3938
J. Phys. Chem. 1981, 85,3938-3944
Carbon-13 NMR Investigations of Aerosol OT Water-in-Oil Microemulsions Craig A. Martln and Linda J. Magid” Department of Chemistry, University of Tennessee, Knoxvilie, Tennessee 379 16 (Received: June 22, 198 I; In Final Form: August 17, 198 1)
The conformational and dynamic changes which occur when HzO is added to Aerosol OT (AOT) inverted micelles have been studied by means of 13CNMR spin-lattice relaxation times (Tl)and chemical shifts (6) in cyclohexane, benzene, and carbon tetrachloride. Chemical shift changes and T1 gradients upon addition of H 2 0 indicate that gauche to trans conformational changes occur throughout the AOT molecule. Solvent penetration decreases in the order benzene > carbon tetrachloride > cyclohexane. Frequency-dependent Tl’s arise as the result of a distribution of correlation times affecting the relaxation of all the carbon nuclei in AOT inverted micelles in cyclohexane. Overall molecular reorientation is the primary contribution to the relaxation of carbons nearest the head group in all three solvents. There exist motional differences in the AOT alkyl chains when going from the inverted micelle region to the water-in-oil (w/o) microemulsions.
Introduction Certain surfactants, when dissolved in nonpolar solvents, exhibit the remarkable ability to solubilize large amounts of water resulting in the formation of water-in-oil (w/o) microemulsions. Systems of this type have been important commercially for some time and are found in many cleaning solutions.l More recently they have been used as models for enzyme catalysis2 and membrane t r a n ~ p o r t . ~ They have important implications for enhanced oil recovery,4 and their ability to promote light-induced charge separation and efficient energy conversion has been investigated. Aerosol OT [AOT, sodium bis(2-ethylhexy1)sulfosuccinate] forms inverted micelles when dissolved in nonpolar media, that is, the sulfonate head groups occupy the structure’s core and the hydrocarbon chains extend outward into the continuous phase. When the molar ratio of added water to Aerosol OT is small ( R = [H20]/ [AOT] < 5-10), all the water is involved in hydrating the head groups. The appearance of free water ( R L 10-12) marks the entrance into the w/o microemulsion region.6 Previous studies of AOT aggregation behavior have been concerned with the overall nature of the aggregates (size, phase behavior, etc.) or the nature of the solubilized watera7p8 With the use of 13C NMR it is possible to probe the dynamic processes and conformational preferences at individual locations within the surfactant molecule itself. Information on the local environment of each nucleus is gained through 13Cchemical shifts. The spin-lattice relaxation times are related to both motional and structural NMR offers the distinct qualities of unique carbons. advantage that a probe molecule, which often perturbs the environment it ~ t u d i e sis , ~not required. The inverted micellar region of AOT has been examined previously by using 13C spin-lattice relaxation times. Segmental motion (Le., an increase in relative motion along the alkyl chains away from the head grouplo) was ob(1)Prince, L. M. In “Microemulsions”, Prince, L. M., Ed.; Academic Press: New York, 1977;pp 1-32. (2) Menger, F.; Yamada, K. J. Am. Chem. SOC.1979,IOI, 6731-2. (3)Fendler, J. H.J. Phys. Chem. 1980,84, 1484-91. (4)Basal, V. K.;Shah, D. 0. In “Microemuleions”,Prince, L. M., Ed.; Academic Press: New York, 1977;pp 149-73. (5)Monserrat, K.;Gratzel, M.; Tundo, P. J. Am. Chem. SOC.1980,102, 5527-9. (6)Zulauf, M.; Eicke, H.-F. J. Phys. Chem. 1979,83,48C+6. (7)Eicke, H.-F. Top. Current Chem. 1980,87,86-145, and references therein. (8) Magid, L. J. In “Solution Chemistry of Surfactants”, Mittal, K. L., Ed.; Plenum Press: New York, 1979; Vol. I, pp 427-53,and references therein. (9) Menger, F. M. Acc. Chem. Res. 1979,12, 111-7.
servedll and addition of water increased the mobility of the alkyl chains.12 The present work represents the first time 13CNMR has been used to explore the w/o microemulsion region of AOT.
Experimental Section Purification of AOT. Since salts profoundly affect the water solubilizing capacity of Aerosol OT in cyclohexane,lg the surfactant was purified as follows. This is a combination of other procedures13-15and was the only method to give consistent results. AOT (50-60 g, Aldrich) was stirred overnight with 5-10 g of cocoanut charcoal in 500 mL of benzene. After filtration through a 0.5-pm FH Millipore filter, 25 mL of water was added, the solution shaken, and the flocculant allowed to settle. The benzene solution was decanted and the procedure repeated with 15 and 10 mL of water, followed by removal of the benzene. The solid was then dissolved in 400 mL 1:3 methanollwater and washed 3 times with 100 mL of 60-80 ligroine to remove any remaining organic impurities. The aqueous methanol was then carefully evaporated (to avoid foaming), after which solid AOT was dried overnight a t 75 “C in vacuo. Dissolution in anhydrous methanol and filtration through a 0.08-pm polycarbonate filter (Nucleopore) removed any additional salts. Methanol was stripped off and the solid dried 48 h in vacuo. Percent recovery was 50-60%; a solution of 10% AOT in cyclohexane incorporated >70 mol of water per mol of AOT. The absence of residual acidic materials was checked by using l-methyl-4-(cyanoformy1)pyridinium oxide (CP0).l6 The ternary phase diagram illustrating the isotropic Lz region is shown in Figure 1. NMR. 13Cchemical shifts (6) and spin-lattice relaxation times (T,) were measured a t 15.1 MHz on a Nicolet TTY-14 system. All samples were run in a 20-mm probe a t 30 f 2 “C. The probe temperature was set before each run with a solution of 15 (v/v) cyclooctane/methylene ~
~~~
(10)(a) Doddrell, D.; Allerhand, A. J . Am. Chem. SOC.1971, 93, 1558-9. (b) DoddreU, D.;Glushko, V.; Allerhand, A. J. Chem. Phya. 1972, 56,3683-9. (11)Ueno, M.; Kishimoto, H.; Kyogoku, Y. J. Colloid Interface Sci. 1978,63,113-9. (12)(a) Dense, A., Ph.D. Dissertation, University of Basel, 1977. (b) Eicke, H.-F.; Zinsli, P. E. J. Colloid Interface Sci. 1978,65, 131-40. (13)Kunieda, H.; Shinoda, K. J. Colloid Interface Sci. 1979, 70, 577-83. (14)Eicke, H.-F.; Christen, H. J. Colloid Interface Sci. 1974, 48, 281-90. (15)Menger, F. M.; Saito, G. J. Am. Chern. Soc. 1978,100,4376-9. (16)Magid, L.J.;Kon-no, K.; Martin, C. J. Colloid Interface Sci. 1981, 83,307-8.
0022-3654/81/2085-3938$01.25/00 1981 American Chemical Society
The Journal of Physical Chemistty, Vol. 85, No. 25, 1981 3939
Carbon-13- NMR Investigations of Aerosol OT
A 01
Figure 2. 15.1-MHz I3CNMR spectrum of Aerosol OT/cyclohexane/ HO , showing the assignments given by Ueno.” Flgure 1. Ternary phase diagram of AOT/cyclohexane/HpO at 30 f 1 O C showing the inverted micelle w/o microemulsion region (L2). The circles indicate the composition of the samples studied by I3C NMR.
iodide.17 Tl’s were measured by using the fast inversion-recovery technique,@calculated via a semilogarithmic least-squares fit of the integrated intensities, and averaged over 3-5 runs. The estimated error is 5 1 0 % for Tl > 0.1 s and 10-20% for T1 < 0.1 s. The usual experimental parameters were as follows: 256 acquisitions; 3000-Hz sweep width; 2-5 delay time; 8K data points in the time domain. Chemical shifts were measured relative to CDC13 in a coaxial insert, are uncorrected, and are accurate to f0.1 ppm. An external capillary of D20,within the probe, was used to maintain lock. Samples were not degassed. All NMR glassware and accessories were soaked in an alkaline EDTA bath as the last stage in the normal washing procedure. To study T1 frequency dependence, measurements of R = 0 (inverted micelle) and R = 30 (w/o microemulsion) samples were performed a t 100.6 MHz in cyclohexane-d12 on a Bruker WH-400 NMR. TIis related to the effective correlation time, Teff, for molecular reorientation of a carbon-hydrogen vector by means of eq l,I9 provided motion is isotropic and the
-1NTl
- yH2yC2h.2 lora
[
Teff
1 + (wH - W
+ +3~eff + wc2r,ff2
C ) ~ T , ~1 ~ ~
]
6Teff (1) 1 + (WH + wc)2Teff2 predominant mechanism causing relaxation is due to dipolar interactions between carbon nuclei and their adjacent hydrogens. YH,yc and OH,oc are the gyromagnetic ratios and Larmor frequencies of carbon and hydrogen, respectively; h. is Planck‘s constant divided by 2 ~r ;is the carbon-hydrogen bond length; and N is the number of directly bound protons. For a C-H vector in a rigid molecule undergoing isotropic motion, Teff is the correlation time for molecular reorientation. When internal rotation occurs, or for the case of anisotropic molecular reorientation, T~ corresponds to an average correlation time for several motions.lg In the latter case, eq 1is an acceptable alternative to the more complete description;1° significant information is still obtained when reffis treated in a semiquantitative manner.lg reffwas calculated by using eq 1, assuming r(CH3) = 1.096 A, r(CH2) = 1.073 A, and r(CH) = 1.070 &z0~21 (17) Vidrine, D. W.; Peterson, P. E. Anal. Chem. 1976, 48,1301-3. (18) Canet, D.; Levy, G. C.; Peat, I. R. J. Mugn. Reson. 1975, 18, 199-204. (19) For a detailed discussion see: Lyerla, J. R., Jr.; Levy, G. C. In “Topics in Carbon-I3NMR Spectroscopy”,Levy, G. C., Ed.;Wiley: New York, 1974; Vol. 1, pp 79-148.
TABLE I: I3CChemical Shifts (6 ) for AOT/Cyclohexane, R = 0 C no. 6 C no. 10, 10’ 9, 9’ 8, 8’ 7, 7’ 6, 6’ 5, 5’ 4, 4’
10.3 23.3 13.4 22.8 28.7 29.8 38.5
3 3’ 2 2’ 1 1‘
6
66.0 66.6 171.1 169.4 61.0 32.9
Sample Preparation. In a glove box AOT was weighed into a 10-mL volumetric flask, the desired amount of water added, and the flask filled with solvent. Concentrations studied in cyclohexane were 0.5 and 0.25 M AOT with R ranging from 0 to 46.3 (see Figure 1). In benzene and carbon tetrachloride, 0.5 M AOT was studied up to a maximum R of 11.1and 15.3, respectively. It was necessary to thermostat samples having high water concentrations overnight. General Procedures. Laboratory deionized water was distilled with a Kontes WS-2 still. Cyclohexane, benzene, and methanol were ACS reagent grade, distilled, and dried over 3-A molecular sieves. Carbon tetrachloride was Aldrich Gold Label (99+%) and dried over 3-A sieves. Cyclohexane-d12was purchased from Merck. Infrared spectra were obtained on a Perkin-Elmer 257 spectrophotometer.
Results and Discussion Chemical Shifts in Cyclohexane. Figure 2 shows the 13C spectrum of AOT/cyclohexane/water. The assignments used are those of Ueno et al.I1 Even at 15.1 MHz, adequate resolution is obtained except between C-7,7’ and C-9,9’ and, to a lesser extent, C-3 and C-3’. The chemical shift of each resonance is listed in Table I for R = 0. Addition of water has no effect on 6 of carbons 4,4’-10,lO’. However, significant changes occur in the head group region, as illustrated in Figure 3. The sharp downfield shift of S(C-1) up to R = 10 is due to hydration of the head group. After the hydration requirements have been met, S(C-1) remains constant. The largest changes occur in the carbonyl chemical shifts, 6(C-2) and 6(C-2’). Carbonyl chemical shifts are extremely sensitive to the nature of the local environThe observed initial upfield shifts (hydrogen bonding induces downfield shifts23)are consistent with (20) The choice of r can have a large effect on the accuracy of ia. Dill, K.; Allerhand, A. J.Am. Chem. SOC.1979, 101, 4376-8. (21) Gordon, A. J.; Ford, R. A. “The Chemist’s Companion”;Wiley: New York, 1972; p 107. (22) Menger, F.; Jerkunica, J. M.; Johnston, J. C. J. Am. Chem. SOC. 1978, 100, 4676-8. Stothers, J. B. “Carbon-13 NMR Spectroscopy”; Academic Press: New York, 1972. (23) Maciel, G. E.; Dallas, J. L.; Miller, D. P. J. Am. Chem. SOC.1976, 98, 5074-82.
3840
Martin and Magid
The Journal of Physical Chemistty, Vol. 85,No. 25, 798 1
TABLE 11: NT,(s) for AOT/Cyclohexane/H,O at 15.1 MHz C no. R=O 2.2 5.3 10.2 10, 10' 9, 9' 8, 8' 7, 7' 6, 6' 5, 5' 4, 4' 3 3' 2'" 2''" 1 1' '"
T,is reported.
1.50 0.34 3.18 0.84 0.50 0.40 0.044 0.044 0.062 0.54 0.74 b b
2.10 0.56 4.44 1.28 0.68 0.42 0.058 0.090 0.088 0.72 0.97 0.026 b
3.24 0.66 5.94 1.82 1.00 0.44 0.15 0.12 0.13 1.23 1.69 0.045 0.062
3.51 1.06 6.27 1.48 0.96 0.62 0.17 0.16 0.18 1.14 1.93 0.068 0.10
19.9
25.2
29.6
46.3
3.57 0.88 5.61 2.04 1.14 0.38 0.16
3.42 0.80 5.82 2.20 1.00 0.54 0.19 0.15 0.17 1.70 2.60 0.061 0.064
3.96 0.76 6.39 2.22 1.48 0.62 0.22 0.22 0.24 2.03 2.53 0.056 0.070
3.75
0.17 0.16 1.54 2.65
0.10 0.10
1.00 6.75 1.92 1.26 0.44 0.18 0.13
0.13 2.21 3.25 0.045 0.030
Significant line broadening resulted in insufficient S/N to measure T,for these resonances. R = 0
09
22
55
a7
147
381
238
172 '171
F
n
"
"
h
V
"
2
I70
c
c
69
6
Figure 4. Infrared carbonyl stretch region at varlous water concentrations. gauche
trans
c, c-c5
c-c //O c4 \o
' 0 1723 cm-1
1740 cm-1
Figure 3. Change in I3C chemical shifts of carbons 1-3 as a function of added water concentration In cyclohexane.
both carbonyls moving into a more hydrophobic environment. Infrared analysis shows two distinct microenvironments initially a t each carbonyl (Figure 4). At R = 0, carbonyl stretches are observed at 1723 and 1740 cm-l. By R = 5.5, one band remains a t 1725 cm-l. Analogous to the interpretation of the Raman bands of phosphatidylcholine^,^^ the 1740-cm-l band is assigned to a gauche conformation about the C(0)-C bond and the 1723-cm-l band to a trans conformation (Figure 5). C-2' comes into closest contact with the head group at R = 0.26 Space-filling models clearly show that this can only occur if the conformation is gauche. The trans conformer is favored after addition of water. The net result is an increase in the surface area a t the surfactantlwater interfacesz6 Tl's in Cyclohexane at 15.1MHz. NT1's a t 15.1 MHz are shown in Table 11. All NT1 increase rapidly up to R = 5-10 indicating the increased mobility of an AOT molecule in the inverted micelle. For carbons 4,4'-10,10', (24) Bicknell-Brown, E.;Brown, K. G.; Person, W. B. J. Am. Chem. SOC.1980,102,5486-91. (25) Ueno, M.;Kishimoto, H.; Kyogoku, Y. Chem. Lett. 1977,594-602. (26) Eicke, H.-F.; Rehak, J. HeEu. Chim. Acta 1976,59, 2883-91.
0
Figure 5. Assignment of the infrared carbonyl stretches to different conformations about the C(0)-C bond.
20 10
,
20 (HD) /(A
1
I
30
40
03
0
Figure 6, Extent of segmental motion, expressed as ~ ( 4 ) / ~ ( 8as ),a function of R: (0)0.5 M in cyclohexane, (X) 0.25 M in cyclohexane, (A)in CCI4, (m) In benzene. The effective area (A,) at the surfactant/oll interface is given by the dotted line.
The Journal of Physical Chemistry, Vol. 85,No. 25, 1981 3941
Carbon-I3 NMR Investigationsof Aerosol OT
3.01
I
I
,
1
I
I
I
IO+ ' IO'
i
'
I
,
lo3 YR s e c .
,
,
,
,
, , , ,1
,
,
I0 .'
,
.05
I , , ,
10-6
Flgure 7. Comparison of ~ ~ f xcalculated 1) by using eq 1 with rR calculated by using eq 3: ( 0 )rh in cyclohexane, R = 2, 5, 10 left to right (Day et al.); (A)rhin isooctane, R = 2, 5, 10, 20, 25, 30 left to right (Zulauf and Eicke); (W) rh in heptane, R = 30, 46 (Gulari et al.). The dotted line has a slope = 1.
N T , remains constant or increases slightly at higher R. Segmental motion is observed at all water concentrations. The extent of segmental motion can be represented by the ~ ( 8 ) . addition of water results in a ratio, ~ , ~ ~ ( 4 ) / 7 , ~ Initial sharp decrease in this ratio (Figure 6). Segmental mobility then gradually decreases to R = 30 and increases at the highest R. Changes in segmental mobility may be due to changes in the relative probability of gauche conformations occurring at individual C-C bonds (an equilibrium property of the system), or to changes in the rate of gauchetrans interconversion (a dynamic property of the system) which may occur either at individual C-C bonds or as part of a correlated motion involving several C-C bonds.27 Correlated motions are discussed in the next section. The large values of ~,ff(4)/7,ff(B)observed a t low R indicate a higher probability of gauche conformations; the lower ratio brought about by addition of water reflects the increasing probability of trans conformers along the chain. This is supported by a calculation of A,, the surface area at the surfactant/oil interface (dotted line in Figure 6), using eq 2,2a where rh is the radius of the a g r e g a t e ~1, ~ ~ is the length of the surfactant molecule (11 ), and A , is the surface area at the surfactant/water interface.
x
[rh/(rh - 012 = A , / A ,
(2)
If the increase in segmental motion at R = 46 were due to aggregate crowding resulting in more gauche conformers, dilution of the samples should decrease ~ , ~ ( 4 ) / ~ , & 3This ). is not observed (cf. 0.25 M AOT, Figure 6). If the time each carbon-carbon bond spends in a trans conformation increases, segmental mobility will increa~e.~'Internal crowding of the alkyl chains causes this behavior. Spin-lattice relaxation times of the carbonyls, 2 and 2', show a general increase with R. The complete mechanism causing this relaxation is unknown but degassing causes only T I of the carbonyls to increase significantly. NTl's for carbons 1and 1' increase up to R = 20, then decrease. These carbons are not expected to exhibit a significant amount of internal motion and their relaxation (27) London, R. E.; Avitabile, J. J.Am. Chem. SOC.1977,99,7765-76. (28) Prince, L. M. In "Emulsions and Emulsion Technology", Lissant, K. J., Ed.; Marcel Decker: New York, 1974; Vol. 6, pp 125-77. (29) rh from ref 6; A , from ref 26.
I
IO
I
I
20 30 (H20Y (AOT)
I
40
I
50
Flgure 8. Internal correlation times ( T , " ~calculated ) for C-5,5' to c 10,lO' as a function of R: (+) 53'; (8)6,6'; (W) 7,7'; (A)8,8'; (V) 9,9'; ( 0 )10,lO'.
should be dominated by overall aggregate reorientation. If micelle size data are available, the rotational correlation time, T ~ can , be calculated by using eq 3, where 1 is the viscosity of the solvent, k is Boltzmann's constant, and T is the absolute temperature. TR
= 47Vh371/(3kr)
(3)
Day et aL30 have determined AOT aggregate sizes for small water concentrations in cyclohexane. Figure 7 compares T R with the effective correlation time of carbon-1, ~dl). The value for R = 10 was obtained by extrapolation. At all R, > TR. This is most likely due to the actual solution viscosity being greater than that of the solvent.30 The most extensive investigation of the effect of water on aggregate size has been performed by Zulauf and Eicke! Their data can be used in eq 3 by assuming equal rh in isooctane and cyclohexane. Correlation is observed up to R = 20-25 (Figure 7). Such good agreement, however, may be fortuitous, since their data consistently predict larger aggregates than the data of other workers.31 At higher R, Teff(l) < 7B. Other, faster motions are occurring (e.g., monomer diffusion) and this is consistent with the decreasing microviscosities measured in this region.32 It is useful to compare T,&) with TR calculated by using r h in heptane at high water concentration^.^^ This is also shown in Figure 7 with good agreement for R = 30. This qualitative analysis indicates that the predominant contribution to relaxation near the head group is due to overall aggregate reorientation, at least up to intermediate water concentrations. An assessment of the effective correlation time for internal motions can then be made by using eq 4.loJ9 The results are shown in Figure 8 for the AOT alkyl chains. 1/Teff
+ 1/Tint
~ / T R
(4)
We obtain the now familiar curve where a sharp change ~ ~ in) the inin a parameter (here a decrease in T ~ occurs verted micelle region and then levels off when w/o microemulsions are formed. This suggests that the average (30) Day, R. A.; Robinson, B. H.; Clarke, J. H. R.; Doherty, J. V. J. Chem. SOC.,Faraday Trans. 1 1979, 75, 132-9. (31) Keh, E.; Valeur, B. J. Colloid Interface Sci. 1981, 79, 465-8. (32) Zinsli, P. E. J. Phys. Chern. 1979,83,3223-31. (33) Gulari, E.; Bedwell, B.; Alkhafaji, S. J.Collozd Interface Sci. 1980, 77,202-12.
3942
The Journal of Physical Chemistry, Vol. 85,No. 25, 1981
TABLE 111: NT, (s) for AOT/Cyclohexane-d,,/H,O a t 100.6 MHz
C no. 10,10' 9,9' 8, 8' 7,7' 6,6' 5, 5' 4,4' 3 3' 1 1' a
R=O 2.70 0.46
30 3.60 0.73
a
a
1.40 0.86 0.50 0.28 0.33 0.33 0.24 0.19
1.94 1.26 0.82 0.43 0.51 0.70 0.31 0.20
Martin and Magld
TABLE IV: NT, (s) for AOT/Benzene/H,O a t 15.1 MHz
10,lO'
9, 9' 8,8' 7, 7' 6,6' 5, 5' 4, 4' 3 3' 2a 2' 1 1'
Longest delay time carbon tetrachloride > benzene for R = 0. At R = 5 and 10, the ratio is about the same in the latter solvents. The results imply more extended alkyl chain conformations, on the average, in benzene and carbon tetrachloride at lower R. We propose that benzene and carbon tetrachloride intercalate the AOT hydrocarbon chains,31while in cyclohexane the voids at the surfactant/oil interface are filled by the hydrocarbons chains themselves. This explains the preference for gauche conformers in cyclohexane at low R. The extent of solvent penetration is, roughly, inversely proportional to ~ ~ ~/ ~~~ (~ 4~ () 8 ) . Solvent properties which may be used to rationalize the observed penetrating abilities are collected in Table VI.
Polariza-
TABLE VII: Comparison of 7 R and ~ ~ f f ( 1 ) in Benzene and CCl,
0 5
3 33 4+
g
20.6 26.7
32 72 94 72 83 88
Extrapolated from data a t Reference 46.
Water is included for comparison. Due to the nonpolar nature of these solvents, any interaction with the AOT head group should be due to dipole-induced dipole interactions. The polarizability parameter, p,43 decreases in the order benzene > carbon tetrachloride > cyclohexane. Other factors will also influence penetration. Benzene exhibits a surprisingly large polarity parameter, occupies the smallest volume per mole, V," and has a slight hydrogen-bonding acceptance tendency, ah." When these factors are combined with the mutual solubilities between each solvent and water,46a convincing argument is made for solvent penetration into AOT inverted micelles decreasing as follows: benzene > carbon tetrachloride > cyclohexane. Aggregation numbers, ri, have been observed to decrease as the solubility parameter increase^.^^ In benzene ri = 14 and in cyclohexane, ri = 18. However, the size of the aggregates is about the same in both solvents.31 Solvent penetration helps explain this apparent anomaly. Finally, the contribution of overall aggregate tumbling to the relaxation process can be estimated. Teff(l) is compared to T~ in benzene and carbon tetrachloride in Table VII, using size data from various sources.30*31~46 In all > 7R ~ (As1in) cyclohexane, the acutal soinstances, ~ ~ ~ lution viscosity is expected to be greater than that of the solvent. Conclusions In AOT inverted micelles in cyclohexane at R = 0, the molecule's head group region is arranged into a compact structure while the alkyl chains are arrayed so that solvent cannot penetrate into the micelle. Addition of water induces conformational changes throughout the molecule, resulting in a more open, extended structure. This extended conformation is observed at lower R in benzene and carbon tetrachloride because of solvent penetration. The (43) Kamlet, M. J.; Abboud, J. L.; Taft,R. W. J.Am. Chem. SOC. 1977, 99, 6027-38.
(44) Barton, A. F. M. Chem. Reu. 1975, 75, 731-53. (45) Merck Index, 9th ed, 1976. (46) Sein, E.; Lalanne, J. R.; Buchert, J.; Kielich, S. J. Colloid Interface Sci. 1979, 72, 363-6.
3944
J. Phys. Chem. 1981, 85,3944-3949
water solubilizing capacity of AOT in the latter solvents is reduced because of more favorable AOT-solvent interactions. In cyclohexane, motional differences in the AOT alkyl chains exist between the inverted micelles and the w/o microemulsions. Frequency-dependent data indicate a complex series of motions in the inverted micelles; motion at each carbon-carbon bond cannot be considered independent of other motional contributions. While NMR offers the promise of a complete description of the motional factors involved, in practice this may be impossible. In all three solvents the relaxation of the carbons nearest the head group is dominated by overall aggregate motion.
This correlation holds up to intermediate R values. At higher R, other motions, such as monomer diffusion, are contributing to the relaxation process. This work has further emphasized the distinction between Aerosol OT inverted micelles, and w/o microemulsions. Acknowledgment. Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for the support of this research and to Dr. Ruth Inners and the South Carolina Magnetic Resonance Laboratory for acquiring the 100MHz spectra for us.
Thermodynamics of a Charged Hard Sphere in a Compressible Dielectric Fluid. A Modification of the Born Equation To Include the Compressibility of the Solvent Robert H. Wood,* Department of Chemistty, University of Delaware, Newark, Delaware 1971 1
Jacques R. Qulnt, and Jean-Plerre E. Groller Laboratoire de Thermodynamique et Cinetique Chimique, Unlversit6 de Clermont-Ferrand, AublGre, 63 7 70 France (Received: May 1, 198 1; In Final Form: July 28, 198 1)
Equations for the thermodynamic properties of a charged hard sphere in a compressible dielectric fluid have been derived. For small effects, a first-order correction term is accurate, but, when effects are large, for instance, near the critical point, the complete set of equations describing the thermodynamic properties must be solved by numerical techniques. For a fluid with the density and dielectric properties of water, the contribution from the compressibility of the solvent is very small at 300 K, but, as the critical point of the solvent is approached, the contribution becomes much larger. In a water-like dielectric fluid at 600 K and 17.7 MPa, the effect is very large; for example, for a 1-1 electrolyte with ions having radii of 0.2 nm, the calculated apparent molal heat capacity changes from -4900 to -2168 J mol-l K-l when the compressibility of the solvent is taken into account. This change results from the very large change in the solvent dielectric constant which rises from 17 at large distances from the ion to 28 at its surface. Similarly, the density near the ion is much higher and the effective pressure goes from 17.7 to 280 MPa. Thus, the compressibility of the solvent makes large contributions to the calculated thermodynamic properties of the ions, and these contributions cannot be ignored in a theory that is expected to be accurate near the critical point. However, since the theory presented here does not accurately represent the heat-capacity measurements of Smith-Magowan and Wood for aqueous NaC1, it seems likely that dielectric saturation must also contribute appreciably to the thermodynamic behavior and must be included in a more complete theory.
I. Introduction The Born equation1 is an equation for the electrostatic free energy of a charged hard sphere in an incompressible dielectric fluid. Ever since its inception, this equation has been used as a primitive model for the electrostatic contribution to the free energy of an ion in a dielectric solvent. Friedman and Krishnan2 have recently reviewed the application of the Born equation as model for electrolyte solutions and shown that it has not been very successful in water and other solvents a t 298 K. The basic reason for this failure is that neglected effects, resulting from the molecular nature of the solvent, are sufficiently important that the quantitative predictions of the model are not accurate. Refined models, which account for dielectric saturation or hydration in the first coordination sphere, (1) M.Born, 2.Phys., 1, 45 (1920). (2) H.L. Friedman and C. V. Krishnan in “Water; a Comprehensive Treatis”, Vol. 3, F. Franks, Ed., Plenum Press, New York, 1973, Chapter 1. 0022-3654/81/2085-3944$01.25/0
have met with more ~ u c c e s s . ~ - ~ In contrast to the situation near room temperature, where it is not very useful, the Born equation has recently been found to provide a surprisingly accurate model for the heat capacities of aqueous solutions at temperatures of 500-600 K and a pressure of 17.7 MPaa6 The apparent molal heat capacities at constant pressure (17.7 MPa) of infinitely dilute solutions are very large and negative (C,,# N -3000 J mol-l K-l at 600 K). The fact that the Born equation is very good at predicting and correlating these very large effects indicates that the effects are primarily electrostatic in origin. Presumably, the Born equation is valid because chemical solvation effects are small compared to electrostatic effects a t this temperature and pressure. (3) M. H. Abraham, J. Lisze, and L. MBszhos, J. Chern. Phys., 70, 2491 (1979). , (4) P. R. Tremaine and S. Goldman, J. Phys. Chern., 82,2317 (1978). (5) D.Smith-Magowan and R. H. Wood, J. Chem. Thermodyn., in press.
0 1981 American Chemical Society
