Rates of desorption

Davies [114] found that the rates of desorption of sodium laurate and of lauric acid films were in the ratio 6.70 1 at 21.5°C at molecular areas of 90 and 60 per molecule, respectively. Calculate o. the potential at the plane CD in Fig. XV-12. 

Temperature-programmed desorption (TPD) is amenable to simple kinetic analysis. The rate of desorption of a molecular species from a uniform surface is given by Eq. XVII-4, which may be put in the form... 

This means that desorption activation energies can be much larger than those for adsorption and very dependent on 6 since the variation of Q with 6 now contributes directly. The rate of desorption may be written, following the kinetic treatment of the Langmuir model. 

Process 2, the adsorption of the reactant(s), is often quite rapid for nonporous adsorbents, but not necessarily so it appears to be the rate-limiting step for the water-gas reaction, CO + HjO = CO2 + H2, on Cu(lll) [200]. On the other hand, process 4, the desorption of products, must always be activated at least by Q, the heat of adsorption, and is much more apt to be slow. In fact, because of this expectation, certain seemingly paradoxical situations have arisen. For example, the catalyzed exchange between hydrogen and deuterium on metal surfaces may be quite rapid at temperatures well below room temperature and under circumstances such that the rate of desorption of the product HD appeared to be so slow that the observed reaction should not have been able to occur To be more specific, the originally proposed mechanism, due to Bonhoeffer and Farkas [201], was that of Eq. XVIII-32. That is. 

If adsorption occurs via a physisorbed precursor, then the sticking probability at low coverages will be enhanced due to the ability of the precursor to diflfiise and find a lattice site [30]. The details depend on parameters such as strength of the lateral interactions between the adsorbates and the relative rates of desorption and reaction of the precursor. In figure Al.7,8 an example of a plot of S versus 0 for precursor mediated adsorption is presented. 

The ACR Process. The first step in the SCR reaction is the adsorption of the ammonia on the catalyst. SCR catalysts can adsorb considerable amounts of ammonia (45). However, the adsorption must be selective and high enough to yield reasonable cycle times for typical industrial catalyst loadings, ie, uptakes in excess of 0.1% by weight. The rate of adsorption must be comparable to the rate of reaction to ensure that suitable fronts are formed. The rate of desorption must be slow. Ideally the adsorption isotherm is rectangular. For optimum performance, the reaction must be irreversible and free of side reactions. 

To derive an explicit expression of the rate of desorption we restrict ourselves to nondissociative adsorption, listing references to other systems— such as multicomponent and multilayer adsorbates with and without precursors—for which such a treatment has been given, later. We look at a situation where the gas phase pressure of a molecular species, P, is different from its value, P, which maintains an adsorbate at coverage 6. There is then an excess flux to re-establish equilibrium between gas phase and adsorbate so that we can write [7-10]... 

This is our principal result for the rate of desorption from an adsorbate that remains in quasi-equihbrium throughout desorption. Noteworthy is the clear separation into a dynamic factor, the sticking coefficient S 6, T), and a thermodynamic factor involving single-particle partition functions and the chemical potential of the adsorbate. The sticking coefficient is a measure of the efficiency of energy transfer in adsorption. Since energy supply from the... 

Langmuir (1916), whp put forward the fir quantitative theory of the adsorption of a gaS, assumed that a gas molecule condensing from the gas phase-would adhere to the surface fora short time before evaporating and that the condensed layer was only one atom or molecule thick. If 0 is the fraction of the surface area covered by adsorbed molecules at any time, the rate of desorption is proportional to 0 and equal to k 0 where is a constant at constant temperature. Similarly the rate of adsorption will be proportional to the area of bare surface and to the rate at which the molecules strike the surface (proportional to the gas pressurep). At equilibrium the rate of desorption equals the rate of adsorption... 

Fig. 5. Dependences of relative concentrations Cj on time variable r (arbitrary units) for consecutive catalytic reactions according to scheme (III) for various values of rate constants of the adsorption k,(ub and desorption fcduB of the intermediate B. Left-hand column (fcdesB/fcs = 0.1) desorption of B is slower than its surface transformation. Middle column (fcde.B/fcs = 1) equal rates of desorption of B and of its surface transformation. Right-hand column (fcdesB/fcj = 10) desorption of B is faster than its surface transformation. From G. Thomas, R. Montarnal, and P. Boutry, C.R. Acad. Sri., Ser. C 269, 283 (1969).

B. Rate of Readsorption Nearly Equal to the Rate of Desorption... 

When the temperature of the analyzed sample is increased continuously and in a known way, the experimental data on desorption can serve to estimate the apparent values of parameters characteristic for the desorption process. To this end, the most simple Arrhenius model for activated processes is usually used, with obvious modifications due to the planar nature of the desorption process. Sometimes, more refined models accounting for the surface mobility of adsorbed species or other specific points are applied. The Arrhenius model is to a large extent merely formal and involves three effective (apparent) parameters the activation energy of desorption, the preexponential factor, and the order of the rate-determining step in desorption. As will be dealt with in Section II. B, the experimental arrangement is usually such that the primary records reproduce essentially either the desorbed amount or the actual rate of desorption. After due correction, the output readings are converted into a desorption curve which may represent either the dependence of the desorbed amount on the temperature or, preferably, the dependence of the desorption rate on the temperature. In principle, there are two approaches to the treatment of the desorption curves. 

The maximum specific rate of desorption Nm is obtained from Eqs. (15) and (31) as... 

The third independent possible estimation of Ed is given by an analysis of the peak shape. To this end, the hyperbolic heating schedule is most convenient. According to Eq. (38), the width w of the peak at a given value of the relative rate of desorption n and for a given desorption order is a universal constant in the e-scale w(n) = ej — h = f(n), which leads directly to... 

With porous materials, a slow diffusion in the pores can sometimes control the rate of desorption. This may give rise to complications because diffusion in the pores may be complex and difficult to treat mathematically. Cvetanovi6 and Amenomiya (48) gave a model treatment for their modification of the thermal desorption technique. 

As discussed in Chapter 7, this form can provide a good fit of the data if the reaction is not too close to equilibrium. However, most reaction engineers prefer a mechanistically based rate expression. This section describes how to obtain plausible functional forms for based on simple models of the surface reactions and on the observation that aU the rates in Steps 2 through 8 must be equal at steady state. Thus, the rate of transfer across the film resistance equals the rate of diffusion into a pore equals the rate of adsorption equals the rate of reaction equals the rate of desorption, and so on. This rate is the pseudohomo-geneous rate shown in Steps 1 and 9. 

In equilibrium, the rate of adsorption equals the rate of desorption. 

If the pumping speed is infinitely high, readsorption may be ignored, and the relative rate of desorption, defined as the change in adsorbate coverage per unit of time, is given by... 

Zero-order desorption occurs if the rate of desorption does not depend on the adsorption coverage, as seen with relatively large silver islands on a ruthenium surface (Fig. 7.7), where the Ag atoms desorb from the edges of the island. As the 0" term in Eq. (12) vanishes, the curves exhibit a clearly recognizable exponential shape on the leading side. Such situations are rare. 

As long as the desorption of CO2 is faster than the surface reaction between CO and O, the rate of desorption equals that of the preceding reaction ... 

As the initial coverages of CO and O are known, and the surface is free of CO at the end of the temperature-programmed experiment, the actual coverages of CO and O can be calculated for any point of the TPD curves in Fig. 7.14. Hence, an Arrhenius plot of the rate of desorption divided by the coverages, against the reciprocal temperature yields the activation energy and the pre-exponential factor ... 

Suppose we successfully measured the sticking coefficient and the activation energy for adsorption of a certain molecule, as well as the rate of desorption. Is it then possible to estimate the equilibrium constant for adsorp-tion/desorption ... 

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