Desorption order

Since generally em > z, these coverages at Tm increase only slightly as the heating schedule becomes less progressive and amount to about c-1 37%, J = 50%, and /3/3 59% of the initial coverage for the first-order, second-order, and third-order desorption, respectively. 

Thus, for the second-order desorption kinetics and the hyperbolic heating schedule, the peaks are symmetric about Tm in the scale (1/T). The first-order peaks are asymmetric in this scale, exhibiting a steeper descent than ascent. These considerations suggest that the hyperbolic heating schedule is especially favorable for an analysis of the peak shapes and for the detection... 

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). 

In estimating the value of Ed by means of the transcendental equations (28), the circumstance utilized is that the variation of em for a given change in Tm is much less than the variation of exp(em) (31). Until now, only particular solutions have been available for the hyperbolic and linear heating schedules and for the first-order and second-order desorptions. They can be found for example in the fundamental papers by Redhead (31) and Carter (32) or in the review by Contour and Proud homme (106), and therefore will not be repeated here. Recently, a universal procedure for the... 

The paper by Dawson and Peng (98) can be quoted as an example of applying Eq. (58) to a kinetic analysis of both the first-order and second-order desorptions with an activation energy varying linearly with the surface coverage. 

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

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. 

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-... 

The right-hand part of Fig. 7.7 corresponds to the second-order desorption of nitrogen atoms from a rhodium surface. As the desorption reaction corresponds to N -I- N —> N2 -I- 2 the rate is indeed expected to vary with A characteristic feature of second-order desorption kinetics is that the peaks shift to lower temperature with increasing coverage, because of the strong dependence of the rate on coverage. 

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 ... 

A similar though more complicated expression exists for second-order desorption kinetics ... 

TPD of the nitrogen-saturated Fe(lOO) surface shows a symmetric feature with a peak maximum at 740 K if we use a heating ramp of 2 K s . Estimate the activation energy for desorption assuming second-order desorption. 

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 ... 

The results of a similar experiment with adsorbed hydrogen is shown in Fig. 2.3b. Only one desorption peak was observed in the temperature range studied [50], The desorption peak temperature lies at 420 K for the experiment with 0.8 L and is shifted to lower temperatures as the H2 concentration increases indicating second order desorption kinetics. Surface states with desorption temperatures at 165 K, 220 K, 280 K and 350 K were reported for the adsorption of H2 and D2 at 120 K [51]. Thermal desorption experiments after H2 adsorption at 350 K show only one desorption state at ca. 450 K [52],... 

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 ... 

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. 

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... 

Plot the surface coverage 6 versus temperature assuming second-order kinetics (n = 2) for the same initial coverages and parameters listed in part 4, above. Are the calculated TPD curves symmetric with respect to temperature Does Tp depend on initial surface coverage You will often see the comment that for second-order desorption kinetics, the surface coverage at Tp is 9P = 9 /2. Do your calculations bear this out ... 

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. 

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