Orientation of Hydroquinone and Benzoquinone Adsorbed on

TABLE 111: Temperature Dependence of Hyperfine Coupling. Constants (Gauss) (IN0 Calculations) single well double well. T, K. (IN an. aN arr. 4. 50. L ...
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J. Phys. Chem. 1984,88. 4583-4586 TABLE 111: Temperature Dependence of Hyperfine Coupling Constants (Gauss) (IN0 Calculations)

single well

T,K 4 50 L 00 :I50 200 250

300 350

(IN

an

13.07 13.07 13.07 13.07 13.08 13.10 13.13 13.15

-9.43 -9.43 -9.43 -9.42 -9.39 -9.34 -9.27 -9.18

double well arr

aN 12.36 12.36 12.36 12.37 12.40 12.44 12.49 12.55

-11.24 -11.24 -1 1.24 -1 1.20 -11.11 -10.98 -10.83 -10.67

with a liow inversion barrier. CI calculations including correlation effects in the valence shell and a first-order treatment of the ?r s stem confirm the nonplanarity of the system26 (NO = 1.292 N H = 1.018 A; H N H = 118O.8; a = 26O.1). The important point is the fact that the potential well for H2N0 inversioln is essentially shallow between 0 and 30'. In Figure 2 it can be seen that geometry of the radical corresponding to the maximum of the probability density for the vibrational wave function in the zeroth and first level differs substantially. Integration of the corresponding coupling constants (eq 4) leads to average splittings (Table 11) which do not vary as much as one would have expected from the static values (Table I). The general trend is the same for all calculations: a slight increase: in ( a N ) "and a net decrease in ( a H ) uwhen adding vibrational quanta of energy. Unfortunately, the energy difference between the lowest two levels is too large (477 cm-') for the upper level to be occupied significantly just above absolute zero. The temperature dependence of the nitrogen coupling is small and will be difficult to observe. One can expect more significative experimental results for the proton (Table 111). The oxygen coupling

i;

( 2 6 ) Y . Ellinger, H. Gritli, and R.Subra, unpublished material,

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which is essentially constant (a,, = -46 G) for all geometries will not provide any supplementary information. The most important result of this study is that, vibrational effects included, the final result for v = 0 is the same as that which would be obtained for a static radical frozen in a nonplanar geometry with a bending angle about 20'. Since calculated equilibrium geometries fall in that range (DZ P calculations), it explains why vibrational effects seem negligible in this molecule. This fortuitous result is best understood in Figure 2 for aN in the case of the most shallow double-well potential obtained in DPT2 calculations. Integration of aN(a) over the range of a gives a large weight to contributions with a C a% and aN C aN(Eq) (domain A Eq in Figure 2) and a less important weight to contributions with a > aQ and aN > aN(Eq) (domain Eq B in Figure 2). Since aN increases rapidly for bending angles greater than the equilibrium value, the two effects balance each other and the final result is close to that corresponding to the equilibrium geometry. For a single-well potential (DZ calculations) the vibrational wave functions are very much the same as those of the double-well case. Thus, they lead to the same results, namely, a value of the coupling constants corresponding to an effective out of plane deviation about 20'. This series of calculations illustrate a crucial problem in the interpretation of ESR experiments. Because of the particular shape of the potential surface, neither the measure of the coupling constants nor that of their temperature dependence can provide a conclusive answer as to the geometry of this radical. Theoretical calculations give that information which at all events is somewhat academical since the first vibrational level masks the actual shape of the energy minimum.

+

-

-

Acknowledgment. H.G would like to acknowledge Dr. J. Douady and the CIS1 Computational Chemistry group for the financial support that made this work possible. Registry No. H2N0, 13408-29-2.

Orientation of Hydroquinone and Benzoquinone Adsorbed on Piatinurn Electrodes: Studies by Reflection-Absorption Infrared Spectroscopy K. Peter Pang, Jay B. Benziger,* Department of Chemical Engineering, Princeton University, Princeton, New Jersey 08544

Manuel P. Soriaga, and Arthur T. Hubbard Department of Chemistry, University of California, Santa Barbara, California 931 06 (Received: March 28, 1984; In Final Form: June 28, 1984)

The adsorption of hydroquinone and p-benzoquinone on Pt electrodes in 1 M HC104 has been examined by reflection-absorption infrared spectroscopy and cyclic voltammetry. At solute concentrations below 0.1 mM no spectral features were observed by RAIS in the 2700-3200-cm-' region. Cyclic voltammetry indicated less than a twofold increase in adsorbate coverage when the solute concentration was increased from 0.075 to 0.75 mM while the infrared spectra clearly showed four absorption bands, characteristic of diphenols. These results indicate a transition from flat to edgewise orientation of the adsorbed species. The results suggest that both hydroquinone and benzoquinone adsorbed from concentration above 0.75 mM as 2 , 3 - ~edge-bonded ~ diphenols. The applicability of separating the electrode from the electrolyte for spectroscopic examination is also demonstrated.

Introduction Thin-layer electrochemical methods have demonstrated that aromatic and quinonoid compounds are adsorbed spontaneously and irreversibly from aqueous solution onto smooth platinum surfaces in specific orientations which depend on solute concentrations and other factors.'s2 This letter reports the application ~

~

of reflection-absorption infrared spectroscopy (RAIS) to study the adsorption and orientation characteristics of complex organic molecules on smooth polycrystalline Pt electrodes. The dependence of molecular orientations on solute concentrations is depicted from the infrared spectra of adsorbates by using the metal-surface selection r ~ l e . ~This . ~ work also demonstrates that the molecular

~~~~~

(1) Soriaga, M. P.; Hubbard, A. T. J. Am. Chem. SOC.1982, 104, 2735.

0022-3654/84/2088-4583$01.50/0

(2) Soriaga, M. P.; Hubbard, A. T. J . Am. Chem. SOC.1982, 104, 3937.

0 1984 American Chemical Society

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The Journal of Physical Chemistry, Vol. 88, No. 20, 1984

Letters

1

I

TO PRE-AMPLIFIER 6 LOCK-IN M1

‘W

a

S

Figure 1. Schematic view of reflection-adsorption IR spectrometer: ( S ) Nernst glower source, (El) Pt electrode, (E2) auxiliary electrode, (E3) reference electrode, (Pl) stationary polarizer, (P2) rotating polarizer, (G) grating, (D) InSb detector, (Ml, M3, M7, M8) spherical mirrors, (M2, M4, M5, M6) plane mirrors, (Sl, S2) slits.

orientation of adsorbate at a liquidsolid interface can be studied by separating the solid adsorbent plus adsorbed layer from the liquid phase before spectroscopic examination. Two compounds were studied: hydroquinone (HQ) and p-benzoquinone (BQ). Experimental Section Apparatus. Surface infrared spectroscopic measurements were made with a combined infrared-electrochemical Cell described in detail el~ewhere;~ the electrochemical attachment is identical with that utilized in UHV-EC experimentsS6 The cell was constructed so that infrared spectroscopy and cyclic voltammetry were carried out under a nitrogen atmosphere. A schematic view of the infrared-electrochemical system is shown in Figure 1. The infrared window used in this work was CaF2. Infrared radiation from a Nernst glower source (Harrick Scientific) was passed through a stationary wire grid polarizer and focused onto the sample at an angle of about 8 2 O . The reflected radiation from the sample was modulated at 30 H z by a rotating wire grid polarizer and focused onto the entrance slit of a grating monochromator (Oriel Corp.). The beam was then focused onto a liquid-N2-cooledInSb detector. The spectral range of the detector was from 2 to 5.5 hm. The grating monochromator was computer controlled. The detector signal was fed to a lock-in amplifier, and the second harmonic was measured. The second harmonic is proportional to difference in the s and p polarization components, which represents absorption of p-polarized light due to the adsorbed layer. Output from the lock-in amplifier was stored by the computer as intensity vs. wavelength. Due to a variety of polarization effects in the optical train of the apparatus, the perpendicular and parallel scalar components of the polarized radiation did not have equal values; this imbalance was compensated by a stationary wire grid polarizer. This allowed a higher gain to be used on the lock-in amplifier, thus achieving maximum sensitivity. Cyclic voltammetry was used to characterize the Pt electrode. A retractable Pyrex cup housed the auxiliary and reference electrodes. Electrolyte entered the cup through a capillary tube by pressurized nitrogen. The Pyrex cup and capillary tube were mounted on a Teflon tube inside a stainless steel sleeve. The whole assembly could be moved up for CV and then retracted to allow infrared spectra to be obtained. A constant nitrogen purge was used to deoxygenate the electrolyte solution and to dry the Pt electrode prior to taking infrared spectra. Procedures. The clean Pt electrode was characterized by CV in 1 M HC104. A minimal oxidation peak at 1 V (vs. 1 M AgC1) indicated the surface to be free of adsorbed hydrocarbons (see Figure 2). After CV characterization the electrode was rinsed in distilled water to remove excess electrolyte from the electrode surface. The Pyrex cup was then lowered, and nitrogen purging dried the excess water on the Pt surface. As water absorbs infrared light to a varying degree over a wide wavelength range,’ it was necessary (3) Greenler, R. G. J . Chem. Phys. 1966, 44, 310. (4) Pearce, H. A,; Sheppard, N. Surf. Sci. 1976, 59, 205. (5) Pang, K. P. M.S.E.Thesis, Princeton University, 1984. (6) Stickney, J. L.; Rosasco, S . D.; Song, D.; Soriaga, M. P.; Hubbard, A. T. Surf. Sci. 1980, 130, 326. (7) Smith, A. L. “Applied Infrared Spectroscopy”; Wiley: New York, 1979; p 109.

I -0.4

i 0.0

W

0.4

I

I 0.8

I

I

I 1

1.2

POTENTIAL, VOLT VS. AgCl

Figure 2. Cyclic current-potential curves for hydroquinone at a polycrystalline platinum electrode: (--) clean surface, (-) presaturated surface, (- * -) presaturated surface rinsed to remove dissolved reactant. The solutions contained initially 0.75 mM reactant and 1 M HC104 (platinum electrode area 1.44 cm2, rate of potential sweep 4 mV/s).

that the electrode surface be as dry as possible when the infrared spectrum was taken. The reproducibility of the IR spectra dpended a great deal on the surface conditions of the sample. Thus, it was important to adopt a standard procedure in performing the RAIS characterization of the Pt electrode: (i) After the CV characterization, two separate base-line spectra of the clean Pt surface were obtained and differenced. The difference would indicate the reproducibility of the surface conditions. It also served a measurement of the noise level. (ii) Electrosorption was carried out at open circuit for ca. 10 min, and then excess electrolyte was removed by distilled water. After nitrogen purging, RAIS characterization of adsorbed layer was carried out and the adsorbed layer and base-line spectra were then differenced to obtain the vitrational spectrum of the adsorbed species. Two scans were coadded for each spectrum. The scan speed used was 2 c d / s with a spectral resolution of ca. 15 cm-’. The spectral range scanned was 2700-3 150 cm-’. Above 3 150 cm-’ the base line and adsorbed layer both showed absorption of ppolarized light due to adsorbed water. Despite the fact that the surface appeared dry, the surface had a thin film of adsorbed water. Results and Discussion Cyclic current-potential curves for the irreversible electrochemical oxidation of hydroquinone adorbed on Pt electrodes are shown in Figure 2. The solid curve is for H Q in dissolved and adsorbed forms; the dot-dash curve was obtained when only adsorbed material was present; the dot curve is for clean Pt electrodes in 1 M HC104. The reversible peak a t 0.55 V is due to the unadsorbed HQ.’ The adsorbed material is comparatively unreactive as illustrated in Figure 2 when the potential scan was continued in the positive direction beyond the first peak; a broad maximum was observed in the vicinity of 1.1 V. This is characteristic of the oxidation of adsorbed hydrocarbon materials* and corresponds to irreversible oxidation of the adsorbed form9 of HQ. This same irreversible oxidation behavior was also observed when the adsorption was followed by thorough rinsing with the pure supporting electrolyte to remove dissolved material prior to recording the scan. Voltammetric curves for oxidation of the adsorbed form are unchanged by thorough rinsing with aqueous perchlorate; therefore, (i) the adsorption of aromatic on Pt electrode is irreversible and (ii) water and supporting electrolyte do not displace the adsorbed aromatic species. (8) Stickney, J. L.; Soriaga, M. P.: Hubbard, A. T.; Anderson, S. E. J . Electroanal. Chem. Interfacial Electrochem. 1981, 125, 73. (9) Soriaga, M. P.; Stickney, J. L.; Hubbard, A. T. J . Mol. Caral. 1983, 21, 211.

The Journal of Physical Chemistry, Vol. 88, No. 20, 1984 4585

Letters

w

0 2 U

c k

s

-,

v)

\

z U

\ \

e

\ \

x'55

\X 2 5

'

2700

2800

2900

WAVENUMBER

3000

3100

Figure 3. Infrared spectra for hydroquinone adsorbed at 0.075 mM (-) and 0.75 mM (-) on smooth polycrystalline Pt foil. Experimental conditions: Pt foil thickness 0.635 mm, surface area 1.44 cm*, scan rate 2 cm-'/s, slit width 0.4 mm, resolution 15 cm-I. TABLE I: CH Bond Positions and Intensities for Hydroquinone" H Q adsorbed H Q adsorbed on Pt solid H O in KBrb on A1,OIc electroded 3050 (0.35) 3030 (1) 3104 (0.1) 3005 (0.6) 2960 (1) 2963 (0.58) 2932 (0.5) 2882 (1) 2880 (0.65) 2820 (0.4) 2810 (0.10) 2852 (0.42) 2700 (0.1) 2755 (0.45) 2722 (0.42)

" Frequency in cm-'; intensities in parentheses. *Taken from ref 11; intensities are scaled relative to major peak at 3030 cm-'. cTaken from inelastic tunneling data of Lewis et al.;lz intensities are scaled relative to major feature at 2882 cm-'. dData presented here; intensities are scaled to major feature at 2960 cm-'. The infrared spectra of H Q at 0.75 mM (solid curve) and 0.075 m M (dashed curve) adsorbed on the Pt electrode are shown in Figure 3. At the low concentration no features were clearly discernible in the spectral region 2700-3 150 cm-', whereas at the higher concentration four bands at 2755,2880,2960, and 3050 cm-' were clearly distinguished. In addition, there is a very weak band at 2810 cm-'. Cyclic voltammetry gives a ratio of the integrated current for oxidation of the adsorbed species a t the two concentrations of 1.16:1, clearly insufficient to account for the dramatic change in the infrared spectra in terms of multilayer adsorption. The relative surface concentrations were estimated using by appropriate values for nox(number of electrons for oxidation) as determined by Soriaga and Hubbardlo to be 1.8, which is consistent with the adsorption isotherm measured by a thin-layer technique.' These results indicate a change in molecular orientation of the adsorbed species with concentration whereby the molecular vibrations become infrared active. According to the surface selection rule for RAIS only molecular vibrations with components normal to the surface are infrared active. The orientational transition from a flat 7-bonded species to the 2,3-q2 adsorbed species as proposed by Soriaga and HubH

rr-bonded

2700

2800

2900

WAVENUMBER

CM-'

H

2 , 3 -g2 bonded

3000

3100

CM"

Figure 4. Infrared spectra of p-benzoquinone adsorbed at 2 mM on smooth polycrystalline t'F foil. Experimental conditions were as in Figure 3.

as indicated in Table I. Also shown in Table I are the bands observed by Lewis et a1.12 for H Q adsorbed on A1203measured by inelatic tunneling spectroscopy. The band positions and relative intensities show reasonable agreement between solid HQ and adsorbed HQ. Interpretation of the shifts and intensities of the various bands is not possible at this time because of the complexity of the system. The multiplicity of C-H stretching modes is the result of hydrogen-bonding interactions, both intramolecular as well as intermolecular. To our knowledge there are no qunatitative models to account for those features. The presence of a solvating layer of water further complicates the hydrogen-bonding interactions in the adsorbed layer. It is not possible to compare the spectra of adsorbed HQ and H Q in aqueous solution because of the low solubility of H Q in water. It should be pointed out that although the infrared spectra do indicate a change in molecular orientation, the 2,3-$ edge-bonded assignment is not unique. An alternative possibility is an oxygen-bonded phenoxy species, which is what Lewis et al.l2 suggested for HQ adsorbed on A1203. Lewis et al. did point out their results could not distinguish between the two possible bonding arrangements. Deuterium labeling at the OH group is unable to resolve these differences due to rapid hydrogen exchange with the water in solution. From the inrared results we can only conclude that the molecular orientation changed from flat to edge bonded. Figure 4 shows the inftared spectra of 2 mM p-benzoquinone adsorbed on the Pt electrode. The base line is sloping in the opposite direction to that of H Q shown in Figure 3 due to a 90° rotation of the compensating polarizer. At concentrations below 0.1 mM the infrared spectrum of BQ was featureless. These results again suggest an orientational transition with concentration. The spectrum for adsorbed BQ is noteworthy in that it shows the same characteristic C H botlds observed for adsorbed HQ. In solid form BQ has a single C H bond at 3060 cm-l;13 the simpler spectrum is due to the absence of hydrogen bonding. The similarity in the spectra for adsorbed HQ and BQ suggests that the adsorbed benzoquinone is structurally similar to a diphenol; for example, BQ undergoes hydrogen shifts upon adsorption to produce a 2,3-$ diphenol. Unfortunately, the adsorbed water has interfered with attempts to identify an OH stretching mode at 3200 cm-' which would clarify this assignment. The results presented here display the utility of combining spectroscopic techniques with electrochemical techniques to probe adsorption. Several other investigators have also shown the utility of infrared spectroscopy to study adsorption at the electrodeelectrolyte interface.14-16 The R A E technique employed here

would result in the C-H stretching modes changing from infrared inactive to infrared active. The observed infrared bands for the edge-bonded HQ are close to those observed for solid H Q

(12) Lewis, B. F.; Bowser, W. M.; Horn, J. L. Jr.; Luu, T.; Weinberg, W. H.J . Vac. Sei. Technol. 1974, 11, 262.

(10) Soriaga, M. P.; Stickney, J. L.; Hubbard, A. T. J. Electroanal. Chem. Interfacial Electrochem. 1983, 144, 207. (11) Hildago, A.; Otero, C. Spectrochim. Acta 1960, Id, 528.

(13) Grasselli, J. G., Ritchey, W. M., Eds. "Atlas of Spectral Data and Physical Constants for Organic Compounds"; Chemical Rubber Co.: Cleveland, OH, 1975. (14) Russell, J. W.; Severson, M.; Scalon, K.;Overend, J.; Bewick, A. J. Phys. Chem. 1983, 87, 293.

J. Phys. Chem. 1984, 88, 4586-4589

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is similar to that employed by Russell et al.I4 and Bewick.I5 In these other investigations spectra were taken in situ by pressing the electrode up against an infrared transparent window. We have taken the different approach of isolating the electrode from the supporting electrolyte for spectroscopic examination. This eliminated materials compatibility problems that have been reported in these other studies and thus eliminated problems of contamination. In the work presented here the irreversible nature of the adsorption permitted the electrode to be removed from the elec(15) Bewick, A. J. Electroanal. Chem. Interfacial Electrochem. 1983,150, 481. (16) Pons, S.J. Electroanal. Chem. Interfacial Electrochem. 1983, 150, 495.

trolyte. Clearly this is a limitation of our approach; however, the influence of contaminants, such as halide ions, on the adsorption process mitigated against any other approach. The results presented here do show conclusively a structural transformation of adsorbed quinoid compounds with solute concentration. This transformation is consistent with the orintational transition model proposed by Soriaga and Hubbard.’ The results also suggest that the edge-bonded H Q and BQ are structurally similar, and its is suggested they both adsorb as 2,3-q2 bonded diphenols. Lastly, these results indicate the feasibility of spectroscopic examination ouf adsorbed layers by separating the electrode and supporting electrolyte. Registry No. Pt, 7440-06-4; HQ, 123-31-9; BQ, 106-51-4.

Evidence for Zero Mean Curvature Microemulsions Ldc Auvray,*t$ Jean-Pierre Cotton,$ Raymond Ober,? and Christiane Taupint Laboratoire de Physique de la Matiere Condensee, College de France, 75231 Paris Cedex 05, France, and Laboratoire Leon Brillouin, C.E.A.-C.E.N.Saclay, 91 191 Gif-sur-Yvette Cedex, France (Received: May 23, 1984)

We studied Winsor type microemulsions containing equal brine and toluene volumes by X-ray and neutron scattering. The contrast factors between the microemulsion constituents are chosen to separate the oil, water, and surfactant contributions to the scattering. The spectra were recorded in different angular ranges. At large angle, the interfacial surfactant film between oil and water is directly evidenced by the asymptotic intensity behavior. At zero angle, the contrast variation method shows that the concentration fluctuations of water and surfactant are not correlated; we deduce from this result that the mean curvature of the interfacial film is zero on average. The oil and water spectra and film spectra suggest that, when the film curvature fluctuates, the water and oil domain size remains well-defined.

In the Winsor phases’ of brine, hydrocarbon (“oil”), ionic surfactant, and alcohol mixtures, as the water ionic strength increases, one observes the following successively: (i) a two-phase equilibrium: an oil-in water microemulsion coexists with an oil excess; (ii) a three-phase equilibrium: the middle-phase microemulsion contains comparable oil and brine volumes and separates the oil and brine phases; (iii) another two-phase equilibrium: a water-in-oil microemulsion coexists with a brine excess. This sequence has raised much interest1” but is not yet fully understood. To interpret it partially, it has been proposed that salt addition changes the c~rvature’g”~ of the surfactant interfacial film between oil and brine, by screening the ionic surfactant polar head repulsion. In the twQ-phase equilibria, the microemulsion is “classical”, Le., made of oil-in-water or water-in-oil droplets; in the middle phase, as the water and oil volumes are very close and the microemulsion is not d i l ~ t a b l ethe , ~ existence of well-defined droplets is very unlikely and bicontinuous structures, where the surfactant interfacial film has no preferred curvature, have been imagined. They are either ordered, generated by minimal surfaces (lamellar,8 cubic9, or random: ’Ovl’ the microemulsion volume is divided into cells, randomly filled by oil and water, and the surfactant is distributed at the oil-water interface. In the original Talmon-Prager model (ref lo), the cells are generated by a Voronoi tessellation and the cell size distribution is large. In ref 11, the interfacial film is flexible and fluctuates, but the curvature fluctuations are important only at scales larger than Ek, the “persistence length” of the film; this fixes the basic size (- 100 %.)of the cells, which are taken to be identical and cubic. In both models, the oil and water domain size 5 (& in ref 11) is related to the chemical composition by the geometrical constraint

t College de France

* Laboratoire LBon Brillouin 0022-3654/84/2088-4586$01 S O / O

($o and +w, oil and water volume fractions; Cs,surfactant concentration; 2, area per surfactant molecule in the interfacial film, 2 = 60 A2). This relation is at variance from the equation giving the radius R of, say, water-in-oil spheres: R = 34W/(CSZ) (2) Phase diagrams of the random models have been constructed in have calculated the X-ray ref 10-12 and Kaler and Prager l 3 (W) scattering by the oil and water parts of the microemulsion using the Voronoi model. They predict that the scattered intensity decreases monotonously as the scattering vector q increases. Recently, the authors of ref 14 and the present authorsI5 have studied the middle-phase structure by small-angle X-ray scattering. We observed that the X-rays were mainly scattered by the in(1) P. A. Winsor, “Solvent Properties of Amphiphilic Compounds”, Butterworths, London, 1954. (2) K. Mittal, Ed., “Micellization, Solubilization, and Microemulsions“, Plenum Press, New York, 1977. (3) A. M. Cazabat, D. Langevin, J. Meunier, and A. Pouchelon, Adu. Colloid Interface Sci., 16, 175 (1982). (4) S. Friberg, I. Lapczynska, and G. Gillberg, J. Colloid Interface Sci., 56, 19 (1976).

(5) M. L. Robbins in ref 2, Vol. 2, p 713. (6) R. Hwan, C. A. Miller, And T. Fort, Jr., J. Colloid Interface Sci., 68, 221 (1979). (7) P. G. de Gennes and C. Taupin, J. Phys. Chem., 86, 2294 (1982). (8) Chun Huh, J. Colloid Interface Sci., 71, 408 (1979); 0. Parodi,

Communication at the Workshop “Colloidal Crystals”, Les Houches, Feb

__19RA..

(9) L. E. Scriven in ref 2, Vol. 2, p 877. (10) Y. Talmon and S. Prager, J. Chem. Phys., 69, 2984 (1978). (1 1) P. G. de Gennes, J. Jouffroy, and P. Levinson, J. Phys. (Orsay, Fr.), 43, 1241 (1982). (12) B. Widom, J. Chem. Phys. 81, 1030 (1984). (13) E. W. Kaler and S. Prager, J. Colloid Interface Sci., 86, 359 (1982). (14) E. W. Kaler, K. E. Bennett, H.T. Davis, and L. E. Scriven, J. Chem. Phys., 79, 5673 (1983); E. W. Kaler, H. T. Davis, and L. E. Scriven, J. Chem. Phys., 79, 5685 (1983). (15) L. Auvray, J. P. Cotton, R. Ober, and C. Taupin, J. Phys. (Orsay, Fr.), 45, 913 (1984).

0 1984 American Chemical Society