Arrhenius equation surface desorption

To calculate thermodynamic equilibrium in multicomponent systems, the so-called optimization method and the non-linear equation method are used, both discussed in [69]. In practice, however, kinetic problems have also to be considered. A heterogeneous process consists of various occurrences such as diffusion of the starting materials to the surface, adsorption of these materials there, chemical reactions at the surface, desorption of the by-products from the surface and their diffusion away. These single occurrences are sequential and the slowest one determines the rate of the whole process. Temperature has to be considered. At lower substrate temperatures surface processes are often rate controlling. According to the Arrhenius equation, the rate is exponentially dependent on temperature ... 

The simplest case to be considered is that of a homogeneous surface the rate constant of desorption k ) is not a function of 6 and its temperature dependence is given by the Arrhenius equation... 

Commonly, the design of a reactor requires the prediction of the rate of reaction. Two different approaches have been used to develop suitable kinetic models for the WGS reaction. The first is based on microkinetics by taking into account the elementary steps from the adsorption of the chemical species to the reaction and the product desorption the second is based on the macrokinetics that are empirical models in which the rate of reaction depends proportionally on the concentration of reactants and products and exponentially on temperature (typically expressed using the Arrhenius equation). The microkinetics approach is more complex, in particular from a mathematical and computational point of view, but it offers the possibility to better model the surface coverage and the enthalpy of the reaction (i.e., the temperature increase on the catalyst surface). Two different mechanisms for the WGS reaction are proposed in the scientific literamre the redox mechanism and the associative mechanism. 

Generally, adsorption steps were taken as temperature independent, whereas the rate parameters of surface reactions and desorption steps were described by Arrhenius equations. The kinetic rate parameters for CO oxidation (steps 1-10) and the catalyst properties were taken from [24] with minor adaptation as mentioned. The rate parameters, e.g. activation energies and pre-exponential factors, for steps 11-28 were determined by non-linear regression. It was found [25] that the rates for NO reactions on ceria are independent of the oxidation state of ceria, so the rate parameters for the corresponding steps were taken as the same (i.e. steps 11 and 12 for oxygen, steps 25-28 for NO). 

The Monte Carlo method as described so far is useful to evaluate equilibrium properties but says nothing about the time evolution of the system. However, it is in some cases possible to construct a Monte Carlo algorithm that allows the simulated system to evolve like a physical system. This is the case when the dynamics can be described as thermally activated processes, such as adsorption, desorption, and diffusion. Since these processes are particularly well defined in the case of lattice models, these are particularly well suited for this approach. The foundations of dynamical Monte Carlo (DMC) or kinetic Monte Carlo (KMC) simulations have been discussed by Eichthom and Weinberg (1991) in terms of the theory of Poisson processes. The main idea is that the rate of each process that may eventually occur on the surface can be described by an equation of the Arrhenius type ... 

Perhaps of more general applicability for the study of the properties of positronium is its production by the desorption of surface-trapped positrons and by the interaction of positrons with powder samples. According to equation (1.15) it is energetically feasible for positrons which have diffused to, and become trapped at, the surface of a metal to be thermally desorbed as positronium. The probability that this will occur can be deduced (Lynn, 1980 Mills, 1979) from an Arrhenius plot of the positronium fraction versus the sample temperature, which can approach unity at sufficiently high temperatures. The fraction of thermally desorbed positronium has been found to vary as... 

When the Bom, double-layer, and van der Waals forces act over distances that are short compared to the diffusion boundary-layer thickness, and when the e forces form an energy hairier, the adsorption and desorption rates may be calculated by lumping the effect of the interactions into a boundary condition on the usual ccm-vective-diffusion equation. This condition takes the form of a first-order, reversible reaction on the collector s surface. The apparent rate constants and equilibrium collector capacity are explicitly related to the interaction profile and are shown to have the Arrhenius form. They do not depend on the collector geometry or flow pattern. 

The model is formulated on the premise that the decomposing hydrate particle is surrounded by a cloud of the product gas hence the driving force for the decomposition process is expressed in terms of the fugacity difference given in Eq. (1). The process of decomposition possibly involves (1) destruction of the clathrate host (water) lattice at the surface of the particle, and (2) and desorption of the guest (hydrate former) molecules from the surface. The particle size distribution was incorporated in the calculations for the determination of the intrinsic rate constants.The following Arrhenius type equation is used to represent the effect of temperature on the intrinsic rate constant ... 

In the discussion so far, orders of one or two have been considered. Surface processes with other orders (and fractional orders) have been found and changes in Arrhenius plot slopes can be caused by changes in desorption mechanism. Equation (94) shows the general form of the dependence of the kinetic parameters on the desorption order in terms of initial coverages. Another important relationship can be derived from the work of Falconer [280] who showed that... 

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