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Langmuir 1991, 7, 1124-1128
A Monte Carlo Approach to Temperature Programmed Reactive Desorption: The Case of H20 on Polycrystalline Pd Films J. M. Heras,+A. P. Velasco,*L. Viscido,+and G. Zgrablich'J Instituto de Inuestigaciones Fisicoquimicas Tebricas y Aplicadas (INIFTA), Divisibn Fisicoqulmica de Superficies, Universidad Nacional de La Plata, Casilla de Correo 16, SUC. 4, 1900 La Plata, Argentina, and Instituto de Investigaciones en Tecnologia Quimica, Universidad Nacional de San Luis-CONICET, Casilla de Correo 290, 5700 San Luis, Argentina Received June 16, 1990 A Monte Carlo model for the simulation of temperature programmed reactive desorption is developed. The model takes into account effecta of adsorbate-adsorbate interactions on the desorption energy and on the activation energy for the reaction, aa well aa surface heterogeneity. Ita potentiality is shown in discussing the case of reactive desorption of H20 from polycrystalline Pd films, where the presence of adsorbed oxygen affectsthe activation energy for the reaction 20H HzO + 0.Similarly,literature data on reactive desorption spectra of D2O in Pd(100) with various 02precoverages were also successfully fitted with comparable adsorbate-adsorbate interaction energies.
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Introduction Temperature programmed desorption (TPD) and temperature programmed reaction (TPR) spectroscopieshave been widely used during the last two decades to study surface reactivity. They are attractive because of the information they yield and the relative low cost and simplicity of the experimental equipment. In fact classical methods of analysis based on global kinetic equations1I2 allow the estimation of activation energies for the different processes involved, preexponential factors and reaction orders. However, these methods are insufficient to obtain a more complete microscopic information about the characteristics of the gas-solid interaction such as the different types of active sites present on the surface, their energetic and geometric distribution and relative abundances, adsorbateadsorbate interactions and their influence on the different processes involved, etc., in spite of their important effects on the spectra. The TPR technique, when performed in ultrahigh vacuum,= makes it possible to obtain "clean" desorption spectra free of obscuring effects even using polycrystalline substrates.&* In turn this possibility acts as a stimulating agent for the development of new microscopic models for the analysis of TPD and TPR spectra, which should take into account at least three factors: (a) adsorbate-adsorbate interactions; (b) energy distribution for active sites; (c) geometric distribution of these sites.
* To whom correspondence should be addressed. + Universidad Nacional de La Plata.
Universidad Nacional de San Luis-CONICET. (1)Lemaitre, J. L. In Characterization of Heterogeneous Catalysts; Delannay, F., Ed.;Marcel Dekker: New York, 1984. (2)Falconer, J. L.;Schwarz, J. A. Catal. Rev. Sci. Eng. 1983,25,141. (3)Heras, J. M.; Papp, H.; Spiees, W. Surf. Sei. 1982,117,91. (4)Ibach, H.; Lehwald, S. Surf. Sci. 1980,91,187. (5)Stuve, W.M.; Jsrgensen, S. W.; Madix, R. J. Surf. Sci. 1984,146, 179. (6)Heras, J. M.; Eetid, G.; Asensio, M. C.; Viscido, L. Actas Simp. Iberoam. Catal., 10, 1986,1,227. (7)Heras, J. M.; Albano, E. V. Thin Solid Films 1983,106,275. (8)Heras,J. M.;Estid, G.;hensio,M. C.; Viscido,L.Thin Solid Films, in press. See also Heras, J. M.; Asensio, M. C.; Vicido, L. 2.Phys. Chem. (Munich) 1988,160,199,and references therein. t
Microscopic descriptions for TPD from perfectly homogeneous surfaces have been introduced by Goymour and King and Adams? for the case of monomolecular desorption, and by Zhdanov et al.,l0 for associative desorption and the Langmuir-Hinshelwood reaction. They use mean field approximations (for example the quasi-chemical approximation) to describe the behavior of the adsorbed lattice gas. Silverberger et al." have used Monte Carlo simulations to study the kinetics of the Langmuir-Hinshelwood reaction on a uniform surface in the case of attractive interactions between adsorbed particles. In particular, thermal desorption spectra of the reaction product have been calculated a t temperatures below the critical for the first-order phase transition in the adsorbed overlayer. Recently,12Js we have shown that, for a more complete treatment of the subject, a numerical simulation method is necessary. Accordingly a Monte Carlo model has been developed to simulateTPD spectra explicitlyincorporating the three above-mentioned factors. The problem of TPR is more complex than that of TPD since the reaction of different adsorbed species and the desorption of reactives and products occur simultaneously and are competing processes. Moreover, lateral interactions may be affecting in different ways the reaction and desorption processes. The purpose of the present work is (i) to develop a model to simulate TPR on the basis of the Monte Carlo model presented in refs 12 and 13and (ii) to analyze experimental spectra for a well-known system to show the potentiality of the method. (9)Goymour, G.C.;King,D. A. J. Chem. SOC.,Faraday Trans 1 1973, 69,749. See ale0 Adams, D. L. Surf. Sci. 1974,42,12. (10)Zhdanov,V. P. Surf.Sci. 1982,123,106;1983,133,649;1984,137, 515. Hellsing, B.; Zhdanov, V. P. Chem. Phys. Lett. 1988,147,613.Zhdanov, V. P.; Zamaraev, K. I. Usp. Phys. Nauk 1986, 149, 635;Sou. Phys.-Usp. (Engl. Transl.) 1986,29,755. (11)Silverberger, M.; Ben-Shad, A.; Relentrost, F. J. Chem. Phys. 1986,83,6501.Silverberger,M.; Ben-Shad, A. Chem. Phys. Lett. 1987, 134,491;J. Chem. Phys. 1987,87,3178. (12)Sales, J. L.;Zgrablich, G. Surf. Sci. 1987,187,1. (13)Sales, J. L.; Zgrablich, G. Phys. Rev. 1987,B35,9520.
0743-7463/91/2407-ll24$02.50/0 0 1991 American Chemical Society
Temperature Programmed Reactive Desorption
Langmuir, Vol. 7, No. 6, 1991 1125
Model A typical situation for TPR arises when we have two kinds of molecules A and B (the reactives) adsorbed on a surface reacting irreversibly to originate products C and D A+B-C+D (1) Generally,one of the products, say C, is monitored during the desorption and TPR spectrum, dBc/dT versus T, is obtained (here Bc is the coverage for species C, and T is the temperature that is assumed linearly related to time t). In order to perform the simulation we take a system consisting of a square lattice of N adsorbing sites, each having an adsorptive energy tix (i = 1, ...,N) for species X (X = A, B, C, D), and initial coverages eA(0) and eB(0) for reactives A and B. Lateral interactions will be considered between molecules adsorbed on nearestneighbor (NN) and next-nearest-neighbor (NNN) sites only. We must consider three elementary processes which may compete with each other: (1)desorption, (2) reaction, and (3) surface migration; for each of them appropriate transition probabilities must be defined. (1)For the desorption process, the activation energy for desorption E d for a molecule of kind X adsorbed on site i is given by
(2)
where the interaction energies for desorption W O ~and -~ W I ~refer - ~ to NN and NNN interactions between species X and Y, respectively, and Sjy is the occupation number of site j (Siy = 1 if occupied by species Y and SjY = 0 otherwise). Consequentlythe probability for the molecule to be desorbed in a temperature interval (T, T + AT) can be calculated as12 (3)
where Yd is the preexponential factor for desorption, p is the heating rate, and R, is the gas constant. (2) For the reaction process, a pair of molecules A-B adsorbed on a pair of NN sites i-j must be considered. If the activation energy for the reaction in the gas phase is ErG,we can assume that a site i contributes with an energy EiS in lowering the activation energy for the reaction in the adsorbed phase (in which case EiSwill be a measure of the "activity" of site i for the given reaction). Moreover, lateral interactions with other adsorbed molecules may also modify the potential energy surface of the reaction. Hence, each pair of molecules X-Y contributes with an interaction energy to the reaction which is for NN pairs, and VI^-^, for NNN pairs. We can then write for the activation energy of reaction for molecules A-B adsorbed on NN sites i - j
E, =
(4)
Given the activation energy, the probability for the pair
of molecules to react in a temperature interval (T,T + AT) can be found following the same arguments used in ref 12 as
pr= vr
AT
exp(-Er/R,T)
where vr is the preexponential factor for reaction. (3)Finally, as regards the surface migration process, we define the probability for a molecule X adsorbed on site i to migrate to an empty NN site j as the classical Metropolis transition probability14
Pm= minll, exp[-(Ed(i) - EdO'))/RgT])
(6)
where E&) and EdU) are given by eq 2 evaluated at site i and j, respectively. Of course other transition probabilities leading to the same final result could be assumed for this process, since migration will be used to reestablish the situation of thermodynamical equilibrium after a number of reaction and desorption steps have occurred. We can now state the simulation scheme as follows: (a) Prepare the surface of N sites with the desired distribution (if heterogeneous) of adsorptive energies ciX and activities E? (i = 1, ..., N), and with a given initial coverage for each species. Fix an initial temperature TO. (b) Select a site in the lattice at random and test it for a transition to a new state. We must differentiate between two situations: bl. The selected site is occupied by one of the reactives (A or B) and it is in condition to react, i.e. at least one of its NN sites is occupied by the other reactive. In this case a Monte Carlo step is executed by comparing the probabilities for reaction, desorption, and null event. b2. The selected site is occupied by a molecule that cannot react. In this case the probabilities for desorption and null event are compared for the Monte Carlo step. (c) Repeat step b until N sites have been tested at random and then obtain the desorption rate -ABc/ATfor the given temperature and other mean values of interest. (d) Apply a relaxation procedure by selecting pairs of sites at random with different occupation states and trying to interchange these states using the migration probability P m until thermodynamic equilibrium is again approximately reestablished. (e) Increase the temperature by AT and repeat from step b until no more molecules are desorbed or reacted. In practice we found that using a square lattice with N = 150 X 150 sites and periodical boundary conditions, good statistics could be obtained with a reproducibility within 1%.
Experimental Results The interaction of H20 molecules with evaporated polycrystalline Pd films has been recently studied in an ultrahigh vacuum system.6 We point out here some of the outstading results (more experimental details can be found in ref 8). The films, with thicknesses varying between 8 and 10 nm, were obtained by sublimation of Pd (99.999% pure from Johnson, Matthey & Co) followed by condensation onto Pyrex glass substrates at 77 K. Different surface morphologies were stabilized through heat treatments in the range 77-473 K and monitored in situ by means of electric resistance (ER) and photoelectric work function (WF). Once the experiments were over, scanning electron microscopy (SEM), X-ray diffraction (XRD), and Auger electron spectroscopy (AES) were performed on separate samples deposited onto glass disks and treated simultaneously in the same vessel. Triple distilled HzO was discontinuously dosed over the film at 77 K monitoring (14)Metropolis, N.; Rosenbluth, A. W.; Rosenbluth, M. N.; Teller, A.
H.;Teller, E.J. Chem. Phys. 1953,21,1087.
1126 Langmuir, Vol. 7, No.6,1991 simultaneously WF and ER. The nominal coverage per dose amounted to 5.7 X 1017m-2 water molecules =l/lO of an ideal monolayer (ML) assuming the ML to be that of closest-packed spheres of 0.452 nm in diameter (the distance of maximum approach of two non-H-bonded HzO molecules16). Absolute coverages depend on surface roughness and were derived from the saturation of the WF decrease upon HzO adsorption. A roughness factor of 4.4was obtained for the case of films annealed at 473 K, which show an extended (111)fiber textureeand whose behavior will be discussed in this paper. Oxygen precoverage was performed by exposingthe films at 77 K to a pressure of lo* Pa of 0 2 (99.998% pure from Messer-Griesheim) up to saturation of the WF change (=+0.65eV). In this condition a precoverage of 0.75ML16 is assumed. However, according to this reference 1 ML of 0 2 corresponds to a coverage BO = 0.5 referred to the number of adsorption sites as it is usual (i.e. Pd atoms at the surface). Hence 0.75 ML means that 00 =0.38. After the films were dosed with oxygen and/or water, mass-resolved reactive thermal desorption spectra were performed with a heating rate about 0.04K/s, monitoring the masses between 2 and 44 uma with a high frequency omegatron type mass spectrometer without memory effect. The only species desorbing into the gas phase was water, at temperature between 180 and 240 K. No H2 evolution could be detected even following the desorbed gas composition up to 450 K. It is worth mentioning that the highly sensitive mass spectrometer used displays a measurable signal when about 10l2 H2 molecules enter the gase phase. In our system, this amount corresponds to -0.002 of a monolayer. Changes in ER and WF were simultaneously monitored throughout. The adsorption of successive H2O doses of Pd films annealed at high temperatures caused a WF decrease up toa saturation value of -0.95 eV. This behavior has always been found on polycrystalline metal films17 and can be ascribed to the building of a double layer with the positive pole pointing outward. That is to say, H2O is adsorbed with the 0 atom on the surface as expected,le with some charge transfer to the metal.Ig Comparison between Pd film behavior and that of single crystals6 under different conditions suggests H20 dissociation below 245 K and indicates that atomic oxygen is a remanent surface species after thermal desorption. In other words we are dealing with TPR rather than TPD. The comparison between the TPR of H2O adsorbed on a virgin Pd film with that of a Pd film precovered with oxygen is particularly interesting. These TPRs show a peculiar behavior which could only be explained by a deeper analysis through the model given above. Figure 1 shows experimental desorption spectra taken in Pd films annealed at 473 K. Three types of experiments are described. The dashed line curve shows the desorption of HzO from a clean film. The full line curve corresponds to H20 desorbing from a film precovered with 0 2 up to WF saturation. We see that the peak is shifted -17 K to lower temperatures and a shoulder appears in the position of the original peak. Such a behavior was also reported in the case of Pd(100) single c r y ~ t a l . ~ Noteworthy,this temperature shift was also observedwhen (16) Eisenberg,D.; Kawzmann, W. In The Structure and Properties of Water; Oxford Univereity Prese: New York, 1969. (16) Hthe, J. E.; Wandelt, K.; Knppers,J.; Ertl, G. Le Vide 1980,201, 108. (17) Heras, J. M.; Vicido, L. Appl. Surf. Sci. 1980, 4, 238. (18) Heras, J. M.; V i d o , L.; Amorebieta, V. Ber. Bunsen-Ges. Phys. Chem. 1978,82, 1035. (19)Heras, J. M.; Aseneio, M. C. Afinidad 1985, 42, 111.
Heras et al. TlOO
.-> -Id
-p1
80
3
60
0
u
c3
v)
40
2
20
I n 150
200 250 300 TEMPERATURE [K]
350
Figure 1. Experimental data of the reactive desorption spectra of H20 from Pd polycrystalline films annealed at 473 K. The mass spectrometer signal relative to the maximum (=loo) is plotted against temperature. Dashed curve, clean film; initial HzO coverage N = 9.4 X 10'8 m-2 molecules; maximum partial HzO pressure during desorption,p , = 9.6X 1WPa. Full curve, oxygen precovered film (up to WF saturation = 0.4 L), N = 4.5 x 10l8 m-2, p , = 3.5 X lo-' Pa. Open circles, after annealing at 473 K in the presence of HzO; N = 5.7 X 10l8m-z; p- = 1.7 X lo-' Pa. Note that only in this case a faint Ha0 desorption peak is found at 180 K.
H2O desorbed from a Pd film previously treated with H2O at 473 K, as the curve with open circles shows. That is, in this case, the presence of 0 atoms on the surface should be a consequence of H20 dissociation during the first adsorption-desorption cycle. Roughness promoted H2O dissociation is a fact observed even in single crystals, for instance, Ni(110).20 Only in films pretreated with H2O and for coverages above 0.7,a H2O desorption peak was observed at 180 K, which was extremely small. Taking into account our results in polycrystallinefilms6 and those obtained by several authors in Pd single crystals:I2l the following mechanism scheme can be postulated for the adsorption and reactive desorption of water from Pd films where (g) indicates gas phase, (ad) adsorbed, and (inc) incorporated: (a) virgin films
'.
H2°(g)
BOK
H20(d)
H20(g)
The main differences between both cases are that in part a, according to step 2, atomic hydrogen is present during the disproportionating reaction (step 31,while in (20) Benndorf, C.; Madey, Th.E. Surf. Sci. 1988,194,63. (21) Nyberg, C.; TengaAI, C. G. J. Chem. Phys. 1984,80, 3463.
Langmuir, Vol. 7, No. 6, 1991 1127
Temperature Programmed Reactive Desorption
part b, if the oxygen precoverage is high enough, there will be a remanent oxygen coverage at the beginning of the disproportionating reaction. In Pd(100) single crystal6it has been found that the OH coverage tracks the 0 atom precoverage for do < 0.10. Above this coverage the 0 atoms remain unreacting on the surface causing, when do 0.31, a shift of the H2O desorption peak from 251 to 230 K. As stated above, our observations in polycrystalline Pd are in full agreement with this peak temperature shift. The presence of H atoms on the surface can hardly explain a higher H20 desorption temperature because actually at a180 K H atoms incorporate into some states below the Pd surface.22 In our experiment, this fact is shown by a WF decrease observed at =180 K, since stable H atoms on the surface increase the WF of a clean Pd film.23 Actually, above 300 K another step should be considered: The reaction between H and 0 atoms, which is known to proceed in Pd(100)with a measurable kinetics at this temp e r a t ~ r e . This ~ ~ step has not been included as it is irrelevant to our discussion of the shift in temperature of the H2O desorption peak, but surely accounts for the peak form distortion at T > 270 K. From another point of view, considering mechanism b, it is known that adsorbed excess oxygen stabilizes molecularly adsorbed water so that higher temperatures are required todesorb it.26 This effect appears to be opposed to the one observed and described in Figure 1. The observed temperature shift in TPR peaks of H2O desorption may be accounted for by the influence of the different adsorbed species on the activation energies for the disproportionating reaction and the desorption process. This influence will be investigated in the following by means of the model introduced above.
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Discussion As stated when introducing the theoretical model, an initial configuration of adsorbed species must be established in order to simulate TPR spectra. On the basis of the WF change observed during oxygen precoverage of our films compared with that in Pd(ll0) single crystals,l6 we can assume that the initial 0 atom precoverage is do = 0.38 referred to the total number of adsorption sites. In polycrystalline films, where LEED techniques are not applicable, the uncertainty of the crystallographic surface morphology and the area of each of the planes actually exposed renders the absolute determination of a real oxygen coverage (expressedin 0 atoms per Pd atom) somewhat difficult. Nevertheless, the similar H20 desorption peak shift6 reported for a Pd(100) single crystal precovered with do 0.31 suggests that our assumption of an oxygen precoverage of ~ 0 . 3 8is fairly good. Moreover, the XRD measurements and the WF value of clean films thoroughly annealed at 473 K (5.40 eV) points to a smooth surface comparable to that of single crystals.8 In Pd(100), the maximum attainable concentration of OH(ed)due to the hydrogen abstraction reaction from the co-adsorbed H2O molecules caused by the randomly adsorbed 0 atoms is OOH = 0.22.6 Such a maximum OOH was also observed in other metals.= From this OOH value it follows that the consumption of 0 atoms or H20 molecules is 0.11.
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(22) Eberhardt,W.;Greuter,F.;Plummer,E. W.Phya.Reu.Lett. 1981, 46,1085.
(23) Watanabe, M.; Wedler, G.; Wiasman, P. Surf.Sci. 1986, 154, L 207. (24) Nyberg, C.; TenstA1, C. G . Surf.Sci. 1983, 126, 163. (26) Stuve, E. M.; Madix, R. J.; Sexton, B. A. Surf.Sci. 1981,111,11. (26) Thiel, P. A.; Madey, T. E. Surf.Sci. Rep. 1987, 7, 211.
From the WF change upon adsorption of H2O on oxygenprecovered filmss a nominal value of 4.5 X 1Ol8 m-2 H2O molecules corresponds to a real coverage of =0.5. Hence, by introduction of the above discussed coverages, the initial balance for the case of oxygen-precovered Pd films would be OOH = 0.22; do = 0.38-0.11 = 0.27; d ~ p 0.5-0.11 = 0.39. From the latter, it follows that the crowding of the surface, forces the remaining undecomposed H2O molecules (about 3.5 X lo1* m-2) to stay in an unfavorable bonding configuration to suffer dissociation, though stabilized through interaction either with the remaining 0 atoms as reported in ref 25 or with the OH formed. However, even considering strong H2O-0 and H20-OH attractive interactions, this unreacted initial H2O coverage would give an important H2O desorption peak at low temperatures (
