Desorption rates

In contrast to adsorption processes, which may or may not be activated as previously discussed, the desorption step is always activated, with a minimum activation energy equal to the heat of adsorption, Qad- The rate of desorption from occupied sites is  

As with adsorption, the rate constant and Edes can vary with coverage on a uniform surface, and the desorption rate can then be expressed as  

For a simple unimolecular desorption step, an adsorbed molecule with the requisite activation energy will desorb within the period of one vibration perpendicular to the surface, hence the rate of desorption is  

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Derive Eq. XI-IS, assuming a Langmuir adsorption process described in Eq. XI-2, where ka and kd are the adsorption and desorption rate constants. Treat the solution... 

A powerful technique in studying both adsorption and desorption rates is that of programmed desorption. The general procedure (see Refs. 36, 84) is to expose a clean metal filament or a surface to a known, low pressure of gas that flows steadily over it. The pressure may be quite low, for example, 10 mm Hg or less, so that even nonactivated adsorption can take some minutes for... 

If the adsorbed molecule occupies two sites because it dissociates, the desorption rate takes on the form... 

It might be thought that since chemisorption equilibrium was discussed in Section XVIII-3 and chemisorption rates in Section XVIII-4B, the matter of desorption rates is determined by the principle of microscopic reversibility (or, detailed balancing) and, indeed, this principle is used (see Ref. 127 for... 

In the case of nitrogen on iron, the experimental desorption activation energies are also shown in Fig. XVIII-13 the desorption rate was given by the empirical expression... 

If the desorption rate is second-order, as is often the case for hydrogen on a metal surface, so that appears in Eq. XVIII-1, an equation analogous to Eq. XVIII-3 can be derived by the Redhead procedure. Derive this equation. In a particular case, H2 on Cu3Pt(III) surface, A was taken to be 1 x 10 cm /atom, the maximum desorption rate was at 225 K, 6 at the maximum was 0.5. Monolayer coverage was 4.2 x 10 atoms/cm, and = 5.5 K/sec. Calculate the desorption enthalpy (from Ref. 110). 

As with the other surface reactions discussed above, the steps m a catalytic reaction (neglecting diffiision) are as follows the adsorption of reactant molecules or atoms to fomi bound surface species, the reaction of these surface species with gas phase species or other surface species and subsequent product desorption. The global reaction rate is governed by the slowest of these elementary steps, called the rate-detemiming or rate-limiting step. In many cases, it has been found that either the adsorption or desorption steps are rate detemiining. It is not surprising, then, that the surface stmcture of the catalyst, which is a variable that can influence adsorption and desorption rates, can sometimes affect the overall conversion and selectivity. 

TPD is frequently used to detenuine (relative) surface coverages. The area below a TPD spectrum of a certain species is proportional to the total amount that desorbs. In this way one can detennine uptake curves that correlate gas exposure to surface coverage. If tire pumping rate of the UHV system is sufiBciently high, the mass spectrometer signal for a particular desorption product is linearly proportional to the desorption rate of the adsorbate [20, 21] ... 

The newly formed short-chain radical A then quickly reacts with a monomer molecule to create a primary radical. If subsequent initiation is not fast, AX is considered an inhibitor. Many have studied the influence of chain-transfer reactions on emulsion polymerisation because of the interesting complexities arising from enhanced radical desorption rates from the growing polymer particles (64,65). Chain-transfer reactions are not limited to chain-transfer agents. Chain-transfer to monomer is ia many cases the main chain termination event ia emulsion polymerisation. Chain transfer to polymer leads to branching which can greatiy impact final product properties (66). 

Dj IE, ratio of a crack is held constant but the dimensions approach molecular dimensions, the crack becomes more retentive. At room temperature, gaseous molecules can enter such a crack direcdy and by two-dimensional diffusion processes. The amount of work necessary to remove completely the water from the pores of an artificial 2eohte can be as high as 400 kj/mol (95.6 kcal/mol). The reason is that the water molecule can make up to six H-bond attachments to the walls of a pore when the pore size is only slightly larger. In comparison, the heat of vaporization of bulk water is 42 kJ /mol (10 kcal/mol), and the heat of desorption of submonolayer water molecules on a plane, soHd substrate is up to 59 kJ/mol (14.1 kcal/mol). The heat of desorption appears as a exponential in the equation correlating desorption rate and temperature (see Molecularsieves). 

The latter kind of formulation is described at length in Sec. 7. The assumed mechanism is comprised of adsorption and desorption rates of the several participants and of the reaction rates of adsorbed species. In order to minimize the complexity of the resulting rate equation, one of the several rates in series may be assumed controlling. With several controlling steps the rate equation usually is not exphcit but can be used with some extra effort. 

Heterogeneous catalytic studies should also be concerned with the significance of adsorption and desorption rates and equilibria of the reactants, intermediates and products. Yang and Hougen (1950) tabulated the expressions for surface catalyzed reactions controlled by various steps. 

Fig. 10 shows the curves for the canister weight and the amount of vapor removed for the example canister during a purge event. In this case, the canister is being purged with an air stream flowing at a rate of about 22.6 liters per minute for a total of 15 minutes. The curves show that the n-butane desorption rate is initially quite rapid, and then it levels out at a lower rate. 

Now, if (kd) is the desorption rate constant, then the mean desorption time (td) for... 

FIG. 16 Variation of the steady-state rate of production, Pcoj, with Pco in the NO + CO lattice gas model with NO desorption (rate d o = 0.5), and CO desorption at various rates (shown). The inset shows the reaction rate measured experimentally at 410 K. (From Ref. 81.)... 

Here Zint is the intramolecular partition function accounting for rotations and vibrations. However, in equilibrium, the chemical potential in the gas phase is equal to that in the adsorbate, fi, so that we can write the desorption rate in (I) as... 

For dissociative adsorption, i.e., for systems in which the gas phase is predominantly molecules which dissociate into fragments A and B on the surface (not necessarily atoms), the desorption rate is given by... 

With the availabihty of computers, the transfer matrix method [14] emerged as an alternative and powerful technique for the study of cooperative phenomena of adsorbates resulting from interactions [15-17]. Quantities are calculated exactly on a semi-infinite lattice. Coupled with finite-size scaling towards the infinite lattice, the technique has proved popular for the determination of phase diagrams and critical-point properties of adsorbates [18-23] and magnetic spin systems [24—26], and further references therein. Application to other aspects of adsorbates, e.g., the calculation of desorption rates and heats of adsorption, has been more recent [27-30]. Sufficient accuracy can usually be obtained for the latter without scaling and essentially exact results are possible. In the following, we summarize the elementary but important aspects of the method to emphasize the ease of application. Further details can be found in the above references. 

FIG. 6 (a) Atomic desorption rates calculated with the two-site lattice gas model... 

For crystal growth from the vapor phase, one better chooses the transition probability appropriate to the physical situation. The adsorption occurs ballistically with its rate dependent only on the chemical potential difference Aj.1, while the desorption rate contains all the information of local conformation on the surface [35,48]. As long as the system is close to equilibrium, the specific choice of the transition probability is not of crucial importance. 

The desorption rate contains an exponential factor with a chemical potential (Iq for desorption into the vapor phase, since it is a thermally excited process. In a nonequilibrium situation, the chemical potential increases by Afi and increases the adsorption rate The rate difference is given as... 

Wetness of a metal surface The lime of wetness of the metal surface is an exceedingly complex, composite variable. It determines the duration of the electrochemical corrosion process. Firstly it involves a consideration of all the means by which an electrolyte solution can form in contact with the metal surface. Secondly, the conditions under which this solution is stable with respect to the ambient atmosphere must be considered, and finally the rate of evaporation of the solution when atmospheric conditions change to make its existence unstable. Attempts have been made to measure directly the time of wetness , but these have tended to use metals forming non-bulky corrosion products (see Section 20.1). The literature is very sparse on the r61e of insoluble corrosion products in extending the time of wetness, but considerable differences in moisture desorption rates are found for rusted steels of slightly differing alloy content, e.g. mild steel and Cor-Ten. 

They varied only the values of the adsorption and desorption rate constants of the reaction intermediate B, and by using the simplest Langmuir kinetics, they calculated time-concentration curves of compounds A, B, and C shown in Fig. 5. Also from this example, which does not consider any step as clearly rate determining, it is evident how very different concentration versus time plots can be obtained for the same sequence of surface reactions if adsorption and desorption of the intermediate B proceed by different rates, which are, however, comparable with the rate of surface reactions. In particular, the curves in the first and second columns of Fig. 5 simulate the parallel formation of substances B and C, at least... 

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 the first one, the desorption rates and the corresponding desorbed amounts at a set of particular temperatures are extracted from the output data. These pairs of values are then substituted into the Arrhenius equation, and from their temperature dependence its parameters are estimated. This is the most general treatment, for which a more empirical knowledge of the time-temperature dependence is sufficient, and which in principle does not presume a constancy of the parameters in the Arrhenius equation. It requires, however, a graphical or numerical integration of experimental data and in some cases their differentiation as well, which inherently brings about some loss of information and accuracy, The reliability of the temperature estimate throughout the whole experiment with this... 

For the model formulated by the above postulates, the specific desorption rate rd, i.e. the molar rate of release of the adsorbed species under consideration from the unit surface, is in general given by the product of four factors ... 

Hence, the most general expression for the desorption rate in this model is... 

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