116
Langmuir 1987, 3, 116-120 concentration, the monomeric species condense to form increasingly complex oligomers containing Ti-&Ti bonds. Evaporation of the TiC14-HC1 solution produces a cubic octamer of titanium, identified as [Ti8012(H20)24]Cls.HC1.7H20. The same structure is present following incipient wetness impregnation of Si02. Calcination of the supported cubic octamer produces Ti02(B)and anatase, the proportion of anatase increasing with increasing weight loading of titanium. The TiOz(B)phase is highly dispersed and cannot be detected by XRD or observed by TEM. The anatase phase exists as 6.0-8.0-nm particles dispersed on the Si02support. Both phases of titania are stable to 1000 "C. A plausible pathway can be shown for the transformation of the cubic octamer to Ti02(B)and from there to anatase.
Figure 9. Transformation of Ti02(B) to anatase and the transformation of anatase to rutile.
ever, are stable to further sintering or conversion to rutile even when heated to temperatures as high as 1000 OC.
Conclusions It has been demonstrated that TiC14-HC1 solutions contain a variety of species. At low titanium and acid concentrations, the predominant species are monomeric ions such as Ti02+. With increasing acid and/or titanium
Acknowledgment. We acknowledge the assistance of Dr. M. L. Sattler in obtaining the TEM results reported here and thank Dr. I. Wachs of Exxon Research and Engineering for providing Raman spectra of the pure phase of Ti02. This work was supported by the Office of Basic Energy Sciences, Chemical Science Division, of the U.S. Department of Energy, under Contract DE-ACOS76SF00098. Registry No. [Ti80,2(H20),,]C18~HCl.7H20, 105638-65-1;Ti02, 13463-67-7.
Virial Coefficients for Nzand CO Adsorbed on the Graphite Basal Plane Mary J. Bojan and William A. Steele* Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802 Received August 18, 1986 Studies of N2and CO adsorbed on exfoliated graphite (Grafoil) were performed with a volumetric adsorption apparatus in the low-coverage region for temperatures ranging from 90 to 210 K. From the isotherms, values for the isosteric heat of adsorption extrapolated to zero coverage [qst(0)],the gas-solid virial coefficient (BAS),and the two-dimensionalsecond virial coefficient (B2D)were determined for these systems. The values obtained for qst(0)agree well with the calorimetric measurements of Piper et a1.loJ2 Calculations of BAS and B2D were carried out by using potentials similar to those used in recent computer simulations. Theoretical curves were fitted to the experimental data by taking the well-depth and size parameters of the gas-solid and gas-gas potentials to be adjustable constants. The results are compared to other estimates of the parameters and possible reasons for the discrepancies found are suggested.
Introduction In developing practical theories for the thermodynamic properties of molecules physisorbed on homogeneous surfaces, it is crucial to know the potential energies that appear in the general statistical mechanical equations for the problem. An excellent approximation to the homogeneous surface is provided by graphitized carbon black (gcb) or exfoliated graphite (exg), both of which possess surfaces that are almost entirely exposed basal planes containing only a few percent of physical or chemical imperfections. For many years, the adsorption of spherical molecules (i.e., the rare gases) has been intensively studied, theoretically and experimentally.' At this time, reasonably (1) Cardini, G.; O'Shea, S.F.; Klein, M. L. Faraday Discuss. Chem. Sac. 1985,80, 227. See other references therein.
accurate curves are known both for the molecule-solid and for the molecule-molecule interactions in these systems. Much of this knowledge has been obtained by measurements of the low-coverage parts of adsorption isotherms over a wide range of temperature, followed by an analysis of the data to give BASand BZD,the molecule-solid and the molecule-molecule surface virial coefficients, respectively. The experimental values were then fitted to appropriate theoretical curves to give the constants of the potentials. More recently, interest has shifted to simple nonspherical molecules such as Nz and CO interacting with graphite. Since there seemed to be almost no suitable data in the literature concerning the low-coverage isotherms and their theoretical interpretation, we have performed such a study for the gases N2 and CO on exg and present the results here. We will see that the outcome is somewhat surprising, especially with respect to the moleculemolecule
0743-7463/87/2403-0116$01.50/00 1987 American Chemical Society
Langmuir, Vol. 3, No. 1, 1987 117
Virial Coefficients for Adsorbed N2 and CO
interactions within monolayers adsorbed on exg. The isotherm equation that provides the starting point for studies of this kind is well-known.2 We write it as (1) In (Na/P) = In (BAs/kT) - 2 (Na/A)BzD + where N,, p , and .A are the moles adsorbed, the pressure, and the surface area, respectively. The constants in this virial isotherm are found to be
...
BAS= S,[g,(r)
- 11 d r
(2)
where volume V is the gas adsorption volume and g,W = exp[-u,(r)/kTi (3) Here r is a generalized coordinate that includes both the molecular position and, for molecules, the angles of orientation relative to the solid surface. The "twodimensional" virial coefficient is actually a many-dimensional integral for nonspherical molecules conveniently given by several equations which are3 (4) w2
= %S$.(rd
dr1 J[gs(r2) - llfl' drz
(5)
f1~ = exP[-umm(rlz)/kTl - 1 (6) where r12= rz - rl. The term in eq 4 containing BBDis a correction term for the nonideality of the gas not in contact with the solid; in this study, it was found to be small, but not quite negligible. The Mayer function f12 involves the interaction potential umm(rlz) between two nonspherical molecules whose position variables are specified by rl and r2 This potential will differ from the free-space function due to various surface-mediated interaction terms. As the molecules involved become structurally more complex, the process of fitting experimental data for BAS and BzDobtained over a range of temperature becomes essentially one of selecting a reasonable model and attempting to characterize some of the parameters. (As will be seen, the number of such parameters is much too large for unambiguous determination even for molecules as simple as N2 or CO.) Perhaps the most widely used explicit model of a molecule-solid interaction for a nonconducting solid like graphite is based on a site-site approach in which each carbon atom interacts with each atom in the gas. For molecular adsorbates, an obvious extension is to assume that each molecule is composed of sites. Although the infinite summations (over C sites) would appear to be very cumbersome to use in either eq 2 or 5, it is now well-known that analytic summations can be performed to yield reasonably simple expression^.^ Formally, one expands the site-solid potential in a two-dimensional Fourier series with periodicity reflecting the periodicity of the solid surface. For the purposes of this paper, it will be sufficient to include only the leading term w0("')(z)which is the surface-averaged potential for site m in an adsorbate molecule. If the site-site interactions are taken to.be Lennard-Jones 12-6 functions, one finds5
Table I. B A# for Nsand CO on the Graphite Basal Plane
co
N"
T,K 671.2 186.0 61.30 12.32 3.18 1.34 0.661 0.383
89.51 99.55 109.54 128.92 151.00 170.12 190.40 210.43
(3) Sokolowski,S.; Stecki, J. Acta Phys. Pol. A 1979,55,611. J . Chem. SOC., Faraday Trans. 2 1981, 77, 406. (4) Steele, W. A. Surf. Sci. 1973, 36, 317.
cm31e
292.8 80.64 29.11 6.324 1.896 0.860 0.456 0.280
where em and u are the well-depth and size parameters for the m site/gsite Lennard-Jones function and a, and d are the site area (5.24 A') and distance between graphite planes (3.40 A), respectively. The sums over planes in eq 7 converge rapidly and can be replaced with analytic approximations, for practical calculations. For the molecules N2 and CO used in this work, there are evidently two sites each, with only one set of c,u parameters needed for Nz/exg but two for CO/exg. The molecule-molecule interactions are modeled in an obvious and by now well-known way5 (for N2, at least). The summation over four pairs of site-site interaction functions must be augmented by the electrostatic interaction which is purely quadrupolar for N, and approximately for CO also. This can be conveniently done by placing three discrete charges in the molecule, two on the sites and one a t the molecular center which is opposite in sign but equal to the sum of the other two. Note that this approach yields a Nz/N2 potential characterized by two or three parameters (E", a", and possibly q, the charge on the N). This charge may be taken to be that which yields the known experimental quadrupole moment of N2 or it may be adjusted to give an "effective" moment valid in a dense medium of polarizable molecules. Unfortunately, the number of free parameters for CO-CO is much larger (€00, ECO, ECC, 000,QCO, UCC, 40, and qc) than for N2. Furthermore, relative absence of simulation studies on the bulk CO phases6means that one has less information concerning the probable values of the parameters. We will see that fairly drastic assumptions are necessary to make progress in this case. Experimental Section Isotherms were measured for Nz and CO over a relatively wide range of temperature (90-210 K) in a moderately conventional volumetric adsorption apparatus. Temperatures were measured to an accuracy of h0.02 K with a platinum resistance thermometer. Pressures were measured either on a Texas Instruments quartz spiral gauge which was calibrated against a mercury manometer or a Baratron capacitance manometer, for low pressures. The capacitance manometer was calibrated against a mercury manometer and a McLeod gauge. The estimated errors in the pressure are less than 1 % . The gas handling system was conventional and was based on a water-jacketed gas buret. The estimated precision in the gas doses was h0.05 cm3and, in the various dead-space volumes, *0.10 cm3. The adsorbent consisted in a sample of 50.274 g of Grafoil,7 held in a brass container sealed with a stainless steel UHV conflat flange which could be heated to 200 "C for outgassing. This container was held in a can that could be evacuated for purposes of temperature control. The isotherm data were analyzed by plotting In ( N , / p ) vs. N,. As shown in eq 1, intercepts gave BAS and the slopes, BZD/A. Values obtained for BAS are given in Table I. These data were ~~
(2) Steele, W. A. The Interaction of Gases with Solid Surfaces; Pereamon: New York. 1974.
Bas,
~
89.63 99.68 109.64 129.07 151.16 170.29 190.69 210.67
~
~~
(5) Steele, W. A. J.Phys. (Paris) 1977, 38, Coll. C4-61. (6)Fracassi, P. F.; Cardini, G.;O'Shea, S.;Impey, R. W.; Klein, M. L. Phys. Reu. E 1986,33, 3441. (7) Grafoil is the trade name of a product of Union Carbide Corp., Carbon Products Div., New York, NY.
118 Langmuir, Vol. 3, No. 1, 1987
Bojan and Steele
I N p on Grafoil
Table 11. Physical Properties DroDerties N2 co dipole moment2' 0 1.2 x lo-'' esu quadrupole moment2' -1.5 X esu -2.5 X esu bond length 1.10 A25 1.13 A26 melting point 63.15 K27 68.15 K27 boiling point 17.34 K28 81.61 Km critical temp 126.2 KZ5 132.9 KZ9 (Y (3 phase trans temp 35.61 K25 61.55 K30
-
- 0.09-
1 I
I
I
I
Table 111. Molecule-Solid Site Potential Parameters elk, K u. 8, N2 this work 33.4 3.36 Piper et al.1° 34.5 3.36
co
I
this work, "Mirsky"
Figure 1. Deviation of the calculated In E&* from linearity as a function of 1 / 1 1 . Experimental values of In BAS* for N2 are and In (Au,) shown with reducing factors In (Au,) = -10.350 (0) = -10.310
(A).
sc so Piper et a1.12 sc so
35.5 42.0
3.39 3.14
34.8 41.2
3.39 3.14
SC(=S)O
37.3
3.31
this work, N2-like fitted to theoretical curves based on eq 2 and 7, using g,(r) = exp[-wJm)(z)/kr] - 1. Since plots of In B u vs. 1 / T were nearly linear over the temperature range studied, the fitting procedure consisted of T i t assuming linear behavior of both the theoretical and experimental curves. A fit of one to the other gave preliminary values of tp/k and uBs.The fit was refined by making a plot of the difference between the actual values of In BASand the linear approximation to this quantity. Thus, one defines A = In B*As - ( S , / P ) - It
where S,and I, are the slope and intercept obtained in the initial linear fit. A plot of the theoretical A is shown in Figure 1. Experimental data are also shown in Figure 1 together with the estimated experimental uncertainty, which is significant only because of the expanded scale of this difference plot. The two sets of data shown are plotted vs. 1 / 1 1 = t,/kT for c,/k = 33.4 K. Two reducing factors for BAS* are taken which correspond to In (Au ) of -10.350 and -10.310 (best fit). Evidently, these data can r e fit to the calculations for a site-site summed 10-4 potential model. We have not examined alternative models but, based on analogous studies of rare gas/gcb systems, feel that it is likely that fits to the curves for other potentials could be made but that the values obtained for ugswould be less realistic than that given by the present model.8 In particular, an arithmetic mean approximation for up [=(uw + um)/2] yields 3.36 A, based on the accepted um = 3.32 8, and the ucc = 3.40 8,used in earlier works4 Consequently, this analysis yields A = 19.7 m2/g which agrees nicely with the BET value of 21.0 m2/g. It is also pleasing to note that this value of t,/k agrees well with the previous value of 31.9 K obtained from a geometric mean argument (tNC = (~cct")~/~) and used by Talbot et al. in computer simulation^.^ It also is consistent with the value of 34.5 K deduced by Piper et al.'O from an analysis of their experimental heats of adsorption at 79 K. In fact, our data yield the zero-coverage heat of adsorption simply by evaluating the slope of In (BAs/kT) vs. 1 / T . In this way, we find qJ0) = 10.1 i 0.2 kJ/mol, compared to 10.4 f 0.1 kJ/mol given by Piper e t al. (Note that our temperature is roughly 60 OC higher than theirs.) The process of fitting B u for CO/exg to theory is made more difficult by the fact that five adjustable parameters are present. We have attempted to reduce these by fixing the ratio tSc/tSO ( = R ) and the values of uSc and USO, thus leaving the fitting parameters 34. and tsC,the well depth for carbon sites in CO and in graphite. The size parameters were obtained from the usually (8)Sokolowski,S.; Stecki, J. J.Phys. Chem. 1981,85, 1741. See other references therein. (9) Talbot, J.; Tildesley, D. J.; Steele, W. A. Mol. Phys. 1984,51,1331; Surf. Sci. 1986, 169, 71; Faraday Discuss. Chem. SOC.1985, 80,91. (IO) Piper, J.; Morrison, J. A.; Peters, C.; Ozaki, Y. J. Chem. SOC. Faraday Trans. 1 1983, 79, 2863.
r( iable arithmetic means but were based on less reliable site-site values obtained from previous limited analyses of bulk CO properties." One possibility is to follow the study of Piper et a1.,12 who used R = 1.18, uSc = 3.39 A, and uSo = 3.14 8,. In the work of Piper, et al. the CO-solid potential was obtained by applying geometric and arithmetic mean combining rules to a CO-CO potential suggested by Mirsky" in which the C-C and the 0-0well depths differed by 40%. We (and others)13-'5 believe this to be unlikely and therefore considered also an approximation in which CO was taken to be N2-like except for its (known) quadrupole moment. For reference, a comparison of a number of physical properties for Nz and CO is given in Table 11, where it can be seen that the two substances are similar in most respects, with the most obvious differences being in the large quadrupole moment and in the small but nonzero dipole moment of CO. Thus, the C-S and the 0-S site parameters were assumed to be identical, which reduces the adjustable parameters to a reasonable number. Furthermore, it was assumed that A = 19.7 m2/g from the Nz study, leaving only tgsand u, to be determined. Table I11 gives a comparison of our determinations of the parameters for CO/exg with those of Piper et al. It is evident that both studies give essentially the same results for the Mirsky potential, which is not surprising considering the complete agreement between the experimental zero-coverage isosteric heats of 10.9 kJ/mol. Although we do not show them here, the quality of the fits of experiment to theory is equally good for the Mirsky-derived and the N2-like potentials. Note that the N2-like parameters shown in Table I11 appear to be reasonable and support the argument that CO and Nz are similar molecules. The theory for the BzD of nonspherical molecules requires a relatively lengthy calculation because one must average over molecular orientation variables as well as center-of-" positions for the two adsorbed molecules. (Indeed, the 2D notation is no longer very appropriate because the probable orientations of these particular molecules are spread over the entire range, especially at T > 100 K, so that no 2D approximation can be invoked.) A second problem arises from the fact that BZD is a slowly varying function of temperature given by the ratio of two strongly temperature dependent quantities W2 and B&2 (see eq 4). Of course, this means that the separate calculations of Wz and BAs must be done to high precision and without simplifying approximations. A third, more severe problem arises from the large number of parameters involved for N2 and especially for CO. They include (11) Mirsky, K. Chem. Phys. 1980,46, 445. (12) Piper, J.; Morrison, J. A.; Peters, @. Mol. Phys. 1984,53, 1463. (13) Belak, J.; Kobashi, K.; Etters, R. D. Surf. Sci. 1985, 161, 390. (14) Peters, C.; Klein, M. L. Mol. Phys. 1985, 54, 895. (15) Fain, S. C. Ber. Bunsenges. Phys. Chem. 1986, 90, 211.
Langmuir, Vol. 3, No. 1, 1987 119
Virial Coefficients for Adsorbed N2 a n d CO Table IV. Experimental B I D / &(mol-') 0.9-
-14.9 (f1.6) -8.1 (f2.4) +3.3 (f2.9) +11.4 (f2.2) +26.7 (f1.4) +36.3 .(f3.9)
89.51 99.55 109.54 128.92 151.00 170.12
89.63 99.68 109.64 129.07 151.16 170.29 190.69
-15.0 -3.7 -5.7 +24.9
(f3.0) (f2.5) (f2.2) (f2.1) +%.8 (f1.4) +29.2 (f3.3) +33.7 (f4.2)
I
I
0.6
-
0.38;o.o-0.3
-
-0.6
-
- 0.91
-I 2
0120
I
I
0176
0232
I
I
028: I/T
0344
0400
0456
Figure 3. Reduced two-dimensional second virial coefficient of Nz and CO on Grafoil: (1)BZD*calculated by using the N2-Nz model potential; (2) BzD* calculated by using cg = 28 K, ugg= 3.32 A, and q = 0.405 e (best fit to Nz data 0); (3) calculated by using c = 27 K, ugg= 3.32 A, and q = 0.388 e (best fit to CO (A) experimental data of Levi.20 data 0);
km*
I
I
E,,
-2.0 -24
t
012
'i
\ I
I
0176
0232
0288 I/TX
0344
I
I
040
0456
-36
vs
T
for
I
I
I
CO
-
-5s-
0
co
-so-
-
Figure 2. Reduced two-dimensional second virial coefficient of CO on Grafoil as a function of 1/P:(1)Bm* calculated by using the Mirsky CO-CO potential," (2) Bm* calculated by using the Mirsky CO-CO potential with well depths reduced by 50%; (0) experimental data for CO on Grafoil. those for the molecule-solid potential as well as those for the molecule-molecule interactions. Of course, we can assume that the molecule-solid potential and the area are given correctly by the BA9analyses. Furthermore, one might use molecule-molecule potentials obtained from studies of bulk Nz and CO, thus leaving no adjustable parameters. We will see that this approach gives quite poor results and leads to the conclusion that substratemediated effects on the molecule-molecule potential are significant, as suggested by a number of theoretical studies.lsJ7 Values of BzDobtained from the experimental isotherms are listed in Table IV. A comparison between the data and theory based on the Mirsky C O C O potential is shown in Figure 2, where it can be seen that this model is not valid for CO/exg, primarily because the CO-CO interactions are much too attractive. Even a 50% reduction in all the site-site well depths did not bring theory and experiment into agreement, primarily because the quadrupolar interaction has been left with its large gas-phase parameter. At this point, this model for the CO interaction was abandoned for the Nz-like model. Figure 3 shows both the Nz and the CO data as well as several theoretical curves. First, note that the N2/N2model potential that gives a good account of the bulk liquid and solid is too attractive for molecules on the surface. However, if one reduces the site-site well-depth parameter cm/k from 36.4 (bulk model) to 28 K, the theory comes into moderately good agreement with experiment. This reduction of 25% is consistent with the arguments of Bruch,'* among others,lg who conclude that the substrate-mediated effect often referred to as (16) Sinanoglu, 0.;Pitzer, K. S. J. Chem. Phys. 1960, 32, 1279. (17) McLachlan, A. D. Mol. Phys. 1964, 7, 381. (18) Bruch, L. W. J. Chem. Phys. 1983, 79, 3148. (19) Rauber, S.; Klein, J. R.; Cole, M. W. Phys. Rev. B 1983,27, 1314.
-
-
Figure 4. Bulk second virial coefficient of CO as a function of T (1) experimental values of B3,, ( o )and ~ ~theoretical curve calculated by using the symmetric Nz-like potential and the experimental quadrupole moment of CO; (2) theoretical curve of BIDvalues calculated by using the asymmetric potential proposed by Mirsky.lo the MacLachlan energy but first estimated by Sinanoglu and Pitzer16 should bring about such a reduction. A closer examination of the CO data is now in order. The similarity of the experimental data for N, and CO shown in Figure 3, taken together with the bulk data, leads one to believe that their interactions should be similar. However, the site-site parameters obtained by Piper et al. from the original calculations of Mirsky are12 ecc/k = 39.9 K ucc = 3.89 A
A
eoo/k = 61.6 K
uoo = 2.89
eco/k = 49.6 K
tco = 3.14 A
Although all interactions appear to be too attractive, it is primarily the large 0-0 well depth that causes the large discrepancy be-
120 Langmuir, Vol. 3, No. 1, 1987
Bojan and Steele
tween theory and experiment shown in Figure 2. Furthermore, these parameters yield poor values for the usual (bulk) second virial coefficient, as indicated in Figure 4. Note that discrete charges were placed in the CO molecule in these calculations to give appropriate values of the dipole and quadrupole moments. Thus, q = 0.927 e on an 0 atom, 0.731 e on a C atom, and -1.658 e at the center of mass, where e is the electron charge. Since it appeared that the Mirsky-derived model was not very realistic, a drastic change (and simplification) was introduced by switching to a Nz/Nz-like description. The dipole moment is deleted in this model, but this is a small factor in the calculation in any case. The "best-fit" curve for CO in Figure 3 is based on the following parameters:
tss/k = 27 K
u s s / k = 3.32 A
q = 0.388 e
where S denotes a site in the N,-like CO model. The site-site well-depth and size parameters are quite close to those for Nz, as anticipated. However, the charge q used here yields a quadrupole moment of -1.19 X lo-%esu, which is closer to the nitrogen gas-phase value than that of CO. It should be emphasized that this reduction is an important part of the calculation, since the BIDevaluated using the full gas-phase quadrupolar energy were noticeably too negative for any reasonable site-site well depth.
Discussion This study represents the first detailed comparison between theory and experiment for the gas-solid virial coefficients for N2 and CO. Indeed, this appears to be the first report of experimental data for the N2/exg and CO/exg systems. Earlier but still unpublished data of Levy20 for N2/gcb are shown in Figure 3. Within the uncertainties produced by the use of samples which differ in surface perfection and in surface area, the two studies agree nicely. The theoretical analysis of the N2/exg experiments produces no great surprises. The N2/exg interaction potential obtained here agrees very well with previous estimates based on the site-site model and Lorentz-Berthelot combining rules. (Note that ccc/k and cm/k are not very different, so that the use of the geometric mean for cNC/k does not really test the accuracy of the rule.) Primarily, this analysis gives one increased confidence in the site-site model for N2/exg (and other similar systems) while providing improved estimates for the potential parameters. In particular, the 25% reduction in the N / N site-site potential for molecules in the monolayer is a significant change from previous assumptions, and it should be included in future theoretical and computer simulation studies. The CO study produced several interesting findings. In the first place, we conclude that molecule-solid and adsorbed molecule-molecule interactions based on the Mirsky model are invalid and should be replaced by models in which the similarity between CO and N2 is exploited. Even given this, the reduction in quadrupole moment needed to produce agreement between theory and experiment is considerable and somewhat unexpected. Nevertheless, it is not without support from the studies (20) Levy, A. C. Ph.D. Thesis, Georgia Institute of Technology, Atlanta, 1976.
of the in-plane orientational disordering transition for CO on gcb.16i21*" These experiments show that the transitions for CO and N2 occur a t roughly the same temperature (-28 K). However, the magnitude of the angle-dependent part of the interaction in these monolayers depends strongly upon quadrupole moment and, based on simulations of N2 with different quadrupole moment^,^ would lead one to expect that the temperature for the CO transition might be as much as twice that for N2. Table I1 indicates a ratio of 1.7 for these temperatures in the bulk phases. Further supporting evidence is provided by the measurements of the coverage dependence of the heats of adsorption by Piper et a1.1°J2 It is known that the initial slope of qstvs. N, for a homogeneous surface is proportional to the average molecule-molecule interaction in the film. Although the presence of residual heterogeneity makes it difficult to accurately estimate these slopes, the curves of qst for N2 and CO are quite similar and show no obvious manifestation of a large quadrupole-quadrupole interaction in the CO monolayer. A possible mechanism for reduction in the effective electrostatic interactions between molecules adsorbed on a dielectric solid comes from the image charge calculation of classical electrostatics. That is, a charge q at a distance d from the surface of a planar dielectric can be viewed as inducing a charge of opposite sign within the dielectric at the same distance from the surface and with a magnitude depending upon dielectric constant. Bruch has already considered this effectla and concluded that it leads to a nonnegligible reduction in the effective quadrupole moments of molecules in the monolayer. However, the approximation of graphite as a continuum dielectric and the arbitrary choice of distance 2d between charge and image charge lead to considerable uncertainty in the calculation, so that the rather small reduction of -20% found by Bruch could be increased without necessitating any conceptually different theory. A t least one unresolved problem remains: a reduction of 20% in quadrupole moment for adsorbed N2 gives agreement between experiment and simulation, but the image charge arguments and our CO results suggest that the change should be considerably larger than this. At present, there is no obvious way to resolve this inconsistency. Acknowledgment. This work was supported by a grant from the Division of Materials Research of the NSF. Computer programs provided by Dr. Stefan Sokolowski are gratefully acknowledged. Helpful discussions with S. Sokolowski, M. Cole, and M. Chan are also acknowledged. Registry No. CO, 630-08-0; NB,7727-37-9; graphite, 7782-42-5. (21) Morishige, K.; Mowforth, C.; Thomas, R. K. Surf. Sei. 1985,151, 289. (22) Feng, Y.; Chan, M. H. W., unpublished results. (23) Dymond, J. H.; Smith, E. B. The Virial Coefficients of Pure Gases and Mixtures. A Critical Compilation; Clarendon: Oxford, 1980. (24) Stogryn, D. E.; Stogryn, A. P. Mol. Phys. 1966, 11, 371. (25) Scott, T. A. Phys. Rep. 1976,27C, 89. (26) Herzberg, G. Spectra of Diatomic Molecules; McGraw-Hill: New York, 1960. (27) Parsonage, N. G.; Staveley, L. A. K. Disorder in Crystals; Clarendon: Oxford, 1978. (28) Giauque, W. F.; Clayton, J. 0. J. Am. Chem. SOC.1933,55,4875. (29) Clayton, J. 0.; Giauque, W. F. J. Am. Chem. SOC.1932,54,2610. (30)Hall, B. 0.;James, H. M. Phys. Rev. E 1976, 13, 3590.
