Langmuir 1988,4, 217-224
217
to chloroform can be understood in terms of effects on the molecular wedge shape. Ethyl ether has a lower anesthetic potency than chloroform, and the affinity for the hydrocarbon core in relation to the aqueous medium is also lower. The pressure reversion of the anesthetic effect is in fact what should take place if the transition corresponds to L, cubic phase. This transition is a consequence of increased disorder, and in well-defined binary systems it is obtained by an increase in temperature and/or increased water content.6 An increase of pressure will act in the opposite direction. It is believed that local anesthetics act specifically on the sodium channel activation gates. In order to find out whether they have additional effect on the lipid bilayer, the addition of lidocain hydrochloride has been examined. The L, phase of EYPC, SBPC, and DOPC solubilizes a limited amount, resulting in an additional swelling of the L, phase. The formation of this L, phase starts at about 0.15% (w/w) of lidocain hydrochloride (with 5% lipid in the dispersion), and at coexistence the d-spacing of the lidocain-containing L, phase is 63.2 A compared to 53.5 %, for the “pure” DOPC L, phase. The corresponding values in the case of SBPC are 64.2 and 55.5 A, respectively.6 It is interesting to note that two lamellar phases with different d-spacings coexist. No cubic phase induced by the presence of lidocain hydrochloride in the bilayer was observed.
-
Figure 2. Schematic illustration of the proposed transition mechanism of the axon lipid bilayer induced by inhalation anesthetics. The region near a sodium channel is shown (with two gates indicated). The transition from a planar into a periodic minimal surface curved bilayer will induce a conformational change cylindrical conical and therefore tend to close the channel at one end.
-
the concentration then goes below this limit (for example, by lateral diffusion within the membrane) the signal propagation is switched on. The phase changes of a phosphatidylcholine with unsaturated chains (DOPC) compared to one with saturated ones (DPPC) are consistent with the phase-transition model based on changes in molecular wedge shape. The chains diverge more toward the center of the bilayer in the case of DOPC compared to DPPC; thus less of the disordering anesthetic agent is needed in order to obtain the transition. Also, the relative effect of ethyl ether compared
Acknowledgment. This work was supported by a grant from the Swedish Natural Science Research Council. Registry No. CHC13,67-66-3; halothane, 151-67-7; ethyl ether, 60-29-7.
Spectroscopic Determination of the Effective Dielectric Constant of Micelle-Water Interfaces between 15 and 85 “C Gregory G. Warr and D. Fennel1 Evans* Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455 Received March 25, 1987. I n Final Form: September 2, 1987 The effective dielectric constant of the interfacial region of several ionic and nonionic micelles has been determined over the range 15-85 O C by using two lipophilic, solvatochromic dye probes. Results are measurably different from the results of bulk solvents investigated and are discussed in terms of the model of Mukerjee and Buff for dipoles at interfaces. This model is examined in detail, resulting in improvements to its predictive power. Specific chemical and solubilizate location effects in sohatochromic dye studies of interfacial dielectric constants are also examined in terms of this model. The consequences of the dielectric behavior for head-group interactions within micelles are discussed.
Introduction This work is concerned with micelle-water interfaces, with how they differ from bulk solvents, and with how they change as a function of temperature. It is motivated by several observations: ionic micelles become smaller and more highly charged with increasing temperature and the cmc’s of almost all classes of surfactants increase significantly with temperature.lS2 Solutions of double-chained (1) Mukerjee, P.; Mysels, K. J. Natl. Stand. Ref. Data Ser. (U.S., Natl. Bur. Stand.) 1971, February. ( 2 ) Evans, D. F.; Allen, M.; Ninham, B. W.; Fouda, A. J. Solution Chern. 1984, 13, 87.
surfactants such as dialkyldimethylammonium halides upon heating transform from dispersed liquid crystalline bilayers and liposomes to vesicles and bilayer^.^^^ In nonionic, poly(oxyethy1ene) surfactants the cloud point is also a signal of changing micellar structure.”8 (3) Kuneida, H.; Shinoda, K. J. Phys. Chem. 1978, 82, 1710.
(4) Miller, D. D.; Bellare, J. R.; Evans,D. F.; Talmon, Y.; Ninham, B. W. J. Phys. Chem. 1987,91, 674. (5) Mitchell, D. J.; Tiddy, G. J. T.; Waring, L.; Bostock, T.; McDonald, M. P.J . Chem. SOC.,Faraday Trans. 1 1983, 79,975. (6) Nonionic Surfactants; Schick, M. J., Ed.;E.Arnold: London, 1967. (7) Triolo, R.; Magid, L. J.; Johnson, J. S., Jr; Child, H. R. J. Phys. Chern. 1982,86, 3689.
0743-7463/S8/2404-0217~01.50/0 0 1988 American Chemical Society
218 Langmuir, Vol. 4,No. 1, 1988
What factors then govern these changes in aggregate properties with increasing temperature? The cmc of tetradecyltrimethylammonium bromide increases by almost a factor of 8 between 25 and 160 "C. This is equivalent to a change in free energy of micellization (RT In cmc) of -10 kJ/mol. Yet the free energy of transferring a hydrocarbon chain from water into the interior of a micelle is almost invariant across this temperature range.2 The difference in ln(cmc) can be attributed to steric, electrostatic, and entropic interactions between the head groups, counterions, and solvent at the charged interface, and this must therefore determine the temperature dependence. There are numerous theoretical and semiempirical models for such interfaces. The head-group region can be described in a variety of ways, and the amount of detail varies widely from mean-field interaction models to more complete pictures that include thickness, discreteness of charge groups, surface fluctuations, and/or the motion of individual surfactant molecules."" Implicit in all of these models are assumptions about the dielectric constant of the interfacial region. Often the bulk dielectric constant is used; more sophisticated models have been alluded to, but without any experimental raison &&re. Here we are particularly concerned with the effective dielectric constant in the head-group region of micelles. The effective dielectric constant, or micropolarity, of micellar solutions has been the subject of many previous studies using numerous solubilized probe molecules. Lipophilic, solvatochromic chromophores, whose absorbance spectra are sensitive to the surrounding microenvironment, are widely used for carrying out such investigation^.'^-" In the absence of the complication of highly polarizable groups such as esters, amides, nitriles, and aromatic moieties in the solvent, the spectra of these dyes can be correlated directly with the dielectric constant of the surrounding medium.15 Interpretation of measurements on micellar solutions is largely predicated on the oil-drop picture of a micelle, with a hydrocarbon-like interior of local dielectric constant near to 2. There must thus be a transition between that small value and that of the bulk solvent, approximately 80, as the head-group region is traversed. Indeed a radially varying dielectric constant highly dependent upon position and microenvironment is anticipated, and this is suggested by the discrepancies between the results of various types of solubilized probe studies on identical micellar solutions. A more sophisticated class of dielectric probes are lipophilic acid-base indicator molecules, whose apparent pK, values depend upon the work of taking a proton from bulk solution to an interface.18J9 However these are only useful in nonionic systems where the pK, contains no
Warr and Evans electrical work contribution due to the surface potential. Where comparisons exist, there is often good agreement between pK, and absorbance maximum determinations of With ionic surfactants, the indicator probes are known to produce artifacts reflecting specific interactions with certain solute moieties. As with all such techniques, careful scrutiny and comparison with different methods are necessary. In this paper we are mainly concerned with how teff changes with temperature rather than with the absolute value of teff. By comparing several calibration solvents we will show that these changes can be measured reliably even when the absolute numbers are disputable. Consequently we can avoid many of the ambiguities in the interpretation of solvatochromic dye studies. This provides a means by which to compare micelle surfaces with bulk solvents or solutions whose behavior is well-known. We find that there are significant differences between bulk ckT and tef&T, which provide some insight into the effect of temperature on the properties of self-organizing assemblies. The calculation of eeff as measured by solvatochromic dyes is also addressed in some detail. A number of effects are present at interfaces which serve to alter the dielectric constant of this region, and solvatochromic probes may respond differently to each contributor. We discuss how best to treat each of these in terms of models that already exist and compare their predictions of temperature behavior with the experimental results. ~
,
~
~
~
~
r
~
~
Experimental Section Materials and Methods. The lipophilic, solvatochromic, merocyanine dye molecule 4-hexadecyl-1-[4-(4-oxyphenyl)buta1,3-dien-l-yl]pyridinium (I) and its 4-propyl analogue (11) were kindly provided by, Calum Drummond of the University of Melbourne and were used as received. The phenol betaine 2,6diphenyl-4-(2,4,6-triphenyl-l-pyridinio)phenoxide (111)was given to us in purified form by Professor Christian Reichardt, University of Marburg.21
f
A
R = C,6H33:I R=C,H,
II
m
The surfactants were used without further purification and were (8)Lum Wan, J. A.; Warr, G. G.; White, L. R.; Grieser, F. Colloid Polym. Sci. 1987,265,528. (9)Warr, G. G.;White, L. R. J . Chem. SOC.,Faraday Trans. 2 1985, 81, 549. (IO) Ljunggren, S.;Eriksson, J. C. J . Chem. SOC.,Faraday Trans. 2 1984,80,489. (11)Stigter, D. J . Phys. Chem. 1964,68,3603. (12)Zachariasse, K. A.; Van Phuc, N.; Kozankiewicz, B. J. Phys. Chem. 1981,85,2676. (13)Drummond, C. J.; Grieser, F. Photochem. Photobiol. 1987,24,19. (14) Ramachandran, C.; Pyter, R. A.; Mukerjee, P. J. Phys. Chem. 1982,86,3189,3198. (15)Drurnmond, C. J.; Grieser, F.; Healy, T. W. Faraday Discuss. Chem. SOC. 1986,81,95. (16)Kalyanasundarum, K.;Thomas, J. K. J . Phys. Chem. 1977,81, 2176. (17)Shinitzky, M. Isr. J.Chem. 1974,13,879. Gitler, C.; Cordes, E. H. Prog. Bioorg. Chem. 1973,2,1. (18)Drummond, C. J.; Warr, G. G.; Grieser, F.; Evans, D. F.; Ninham, B.W. J. Phys. Chem. 1985,89,2103. (19)Fernandez M. S.;Fromherz, P. J . Phys. Chem. 1977,81, 1755.
dodecyltrimethylammonium bromide (DTAB, Kodak), tetradecyltrimethylammonium bromide (TTAB, Aldrich), hexadecyltrimethylammonium bromide (CTAB, Aldrich), hexadecyltrimethylammonium chloride (CTAC, Kodak), sodium dodecyl sulfate (SDS, BDH specially pure), n-dodecyl P-D-mdtoside (DM, CalBioChem), and octa(ethy1ene glycol) mono-n-dodecyl ether (CI2Es,Nikkol). Tetramethylammonium dodecyl sulfate (NMe,DS) was prepared from SDS as described elsewheren and was recrystallized twice from methanol. Diethanolamine (DEA, Aldrich) was listed as 99% pure, and ethylene glycol (EG) was Fisher certified. Both solvents containing dissolved probe molecules exhibited the expected spectral properties. Tetra(20)Drummond, C.J. Ph.D. Thesis, University of Melbourne, 1987. (21)Reichardt,C.;Harbusch-Gornet, E. Justus Liebigs Ann. Chem. 1983,721. (22)Evans, D. F.;Evans, J. B.; Sen, R.; Warr, G. G. J. Phys. Chem., in press.
Langmuir, Vol. 4,No. 1, 1988 219
Dielectric Constant of Micelle- Water Interfaces 700
I
5 20
I
I
I
I
I
20
40
60
00
Diethylethanolomine / H20 o Dioxane / H20 0 EG / H20 rn EG at elevated Temp. 0
I
650
-
6 600
I F
a Z W
d
>
550
s
0
DIELECTRIC CONSTANT
Figure 2. Absorbance maximum (nm) of I1 versus dielectric constant of various organic solvent/water mixtures. Data for dioxane/H20 mixtures taken from ref 20.
500
450
I
t-
constant of various organic solvent/water mixtures. Data for EG/H20 and dioxane/H20 taken from ref 15.
I
I
0 7 5 / 2 5 H20/EG 0 50/50 H20/EG
00-
DIELECTRIC CONSTANT
Figure 1. Absorbance maximum (nm) of I11 versus dielectric
I
-
U J
2
0 0
60-
-
0 LL
methylammonium bromide (NMe4Br, Kodak), tetraethylammonium iodide (NEt41, Aldrich), tetra-n-butylammonium bromide (NBQBr,Kodak), sodium sulfate (Na2S04,Matheson), and potassium chloride (KCl, Fisher) were all used as received. All solutionswere prepared in distilled, Millipore Milli-Q fiitered water. Solvatochromic dyes were solubilizedinto micella by sonication of the crystals in surfactant solution until all had dissolved. Complete dissolution was ascertained spectrophotometrically. All solutions were adjusted to be slightly basic to ensure that the deprotonated form of the dye was present in sufficient quantity to give reliable absorbance maxima. Room temperature (20"C)calibration spectra of 11and 111were recorded on a Beckman DU-50 spectrophotometer against a background of water. I1 is highly water soluble, but I11 is much less so, particularly at high pH where the deprotonated, solvatochromic species is dominant. In all cases absorbances were sufficient that any error due to the background spectrum was negligible. In certain of the tetraalkylammonium salts some highly colored impurities were present, so all spectra for these salts containing dissolved dye were recorded against an equimolar background solution of the salt. Wavelength maxima,, ,A are accurate to approximately i1 nm. Temperature-dependent spectra were recorded on a Beckman DU-8scanning spectrophotometer, with cells thermostated to within 0.1 "C. The wavelength of maximum absorbance was determined from the smoothed experimental spectrum after subtraction of a background solvent: either water for surfactant solutions or an appropriate EG/water mixture. Calibration of Spectroscopic Probes. As has been shown for I11 in various solvents and solvent mixtures, determination of dielectric constants from probe spectra is prone to give spurious results. Even organic solvent/water mixtures show significant disparities in their A, versus e properties. The agreement between solvents is actually at its worst in just that region which is of most use for studying surfactant systems. Figure 1 shows several such calibration curves for I11 in ethylene glycol/water, dioxane/water, and diethylethanolamine/watermixtures. Figure 2, likewise,shows calibration curves for A,- of I1 against dielectric constant in the same organic solvent/water systems. Dielectric constants were taken from a number of literature source^.^^-^^ DEA was selected as a solvent for calibration of I1 and I11 as it is completely miscible with water and should better mimic quaternary ammonium compounds than solvents like dioxane, acetone, etc., which have been used previously. As Figures 1and (23) uerlof, G. J. Am. Chem. SOC.1932, 54, 4125. (24) Gaboriaud, R. C . R. Seances Acad. Sci., Ser. C 1967, 264, 157. (25) Critchfield, F. W.; Gibson, J. A.; Hall, J. L. J. Am. Chem. SOC. 1953, 75, 1991.
I-
0 W
-
40-
I
I
I
I
I
20
40
60
00
I
TEMPERATURE (" C 1
Figure 3. Dielectric constant of EG/H20 mixtures versus temperature, determined from A,- of III. Solid lines are interpolated
from the data of A k e r l ~ f . ~ ~
2 show clearly, the absorbance maximums of both I1 and I11 are shifted to longer wavelength at a given value of e in DEA/water mixtures than in either dioxane/water or EG/water. The only mixed solvent systemsthat agree well in their absolute A,- versus e response are EG/water and dioxane/water mixtures containing compound 11. However, in the region of interest (15 < e < 60) the calibration lines are almost parallel for these mixed solvents, so that changes in A, should reliably reflect changes in the effective dielectric constant with temperature where the chemical nature of the species present is not changing. For comparison with previous work using I11 as a dielectric probe,16 all results for micellar solutions are reported as effective dielectric constant, eeff, derived from the dioxane/water calibration lines. Thm choice can be vindicated a posteriori by both the agreement between e& results from I and 111and the small difference between measured teff obtained by using different calibration lines, for cationic and nonionic micelles. It was first ascertained that I11 was well-behaved in mixed solvent systems at elevated temperatures. As shown in Figure 3, a 50 wt % aqueous solution of EG gives excellent agreement between spectroscopicallydetermined eeff and the literature. For a 25% aqueous solution of EG the agreementis also good, although there is more experimental scatter in the data, due in part to the low solubility of 111. In these systems E& were obtained from the 20" EG/water calibration line. Similarly, e versus ,A, for pure ethylene glycol at elevated temperatures lies on a straight-line extrapolation of the mixed solvent calibration line and parallel to the dioxane/water line (see Figure 1).
Results Figure 4 and Table I show teff versus temperature for a number of micellar solutions containing I and I11 as solubilized probes. With only two exceptions, teffvalues derived from use of both probes lie between 25 and 33 for these surfactant systems. These results agree well with a number of previous studies at and around room temperature. Our results at 20 OC are compared with other work in Table II. The agreement between our results and others is generally good, although the correlation with
220 Langmuir, Vol. 4, No. 1, 1988
Warr and Evans
Table I. Dielectric Constants of Micelle-Water Interfaces As Determined by the Spectral Behavior of I and 111 I I11 15.2 20.1 25.0 30.0 32.0 34.9 36.9 40.0 41.7 47.0 50.0 53.3 57.1 57.6 60.0 64.0 68.0 70.0 72.0 73.0 74.0 75.0 76.0 78.9 80.0 85.0 85.8
48.0 48.0 48.0
30.5 29.0 30.0
26.0 28.0 24.0
32.0 29.0 29.0
48.0
27.0
27.0
29.0
28.5
33.0
35.0
33.0
30.0
26.0
32.5
34.0
32.0
29.0
26.0 25.0
32.0
33.0
31.0
29.0
25.5 25.0
31.0
32.0
29.0
28.0
24.0
30.0
30.0
29.0
28.0
29.5
29.0
28.0
26.0
29.0
29.0
28.0
26.0
27.0
28.0
28.0
26.0
26.0
47.0
27.0
26.0
28.0
46.5 46.5
25.0 25.0
26.0 23.0
28.0 28.0
46.0
24.0
24.0
28.0
45.0
22.0
23.0
27.0
25.0
42.5
21.0
22.0
26.0
43.0
21.0
21.0
26.0
43.5
18.0
21.0
24.0
43.5
18.0
21.0
23.0
25.5 26.5 25.5 25.5 13.0 16.0 15.0
Table 11. Effective Dielectric Constants, c,~, of Micellar Solutions at 20 OC Determined by Using Various Probe Techniques this work
NMe4DS SDS
other sources
I"
IIIb-'
46
56
30
34
29 29
29
33 36 31 32 33 34
I
I11
48 48
49
HHCd
ONAd Anionic
ANS'
PyCHOf
TEMPW
25
45
48
eq 1 (4 49, NazS04(80) 49, Na2S04(80)
Cationic DTAB TTAB CTAB
28
CTAC
29
C12E8 Brij-35 Triton X-100 Igepal CO-630 DM
29
29
36
28, NMe4/NEt4 (45) 28, NMe4/NEt4 28, NMe4/NEt4
16 18
33
28, NMe4/NEt4
Nonionic 27
33
29
32
29 29 30
28, 90% (as) EG (45)
28 32 60
35 35
15 12
35
34, 70% (as) sucrose (55)
OGk
40
a Reference 20. Reference 12. Reference 15. dReference 17. Solubilized indicator titration. /Reference 16. Fluorescence maximum. #Reference 14. OG = n-octyl b-D-glucoside.
certain other kinds of probe measurements in some miceles is less satisfactory. The single feature common to all types of probe determinations of teff is that the results lie at intermediate values between water and liquid alkanes, which at least is reassuring. Beyond that generality, however, there is disparity exceeding experimental uncertainty that needs resolution. We shall defer consideration of this until a somewhat sturdier basis for interpreting teff has been constructed. Nonionic Surfactants. The nonionic, disaccharide head-group surfactant DM has been the focus of a number of recent studies.l8JB In particular, the contrast between its behavior and the behavior of alkyl poly(oxyethy1ene) surfactants has been of interest, and this is again mani(26) Warr, G. G.; Drummond, c. J.; Grieaer,F.; Evans,D. F.; Ninham
B. W. J. Phys. Chern. 1986,90, 4581.
'Reference 17.
Fluorescence maximum.
fested in the temperature behavior of teff. Across the temperature range studied, eeff of DM varies only very slightly. Indeed it acta in this respect almost precisely like the teff of ionic surfactants examined. Clz& provides the most striking feature of Figure 4 by the step change which teff undergoes at its cloud point of 74 "C. In going from teff = 25 to -15, I11 demonstrated a shift in wavelength of maximum absorbance of over 30 nm. This was accompanied by an increase in absorbance as the solution became turbid. At 74 "C two maxima were observed in solution. The change in teffat this temperature must be due to a change in the microenvironment of the probe and is probably due to the expulsion of water of hydration from the ethoxy groups near the hydrophobic/hydrophilic interface of the micelle. In contrast, I exhibits no such sudden change but rather a gradual decrease across the temperature range studied.
Langmuir, Vol. 4, No. I, 1988 221
Dielectric Constant of Micelle- Water Interfaces
G
E 0
I
301
I
20
that measured for pure and mixed solvents of comparable dielectric constant, e.g., see Figure 2. The decrease is so slight in fact that tkT goes from being a decreasing function of T , as it is in bulk solvents, to an increasing one here. This subtle difference bears, as we shall see, upon the nature of intramicellar electrostatic interactions and thus upon the temperature behavior of micellar surfactant solutions.
Discussion The discrepancy between teff values in anionic and cationic micelles is a troublesome one. There is mounting zW indirect evidence which suggests that real differences exist 30 between micelles of SDS and of alkyltrimethylammonium a halides, the effects of which may be manifested most oba 20 viously in the micelle head-group region.28 At the same time, the interpretation of molecular probe techniques I I 1 1 warrants a modest preoccupation with possible artifacts, 20 40 60 80 arising mainly from specific chemical interactions between TEMPERATURE ("C) the probe and some species in solution: Bunton and Figure 4. Apparent dielectric constant of aqueous micellar soMinchZ9showed, for example, that solubilized aromatic lutions versus temperature, determined from, A of solubilized acids interact strongly with highly polarizable quaternary I and m.(e)SDS (A)CTAC; (v)CTAB; (0)?TAB, (0) DTAB, ammonium cations, changing both their pK,'s and their (0) DM; (w) C&s. spectra. In what follows, we develop a semiempirical description of the effective dielectric constant at micelleAlkyl poly(ethy1ene oxide) surfactants are rather persolution interfaces, apply it to the surfactant systems under verse entities in comparison with DM and ionic amphiinvestigation, and then compare it to the measured temphiles as their "head groups" are actually oligomeric chains perature profiles. that are often considerably longer than the hydrophobic The environment sensed by a solubilized dye molecule moiety. Water penetration into the ethoxy chains is still at an ionic micelle-solution interface is substantially difa subject for some debate, although at least one ethoxy group near the core would appear to be ~ n h y d r a t e d . ~ ~ ferent ~ ~ from that of a homogeneous, bulk solution. The polarizability of its immediate vicinity can be ascribed to The hydrophobic/hydrophilic interface is likely then to at least three identifiable factors,30namely, the presence be quite a diffuse region in such systems, and the radius of a low dielectric region (the micelle core), dielectric of the hydrophobic core of the micelle is an ill-defined saturation in the high electric field, and the presence of quantity. It should, however, be slightly greater than the a high concentration of ions. Some or all of these effects fully extended length of a dodecyl chain. should be reflected in the local dielectric constant, as The probe I and I1 are solubilized into micelles by sensed by the spectroscopic probe. In addition, the orislightly differing mechanisms. I11 is quite hydrophobic, entation and location of a solubilized molecule are not and it is believed to reside on average near the fmt ethoxy precisely known for many systems and may lead to apgroup of polyethoxylate micelles. The aromatic group I parent differences between similar ~ y s t e m s . ' ~ J ~ ,It~ 'is is, however, quite water soluble and is only anchored into almost impossible to experimentally examine the effect of micelles by the covalently attached hexadecyl chain, which dielectric saturation directly upon spectral properties; may leave the chromophore protruding beyond the lipohowever, the other two factors may be studied in isolation philic/ hydrophilic interface. We can therefore reconcile by using concentrated salt solutions or nonionic surfacthe differing teff(T)profiles derived from I and 111: the tants. merocyanine group of I resides way out into the poly(oxNonionic surfactants provide an interface free from yethylene) chains and senses the gradual change in eeR due charge and electric field effects, so we can examine the to thermal excitation and breaking of ethoxylwater H effect solely of proximity of a low dielectric region. The bonds, whereas I11 is nearer the core and is only affected adsorption potential of a dipole at such an interface was very close to (or at) the phase transition. described by Buff et al.32in terms of the image interactions Ionic Surfactants. The temperature profile of teff for of a dipole as it approaches a dielectric cavity. For a point all ionic surfactants studied here using both probes is dipole inside a sphere, and oriented perpendicular to the almost flat, as is that of DM. There is, however, a striking interface, the work of moving from infinity in a medium difference in the magnitude of teff between cationic and having bulk dielectric constant t, up to a distance from the anionic micelles. Tetramethylammonium and sodium interface equal to the radius of the sphere can be expressed dodecyl sulfate both have effective dielectric constants of in closed form. By equating this quantity with the work 48 at 20 "C, and for SDS this drops to 43 at 85 O C . All of moving the dipole into a medium of lower dielectric of the alkyltrimethylammonium halides studied here have constant, Mukerjee14derived an expression for teff: lower teffvalues, approximately 30 at 20 "C, and decreasing by around 3 units over the range studied. At all temtI - 1 teff - 1 peratures the measured values of eeff decrease with in(1) 0.4546 = cI[ 2e, + 1 26,ff + 1 creasing alkyl chain length for the cationics, and CTAC has an teffslightly greater than does CTAB, both of which observations are in agreement with previous reports. (28) Hayter, J. B.; Penfold, J. Colloid Polym. Sci. 1983, 261, 1022. (29) Bunton. C. A.: Minch. M. J. J. Phvs. Chem. 1974, 78, 1490. In all of the micellar solutions examined (excepting I in (30) Mukerjee, P.;'Desai, N. R. Nature (London) 1969, 223, 1056. Cl2Es) the change in teffwith temperature is much less than (31)Pleininger, P.; Baumgiirtel, H.Justus Liebigs Ann. Chem. 1983, Q
I
-1
860. (27) Cebula, D. J.; Ottewill, R. H. Colloid Polym. Sci. 1982,260,1118.
(32) Buff,F. P.; Goel, N. S. J. Chem. Phys. 1972,56, 2405. Buff, F. P.; Goel, N. S.; Clay, J. R. J. Chem. Phys. 1975, 63, 1367.
222 Langmuir, Vol. 4, No. I, 1988 100
Warr and Evans
1 I I
(1
I +
t
a
2 0 / [
"0
2
6
4
8
Scaled Distance, z
Figure 5. Calculated distance dependence of the apparent dielectric constant according to the model of Buff et al. for the adsorption of dipoles, calculated for several values of the bulk dielectric constant, e,. z is the distance of the dipole from the interface divided by the dipole radius.32
This equation describes a dipole with one center of charge between the micelle head groups and the second charge some distance out into the aqueous medium. Mukerjee took his reference state, E,, to be the bulk dielectric of water and obtained an effective interfacial dielectric constant of 48.6at 20 "C, irrespective of the nature of the surfactant. This value gives good agreement with experimental results for both NMe4DS and SDS but is much higher than that observed for nonionic or cationic micelle^.'^ In these systems there is a further decrease of 15-20 for which we must account. The popular explanation for this effect is that solubilized probes are located at a different distance from the micelle surface than in the above, idealized case. We can use an approximate series representation for the adsorption potentia132rather than the above exact solution at a specific distance and replace the numerical value of 0.4546 in eq 1 with a distance-dependent function. In the series expansion of Buff et al., distance from the interface is scaled with the radius of the cavity containing the dipole. The scaled distance is denoted by z , and eq 1 becomes
32
2€,
+1
+1
2Eeff
(2)
A t z = 1 this approximate solution underestimates the adsorption potential by 61%,32 but teff is only overestimated by 15% (cf. eq 1). This error is worse for z < 1 and becomes less for larger distances. It is therefore a useful description of the distance dependence of Eefp Figure 5 shows teffversus scaled distance between z = 0.5 and 8 for various e, values typical of water between 20 and 100 "C. Taking as an example the e, = 80 curve of Figure 5, a small displacement of the probe from z = 1 (particularly toward lower z ) results in a large change in teff,and it is apparent why structurally different dye probes and average solubilization sites can lead to substantially differing effective dielectric constants. There is independent evidence, however, that the differences in teff observed here are not due to different probe locations in the surface region of the micelle. Two NMR studies, one on CTAB12and another on SDS, DTAB, and dimethyldodecylammonium propane~ulfonate,~' both suggest that the dipole of I11 resides perpendicular to the surface, with one charged center in the layer of charge of the ionic surfactants (z = 1). This difference in orientation
is also supported by spectral difference^'^^^^ between probes solubilized in SDS and DTAB micelles and by changes in the spectral response of 111in SDS solution, when modified by attachment of an alkyl chain.% To our knowledge there are no similar studies on nonionic surfactants, but the amphiphilic nature of both I1 and I11 should lead them to also be solubilized in the surface region of nonionic micelles. The proximity of the micelle core thus explains much but not all of the observed lowering of the apparent dielectric constant. The most likely cause for discrepancy between eq 1 and experiment is the choice of reference state, E,. The surface of a micelle is not simply a waterhydrocarbon interface but is an environment more akin to a concentrated aqueous solution of the head-group species in contact with hydrocarbon. Instead of using water for the t, of DM and ClzE8 micelles, we found a more appropriate reference state of concentrated sucrose or ethylene glycol solution vastly improves the agreement of eq 1with experiment, at approximately room temperature. The best agreement is obtained for 70 wt % aqueous sucrose as a reference state for DM and 90 wt % ethylene glycol in water for C12E8. (A better choice of reference for C&8 would be a poly(ethy1ene glycol) solution at
