J. Phys. Chem. 1995,99, 14893-14902
14893
Diffusion-Controlled Reactions of Molecular Oxygen on Porous Silica Glass: Coverage Dependence of Reaction and Diffusion Rates and Evidence for Surface Heterogeneity Ohad Katz, Joshua Samuel, David Avnir,* and Michael Ottolenghi* Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel Received: May 30, 1 9 9 9
At relatively low temperatures (T I 130 K) and low coverages the bimolecular, fluorescence quenching, reaction of Ru(bpy)32+by molecular oxygen on porous silica surfaces is essentially Langmuir-Hinshelwood (LH) as well as diffusion controlled. We have studied the reaction on controlled porous silica glass, with an average size of 95 8, (CPG-75), over the 80-253 K temperature range, varying the degree of 0 2 coverage. An analysis of the second-order quenching rate constants was carried out based on the classical expressions for diffusion-influenced and diffusion-controlled reactions. As the temperature is increased above 130 K, the reaction turns from diffusion-controlled to diffusion-influenced, with substantial contributions from both diffusion and activation terms. Above 160-190 K (at high coverages) the mechanism becomes substantially Eley-Rideal (target annihilation) in nature, preventing the separation of the LH component from the overall rate constant. The rate constants in the predominantly diffusion-controlled range (75- 125 K, at low coverages) were analyzed using the two-dimensional (Smoluchowski-type) diffusion model of Freeman and Doll. The treatment leads to the determination of the diffusion coefficient (0)of 02 adsorbed on the porous surface. The diffusion-controlled rate constants and the corresponding diffusion coefficients are found to be markedly affected by the degree of 02 surface coverage. This behavior is accompanied by an analogous coverage effect on the 0 2 heat of adsorption (Q). The findings are interpreted in terms of the heterogeneity of adsorption sites which leads to the preferential occupation of high Q and, consequently, low D locations. We therefore demonstrate that the mechanism of diffusion-influenced LH reactions on amorphous solid-gas interfaces may be tuned by both temperature and degree of surface coverage. N
Introduction Diffusion-influenced or diffusion-controlled processes, in which the rate of the reaction is affected by the mutual diffusion of the reactants, are well characterized in homogeneous solutions. Much less is known, however, on the mechanism of diffusion-controlled (DC) reactions in nonhomogeneous media such as interfaces, especially in the case of amorphous solids. A primary goal in defining a diffusion-controlled reaction at a solid-gas (or solid-liquid) interface is that of identifying a system in which the reaction is exclusively surface bound, obeying a Langmuir-Hinshelwood (LH) type mechanism.’ Due to the contribution of target annihilation of Eley-Rideal (ER) mechanisms? this problem represents a challenge when studying processes in which at least one of the two reactants is also present in the gas (or liquid) phase. (A distribution of one of the reactants between the interface and the gaseous or liquid bulk is frequently implied by the requirement of a substantial surface mobility of at least one of the two reactants.) The problem of discriminating between pure LH and ER, or “mixed” mechanisms, on an amorphous surface such as porous silica has been treated by Gafney and co-workers3and Thomas and co-workers4 as well as by us5 In the case of the luminescence quenching of Ru(bpy)32+ by molecular oxygen on porous silica and on controlled porous glass (CPG) solidgas interfaces, we have been able to d e f i e the conditions under which the reaction is exclusively LH.5 Moreover, we have discriminated between a low-temperature range in which the LH reaction is controlled by the surface diffusion of 02 and a (higher temperature) range in which the reaction becomes substantially affected by the reaction-controlled (RC) term. An @
Abstract published in Advance ACS Abstracts, September 1, 1995.
analysis of our data for the LH duffusion-limited reaction on the basis of the theoretical approach of Freeman and Doll6 led, for the first time, to the determination of surface diffusion coefficients of an adsorbed gaseous molecule ( 0 2 ) at an amorphous solid interface. An analogous treatment, though applying a different theoretical approach, was carried out by Wong et ale7in the case of a bimolecular reaction occurring at a solid (silica)/liquid interface. The rates of surface reactions and diffusion are predicted and known to be dependent on the degree of surface coverage, due to adsorbate-adsorbent and adsorbate-adsorbate interactions.* No data are however available in this respect in the case of irregular surfaces of amorphous solids such as the widely used metal oxides (silica, alumina, etc.). In the present study we investigate the effects of 0 2 surface coverage on the mobility of 02 on porous silica by analyzing the quenching reaction of R~(bpy)3~+ by 02 on a “controlled porous glass”, CPG-75. After defining a low-temperature range in which the reaction is exclusively LH, we carry out an analysis for determining the relative weights of -the diffusion-controlled and reactioncontrolled components. The respective contributions to the observed quenching rate constant are both temperature and ( 0 2 ) coverage dependent. We proceed by analyzing the diffusioncontrolled component in terms of the theoretical model of Freeman and Doll: deriving surface diffusion coefficients from the rates of diffusion-controlled rate constants. The data lead to the conclusion that the surface mobility of molecular oxygen is markedly affected by the degree of surface coverage. The observation is interpreted in terms of the preferential occupation of adsorption sites with stronger adsorbate-adsorbate interactions, therefore providing direct evidence for the heterogeneity of the CPG adsorbent.
0022-3654/95/2099-14893$09.00/0 0 1995 American Chemical Society
14894 J. Phys. Chem., Vol. 99, No. 40, 1995
Experimental Details CPG-75. Controlled porous glass-75 (CPG-75), with an average pore size diameter of 95 8, and a specific surface area of 180 m2 g-I, was obtained from Electro Nucleonics Inc. Ruthenium tris(bipyridy1) chloride, (Ru(bpy)32+, was used as received from Aldrich. Oxygen gas (99.5% purity) was used as received from Merkaz Hahamtzan Inc., Israel. Water was Millipore filtered and triply distilled. Surface Area Measurements. The CPG-75 surface area measurements were carried out with a Micromeritics ASAP 2000 surface area analyzer, using N2 at liquid nitrogen temperature. The CPG 75 samples were degassed for 24 h at 50 "C until a 1-3 mTorr pressure was achieved with vacuum cutoff. Measurements were carried out with a varying (5 or 10 s) equilibrium time. Sample Preparation. Special care was therefore taken in the present work to assure complete equilibration by relatively long exposures of the CPG-75 samples both to the R~(bpy)3~+ solutions and to the 0 2 gaseous phase. We observed that insufficient equilibration times associated with the adsorption of Ru(bpy)32+ and 0 2 on the porous CPG matrix may affect the observed quenching rate constants. Samples were prepared by adding Ru(bpy)P in 50 mL of triply distilled water to 2 g of degassed CPG-75. The amount of Ru(bpy)s2+ was set to as to correspond to 6% coverage of the surface area. The samples were allowed to equilibrate in the dark for 7 days and were then filtered and dried. The amount of R~(bpy)3~+ adsorbed was determined by measuring the residual absorption of the filtrate. The percentage of surface coverage by R~(bpy)3~+ was determined on the basis of the amount adsorbed and of the N2 BET surface area, assuming an adsorbate cross section area of 172 A2 and assuming a smooth surface for CPG.I8 The CPG75 samples covered with Ru(bpy)32+were placed in an optical cell attached to an M.K.S. Baratron transducer and degassed at 50 "C for about 1 week, until a stable pressure (1-3 mTorr) was achieved with vacuum cutoff. Oxygen was then introduced at room temperature and the pressure recorded. The cell was subsequently placed in a DN-704 Oxford Instruments cryostat, cooled to a temperature in the 85-253 K range, and allowed to equilibrate for 15 h. The 0 2 surface concentration (r,mol m-2) was determined at each temperature by measuring the 0 2 pressure in the calibrated total volume of the sample cell. Correction for the pressure change component not caused by adsorption was carried out by replacing oxygen with helium, which under identical conditions shows no detectable absorption. Luminescence Measurements. Luminescence measurements were carried out as previously described using a P.R.A. (LN 102) dye laser (0.7 ns, 452 nm) pumped by a P.R.A. (LN 1000) NZ laser. Fluorescence decay profiles at 610 nm were obtained using an Applied Photophysics monochromator and a Hamamatsu R 15644 multichannel plate. The signals were amplified and digitized, using a Tektronix 7912 AD oscilloscope or a Tektronix TDS 520 two-channel oscilloscope, followed by averaging and storing with an Olivetti 386 M-24 PC.
Results and Discussion Adsorption Isotherms on CPG-75. We have recently shown9 that, in highly porous silica systems at relatively low temperatures, the adsorption of gases such as 0 2 and N2 may be substantially slow and in some cases even incomplete. The effect is due to the (activated) diffusion of the gases into the porous network. To ascertain that in the present CPG-75/6% R~(bpy)3~+ systems equilibration with 0 2 is complete, namely, that no complications arise from slow diffusion phenomena, we performed adsorption experiments as presented in Figure 1. The
Katz et al.
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nitrogen temperature: (0)adsorption, (0)desorption. (a) CPG-75, 10 s equilibration time. (b) CPG-75 + 6% adsorbed Ru(bpy)3Z+, 5s equilibration time. close nature of the isotherms, and the observation that variation of the equilibration times does not affect the shape of the isotherms, suggests that at liquid N2 temperature nitrogen equilibration is fast and complete. This is quantitatively confirmed by showing that the surface area determined by means of the BET model,l0 using NZat liquid nitrogen temperature, is independent of of the equilibration time. The data are given in Table 1, along with the calculated pore diameter values for two (5 and 10 s) equilbration times (see also Experimental Section). We have shown9 that the same conclusion, namely that of fast equilibration with the gas phase, may be extended to the case of 0 2 which is used as a reactant in our present quenching experiments. Quenching Rate Constant: Temperature and 0 2 Coverage Effects. As shown in Figure 2 and previously reported by US,^ both the self-decay and the 0 2 quenching reaction of R~(bpy)3~+ adsorbed on porous silica surfaces are nonexponential. Very good fits are obtained with a Gaussian m0de1~9'~ in which the distribution of decay rate constants, ki, is associated with a normal distribution of activation energies due to the inherent heterogeneity of the porous solid. The distribution of log ki around log(kav)(the average rate constant) is determined by the dispersion parameter, 7, so that ki = kav exp(-fy) represents the rate constant when the distribution falls to l/e of its maximum value. The average observed fiist-order rate constants, k, reported in the present work are given by k = kav kava, where kavOis the average rate constant of the self-decay measured in the absence of 0 2 . Although representing the experimental data quite well, it should be recalled that the model is based on the approximation that the transition state energies
Reactions of
J. Phys. Chem., Vol. 99,No. 40, 1995 14895
on Porous Silica Glass
0 2
TABLE 1: Surface Area (S), Total Pore Volume (PJ, and Average Pore Diameter (dD)for CPG-75 Samples dp(A)
equilibration time, s 10 5 5
sample CPG-75 CPG-75 CPG-75 + 6% Ru(bpy)s2+
S," mz g-l
Pvt()cm3g-l
d
e
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0.60
131
0.59
125
95 95
134 130
184
180 182
a All measurements performed at liquid N2 temperature in the range plp" = 0.06-0.3. A 16.2 A2 value for the Nz cross-sectional area was used. Calculated from adsorption-desorption data above plp" = 0.98. BET model,1° adsorption data. BJH model," adsorption data. e BJH model," desorption data.
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Figure 3. Temperature dependence of first-order 02-quenching rate constants of excited Ru(bpy)s2+on CPG-75 for different oxygen , = 0.0015 (initial 0 2 pressure, 1.0 Torr), (slanted coverages: (0)0 0) 0 , = 0.0029 (initial 0 2 pressure, 1.99 Torr), (0) 0 , = 0.0058 (initial 0 2 pressure, 4.0 TOIT),(0)0, = 0.010 (initial 0 2 pressure, ,, = 0.029 (initial 0 2 presssure, 19.9 Torr). 6.89 Torr), and (0) e
00 1
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Figure 2. Characteristic experimental and calculated (see text) luminescence decay profiles (superimposed) of excited Ru(bpy)32+ adsorbed on CPG-75 (6% Ru(bpy)Z+)in the presence of molecular 0 2 at 103 K. I denotes the normalized luminescence intensity. (a) e ,, = 0.0015 (initial 0 2 pressure of 1.00 TOIT).(b) e,, = 0.012 (initial 0 2 pressure of 8.00 Torr). and geometries are the same for the self-decay and the quenching rate constants. Figure 3 presents the temperature dependence of k, over the 85-253 K range, for a variety of initial (room temperature) oxygen pressures. Upon lowering the temperature, a rise in k is observed, leading to a maximum which is followed by a sharp drop at lower temperatures. This type of behavior, which prevails at temperatures below -250 K, has been previously interpreted by us in terms of a bimolecular LangmuirHinshelwood (LH), quenching reaction mechanism, between adsorbed 0 2 and excited Ru(bpy)32t adsorbed at the CPG interfa~e.~ Accordingly, the initial rise in k is caused by an increase in the amount of adsorbed oxygen, due to the decrease in temperature. The subsequent drop in k upon lowering the temperature is due to slowing down of the surface diffusion of 0 2 which is not offset by an increase in the amount of adsorbed oxygen. This picture is consistent with Figure 5, showing the temperature dependence of r, the two-dimensional concentration of 02, for a variety of initial oxygen pressures. The constant surface coverage, corresponding to total 0 2 adsorption, is obtained (depending on coverage) in a temperature range (1 10130 K)which is close to that (115-138 K) where the maximum in the k values is attained in Figure 3. The increase of k with
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Figure 4. Temperatureand 0 2 coverage dependence of the half-width 0 , = of the Gaussian, y , used in the fitting procedure for k: (0) 0.0015, (slated 0) e,, = 0.0029, and (0) 0 , = 0.0058. increasing oxygen coverage is consistent with the postulated LH mechanism. It should be noted, however, that the maximum in the curves of Figure 3 shifts to lower temperatures upon increasing the maximum coverage value (as shown in Figure 5). This indicates that the temperature effect responsible for the fall of the curves in Figure 3 at low temperatures is weaker for higher maximum coverage values. In other words, the activation energy of the postulated LH process decreaes at higher oxygen coverages. This suggestion will be quantitatively analyzed below and interpreted in terms of the heterogeneity of adsorption sites. It is worthwhile noting that, as shown in Figure 4, the dispersion parameter, y, depends on both surface coverage and temperature. The increase in the maximum value of y with increasing oxygen coverage is interpreted in terms of a higher degree of heterogeneity upon the occupation of a larger fraction
14896 J. Phys. Chem., Vol. 99, No. 40, 1995
Katz et al.
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Figure 5. Temperature dependence of the two-dimensional 0 2 surface concentration, r,for different oxygen coverages: (0)Om, = 0.0015, (slated 0 ) Om, = 0.0029, (0) Om, = 0.0058, (0)Om, = 0.010, and (0)Om, = 0.029. of binding sites. As to the temperature effect, Figure 4 shows that y passes through a maximum at around 140 K. The two opposing effects leading to the appearance of the maximum are attributed to the following: (a) An increase in the relative occupation of lower adsorption energy occurs upon increasing the coverage (see detailed arguments below). This effect is dominant up to -140 K. (b) Below this temperature displacement of 02 from the less favorable adsorption sites to the stronger ones, as well as desorption from the weakest sites, counterbalances the coverage effect. (Compare with Figure 5 where the bending occurs at 140 K as well.) Temperature Dependence of the Bimolecular Rate Constants of the LH Reaction. The meaningful parameter in a LH mechanism is the second-order rate constant defined as K = WT, where r is the two-dimensional concentration of surfaceadsorbed oxygen. The temperature dependence of #, calculated using the r values of Figure 5, is given in Figure 6. The curves in Figure 6a and the corresponding Arrhenius plots in Figure 6b show that K is affected by both 02 coverage (K increases with surface coverage) and temperature. For all oxygen coverages three distinct temperature ranges are evident: The low-temperature range (approximately 85- 125 K) where the curves are relatively steep, an intermediate range (125-160 K) with lower slopes, and (for the highest oxygen pressure) a high temperature range, above -170 K, where the slope increases again.
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Figure 6. Temperature dependence (a) and corresponding Arrehnius plot (b) of the second-order 02-quenching rate constant, k', of excited Ru(bpy)3*+on CPG-75: (0)Om, = 0.0015, (slated 0)0, = 0.0029, (0) Om, = 0.0058, (0)Om,,= 0.010, and (0)Om,,= 0.029. Our subsequent analysis will be based on the assumption that below -160 K the contribution of an ER mechanism is negligible, so that the K values represent a pure surface LH r e a ~ t i o n .This ~ assumption, which will be justified a posteriori on the basis of the very good fits with the LH mechanism, is in keeping with Table 2, which displays the observed values of k and K as a function of temperature between 88 and 148 K for two representative (lowest and highest) 02 coverages, along with the corresponding oxygen pressures @(02)). It is evident from Table 2 that for both coverages the temperature-induced changes
TABLE 2: Oxygen Surface Concentration (r),Pressure (~(OZ)), Observed First-Order (k),and Second-Order (k') Rate Constants as a Function of Temperature in the 80-148 K Range0 88
r x 10-7, mol m-2 p(Oz), Torr k, s-l x lo8 k', mz mol-' s-l x lOI4
108
118
128
138
148
3.02 2.2 1.77 5.86
2.34 5.4 1.65 7.05
1.62 8.9 1.37 8.45
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1.66
1.45 0.13 5.20 3.59 16.1 39.7 32 1.96
1.04 0.33 6.24 6.00 15.6 21.1 22 1.41
0.61 0.54 4.99 8.13 16.3 22.4 23 1.38
Om, = 0.029 3.49 0.02 0.53 1.52 1.75
p(Oz), Torr k, s-l x lOI4 k', mz mol-I r(o.o29)/r(o.oois) p(~2)(~.~~9)~p(O2)(0.O01 5) k(0.029)/k(0.00015) k'(0.029)lk'(0.0015)
98
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3.48 0.08 0.89 2.56
3.31 0.56 1.44 4.26 0,- = 0.0015 1.76 1.75 0.003 0.85 1.83 0.64 1.05 19.9 19.2 187 105 79 3.27 4.06
0.04
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Values are for two representative (maximum) coverage values (e,,,= = 0.029 and Om, = 0.0015) and correspond to the data of Figures 3 and 6a.
Reactions of 3450
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J. Phys. Chem., Vol. 99, No. 40, 1995 14897
on Porous Silica Glass
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in ~ ( 0 2 )are about 1 order of magnitude higher than the corresponding changes in k and K. The effect is in variance with that expected for an ER reaction for which the rate linearly increases with pressure (eq 6, neglecting the TIn effect). A further analysis c o n f i i n g the LH character of the reaction below -150 K will be presented below. The same conclusion also applies to the range 150-190 K where a decrease in k rather than an increase with increasing T (and consequently ~ ( 0 2 ) is ) observed. It is only above -160 K, in the case of the highest 0 2 pressure which shows a sharp rise in K (see Figure 6), that a substantial contribution of an ER mechanism becomes evident. We proceed with the analysis of the temperature effects on K, the bimolecular rate constant of the LH reaction, on the basis of assumption (see above and ref 5 ) that the drop in k below -125 K, shown in Figure 3, is mainly due to inhibition of the diffusion of 0 2 to excited Ru(bpy)3*+. The initial slopes (below -125 K) shown in Figure 6, presented on an expanded scale in Figure 7% are therefore attributed to the temperature dependence of an essentially diffusion-controlled rate constant. It is evident from the decrease in the initial slope upon increasing r that the diffusion barrier decreases with increasing oxygen coverage. The decrease in slope in the intermediate, 125-150 K, temperature range (see Figure 7b) is interpreted by assuming that the rise in temperature induces an increase in the diffusion rate to a level which is sufficient for transforming the reaction from diffusion-controlled to diffusion-influenced, namely, one which obeys the expre~sion'~
in which kd, is the rate constant of the purely diffusion-controlled reaction and krc (the purely reaction-controlled rate constant) is the rate constant once the reactants have reached the critical reaction distance. The temperature dependence of the two rate constants is given by
where Edc and Erc are the activation energies of the diffusioncontrolled and the reaction-controlled reactions, respectively, and Adc and A, are the corresponding preexponentid factors. According to our analysis the observed activation energies, E(obs), derived from the slopes of the k h e n i u s plots in the low-temperature range (Figure 7a), should be identified as a first approximation with Edc. As shown in Figure 8a, Edc shows a pronounced dependence on 0 2 coverage. (In the intermediate range, where k and kdc are assumed to have comparable contributions, the observed activation energies derived from Figure 7b and presented in Figure 8b do not have a simple meaning.) A quantitative analysis of our data in terms of eq 1 was carried out by first determining Adc and Edc for d l oxygen coverages from the initial slopes of the k h e n i u s plots in the 85-125 K range, where we assume kdc .*: krc and thus 'k = kdc. This assumption is strictly valid only for the lowest coverage values. On the basis of these data, we have roughly estimated the contribution of hcin the 125-150 K range, where the reaction is assumed to be diffusion-influenced, obtaining an approximate estimate of k,. The values obtained for Ercand A, are then
Katz et al.
14898 J. Phys. Chem., Vol. 99, No. 40, 1995 d IQ'
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Figure 9. Comparison between the experimental k' values (points) and the corresponding calculated values (continuous lines, obtained by using eqs 1-3.
used as the basis for fitting the experimental values of K to eqs 1-3. The best fits are obtained with the values A, = 2 x 10l6 m2 mol-' s-I and E,, = 1.5 kJ mol-', which are assumed to be equal for all 0 2 coverages. The full comparisons between the experimental and calculated K values in the 85-168 K temperature range are given in Figure 9. Very good fits are obtained, in agreement with eq 1. It is interesting to consider separately the temperature dependence of the calculated values of krc and kjc (eqs 2 and 3), which have been used in drawing the continuous curves of K in Figure 9. Particularly, we would like to determine the conditions under which the reaction may become exclusively reaction-controlled. The corresponding curves are presented in Figure 10, hypothetically assuming that the present LH reaction may take place at temperatures as high as 700 K. It is evident that although (as shown above) at low temperatures k' 3: kdc,
the comparable situation, 'k = k,, is not achieved by raising the temperature within the 85-170 K range where the LH reaction is experimentally attainable. In other words, in the high-temperature limit of the range in which the reaction is predominantly LH, it becomes diffusion-limited but not reactioncontrolled. It is also evident that the increase of kdc with 0 2 coverage is maintained only at low temperatures. At about 190 K a crossing point of the kdc curves is observed, showing an "inverted" 0 2 coverage effect at high temperatures. In this range the entropic factors associated with the preexponent Adc (see below) overcome the effects of the diffusion barrier ( E d c ) leading to a decrease, rather than to an increase, of kdc with Om,,.It also becomes evident from Figure 10 that the effect of decreasing the difference between kdc and k, with increasing temperature (which is responsible for the diffusion-influenced behavior in
J. Phys. Chem., Vol. 99,No. 40, 1995 14899
Reactions of 02 on Porous Silica Glass
TABLE 3: Comparison of Observed Activation Barriers (E(obs) and Those Calculated Using Eq 4 (E(calc)Y 85-128 K
128-148 K
Om,
E(obs), klmol-l
E(calc), klmol-I
E(obs), klmo1-I
E(calc), kTmo1-I
0.0015 0.0029 0.0058 0.010 0.012 0.029
1.12 7.36 6.61 6.15 5.91 3.95
1.58 1.20 6.44 5.93 5.15 3.12
6.65 6.48 5.03 4.25
7.01 6.13 6.02 5.46 5.36 3.55
3.59
a Low (85-128 K) and intermediate (128-148 K) temperatures ranges are given as function of Om. Error estimates are f5% for E(obs) and f 1 2 % for E(ca1c).
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200
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80
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Figure 10. Temperature dependence of the parameters kd, and k , used for the calculation of the tempearture dependence of k' as shown in Figure 9 (continuous lines).
the intermediate temperature range) is also inverted at higher temperatures. Thus, a crossing point at about 220 K is predicted between krCand kdc (except for the highest coverage (Om= = 0.029) for which the point is expected at about 600 K). In this range the effect of increasing temperature is one of increasing, rather than decreasing, the gap between kdc and kc. The consequence (with the exception of the higher coverage case) is that only above -1000 K is the reaction expected to become essentially reaction-controlled. This "inverted" region is not attainable experimentally in our present system, primarily due to the transition from the LH to the ER mechanism at about 170 K and, obviously, due to the lack of thermal stability at such higher temperatures. It cannot be excluded, however, that in other systems, with different activation and preexponential parameters, effects characteristic of the inverted region may have to be considered in a lower temperature range where the LH reaction is experimentally feasible. An interesting demonstration of the applicability of eq 1 in the present system, in the range where kdc and k, are comparable, may be carried out on the basis of expression 4, derivable6 from eqs 1-3, in which E is the apparent activation energy of the reaction.
(4) As shown in Table 3, the calculated values, E(calc), are in excellent agreement with the experimental ones, E(obs). The dependence of E(calc) on temperature for different coverage values is shown in Figure lla. The change in slope at low oxygen coverages is due to the change in mechanism, from diffusion controlled at low temperatures to diffusion influenced at high temperatures. The effect is essentially undetectable in the case of the highest coverage where the reaction is not purely
120
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160
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Temperature, T
