12014
J. Phys. Chem. 1993,97, 12014-12019
NMR Study of Diffusion of CO on Alumina-Supported Pt Clusters Lino R, Becerra, Christopher A. Klug, and Charles P. Slichter’ Department of Physics and Materials Research Laboratories, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801 -3080 John H. Sinfelt Exxon Research and Engineering Co., Annandale, New Jersey 08801 Received: June 21, 1993; In Final Form: August 26, 1993” The authors report an N M R study of carbon monoxide diffusion on surfaces of supported Pt clusters. They have implemented an N M R technique complementary to the other ones used in N M R to measure diffusion. They found that the rate of diffusion of CO on Pt depends on cluster size. For the large clusters (average diameter 100 A), the activation energy is about 6.5 f 0.5 kcal/mol, in agreement with the value obtained by other methods for CO on Pt( 111). For the small clusters (diameter about 12 A), the activation energy is about 10.5 f 1 kcal/mol. The authors also found that CO is more mobile on a partially covered surface than on a saturated one. They found that, in the temperature range investigated, only about 50% of the molecules are moving. The authors explain the data by a model in which only bridge-bonded CO molecules are capable of moving, by jumping to other bridge sites, while CO molecules linearly bonded are immobile.
Introduction The study of surface diffusion is not only relevant for understanding the behavior of adsorbed molecules but may also be important for catalysis. The system CO on Pt has been extensively studied for the case of Pt single-crystal surfaced-3 and supported Pt clusters.4 Recently, newly developed experimental techniquesH were applied to the study of diffusion but were limited to single-crystal surfaces. Due to the relevance that supported Pt clusters have in catalysis, a study of diffusion on these materials is important. Our group has studied diffusion of CO on Pt and on Pd clusters using NMR9J0 in the past. The motion of CO molecules on the surface is reflected in many NMR parameters. It is a wellknown effect in NMR that motion narrows the NMR absorption line when the rate of motion is comparable with the line width” (motional narrowing). By following the line shape as a function of temperature, it is possible to deduce an activation energy for diffusion (Ed). For the case of CO on Pt, Ansermet12 found that co seems to show two activation energies Ed for diffusion: 13 and 16 kcal/mol. Using a similar analysis, Shore et al.IO found that for the case of CO on Pd Ed is 6 kcal/mol. Zilm and coworkers have also used NMR13J4 to study diffusion of CO on Pt and Pd. Their results14agree with the model previously proposed by Ansermet12 for diffusion of CO on Pt, but they propose a detailed picture which, however, differs from our conclusion. A particularly important aspect of their studies was the useof magic angle spinning (MAS). They demonstrate that MAS does not narrow the CO spectrum and propose that there is a spread in the size of the isotropic shift of 13C. Diffusion of the molecules affects the spin-spin relaxationtime T2 as has been seen in the CO/Pt9 as well as in the CO/Pd10 system. Spin-lattice relaxation times TI can also be affected by diffusion. The rateof motion must becomparablewith theLarmor frequency to affect T I . This effect has not been seen for CO, but it was observed by Wang et aL15for the case of carbon atoms on Pt. Nevertheless, if different sites present different relaxation times for CO, exchange of CO molecules among the different kinds of sites will average out the different relaxation times if the motion rate is comparable with TI (as Ansermetl6 has found for CO on Pt). From LEED studies” of CO on Pt( 11l), it is known that CO bonds in a ~ ( 4 x 2 pattern ) for a coverage of 8 = 0.5 with half Abstract published in Advance ACS Abstracts, October 1, 1993.
of the molecules on bridge sites and the other half on on-top (linear) sites. For supported Pt clusters, IR results (see references in ref 4) show that as much as 50% of adsorbed CO is bridgebonded. It also is known that CO bonds more strongly to linear sites than to bridge sites, which suggests that it might be possible that defects exist in the bridge sites (e.g., missing molecules) so that CO is able to diffuse among bridge sites while CO linearly bonded is immobile on the surface (although exchangeof linearly and bridge bonded CO will provide a mechanism for an effective motion of linearly bonded CO). We cannot confirm this model by using NMR with the classical analysis. For the analysis of line shapes, motion of the molecules has to be fast enough to narrow the line. If some molecules are to remain at rest, they will not narrow the line, and we cannot distinguish which are moving and which are not. The averaging of T I only indicates that there is exchange of COS, but we cannot determine if CO is moving among bridge sites. We have implemented a technique in which we use the fact that CO molecules bound to different parts of the clusters will have different 13Cresonance frequencies depending on the relative orientations of the molecules with respect to the external magnetic field. The angular dependence derives mainly from the chemical shift anisotropy and the cluster’s magneticsusceptibility. Hence, when the molecules diffuse over the surface of the cluster, their resonant frequencies change. A preliminary form of our method was first performed in our laboratory by Ansermet. A similar scheme was developed independently by Duncan et a1.18 The basis of these methods is to “label” some of the molecules by inverting their 13C spin orientation. But rather than using a weak pulse13or a long combination of pulses1*that restrict the rate of motion to that determined by the rate of “preparing” the spins, we use two strong pulses to label the spins.19 The exact pulse sequence is described below. We call the sequence an “S-shape” sequence because it caused one-half of the absorption line to be inverted. With this sequence, the preparation time is on the order of the inverse of the line width. When the molecules diffuse, labeled and unlabeled molecules mix, altering the magnetization at different frequencies. The study of these changes yields information about the diffusion parameters. We have applied the “S-shape” technique to the study of CO on Pt clusters of different sizes at various coverage. We have found that our results agree with the idea that CO diffusion occurs in one sublattice formed by CO molecules bridge bonded while CO molecules in the other sublattice (linearly bonded) are
0022-3654/93/2097-12014$04.00/0 0 1993 American Chemical Society
NMR of CO Diffusion on Pt Clusters
The Journal of Physical Chemistry, Vol. 97, No. 46, 1993 12015
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pulse (with the rf field along theXaxis) brings the magnetization along the -Y axis; due to the several shifts, the spins rapidly dephase, and after a time Tm, some are along the +X axis and some along the -X. At that time, a second 90' pulse shifted 90' in phase from the first pulse is applied so that the magnetization is brought back to the Z axis. Now the "fast" spins are pointing along the -2 axis while the "slow" ones are pointing along the +Z axis. If the magnetization along the Z axis is later allowed to evolve for a time T , and then is inspected by an echo sequence, the effects of diffusion can be observed in the changes in line shape. We use an eight-phase cycling sequence to get rid of any ring down due to the preparing pulses as well as the inspecting ones. The main advantage of the S-shape labeling sequence is that the spins are prepared in a time of the order of 10-15 ps compared to 1 ms, which is required in typical hole-burning sequences. We can see that this is a major advantage by doing the following analysis: Suppose that the diffusion parameter D is defined as D = R ~ / Twhere , R is the radius of the cluster and T is the time that it takes a molecule to diffuse over the cluster. Motional narrowing requires that T should be shorter than the inverse of the linewidth 6w or that 1 / >~ 6w. That means that D > R26w. We wish to observe diffusion at a rate that does not affect the line, so the upper limit for D is D < R26w. However, if D is too small, the spins are relaxed back by TI processes, so T has to be shorter than T I or D > R2/T1 which represents the lower limit for D. During the preparation time, diffusion should be minimal. Therefore, T must be larger than Tpmp That is, D < R2/Tp,. For the case of CO on Pt, TI is in the range 100-150 ms and 6w is about 25 kHz. Using the weak pulse scheme, D can vary by about 2 orders of magnitude. In contrast, by using the S-shape sequence the dynamic range of D is extended to about 4 orders of magnitude.
90
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Figure 1. Vector diagrams of S-shape sequence: "s" represents the slow spins and "T the fast ones.
immobile. We also found that motion is easier on larger clusters than on small ones and that the activation energies found for these large clusters are closer to those encountered in singlecrystal studies. In addition, we observed that CO diffusion is enhanced on partially covered samples. In the remaining sections of the article, we will use diffusion meaning molecular diffusion. As Ansermet determined,12 13C spin diffusion is negligible due to the larger frequency shift that exists from site to site compared to the 13C dipole-dipole interaction.
Results Experimental Section Samples. We have described our samples elsewhere.lO Briefly, our samples consist of Pt clusters supported on 7-alumina. For purposesof a working model, we visualize them as cubooctahedra with 80%of the surface coming from (1 11) planes and 20% from (100) planes. The samples are characterized according to their dispersion,which is the fraction of metal atoms occupying surface sites. Samples are cleaned by alternating flows of H2 and 0 2 at high temperatures, followed by evacuation to 10-6 Torr. Cleaned samples are exposed to the desired gas (l3CO) at room temperature, and adsorption is determined by thedrop in the gas pressure. Any excess gas and physisorbed molecules are pumped away before the sample is transferred to a 2-cm3 glass tube which is flame-sealed. We label our samples according to the metal, its dispersion, and the coating gas: for example, Pt23CO. If the coverageisdifferent from saturation, it is indicated by a percentage at the end of the label: PT73C030% means that the coverage is 30% of the saturation coverage. NMR. Our spectrometer is a homemade one with an 8.2Tesla Oxford superconducting magnet. The I3C resonance frequency is 87.695 MHz. The rf pulse power is about 400 W giving us 90° pulses with durations of about 3.5-4 ps. The S-shape sequence consists of two preparing pulses and two inspecting ones. The inspecting pulses form the regular echo sequence: 90-Td,,ay-1 IO-echo. Spectra are obtained by Fourier transforming the second half of the echoes. The preparing sequence consists of applying 90x-T,ep-90y. Tplcpis chosen about equal to the inverse of the frequency width of the resonance line. A simple vector picture is shown in Figure 1 (assuming right-handed rotation about the magnetic field as would result from a negative gyromagnetic ratio.) The first 90°
Figure 2a shows the evolution in time, T, of the NMR line of Pt73CO at 77 K. At this temperature, diffusion is negligible and the line relaxes back to its equilibrium form by 2'1 processes. Since the S-shape sequence modulates the NMR absorption spectrum with a sinusoidal form, most of the line has a different amplitude after the preparation sequence than the equilibrium line. Therefore, not only will the inverted part of the line grow back but also the noninverted one will grow as well. If the experiment is repeated at a higher temperature as shown in Figure 2b, we can see by looking at the positive peaks that the line gets smaller in size before it relaxes back to equilibrium. If there were only a single activation energy for diffusion for all CO molecules, there would be a temperature above which diffusion is fast enough to completely cancel the line before it relaxes back to equilibrium. We have verified this type of effect using a previously studied system with two chemical sites and two welldefined NMR lines.20 However, for the case of CO on Pt, we have not been able to see the line intensity go to zero at any temperature in any of our samples. We believe that the explanation for this failure is that at our temperatures some of the CO is unable to diffuse. We found that to quantify diffusion it is convenient to follow the amplitude M+(T,) of the positive peak in the low-frequency part of the line. If only T1 processes are involved, M+(T,) will grow back to its equilibrium value from the beginning. On the other hand, if diffusion is mixing labeled and unlabelled spins, the amplitude might initially decrease before relaxing back. We have defined a normalized amplitude A+(Tcy)(see Appendix) as the ratio of the experimental amplitude M+(T,) to the value of M+(T,) if only T1 processes were responsible for the time dependence of the magnetization. A formula for it, based on the fact that the NMR line shape is nearly Gaussian, is given in eq
Becerra et al.
12016 The Journal of Physical Chemistry, Vol. 97, No. 46, 1993 l
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Figure 2. Evolution of NMR line shape with Tw for Pt76CO at (a, top) 77 K and (b, bottom) 337 K.
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According to that definition, without diffusion A+( TW)= 1 for all T,. With diffusion, A+(T,) might get smaller than 1. In Figure 3, we show the variation of A+ with T,/Tl for Pt73CO at three different temperatures. We have used T,/T, instead of T , because T I changes with temperature. When the temperature is raised, CO is able to diffuse faster, causing more mixing of labeled and unlabeled molecules which in turn is reflected as a deeper drop in A+. We also have investigated the effects of reducing the amount of CO on the surface by preparing a sample with partial coverage, Pt73C030%. This sample has a larger number of vacanciesthan the saturated one, which could affect the capability of CO molecules to diffuse. In Figure 4, we present the results of A+ for Pt73CO and Pt73C030% at room temperature. We can see that the partially covered sample has a deeper decay of A+, indicating that it is easier for CO to diffuse. We cannot fit A+ if we assume that there is a single activation energy for diffusion for all the molecules. We therefore assume that part of the molecules are moving and part are not and define a fitting function f(Tev):
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size is rather narrow as has been observed by electron microscopy in our group21 for other Pt samples. This in turn permits us to assume that all the clusters are about the same size and that no corrections for a distribution of sizes are necessary. Using eq 2 and eq A9 in the Appendix, we find for Pt73CO and R73CO30% a diffusion parameter 0,for each temperature. For the samples Pt23CO and PtllCO, the distribution of clusters is fairly large and should be included in the analysis. We have incorporated the distribution of cluster size by using the results of previous studies in our group.21 We found that the distribution of clusters follows a log-normal distribution. Equation 2 is then modified as follows:
(3) d
where p(d) is the probability for a cluster of diameter d in the sample. f(T,) is the fitting function similar to the one in eq 2. A: is the normalized amplitude in which the dependence on the cluster's size is made explicit. In principle, we should include C m in the sum as C,(d). As explained later, for the samples utilized in this study, we think that C, is not far from being independent of diameter.
*
The Journal of Physical Chemistry, Vol. 97, No. 46, 1993 12017
NMR of CO Diffusion on Pt Clusters A+
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In Figure 5 , we show the variation of A+ for PtllCO with T,/TI. Utilizing eq 3, we obtained D, for each temperature. As explained in the Appendix, we assume that 0,has an Arrhenius type of dependence on temperature:
D, = 0:exp(-Ed/kT) (4) Figure 6 shows D, vs 1/ T for all our samples. To obtain the activation energies and the preexponential factors, we proceeded as follows: For each set of data for samples with saturation coverage (Pt73CO,Pt23CO,andPtl lCO), wedeterminedarange of possible preexponential factors in each sample from straightline fits through the data. The ranges overlap around certain values. We then assumed a common preexponential factor for all the samples and extracted an activation energy for each sample. Assuming a common preexponential value seems to be a reasonable choice. Preexponential factors are determined by the local characteristics of motion such as jump distance and rate of jump attempts. Thesequantitiesshould not vary from sampleto sample if the local environment does not change much. One might expect for the partially covered sample (see Figures 4 and 6) that the increase in the diffusion rate (about a factor of 5 at the temperatures studied) probably is due to a vacancy mechanism which would modify the preexponential factor as well as the activation energy for diffusion. In solids, the vacancy concentration is determined by an activation energy for the formation of a vacancy. In our samples, even the saturated
TABLE I: Fraction of Moving Molecules and Activation Energies for Diffusion for the Different Samples sample G O Ed (kcal/mol) PtllCO 0.5 0.07 6.5 0.5 Pt23CO 0.4 f 0.10 7.4 0.7 Pt73CO 0.4 0.05 10.5 1 Pt7 3C030% 0.5 0.07 9.6 1
* *
samples have some empty sites available (saturation coverage is approximately50% of the surface sites). It is difficult to estimate the preexponential factor in the saturated sample and thus how it gets modified when the amount of gas is reduced. In a simple picture in which only jumps to nearest unoccupied sites are allowed, we would expect that the preexponential factor should have a dependence on coverage like 1 - 8, where 8 is the coverage (expressed as a fraction of full coverage). However, if only motion of bridge-bonded CO is allowed, we do not know the values of 8 even for unsaturated samples. We can only predict that the preexponential factor for the unsaturated sample should be somewhat larger. To prepare Table I, we have assumed that the preexponential factor is the same for all the samples, although it might be somewhat off for the partially covered sample. The activation energy in Table I for the partially covered sample is then an underestimate of the value. Table I also presents the fraction of moving CO as well as the activation energies for diffusion for each sample. The first striking result from Table I is the lower activation energy for diffusion for the large clusters (PtllCO, Pt23CO). Its value is close to those cited for the case of CO on Pt( 111) planes: 7 kcal/mol. This probably reflects the fact that the surfaces of large clusters resemble single-crystal planes. By contrast, the small clusters (Pt73CO) have higher activation energies for diffusion which may reflect how their surfaces differ from single-crystal planes: a large fraction of the surface sites which exist are edges and corners. There may be a slight difference in C, for the large cluster sample (PtllCO) and the small cluster one (Pt73CO). The smaller fraction of moving CO on Pt73CO may be due to CO bonded to edges and corners, these sites have been associated with linear sites and represent a larger fraction of all sites in the small clusters. In our model, CO bonded to those sites should remain immobile in the temperature range studied here. We expect then to observe a smaller fraction of moving CO on small clusters where there are more edges and corners. Having a larger activation energy for diffusion for small clusters will contradict the model described in the Appendix in which we assumed that CO has the same dynamic characteristics of motion regardless of particle size. To justify our assumption, we look into the distribution of clusters accordingto diameter. We found that for Pt73CO the distribution is narrow enough that we can assume a singlecluster size. There is no overlap in the distribution of clusters between PtllCO and Pt73CO (Figure 7). Furthermore, the sample Pt23CO has a different distribution of clusters than Ptl 1C0, Pt23CO has a distribution of clusters that roughly representsa subset of the Pt 11CO sampleemphasizingthe smallclusters region. We can test if all the clusters in PtllCO give the same characteristics for the diffusion of CO by comparing Pt23CO with Ptl 1CO. We see from Table I that the differences are small and that it is permissible to assume for PtllCO that CO has the same properties of motion regardless of cluster size. The preexponential factor DZ gives us the diffusion constant in frequency space. In real space, the diffusion constant D, can be calculated using eq A1 5 from the Appendix in which we work out the relationships between a jump on the surface ("real" space) and its equivalent in frequency. With DZ = 2 X 101 s-3, we get for 0,": Di = 6 X lo-' cm2 s-' (5) In single-crystal studies, it was found that D, 10-9-1W cm2 g1.m
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12018 The Journal of Physical Chemistry, Vol. 97,No. 46, 1993
that 6w,j is independent of 8, the polar angle which describes the location of the CO molecule on the particle. Unfortunately, there is no explicitway to calculate the frequencyof a CO molecule as a function of 0 and to determine 6wj,,(8) accurately. Our assumption therefore relies on the size and shape of the particle being such that a single jump results in a small 68 and a correspondinglysmall 6wjump.swhich therefore leads to a frequently independent 0,. We have made attempts at accurately including 8 dependencies and found that the results are not significantly changed. In solving eq A2, the initial condition M,(o,t) is that M,(w) is modulated by sin(wTprcp):
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Becerra et al.
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Figure 7. Calculated cluster size distribution according to diameter for different dispersions. The average diameter for each dispersion is also shown.
Conclusions We implemented an NMR sequence (which we call the 'Sshape sequence") capable of detecting diffusion of CO on metal surfaces. The sequence has the advantage of preparing the spins in a time short compared to other sequences and hence enables us to detect faster rates of diffusion. We applied the S-shape sequence to CO molecules adsorbed on Pt clusters. We explored the possibility that not all the molecules diffuse on the surface at the same rate. We have results, for the range of temperatures studied here, that show that about 50% of the molecules diffuse while the others remain fixed. We conclude that bridge-bonded CO molecules are moving among bridge sites while linearly bonded CO molecules remain at rest. We determined the activation energy for diffusion for samples of different cluster distributions. For the small-cluster sample (Pt73CO), we found a higher activation energy for diffusion than for the large-cluster one (Ptl 1CO). The activation energy for diffusion for Pt 11CO is close to that found in single-crystalstudies (7 kcal/mol). We attribute the larger activation energy for diffusion on smaller clusters to CO linearly bonded to edges and corners. Acknowledgment. We are grateful to the IBM Corp. for providing a Fellowship (held by L.R.B.) to assist our work. This research was supported by the Department of Energy, Division of Materials Science,under Contract No. DEFG02-8 1ER45439. Appendix The rate equation that describes the recovery of the magnetization in NMR is given by the Bloch equation:
dM,(w) - M,(w) - M,(w) --
(All dr Tl where M,(w) is the magnetization along the Z axis with resonant frequency w , Mo(w) is the equilibrium value of M,(w), and TIis the spin-lattice relaxation time and is the same for all l3C nuclei. M,(w) might be taken as the function that describes the line shape. To this equation, a diffusion term should be added: dM,(w) -- Mob)- M J w ) + D,-a21Cl,(4
M,(w,t=O) = Mo(o)sin(wTprcp) (A31 0 3 , the magnetization should have its equilibrium
(A21 dt T, aw2 where 0,is the diffusion coefficient in frequency space. We assume in eq A2 that the change in frequency due to a jump is small compared to the total line width (i.e,, 6wj,,
