Zero order desorption

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. 

In the low coverage region (Figure 4a) the initial buildup of Cu can be seen. The initial stage of Cu growth is indicated by the appearance of an approximately zero order desorption peak and, following the notation of Christmann and co-workers (34), is noted as. This state reflects Cu coverages up to approximately one monolayer (one Cu atom per surface Ru atom). The saturated f state has a desorption maximum at -1210 K. 

Multilayer adsorption models have been used by Asada [147,148] to account for the zero-order desorption kinetics. The two layers are equilibrated. Desorption goes from the rarefied phase only. This model has been generalized [148] for an arbitrary number of layers. The filling of the upper layer was studied with allowance for the three neighboring molecules being located in the lower one. The desorption frequency factor (CM) was regarded as being independent of the layer number. The theory has been correlated with experiment for the Xe/CO/W system [149]. Analysis of the two-layer model has been continued in Ref. [150], to see how the ratios of the adspecies flows from the rarefied phases of the first and the second layers vary if the frequency factors for the adspecies of the individual layers differ from one another. In the thermodynamic equilibrium conditions these flows were found to be the same at different ratios of the above factors. 

Examples of the dependence for a fixed rate constant are given in fig. 17. Zero-order desorption shows an increase in peak temperature with coverage and a precipitate drop in desorption rate when all the materia is... 

The desorption order x describes the coverage dependence of the desorption rate. For organic molecules only the desorption orders x = 1 (first order) and x = 0 (zero order) are relevant. Zero order desorption takes place in the presence of multilayers. In this case the maximum number of molecules per surface unit is always available and therefore no coverage dependence exists (A 0). When it comes to desorption of the last monolayer the desorption rate is proportional to the number of available molecules, i.e. proportional to A1. 

Fig. 1. Calculated desorption spectra for pure zero-order desorption (a), for changing the desorption order from zero to first order at 1 monolayer (b), for pure first order desorption (c) and for first order desorption with repulsive lateral interaction (d).

The desorption energy of multilayers (heat of evaporation) can be easily obtained as outlined in section 2. As an example we show the multilayer desorption of p-4P from a carbon covered polycrystalline Au-foil (Fig. 4a) and the corresponding Inf vs. 1/7 plot (Fig. 4b). In Fig. 4a one can clearly see the zero order desorption behavior as described above (common leading edge, sharp cutoff of trailing edge). The determination of the desorption energy from Fig. 4b yields Edes =1.6 eV. For the pre-exponential factor one obtains i = 5 x 1021 s [19],... 

It has been shown, in general, that zero-order desorption is likely from desorbing layers of surface compounds [291], as has been seen for Xe on C 0001 [292] and for oxide films on W [293] (W02 oxide states are observed in the desorption spectra). Following the Venables and Bienfait analysis [291], the coverage, N, is made up of atoms in a solid phase, S, in the first layer which covers a fraction, A, of the substrate and an adsorbed gas phase, 1, is in the first layer while 2 denotes second layer adsorbed gas species. If the atoms arrive from the vapour phase at a rate R (per unit area) and are accommodated and the layer evaporates at a rate Re, then... 

Adsorption/Desorption. There is earlier evidence for the dominance of a zero-order desorption mechanism at low to moderate temperatures in pure carbon systems. Rosner and Allendorf (48) observed a change in activation energy of 31 kcal/mole at 1300°K to 0 at 1600°K and a change in order from 0.56 at 1200°K to unity at 1440°K. If pore diffusion were a factor, the change in oxygen reaction order would... 

The optimum temperature could be deduced from thermal desorption measurements in which 5T films were heated up to 474 K (Figure 13.9). They show a main peak with a sharp cut-off pointing at a zero-order desorption kinetic with a desorption energy of 210 kJ/mol. The secondary peak at lower temperature can be attributed to a temperature-induced less ordered and probably more mobile phase [36]. Therefore, a deposition temperature should be chosen which is high enough for molecular diftiision but low enough that the molecules are not evaporated, i.e. around 363-383 K. 

The two most common temporal input profiles for dmg delivery are zero order (constant release), and half order, ie, release that decreases with the square root of time. These two profiles correspond to diffusion through a membrane and desorption from a matrix, respectively (1,2). In practice, membrane systems have a period of constant release, ie, steady-state permeation, preceded by a period of either an increasing (time lag) or decreasing (burst) flux. This initial period may affect the time of appearance of a dmg in plasma on the first dose, but may become insignificant upon multiple dosing. 

The reaction of Si02 with SiC [1229] approximately obeyed the zero-order rate equation with E = 548—405 kJ mole 1 between 1543 and 1703 K. The proposed mechanism involved volatilized SiO and CO and the rate-limiting step was identified as product desorption from the SiC surface. The interaction of U02 + SiC above 1650 K [1230] obeyed the contracting area rate equation [eqn. (7), n = 2] with E = 525 and 350 kJ mole 1 for the evolution of CO and SiO, respectively. Kinetic control is identified as gas phase diffusion from the reaction site but E values were largely determined by equilibrium thermodynamics rather than by diffusion coefficients. 

Figure 7.7 shows three different sets of TPD measurements, corresponding to zero-, first- and second-order desorption processes. 

For a first-order desorption, a useful relation between Edes and v arises if we consider the peak maximum, which occurs when the derivative of the rate becomes zero ... 

Give examples of desorption systems following first-, second- and zero-order kinetics. Can you give a physical interpretation for the latter ... 

Figure 2.11 Thermal desorption spectra of silver from the close-packed surface of ruthenium for different initial Ag coverages. Desorption from the second layer of silver occurs at lower temperatures, indicating that Ag-Ag bonds are weaker than Ag-Ru bonds. Note the exponential increase of the low temperature sides of the peaks, indicating that the desorption follows zero-order kinetics (from Niemantsverdriet et al. [18]).

Figure 2.13 Activation energies and prefactors for the desorption of Ag from Ru(001) as determined with the complete analysis. The desorption parameters become essentially constant for coverages above 0.15 ML, indicative of zero-order kinetics. This suggests that Ag atoms desorb from the edges of relatively large two-dimensional islands (data from Niemantsverdriet et al. [18]). 

Higher Cu exposures (Figures 4b, 4c, and 4d) cause the appearance of a second binding state, fi., with a desorption maximum at a temperature below that of the state. The kinetics of the desorption process of the state are approximately zero order, indicating that the rate or the desorption is independent of the Cu concentration on the surface. The general adsorption behavior and peak temperatures in Figure 4 are completely in agreement with the work of Christmann, et al. (34). 

While first-order models have been used widely to describe the kinetics of solid phase sorption/desorption processes, a number of other models have been employed. These include various ordered equations such as zero-order, second-order, fractional-order, Elovich, power function or fractional power, and parabolic diffusion models. A brief discussion of these models will be provided the final forms of the equations are given in Table 2. 

Reaction temperature can also affect the order of a reaction. It is generally agreed that the rate constant for the conversion (or desorption) of the surface-oxygen complex has a higher activation energy than the rate constant for the formation of the complex. Therefore, a reaction which is zero order at low temperatures and a given pressure can become first order at the same pressure and a sufficiently high temperature. 

Kinetic Considerations. The reaction kinetics are masked by a desorption process as shown below and are further complicated by rate deactivation. The independence of the 400-sec rate on reactant mole ratio is not indicative of zero-order kinetics but results because of the nature of the particular kinetic, desorption, and rate decay relationships under these conditions. It would not be expected to be more generally observed under widely varying conditions. The initial rate behavior is considered more indicative of the intrinsic kinetics of the system and is consistent with a model involving competitive adsorption between the two reactants with the olefin being more strongly adsorbed. Such kinetic behavior is consistent with that reported by Venuto (16). Kinetic analysis depends on the assumption that quasi-steady state behavior holds for the rate during rate decay and that the exponential decay extrapolation is valid as time approaches zero. Detailed quantification of the intrinsic kinetics was not attempted in this work. 

Here M and T represent methylcyclohexane and toluene in the gas phase, and Ttt represents adsorbed toluene. The first step in the above reaction sequence represents the adsorption of methylcyclohexane with subsequent reaction to form toluene, while the second step is the desorption of toluene from the surface. Very likely the first step represents a series of steps involving partially dehydrogenated hydrocarbon molecules or radicals. However, at steady-state conditions the rates of the intermediate steps would all be equal, and the kinetic analysis is, therefore, not complicated by this factor. To account for the near zero-order behavior of the reaction, it was suggested that the active catalyst sites were heavily covered with... 

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