J. Chem. SOC., Faraday Trans. I, 1987,83, 1363-1367 The Role of Electron Transfer Processes in Determining Desorp tion Kinetics Philip J. Pomonis Department of Chemistry, University of Ioannina, Ioannina 45332, Greece The desorption step of heterogeneous processes taking place on solid-gas interfaces may be influenced by the bulk conductivity of the solid. This might be seen in systems where, during adsorption, negative charge is transferred to adsorbed species, leaving a positive hole. If the n-type conduction of the solid is high, then this hole may be filled by an electron, not from the adsorbed species but from the bulk of the solid. Desorption is thus shown to be a second-order process necessitating, apart from the adsorbed species, electronically vacant sites. Application of transition-state theory shows that the second-order desorption of monomolecular processes should appear at sufficiently low pressures, while at higher ones normal first-order kinetics applies.In a typical catalytic process, taking place on a solid surface, the net reaction contains the three necessary and distinct steps of adsorption, reaction and finally desorption. For a monomolecular decomposition reaction this consequence can be represented as follows. Adsorption H eac tio n Desorption A I I I A(&+-VS--+-VS- A X -vs- +- -vs- X I I I I I -vs- +X(g) + -vs- I I where VS stands for a vacant surface site. The sequence of reactions (1 a), (1 b) and (1 c ) does not tell us anything about the charges transferred to, or from, the solid. A more detailed representation of the same process should take these effects into account.Thus for a reaction where electrons are transferred from the solid to the adsorbed molecule during adsorption, reactions (1 a), (1 b) and (1 c ) can be written as follows. Adsorption A- t I I A(g) +-VS- + -EVS- 1363Electron Transfer Processes in Desorption Kinetics 1364 Reaction Deso rp t ion A- X- -EVS- -+ -EVS- I I 1 I X- I -EVS-+X(g)+-VS- I I A- T X- T Fig. 1. The species A adsorbed on the surface as A- remains adsorbed on the surface as X- (11). Then (I) may yield the product X, the last of which X- may desorb as X(g) by the return of the electron to the electronically vacant site (111) if this site has not been filled’by-electrons from the bulk of the solid (IV). In the above scheme EVS stands for an electronically vacant surface site and is a hole left behind by an electron transferred to adsorbed molecule A.Step (2c) involves the transfer of an electron from X-, which represents the product of the reaction, to the EVS, which is then transformed to a VS. However, if the n-type conductivity of the solid is high the EVS might be filled by an electron from the bulk of the solid. As a result step (2c) will be prohibited (fig. 1) and species X will be trapped on the surface.l The purpose of this paper is to examine the consequences of this effect. The discussion which follows is not affected significantly if the reaction is diatomic, as the majority of heterogeneous catalytic reactions usually are, and the charge is transferred to one or both molecules.However, for simplicity we shall refer to a typical monomolecular reaction, e.g. the decomposition of N,O, which has been studied extensively.2yP. J. Pomonis 1365 Discussion Many studies of the decomposition of N,O on different solid catalysts have shown that the rate-determining step is the desorption of oxygen,’. written as (3) 20-(ads) + 2EVS -+ O,(g) + 2VS or 0-(ads) + EVS + N,O(g) --+ VS + (N, . . . O,)(g) -+ VS + N,(g) + O,(g). (4) The desorption can be written in a general way so as to contain the ‘transition complex ’ : where X# stands for the intermediate (transition) complex transformed without con- sumption of energy to the final product X(g). Then, according to transition-state theory (TST),4 we obtain the following expression for the rate of desorption Rd from reaction A-(ads) + EVS -+ X # (g) + VS ( 5 ) ( 5 ) : (6) R d = CA(ads) cEVS f i f V S exp (- E;/RT) cvs h f*(ads)fEVS where Cvs and C,,, refer to the concentration of vacant and electronically vacant surface sites while the f are partition functions having their customary significance.Eqn (6) may be compared with the expression describing, according to TST, the rate of desorption, which equals the rate of formation of the transition complex for monomolecular processes :4 A(ads) --+ Xf(ads). (8) Eqn (6) and (7) are similar, apart from the terms C,, and C,,, and the corresponding partition functionsf,, andf,,,. However, eqn (6) should be nearer to reality since it takes into account the necessity that desorption requires EVS. The question arising now is, on what does the CEVS depend? We believe that the main factor affecting it is the conductivity of the solid.Namely, for the system described by reactions 2(a)-(c) and shown in fig. 1, if the n-type conducting on of the solid tends to zero, as in a perfect insulator, then step (IV) in fig. 1 is totally avoided and the EVS created by step (I) in the same figure has the unique possibility of being filled by the electron returning to it from the adsorbed species X-. This will be done to an extent which, among other things, depends on the activation energy of desorption E:. If on the other hand the n-type conductivity CT, of the solid is high, step (IV) should prevail and therefore the rate of desorption, which is equal to the rate of the process, should tend to zero.These arguments can be put formally into theory by setting cEVS = CA(ads) d o n ) (9) where g(an) is a conductivity function such that for small an, g(on) -+ 1 while for large on, d o n ) -+ 0. Substitution of eqn (9) into eqn (6) yields exp (- E:/RT). ‘k(ads) d o n ) kT - f # f V S R, = cVS fA(ads)fEVS1366 Now we can consider that Electron Transfer Processes in Desorption Kinetics CA(ads) = GSO and c,, = C&( 1 - 0) (12) where 0 is the fractional coverage and Cvs is the initial concentration of vacant sites. Substitution of eqn (1 1) and (12) into eqn (10) provides kT fifvs exp (- E:/RT). o2 Rd = CVS -don) ' fA(ads1fEVS Then by using the Langmuir isotherm we obtain For sufficiently small values of pressure KP 6 1, and eqn (14) is written as Rd = C&(KP)'g(a,) kT f i f v s exp (- Eg/RT).fA(ads)fEVS Conversely, for high values of pressure KP + 1, and eqn (14) is reduced to the form In other words we observe that the general equation (14) describes kinetics of second order at sufficiently low pressures, but kinetics of first order at relatively higher pressures. This result is similar to that described in the theory of homogeneous monomolecular reactions of Lindeman.5 However, in order to derive it for surface reactions we have introduced the term for conductivity of the solid, and especially the EVS which corresponds to the second atom, necessary for collision, in Lindemann's theory. In spite of our efforts we have not been able to find in the relative literature clear experimental evidence corresponding to the transition from first- to second-order kinetics, as the pressure decreases, in monomolecular heterogeneous reactions.It might be the case that the observation of such a transition could be restricted by factors similar to those operating in homogeneous This matter requires further attention. A second point about the general equation (14) is that under constant pressure, P, and temperature, T, and considering that the values of K and f are approximately constant, it is reduced to the form Eqn (1 7) indicates that, according to the definition given above, as the n-type conductivity 0, of the system increases, then g(a,) decreases and the rate of desorption should drop. In this respect the observation* that p-type semiconductors are good catalysts for the N20 decomposition, whereas n-type materials are not, fits well with the above discussion.The holes created by step (I) in fig. 1 should be filled much more easily in an n-type material than in a p-type one, although their net conductivity due to n- and p-type carriers might be of the same magnitude. We also believe that the results described in ref. (I) may also be explained according to this model. Namely, in this work some doped insulators of the form Al,-,Cr,O, and MgAI,-,Cr,O, were examined with regard to different catalytic reactions. For small values of x (x 5 0.2) the material showed a low conduction (1 0-lo R-l cm-l), while the catalytic activity increased almost linearly with the degree of doping, x. This means that g(a,) z 1, so that eqn (1 7) is written as Rd = kc& eXp ( - E : / R T ) .(18)P. J . Pomonis 1367 This shows that the activity depends only on C&, which corresponds to doped active centres (x). For large values of x(x 2 0.4) the material showed a stabilized conductivity of ca. W1 cm-l, while the activity again increased almost linearly with doping. This may also show that the term g(a,) was stabilized between its two extreme values (zero and unity) and therefore that an equation similar to eqn (18) was again operating. Finally, in the region 0.2 < x < 0.4 the conduction of the solid showed a sharp drop by ca. five orders of magnitude, while the activity dropped by ca. one order of magnitude. This phenomenon could also be explained according to eqn (17). A similar explanation may also be proposed for the system La,Cu,-,Ni,O, examined recentlyg in the decomposition of N,O. References 1 P. Pomonis and J. C. Vickerman, J. Catal., 1978, 55, 88. 2 A. Cimino, Chim. Ind. (Milan), 1974, 56, 27. 3 J. C. Vickerman, in Catalysis, ed. C. Kemball and D. A. Dowden (Specialist Periodical Reports, the 4 J. M. Thomas and W. J. Thomas, Introduction to the Principles of Heterogeneous Catalysis (Academic 5 F. A. Lindeman, Trans. Faraday SOC., 1922, 17, 597. 6 Theory of Kinetics, ed. C. H. Bamford and C. F. Ripper, vol. 2 of Comprehensive Chemical Kinetics 7 K. J. Laidler, Reaction Kinetics (Pergamon Press, Oxford, 1963), vol. 1. 8 R. P. De, F. S. Stone and R. F. Tilley, Trans. Faraday SOC., 1953,49, 201. 9 K. V. Ramanujachary and C. S. Swamy, J. Catal., 1985, 93, 279. Chemical Society, London, 1979), vol. 2, p. 107. Press, London, 1967). (Elsevier, Amsterdam, 1969). Paper 6/289; Received 10th February, 1986