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J. Phys. Chem. C 2009, 113, 3254–3258
Monte Carlo Theory Analysis of Thermal Programmed Desorption of Chiral Propylene Oxide from Pd(111) Surfaces V. Bustos,† D. Linares,† A. Gil Rebaza,† W. T. Tysoe,‡ D. Stacchiola,‡ Luke Burkholder,‡ and G. Zgrablich*,† Instituto de Fı´sica Aplicada, UniVersidad Nacional de San Luis, Chacabuco 917, 5700 San Luis, Argentina, and Department of Chemistry and Biochemistry, UniVersity of WisconsinsMilwaukee, Milwaukee, Wisconsin 53211 ReceiVed: September 26, 2008; ReVised Manuscript ReceiVed: December 3, 2008
Thermal programmed desorption spectra for chiral propylene oxide molecules adsorbed on Pd(111) are analyzed through dynamic Monte Carlo simulation and density functional theory calculations of the binding energy of adsorbed species. A model of the adsorbed phase is developed in such a way that the observed spectra are satisfactorily reproduced. The model reveals that propylene oxide adsorbs in configurations with different tilt angles, depending on the crowding of the surface around each adsorbed molecule, providing desorption energies varying over a wide range from about 9.2 to 13.6 kcal/mol. 1. Introduction A chiral molecule is characterized by a particular geometric symmetry, such that it cannot be superimposed onto its mirror image. Such molecules can appear in two forms, enantiomers, R and S, each being the mirror image of the other, and the two enantiomers can interact differently with living organisms. For this reason, the production of enantiomerically pure chiral compounds is a subject of great interest to the pharmaceutical industry.1 In recent years an approach that has received particular attention for this purpose is the enantioselective modification of the catalyst surface by the adsorption of chiral species.2-6 This approach consists of producing an assembly of chiral adsorbate structures on the surface of the catalyst to create chiral sites that are capable of promoting the desirable enantioselective reactions. In particular, this approach has been applied to the enantioselective adsorption of propylene oxide (PO) on surfaces templated by the preadsorption of S- or R-2-butanol.7-9 The system showed a peak in enantioselectivity around a template coverage of 0.25, adsorbing almost twice the amount of R-PO as compared to S-PO when the surface was templated using R-2-butanol.7 Theoretical models to explain the observed behavior have been attempted based on the assumption that some particular template structures would produce enantioselective sites (or pockets)10,11 and also on the assumption that a geometrical effect caused by the different footprints of R and S enantiomers may induce selectivity.12 However these models must be considered as a first step in understanding the process at a molecular level, and further development of such models will rely on a more detailed determination of the structure of the template and probe molecules. The structure of 2-butanol on a palladium surface has recently been examined,13 and this work explores the adsorption and desorption behavior of PO. A key issue in understanding enantioselective interactions between a chirally modified surface and a probe molecule is the differences in interaction energy between different enanti* Towhomcorrespondenceshouldbeaddressed.E-mail:
[email protected]. † Universidad Nacional de San Luis. ‡ University of WisconsinsMilwaukee.
omers on the surface. These energetic differences are likely to be rather small. Temperature-programmed desorption (TPD) is capable of yielding desorption activation energies, and in cases in which adsorption is not activated, this is equal to the heat of adsorption. Approximate heats of adsorption can be obtained from peak temperatures for first-order desorption processes by using the Redhead equation.14 However, to apply this equation, assumptions must be made concerning the value of the preexponential factor (generally assumed to be 1 × 1013 s-1 for a first-order process) and any lateral interactions between adsorbates are neglected. In addition, when the adsorbed species are rather complex, they may adopt different local configurations depending on the crowding of the surface around each particular adsorbate, thus inducing a complex variation in desorption energy during the TPD process, which cannot be accurately taken into account by analytical methods. However, such effects can be straightforwardly included by analyzing the TPD data using Monte Carlo methods and the purpose of the present work is to develop a model for the adsorption of PO on Pd(111) and describe the thermal desorption process through dynamic Monte Carlo simulations to determine the structural properties that are necessary to reproduce the observed TPD spectra. To provide a reasonable theoretical basis for the model to be used in Monte Carlo simulations, density functional theory (DFT) calculations were also performed to determine the possible range of binding energies for a PO molecule adsorbed on Pd(111) in different configurations. 2. Experimental Methods TPD data were collected in an ultrahigh vacuum chamber operating at a base pressure of 8 × 10-11 Torr that has been described in detail elsewhere15 where desorbing species were detected using a Dycor quadrupole mass spectrometer placed in line of sight of the sample. The sample could be cooled to 80 K by thermal contact to a liquid-nitrogen-filled reservoir and resistively heated to ∼1200 K. The temperature ramp and data collection were controlled using LabView software. This chamber was also equipped with a double-pass, cylindrical mirror analyzer for Auger spectroscopy measurements and an ion-sputtering gun for sample cleaning.
10.1021/jp808555p CCC: $40.75 2009 American Chemical Society Published on Web 02/03/2009
TPD of Chiral Propylene Oxide from Pd(111) Surfaces
Figure 1. A series of 58 amu (PO) TPD spectra following the adsorption of PO on clean Pd(111) collected using a heating rate of 6.5 K/s as a function of PO exposure, where the exposures in Langmuirs (1 L ) 1 × 10-6 Torr s) are indicated on the figure.
Infrared spectra were collected using a Bruker Equinox infrared spectrometer and a liquid-nitrogen-cooled mercury cadmium telluride detector. The complete light path was enclosed and purged with dry, CO2-free air. Data were typically collected for 1000 scans at 4 cm-1 resolution.16 The Pd(111) substrate (1 cm diameter, 0.5 mm thick) was cleaned using a standard procedure, which consisted of cycles of argon ion bombardment (2 kV, 1 µA/cm2) and annealing in 2 × 10-8 Torr of O2 at 1000 K. The cleanliness of the sample was judged using X-ray photoelectron spectroscopy (XPS) and oxygen titration where O2 instead of CO desorbs following O2 adsorption when the sample is carbon free. The PO (Aldrich, Research grade) was transferred to a glass vial and purified using several freeze-pump-thaw cycles and its purity determined by mass spectroscopy. 3. Results Figure 1 displays a sequence of TPD spectra for PO adsorbed on Pd(111) collected using a heating rate of 6.5 K/s monitoring desorption at 58 amu (the parent peak for PO) as a function of PO exposure, where exposures are indicated on the figure. At the lowest exposure (0.4 L, 1 L ) 1 × 10-6 Torr s), a single desorption peak is found centered at ∼230 K. Note that exposures have not been corrected for ionization gauge sensitivities. This feature shifts to lower temperatures as the PO exposure increases. At the highest exposure (3.0 L), the desorption maximum appears at ∼175 K, while at PO exposures greater than 1.8 L, a second-layer desorption state starts to appear as evidenced by a low-temperature shoulder (at ∼160 K). At exposures of 2.7 and 3.0 L, this evolves into a sharp peak at ∼120 K. Exploring other masses confirms that all mass spectrometer fragments can be assigned to PO and that there is no detectable thermal decomposition on the clean surface. PO desorbs completely molecularly.
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Figure 2. RAIRS for PO adsorbed on clean Pd(111) at 80 K as a function of exposure and the effects of annealing to various temperatures. Both the PO exposures and annealing temperatures are indicated adjacent to the corresponding spectrum.
Attempts to fit the shape of the desorption profile and the shift with coverage to a single desorption state with lateral interactions failed to reproduce the experimental profile (see below). In addition, the reflection-absorption infrared spectra (RAIRS) for PO adsorbed on clean Pd(111) at 80 K and after annealing to various temperatures are displayed in Figure 2. There is clear evidence for multilayer condensation from the ring deformation mode at ∼830 cm-1. While there are some variations in relative intensities of the vibrational features as a function of exposure suggestive of the formation of different PO adsorption states, of particular note is the spectrum produced on heating to ∼220 K where the relative intensities of the infrared peaks are significantly different from those formed at ∼150 K. Note in particular the relative intensities of the 1441 and 1399 cm-1 modes and those at 1021 and 940 cm-1. This suggests the formation of various PO adsorption states. A. Adsorption Model and Simulation Method. An adsorption model is proposed based on the general characteristics of the experimental information available for PO on Pd(111), namely, TPD and IR spectra, and on DFT calculations of the binding energy of the molecule in configurations with different tilt angles with respect to the metal surface. The TPD results, measured for different initial coverages, show a significant shift in peak maxima toward higher temperatures as the initial coverage decreases. Such a shift in a firstorder, monomolecular, desorption state such as the one we have here is usually produced by repulsive interactions among adsorbates. However, this cannot be the case when, as in Figure 1, the shift still occurs (or even increases) as the coverage decreases to very low values. Thus, at low coverages, adsorbates are far apart from each other and would require very long-range interactions to produce such a shift. However, even if such longrange interactions were possible, the shift in the temperature of
3256 J. Phys. Chem. C, Vol. 113, No. 8, 2009 the peak would continue to decrease as the initial coverage decreases, which clearly does not occur in Figure 1. Auxiliary Monte Carlo simulations confirmed that the observed set of TPD spectra cannot be explained in terms of interadsorbate interactions alone. Under these circumstances we must assume the possibility that PO may adsorb on the Pd(111) surface in different configurations with different binding energies as a function of coverage. To examine this possibility, PO adsorption was explored using DFT calculations, as described below. We note that the TPD spectra show desorption from the second layer at very low temperatures, represented by a sharp peak at ∼120 K. However, this desorbs before any PO adsorbed directly on the palladium surface has desorbed, so that our DFT calculations will be restricted to PO molecules adsorbed on clean palladium. Our calculations used plane-wave DFT calculations through the Vienna Ab Initio Simulation Package (VASP),16-19 where electronic interactions are described by the Projector Augmented Wave (PAW) method. The Perdew-Bruce-Erzenhof (PBE) functional was used for exchange and correlation energies because of its good performance for the system to be studied. All calculations were performed using a cutoff energy value of 450 eV, which results after a convergence study using the Monkhorst-Pack scheme for integration over the first Brillouin zone. The size of the unit cell was 4 × 4, corresponding to an effective coverage of 0.18 measured as the number of metal atoms covered by the projection of the molecule on the surfaces divided by the number of total metal atoms. The molecule was adsorbed on the high-symmetry adsorption sites: on-top, bridge, face-centered cubic (fcc), and hexagonal close-packed (hcp) hollow sites. In each case, the molecule is located with its oxygen atom on the chosen site at a large distance, which is progressively decreased in order to find the maximum adsorption, or binding, energy (minimum energy for the system), the heats of adsorption calculated in the usual way from the difference in energy between the isolated molecule and clean surface, and the molecule-surface combination. It was found that the most favorable adsorption site is the on-top position for all configurations. After finding the most favorable adsorption site and the molecule-surface bond length, the molecule was allowed to relax and the energy of the system calculated. All these calculations were performed for different inclinations of the plane formed by the carbon atoms (above the oxygen atom) with the surface of 34, 0, and -15°, which was fixed while all the other structural parameters were allowed to relax. These different configurations and their binding energies are depicted in Figure 3. The adsorption, or binding energy is calculated from the relation Eads ) Etot - Esurf - Emol, where Emol is the minimum energy of the isolated molecule, Esurf that of the clean solid, Etot that of the solid plus the adsorbed molecule, and Eads is the resulting adsorption or binding energy. The influence of rotations of the molecule around an axis perpendicular to the surface was also considered. Taking into account the triangular geometry of the Pd(111) surface and the presence of fcc and hcp sites, the surface presents a configurational invariance under rotations of 120° so that the variation in adsorption energy due to molecular rotation around an axis perpendicular to the surface was calculated in this range for configurations with azimuthal angles going from 34 to -60°. It was found that the energy variation is a negligibly small, on the order of 0.5%, value which represents the estimated error of the values found for the binding energies. Furthermore no activation energy was found to reach the minimum energy for each configuration during the relaxation process. From Figure
Bustos et al.
Figure 3. Representation of adsorbed PO on Pd(111) in different tilt angles with respect to the surface obtained by DFT calculations for tilt angles of (a) 34, (b) 0, (c) -15°. The calculated binding energies are indicated below each structure.
3, it is seen that the most stable configuration at low coverages has a tilt angle of -15°, with an adsorption energy of 14.8 kcal/ mol, while the least stable is that corresponding to 34°, with an adsorption energy of 11 kcal/mol. This suggests that the PO is stabilized by an agostic interaction between the methyl groups and the palladium surface. However, the area occupied by the more stable surface species depicted in Figure 3c is larger than that shown in Figure 3a. This suggests that, as the surface coverage increases, the adsorption geometry of PO will change such that the tilt angle increases from -15° to larger angles, with a concomitant decrease in heat of adsorption. This picture accounts for the experimentally observed decrease in desorption activation energy with increasing coverage shown in Figure 1. To explore these ideas more quantitatively, we propose the following adsorption model. The Pd(111) surface forms a triangular lattice (each site has 6 nearest neighbors). However, PO, in any configuration, will occupy a certain number of these sites. We do not lose generality at this stage of our study if we consider an effective lattice, say a square lattice, where each species occupies just a single site. In such a lattice we assume that a PO molecule, adsorbed at a given site characterized by a surrounding R, will have an adsorption energy ER. According to our discussion above, parameter R should represent the local crowding of the surface coverage. For this we have taken the fraction of occupied sites within up to the fourth neighbors from the given PO molecule. Thus, if N0 is the total number of surrounding sites up to the fourth neighbor (20 in a square lattice) and n is the number of occupied sites in this surrounding, then R ) n/N0. Therefore, ER will be a continuously decreasing function of R, which will be determined by fitting simulated spectra to the experimental ones. Intermolecular interactions between neighboring adsorbed species are also allowed, with interaction energies 1 and 2 between nearest- and next-nearestneighbors, respectively. The thermal desorption process is simulated by a dynamic Monte Carlo method, which has been discussed in more detail elsewhere.20,21 We consider a square lattice of M ) L × L sites,
TPD of Chiral Propylene Oxide from Pd(111) Surfaces
J. Phys. Chem. C, Vol. 113, No. 8, 2009 3257
with periodic boundary conditions, and prepare the initial surface with a given coverage of randomly adsorbed molecules. Desorption of a given molecule adsorbed at site i is considered as an activated process with a transition rate given by
wi ) V exp {-[EiR - Ui(ε1, ε2)]/kBT}
(1)
where V is the pre-exponential frequency factor, EiR the adsorption energy at site i with surrounding R, Ui the interaction energy of the molecule adsorbed at site i with other neighbor adsorbed molecules, kB the Boltzmann constant, and T the temperature. Let r be the maximum desorption rate in the system, i.e., r ) max(wi), and R ) N(t)r, where N(t) is the number of adsorbates at time t. Then a Monte Carlo trial consists of the following steps: (i) an occupied site i is chosen at random, and the corresponding value of wi is calculated; (ii) a random number ξ1 uniformly distributed in the interval (0,1) is obtained and the desorption of the species adsorbed at site i is executed if ξ1 < wi/r, otherwise it is not; (iii) a random number ξ2 is obtained and the time is increased by ∆t ) -ln(ξ2)/R, with a corresponding increase in temperature given by ∆T ) V∆t, where V is the heating rate. The process is repeated, starting from sufficiently low temperatures that the desorption rate is negligible and ending when no more molecules are present on the surface. Each run at a given coverage is averaged over a large number of replicas of the system in order to minimize fluctuations in the simulated spectra. B. Results of Monte Carlo Simulations. A lattice size of L ) 100 was used in all simulations, which was sufficient to avoid finite size effects, and the heating rate was fixed at V ) 6.5 K/s (the experimental value). Peaks corresponding to second-layer adsorbed PO were subtracted from the experimental data in order to compare with simulations. After this subtraction the initial coverage of the largest-area TPD spectrum was taken as θ ) 1; therefore the initial coverages of the remaining TPD spectra correspond to 0.85, 0.74, 0.65, 0.45, 0.21, 0.12, and 0.07. These, of course, should be considered as effective coverages corresponding to the effective square lattice. Preliminary simulations were performed in order to determine the appropriate value of the pre-exponential frequency factor and the influence of lateral interactions. It was found that a value of V ) 6.5 × 1011 s-1 reproduced the widths of desorption peaks very well with a simple trial function ER and that interaction energies between adsorbed molecules should be negligibly small, so that they were set as 1 ) 2 ) 0. After this, new simulations were performed using ER as a fitting function in order to obtain a satisfactory agreement between simulated and experimental spectra for each value of the total initial coverage θ. The best-fit values of ER are plotted in Figure 4, where it can be seen that the binding energy varies in a continuous way from ∼9.2 to ∼13.6 kcal/mol. This variation is consistent with our DFT calculations corresponding to configurations of the PO molecule with tilt angles between ∼-15° at the lowest coverages to ∼34° at the highest. A comparison between the simulated and experimental TPD spectra is shown in parts a-f of Figure 5. As can be seen, there is excellent agreement between the model prediction and the experimental results. In fact, the only significant deviations occur in the high-temperature tail of each spectrum, which could be attributed to the presence of defects on the real Pd(111) surface used in experiments. These defects would provide a variety of stronger adsorption sites, which are not taken into account in the simulations. The model correctly reproduces the shift in the temperature of the experimental spectra as θ decreases as well as the shape of the peaks and shoulders. In particular, the width
Figure 4. Variation of binding energy of PO on Pd(111) as a function of the crowding of the surface up to fourth order neighbors, values found in Monte Carlo simulations to fit experimental TPD spectra.
Figure 5. Comparison between simulated (hollow symbols) and experimental (solid symbols) TPD spectra for different total initial coverages: (a-f) θ ) 0.12, 0.21, 0.45, 0.65, 0.85, 1.0, respectively.
of the calculated desorption features agrees well with the experimental data implying that the value of the pre-exponential factor is correct. We emphasize that this agreement cannot be obtained on the basis of adsorbate-adsorbate interactions alone, that the function ER is unique for all TPD spectra corresponding to different initial coverages, and that it is consistent with DFT calculations of PO adsorbed on Pd(111). Some comments are in order regarding the desorption energies obtained in our Monte Carlo simulations. In the first place, the goodness of fit of simulated to the experimental spectra is not characterized by the usual mean-square deviations but by comparing the experimental and theoretical profiles by eye. Thus we cannot define quantitative fitting errors but only a sensitivity range for each value of the desorption energies obtained. This range is the amount by which each desorption energy can be changed without observing significant variations in the spectra. These ranges are represented in Figure 4 as “error bars”. Second, Redhead values of the desorption energy were calculated from
3258 J. Phys. Chem. C, Vol. 113, No. 8, 2009 TABLE 1: Redhead Estimates of Desorption Energies for Each TPD Peak coverage
peak temperature (K)
desorption energy (kcal/mol)
0.12 0.21 0.45 0.65 0.85 1.0
217.8 209.6 190.2 189.8 187.9 186.2
10.8 10.6 9.88 9.99 9.98 9.95
the peak temperature of each experimental desorption profile. The resulting values of these desorption energies are shown in Table 1. As can be seen, these values differ from those obtained by Monte Carlo simulations. It should not be surprising that in fact the Redhead equation, as any Arrhenius type of equations, is the result of mean field kinetic equations, which ignores fluctuations in the density22 and should lead to erroneous results when the kinetics are strongly dependent on local density fluctuations as is the case for the process studied here. 4. Conclusions We have used TPD data of chiral PO species to obtain information about the structure of these molecules when adsorbed on Pd(111) at different coverages by simulating the TPD process through a dynamic Monte Carlo method through a model suggested by DFT calculations of the binding energies of the molecule to the metal surface. Our study indicates that experimentally observed spectra cannotbereproducedsatisfactorilyonthebasisofadsorbate-adsorbate interactions alone and that experiments are reproduced satisfactorily when it is assumed that adsorbed PO is present on the surface in a variety of states corresponding to different tilt angles, ranging from 34 to -15°, with binding energies varying continuously between ∼9.2 and 13.6 kcal/mol according to a function ER which is unique for all initial coverages. This kind of analysis is helpful as long as the adsorbate structure cannot be determined through low-energy electron diffraction or scanning tunneling microscopy experiments.
Bustos et al. Acknowledgment. The Consejo Nacional de Investigaciones Cientı´ficas y Te´cnicas and the US Department of Energy, Division of Chemical Sciences, Office of Basic Energy Sciences, under Grant No. DE-FG02-03ER15474 are gratefully acknowledged for providing partial support to this research. References and Notes (1) Stinson, S. C. Chem. Eng. News 2000, 78, 55. (2) Blaser, H. U.; Jalett, H. P.; Lottenbach, W.; Studer, M. J. Am. Chem. Soc. 2000, 122, 12675. (3) Lorenzo, M. O.; Baddeley, C. J.; Muryn, C.; Raval, R. Nature 2000, 404, 376–379. (4) Raval, R. CATTECH 2001, 5, 12. (5) Humblot, V.; Barlow, S. M.; Raval, R. Prog. Surf. Sci. 2004, 76, 1. (6) Stacchiola, D.; Burkholder, L.; Zheng, T.; Weinert, M.; Tysoe, W. T. J. Phys. Chem. B 2005, 109, 851. (7) Stacchiola, D.; Burkholder, L.; Tysoe, W. T. J. Am. Chem. Soc. 2002, 124, 8984. (8) Gao, F.; Wang, Y.; Burkholder, L.; Tysoe, W. T. J. Am. Chem. Soc. 2007, 129, 15240. (9) Gao, F.; Wang, Y.; Li, Z.; Furlong, O.; Tysoe, W. T. J. Phys. Chem. C 2008, 112, 3362. (10) Roma´, F.; Zgrablich, G.; Stacchiola, D.; Tysoe, W. T. J. Chem. Phys. 2003, 118, 6030. (11) Roma´, F.; Stacchiola, D.; Tysoe, W. T.; Zgrablich, G. Physica A 2004, 338, 493. (12) Lo´pez, R. H.; Roma´, F.; Gargiulo, V.; Sales, J. L.; Zgrablich, G. J. Phys. Chem. B 2008, 112, 8619. (13) Gao, F.; Wang, Y,; Burkholder, L.; Hirschmugl, C.; Saldin, D. K.; Poon, H. C.; Sholl, D.; James, J.; Tysoe, W. T. Surf. Sci. 2008, 602, 2264. (14) Redhead, P. A. Vacuum 1962, 12, 203. (15) Kaltchev, M.; Tysoe, W. T. J. Catal. 2000, 196, 40. (16) Wu, G.; Kaltchev, M.; Tysoe, W. T. Surf. ReV. Lett. 1999, 6, 13. (17) Kresse, G.; Hafner, J. Phys. ReV. B 1993, 47, 558. (18) Kresse, G.; Furthmu¨ller, J. Phys. ReV. B 1996, 54, 11169. (19) Kresse, G. J. Phys.: Condens. Matter 1994, 6, 8245. (20) Binder, K. Monte Carlo Methods in Statistical Physics; SpringerVerlag: Berlin, 1978; Vol. 7. (21) Sales, J. L.; Un˜ac, R. O; Gargiulo, M. V.; Bustos, V; Zgrablich, G. Langmuir 1996, 12, 95. (22) Hinrichsen, H. AdV. Phys. 2000, 49, 815.
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