J. Phys. Chem. lS81, 85, 722-723
722
er-chain decyltrimethylammonium ion in the disk micelles. There is a large difference in bilayer thickness indicated for pure laurate and pure decyl sulfate because the normalized ratio increases to 1.461 at the tail methyl group. Curve 9 is interesting because it corresponds to the derived normalized ratios for palmitic acid as a dilute guest in pure hexadecyltrimethylammonium (HDTMA) bilayers/pure decyl sulfate bilayers, an extreme case.20,24 A large increase in the normalized ratio occurs up to carbon 12, which evidently corresponds to the thickness of the decyl sulfate bilayer in terms of the segments of the palmitic acid guest. After this point for CI3-Cl6 there is a steady decrease in the normalized order ratios, the meaning of which is not covered by this article. Curves 15-17 are columns 3-5 of Tables I1 and I11 of this paper, which now show up as indicating a small but steady increase in bilayer thickness as the detergent LAK substitutes detergent G in the micelle. The vertical scale for all ratios plotted is the same; consequently the differences in bilayer thickness in this case are the smallest encountered, a reasonable conclusion based on the identical chain lengths of the two detergents. Curve 10 compares bilayer thickness by using the order profile for hexadecylpyridinium (HDP) chains26 in the form of pure hexadecylpyridinium bilayers/ 14% hexadecylpyridinium-86% hexadecyltrimethylammonium bromide. The numerator micelle bilayer has a larger thickness. Curve 14 is an example of the use of a profile for hexadecyltrimethylammonium ions in the form 12.9% HDTMA-87.1% HDP/84% HDTMA-16% HDP showing (24) B. J. Forrest and L. W. Reeves. Chem. Phvs. - Lioids,24. 183 (1979). (25) L. W. Reeves, A. S. Tracey, and M. M. Tracey, Can. J.Chem., 57, 747 (1979).
the numerator bilayer of greater thickness.2s Curve 11corresponds to a case using the order profile of decan01~~ as a guest amphiphile, the plotted ratio being the same as for curve 14. The results are in agreement, namely, that the numerator bilayer is thicker. This case is interesting because it shows that, even when the probe of bilayer thickness is a 10-carbon chain, the change in thickness of a 16-carbon bilayer is detectable, though the change in ratios is small. The results for decylammoniuml’ profiles also show that the hexadecylpyridinium bilayers have a greater thickness than hexadecyltrimethylammonium. The effect is again small for the shorter chain, but still detectable (curve 13). Curve 12 is another confirmation of the same effect for the hexadecyl chains using profiles for decyl sulfate i0ns.l’ A small but definite change in normalized ratios occurs even in 10-carbon chains immersed in a 16-carbon bilayer. The method proposed here has therefore been experimentally tested in a wide variety of situations. The results show that lipids accommodate to bilayers of different thicknesses by an increase of a decrease in the population of single gauche rotamers near the nonpolar tail but that the king/jog motion nearer the polar head group is not affected and remains largely a property of the chemical identity of the lipid head group. Acknowledgment. This work was made possible by operating grants available to L.W.R. by the National Science and Engineering Research Council of Canada. M.E.M.H. thanks the Conselho Nacional de Pesquisas of Brazil for scholarship support. Equipment grants from Banco Nacional de Desenvolvemento Economico do Brasil and Fundacgo 6 Ampara de Pesquisa do Estado de Sao Paulo were also important.
Contribution to the Interpretation of a General Scale of Solvent Polarities Vojtgch Bek5rek Faculty of Sciences, Paiacky University, 771 46 Olornouc, Czechoslovakia (Received: June 24, 1980)
A model is developed which allows one to express the solvent polarity effects as a simple function of the relative permittivity ( E ) and the refractive index (n)of the solvents. A very good correlation between the proposed solvent function (e - l)(n2- 1)/(2e + 1)(2n2+ 1)and Taft and Kamlet’s ?r* solvent polarity parameters is found.
Great attention has recently been paid to the problem of solvent effect on spectral, chemical, and reactivity data by Taft, Kamlet, and their co-workers.l-1° The authors (1) M. J. Kamlet and R. W. Taft, J. Am. Chem. Soc., 98, 377 (1976). (2) R. W. Taft and M. J. Kamlet, J. Am. Chem. Soc., 98,2886 (1976). (3) T. Yokoyama, R. W. Taft, and M. J. Kamlet, J. Am. Chem. Soc., 98, 3233 (1976). (4) R. R. Minesinger, M. E. Jones, R. W. Taft, and M. J. Kamlet, J. Org. Chem., 42, 1929 (1977). ( 5 ) M. J. Kamlet, J. L. Abboud, and R. W. Taft, J. Am. Chem. SOC., 99, 6027 (1977). (6) J. L. Abboud, M. J. Kamlet, and R. W. Taft, J . Am. Chem. SOC., 99, 8325 (1977). (7) J. L. Abboud and R. W. Taft, J. Phys. Chem., 83, 412 (1979). (8) M. J. Kamlet and R. W. Taft, J. Chem. Soc., Perkin Trans. 2,337 (1979). (9) M. J. Kamlet, M. E. Jones, R. W. Taft, and J. L. Abboud, J . Chem. Soc., Perkin Trans. 2, 342 (1979).
consider the total solvent effect to be composed of three independent contributions-polarity, acidity, and basicity-and they introduced corresponding empirical solvent polarity (a),acidity (a),and basicity ( p ) scales. As far as the ?r generalized solvent polarity scale is concerned, quite good correlations have been found with the other most widely used empirical polarity scales and with a great number of experimental data. The .rr scale is based on the solvent solvatochromic shifts of different indicators, and ?r parameters of -70 solvents were published. On the basis of extensive studies, 28 aliphatic, aprotic, monofunctional solvents (henceforth called “select solvents”) for which ?r values are very nearly proportional (10)M. J. Kamlet and R. W .Taft, J. Chem. SOC., Perkin Trans. 2,349 (1979).
0022-3654/8112085-0722$01.2510 0 1981 American Chemical Society
A General
Scale of Solvent Polarities
The Journal of Physical Chemistry, Vol. 85,No. 6, 1981 723
to molecular dipole moments were selected and recommended for practical studies of solvent effects.6 As far as the relations of these T factors to relative permittivity ( E ) and refractive index ( n )solvent functions are concerned, the authors originally concluded that these could be considered rather in a qualitative way? Recently Abboud and Taft' carried out the correlation of the T factors of the select solvent set with the e(€) solvent function of Block and Walker" and obtained an equation which had the form 7~ = 2.528(~)- 0.23, with the correlation coefficient being 0.964. We would like to present here a simple model which makes it possible to express the solvent-induced shifts by reaction field functions of the refractive index and the relative permittivity of solvents. Only the shifts caused by polarity effects are considered. Two kinds of polarization of cybotactic solvent molecules by solute can be considered: the polarization by the equilibrium dipole moment of the solute molecule, and the additional polarization accompanying the change of the dipole moment during excitation. The reaction field due to polarization by the equilibrium dipole moment is proportional to (e - 1)/(2c + 1) = f(€) because electronic, atomic, and orientational polarizations of solvent molecules take place. The additional polarization of the cybotactic solvent molecules during excitation is only electronic and atomic because the excitation process is too rapid to be followed by reorientation of solvent molecules. The corresponding change of the reaction field of these cybotactic solvent molecules is therefore proportional to (n2- 1)/(2n2 + 1) = f(n2). This change in the reaction field and therefore the f(n2)function is of primary significance for the evaluation of the solvent-induced shifts. The size of this excitation polarization change depends on the distance between solute and cybotactic solvent molecules. The shorter the distance, the more intense the polarization and corresponding reaction field and thus also the solvent-induced shift. It seems reasonable to consider the distance to be dependent on the reaction field induced in cytotactic solvent molecules by the equilibrium dipole moment of solute molecules and thus to be proportional to f(e). The primary effect of f(n2) on solute molecules can thus be considered to be modified by the f(t) term so that a relationship between the solvent-induced shifts and the f(n2) f(e) product function should exist. To confirm these ideas, we carried out the correlation of T solvent parameters with the f(n2)f(e) = f(E,n2)term. The correlation was performed with all known T parameters including also the secondary and tertiary values (eq l ) , with T of only aprotic solvents (eq 2), with T of the T
= 15.24f(e,n2)- 0.570
R = 0.841
F = 135 (1)
T
= l5.52f(e,n2) - 0.514
R
F = 205 (2)
= 14.65f(€,n2)- 0.573
R = 0.989
F = 1195 (3)
= 8.09f(6,n2)- 0.058
R = 0.963
F = 129
T
T
= 0.904
(4)
select solvent set (eq 3), and with T of aromatic solvents (eq 4). (Cf. Figure 1.) R and F are the correlation coefficient and the Fisher F criterion, respectively. As is apparent from eq 3 and the corresponding correlation characteristics, the correlation of the T parameters of the 29 selected solvents with the f(&) function is of the same significance as the correlation of these m with various spectroscopic and reactivity and it is better than the correlation of T with the e(€) function.' In connection (11)H.Block and S. M. Walker, Chem. Phys. Lett., 19,363 (1973).
Figure 1.
with the correlation of T with e(€), we would like to note that this dependence cannot be expected to be obeyed by solvents of considerably higher refractive index as, for example, CS2,CH2Br2,CHBr3, or CH212.We have found these solvents to be suitable for solvent-effect studies when f(e,n2)has been used for the evaluation of solvent-induced shifts.12 As far as the solvent effect of aromatics is concerned, the correlation of their T parameters with f(e,n2)(eq 4) is quite satisfactory. Different values of the regression coefficient and the intercept probably result from weak specific interactions of these solutes with the aromatic solvents (overlap of solvent molecule orbitals with those of the solute leading to exiplex formation). In our opinion, dielectric saturation can influence the solvent effects with only the most dipolar solvents such as H 2 0 or HCONH2. As far as applicability of the ?r parameters is concerned, the behavior of the dipole moment of the solute molecule during excitation is important. If the direction of the dipole moment is not changed during excitation (which is probably the case of the indicators which served for adjusting the T scale), the solvent-induced shifts should depend on T or f(e,n2)only. If, however, the direction of the dipole moment of the solute molecule is changed during excitation, the part f(e) of the f(c,n2) loses its meaning (the orientational polarization of cybotactic solvent molecules decreases or even cancels out, and = n2 in this case), and a dependence of the studied property on the combination of T and f(n2) or f(c,n2)and f(n2) or even on the f(n2) term only should be expected. In our opinion the use of the combination of two terms (?r and f(n2) or f(e,n2) and f(n2)) seems to be general for the evaluation of the solvent polarity effects. (12)V. Beklrek and A. Mikuleckb, Collect. Czech. Chern. Comrnun., 43,2879 (1978).
