Desorption processes

XVIII-11 (the paradox of desorption heat exceeding adsorption heat is explainable in terms of a partial irreversibility of the adsorption-desorption process). 

The steps may be so chosen as to correspond to consecutive points on the experimental isotherm. In practice it is more convenient to divide the desorption process into a number of standard steps, either of relative pressure, or of pore radius, which is of course a function of relative pressure. The amount given up during each step i must be converted into a liquid volume i , (by use of the normal liquid density) in some procedures the conversion is deferred to a late stage in the calculation, but conceptually it is preferable to undertake the conversion at the outset. As indicated earlier, the task then becomes (i) to calculate the contribution dv due to thinning of the adsorbed film, and thus obtain the core volume associated with the mean core radius r by the subtraction = t ... 

Consider stage i in the desorption process where the thickness of the adsorbed film is and the pores of radius r, have just lost their capillary condensate. The volume of multilayer lining the pores of any radius r, where r > ri, will then be (since the pores are cylindrical) ... 

M ass Transfer. Mass transfer in a fluidized bed can occur in several ways. Bed-to-surface mass transfer is important in plating appHcations. Transfer from the soHd surface to the gas phase is important in drying, sublimation, and desorption processes. Mass transfer can be the limiting step in a chemical reaction system. In most instances, gas from bubbles, gas voids, or the conveying gas reacts with a soHd reactant or catalyst. In catalytic systems, the surface area of a catalyst can be enormous. Eor Group A particles, surface areas of 5 to over 1000 m /g are possible. 

For adsorbed hydrocarbons, the adsorption—desorption process can be thought of as a reaction and the adsorption isotherm as a description of the reaction at equihbtium. For the Langmuir isotherm,... 

The desorptive process may be analyzed before boiling. The key assumption is that the vapor and adsorbed phases are ia equiUbrium ia the bulk of the bed. This assumption eliminates iatraparticle resistances from further consideration and is reasonable for rotary kiln appHcations. The two remaining resistances are associated with hydrocarbon diffusion out of the bed and with convection from the bed surface to the bulk gases. The flux of species Fi from the desorbiag bed becomes... 

The I2 formed stays in solution, exerting a certain vapor pressure, and is extracted from the brine in a countercurrent air blow-out process. The extracted brine leaves the extraction tower and is discarded or reinjected into the wells to avoid sinking of the soil. The iodine-loaded air is then submitted to a cocurrent desorption process by means of an acidic iodide solution to which SO2 is added. By this solution the iodine is reduced to iodide by the following reaction ... 

Sorption and Desorption Processes. Sorption is a generalized term that refers to surface-induced removal of the pesticide from solution it is the attraction and accumulation of pesticide at the sod—water or sod—air interface, resulting in molecular layers on the surface of sod particles. Experimentally, sorption is characterized by the loss of pesticide from the sod solution, making it almost impossible to distinguish between sorption in which molecular layers form on sod particle surfaces, precipitation in which either a separate soHd phase forms on soHd surfaces, covalent bonding with the sod particle surface, or absorption into sod particles or organisms. Sorption is generally considered a reversible equdibrium process. 

The above stm study also discovered a facile transport of surface gold atoms in the presence of the Hquid phase, suggesting that the two-step mechanism does not provide a complete picture of the surface reactions, and that adsorption/desorption processes may have an important role in the formation of the final equiHbrium stmcture of the monolayer. Support for the importance of a desorption process comes from atomic absorption studies showing the existence of gold in the alkanethiol solution. The stm studies suggest that this gold comes from terraces, where single-a tomic deep pits are formed (281—283). 

The first term in the second integral will not have the same magnitude as in the desorption process because the latent heat L will now be that at the evaporating... 

This review is structured as follows. In the next section we present the theory for adsorbates that remain in quasi-equilibrium throughout the desorption process, in which case a few macroscopic variables, namely the partial coverages 0, and their rate equations are needed. We introduce the lattice gas model and discuss results ranging from non-interacting adsorbates to systems with multiple interactions, treated essentially exactly with the transfer matrix method, in Sec. II. Examples of the accuracy possible in the modehng of experimental data using this theory, from our own work, are presented for such diverse systems as multilayers of alkali metals on metals, competitive desorption of tellurium from tungsten, and dissociative... 

We consider desorption from an adsorbate where surface diffusion is so fast (on the time scale of desorption) that the adsorbate is maintained in equilibrium throughout the desorption process. That is to say that, at the remaining coverage 9 t) at temperature T t), all correlation functions attain... 

Note that if sticking is controled by site-exclusion only, i.e., if S 6,T) = 5 o(P)(l — 0), this rate is that of a first-order reaction at low coverage. This simple picture breaks down when either the sticking coefficient depends dilferently on the coverage, as it does for instance for precursor-mediated adsorption, or when lateral interactions become important. It then does not make much physical sense to talk about the order of the desorption process. 

The simplest case to be analyzed is the process in which the rate of one of the adsorption or desorption steps is so slow that it becomes itself rate determining in overall transformation. The composition of the reaction mixture in the course of the reaction is then not determined by kinetic, but by thermodynamic factors, i.e. by equilibria of the fast steps, surface chemical reactions, and the other adsorption and desorption processes. Concentration dependencies of several types of consecutive and parallel (branched) catalytic reactions 52, 53) were calculated, corresponding to schemes (Ila) and (lib), assuming that they are controlled by the rate of adsorption of either of the reactants A and X, desorption of any of the products B, C, and Y, or by simultaneous desorption of compounds B and C. 

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. 

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. 

In general, the flow rate F(t) consists of the following additive components the controlled flow rate Fd of the entering gas, the flow rate Fi which is due to parasitic leaks and/or diffusion, and the flow rate Fw resulting from possible adsorption-desorption processes on the system walls (in Section I, references are given to papers dealing with the elimination or control of the wall effects in the flash filament technique). In each of these flow rate components a particular ratio of the investigated adsorbate and of the inert gas exists and all these components contribute to the over-all mean values Fh(t) and F (t). 

In actual experiments we do not usually observe directly the desorbed amount, but rather the derived read-out quantities, as is the time dependence of the pressure in most cases. In a closed system, this pressure is obviously a monotonously increasing function of time. In a flow or pumped system, the pressure-time dependence can exert a maximum, which is a function of the maximum desorption rate, but need not necessarily occur at the same time due to the effect of the pumping speed S. If there are particles on the surface which require different activation energies Ed for their desorption, several maxima (peaks) appear on the time curve of the recorded quantity reflecting the desorption process (total or partial pressure, weight loss). Thereby, the so-called desorption spectrum arises. It is naturally advantageous to evaluate the required kinetic parameters of the desorption processes from the primarily registered read-out curves, particularly from their maxima which are the best defined points. 

For the desorption processes that follow the first-order kinetics, we thus obtain [neglecting again ([Pg.360]

Taking i m = 0, we obtain an equation for the desorption process alone, i.e. for the case where the rate of readsorption is negligible. On the other hand, if only the last term in the brackets is considered, one has the equation for the equilibrium desorption. 

If the desorption process follows the second-order kinetics, it is necessary to solve a quadratic equation for 0 resulting from Eq. (8) and the general expression (17) becomes rather complex. 

From Pm still further information about the parameters of the desorption process can be obtained. To this end, Eq. (8) must be solved. The solution, however, is accessible only in the case of desorption alone. If the contribution of the second term in Eq. (8) is appreciable, it is necessary to insert for P from Eq. (13). Thus, nonlinear differential equations result even for the most simple cases (x = 1, or the equilibrium desorption), which can be solved by numerical methods only or by iterative methods provided the second term in Eq. (8) is small. 

Most often, the primary experimental desorption data [[mainly the P(t) or P(T) function] represent, after due corrections, the temperature dependence of the desorption rate, —dnjdt = Nt vs T. The resulting curves exhibit peaks and their most reliable point is the maximum at the temperature Tm, corresponding to the maximum desorption rate Nm. Its location on the temperature scale under various conditions is essential for estimating the kinetic parameters of the desorption process. 

The minimum number of postulates of the model of a desorption process with no explicit analytical expression of the heating schedule are required if the primary output data are treated according to Eqs. (10) and (12), viz. by numerical or graphical derivations and integrations of the recorded pressure data. After an adaptation of the analyzer, these operations can be performed by means of electrical circuits. The known temperature-time relationship (either in the form of an analytical function or established... 

The order of the desorption process is estimated in the first place from the shape of the desorption peak, preferably in the l/T scale. The first-order peaks here are clearly asymmetric, the falling branch being steeper than the ascending one. The second-order peaks are near symmetric and are broader. The third-order peaks are even broader and are again asymmetric, but in this case the ascending branch is steeper than the falling one. 

An analysis of the rate of release of adsorbed atoms from sites with a continuous energy spectrum for the case of an arbitrary distribution function of initial site populations was given by Carter (32). The rate equation for the t th desorption process with x = 1 and negligible readsorption is... 

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