Desorption first order

Its main features are given by the use of a stream of inert carrier gas which percolates through a bed of an adsorbent covered with adsorbate and heated in a defined way. The desorbed gas is carried off to a detector under conditions of no appreciable back-diffusion. This means that the actual concentration of the desorbed species in the bed is reproduced in the detector after a time lag which depends on the flow velocity and the distance. The theory of this method has been developed for a linear heating schedule, first-order desorption kinetics, no adsorbable component in the entering carrier gas (Pa = 0), and the Langmuir concept, and has already been reviewed (48, 49) so that it will not be dealt with here. An analysis of how closely the actual experimental conditions meet the idealized model is not available. 

Even if the peak behavior fits well for a given apparent desorption order, the real kinetic situation may be a different one. As a rate controlling step in a second-order desorption, random recombination of two particles is assumed most frequently. However, should the desorption proceed via a nonrandom recombination of neighboring particle pairs into an ordered structure, the resulting apparent first-order desorption kinetics is claimed to be possible (36). The term pseudo-first-order kinetics is used in this instance. Vice versa, second-order kinetics of desorption can appear for a nondissociative adsorption, if the existence of a dimer complex is necessary before the actual desorption step can take place (99). A possibility of switching between the apparent second-order and first-order kinetics by changing the surface coverage has also been claimed (60, 99, 100). 

The first-order and second-order kinetics of desorption are by far the most common and practically considered cases. Less than first-order desorption kinetics indicates multilayer adsorption or transport limited desorption (101). An actual significance of the third-order kinetics in desorption has been found recently by Goymour and King (102, 103). 

The second case in Fig. 7.7 corresponds to first-order desorption of CO from a stepped Pt(112) surface. This surface consists of (111) terraces and (100) steps. At coverages below one-third of a monolayer, CO only occupies the step sites, while at higher coverage the terraces are also populated, resulting in two clearly distinguish-... 

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 ... 

Desorption Rates. Using the above model for the temperature jump associated with pulsed laser heating, the rate of desorption versus time and the total number of molecules desorbed from a finite surface area heated by the laser can be calculated. For the particular case of first-order desorption kinetics, the desorption rate is ... 

Expression (2-16) is approximately correct for first-order desorption and for values of vt[ between 108 and 1013 K l. It is very often applied to determine from a single TDS spectrum. The critical point however is that one must choose a value for v, the general choice being 1013 s, independent of coverage. As we explain below, this choice is only valid when there is little difference between the entropy of the molecule in the ground state and that in its transition state 125, 27], The Redhead formula should only be used if a reliable value for the prefactor is available ... 

Another popular method has been developed by Chan, Aris and Weinberg [28], These authors expressed E ( 8) and v(8) in terms of the peak maximum temperature Tmax and the peak width, either at half or at three quarters of the maximum intensity. Their expressions for first order desorption are ... 

D Evelyn, M. P., Cohen, S. M., Rouchouze, E. and Yang, Y. L. Surface bonding and the near-first-order desorption kinetics of hydrogen from Ge(100)2x 1. Journal of Chemical Physics 98, 3560-3 (1993). 

For first-order desorption kinetics (i.e., n = 1), Redhead [331] gave an approximate relationship between the activation energy Ea and the temperature Tp at which the desorption rate is a maximum... 

Kd is the desorption coefficient for product D. The first-order desorption term should be strictly Kd(Cdp — H Cdg), allowing for an equilibrium backpressure, where H is an equilibrium adsorption constant relating mole fractions in the gas and zeolite phases. H Cdg was shown empirically to be small compared with Cdp under our conditions. 

For the simple case of a first-order desorption process we briefly describe the analysis a first order desorption is described by dO/dt = —kde9. Desorption is assumed to be an activated process. The desorption rate, that is the decrease in coverage or the number of molecules coming off the surface per unit time, is... 

The TPD spectra of three different adsorbate systems, corresponding to zeroth-, first- and second-order kinetics, are shown in Figure 2.9. Each trace corresponds to a different initial adsorbate coverage, as indicated in the figure. The simplest case in TPD corresponds to first-order desorption kinetics, represented by the CO/Rh(lll) series in Figure 2.9 [17, 18]. For CO coverages up to 0.5 monolayer (ML), the CO molecules do not interact on Rh(lll) and the desorption traces all fall in the same temperature range, all with the same peak maximum temperature. Hence, the rate of desorption is proportional to the surface concentration of CO. Above 0.5 ML, CO starts to populate additional sites (from vibrational spectroscopy studies we know that in addition to on-top sites also threefold hollow sites are occupied see Fig. 8.15), and a faster reaction channel for desorption opens up, as seen by the development of a shoulder at lower temperatures [18]. 

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