Langmuir 1987, 3, 1123-1127
Amount of chemisorbed HzO, OH groups n d
Figure 8. Relation between electrostatic field strength and surface H20content on each of two kinds of surfaces: ( 0 )(110) surface; (0) (100) + (101) surface. other hand, the F value of the (110) plane, F(,,,), remains constant at 1.54 X lo4 statvolt cm-l at evacuation temperatures from 25 to 150 OC. The F(llo,value then increases almost linearly with decreasing amount of surface hydroxyls, which also impliesthe (110) surface to be homogeneous. Strictly speaking, on the extremely dehydroxylated surfaces the F(',,) curve deviates slightly to higher values from the straight line, probably because af the presence of active sites or various kinds of surface defeds. In conclusion, the two kinds of surfaces, (110) and (100) + (101), are found to be homogeneous, respectively.
1123
Furthermore, it is interesting to see that the F(llo) value on the bare (110) surface is 3.26 X lo5 statvolt cm-', being remarkably larger than the average F value of the actual surface (Figure 4). In the bulk of the rutile crystal, the coordination numbers of Ti4+and 02-are 6 and 3, respectively, so that the formal charges of Ti4+and 02-are +2/3e and -2/3e per bond, respectively, where e is the electronic charge. On the other hand, in the bulk of the wurtzite crystal the coordination numbers of both Zn2+and 02-are 4, so that the formal charges of Zn2+are 02-is + 1 / 2 eand -1/2e per bond, respectively. Thus it can be expected that the F value of the bare (110) surface of rutile is larger than that of the bare (10x0) plane of ZnO. However, the experimental F values of rutile and ZnO are found to be almost equal, Le., 3.26 X lo5 and 3.38 X lo5 statvolt cm-l, respectively. Upon the analysis procedure of heat of adsorption stated above, it is assumed that the heat values of the organic adsorbates on the hydroxylated (110) surface are identical with those on the hydrated (100) + (101) surface, but in practice the former may be larger than the latter. With this point of view taken into account, the true F value of the (110) surface of rutile may be larger than the F(',,, value shown in Figure 8.
Acknowledgment. I thank Professor Tohru Takenaka of Kyoto University for his kind advice and helpful suggestions and Professor Mahiko Nagao of Okayama University for much help in the heabof-immersion experiments. I also thank Professor Tetsuo Morimoto of Okayama University for his helpful discussions and constant encouragement throughout this work. Registry No. H20, 7732-18-5;Ti02, 13463-67-7; 1-BuOH, 71-36-3; l-BuCI, 109-69-3;n-C,Hle, 142-82-5.
Interactions of Diatomic Molecules with Graphite Mary J. Bojan and William A. Steele* Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802 Received March 31, 1987. In Final Form: June 24, 1987 Low-coverage isotherm data for the adsorption of 02 on exfoliated graphite are reported and analyzed by using the virial adsorption isotherm. The molecule-solid and the adsorbed molecule-molecule second virial coefficients are obtained for this system over a range of temperature. These data are compared with theory, and best-fit parameters for the site-site moleculesolid interaction potential are given. In addition, a comparative study of the molecule-molecule interactions for 02,N2,and CO is presented, based on the molecule-molecule virial coefficients reported here (and elsewhere for N2and CO). It is concluded that the solid produces an alteration in the site-site well-depths for these systems in agreement with theoretical arguments. 1. Introduction The thermodynamics and phase equilibria of simple molecules adsorbed on the (nearly) homogeneous exposed basal plane of graphite have been a subject of great interest over the past decade or so. An understanding of the interaction of these molecules with the solid and with each other when in an adsorbed film is essential for these systems both to the development of an adequate theoretical understanding and to the elucidation of molecular behavior via computer simulation. The virial adsorption isotherm is a powerful tool for analysis of experimental data, since 0743-7463/87/2403-1123$01.50/0
it enables one to extract unambiguous information concerning single adsorbed molecules and pairs of such molecules from the measurements.l This approach has led to reasonably good interaction potentials for the rare gases on graphite, judged by the success of computer simulations in reproducing the phase behavior of these systems.2 Applications to nonspherical adsorbate molecules (1) Steele, W. A.; Haleey, G. D., Jr. J. Chem. Phys. 1954, 22, 979. Sams, J. R., Jr.; Constabaris, G.; Halsey, G. D., Jr. J.Phys. Chem. 1960, 64, 1689. Sams, J. R., Jr.; Constabaris, G.; Halsey, G. D., Jr. J. Chem. Phys. 1962,36, 1334.
0 1987 American Chemical Society
Bojan and Steele
1124 Langmuir, Vol. 3, No. 6, 1987
are less advanced, due partly to the need for more extensive computations and partly to the increase in complexity of the interactions of molecules with shape factors in the dispersion-repulsion energy and with permanent electrostatic multipoles, to name only the most significant differences from rare gas interactions. In a previous paper3 (hereafter referred to as I), we have reported experimental data for N2 and CO on exg (exfoliated graphite). These data were analyzed to obtain the first two virial coefficients for these adsorbates over a range of temperature, and the results were compared with the coefficients calculated from model potentials. In this paper, we report the data for oxygen on the same adsorbent. In light of the great similarity in physical properties (molar volume, melting and critical point parameters, boiling point, bulk second virial coefficients, etc.) for 02, N2, and CO, it seemed of interest to compare the results obtained for the three molecules on graphite and to attempt to generate a consistent set of model interaction potentials for the three gases. The procedure followed in this study was identical with that of the previous work: low coverage experimental isotherm data were fitted to the virial expression that is' In (n,/p) = ln (BAs/kT) - ~ ( B z D / & )-k~ ,... (1.1) Thus, the intercepts and limiting slopes of plots of In (n,/p) versus n,, where n,, p , and A are the moles adsorbed the pressure, and the surface area, respectively, will yield the desired virial coefficients BASand B2D. Results obtained over a range of temperature were then fitted to the theoretical expressions for these quantities
BAS = l(exp[-u,(R)/kT]
- 1) dR
(1.2)
where u,(R) is the adsorbate-solid interaction energy of a molecule at position r, with orientation Q relative to the adsorbent surface. For nonspherical molecules, B2Dloses its convenient approximation as a two-dimensional gaslike second virial and must be calculated from the more complicated general expression that can be written as6 B2D _ -- -B3D- - w2 A BAS B A S ~ The term in B3Dis a small correction for nonideality of the bulk gas in the adsorption volume. W2 is the surfacesensitive term that can be written
W2 =
'/2$
exp(-u,(Rl)/kT) d R l l [exp(-u,(RJ/kT) - ll[ex~(-u,,(R~~)/kT)- 11 dR2 (1.4)
where u,,(RI2) is the interaction energy of a pair of adsorbed molecules, with relative position variables R12 = rl - r2, Q1, Q2. Computer programs developed previously for the N2and CO studies were used in the present work. Evidently, one needs models for the interactions of the adsorbate molecules with each other and with graphite surface. For N2 and CO, we found that the molecule-solid energies appear to be nicely approximated by a site-site approach in which the solid is represented as a collection of C atom sites, each (2) See, for example: Abraham, F. F.; Rudge, W. E.; Auerbach, D. J.; Koch, S. W. Phys. Rev. Lett. 1984,52,445. Abraham, F. F.; Koch, S. W. Phys. Rev. B: Condens. Matter 1983,27, 2964. (3) Bojan, M. J.; Steele, W. A. Langmuir 1987, 3, 116. (4) Steele, W. A. The Interactions of Gases with Solid Surfaces; Pergamon: New York, 1974. (5) Sokolowski, S.; Stecki, J. Acta Phys. Pol., A 1979, A55, 611. Sokolowski, S.; Stecki, J. J. Chem. Soc., Faraday Trans 2 1981, 77, 405.
of which interacts with two sites in the diatomic adsorbates via spherical Lennard-Jones functions. Furthermore, it emerges that the periodic part of the molecul-olid energy is quite negligible in the problems under consideration here. Thus, u,(R) is approximated as wo(z),a function which gives the surface-averaged interaction of an adsorbate site with the solid. The explicit expression for wo(z) is6
(1.5) where tgsand ugsare the well-depth and size parameters, respectively, in the molecule site-carbon site interaction function, d is the interplanar distance (3.40 A), and a, is the area per C atom in the basal plane of graphite (5.24 A2). The sums over planes can be replaced by analytic approximations for convenience in evaluating the integrals in BAS and B ~ D . For the diatomics considered here, the adsorbate-adsorbate interactions are based on two sites per molecule interacting via Lennard-Jones functions. In addition, electrostatic quadrupolar energies were included, since the known quadrupole moments for N2 and CO indicate that these energies form a significant part of the total. However, the quadrupolar energy for O2 is much smaller-by roughly a factor of 10 compared to that for N2-so that this contribution could safely be omitted in the O2 calculations.' One of the most interesting features of this study arises from the theoretical predictions that adsorbateadsorbate interactions will be modified from their bulk values when the pair is in the vicinity of a s0lid?1~ In fact, for molecules at their first layer distance from the solid, the estimates of these changes amount to -25% decreases in the well-depths. One goal of this analysis was to ascertain whether this has a noticeable affect on the comparison between calculated and the measured BPDvalues. Comparative analyses of the three rather similar adsorbates on the same solid will strengthen any conclusions concerned with these questions. Another problem which will be studied arises in the parameterization of the molecule site-solid site interactions. One hope is that the simple Lorentz-Berthelot rules that are often used to specify unlike molecular pair interactions in bulk solutions will apply here. Even in bulk, there is little theoretical justification for using these rules for the site-site functions. Nevertheless, studies of the rare gases on graphite'O as well as our previous analysis of N2 and CO on this solid indicate that an arithmetic mean calculation of ugcis satisfactory and, also, that a geometric mean for tgsworks moderately well. In fact, most of the criticism of these rules is (correctly) directed at the geometric mean rule for tl2, since it seems to fail badly when ell and tZ2are very different." As it turns out, the site-site tgg/k for the three diatomic molecules considered here are not so different from the value of 28 K chosen for tcclk. We will show that the BAS data for O2 can be fitted by using a site-site model with well-depth and size parameters that agree well with the Lorentz-Berthelot estimates obtained with the same values of t C C / k and a C C used in previous studies of rare gases as well as Nz and CO. Steele, W. A. J. Phys. C o l l i . 1977, 38, C4, 61. Stogryn, D. E.; Stogryn, A. P. Mol. Phys. 1966, 11, 371. Sinanoglu, 0.;Pitzer, K. S. J. Chem. Phys. 1960,32, 1279. McLachlan, A. D. Mol. Phys. 1964, 7, 381. (IO) Steele, W. A. J. Phys. Chem. 1978, 82, 817. (11) Henderson, D. Annu. Rev. Phys. Chem. 1974,25, 461.
(6) (7) (8) (9)
Langmuir, Vol. 3, No. 6, 1987 1125
Interactions of Diatomic Molecules with Graphite I
Table I. Experimental B M and BZD/Afor O2 on exg temp, K Bm, cm3/g BZD/A,mol-' 89.60 241.9 -70.8 99.65 70.45 -47.3 109.64 24.79 -34.9 129.04 5.603 -14.5 151.14 1.719 -3.7 170.26 0.844 190.58 0.429
2. Data Analysis The apparatus and experimental procedure employed in the measurement of the low coverage parts of O2 isotherms on exg (exfoliated graphite) were the same as in I. Furthermore, the same sample of exg was used, so that the total (and specific) area A of the solid is the same in all three studies. Results for BAS and BPDare given in Table I. Because there are three adjustable parameters involved in the calculation of BASand only two can be uniquely determined in the fitting process, one of the three must be specified prior to the calculation. The value of upswas chosen to be a constant given by the arithmetic mean rule. As in previous calculations for rare gases on graphite,1° ucc was taken to be 3.40 A. aOO was chosen to be 2.988 A, the value used by Laufer and Leroi in their calculation of the lattice frequencies of the y and p solid phases of In a more recent calculation by Klein et al.13 it was shown that this choice of u00, along with a value of 52 K for toolk, reproduced the bulk experimental virial coefficient data of O2rather well. With this parameter fixed, the integrand of eq 1.2 was evaluated by using an expression for w&) equivalent to eq 1.5 and reduced units for temperature (P = kT/eoc). The calculated BAs/kT were fitted to experiment following the procedure described in I. The best fit gave a value of toc/k of 37.6 K, which is in satisfactory agreement with 38.2 K obtained from the geometric mean argument when too/k = 52 K and ecc/k is taken to be 28 K. In addition A was found to be 19.7 m2/g, in excellent agreement with the surface area obtained in the analysis of the data for N2 adsorbed on the same sample. Our measured BASvalues produce a value for the limiting low coverage isosteric heat of O2 of 10.0 f 0.10 kJ/mol, which is close to the 10.5 kJ/mol measured by Gale and Beebe14 at nearly the same temperature. This result was further confirmed in a calorimetric study by Smith and Ford.15
3. Comparison Of 02,N2,and CO on Graphite As is well-known, the three diatomic molecules considered here have very similar bulk properties. The fact that CO is heteronuclear is almost irrelevant for present purposes, since the dipolar interaction for this moelcule is negligible under the conditions of these experiments.16 The plots of BAS shown in Figure 1 indicate that the interactions of these molecules with graphite are not very different. This is borne out by the parameters found for the site-site potential curves by fitting the experimental BASto theory. Not only are the results shown in Table I1 close to one another, but also they agree reasonably well with estimates based on the combining rules. This is particularly gratifying in the case of the N2-likemodel for CO, since the simplification introduced by letting both ends of the molecule be identical is extremely helpful in (12) Laufer, J. C.; Leroi, G. E. J. Chem. Phys. 1971,55,993. (13) Klein, M. L.; Levesque, D.; Weis, J. J. Phys. Reu. E Condens. Matter 1980,21, 5785. (14) Gale, R. L.; Beebe, R. A. J. Phys. Chem. 1964, 68,555. (15) Smith, W. R.; Ford, D. G. J . Phys. Chem. 1965, 69,3587. (16) You, H.; Fain, S. C., Jr. Surf. Sci. 1985, 151, 361.
I
I
I
I
I
I
Ifcar
6L
543-
2-
cn
m'
c I-
o(
-
0-
-I
-
-T
-3
-43
'
4
5
6
7 8 I / T x IO3
9
IO
II
12
Figure 1. Experimental values of BAS for N2, 02,and CO on exfoliated graphite plotted versus 1/T on a logarithmic scale. Table 11. Summary of Molecule-Solid Interaction Site Parameters and Related Quantities O2 CO (NJike) Nz tr/k (K) fit to Bm combining rule up
(A)
33.4 * 31.9" 3.36*
37.6 38.2O 3.1gb
37.3 31.9 3.31e
10.1 10.421
10.0 10.514
10.9 10.922
qBt(kJ/mol)
this work results of other workers
"From combining rule using = 36.4 K,23€00 = 52 K12 (obtained from studies of bulk phases), and tCC = 28 K.l0 bFrom um = 2.99 (obtained from combining rule using uNN = 3.32 studies of bulk phases), and ucc = 3.40 %..lo cFrom fit to BASusing A = 19.7 m2/g, as obtained from the O2 and N2 analyses.
the analysis of the BzDdata. As indicated in I, the analysis of the BZD,which involve the interactions of a pair of molecules in the vicinity of the surface, is a more difficult task than that for the singlemolecule quantity BAS. This calculation benefits considerably from a comparative analysis of the three gases. Other than minor differences in the site-site interaction parameters for the molecules considered here, one must take careful account of the very considerable differences in electrostatic quadrupole interactions, which are negligible for 02-02, significant for N2-N2 (roughly, a factor of 10 larger than for 02),and large for CO-CO (a factor of 3 larger than for N2). Furthermore, preliminary analyses of the Bm data show clearly that the bulk phase interaction potentials are modified in the vicinity of the solid adsorbent, with reductions in the attractive wells amounting to -20%. Two questions that we hope to answer are: does this reduction affect all three molecules equally and does it affect the quadrupolar part in the same way as the site-site dispersion-repulsion part? Of course, the absence of significant quadrupolar interactions is helpful in unraveling the O2 case, so we consider this first. Figure 2 shows the experimental Bm data for O2on exg together with two theoretical curves: one calculated by using site-site well-depth and size parameters appropriate for bulk O2 and the second (which gives a reasonable fit to the data) calculated by using well-depths reduced by -20% from the bulk phase values. In the previous study of N2and CO, similar substratemediated changes in well-depth were needed to fit the data, but an extensive analysis was not carried out because of questions concerning the relative importance of the quadrupolar and the dispersion-repulsion parts of the interaction. We will now use the O2results as support for
1126 Langmuir, Vol. 3, No. 6, 1987 I
0.4
Bojan and Steele I
I
I
-
1
0.0-
-0.4-
-0.8-
-1.20120
0 176
0.232
-1.6-
0288 I/T*
0.344 0 4 0 0
Figure 4. Second virial coefficients for CO shown by the squares, with estimated experimental uncertainties indicated by the vertical lines. Curves are calculated by using the following parameters for the N,-like potential: (1) talk = 20 K, u = 3.32 A, qeff= 0.82 e; (2) various parameter sets listed in Tabye I11 all give this curve. Figure 2. Experimental values of E ~ for D 02 on exg plotted as a function of 1/T together with the uncertainties. Reduced units for Em and Tare defiied by Bm* = BD/uP2N,,and P = kT/em. Curves are calculated by using the following parameters for the 02-02 sitesite potential: (1) bo/k = 52 K, 000 = 2.99 A; (2) k = 40 K, uo0 = 2.99 A. (Quadrupolar energies are neglected in both cases.) - 2 . 1
0.6
00-
-0 3-06BD :
-09-I 2-I 5 -I 8-
Table 111. Parameters for the 'Best-Fit" CO Site-Site Potentials"
clk
U
28 27 25
3.32 3.32 3.32
Q/Qo 0 0.47 0.75
"Experimental quadrupole moment Qo = -2.5
X
em7
needed depends upon the effective quadrupole moment used. Given the experimental uncertainties indicated in the figure, more detailed conclusions are unwarranted. We now reconsider the CO data for BZD. In I, it was argued that an N2-like model is more realistic than the alternative suggested by Mirsky." Using this approach and neglecting dipolar energies, we have attempted to fit calculated curves to the data by using the first known quadrupole moment and a variable site-site well-depth. Figure 4 shows that the best fit is obtained by using a well-depth reduced by 44% from the site-site value u l k = 36 K which fits the bulk virial coefficient data. Alternatively, we attempted to maintain consistency with the 0,and N2 systems by constructing curves using site-site well-depths reduced by 20% and looking for the best-fit quadrupole moments. Several different potentials produced essentially the same "best-fit" theoretical plot (shown as curve 2 in Figure 4). The parameters of these potentials are shown in Table 111. We conclude that a significant reduction in the quadrupolar interaction for CO molecules on graphite is needed to fit the data while being consistent with the Nz and O2 results. I t is not possible to say precisely how much reduction is needed, but a reduced value in the range of 5@75% of the known moment could easily account for the data, which are obviously not highly precise. N
-2 I-2 4I
I
I
I
0 I20 0176 0232 0288 0 3 4 4 0 4 0 0 I/T*
Figure 3. BD values plotted for N2 on exg as a function of 1/T (reduced units are defined as in Figure 2). Curves are calculated by using the following parameters for the N2-N2 potential: (1) &k = 36.4 K, U" = 3.32 A, qaff= 0.41 e (for quadrupolar interaction); (2) em/k = 28 K, u m = 3.32 & qsIr= 0.49 e; (3) w / k = 28 K, "U = 3.32 A, qetf= 0.41 e; (4) em/k = 28 K, um = 3.32
A, qeff= 0. an assumption of a -20% reduction in well-depth for both N2and for the N,-like CO model. A number of calculations are compared with the BzDdata for N2 in Figure 3. In addition to using the bulk-phase well-depth ( t - / k = 36.4 K) and a quadrupole moment decreased by 20% from the best experimental value (curve l), several potentials were studied that were characterized by a 20% reduction in em and various quadrupole moments. I t is evident that the quadrupolar interaction has only a minor effect on the calculated BzD and that a reduction in the site-site welldepth is required to fit the data. The magnitude of this reduction must be close to 20%, but the precise value
4. Discussion This work, combined with similar analyses of the data for the rare gases interacting with graphite, leads to the conclusion that the molecule-solid potentials constructed by summing over the sites in the adsorbate molecules and in the solid are in rather good agreement with experiment. Attempts to estimate the parameters of the potentials using Lorentz-Berthelot combining rules are moderately successful, with significant errors appearing primarily in (17)Mirsky, K. Chem. Phys. 1980, 46,445.
Langmuir, Vol. 3, No. 6, 1987 1127
Interactions of Diatomic Molecules with Graphite the geometric mean rule for well-depth when the gas-gas well-depth differs considerably from the 28 K taken for elk for carbon sites. In fact, the well-depths given here and in I do not depend upon the combining rule for their accuracy-we discuss this approximation only in respect to its possible utility for other gases on graphite where suitable BASdata may not be available. We note also that these data are not very sensitive to the corrugation of the surface energies, since calculations of BAS under conditions relevant to the experiments yield essentially the same values whether or not the sitesite corrugation is included. It is interesting to find that the BZDdata for the gases on graphite imply a significant reduction in both the site-site well-depths and in the effective quadrupole moments for molecules on the surface. Of course, theoretical studies of substrate-mediated changes in intermolecular interactions have indicated that effects of the magnitude found in this work should be present.l* Indeed, Bruch has published an explicit calculation for the N2/graphite system that includes an estimate of the alteration in electrostatic interaction due to the presence of a dielectric solid as well as the better-known substrate-mediated change in site-site well-depth.lg If one represents the quadrupole moment as a symmetric arrangement of discrete charges on the atoms plus a pair of neutralizing charges located at the molecular center, the effect of the nearby solid can be viewed in terms of a production of image charges in the solid with sign opposite to the real charge and magnitude. (For convenience, this discrete charge representation of the quadrupolar interaction was used throughout the present calculations. The experimental quadrupole moments for N2 and CO are obtained by placing charges of 0.49 e on the N atoms and 0.82 e on the C and the 0 atoms as well as -0.92 e and -1.64 e at the respective molecular centers.) The resulting image quadrupole will interact with the real inducing quadrupole to produce an extra attractive term in u&R)that is proportional to quadrupole moment and, thus, is largest for CO. Evidently this energy is not explicitly included in the calculations reported here. In addition, the images interact with the quadrupoles of neighboring adsorbates to give an effectively repulsive interaction term. The effect of this upon the total electrostatic interaction depends upon the molecular size, which determines the distance between the quadrupole and the dielectric solid and, through this (18) Rauber, S.;Klein, J. R.; Cole, M. W. Phys. Reu. B Condens. Matter 1983,27, 1314. (19) Bruch, L. W. J. Chem. Phys. 1983, 79, 3148.
distance, the magnitude of the image charge. On an atomic scale, this model is defective in this representation of the solid as continuous dielectric with discontinuous change in density a t the surface. Consequently, one cannot reliably use the model in a quantitative calculation of the effects of the substrate upon the electrostatic interactions of adsorbed molecules. Nevertheless, the sign and the general order of magnitude of the effect do correspond to our conclusion that the quadrupolar interactions for N2 and CO on exg are reduced by perhaps 25% relative to that for the bulk gas. The estimated reduction of 20-25% of the site-site well-depth due to the substrate mediation is on somewhat more solid ground, since (a) the data now include the nonquadrupolar O2 molecule and (b) the calculated BzD are much more sensitive to this part of the interaction than to the electrostatic terms. Here, the choice of a graphite substrate is fortunate, since interference due to induction by an electric field at the solid surface or to corrugation in the nonelectrostatic part of the gas-solid potential is minimal. It should be noted that ugs,which was taken to be a fixed parameter in the fitting process, depends on the value chosen for u,. While the value of 3.40 A used here has been widely used in previous studies, an analysis of He scattering data has led Cole and Klein to propose 2.84 A for the graphite uwZo If this value is used in the combining rule, the resulting values of agsare approximately 10% lower than those assumed in this study. In order to obtain an equivalent fit of experiment to theory with the modified ugs,the value of cgs must be increased by nearly 20% and the value of the surface area by -3%. Since the quality of the fits obtained with these parameters is not significantly inferior to that for the original set, the data give no support for one set over the other. Of course, the original value of 3.40 A was selected to give the proper interplanar spacing in the graphite crystal, assuming that only the site-site interactions are acting to hold the planes in place. A better argument and a more reliable estimate of a, would be helpful not only for diatomic5 on graphite but also for rare gases as well. Registry No. 02,1182-44-1; N2, 1121-37-9; CO, 630-08-0; graphite, 7182-42-5. (20) Cole, M. W.;Klein, J. R. Surf. Sci. 1983, 124, 547. (21) Piper, J.; Morrison, J. A.; Peters, C.; Ozaki, Y. J. Chem. SOC., Faraday Trans. 1 1983, 79, 2863. (22) Piper, J.; Morrison, J. A.;-Peters,C. Mol. Phys. 1984, 53, 1463. (23) Murthy, C. S.;Singer, K.; Klein, M. L.; McDonald, I. R. Mol. Phys. 1980,41, 1387.
