J. Phys. Chem. 1981, 85,3577-3581
in the range accessible by chemical activation. At sufficiently high temperatures, it appears that C-H bonds will be preferred over C-F; however, at such energies, electronic states become accessible. The net effect is that in our systems, both the frequency and very strong Aio,lfor C-F greatly increases radiative emission. Other systems provide further support for this analysis. Only a small amount of clustering is seen for 1-butanol in the ICR, while 2-methoxyethanol does so readily. This is presumably similar to the fluorinated alcohols: a C-0 stretch is both intense and in the right frequency range to increase k, and decrease k , compared to a C-C bond. We note that nearly all the reported cases of bimolecular clustering in the laboratory involve compounds with C-0 bonds, or the S-F bond a t comparable f r e q ~ e n c y . ~ - ~ Benzyl mercaptan does not cluster with its mercaptide, while benzyl alcohol is comparable in clustering rate to the largest alcohols here. The C-S stretch, while at 650 cm-l is lower than the C-0 stretch,33nevertheless is still at a favorable frequency from Figure 3. The weak absorbance of the S-H stretch relative to 0-H may be a factor here; however, the well depth Eois also important. The shallower the well, the slower the overall reaction. It is well-known that thiols are much weaker at hydrogen bonding in solution than alcohols.34 If RS--.HSR bond was only 2.5 kcal/mol weaker than predicted by eq 3, the clustering rate would be slower than our time window in the ICR. We are currently measuring such bond strengths by an equilibrium method.35 Diisopropylamine does not cluster with its amide, while c6 alcohols do. The weakness of the C-N stretch33may be the cause of this. (33)Silverstein, R. M.; Bassler, G. C. “Spectrometric Identification of Organic Compounds”; Wiley: New York, 1967;2nd ed, pp 86-100. (34)Pimentel, G. C.; McClellan, A. L. “The Hydrogen B o n d ; W. H. Freeman: San Francisco, 1960. Vinogradov, S. N.; Linell, R. H. “Hydrogen Bonding”; Van Nostrand-Reinhold New York, 1971. (35)McIver, R.T., Jr.; Scott, J. A.; Riveros, J. M. J.Am. Chem. SOC. 1973.9*5.2706-8. Bartmess. J. E.:Caldwell. G . 29th Annual Conference on Mass’Spectrometry and Allied’Topics, Minneapolis, MN, May 24-29, 1981,Paper MPAIO.
3577
There has been considerable recent interest in advancing the analytical capability of ICR spectrometry due to its instrumental simplicity, high mass resolution,36and capability for use of selective polar reagent gases in chemical ionization mode.37 The problem with the use of polar reagent gases in conventional chemical ionization mass spectrometry is the termolecular clustering of such polar molecules onto ions at the reagent pressures of ca. 1 torr. This results in a variety of ions for each sample, rather than the single peak desired. At the low pressures used in the trapped ICR spectrometer, such clustering is much less likely to 0ccw.3~The recent developments in ICR have involved using lower pressures and higher magnetic fields. These are necessary to increase mass resolution, which goes as the reciprocal of pressure, while maintaining total collision number to effect chemical ionization, since trapping time is a function of the square of the magnetic field. The present work indicates that reagent plus sample cluster ions can still form no matter how low the pressure. Both sample ionization and clustering are bimolecular reactions at low pressure. If the simplest possible mass spectrum is desired, it would be advantageous to avoid the use of reagent gases containing C-0 or C-F moieties. Conversely, the presence of cluster ions may be indicative of such structural features in the sample.
Acknowledgment. We thank the Research Corporation and the National Institutes of Health, Grant GM-27743-01, for support of this work. We are grateful to Professors G. E. Ewing and C. S. Parmenter, and Mr. Rex Pendley for helpful discussions. (36)Comisarow, M.;Marshall, A. G. Chem. Phys. Lett. 1974, 25, 282-3. Comisarow, M. In “Ion Cyclotron Resonance Spectrometry”, Hartmann, H.; Wanczek, K.-P., Ed.; Springer-Verlag: Berlin, 1978;pp 136-45. White, R. L.; Ledford, E. B., Jr.; Ghaderi, S.; Wilkins, C. L.; Gross, M. L. Anal. Chem. 1980,52,1527-9.Allemann, M.; Kellerhals, Hp.; Wanczek, K.-P. Chem. Phys. Lett. 1980,75,328-31. (37)McIver, R. T.,Jr.; Ledford, E. B., Jr.; Miller, J. S. Anal. Chem. 1975,47,692-7. (38)Bartmess, J. E.;Caldwell, G., Int. J.Mass Spectrom. Ion Phys. 1981,40,269-74.
Adsorption Kinetics of Ammonia on an Inhomogeneous Gold Surface R. E. Richton” and L. A. Farrow Bell Laboratories. Murray Hill, New Jersey 07974 (Received: March 27, 198 I)
Adsorption kinetics of ammonia onto a gold surface have been studied by monitoring gas concentration as a function of time using the optoacoustic effect. The data can be understood by applying a theory recently formulated by Aharoni and Ungarish which takes into account the inhomogeneity of adsorption energy and site characteristicsof a “dirty” surface. If the optoacousticdata are used to obtain the parameters of this theory, differential heat as a function of time can be found. The differential heat of adsorption of ammonia onto gold is found to range from -2 to -35 kcal/mol.
Introduction Experiments in gas-phase kinetics are often complicated by adsorption onto reactor cell surfaces. If such heterogeneous processes between the gas and the wall could be quantitatively predicted, then homogeneous gas-phase rates could more readily be derived from kinetic data. For example, determination of the rate constant for the reac0022-3654/81/2085-3577$01.25/0
tion of nitric acid vapor and ammonia vapor has been complicated by the strong adsorption of these gases onto both wet and dry surfaces.’ In examining this system by an oPtoacoustic technique? we found the theory of &em(1) K. J. Olszyna, R. G. DePena, and J. Heicklen, Int. J. Chem. Kinet., 8,357 (1976).
0 1981 American Chemical Society
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The Journal of Phys!cal Chemistty, Vol. 85, No. 24, 7987
Richton and Farrow 1 .o
b
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TIME (seconds) Flgure 1. Concentration in torr of gas-phase ammonia as a function of time in seconds on a logarithmic scale. The points are experimental. The solid curve shows the best fit to eq 13, and the dashed curve shows the best fit to eq 18.
isorption kinetics recently formulated by Aharoni and UngarishW to be useful. This theory is formulated for an inhomogeneous surface and therefore could potentially be applied to many practical problems. We present the application of this theory to adsorption of ammonia vapor onto a gold surface. Optoacoustic observations that could not be explained by simpler theories such as Langmuir’s,’ Elovich‘s,8or Ritchie’sgequations or by the conservation equations given by TompkinslO are shown to fit the theory of Aharoni and Ungarish. Relationship to other models and heats of adsorption are discussed. Experimental Section The construction of the optoacoustic cell and the arrangement of the associated equipment have been published in detail elsewhereS2Briefly, the optoacoustic cell is stainless steel gold-plated to a thickness (0.013 mm) sufficient to prevent migration of NH3through the plating. The surface is rough and untreated except for cleaning by solvents. Surface heterogeneity will therefore arise because of the various geometries, impurities, and traces of previously adsorbed gases. The electret microphone” has a gold foil diaphragm. Before each run, the cell was evacuated to a pressure of lo4 torr for several hours and was (2) L. A. Farrow and R. E. Richton, J.Appl. Phys., 48,4962 (1977). (3) C. Aharoni and M. Ungarish, J. Chem. SOC.,Faraday Trans. I , 72, 400 (1976). (4) C. Aharoni and M. Ungarish, J. Chem. SOC.,Faraday Trans, I , 73, 456 (1977). (5) C. Aharoni and M. Ungarish, J.Chem. SOC.,Faraday Trans, I , 73, 1943 (1977). (6) C. Aharoni and M. Ungarish, J.Chem. SOC.,Faraday Trans, 1,74,
.--.-,.
7
‘
I507 (1978).
(7) K. J. Laidler, “Chemical Kinetics”, McGraw-Hill, New York, 1965. (8) M. J. D. Low, Chem. Rev., 60, 267 (1960). (9) A. G. Ritchie, J. Chem. SOC.Faraday Trans. 1, 73, 1650 (1977). (10) F. C. Tompkins, “Chemisorption of Gases on Metals”, Academic Press, New York, 1978. (11) G. H. Sessler and J. E. West, J.Acoust. SOC.Am., 53,1589 (1973).
TIME (seconds) Figure 2. Same as Figure 1 for a run starting at lower concentration.
filled to a pressure of 25 torr with research-purity nitrogen. A high-pressure reservoir containing a mixture of NH3 in nitrogen was separated from the cell by means of a solenoid valve and was kept at such a pressure that, after the solenoid was opened, the cell contained 50 torr of an NH3-Nz mixture. This sudden injection into the cell gives rise to turbulence, which results in very rapid mixing of the gases. By the time the microphone recovers, which takes -2 s, the mixing is complete. The cell was illuminated with the CO laser line12at 1801.8568 cm-’, which is absorbed in the v4 band13 of NH,. The resulting optoacoustic signal was examined periodically for at least 1 week and then translated into absolute concentration.2 Figures 1 and 2 show some typical data obtained by this procedure.
Theory The theories that failed to explain our results are largely empirical and fail to account for the heterogeneous nature of the surface which we used. Aharoni and Ungarish have formulated a detailed theory for heterogeneous surfaces and have derived an expression for the time dependence of adsorption. They assume a surface consisting of a large array of homogeneous regions each of which has a characteristic range of adsorption enthalpies between H and H + dH. Overall, H varies from Ho,the minimum heat of adsorption at any region, to H,, the maximum. Further, each region has a site-energy distribution, nH(H). The activation energy E, at a given time t is assumed to depend both on H and on the coverage of the region: E t / R T = a H / R T + In (gy,/nH y) (1) where g, y, and a! are constants. gyt/nH >> y even at low coverage; so we shall make the approximation y = 0. Here the coverage is expressed as y t / n H ,where Yt = (2)
+
(12) T. R. Todd, C. M. Clayton, W. B. Telfair, T. K. McCubbin, Jr., and J. Pliva, J. Mol. Spectrosc., 62, 201 (1976). (13) L. A. Farrow and R. E. Richton, J. Chem. Phys., 70,2166 (1979).
The Journal of Physical Chemistry, Vol. 85, No. 24, 1981 3570
Adsorption Kinetics of Ammonia on a Gold Surface ,123
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H/RT Flgure 3. Coverage as a function of adsorption energy for ammonia on gold. The two rlslng curves give the equilibrium coverage yw in torr/(kcal/mol) according to eq 3 of the text, whereas the falling curves give the coverage y, according to eq 5 of the text. At a given time, the rising and falling curves intersect at H,, given by eq 7 of the text. The shaded area to the right of H, minus the shaded area to the leit glves the change in the amount adsorbed as time advances.
q, is the total amount of gas adsorbed onto the surface at time t. Through eq 1E, is proportional to H. Therefore eq 1 implies that the surface comprises regions with low H and low E, (as in physisorption) and regions of high Hand high E, (as in strong chemisorption). Aharoni and Ungarish further assume that in any given region equilibrium is attained when yt becomes equal to yes as given by Yeq/nH = ke exp(H/RT) (3) where k, is a pressure-dependent constant. The ascending curves in Figure 3 show y9 at two different times, with the ascending curve on the right occurring at the later time. These points correspond to two points from Figure 1. Those regions with H 5 H,are at equilibrium; Figure 3 shows Ht for the later time curves. To complete the theory, the rate of adsorption in a given region is given by14 dy,/dt = konH exp(-E,/RT) (4) where ko is a pressure-dependent constant. Unlike most other heterogeneous-surfacemodels found in the literature, this is neither a “kinetic model” nor an “equilibrium model”. In the kinetic models, sites have different activation energies, and the low-activation-energy sites are occupied While these first-occupied, low-E, sites are being filled, the coverage-energy distribution y(E,) is similar to the site-energy distribution nH(E,). There will be no coverage of high-E, sites. In the equilibrium models, sites have different adsorption (binding) energies, and the high-binding-energysites (14) C. Aharoni and M. Ungarish, to be submitted for publication.
are occupied first.16J6 The term high-binding-energy sites refers here to the sites having the deepest potential wells. This would correspond to the lowest overall energy if we were also to include the energy of the surface itself. The equilibrium model can be thought of as allowing surface mobility of the adsorbate, which leads to highest coverage of the sites with the deepest wells. In an equilibrium model the coverage-energy distribution y(H) is similar to the site-energy distribution nH(H) at high H. There will be no coverage at low-H sites. The Aharoni and Ungarish model has elements of agreement and elements of disagreement with both models. Equation 1states that the activation energy is proportional to adsorption energy. This means that the coverage-energy distribution is basically different from the site-energy distribution. Coverage is low in the low-energy regions because equilibrium is easily attained. This aspect is similar to an equilibrium model but not to a kinetic model. On the other hand, the covering of these low-E sites first is consistent with a kinetic model. Similarly, the Aharoni and Ungarish model has low coverage in high-energy regions because adsorption is slow. A kinetic model would agree while an equilibrium model would disagree. The model that we use has high coverage in an intermediateenergy region, which has some implications for the derived heats of adsorption, as will be discussed later. Combining eq 1 and 4 and rearranging gives Yt/nH = A exp[-aH/@RT)I (5) where A = (2ko/g)1/2t1/2 (6) Figure 3 shows yt as the descending curves at two different times. In each case, the intersection of yes and y, is H,, given by Aharoni and Ungarish as H,= [2RT/(a t 2)] In ( A / k , ) (7)
It has been shown5that the amount q adsorbed onto a surface at any given time, pressure, and temperature is given by
This equation can be integrated and combined with eq 3, 5, and 7 to yield q as a function of time: q/(nHRT) = [(a+ 2)/,]k,I*/(*+2)IA[2/(*+2)1 ke exp(Ho/RT) - (2A/a) exp[-aHm/(2RT)1 (9) In this work, the pressure dependence for ko and k, will be taken as linear, so that k , = k i p and ko = kdp. We assume that, at the final equilibrium time teq,Ht = H,; therefore
At first glance, it may seem that a fit to experimental data involves the unknown parameters g, nH,a,k:, k,,’, and H,,.However, these parameters are not all independent, and their number will be reduced. First of all, Ho, the minimum heat of adsorption at any region, may safely be assumed to equal zero without affecting any of the discussion to follow. We form the ratio P
= M/kki2)
(11)
(15) A. M. Bar0 and H. Ibach, J.Chem. Phys., 71,4812 (1979). (16) K. Christman, 0. Schober, and G. Ertl. J. Chem. Phys., 60,4719 (1974).
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The Journal of Physical Chemistry, Vol. 85, No. 24, 1981
and then set q, the amount adsorbed, equal to (po- p ) , where p o is the pressure of adsorbing gas in the cell at t = 0. It is possible to form the following new parameters: = nHk,'RT 7 = X(~/,L)'/(~+~) = 7(t / )-a/Ma+2)1 (12) eq Pes x is an unknown parameter in cases where data are not followed out to the true equilibrium condition. If t , and pes are measured directly, then x is not needed as a parameter, and the only parameters are a,A, and 7. When x is written in explicitly, then eq 9 becomes
(13) Pressure vs. time data can be fitted to eq 13 by using nonlinear least squares to find the parameters. However, this procedure requires that the fitting routine call a numerical root finder because of the transcendental form of eq 13. In the past, this method often led to difficulties with the fitting routine asking to have the function evaluated in a region where no root exists. These difficulties can be avoided by noting that eq 13 contains only one nonlinear parameter (a).The equation is linear in X and 7 (and x if it is needed) and may therefore be fitted by a variable projection technique.l' This technique has the further advantage of not requiring the evaluation of any derivatives. Sometimes the intital concentration, po, is unknown. In such a case it would seem logical to treat p o as an additional parameter to be fitted (poappears linearly). This straightforward approach fails, since the fit is sensitive to p o only for data at early times where po has an influence. At these early times the equation breaks down, as can be seen by examining eq 13 for the conditions t = 0, p = p,,. This breakdown of eq 13 at t = 0 can be traced to the approximationof neglecting y in eq 1, creating a singularity at t = 0. Inclusion of y, however, results in an awkward mathematical form that would greatly complicate the analysis. Fortunately, a simpler approach is possible. For low t, the first term of eq 8 is negligible because Ht = H,,.The second term of eq 8 may then be integrated by using eq 5 and assuming exp(-aH,/RT)
