Mesoscale Structures in the Adlayer of A-B2 Heterogeneous Catalysis

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Mesoscale Structures in the Adlayer of A‑B2 Heterogeneous Catalysis Fei Sun,†,‡ Wen Lai Huang,*,† and Jinghai Li† †

State Key Laboratory of Multiphase Complex Systems, Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China ‡ University of Chinese Academy of Sciences, Beijing 100049, People’s Republic of China ABSTRACT: This article explores the adsorbate distributions in the adlayer for a model A-B2 system of heterogeneous catalysis, i.e., A + 1/2B2 → AB, via kinetic Monte Carlo (KMC) simulations. In comparison with our previous work on the A-B model (Sun, F.; Huang, W.; Li, J. Structural characteristics of the adlayer in heterogeneous catalysis. Chem. Eng. Sci. 2016, 153, 87−92), species B2 here brings about significant new features due to its special site requirement during adsorption and desorption and a different stoichiometric ratio in reactions. The effects of various kinetic processes on the adsorbate distribution are found to be similar to those in the A-B system; that is, both desorption and diffusion (besides adsorption) processes contribute to the adlayer uniformity while reactions account for clustering. However, desorption exhibits a stronger role than diffusion in homogenizing the adlayer, which is opposite to the finding in the previous A-B model. Under a fixed partial pressure, different reaction and desorption rate constants can lead to steady states with different dominant species, which has not been observed in the A-B system. The regime of species B poisoning shrinks as well, leading to the spreading of the coexisting regime, in comparison with the A-B model.

1. INTRODUCTION Complex behavior (including stationary patterns, temporal oscillations, and so on) in nonequilibrium heterogeneous catalysis is of great interest, e.g., in the catalytic oxidation of CO 1−5 or hydrogen,6 and various models have been proposed.7−11 These models can explain a wide range of experimental results associated with catalysis and are also very useful for optimizing relevant processes,12 but restrictions still remain.3,6,9 To establish more effective models, we need to improve our understanding, and a good way is to conduct microscopic simulations based on Monte Carlo (MC) or kinetic Monte Carlo (KMC) approaches13 to reveal detailed behavior and relevant factors. Ziff and co-workers14 conducted MC simulations on the oxidation of CO on a catalyst surface based on their kinetic model, the so-called Ziff−Gulari−Barshad (ZGB) model, under the Langmuir−Hinshelwood (LH) scheme,15−17 which raised an animated tide of research on the nonequilibrium behavior in heterogeneous catalysis. For example, Brosilow and Ziff extended the ZGB model by including the spontaneous desorption of CO.18 Kaukonen and Nieminen developed two types of more sophisticated versions19 involving desorption, diffusion, and the finite reaction probability or taking into account nearest-neighbor (NN) interactions explicitly, successfully showing their effects on the heterogeneity in the adlayer. A large number of papers about MC simulations on heterogeneous catalysis soon followed.20,21 However, most papers focus on CO-O2 catalysis on various catalysts or on various catalyst surfaces, and the specific characteristics of some adsorbates, e.g., the immobility of adsorbed oxygen, were considered.19,22 A general investigation (without constraints on the characteristics © XXXX American Chemical Society

of adsorbates) on the influence of kinetic processes on the adsorbate distribution is still lacking. The complex structures in the adlayer are mesoscale structures, emerging at the mesoscale between the microscale (the adsorbate scale) and the macroscale (the adlayer scale). Such mesoscale structures can be understood through the compromise in competition between dominant mechanisms23 (that may be relevant to energy dissipation24), therefore revealing that the dominant mechanisms are desirable. In our previous work,25 kinetic processes including desorption, diffusion, and reactions are assigned to two competing mechanisms (clustering and homogenizing) in the A-B model. In this article, we move to a more sophisticated model, the so-called A-B226 or the monomer−dimer27 model. Different from CO-O2 catalysis, this A-B2 model does not restrain the characteristics of the species (in comparison to the immobility and no desorption of the adsorbed oxygen in the CO-O2 catalysis), so more comprehensive phenomena may be observed. KMC simulations were performed systematically here using this model, and the effects of various processes (especially the adsorption and desorption of B2) on the adsorbate distribution have been analyzed. Accordingly, relevant mechanisms for clustering and homogenizing have been revealed. Special Issue: Tribute to Keith Gubbins, Pioneer in the Theory of Liquids Received: June 8, 2017 Revised: July 18, 2017 Published: July 21, 2017 A

DOI: 10.1021/acs.langmuir.7b01930 Langmuir XXXX, XXX, XXX−XXX

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neglected. All sites were vacant initially, the simulation time was set to 1000 to ensure the arrival of steady states, and the results were averaged over the last 500 time units. More KMC details are available in our previous work.25

New features for the A-B2 model were highlighted in comparison to the previous A-B model.

2. MODEL AND METHOD The overall process (eq 1) in the A-B2 model system for heterogeneous catalysis (under the LH mechanism) includes detailed procedures 2−6. 1 A + B2 → AB (1) 2 A(g) + * ⇆ A(ads)

(2)

B2(g) + 2* ⇆ 2B(ads)

(3)

A(ads) + * ⇆ * + A(ads)

(4)

B(ads) + * ⇆ * + B(ads)

(5)

A(ads) + B(ads) → AB(g) + 2*

(6)

3. RESULTS AND DISCUSSION In our previous work on A-B heterogeneous catalysis,25 we observed that reactions account for the clustering of the

Here “*” stands for a vacant adsorption site, and “ads” means that the corresponding species are adsorbed. Processes 2 and 3 represent the adsorption/desorption of species A and B, respectively, where the adsorption of monomer species A occupies a single vacant site, while that of dimer species B2 occupies a pair of NN vacant sites. Adsorbed species B can desorb only in the form of B2, releasing a pair of NN sites. If there exist NN vacant sites, then adsorbed species A or B diffuses, as described in processes 4 and 5. Process 6 represents the reaction between species A and B adsorbed at NN sites. Product AB desorbs immediately after reaction, creating two NN vacant sites. KMC simulations were conducted in accordance with the above procedures and are similar to those in our previous work,25,28 where a square lattice containing 100 × 100 adsorption sites was adopted with periodic boundary conditions and each site has four NN sites. The partial pressure p of both species A and B2 in the gas reservoir was fixed in each case, and product AB was removed immediately from the system after reaction, both of which are essential to keeping the system away from equilibrium. Kinetic constants were tailored via corresponding energy barriers through the Arrhenius expression (and the pre-exponential factors are assumed to be unity for species A, B, and B2), and Qads_i, Qdes_i, Qdiff_i, and Qr represent the energy barriers for adsorption, desorption, diffusion, and reaction processes of species i (i = A, B for diffusion and i = A, B2 for adsorption and desorption), respectively. The barriers here are taken as dimensionless quantities so that the kBT term (kB is the Boltzmann constant, T is the temperature) is incorporated implicitly. For instance, the adhesive coefficient for species i is si = exp(−Qads_i), and the adsorption rate at a vacant site or a pair of NN vacant sites is sipi for species i. The rate for the desorption of one molecule of species i is exp(−Qdes_i). The jump frequency of one adsorbate i to a NN vacant site is exp(−Qdiff_i), and the reaction rate of one adsorbed A-B pair at NN sites is exp(−Qr). And we set Qads_i = 0 here. The immediate removal of product AB may be viewed as pAB = 0 (so the adsorption rate of one AB molecule is zero for a finite sAB, the adhesive coefficient for species AB), and kdes_AB_0 = +∞. (Here kdes_AB_0 is the pre-exponential factor for the desorption rate constant of species AB, so the desorption rate of one AB molecule is kdes_AB = kdes_AB_0 exp(−Qdes_AB) = +∞ for finite Qdes_AB.) In order to reveal the roles of kinetic processes, the lateral interactions among adsorbates were

Figure 1. Change in NA‑B/(NA + NB) with the diffusion energy barrier at pA = 0.5. In case #xxyyz, Qdes_A = Qdes_B = x, Qdiff_A = Qdiff_B = y, and Qr = z. Lines are drawn to guide the eye.

Figure 2. Change in NA‑B/(NA + NB) with the desorption energy barrier at pA = 0.5. In case #xxyyz, Qdes_A = Qdes_B = x, Qdiff_A = Qdiff_B = y, and Qr = z. Lines are drawn to guide the eye.

adsorbates, whereas diffusion and desorption (besides adsorption) processes tend to homogenize the adsorbate distribution, and diffusion has a relatively stronger role. In this work, first we revealed the corresponding behavior in the A-B2 model; furthermore, we explored the effects of kinetic processes on the width of the coexisting regime (where adsorbed species A and B coexist and reactions can occur) and regime transition behavior, in comparison to the A-B model. A large series of cases have been investigated in this work. To facilitate comparison, the case number is taken from the kinetic parameters in the sequence of Qdes_A, Qdes_B, Qdiff_A, Qdiff_B, and B


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Figure 3. Change in NA‑B/(NA + NB) with the reaction energy barrier at pA = 0.5. In case #xxyyz, Qdes_A = Qdes_B = x, Qdiff_A = Qdiff_B = y, and Qr = z. Lines are drawn to guide the eye.

Figure 5. (a) NA and (b) NB for the A-B model as a function of pA for different desorption energy barriers at a relatively low diffusion energy barrier. In case #xxyyz, Qdes_A = Qdes_B = x, Qdiff_A = Qdiff_B = y, and Qr = z. Lines are drawn to guide the eye.

number of adsorbed species A, NB is the number of adsorbed species B, and NA‑B denotes the number of all possible NN A-B pairs in the adlayer. This quantity can roughly reflect the extent of A-B mixing and thus the A-A (or B−B) clustering as well. With Qr = 0, changes in the values of NA‑B/(NA + NB) with the diffusion energy barrier under different desorption energy barriers are plotted in Figure 1. It is observed that for a fixed desorption energy barrier for both species A and B2, NA‑B/(NA + NB) increases with the decline in the diffusion energy barrier, indicating that fast diffusion processes are responsible for the uniform distribution of the adsorbates. Next, the effects of desorption processes on the adsorbate distribution are presented in Figure 2, showing changes in NA‑B/(NA + NB) with the desorption energy barrier under fixed diffusion energy barriers. The results suggest that adsorbate clusters in the adlayer become increasingly obvious with the decline in the desorption rate constant, showing that desorption also promotes the uniform distribution of adsorbates. Another interesting phenomenon is the difference of decrease amplitudes between Figures 1 and 2, which indicates the difference in the influential strength between diffusion and desorption. The slope of changes in the NA‑B/(NA + NB) values with respect to the desorption energy barrier in Figure 2 is higher than that of NA‑B/(NA + NB) with respect to the diffusion barrier in Figure 1; that is, desorption has a relatively stronger role in the adsorbate distribution than diffusion, which is opposite to the behavior in the A-B model.25 The above point may be described in another way. In comparison with case with

Figure 4. (a) NA and (b) NB for the A-B model as functions of pA for different desorption energy barriers at a high diffusion energy barrier. In case #xxyyz, Qdes_A = Qdes_B = x, Qdiff_A = Qdiff_B = y, and Qr = z. Lines are drawn to guide the eye.

Qr. For example, case #xxyyz means that Qdes_A = Qdes_B = x, Qdiff_A = Qdiff_B = y, and Qr = z. 3.1. Influence of Kinetic Processes on the Adsorbate Distribution. For simplicity and to facilitate the comparison with the A-B system, a fixed partial pressure of pA = 0.5 (and thus pB2 = 1 − pA = 0.5 as well) was adopted. The distribution of adsorbates here is characterized via one structural quantity we proposed previously,28 i.e., NA‑B/(NA + NB), where NA is the C


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Figure 6. (a) NA and (b) NB for the A-B2 model as a function of pA for different desorption energy barriers at a high diffusion energy barrier. In case #xxyyz, Qdes_A = Qdes_B = x, Qdiff_A = Qdiff_B = y, and Qr = z. Lines are drawn to guide the eye.

Figure 7. (a) NA and (b) NB for the A-B2 model as a function of pA for different desorption energy barriers at a relatively low diffusion energy barrier. In case #xxyyz, Qdes_A = Qdes_B = x, Qdiff_A = Qdiff_B = y, and Qr = z. Lines are drawn to guide the eye.

x > y, the case with x < y has a higher NA‑B/(NA + NB) value, indicating a more uniform adsorbate distribution. For example, NA‑B/(NA + NB) under case #55330 is lower than that in case #33550. This might mainly be attributed to the site requirement for the desorption of B2. Different from the previous A-B model, in the current A-B2 system, the desorption of one B2 needs one pair of nearest-neighbor B adsorbates, which is more difficult than the desorption of a single adsorbed B in the A-B system. In other words, the number of adsorbed B−B pairs in this A-B2 system is smaller than the number of adsorbed B in the previous A-B system under pA = 0.5. The whole desorption rate is the product of the number and the desorption constant. Therefore, when the desorption constant decreases, the whole desorption rate in A-B2 systems decreases more rapidly than that in the A-B system, leading to structures with lower NA‑B/(NA + NB) values at large x values. Typical results with different reaction energy barriers are plotted in Figure 3, where various desorption and diffusion kinetic constants were accompanied. It is worth noting that the influence of various kinetic processes on the adsorbate distribution can be well revealed when the coverage of each species is comparable among the compared cases. Ideally, for example, if NA and NB in the first case are identical to those in the second case but the distribution of these species in the first case is different from that in the second case, then it is obvious that the difference in the species distribution is due to the difference in case conditions, and the distribution may be readily correlated to the conditions. Practically, if the coverage is similar, such inference of the correlation may still seem reasonable. In the preceding cases as shown in Figures 1 and 2,

the coverage of each species along each line is not constant but similar, so the above analyses seem acceptable. In Figure 3, for cases with x = 0, along each line, the coverage of each species does not vary dramatically, so the monotonic increase in NA‑B/ (NA + NB) with z indicates that reactions lead to clustering in these cases. However, for high x values, e.g., x = 3, the line in Figure 3 has been broken because NA/NB < 1 within z ≤ 1 but NA/NB > 1 within z ≥ 2; that is, the coverage of each species is incommensurable between the case with z = 1 and that with z = 2. In each regime (z ≤ 1 or z ≥ 2) where the coverage of each species is similar, the trend in NA‑B/(NA + NB) with z remains the same as for other lines, confirming that reactions lead to clustering. Such a transition from one steady state with NA > NB to the other with NA < NB under a fixed pA due to the changes in kinetic conditions (mainly reactions and desorption) has not been observed in the A-B system and can be understood by considering the different site requirement for the adsorption and desorption of B2 and the different stoichiometric ratio of reactions in A-B2 from that in A-B. On the basis of the above comparative simulations and analyses, it is evident that in the A-B2 model reactions lead to clustering, while both diffusion and desorption processes promote the uniformity of the adsorbate distribution. This is similar to that in the A-B model, whereas for the homogenizing, desorption plays a stronger role than diffusion due to the fact that the desorption of the dimer is different from that of the monomer. It is apparent as in the A-B model that two competing mechanisms govern the adsorbate distribution. The clustering mechanism due to reaction processes tends to form clusters of species, and the homogenizing mechanism resulting D


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Figure 8. (a) NA and (b) NB for the A-B model as a function of pA for different diffusion energy barriers at a high desorption energy barrier. In case #xxyyz, Qdes_A = Qdes_B = x, Qdiff_A = Qdiff_B = y, and Qr = z. Lines are drawn to guide the eye.

Figure 9. (a) NA and (b) NB for the A-B model as a function of pA for different diffusion energy barriers at a relatively low desorption energy barrier. In case #xxyyz, Qdes_A = Qdes_B = x, Qdiff_A = Qdiff_B = y, and Qr = z. Lines are drawn to guide the eye.

from the desorption and diffusion processes favors the homogeneous distribution of the species. Complex adlayer structures with both species coexisting reflect the compromise of these two competing mechanism; that is, neither of them can dominate the other. In the following section, we will describe the change in this coexisting regime with respect to kinetic conditions, especially pA. 3.2. Phase Transitions and Coexistence Regime. The ZGB model has already captured two types of kinetic phase transitions between the coexisting phase (i.e., the phase within the coexisting regime) and the poisoning phase (with only one species) (i.e., first and the second order at high and low partial pressures of CO, respectively, which were attributed to adsorption and reaction processes).14 In the improved model,19 more systematic effects on the phase transitions were revealed. Here we present results based on KMC simulations, revealing the features of the phase transitions and the window with the coexisting phase for the A-B2 system in comparison to the A-B system. Figure 4 shows NA and NB for the A-B model as a function of pA for different values of desorption energy barriers (x = 0 to 5) at a low diffusion rate constant (y = 5) and a high reaction constant (z = 0). For cases with high x values, continuous phase transitions at both low and high pA are obvious, showing three successive phases with increasing pA, namely, the species B poisoning phase, the coexisting phase, and the species A poisoning phase. When the desorption rates of both adsorbed species are very low, species A (B) occupies the surface rapidly with increasing (decreasing) pA, and the window for the coexisting phase shrinks. For cases with low x values (high

desorption rates), the windows for poisoning phases shrink and even disappear, and the coexisting phase expands (even covering the whole range). The obvious effects of desorption processes on the windows might mainly be attributed to their influence on the coverage directly through desorption and indirectly through their homogenizing roles that promote reactions and thus reduce coverage as well. With decreasing desorption rates, the coverage increases, promoting poisoning, and leaving fewer vacant sites for diffusion that improves mixing. It is also worth noting that the AB production rate reaches its maximum when the numbers of species A and B are equal, where pA is around 0.5 in this system. Similar simulations for the A-B model were carried out at a relatively high diffusion rate, and NA and NB as functions of pA for different desorption energy barriers are given in Figure 5. The tendencies of the lines are quite similar to those in Figure 4. That is to say, the effects of diffusion (within the present range) on the windows are very limited, though diffusion may promote mixing. This indicates again that the change in coverage is more important to the change in windows. Diffusion cannot directly modify the coverage though indirectly through promoting reactions. The effect of desorption on the phase transition for the A-B2 model shows some differences due to the special site requirement of adsorption and desorption for species B2, as presented in Figures 6 and 7. When the diffusion rate constant is low, NA and NB as functions of pA with different desorption energy barriers are plotted in Figure 6. The first obvious point is the characteristic first-order transition at high pA under cases E


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Figure 10. (a) NA and (b) NB for the A-B2 model as a function of pA for different diffusion energy barriers at a high desorption energy barrier. In case #xxyyz, Qdes_A = Qdes_B = x, Qdiff_A = Qdiff_B = y, and Qr = z. Lines are drawn to guide the eye.

Figure 11. (a) NA and (b) NB for the A-B2 model as a function of pA for different diffusion energy barriers at a relatively low desorption energy barrier. In case #xxyyz, Qdes_A = Qdes_B = x, Qdiff_A = Qdiff_B = y, and Qr = z. Lines are drawn to guide the eye.

#55550 and #44550, and the other interesting point is that the B poisoning phase cannot be reached (probably through a second-order transition) in the present cases, even when the desorption rate constant is very low. The latter point might be due to the fact that the requirement of two adjacent vacant adsorption sites is difficult to meet. With the increase in the desorption rate constant, desorption slows down the growth of both species A and B clusters, resulting in an extension of the regime for the coexisting phase. The results for the effect of desorption on the phase transition for the A-B2 model at a relatively high diffusion rate constant are presented in Figure 7, which are very similar to those in Figure 6, indicating that changing the diffusion to such an extent plays a very weak role in modifying the transitions. Comparative simulations were also carried out at different desorption energy barriers, Qdes_A = Qdes_B = 5 and Qdes_A = Qdes_B = 3, revealing the effects of diffusion on the phase transition. For the A-B model, three regimes are obviously observed in Figure 8, where all curves overlap each other, indicating a slight influence of the diffusion processes on the adsorbate numbers at least within the current range of y values. Smooth phase transitions are found when the desorption rate constant is relatively high, as shown in Figure 9, and again the effects of diffusion are negligible. For the A-B2 model, the effects of diffusion on the phase transitions are presented in Figures 10 and 11 with two typical desorption settings, respectively. The role of diffusion is also very weak in this system but seems a little stronger than that in the A-B system (Figures 8 and 9). Such a small improved

Figure 12. Number of species A and B for the A-B and A-B2 models as a function of pA for case #55550 (Qdes_A = Qdes_B = Qdiff_A = Qdiff_B = 5, and Qr = 0), respectively. Lines are drawn to guide the eye.

influence might be owing to the fact that diffusion slightly modifies the adsorbate distribution and thus the number of pairs of adsorbed B−B. Therefore, the desorption rate of B2 changes slightly under a fixed desorption constant, and thus the coverage changes slightly. A typical comparison is further presented in Figure 12. NA and NB for the A-B and A-B2 models are plotted with pA under case #55550. The maximum reaction rate is achieved at the intersection point, and a shift of this point to a higher pA is apparent for the A-B2 model in comparison to the A-B system. A spreading window for the coexisting phase can also be F


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Figure 13. Snapshots of typical cases in (a) the A-B and (b) the A-B2 systems, aligned according to the homogenizing/clustering mechanism and the partial pressure. In case #xxyyz, Qdes_A = Qdes_B = x, Qdiff_A = Qdiff_B = y, and Qr = z.

observed for the A-B2 model (in comparison to the A-B system), and the B poisoning phase can never be reached here. The coexisting phase and the poisoning phases were observed long ago within different regimes in the CO-O2 system.29,30 Although we adopted a more general model (allowing both adsorbed species to diffuse and desorb, which is different from the CO-O2 system), we have reproduced the main features as well. 3.3. Short Summary. The preceding results can be briefly summarized in Figure 13 with the final snapshots of typical cases, where the homogenizing/clustering effects on the adsorbate distribution form one axis and the partial pressure of each species (which determines the operating regime) forms the other axis. Along the former axis, when the homogenizing mechanism dominates (adsorption, desorption, and diffusion processes prevail while reactions are suppressed), the adsorbate distribution is more homogeneous. When the clustering mechanism dominates (adsorption, desorption, and diffusion processes are suppressed while reactions prevail), adsorbate clusters are more obvious. The compromise between these two mechanisms leads to the complex distributions of adsorbates. Along the axis of pA, the system changes from an adsorbate B-dominated regime to an adsorbate A-dominated regime, and the intermediate regime is the A-B coexisting regime. Phase transitions and poisoning may occur depending on the system and other operating conditions. It is observed as well that in the A-B2 system with z = 0 adsorbate B is still the majority at pA = 0.5, showing that the maximum reaction rate shifts to a higher pA.

desorption processes play a stronger role than diffusion in homogenizing the adsorbates, which is contrary to the trend in the A-B model. Similar to the A-B system, there exist two competing mechanisms in the A-B2 model, namely, the clustering mechanism due to reaction and the homogenizing mechanism resulting from desorption and diffusion, especially desorption. The compromise between these two competing mechanisms leads to the steady states with complex distributions of both species. The effects of diffusion and desorption on the phase transitions were investigated as well. Desorption not only reduces the number of adsorbates but also homogenizes the adsorbate distribution, leading to the smoothing of the phase transitions and expanding the coexisting window. However, differences are observed for the A-B2 model in comparison to the A-B model. The first-order transition has been observed for the A-B2 system, but only second-order transitions are observed for the A-B system in the adopted cases. The pA with the maximum reaction rate is higher in the A-B2 system than that in the A-B system, and the A-B2 system exhibits a wider pA window for the coexisting phase due to the fact that the species B poisoning phase is difficulty to achieve.

4. CONCLUSIONS Without considering the lateral interactions among adsorbates, KMC simulations were performed for the A-B2 system, and the kinetic mechanisms for the adsorbate distribution in the adlayer were explored. Significant new features were observed in comparison to the A-B model, mainly due to the special site requirement for the adsorption and desorption of species B2. Under a fixed adsorption setting, the results suggest that as in the previous A-B model, reactions account for the clustering of adsorbates while desorption and diffusion processes contribute to the uniformity of the adsorbate distribution. However,

Jinghai Li: 0000-0002-5026-7104

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Corresponding Author

*Tel: 86-10-62614215. Fax: 86-10-62558065. E-mail: [email protected]. ORCID Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We appreciate the financial support from the National Natural Science Foundation of China (grant nos. 91334102 and 91534104) and the Research Center for Mesoscience at Institute of Process Engineering, Chinese Academy of Sciences (grant no. COM2015A002). G


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Mesoscale Structures in the Adlayer of A-B2 Heterogeneous Catalysis

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