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Monte Carlo Analysis of Hydrogen Interaction with Promoter- and Inhibitor-Modified Nickel Surfaces V. Bustos,† M. V. Gargiulo,‡ J. L. Sales,‡ R. O. Un˜ac,‡ and G. Zgrablich*,† Departamento de Fı´sica y Centro Latinoamericano de Estudios Ilya Prigogine, Universidad Nacional de San Luis, Chacabuco 917, 5700 San Luis, Argentina, and Instituto de Energı´a Ele´ ctrica y Departamento de Geofı´sica y Astronomı´a, Universidad Nacional de San Juan, Av. Libertador 1100 Oeste, 5400 San Juan, Argentina Received June 27, 1996. In Final Form: April 14, 1997X A Monte Carlo simulation analysis is performed of the kinetics of adsorption and desorption for the systems H + K/Ni(111) and H + O/Ni(111). Fundamental energetic parameters are determined by fitting simulation results to experimental data for thermal desorption spectra and sticking coefficients.
1. Introduction The use of Monte Carlo simulation for the analysis of molecular processes ocurring on solid surfaces is becoming a powerful tool for the understanding of the elementary steps and mechanism of the kinetics of heterogeneous reactions.1-12 This is especially true for complex systems where the application of approximate analytical solutions to the kinetic equations, like the quasi-chemical approximation,13,14 may be unpractical. One of such complex system, which has been experimentally studied recently and for which complete sets of data are available, is the coadsorption of hydrogen and potassium and hydrogen and oxygen on Ni(111) surfaces.15 In that study the inhibitor action of potassium and the promoter action of oxygen were shown and discussed. The purpose of the present work is to present a microscopic model for the coadsorption of H + K and H + O on Ni(111), inspired by the observations of ref 15, and use it in a Monte Carlo simulation scheme to predict thermal desorption spectra and sticking coefficients and to obtain, by fitting experimental results, the fundamental interaction parameters. These can be used to check, or stimulate, abinitio calculations of adsorbate-adsorbate and adsorbatesubstrate interactions. We model first the hydrogen adsorption on clean metal in section 2 and then consider the inhibitor action of * To whom correspondence should be addressed. † Universidad Nacional de San Luis. ‡ Universidad Nacional de San Juan. X Abstract published in Advance ACS Abstracts, July 1, 1997. (1) Silverberg, M.; Ben Shaul, A. Chem. Phys. Lett. 1987, 134, 491; J. Chem. Phys. 1987, 87, 3178; J. Stat. Phys. 1988, 52, 1179; Surf. Sci. 1989, 214, 17. (2) Sales, J. L.; Zgrablich, G. Surf. Sci. 1987, 187, 1; Phys. Rev. 1987, B35, 9520. (3) Lombardo, S. J.; Bell, A. T. Surf. Sci. 1988, 206, 101; Surf. Sci. 1989, 224, 451; Surf. Sci. Rep. 1991, 13, 1. (4) Fichthorn, K. A.; Weinberg, W. H. Langmuir 1991, 7, 2539. (5) Ramirez Cuesta, A.; Zgrablich, G. Surf. Sci. 1992, 275, L636. (6) Tysoe, W. T.; Ormerod, R. M.; Lambert, R. M.; Zgrablich, G.; Ramirez Cuesta, A. J. Phys. Chem. 1993, 97, 3365. (7) Meng, B.; Weinberg, W. H. J. Chem. Phys. 1994, 100, 5280. (8) Corte´s, J.; Valencia, E. Phys. Rev. 1994, B49, 16793. (9) Corte´s, J.; Valencia, E.; Araya, P. J. Chem. Phys. 1994, 100, 7672. (10) Ramirez Cuesta, A.; Zgrablich, G.; Tysoe, W. T. Surf. Sci. 1995, 340, 109. (11) Meng, B.; Weinberg, W. H. J. Chem. Phys. 1995, 102, 9435. (12) Sales, J. L.; Un˜ac, R. O.; Garginlo, M. V.; Bustos, V.; Zgrablich, G. Langmuir 1996, 12, 95. (13) Zhdanov, V. P. Elementary Physicochemical Processes on Solid Surfaces; Plenum: New York, 1991. (14) Tovbin, Y. K. Theory of Physical Chemistry Processes at a GasSolid Interface; CRC Press: London, 1991. (15) Resch, C.; Zhukov, V.; Lugstein, A.; Berger, H. F.; Winkler, A.; Rendulic, K. D. Chem. Phys. 1993, 177, 421.
S0743-7463(96)00644-0 CCC: $14.00
potassium in section 3 and the promoter action of oxygen in section 4. Section 5 is devoted to discussion and conclusions. 2. Hydrogen Adsorption on Ni(111) The most stable positions for an H atom on the Ni(111) face are 3-fold sites (we do not make distinction between hcp and fcc 3-fold sites) with a binding energy of approximately 63 kcal/mol.16 Since the binding energies for bridge and on top positions have been calculated to be approximately 59 and 54 kcal/mol, respectively,17 we conclude that activation energy for atomic H surface diffusion is between 4 and 9 kcal/mol, which is much lower than the associative desorption energy for H2 (≈23 kcal/ mol). We can then consider that the adsorbate is in thermodynamical equilibrium. The dissociative adsorption of H2 on Ni(111) has been recently studied using ab-initio calculations by Yong et al.17 who propose two main pathways, Figure 1, (a) on-top dissociation and (b) nearly-on-top dissociation. We have represented (right side) the energy variation along the reaction coordinate for each case, resulting from the energy values they obtained. According to their calculations, four cases are possible for the relative position of two H atoms, Figure 1c; however interaction energies V for each configuration are such that V2 - V1 ) +2.3 kcal/mol, V3 - V1 ) +5.5 kcal/mol, and V4 - V1 ) +35.5 kcal/mol, so that the last two configurations are very improbable due to strong repulsion, and we shall only consider the first two configurations. According to these considerations, we propose the following simulation schemes for the adsorption and desorption processes of H2 on Ni(111). Adsorption Kinetics: Sticking Coefficient. Adsorption kinetics is conveniently described through the sticking coefficient S(θ), as a function of coverage θ, which in the framework of the lattice-gas model (without precursor states) and the transition state theory, can be written for dissociative adsorption A2 (g) f 2 A (a) as18
∑i P00,i exp (s∆i/KBT)
S(θ) ) S0
(1)
where S0 is the sticking coefficient at zero coverage and infinite temperature, P00,i is the probability of finding a pair of vacant “contiguous” sites with an environment “i” (16) Christmann, K.; Schober, O.; Ertl, G.; Neumann, M. J. Chem. Phys. 1974, 60, 4528. (17) Yang, H.; Whitten, J. L. J.Chem. Phys. 1993, 98, 5039. (18) Zhdanov, V. P. Surf. Sci. 1981, 111, 63.
© 1997 American Chemical Society
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Figure 1. Energetics of H2 dissociative chemisorption on Ni(111): (a) on top dissociation; (b) nearly on top dissociation (curves on the right represent the energy variation along the reaction coordinate ξ); (c) possible relative configurations of two neighbor H-atoms with their interaction energies, Vi (i ) 1, 2, 3, 4).
of adsorbed particles, and ∆i ) a + i*, a is the activation energy for adsorption at zero coverage and i* the interaction energy of the activated complex A*A* with the environment i. In our case of H2 adsorption on Ni(111), by “contiguous” sites we shall consider those of configurations 1 or 2 of Figure 1c, depending on which adsorption pathway is occurring, (a) or (b). Monte Carlo simulation of the sticking coefficient is easily achieved through the following steps: (i) Produce an initial surface configuration of adsorbed H atoms at random with a given coverage θ. The energy of the system is given by
E ) Vl
∑ ninj + V2 ∑ ninj + H∑i ni
(i, j)1
(2)
(i, j)2
where nk is the occupation number of a site k (nk ) 1 if occupied by an H atom, nk ) 0 if empty), H is the adsorption energy of an H atom (≈63 kcal/mol), and (i, j)l stands for a pair of sites i and j in the configuration l (l ) 1, 2 of Figure 1c; l ) 3 and 4 are forbidden). (ii) The surface is relaxed until thermodynamic equilibrium is established. To do this we select a pair of sites with different occupation numbers and try to exchange them. The exchange is accepted with probability min{1, exp(-∆E/kT)}, where ∆E is the change in E from the initial to the final state. Exchange attempts are repeated until E fluctuates around a mean value. (iii) A measure of S(θ)/S0 is taken on the actual surface configuration by obtaining the mean value 〈p00 exp(-∆i/ kT)〉00, where p00 is the probability of finding a pair of empty sites, in configurations 1 or 2, and the mean value is taken over all pairs of empty sites (of course, for a pair in configuration l ) 1, 2 the activation energy a is the one corresponding to on-top and nearly-on-top dissociation, respectively).
(iv) Steps ii and iii are repeated a number of times, and the overall mean value of S(θ)/S0 is finally obtained. The jamming coverage θJ is the one for which S becomes zero. We obtain θJ ) 1 for adsorption of H2 on clean Ni(111) (i.e., one H-atom per Ni-atom), in good agreement with experimental observations,15 while the maximum coverage if all 3-fold sites were occupied would be θ ) 2. Desorption Kinetics. Simulation of reactive thermal desorption processes (and in particular associative desorption) has been discussed in detail in ref 19. Here we only point out briefly the procedure as applied to the system H/Ni(111). The activation energy for desorption of a pair of H-atoms adsorbed on contiguous sites ij is given by
∑k nk + V2∑l nl
Ed ) Em0 + V1
(3)
where Em0 ) 1, 2) is the activation energy for desorption at zero coverage for configurations “m” of the pair of H-atoms, the sum on k is taken over all sites which are in a configuration 1 relative to either i or j and the sum on l is taken over all sites which are in a configuration 2 relative to either i or j; see Figure 2. The desorption probability in a differential temperature interval, dT, is then given by
Pd )
ν dT exp(-Ed/kBT) β
(4)
where ν is the adsorbate vibrational frequency and β ) dT/dt, the heating rate (l0 K/s). This probability is used at each Monte Carlo desorption step to accept or reject an attempt of desorption. The adsorbate is mantained in (19) Heras, J. M.; Velasco, A. P.; Viscido, L.; Zgrablich, G. Langmair 1991, 7, 1124.
Nickel Surface Interactions
Figure 2. Different configurations of adsorbed H-atoms (empty circles) around a couple which is attempting an associative desorption (full circles).
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Figure 4. Right scale, activation barrier variation with K coverage calculated theoretical. Left scale, H-H interaction energy as a function of θK obtained by fitting TPD spectra: 9, V1; (b), V2.
calculations since we found out that the TPD spectrum is very sensitive to H-H interactions.
Figure 3. TPD spectra of H2 for H + K/Ni(111) for K coverages 0.0, 0.03, 0.06, 0.14, 0.19, and 0.24 ML (from left to right): (a) experimental data of ref 15; (b) simulation results.
thermodynamic equilibrium by the procedure described in step ii for the simulation of the sticking coefficient. All Monte Carlo simulations were carried out on an hexagonal lattice of 104 Ni atoms and the number of observations for mean values calculations was such that statistical fluctuations were below 1%. Excellent agreement is obtained between simulation and experimental temperature-programmed desorption (TPD) spectra for H on clean Ni(111); see in Figure 3 the leftmost spectrum corresponding to zero K coverage, with ν ) 1012 s-l, E10 ) 23.63 kcal/mol, E20 ) 23.24 kcal/mol, V1 ) 0.01 kcal/mol, and V2 ) 0.223 kcal/mol. The values found for Em0 are exactly those predicted in ref 17, i.e., 22.0 + 1.63 ) 23.63 for configurations 1 and 19.7 + 3.54 ) 23.24 for configurations 2. The value of V2 - V1 ) 0.222 kcal/mol, however, differs from the predicted 2.3 kcal/ mol. This point should be checked in the theoretical
3. Inhibitor Action of Potassium Coadsorption of K affects the H-Ni(111) interaction by lowering the work function of metal and, as a consequence of this, by increasing the energy barrier for H2 dissociative adsorption and for H-H associative desorption. According to Resch et al.15 the process is totally inhibited within a radius of about 5.5 Å from the center of the K atom. This includes up to the 7th order neighbor site in a hexagonal lattice. Out of this range the adsorption of K produces a variation in the activation barrier which does not depend on the distance to the adsorbed K atom. This is taken into account by adding to a a term δa where δa will depend on K coverage θK, and modifying accordingly δi in eq 1 and Em0 in eq 3. This effect, δa(θk), can be quantitatively calculated by the procedure proposed by Brown et al.20 and using the variation of work function φ as a function of θK obtained in ref 21. With this, δa as a function of θk turns out to be the curve represented in Figure 4 (full line with right axis). Another effect which may also take place, and in fact is suspected by inspecting the experimental desorption spectra, is that K will influence H-H interaction energies. However, this effect cannot be calculated a-priori and the variation of V1 and V2 with θK will be a result of fitting simulated spectra to the experimental ones. H2 desorption spectra were simulated for θk ) 0.0, 0.03, 0.06, 0.14, 0.19, and 0.24 ML (curves from left to right in Figure 3b) and compared to experimental spectra, Figure 3a. The variation of H-H interactions V1 and V2 with θK is represented in Figure 4, and this accounts for the relative displacement of the two peaks in the spectra as θK increases. As already pointed out, this relative displacement is very sensitive to the values of V1 and V2. On the other hand, the initial sticking coefficient (at zero H coverage) was also simulated with no new parameters and compared to experimental results in Figure 5. The observed agreement reconfirms, in an independent way, that the variation of δa with θK (Figure 4), calculated on the basis of theoretical grounds represents satisfactorily the effect of K on the activation barrier for H2 dissociative adsorption. 4. Promoter Action of Oxygen The effects of oxygen coadsorption can be modeled as follows: (20) Brown, J. L.; Lundz, A. C.; Schultz, P. A. J.Chem. Phys. 1991, 95, 3767. (21) Un˜ac, R. O.; Sales, J. L.; Gargiulo, M. V.; Zgrablich, G. J. Phys. C, in press.
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Figure 5. Initial sticking coefficient for the dissociative chemisorption of H2 on Ni(111) as a function of K coverage: (2) experimental data of ref 15; s, simulation results.
Bustos et al.
Figure 7. Initial sticking coefficient for the dissociative chemisorption of H2 on Ni(111) as a function of θ coverage: (2) experimental data of ref 15; s, simulation results.
Thermal desorption spectra were simulated for oxygen coverages θO ) 0.0, 0.04, 0.09, 0.15, 0.19, and 0.25 and results are shown in Figure 6b and compared to experimental spectra of Figure 6a, with δa ) -5 kcal/mol, V1 ) 0.0 kcal/mol, V2 ) 0.23 kcal/mol, and W1 ) W2 ) W3 ) 0.35 kcal/mol for all oxygen coverages. Again, desorption spectra are quite sensitive to the values of lateral interactions. On the other hand the initial sticking coefficient (at zero H coverage) was simulated for different oxygen coverages, and the result (full line) is compared to experimental data in Figure 7. The good agreement with this independent experiment reconfirm the value of δa ) -5 kcal/mol, expressing the promoter effect of oxygen on dissociative adsorption of H2. The maximum in the initial sticking coefficient reflects the competition between the promoter and the blocking action of oxygen. The small minimum at low θO is due to the presence of strongly adsorptive defect sites which are rapidly filled by oxygen at low coverage.15 This effect is not taken into account in our simulation in order to keep the model simple. 5. Discussion and Conclusions
Figure 6. TPD spectra of H2 for H-O/Ni(111) for K coverages 0.0, 0.04, 0.09, 0.15, 0.19, and 0.25 ML (from right to left): (a) experimental data of ref 15; (b) simulation results.
(a) Each oxygen atom adsorbed on a 3-fold site produces the blocking of its three nearest-neighbor sites (due to its dimensions) for hydrogen adsorption. (b) Oxygen adsorption produces an increase in the work function and consequently a lowering in the activation barrier for hydrogen dissociative adsorption and for associative desorption. This effect is taken into account by considering that each oxygen atom produces a lowering δa in the activation energy affecting the three next-nearest neighbor sites. This must be used in eq 1 and eq 3. (c) Repulsive H-O interactions must be taken into account up to third-order neighbors (outside the nearestneighbor blocked sites), Wi (i ) 1, 2, 3), to account for the strong shift to low temperatures observed in desorption spectra as the oxygen coverage θO increases. These interactions should be added in eq 3.
By using Monte Carlo simulation we have modeled the coadsorption of H-K and H-O on Ni(111) to study the adsorption and desorption kinetics of H2. The model is inspired in experimental observations. By comparing its predictions with experimental data, it was possible to determine fundamental interaction energies concerning both adsorbate-adsorbate interactions with the modifications of activation energy produced by the inhibitor action of potassium and the promoter action of oxygen. The sensibility of desorption spectra of lateral interactions, specially H-H and H-O interactions, make the obtained values reliable ones, which can be used to contrast abinitio calculations.17,22 In particular, our value of V2 - V1 ≈ 0.23 kcal/mol is not in agreement with the value 2.3 kcal/mol reported in ref 17, although the binding and activation energies calculated in the same work produce good agreement between simulation and experimental results. Acknowledgment. This research was supported by CONICET and the European Economic Community Project ITDC-240 who provided the PARIX computer on which calculations were performed. LA960644D (22) Ferullo, R. M.; Castellani, N. J. J. Alloys Compd. 1993, 191, 173.
