Desorption kinetics analysis

Temperature-programmed desorption (TPD) is amenable to simple kinetic analysis. The rate of desorption of a molecular species from a uniform surface is given by Eq. XVII-4, which may be put in the form... 

In this review we put less emphasis on the physics and chemistry of surface processes, for which we refer the reader to recent reviews of adsorption-desorption kinetics which are contained in two books [2,3] with chapters by the present authors where further references to earher work can be found. These articles also discuss relevant experimental techniques employed in the study of surface kinetics and appropriate methods of data analysis. Here we give details of how to set up models under basically two different kinetic conditions, namely (/) when the adsorbate remains in quasi-equihbrium during the relevant processes, in which case nonequilibrium thermodynamics provides the needed framework, and (n) when surface nonequilibrium effects become important and nonequilibrium statistical mechanics becomes the appropriate vehicle. For both approaches we will restrict ourselves to systems for which appropriate lattice gas models can be set up. Further associated theoretical reviews are by Lombardo and Bell [4] with emphasis on Monte Carlo simulations, by Brivio and Grimley [5] on dynamics, and by Persson [6] on the lattice gas model. 

In one dimension the truncation of the equations of motion has been worked out in detail [59]. This has allowed an accurate examination of the role of diffusion in desorption, and implications for the Arrhenius analysis in nonequilibrium situations. The largest deviations from the desorption kinetics of a mobile adsorbate obviously occur for an immobile adsorbate... 

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. 

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. 

Having chosen a particular model for the electrical properties of the interface, e.g., the TIM, it is necessary to incorporate the same model into the kinetic analysis. Just as electrical double layer (EDL) properties influence equilibrium partitioning between solid and liquid phases, they can also be expected to affect the rates of elementary reaction steps. An illustration of the effect of the EDL on adsorption/desorption reaction steps is shown schematically in Figure 7. In the case of lead ion adsorption onto a positively charged surface, the rate of adsorption is diminished and the rate of desorption enhanced relative to the case where there are no EDL effects. 

As an example of the manner in which EDL effects are incorporated into the kinetic analysis, consider the following bimolecu-lar adsorption/desorption mechanism ... 

In arriving at Equation 32 it is assumed that the magnitude of the activation potentials for adsorption and desorption are equal and opposite in sign (a reasonable assumption if the surface potential is relatively unchanged during the course of the reaction, which would be the case for small perturbation of the equilibrium). In this manner the EDL properties are developed consistently for both the equilibrium and kinetic analysis based on the TLM. 

The first attempt to account for surface contamination in creeping flow of bubbles and drops was made by Frumkin and Levich (FI, L3) who assumed that the contaminant was soluble in the continuous phase and distributed over the interface. The form of the concentration distribution was controlled by one of three rate limiting steps (a) adsorption-desorption kinetics, (b) diffusion in the continuous phase, (c) surface diffusion in the interface. In all cases the terminal velocity was given by an equation identical to Eq. (3-20) where C, now called the retardation coefficient , is different for the three cases. The analysis has been extended by others (D6, D7, N2). 

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... 

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. 

The next step in the reaction kinetics analysis is to choose for each family of reactions (i.e., adsorption/desorption, oligomerization//-) -scission, isomerization, and hydride transfer) whether to parameterize the kinetic model in terms of either the forward or the reverse rate constant (kj,for or khrey) since the ratio of the forward and the reverse rate constants must equal the known value of Kit q ... 

The polymer was 10 times as effective as a small-molecule analog, dimethy-benzylamine 10 in the case of p-nitrophenyl caproate 6. The rate enhancement is larply attributed to favorable binding. No difference in catalytic activity was found between linear and branched polyethyleneimine derivatives. It is curious that desorption of the product is rate-limiting according to the kinetic analysis. 

Fig. 38. (a, b) SFG spectra of CO adsorbed on Rh(l 11) at 300K at pressures between 10 and 1000 mbar. (c) Analysis of the on-top CO intensity (surface density), resonance position, and CO coverage as a function of the CO pressure. The open symbols indicate the pressure range of irreversible CO adsorption. The equilibrium CO surface coverage in (c) was calculated from adsorption/desorption kinetics adapted from Pery et al. (314). Copyright (2002) The Combustion Institute. 

Whitley, R. D., Van Cott, K. E., Wang, N.-H. Analysis of nonequilibrium adsorption/ desorption kinetics and implications for analytical and preparative chromatography, Ind. 

For both the Langmuir and Jovanovic isotherms several exact methods exist for the determination of the energy distribution function adsorption isotherm is precisely known. Rather than trying to modify these exact methods for desorption kinetics, this work will use two approximate methods which give simple analytical expressions for the distribution function in terms of derivatives of the overall isotherm, and which allow a better and more friendly analysis of results. 

The asymptotically correct approximation (ACA) was first introduced by Hobson [44] for the description of adsorption equilibrium on heterogeneous surfaces it has however become of wide use in the analysis of adsorption isotherms only after Cerofolini s investigation of the involved errors (which are of the same order as in the CA) and demonstration of its usefulness in determining the maximum adsorption energy [28]. The ACA can be extended to desorption kinetics by replacing the supposedly true desorption isotherm kinetics A (t,E) with their asymptotic limits. Since... 

Cerofolini and Re have extended the analysis of the overall desorption kinetics beyond the 2-nd order approximation by using the methods developed for equilibrium adsorption by Nederlof et al. (logarithmic symmetrical local isotherm approximation) [45], Rudzihski and coworkers (3-rd order approximation) [46, 47, 48, 49], and Re (n-th order approximation) [50]. Details are given in Ref. [39]. 

Thus, the most suitable route for obtaining information on the adsorption/desorption kinetics is from the short-time transient behavior. Under these conditions, surface diffusion effects are negligible and the short-time current response depends only on Ka, Kd, and A for a given tip/substrate separation. Provided that an independent measurement of A can be made, an absolute assignment of the interfacial kinetics is possible. Furthermore, analysis of the long-time current allows the importance, and magnitude, of surface diffusion to be determined. 

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