ARTICLE pubs.acs.org/JPCC
Kinetics of Nitric Oxide Adsorption on Pd(111) Surfaces through Molecular Beam Experiments: A Quantitative Study Sankaranarayanan Nagarajan,† Kandasamy Thirunavukkarasu,†,§ Chinnakonda S. Gopinath,*,† and Sudarsan D. Prasad*,‡ †
Catalysis Division and ‡Physical Chemistry Division, National Chemical Laboratory, Dr. Homi Bhabha Road, Pune 411 008, India ABSTRACT: A detailed kinetic picture derived by molecular beam studies of the adsorptiondesorption of the NO/Pd(111) system is presented. Numerical simulations and detailed kinetic analysis show that the precursor state model of adsorption provides a valid picture of the sticking coefficient variation with surface coverage, especially at low temperatures. At higher temperatures, the precursor model gives way to the Langmuir molecular model of adsorption. All the parameters of the precursor state model have been quantified. Temperature programmed desorption (TPD) studies further show that there is a slight repulsive interaction between adsorbed NO molecules and there is only a negligible fraction of dissociated molecules on the surface for temperatures less than 500 K, as the Pd(111) surface is defect free. A BraggWilliams (BW) lattice gas model with repulsive interactions, within the framework of mean field approach (MFA), is shown to describe the TPD spectra reasonably well.
1. INTRODUCTION Invention of three-way automotive exhaust control catalysts has been one of the crowning achievements of modern day catalysis. Reduction of the NO to N2 (often called deNOx catalysis) is an integral part of the catalyst spectrum. Often there is a trade-off as the air-rich fuel is necessary for complete oxidation of CO and volatile organic components, which is mandatory in all modern (Euro III low emission vehicles and ultralow emission vehicles) emission norms.1 In sharp contrast to this, fuel-rich conditions favor the reduction of NO, which is an important constituent of photochemical smog.24 Sophistication in the design of novel catalysts, especially effective under net oxidizing conditions, such as zeolite-based ones with a NOx storage function, is increasing.5,6 Introduction of Pd is comparatively a recent development, nevertheless it is the focus of several studies.712 Pd has several advantages over Rh in effectively reducing NOx to N2 even at oxidizing conditions, including a cost advantage. There have been several papers dealing with the fundamental aspects of NO reduction with CO on Pd, including Pd(111), which is the most active plane for the NO + CO reaction among the Pd surfaces.913 N2O decomposition that occurs as an intermediate step has also been pursued. It has been claimed that defect sites are particularly active for NO decomposition but nevertheless has been shown to occur even on atomically smooth Pd(111) planes.9,11,12 There has been a paucity of studies in the fundamental aspects of NO adsorption, especially with techniques involving molecular beam instrument (MBI).12,16,17 MBI can measure absolute sticking rates and coefficients with high accuracy, under ultrahigh vacuum (UHV) conditions needed for maintaining surface cleanliness. MBI has been shown to be an effective tool in unraveling the elementary steps in a catalytic reaction sequence. It has been suggested by experimental10,14,15 and theoretical studies18 that r 2011 American Chemical Society
NO occupies face-centered cubic (fcc) hollow sites at low coverage, a mixture of fcc and hexagonal close packed (hcp) sites at intermediate coverage and on-top sites in addition to the above sites at high coverages. NO adsorption kinetics on Pd(111) surfaces has been studied by very few groups. Schmick and Wassmuth19 measured NO adsorption kinetics on stepped Pd(111) surfaces and concluded that the initial sticking coefficient was neatly fitted by the precursor state model for just one temperature. In contrast to their work, we are using a defect-free Pd(111) surface as a model surface over a large range of temperatures. Recently we have undertaken a systematic study of the different aspects of NO adsorption and NO + CO reactions on Pd(111) surfaces.1012 The present communication is a part of our ongoing efforts to understand the molecular level aspects of three-way catalytic converter reactions, with a view to designing better automotive exhaust control catalysts.2023 The work is presented as follows: First, we develop detailed equations for the variation of the chamber partial pressure as a function of dose rate, pressure, and pumping rate for three kinetic models. Then we solve the two-coupled differential equations for the gas-phase concentration (partial pressure) and also the surface concentration (fractional surface coverage). The sticking coefficients will be estimated to show that the precursor state model is valid for low temperatures. The Langmuir model is perhaps more appropriate for the high temperature regime when desorption also starts becoming appreciable. Further, temperature-programmed desorption (TPD) studies have been made to understand the state of NO adsorption on Pd(111), viz., Received: April 29, 2011 Revised: June 29, 2011 Published: July 19, 2011 15487
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predominantly molecular with perhaps only a small fraction dissociating at high temperature.
2. EXPERIMENTAL SECTION, FORMULATION METHODS AND MODELS For the purpose of quantitative analysis, we assume a defectfree Pd(111) surface. So the effects of surface heterogeneity and intermolecular interactions (dipoledipole interactions) among the adsorbed NO molecules are ignored, especially in the initial part of (low coverage) adsorption. However, for the analysis of the TPD spectra, where we start with a high initial surface coverage, we do have to take into account the role of adsorbateadsorbate interactions. Three models will be employed for the data analysis.2538 These are (a) the molecular Langmuir model (MLM), (b) the dissociative Langmuir model (DLM), and (c) the precursor state model (PSM). We will, in turn, examine the validity of each of these models, in providing a valid picture of NO adsorption. In the initial stages of adsorption, desorption is not appreciable, and hence we are essentially measuring adsorption (sticking rates). The rate of change of surface coverage with time for each of these models is MLM2528 ra ¼
dθ ¼ kma Pð1 θÞ kmd θ dt
ð1Þ
DLM2528 ra ¼
dθ ¼ kda Pð1 θÞ2 kdd θ2 dt
ð2Þ
PSM23,24,39 dθ ¼ SðθÞFt dt
ð3aÞ
SðθÞ ¼ ðθmax θÞðθmax ð1 kÞθÞ1 Ft
ð3bÞ
In eqs 1 and 2 ra denotes the net rate of adsorption and P m represents the partial pressure of NO in the chamber. km a , kd , and θ represent the kinetic constants for adsorption, desorption, and the surface coverage, respectively. If N0 is the total number of adsorption sites, and NS is the number of adsorbed molecules, then θ = NS/N0; this is the coverage (θ) definition adopted throughout this work. In eqs 3a and 3b, we do not account for desorption; as in PSM, under conditions of the experiment, it does not contribute appreciably. This assumption is valid for the sticking coefficient measurements in the initial part of adsorption. This is also true, likewise, for the MLM and DLM too. Ft is the total flux striking the crystal including the random background flux. In addition to these, for the gas phase, we have a separate mass balance V dP=dt ¼ Ft π N0 ra λe P
ð4aÞ
Ft ¼ F0 þ Fb
ð4bÞ
where V represents the volume of the chamber, Ft, the total flux from the doser and background in molecules/(s 3 cm2) and the capacity factor π, which depends on the distance between doser tip and the surface, and the solid angle extended by the doser to the adsorbing Pd(111) surface. In our experiments, Vo = 12.2 L, and the diameter of the crystal disk is 8 mm. ra is the net rate of
Figure 1. (a) A typical gas phase profile vs time for NO adsorption. Note the shallow basin-like structure, especially at low temperatures, suggesting the precursor state model (PSM). (b) Graph illustrating the log plot of chamber pressure vs time for pumping speed (mass flow rate) calculation.
adsorption, which is the rate of adsorption minus the rate of desorption. N0 is the total number of adsorption sites present on the defect-free Pd(111) surface. F0 and Fb represent the flux from the collimated molecular beam striking the surface and the random background flux striking the crystal in that order. Fb is only a few percent of the total flux, Ft, in most of the experiments. For accurate flux calibration and finding the F0, π, the flux from the doser and the fraction impinging on the crystal, respectively, we employed a standard procedure involving the condensation of cyclohexane at low temperature.16 The capacity factor π is determined to be about 0.45 as shown in the previous work.16 λe is an effective pumping constant involving the pumping speed of the turbopump and the mass flux through it. It also depends on the conductance of the pipe connecting the vacuum chamber to the turbo molecular drag pump. In all the experiments, the clean Pd(111) metal surface was kept at a constant temperature and exposed to an effusive NO molecular beam. All the relevant gas-phase species formed during the reaction are detected by a quadrupole mass spectrometer as a function of time. Typical experimental details are available in our earlier publications.11,12,16,23 In a typical molecular beam adsorption experiment, the NO molecular beam was first allowed to enter the UHV chamber with the shutter in a closed position to block the surface, so as to avoid the direct interaction of NO molecules and the Pd(111) surface (Figure 1a). Still, a small amount of NO adsorption from the background cannot be prevented. After a few seconds, at t = 14 s, the shutter was removed to allow the beam to directly impinge on the Pd(111) surface. An instantaneous decrease in the partial pressure of NO for the next few seconds can be noticed in the mass signal as a result of NO adsorption on Pd(111) surface from the beam (Figure 1a). This adsorption in the transient state continues until the surface is saturated with NO. Sticking probability and coverage calculations have been carried out by a method described in detail (see eq A1) by Zaera et al.23a Briefly, the time dependence of the sticking probability, S(t) is calculated by using the formalism originally proposed by 15488
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Madey in 1972.24 According to Madey SðtÞ ¼
1 Peq ðtÞ PðtÞ 1 ΔPðtÞ ¼ π Peq ðtÞ Pbase ðtÞ π Peq ðtÞ Pbase ðtÞ
ðA1Þ
where P(t) denotes the NO partial pressure measured experimentally, Peq(t) represents the NO partial pressure expected if the direct beam was blocked (calculated by a least-squares method), Pbase(t) is the original base pressure, and π is the fraction of impinging NO flux intercepted by the crystal surface. The fraction of the impinging reactant molecules has already been measured and given in our earlier publication.16 For further details of the calculation, previous reports23 may be referred to. PSðθÞ ra ¼ F0 πSðθÞ þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rd 2πmRT
ð5Þ
where ra and rd represent the net adsorption rate and the desorption rate, respectively. S(θ) represents the sticking coefficient and varies with a functional depending on the adsorption model chosen (see eqs 13). At higher temperatures, when the desorption becomes significant, the sticking coefficient (which measures only the adsorption) becomes irrelevant, and the net adsorption rate ra becomes more meaningful. The first and second terms on the right-hand side of eq 5 represent the adsorption rate from the collimated molecular beam and background adsorption from the chamber due to the random diffusive flux, impinging on the surface, respectively. At steady-state conditions, when we have ra ¼ 0 V
ð6Þ
dP ¼0 dT
ð7Þ
F e ¼ λe P e
ð8Þ
where F and P represent the equilibrium flux of the doser, and the pressure in the chamber, respectively. Equation 8 provides a relationship between doser flux and the pumping speed λe, which is independent of the temperature. We also make use of eq 8 to eliminate the flux term and rewrite eq 5 as e
e
dP ¼ λe ðPe PÞ ra ð9Þ dT At this juncture, we bear in mind that neglecting the random flux in eq 5 only causes a marginal change in the gas phase temporal profiles and can be safely neglected in actual numerical computations. Equations 5 and 9 have to be simultaneously solved to predict the evolution of the pressure, once the doser is on until the point at which P = Pe. Once, this steady state has been reached (eq 6), from this point onward, the gas and surface phase concentrations remain invariant with time (see Figure 1) The numerical value of the flux Ft is of the order =1014 molecules/(s 3 cm2). This is the total flux Ft which is typical for showing maximum variation in the pressure versus time. Figure 1a represents a typical gas phase temporal profile for the NO adsorption. Notice the sudden dip in the concentration, once the shutter is opened, signaling the onset of rapid adsorption. Notice the “basin”-like structure, especially at the low temperature runs. This implies that the gas phase concentration of NO remains constant for a considerable period of time before it suddenly rises again. This demonstrates an almost constant rate of adsorption, viz., a constant sticking coefficient, especially in the V
initial part of adsorption. This is a typical feature of the PSM for the sticking coefficient of adsorption. Further, the well depth and breadth decrease with increasing temperature, as it should, as the competing desorption increases substantially with temperature from 375 K and above. At T g 400 K, the PSM is no longer adequate and the basin-like feature disappears.12 A few words are in order regarding the estimation of the pumping constant, λe, which is of great interest in the quantitative analysis. At t = 75 s, the doser is switched off, and hence the molecular beam flux is stopped. Some background adsorption will still occur, as implied by the second term in eq 5. The molecules pumped out by turbopump will be much larger than that disappearing by readsorption. The pressure will fall exponentially, as implied by eqs 10 and 11. V
dP ¼ λe P dT
ð10Þ
as ra = 0
e λt P ¼ Pe exp V
ð11Þ
Thus the plot of ln P versus time will yield a straight line which can be used for the estimation of the effective pumping constant λe. (In our experiments λe is of the same order as Ft.) Figure 1b indeed shows that the above relationship is valid and directly leads us to the pumping speed in a straightforward least-squares procedure using a simple logarithmic transformation. As is shown in the inset in Figure 1b, some tailing of the gas phase concentration is evident at higher times, due to desorption from the walls, but this can be corrected by a least-squares fitting of the background to a linear relationship. However, the exponential fall (implied by eq 11) means that the experimental pressure values immediately after the closing of the shutter of the doser is important in evaluating the pumping speeds, and rightly gives us this quantity. 2.1. Numerical Procedures. The governing equations for the temporal profiles, viz., eqs 15 and the concise eq 9 cannot be integrated analytically, except under very restrictive conditions. So we employ a fourth-order RungeKuttaGill algorithm to numerically integrate the relevant equations in simulations. A standard package from a Fortran Library was used. Representative parameter values are used from the literature to get a feel of the “temporal profiles” of both the gas and surface phases for the NO/ Pd(111) system. Also, some smoothening procedures are needed to numerically compute the amount of adsorbed NO as a function of time. Figure 2 illustrates the point for a typical molecular beam experiment. Basically it is equivalent to computing the areas of the “basins” shown in Figure 1a for various temperatures. Due to the presence of experimental noise, the raw data have a typical sawtooth structure, which has been smoothened by a fivepoint sliding data window. Further, a nine-degree polynomial fit was carried out. The time integrals of the gas phase concentration were then evaluated by termterm analytical integration of the fitted polynomial, which is fairly straightforward. This, in turn, was compared with a standard GaussLegendre Quadrature computer package for the numerical integration of the temporal profiles, which only needs inputs of the smoothened data in an ASCII format. The agreement between both these methods was within a few percent, which is of the same magnitude as the experimental error variance, thus illustrating the validity of the procedure. 15489
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be easily expressed as θ ¼ 1 eðS0 Ft =NÞðt t0 Þ
ð17Þ
t0 is the extent of time origin shift needed to get physically meaningful surface coverages. This is because, immediately upon blocking the beam, there is a noticeable pressure surge, which gives to many artifacts, manifested by even a transient increase in the sticking coefficient as a function of surface coverage. This unphysical artifact has to be ignored for quantitative treatment. In giving these analytical expressions, we bear in mind that, since dissociation is not observed, we are not considering DLM. However, for the sake of completion, we will also consider the DLM in the next section for computer simulation. Figure 2. A typical experimental concentration profile of NO vs time in the gas phase. The raw data with sawtooth is first smoothened by a five point interval averaging and fitted by a nine-degree polynomial (line).
2.2. The Adsorption Rate Models. We roughly classify the adsorptiondesorption events involving NO in three regions, viz., (i) the region where the PSM is valid (eqs 3a and 3b), (ii) the region where molecular adsorption occurs as reflected in the MLM (eq 1), and (iii) the region where dissociation occurs, where the DLM is valid (see eq 2). In most of our studies, the last regime is seldom encountered. Accordingly, we first stimulate the pressure profiles of each of these models with representative values. The PSM can be written as
rads ¼ Ft SðθÞ
ð12Þ
SðθÞ ¼ S0 ðθmax θÞðθmax ð1 kÞθÞ1
ð13Þ
Here the θ denotes the maximum surface coverage and k is the kinetic constant ratio, which is a characteristic of the PSM. It would be interesting to analyze the temporal profile of the θ(t) as a function of time, within the framework of the PSM. To achieve this end, we integrate the following equation. max
dθ ¼ S0 ðθmax θÞðθmax ð1 kÞθÞ1 Ft dt
ð14Þ
ð1 kÞθ k lnðt max θÞ ¼ t Ft Ft
ð15Þ
t is the time at which, the surface coverage tends to θ , i.e., saturation. 2.3. The Molecular Langmuir Model (MLM). True to its name, the precursor state gradually leads to a more strongly chemisorbed layer, which can be described by Langmuir kinetics. This is especially true at higher temperatures. The new governing equation is given by max
N
3. RESULTS AND DISCUSSION 3.1. Computer Simulation of Adsorption Models. First, we analyze the PSM (Figure 3, panels a and b) which describes the gas phase and surface concentration profile of NO as a function of time. The impinging gas flux Ft is normalized to a scale of 1, the effective pumping constant λe = 0.5, and the remaining constants indicated on the figure are the lumped rate constants, which in effect reflect the rate processes. In absolute units, it amounts to a molecular beam flux of the order of (14) 1014 molecules/ (s 3 cm2). These figures are simulated profiles, representative of our experimental conditions. The lumped rate constant (k) appearing in panels c and d of Figure 3 accounts for the probability of adsorption and desorption from the precursor state and also of the migration to another vacant site in the precursor state. Notice that as the precursor state constant (k in eqs 13 and 14) becomes smaller, the sticking coefficient shows a constant region, independent of surface coverage, exhibiting the “basin-like feature” in the gas phase concentration vs time profile mentioned as above (see Figure 1a). Panels c and d of Figure 3 display the sticking coefficient variation with respect to time and surface coverage for the PSM. When k = 1, the S(θ) vs θ plot becomes identical with the Langmuir model, as it should. Subsequently the plot becomes linear, as will be shown later, in computer simulation studies. It is common knowledge (ref 39 as and in particular ref 23a) that the precursor state constant k in eq 3b is not a simple constant but is as given by Zaera et al.23
k¼
max
dθ ¼ S0 ð1 θÞFt dt
ð16Þ
where N is the total number of adsorption sites and So is the initial sticking probability. This is because in the shallow basins of Figure 1a, the overall coverages are in general small. Here, we are neglecting the desorption events and are concerned only with the process of adsorption. Equation 16 can be easily integrated and the surface coverage as a function of time can
kd kd þ km
ð18Þ
0
1 km ½Em Ed 1 ¼ d0 exp k RT k 0
ð19Þ 0
where km, kd, Em, Ed, km , and kd represent the rate constants, activation energies, and the pre-exponential factors for migration on the surface and desorption to the gas phase from an extrinsic precursor state in that order. The k values for the precursor state vary from (T = 300 K, k = 0.0507) to (T = 400 K, k = 0.687). As said before, at some intermediate temperature when k becomes unity, Langmuir kinetic behavior will be observed. The parameters are presented in Tables 1-3 In panels f and g of Figure 3 the Arrhenius plots for the precursor and the modified kinetic constant 1/kprec 1 are shown. The Arrhenius plot in Figure 3f, even though it looks 15490
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Figure 3. (a, b) Typical gas phase concentration and surface coverage variation profile vs time for NO with the precursor state model (PSM). (c, d) Variation of the sticking coefficient with time and surface coverage for the PSM. (e) Plots illustrating the excellent fit of the sticking coefficients as a function of surface coverage. Note that higher temperature data T > 375 K can be as well fitted by a MLM. (f) Arrhenius plot for precursor state kinetic constant. (g) Arrhenius plot for the modified precursor state kinetic constant 1/kprec 1. (h) Precursor state constant curve fitted (eq 18) as a function of temperature to estimate the activation energies and pre-exponential factors of km and kd.
Table 1. Precursor State Constant “k” as a Function of Temperature T Ka
a
T, K
k
300
Table 2. Pre-Exponential Factors and Activation Energies for k and ((1/k) 1) of the PSM rate constant
Eo, kcal/mol
0.0507 ( 0.0045
k
6.28 ( 0.173
103.28(0.11
325
0.1167 ( 0.008
((1/k) 1)
8.76 ( 0.683
105.038(0.43
350
0.218 ( 0.016
375
0.452 ( 0.0381
400
0.687 ( 0.107
Initial sticking coefficient So = 0.52 ( 0.04.
good, is not very rigorous, as kd < km, k ≈ kd/km, and kd can be neglected in the denominator of eq 18. On the other hand, plotting ln((1/k) 1) vs 1/T, is a rigorous procedure, (see Figure 3g) but again has a shortcoming, as only EdE m0 can be 0 measured. Also the ratio of pre-exponential factors km /kd will be
pre-exponential factor
less than unity. The positive value of EdEm results in an unusual Arrhenius plot with a positive slope, but there is nothing unphysical, as we are measuring EdEm . Another independent way of doing this is to fit eq 18 as a function of temperature and estimate all Ed and Em parameters directly. Figure 3h indeed displays an excellent fit, and the parameters are presented in Table 3. The excellent agreement of the pre-exponential factor and the activation energy arrived at by two independent means, viz., by Arrhenius plot in Figure 3g and 15491
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by curve fitting in Figure 3h, shows that the procedure is selfconsistent, as is easily seen from Table 3. The Arrhenius plot gives EdEm values 9.44 ( 0.683, compared to 10.3 ( 0.01 obtained from the curve fit. The corresponding values for the preexponential factor are 3.64 106 and 1.2 106, respectively, demonstrating the consistency of the procedure. We bear in mind that the experimentally measured precursor state kinetic constant is a lumped rate constant, weighing the different probabilities for desorption, migration, and also adsorption on a preadsorbed adsorption site. The activation energy for the precursor state kinetic constant is about 6.40 ( 0.14 kcal/mol. A similar analysis and interpretation of the precursor state kinetic constant has been carried out by Zaera et al. in the previous work employing molecular beams.23 We may add that the Kisliuk model works in the low gas phase flux (low surface coverage) limit and, therefore, does not work very well at high surface coverages as shown by Zhadnov et al.37 Herein the sticking coefficient S(θ), θ behavior is far more complex than predicted by the simple precursor state model PSM. Panels a and b of Figure 4 describe the simulated profiles of gas and surface phase NO concentrations within the purview of the MLM. The dips in the gas phase concentrations are much sharper Table 3. Pre-Exponential Factors and Activation Energies for km, kd [see eq (18)] Obtained by Curve Fitting k vs T for the PSM rate constant
pre-exponential factor, s1
d
k
1.02 10 ( 10
km
12.3 ( 0.13
curve fittingb Arrhenius plota a
7
5
activation energy, kcal/mol Ed 10.9 ( 0.002 Em 0.6 ( 0.001 0
0
Ed Em, kcal/mol
km /kd
10.3 ( 0.001 9.44 ( 0.683
1.2 106 3.647 106
From Figure 3g. b From Figure 3h.
in the MLM (when compared with PSM). Panels c and d of Figure 4 analyze the S(t) and S(θ) behavior with respect to time and surface coverage in that order. The most notable feature is the straight line fall of the sticking coefficient with respect to the surface coverage for the MLM. In Figure 4e, the experimental gas phase concentrations are fitted to an MLM. As has been shown in previous simulations, the fitting of the pressure P(t) profiles is not very sensitive to the finer details of the adsorption model, irrespective of whether they are PSM, MLM, or DLM. The simulated profiles of the gas phase and surface concentrations within the framework of the DLM are presented in panels a and b of Figure 5. The sticking coefficient behavior with respect to t and θ is revealing entirely different pictures for the DLM and MLM (see Figure 5c,d). In fact, the last point further shows that a judicious study of the sticking coefficient versus θ is the best way of discriminating between PLM, MLM, and DLM. In addition, TPD studies of adsorbed NO on Pd(111) will tell us whether the molecule is dissociated to an appreciable extent. Below 400 K, dissociation is not appreciable, in any case, as pointed out by several groups including that of Ertl.26 kL and kD represent the relative values of kinetic constants for adsorption in the MLM and DLM scaled to a flux Ft of unity. So far, in these simulation studies, the effect of surface heterogeneity has been neglected.2738 The adsorbateadsorbate interactions30,32,33,37,38 which are important, especially at high coverages, do not much matter in these simulations of transient adsorption, as most often the surface coverages in our experimental conditions remain low, for most of the runs. However, after a long period of time when the surface coverage has been allowed to attain saturation, and subsequently when we do TPD experiments, adsorbateadsorbate interactions do matter. We are not considering surface heterogeneity,29,31 as our surface is defect free, in contrast to a previous study where NO adsorption has been considered.19
Figure 4. (a, b) Typical gas phase concentration and surface coverage variation profile vs time for NO when the molecular Langmuir model (MLM). (c, d) Variation of the sticking coefficient with time and surface coverage for the MLM. (e) Relative amounts (arbitrary units) adsorbed vs time fitted by the molecular Langmuir model. 15492
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Figure 5. (a, b) Typical gas phase concentration and surface coverage variation profile vs time for NO, when the dissociative Langmuir model (DLM) is simulated. (c, d) Variation of the sticking coefficient with time and surface coverage for the DLM.
The sticking coefficients estimated from the concentration profiles can be neatly fitted by the PSM. A reference to panels d and e of Figure 3 clearly shows that for NO adsorption on Pd(111), the sticking coefficient variation can be neatly represented by eq 13, except for the high temperature data above 400 K; indeed the plots show excellent agreement with the PSM. 3.2. Temperature-Programmed Desorption. In TPD, the surface temperature T is uniformly increased in a linear temperature ramp as a function of time39 T ¼ T0 þ βt
ð20Þ
where β is the heating rate. In our own studies, β has been kept at a constant value of 10 K s1. Since equilibrium adsorption decreases with temperature, the evolving desorption profile clearly gives a measure of the underlying desorption kinetics, viz., molecular (first order) or associative (second order). This, in turn, is monitored as a function of the pressure rise in the vacuum chamber. For our experimental system NO/Pd(111), there has been a lot of supporting evidence to suggest molecular (nondissociative) adsorption. Therefore, we would expect, a priori, essentially firstorder kinetics to prevail, viz. dθ ¼ Kd θ ð21Þ dt TPD studies have been carried out mainly to diagnose dissociation or the absence of it. The presence of interaction between adsorbed molecules (especially due to NONO dipole repulsion) adds one more interesting complication to the interpretation of TPD profiles. In the absence of adsorbateadsorbate interactions,39 an asymmetrical TPD profile suggests MLM.31 In sharp contrast to this, a symmetric TPD profile suggests DLM, as the molecule fragments (which are present with equal concentrations on the surface) have to recombine to form the original molecule, before it can desorb to the gas phase. However,
neither of these statements is true when adsorbateadsorbate interactions are present. This is also true, irrespective of whether repulsive or attractive interactions are operative. A large body of experimental evidence and previous studies suggest that there are repulsive interactions between NO dipoles, resulting in the broadening of the TPD peaks. We use a Bragg Williams lattice gas model,27,28 within the framework of the MFA27,28,33 to model desorption. This is necessary, as the starting coverage is large in most of the TPD studies. With these considerations, the governing equations are V
dP dθ ¼ N λe P dt dt
ð22Þ
dθ dt
ð23Þ
rd ¼ N
for large pumping rate λe, V(dP/dt) = 0, and we also keep in mind of a linear temperature ramp, viz. T = T0 + βt (see eq 20). Further, within the BW model dθ E0 Rθ θ ð24Þ rd ¼ N ¼ Nυ0 exp dt RT Equating the rate of desorption, equal to the pumping rate, finally we get N
dθ dθ ¼ Nβ ¼ λe P dt dT
βNυ0 E0 Rθ P ¼ exp θ RT λe
ð25Þ ð26Þ
Note that the sharpness of the TPD profile is dependent on the pumping speed and also on the adsorbateadsorbate interaction parameter R within the BW-MFA model,3237 and the 15493
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Figure 6. Simulated surface coverages and desorption rate as a function of the interaction parameter R (repulsive) for various temperatures for BW lattice gas model.
Figure 7. Fit of desorption rate for BW lattice gas model at (a) T = 300 K, and (b) T = 325 K.
activation energy Eo, at surface coverage extrapolated to zero. υ0 is the frequency factor which is of the order of 1013 s1. In our simulations, we proceed as follows. First from a rough Redhead39-like TPD analysis, we have E0 ¼ 230T m =KJ
ð27Þ
This value is used as an initial trial value, so as to match the computed TPD profile temperature maximum Tm with the experimentally observed one. Before we undertake detailed comparisons with the experimental TPD profiles, it is instructive to have a detailed simulation of expected behavioral patterns. Figure 6 precisely does this. We have chosen representative values of interaction parameter and
Eo = 30.2 kcal/mol, and the pre-exponential factor is 1013. It is very evident that the width and the Tmax (temperature maximum) of the TPD profile depend a lot on the value of the interaction parameter R (see Figure 6). When repulsive interactions are present, the temperature maxima of the TPD should shift to lower temperatures with increasing values of R parameter, as evident from the figures. We find that the best agreement with the experimental TPD profile is obtained with E0 = 30.2 ( 0.6 kcal/mol and a preexponential υ0 of 1013(1. This is in close agreement with previous studies from Ertl’s group.26 However, the value of the BW interaction parameter R is about 1.5 kcal/mol, which is slightly smaller than their reported value. In all probability this high 15494
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The Journal of Physical Chemistry C temperature state corresponds to a “random disordered state” of the adsorbed NO molecules. Actual detailed comparison shows that there is a discrepancy between the experimentally observed width of the TPD profiles and the computed ones, as shown in Figure 7. This may partially arise from the presence of a small percentage of surface defects which may add to the broadening of the peak. Since this is mainly observed at high temperatures, it is obvious that as “surface roughening” is more likely to be large at higher temperatures, rather than at lower temperatures.
4. CONCLUSIONS Molecular beam experiments of NO adsorption on Pd(111) surfaces have been subjected to quantitative kinetic analysis. Numerical simulations show that the gas phase concentration time profiles are not very sensitive to the choice of the detailed kinetic model. On the other hand, a judicious study of the sticking coefficient vs surface coverage reveals that the precursor state model is adequate, especially at low temperatures. We have validated the PSM with full quantification of all the relevant parameters, and this constitutes a novel feature of the present work. At high temperatures, this model in turn, gives way to the Langmuir model of adsorption, as it should. TPD studies further show that, since the surface is virtually defect free, decomposition of NO occurs to a negligible extent. A BraggWilliams lattice gas model with weak repulsive adsorbateadsorbate interactions between the NO dipoles is shown to describe the TPD, gas-phase concentration temporal patterns fairly well. ’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected], www.ncl.org.in/csgopinath (C.S.G.);
[email protected] (S.D.P.). Present Addresses §
National Centre for Catalysis Research, Indian Institute Technology, Madras, Chennai 600 036, India.
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