J. Phys. Chem. C 2007, 111, 7795-7800
7795
On the Formation of Nitrogen Islands on Rhodium Surfaces F. Zaera Department of Chemistry, UniVersity of California, RiVerside, California 92521
J. L. Sales and M. V. Gargiulo Instituto de Energı´a Ele´ ctrica and Departamento de Geofı´sica y Astronomı´a, UniVersidad Nacional de San Juan, San Juan, Argentina
M. Ciacera and G. Zgrablich* Laboratorio de Ciencias de Superficies y Medios Porosos, UniVersidad Nacional de San Luis, San Luis, Argentina ReceiVed: December 1, 2006; In Final Form: February 12, 2007
The possibility of N island formation during the conversion of NO + CO mixtures on Rh(111) and the kinetics observed in thermal desorption experiments from this system were studied by kinetic Monte Carlo simulations. Three models were proposed and tested to account for the behavior observed: (a) one where the free formation of islands through N diffusion on the surface is combined with nearest-neighbor (NN) attractive and repulsive second- and third-order neighbor interactions. (b) A second where compact islands with size similar to that suggested by experiments are produced by an alternative mechanism such as a preferential NO dissociation rate in the presence of an already dissociated N atom. In this model, thermal desorption is still assumed to be affected by adsorbate-adsorbate interactions as in model a. (c) A third where the nitrogen islands are formed as a result of adsorbate-substrate rather than adsorbate-adsorbate interactions, that is, where a “surface stress” mechanism is operative, and the same interactions affect the thermal desorption process. It was found that the experimental data can only be satisfactorily reproduced by model c.
1. Introduction The formation of adsorbate islands on transition metals due to strong intermolecular interactions has been observed in several systems.1-10 These islands affect the kinetics of subsequent surface reactions, sometimes in dramatic ways.11-12 A typical case of island formation is provided by chemisorbed oxygen on some transition metals, as indicated directly by both lowenergy electron diffraction (LEED)8 and scanning tunneling microscopy (STM)9,10 experiments. In some instances the presence of adsorbate islands has not been established directly, but has been inferred from kinetic experiments instead. This is the case of the formation of nitrogen islands on Rh(111) during the reduction of NO by CO. Despite the similarities between oxygen and nitrogen atoms, much less is known about the adsorption of the latter on metals.13 Disordered structures have been often proposed for N atoms on some hexagonal basal planes, but (x3 × x3) R30° and (2 × 2) ordered phases are known only on Ru(0001).14,15 On Rh(111), a diffuse (1 × 1) LEED pattern has been interpreted as a sign of disordered adsorption, apparently associated with high saturation coverages, on the order of 2/3 ML.16,17 A (2 × 1) structure with much lower coverage, on the order of 0.11 0.15 ML, has been reported for nitrogen on Rh(111) when in the presence of some coadsorbed oxygen, but the accompanying STM evidence supporting this conclusion is less than conclusive.18 On the other hand, some kinetic studies suggest that nitrogen atoms may order and form islands on this surface. * Corresponding author. E-mail:
[email protected].
Indeed, our molecular beam kinetic measurements on the reduction of NO by CO on Rh(111) concluded that below 500 K the surface of the rhodium catalyst is partially covered by atomic nitrogen during the steady-state reaction.19-25 Additional isotope-labeling experiments showed that the rate of replacement of 14N by 15N on the surface upon switching from 14NO + CO to 15NO + CO reaction mixtures follow a complex kinetic behavior explainable by the preferential removal of atoms from the periphery of surface N islands.21 The nitrogen molecules made during the steady-state conversion of the NO + CO mixtures were also determined to always contain at least one 15N atom, even immediately after the isotopic switchover, an observation that was interpreted as the result of reactions between newly adsorbed 15NO molecules and nitrogen atoms from the edges of the surface N islands via the formation of a N-NO intermediate.23 Finally, a study combining isotopelabeling experiments with Monte Carlo simulations based on an islanding model added more indirect evidence for this N island formation model on Rh(111).26 The purpose of the present work was to further test the islanding model by using kinetic Monte Carlo simulations to emulate N2 temperature-programmed desorption (TPD) and isothermal desorption data. A number of hypothesis were tested about the driving forces acting in the formation of the proposed N islands. In Section 2 the experimental background is briefly outlined, and in Section 3 the theoretical model and the Monte Carlo simulation method are described. The results and their discussion are presented in Section 4 and, finally, the main conclusions are summarized in Section 5.
10.1021/jp068270c CCC: $37.00 © 2007 American Chemical Society Published on Web 05/10/2007
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Figure 1. Experimental N2 TPD spectra from N atoms adsorbed on a Rh(111) single-crystal surface.20
2. Experimental Background The molecular beam apparatus and experimental procedures used to obtain the data presented below have been described in detail elsewhere.27 N2 TPD spectra were obtained by first depositing N atoms on the Rh(111) surface via exposures to NO + CO beams of different NO:CO composition ratios (typically around 1:7) while keeping the temperature of the crystal at a constant fixed value. The surface was allowed to reach steady state, at which point some N is continuously present on the surface but there is no oxygen buildup because of its rapid removal by reaction with CO to produce CO2. The coverage of N obtained in this way depends on both the beam composition and the reaction temperature, and in the case of the 1.7 NO:CO beam goes from about 0.5 ML at 400 K to less than 0.1 ML above 600 K. After the steady-state regime was achieved for each temperature, TPD spectra were measured using a heating rate of 10 K/s. Figure 1 reproduces the resulting reported TPD traces,20 and shows how the peak maximum in these spectra shifts from about 750 K to less than 600 K as N coverage increases. Although a temperature shifting in the same direction is expected for any second-order process (as the formation of N2 by N recombination is expected to be), in this case it has already been established that the observed shifts can only be explained by significant N-N repulsive interactions.17 Similar conclusions have been reached from isothermal desorption (ID) kinetic experiments. In those, the surface was exposed to a 1:9 NO:CO beam at 450 K for 200 s, and the oxygen atoms were titrated off the surface by using CO. After that, the temperature of the Rh crystal was set to the desired value and kept constant for 100 s, the time necessary to acquire the ID data. Finally, the surface was flashed to 700 K for another 100 s and then to 1000 K to drive the desorption of nitrogen to completion. Figure 2 reports the key experimental ID data for T ) 550, 575, 602, 628, 661, and 700 K (thin lines). Additional experiments using isotopic labeling further supported the suggestion that N forms islands on the surface.21,26 In those experiments, a normal isothermal (T ) 480 K) kinetic experiment was run first using a 1:1 14NO:CO molecular beam mixture. That initial run was maintained for over 200 s in order to reach steady state. The beam was then switched to a second identical one but with 15N-labeled nitrogen oxide (a 1:1 15NO: CO beam at the same total flux as before), and the reaction
Zaera et al.
Figure 2. Isothermal desorption data for N atoms recombination from a Rh(111) surface. The traces correspond to desorption temperatures of, from top to bottom, 550, 575, 602, 628, 661, and 700 K.
carried out for an additional specified t time before turning the beam off again. This experimental sequence was designed to deposit a steady-state coverage of nitrogen atoms on the surface with varying proportions of 14N and 15N isotopes depending on the reaction time t used in the second half. That isotope ratio was measured afterward by recording the nitrogen TPD spectra for 14N2 (28 amu), 14N15N (29 amu), and 15N2 (30 amu). The experimental TPD spectra obtained this way for selected values of t are shown in Figure 3 (thin lines).26 Perhaps the most important observation here is the significant deviations in the distribution of 14N and 15N isotopes among the desorbing nitrogen molecules from statistical. Monte Carlo simulations performed to interpret the data yielded the best fit when assuming rather compact N islands on the surface (of 5 atoms average diameter), and the 14N isotope occupying the inner core and the 15N atoms the periphery.26 In summary, the complete set of experimental data provides two apparently contradictory views of this system. On one hand, the increase in desorption temperature for N2 with increasing N coverage suggests N-N repulsive interactions.17 On the other, however, the behavior of the mixed isotope N adsorbates, which leads to the desorption of molecular nitrogen with isotopic distributions significantly different from those expected from statistical consideration, could only be explained by assuming the formation of N islands,26 and that usually implies attractive N-N interactions. In what follows we intend to reconcile this apparent contradiction by testing different adsorption models for N on Rh(111) via Monte Carlo simulations. 3. Adsorption Model and Simulation Method The Rh(111) surface is represented by a triangular lattice of 104 adsorption sites for N atoms. This size of the lattice, with periodical boundary conditions, was found sufficiently big in order to have negligible border effects. An expression for the energy of an adsorbed N atom at site i is written in a general way as
Ui ) + wR(i)
(1)
where the first term represents the adsorption energy at zero coverage (which is assumed to be the same for all sites) while
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Figure 3. TPD spectra for the different isotopically labelled molecular nitrogen produced by recombination of mixtures of adsorbed on Rh(111) surfaces. Thin lines: smoothed experimental results.26 Thick lines: simulation predictions.
the second corresponds to the interaction energy of the N atom adsorbed at site i with its neighbors (indicated collectively as R(i)). This way, different models for which interactions dominate in the second energy term can be tested by varying the way the overall neighborhood around site i is defined. As the adsorption energy is the same for all sites (homogeneous surface), the processes to be considered will not depend on the value of . Adsorbed N atoms may undergo two processes: (a) Surface diffusion: A nitrogen atom adsorbed at site i can make a diffusive jump to a nearest-neighbor (NN) vacant site j with a rate given by
Wd ) νd exp[-(Uj - Ui)/kBT]
(2)
where Vd is a frequency factor for diffusion, kB the Boltzmann constant, and T the temperature. (b) N + N recombination and desorption: Two nitrogen atoms adsorbed at NN sites (i,j) may recombine and immediately desorb as N2 with a rate given by
Wr ) Vr exp[-(r + wR(i,j))/kBT]
(3)
where Vr is the frequency factor and r is the activation energy for N + N recombination at zero coverage. The evolution of the system, consisting of N nitrogen atoms adsorbed on the surface in a canonical ensemble, is simulated through a kinetic Monte Carlo procedure using the random selection method which, adapted to our system, goes as follows: (i) a surface site is selected at random with probability 1/N; (ii) a given i-type reaction step (i.e., diffusion or recombination) is chosen at random with probability Wi/R, where R is the sum of the rates of all possible processes, i.e., the total transition rate constant of the system; (iii) if the selected i-type reaction step is viable for the chosen site, then it is executed; and (iv) the time is increased by ∆t according to
∆t ) -
ln ξ R
(4)
14N
and15N atoms
where ξ is a random number uniformly distributed between 0 and 1. A detailed application of this method to the simulation of thermal desorption processes has been described elsewhere.28 Modeling the thermal chemistry of adsorbed N atoms on Rh(111) surfaces requires exploring which kind of interactions are capable to reproduce both the N islands structures suggested by experiments and the measured desorption data. To this end, three kinds of models were tested in this study: (a) Isolated N atoms with attractive and repulsive interactions: N atoms were initially adsorbed at random. Attractive NN (firstorder neighbor) interactions, w1, were considered in order to allow for the formation of N islands, which grow by a diffusion process. Second- and third-order neighbor repulsive interactions (w2 and w3, respectively) were also included in order to allow for the shift in desorption peak temperature to lower values as the N coverage increases. After the initial N random distribution was established, the diffusion of N atoms was allowed until N islands were formed and their number, size, and structure were stabilized. Once this process reached a stationary state, desorption spectra were simulated. In this model, for each adsorbed N atom, the following expression was used for the interaction energy with a given neighborhood R:
wR ) n1w1 + n2w2 + n3w3
(5)
where wi is the ith order interaction energy (negative for attractive interactions and positive for repulsive ones) and ni is the number of ith order occupied sites. (b) Compact islands with attractive and repulsive interactions: N atoms were initially arranged in compact hexagonal islands similar to those suggested by our previous analysis of the experimental data. Again, attractive NN interactions combined with second- and third-order neighbor repulsive interactions were assumed. Note that in this case no attempt was made to justify the formation of the islands. Rather, it was assumed that the compact N islands were produced sometime during the NO + CO reaction, perhaps through the preferential dissociation of NO in sites adjacent to N adsorbed atom followed by N
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diffusion to fill any holes formed, as proposed in previous studies.29,30 For this model the interaction energies were also defined by eq 5. (c) Islands formation due to surface stress: In this case it was assumed that N-N interactions are weak, and that the formation of N islands is a consequence of surface stress around a chemisorbed N atom which can only be reduced by the subsequent accumulation of more N atoms around it (an adsorbate-substrate interaction). This idea of a “surface stress” interaction is not new, and has been proposed in the past to explain the behavior of some catalytic systems.31,32 In this model, the N + N recombination reaction is expected to proceed preferentially from the outer shell of a compact island toward its interior as in the exfoliation of a “two-dimensional onion”. This is so because the interaction energy wR with a neighborhood R in eq 3 in a shell of atoms with a radius r (measured from the island center) decreases as r increases, so that N atoms belonging to the outer shell react at lower temperatures than those in the inner shells. In addition, since the quantity wR in eq 1 has the same characteristics as in eq 3, surface diffusion is also expected to refill the holes that could possibly be produced upon N2 desorption from the inside of the islands. Accordingly, for this model, the following expression was assumed for the neighborhood interaction energy wR(r) at the rth shell of a given island:
( )
wR(r) ) -cr + c 1 -
nr nt
(6)
Here, c is a proportionality parameter, nr is the actual number of N atoms in the rth shell, and nt the total number of N atoms in a complete rth shell. 4. Results and Discussion Next, the main results obtained by using the three models described in the previous Section are presented and discussed. For each model, simulated spectra were averaged over 103 replicas of each particular system considered in order to reduce fluctuations. a. Isolated N Atoms with Attractive and Repulsive Interactions. Many combinations of attractive NN and repulsive second- and third-order neighbor interactions were tested within this model. The values of interaction energy tested are in a reasonable range for interactions resulting from a combination of dispersive forces and “through the substrate” forces produced by the perturbation of the surface electronic distribution by the adsorbate. Figure 4 shows typical results in the form of island frequency (number of islands formed) versus island size (measured in number of N atoms), in this case for a total N coverage of 0.4 and two sets of interaction energies (w1 ) -1 kcal/mol, w2 ) 0.5 kcal/mol, w3 ) 0.5 kcal/mol; and w1 ) -2 kcal/mol, w2 ) 1.5 kcal/mol, w3 ) 0.5 kcal/mol). It can be seen there that in both cases the distribution is heavily skewed toward very small islands; there are practically no islands of the size (around 60 atoms) estimated from the experimental data cited above. In fact, it was observed that at lower N coverages these distributions shift toward even smaller sizes, and that although very big islands appear at higher coverages, the region around 60 atoms remains unpopulated. Moreover, the resulting islands are not compact, and the simulated TPD spectra corresponding to the two sets of parameters of Figure 4 do not compare well, even at a qualitative level, with experimental results, as shown in Figure 5. b. Compact Islands with Attractive and Repulsive Interactions. TPD spectra were also simulated starting from compact
Figure 4. Statistics for the size distribution of the N islands obtained by applying model a, as described in the text, for the case of a N coverage of 0.4 ML and two sets of interaction energy values: (a) w1 ) -1 kcal/mol, w2 ) 0.5 kcal/mol, w3 ) 0.5 kcal/mol; (b) w1 ) -2 kcal/mol, w2 ) 1.5 kcal/mol, w3 ) 0.5 kcal/mol.
islands of different sizes, having 2-9 layers, and representing different initial N coverages. For each size the averaging process over 103 replicas, described above, was used. Again, many combinations of attractive NN and repulsive second- and thirdorder neighbor interactions were tested. Typical N2 TPD spectra for two sets of interaction energies are shown in Figures 6 (r ) 35.7 kcal/mol, w1 ) -1 kcal/mol, w2 ) 0.5 kcal/mol, w3 ) 0.5 kcal/mol) and 7 (r ) 35.7 kcal/mol, w1 ) -2 kcal/mol, w2 ) 1.5 kcal/mol, w3 ) 0.5 kcal/mol). When repulsive interactions are moderate, as in Figure 6, the N2 desorption peak shifts toward lower temperature as the N coverage increases, but not sufficiently to account for the experimental observations (Figure 1). On the other hand, if the repulsive energy is increased (together with an increase in the attractive NN interaction, which is necessary to prevent the islands from spreading out), most of the spectra (except the two corresponding to the lowest coverages) display a double peaked structure (Figure 7). No combinations of interaction energies could be found to reproduce the experimental measurements. c. Islands Formation due to Surface Stress. Starting from compact N islands with 5 layers (61 atoms), as suggested by experiments, ID data were calculated from simulations at different temperatures using eq 6 for the interaction energy and eq 3 for the recombination rate. The values of Vr, r, and c in those equations were varied to best fit the experimental data.
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Figure 7. Simulated N2 TPD spectra from N atoms recombination on a Rh(111) surface obtained by using model b. The different traces correspond to island sizes going from 9 (top) to 2 (bottom). r ) 35.7 kcal/mol, w1 ) -2 kcal/mol, w2 ) 1.5 kcal/mol, w3 ) 0.5 kcal/mol.
Figure 5. Simulated TPD spectra from N atoms recombination on a Rh(111) surface obtained by using model a, for the case of a N coverage of 0.4 ML and two sets of interaction energy values: (a) w1 ) -1 kcal/mol, w2 ) 0.5 kcal/mol, w3 ) 0.5 kcal/ mol; (b) w1 ) -2 kcal/ mol, w2 ) 1.5 kcal/mol, w3 ) 0.5 kcal/mol.
the stated temperatures in the kinetic experiments. A much more rigorous test for the model is its ability to predict the TPD spectra of different isotopically labeled molecular nitrogen using the same set of parameters already determined by the isothermal simulations. In order to do this, TPD spectra were simulated for compact five-layers islands with compositions dictated by experiments using different times t (Section 2). Figure 3 contrasts the model predictions (thin lines) to the experimental results (thick lines). Again, a general good agreement is seen between experiments and model predictions, in particular given that in the real system there is likely to be a distribution of N islands sizes centered around 5 layers rather than a collection of identical 5-layer islands. Note in particular the good agreement obtained for the extent to which the production of 14N15N and 15N15N increases at the expense of a lower production of 14N14N as the proportion of 15N on the surface increases. This is one clear indication that the recombination reaction proceeds from the outside toward the inside of the islands. 5. Conclusions
Figure 6. Simulated N2 TPD spectra from N atoms recombination on a Rh(111) surface obtained by using Model (b). The different traces correspond to island sizes going from 9 (top) to 2 (bottom). r ) 35.7 kcal/mol, w1 ) -1 kcal/mol, w2 ) 0.5 kcal/mol, w3 ) 0.5 kcal/mol.
The model predictions obtained by using Vr ) 1.5 × 107 s-1 (see ref 33), r ) 38 kcal/mol, and c ) 2 (thick lines) are compared with the experimental data (thin lines) in Figure 2. It can be observed that, except for very short times, the reproduction of experimental data is acceptable, especially in terms of the separation between the plateaus corresponding to the different desorption temperatures; the short time discrepancies may very well be explained by the finite time needed to reach
In this work, different hypothesis, described in Section 3 as models a, b, and c, were tested for their ability to predict the formation of N islands during the conversion of NO + CO mixtures on Rh(111) surfaces, and also the N2 thermal desorption behavior observed in experiments after heating the surfaces resulting from that reaction. The assumption of the formation of islands by N diffusion on the surface, driven by attractive NN and repulsive secondand third-order neighbor interactions (model a), is unable to predict the growth of islands with the appropriate size to reproduce experimental TPD spectra. Assuming the prior formation of compact N islands during reaction with sizes similar to those suggested by experiments (model b), in combination with attractive and repulsive interactions such as those used in model a, is also insufficient to reproduce TPD spectra. Only when a driving force of a different nature, based on adsorbate-substrate, like the “surface stress”, rather than adsorbate-adsorbate interactions, are considered (model c), both the formation of compact islands of the appropriate size and the experimental thermal desorption spectra could be satisfactorily reproduced.
7800 J. Phys. Chem. C, Vol. 111, No. 21, 2007 The agreement between the predictions using model c and experimental data obtained here is quite acceptable, considering that the real systems are likely to consist of N islands with varying sizes distributed around an average of 5 layers rather than a collection of identical islands all of exactly the same size. It should be said that this does not exclude other possible mechanism for islands formation such as that based on a preferential NO dissociation rate in presence of NN coadsorbed N atoms. Ruling those ideas will require additional simulations. Nevertheless, the present study reinforces the idea of the formation of compact N islands during the NO + CO reaction on Rh(111) advanced in ref 26 and provides additional insight into the possible surface processes contributing to that behavior. Acknowledgment. CONICET and FONCYT of Argentina are kindly acknowledged for financial support to the present research. Additional funds for this work were provided by the US National Science Foundation. References and Notes (1) Goymour, C. G.; King, D. A. J. Chem. Soc., Faraday Trans. 1 1973, 69, 749. (2) Adams, D. L. Surf. Sci. 1974, 42, 12. (3) Lagally, M. G.; Wang, G.-C.; Lu, T.-M. CRC Crit. ReV. Solid State Mater. Sci. 1978, 7, 233. (4) Silverberg, M.; Ben-Shaul, A. J. Chem. Phys. 1987, 87, 3178. (5) Thiel, P. A.; Yates, J. T. Jr.; Weinberg, W. H. Surf. Sci. 1979, 82, 22. (6) Brundle, C. R. In The Chemical Physics of Solid Surfaces and Heterogeneous Catalysis; King, D. A., Woodruff, D. P., Eds.; Elsevier: Amsterdam, 1990; Vol. 3A (Chemisorption Systems), pp 132-388. (7) Besenbacher, F.; Nørskov, J. K. Prog. Surf. Sci. 1993, 44, 5. (8) Gland, J. L.; Sexton, B. A.; Fisher, G. B. Surf. Sci. 1980, 95, 587. (9) Stipe, B. C.; Rezaei, M. A.; Ho, W. J. Chem. Phys. 1997, 107, 6443. (10) Zambelli, T.; Barth, J. V.; Wintterlin, J.; Ertl, G. Nature (London) 1997, 390, 495.
Zaera et al. (11) Akhter, S.; White, J. M. Surf. Sci. 1986, 171, 527. (12) Zgrablich, G.; Sales, J. L.; Unac, R.; Zhdanov, V. P. Surf. Sci. 1993, 290, 163. (13) Comelli, G.; Dhanak, V. R.; Kiskinova, M.; Prince, K. C.; Rosei, R. Surf. Sci. Rep. 1998, 32, 165. (14) Trost, J.; Zambelli, T.; Wintterlin, J.; Ertl, G. Phys. ReV. B 1996, 54, 17850. (15) Dietrich, H.; Jacobi, K.; Ertl, G. J. Chem. Phys. 1996, 105, 8944. (16) Berko, A.; Solymosi, F. Appl. Surf. Sci. 1992, 55, 193. (17) Belton, D. N.; DiMaggio, C. L.; Ng, K. Y. S. J. Catal. 1993, 144, 273. (18) Xu, H.; Ng, K. Y. S. Surf. Sci. 1996, 365, 779. (19) Aryafar, M.; Zaera, F. J. Catal. 1998, 175, 316. (20) Gopinath, C. S.; Zaera, F. J. Catal. 1999, 186, 387. (21) Zaera, F.; Gopinath, C. S. J. Chem. Phys. 1999, 111, 8088. (22) Gopinath, C. S.; Zaera, F. J. Phys. Chem. B 2000, 104, 3194. (23) Zaera, F.; Gopinath, C. S. Chem. Phys. Lett. 2000, 332, 209. (24) Zaera, F.; Gopinath, C. S. Stud. Surf. Sci. Catal. Ser. 2000, 130, 1295-1300. (25) Zaera, F.; Gopinath, C. S. J. Mol. Catal. A 2001, 167, 23. (26) Zaera, F.; Wehner, S.; Gopinath, C. S.; Sales, J. L.; Gargiulo, V.; Zgrablich, G. J. Phys. Chem. B 2001, 105, 7771. (27) Liu, J.; Xu, M.; Nordmeyer, T.; Zaera, F. J. Phys. Chem. 1995, 99, 6167; Zaera, F. Int. ReV. Phys. Chem. 2002, 21, 433-471. (28) Sales, J. L.; Un˜ac, R. O.; Gargiulo, M. V.; Bustos, V.; Zgrablich, G. Langmuir 1996, 12, 95. (29) Avalos, L. A.; Bustos, V.; Un˜ac, R.; Zaera, F.; Zgrablich, G. J. Mol. Catal. A 2005, 228, 89. (30) Avalos, L. A.; Bustos, V.; Un˜ac, R.; Zaera, F.; Zgrablich, G. J. Phys. Chem. B, in press. (31) Levine, R. D.; Somorjai, G. A. Surf. Sci. 1990, 232, 407. (32) Somorjai, G. A. Surf. Sci. 1991, 242, 481. (33) The values of Vr are widespread in the literature. This is so because usually both the frequency factor and the activation energy are determined by fitting an Arrhenius expression to the experimental TPD spectra. This procedure is questionable and subject to the compensation effect between the two quantities to be determined. A higher frequency factor produces a narrower TPD spectrum shifted to lower temperatures, which could be compensated by a higher value of the activation energy. In our simulations we have fixed the activation energy to a value which is close to those appearing in the literature, and we have adjusted the frequency factor in order to obtain the adequate wideness in the TPD spectra.
