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coefficient. It is appropriate, therefore, to take the partition function as unity, as has also been done for the isotopic abundance. The necessary spectroscopic data are available for benzene and h e x a f l ~ o r o b e n z e n e ~but, ~ * ~unfortunately, ~ not for 1,3,5-trifluorobenzene. Table I11 summarizes the analysis of the vibrational contribution to the static polarizability anisotropy of these two molecules; and Table IV details the polarizations, wavenumbers, and absorption coefficients of the four infrared-active vibrations, together with the individual contributions which these make to the parallel and perpendicular components of the polarizability. A similar treatment of the infrared spectra of benzene and hexafluorobenzene has been given by Bishop and C h e ~ n g , ~ ' although their results are approximate in that the population of excited states was assumed to be negligible; polarizabilities in agreement with theirs emerge if the factors Fjare taken as unity. Comparison ofAa0,, and AaoeXpt.With the assumptions made in the extrapolation procedure and the level of reliability of the infrared intensities in mind, the agreement between the values of Aao estimated in the manner described here and those obtained from the temperature dependence of the Kerr effect is good. Tables I11 and IV also reveal the reason for the unexpectedly different values of the ratio A a O / A a for benzene and hexafluorobenzene; for the former, AaoVibis of opposite sign to Aaoel, Aao < Aa, and AaO/Aa < 1; but for the latter, Aaoib has the same sign as Aaoel, Aao > A a , and A a o / A a > 1 . It is also of interest to note that the vibrational polarizability is dominated in the case of benzene by the low-wavenumber out-of-plane C-H bending ( v 4 ) mode, but in the case of hexafluorobenzene by the high-inmodes. As already mentioned, tensity in-plane stretching (Y~~.Y,~) infrared intensities are unavailable for 1,3,5-trifluorobenzene; however, the experimental results reported here, in particular the (25) Spedding, H.;Whiffen, D. H . Proc. R . Soc. London, Ser. A 1956, 238, 245-255. (26) Steele, D.;Wheatley, W. J . Mol. Spectrosc. 1969, 32, 265-275. (27) Bishop, D.M.;Cheung, L. M. J . Phys. Chem. ReJ Data 1982, 11, 119-133.
value of Aa0/Aa, indicate that A a o ~ is b negative for this molecule and comparable in magnitude to that of hexafluorobenzene.
Summary The present investigation of the temperature dependence of vapor-state electric-field-induced birefringence has demonstrated that for benzene, 1,3,5-trifluorobenzene, and hexafluorobenzene the temperature-independent contributions to the effects at normal temperatures are negligibly small. In consequence, the assumption commonly made in single-temperature solution-phase Kerr-effect studies, to the effect that the second hyperpolarizabilities can be ignored, appears to be acceptable, at least for these and similarly anisotropic molecules. Analyses of the temperature dependences in conjunction with the known optical-frequency polarizability anisotropies have also yielded reliable static polarizability anisotropies. In the cases of benzene and hexafluorobenzene these are reasonably predicted from the dispersion in the dominant electronic component, together with appropriate allowance for the much smaller contribution (-1 5%) from molecular vibrations. It is of particular interest to note that, because of the oppositely signed vibrational contributions in these two molecules, the ratio of the static to the optical-frequency anisotropy is less than unity for benzene, as expected, but significantly greater than unity for hexafluorobenzene. Such an outcome greatly reduces the reliability and the usefulness of the assumption which usually underlies the analysis of solution-phase Kerr constants, namely that the ratio of the anisotropies can be approximated by the ratio of the mean static and optical-frequency polarizabilities. Acknowledgment. A Commonwealth Postgraduate Research Award (to I.R.G.), financial support from the Australian Research Council (to G.L.D.R.), technical assistance from Dr. D. R. Laver (University of Sydney), and helpful discussions with Professor B. J. Orr (Macquarie University) and Dr. M. A. Spackman (University of New England) are gratefully acknowledged. Registry No. Benzene, 71-43-2; 1,3,5-trifluorobenzene,372-38-3; hexafluorobenzene,392-56-3.
COMMENTS Comments on "On the Structure of Aggregates of Adsorbed Surfactants: The Surface Charge Density at the Hemimkelle/Admicelle Transition"' Sir: In a recent paper, Yeskie and Harwell' have suggested that
formation of bilayered admicelles is favored during the adsorption of ionic surfactants from aqueous solutions onto charged minerals at surface charges away from the point of zero charge of the mineral; conversely, the formation of monolayered hemimicelles is thought to be favored close to the point of zero charge. The above conclusion was based on a theoretical approach which relied solely on the calculated chemical potentials of the surfactant molecules in hypothetical hemimicellar and admicellar aggregates. Lower values of chemical potential were arrived at for the admicellar case and higher values for the hemimicellar case. They further inferred that both hemimicelles and admicelles might be formed simultaneously on a heterogeneous surface where most highly charged patches may favor bilayers and less highly charged patches may favor hemimicelles. We do not intend to discuss the validity of the assumptions involved in the derivations presented, but do want to alert caution Due to editorial error, a reply to this Comment was published previously. See: Harwell, J. H.; Yeskie, M. A. J . Phys. Chem. 1989, 93, 3372.
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before accepting generalizations based on thermodynamic treatment alone, of hypothetical aggregate systems. The evolved model should be able to contain the experimental results from both bulk and spectroscopic studies reported on these systems. We felt it necessary to clarify certain pertinent points about hemimicelles relevant to this context so that some of our recently published and forthcoming works on adsorbed layers of sodium dodecyl sulfate on alumina (same system as studied in ref 1) could be viewed in the right perspective in relation to the model we suggested earlier. In the bilayer model, a rigid parallelism has been sought between surfactant aggregation processes in solution and on the solid surface mainly to account for the micelle-like nature of the adsorbed aggregates. The aggregation number and other solution properties of micelles remain the same over a wide concentration range whereas the aggregation number of the surfactant adsorbates undergoes continuous changes. The bilayer model fails to adequately represent the evolutionary changes of the aggregates before maximum adsorption density is attained. The bilayered admicelles, if formed from the beginning of the aggregation process, would be expected to result in a similar microenvironment within the aggregates. The limitation of this model is to be understood not only in the light of the contact-angle studies and particle flotation ( I ) Yeskie, M . A.; Harwell, J. H . J . Phys. Chem. 1988, 92, 2346
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J . Phys. Chem. 1989, 93, 7745-7746
7745
E
-. .*-***+-*-*.*-*-*-
-*-*-*
-**-*-.-**e..-.
*-e
I
+ + + +
I
+ - I +
+
Figure 1. Representation of reverse orientation model (left) and the bilayer model (right) for the evolution of sodium dodecyl sulfate on alumina. Curve shows the regions in a typical isotherm.
behavior but also from the supporting spectroscopic evidence which we reported earlier on the same system. Variation of praperties within the hemimicellar microstructure cannot be assumed to be a constant especially when a quantitative evolutionary picture of the aggregate is required. Since all the probes may not be equally sensitive to register the variations in the microenvironment, the normal practice is to study the system with different probes and techniques. Before detailing our arguments supporting the hemimicellar reverse orientation model, it is expedient to get familiarized with the schematic representation of the twin models on a typical isotherm. This is represented in Figure 1. The onset of aggregation is characterized by two types of aggregates: manolayered hemimicelles as shown on the left-hand side ahd bilayered admicelles as depicted on the right-hand side of the figure. As the adsorption progresses, some of the molecules can interpenetrate into the hemimicellar aggregates leaving the charged ends in the liquid phase. This phenomenon may ultimately result in a structure comparable to bilayers at high adsorption densities. Aside from the hydrophobicity data on the solid,6 a multipronged spectroscopic approach adopted by us gave cleat indication of the hemimicellar mechanism operating even when the adsorption system was far away from its point of zero charge in an aqueous environment. Here are the essential results: 1. ESR spin probing within the hemimicelle4v5at three different locations, using doxylstearic acid nitroxide probes, reported different and very high values of microviscosities-ane order of magnitude higher than those in micelles. Microviscosities estimated with fluorescence probes also indicated the same average value. The bilayer model "...supports the interpretation of Bisio et al. that the tail groups of the upper layer of the bilayered aggregate do not significantly interpenetrate the tail-group region of the bottom layer...". This would result in microviscosities comparable to those existing in micellar solutions. 2. Analysis of luminescence spectra of Ru(bpy)?+ in different hemimicellar regions' showed that the microstructure of the ad(2) Somasundaran, P.; Turro, N. J.; Chandar, P. Colloids Surf. 1986,20, 145. (3) Chandar, P.; Somasundaran, P.; Turro, N. J. J . Colloid Inferface Sci.
. - -. - -
19117. 117. 31. .. -
(4) Waterman, K. C.; Turro, N. J.; Chandar, P.; Somasundaran, P. J. Phys. Chem. 1986, 90, 6830. (5) Chandar, P.; Somasundaran, P.; Waterman, K. C.; Turro, N. J. J . Phys. Chem. 1987, 91, 190. ( 6 ) Somasundaran, P.; Chandar, P.; Chari, K. Colloids Surf:1983.8,121. (7) Kunjappb, J. T.; Somasundaran, P. Colloids Surf:,in press.
sorbed surfactant changes continuously as the the adsorption density increases. Changes in luminescence maxima and intensity monitored at various points in the isotherm corroborated the adsorption data of the positively charged probe at the solid/liquid interface. 3. Time-resolved resonance Raman spectra of Ru(bpy)3Z+in the same system* also registered systematic changes in frequencies and variation in intensities, again indicative of changing environments within the hemimicelles. The above observations may be explicable by resorting to the hemimicellar reverse orientation model for the growth of surfactant aggregates on a solid. Interestingly enough, all the above observations were made with the alumina/sodium dodecyl sulfate system under in situ conditions where a bilayer was predicted to be predominant in the paper under discussion. Furthermore, most of the features of the bilayer model are implicit in the reverse orientation model. (8) Somasundaran, P.; Kunjappu, J. T.; Kumar, C. V.; Turro, N. J.; Barton, J. K. Langmuir 1989, 5, 215.
Langmuir Center f o r Colloids and Interfaces Columbia University New York, New York 10027
Joy T.Kunjappu P.Somasundaran*
Received: August 8, 1988; In Final Form: May 31, 1989
An Alternative Interpretation of Coulomb Explosion Data on C,' Sir: Coulomb explosion experiments provide information about the fully correlated nuclear density distributions within small molecules.' The raw data obtained are ensemble-averaged probability distributions. When such experiments are performed with molecules prepared in well-defined states, this information can be directly related to the structures of those states. However, when the internal energies of the molecules studied are unknown, care must be exercised in interpreting these results. It is the purpose of this Comment to demonstrate that previously reported ( I ) Vager, Z.; Naaman, R.; Kanter, E. P. Science 1989, 244, 426.
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