oxidation and at the same time to validate the previously fitted kinetics of the ammonia adsorption-desorption process. 

Thus for each zone, during a given cycle, the adsorption-desorption process is separated into two distinct events with F or G describing the kinetics of each event. Such an approach is of course valid only for first order rate reactions. In the limit of low concentration, (such as that resulting from slow leaching from a repository) the reaction sites on the rock will not approach saturation and the number of reaction sites can be considered to remain constant during adsorption. Therefore, for a single species in solution at tracer concentrations the reaction should approximate a first order reaction (i.e., where no complications such as concentration effects, step-wise dehydration, dissociation, etc., are present). 

Griffin and Jurinak (1974) calculated pseudothermodynamic parameters for phosphate interactions with calcite using reaction-rate theory. Gonzalez et al. (1982) applied reaction-rate theory to a treatment of adsorption-desorption processes on an Fe-selica gel system. In 1981, Sparks and Jardine applied reaction-rate theory to kinetics of potassium adsorption and desorption in soil systems for the first time (Table 2.5). 

Lindstrom, F. T., Haque, R., and Coshow, W. R. (1970). Adsorption from solution. III. A new model for the kinetics of adsorption-desorption processes. J. Phys. Chem. 74, 495-502. 

Gonzalez, J. L., Herraez,M. A., and Rodriguez, S. (1982). Kinetic treatment of adsorption-desorption processes of Fe(III)—silica gel system by a theoretical generalized model. J. Colloid Interface Sci. 88, 313-318. 

These applications are described comprehensively for several different mechanistic models of the adsorption-desorption process at equilibrium by S. Goldberg, op. cit.8 Kinetics applications are discussed by D. L. Sparks and D. L. Suarez, Rates of Soil Chemical Processes, Soil Science Society of America, Madison, WI, 1991. 

The lossy character of the adsorption impedance stems in the finite-rate response of coverages to potential changes T = )( , t). Assuming one adsorption-desorption process, the adsorption-related current at a certain potential contains a dqM/dt = (dqM/dr) dr/ df term which, through the dT/ df term, depends on the (eventually diffusion-controlled) kinetics of the adsorption process. 

Heterogeneously catalyzed reactions are usually studied under steady-state conditions. There are some disadvantages to this method. Kinetic equations found in steady-state experiments may be inappropriate for a quantitative description of the dynamic reactor behavior with a characteristic time of the order of or lower than the chemical response time (l/kA for a first-order reaction). For rapid transient processes the relationship between the concentrations in the fluid and solid phases is different from those in the steady-state, due to the finite rate of the adsorption-desorption processes. A second disadvantage is that these experiments do not provide information on adsorption-desorption processes and on the formation of intermediates on the surface, which is needed for the validation of kinetic models. For complex reaction systems, where a large number of rival reaction models and potential model candidates exist, this give rise to difficulties in model discrimination. 

The adsorption/desorption process was assumed to be relatively slow compared with the mass transfer and the assumption of local equilibrium is no longer valid. Consequently, the solid phase concentration must be related to the adsorption and the desorption rates, via a kinetic equation. The second-order kinetic is accoimted for by the following equation... 

It was proposed by Andricacos et al This mechanism considers one-additive system. It is noted in Ref. 47 (Ch. 10, Sections 10.4 and 10.5) that in general, adsorption of additives (inhibitor) at the cathode affects the kinetics and growth mechanism of electrodeposition. The surface coverage of the additive (inhibitor), 0, is a function of the diffusion controlled rates of the adsorption-desorption processes. In the differential-inhibition mechanism it is assumed that a very wide range of additive fluxes over the micro-profile (vias and trenches) exists, that is, extremely low flux in deep interior comers, low flux at the bottom center, moderate flux at the sidewalls, and high flux at shoulders. 

When the adsorption/desorption kinetics are slow compared to the rate of diffusional mass transfer through the tip/substrate gap, the system responds sluggishly to depletion of the solution component of the adsorbate close to the interface and the current-time characteristics tend towards those predicted for an inert substrate. As the kinetics increase, the response to the perturbation in the interfacial equilibrium is more rapid and, at short to moderate times, the additional source of protons from the induced-desorption process increases the current compared to that for an inert surface. This occurs up to a limit where the interfacial kinetics are sufficiently fast that the adsorption/desorption process is essentially always at equilibrium on the time scale of SECM measurements. For the case shown in Figure 3 this is effectively reached when Ka = Kd= 1000. In the absence of surface diffusion, at times sufficiently long for the system to attain a true steady state, the UME currents for all kinetic cases approach the value for an inert substrate. In this situation, the adsorption/desorption process reaches a new equilibrium (governed by the local solution concentration of the target species adjacent to the substrate/solution interface) and the tip current depends only on the rate of (hindered) diffusion through solution. 

The adsorption process is usually fast on evaporated films. However, on bulk solids, e.g. porous catalyst carriers, adsorption rates are usually slow and activated with activation energies typically in the range 10-40 kcal/g mole (Hayward and Trapnell, 1964). Some activation energies for typical activated chemisorption process are given in Table 5.9. In their investigation of the catalytic dehydration of methylcyclohexane, Sinfelt et al. (1960) found that to obtain a suitable kinetic expression finite rates of the adsorption-desorption process must be taken into consideration. In this section allowance is made for finite rates of adsorption and both activated and non-activated adsorption are considered ... 

The kinetics of the adsorption/desorption process are complex and consist of an initial period where equilibrium is achieved essentially in a few seconds. 

The model of Nijhuis et al. [39] expHcitly accounts for adsorption/de-sorption at the crystal boundary, assuming Langmuir adsorption kinetics. As the TEX-PEP experiments are conducted under steady-state conditions, this mechanism can be replaced by a simple first-order adsorption/desorption process... 

The term C is associated with the mass transfer of molecules between the mobile phase. Cm, and the stationary phase, Cj. The molecules are delayed in the column due to their interaction with the stationary phase. The term C expresses the resistance of the solute molecules between the fluid phase and the stationary phase—often this region through which the molecules diffuse is referred to as the boundary layer, as shown in Figure 8.11. This phase shift increases with increasing velocity it is the result of the limitation of the kinetics of the adsorption-desorption process. The peak profile resulting from the resistance to mass transfer is directly proportional to the velocity of the mobile phase HETP = Cm (Figure 8.12). 

Because of its simplicity and wide utility, the Langmuir isotherm has found wide applicability in a number of useful situations. Like many such classic approaches, it has its fundamental weaknesses, but its utility generally outweighs its shortcomings. The Langmuir isotherm model is based on the assumptions that adsorption is restricted to monolayer coverage, that adsorption is localized (i.e., that specific adsorption sites exist and interactions are between the site and a specific molecule), and that the heat of adsorption is independent of the amount of material adsorbed. The Langmuir approach is based on a molecular kinetic model of the adsorption-desorption process in which the rate of adsorption (rate constant /ca) is assumed to be proportional to the partial pressure of the adsorbate (p) and the number of unoccupied adsorption sites (N - n), where N is the total number of adsorption sites on the surface and n is the number of occupied sites, and the rate of desorption (rate constant d) is proportional to n. 

We note here that there are other theories of adsorption/desorption kinetics that offer expressions for the adsorption/desorption rate that are different from the ART expression but also lead to the Langmuir isotherm when d0/dt = 0. It is rather strange that adsorption systems with different kinetics of the adsorption/ desorption processes have the same form at equilibrium. 

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