Conformational Analysis of Amphiphilic Molecules Incorporated in

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Conformational Analysis of Amphiphilic Molecules Incorporated in Hexagonal, Lamellar, and Reversed Hexagonal Aggregates of a Ternary System of Sodium Octanoate, 1-Decanol, and Water by the Rotational Isomeric State Scheme Combined with the Maximum Entropy Method Akihiro Suzuki, Nobuyuki Miura, and Yuji Sasanuma* Department of Materials Technology, Faculty of Engineering, Chiba University, 1-33 Yayoicho, Inageku, Chiba 263-8522, Japan Received August 17, 1999. In Final Form: April 18, 2000 Conformational and orientational characteristics of amphiphiles incorporated in the hexagonal, lamellar, and reversed hexagonal aggregates formed by a ternary lyotropic system of sodium octanoate, 1-decanol, and water have been investigated. Deuterium NMR quadrupolar splittings observed from the randomly and selectively deuterated compounds were simulated by a combined use of the rotational isomeric state scheme and the maximum entropy method. For the individual mesophases, the bond conformations and orientational order parameters of octanoate and 1-decanol were evaluated and related to the aggregate structures. In the lamellar phase, in particular, the 1-decanol chain was found to exhibit peculiar conformations; the C-C bond nearest the OH group is fixed in the gauche state, the adjacent C-C bond also shows a gauche preference, and the second C-C bond from the methyl terminal has a high gauche probability. It follows that the chain length of 1-decanol is almost equal to that of octanoate in the all-trans conformation. Ab initio molecular orbital calculations at the MP2/6-31+G*//HF/6-31G* level for 1-butanol have revealed the inherent conformational preference of the head portion of the alcohol chains; the first C-C bond from the headgroup prefers the gauche state to the trans state by 0.27 kcal mol-1, and the g( g( states in the first and second C-C bonds from the OH group have a comparatively small free energy of 0.42 kcal mol-1 relative to the tt state.

1. Introduction Of a large number of lyotropic systems, a ternary mixture of sodium octanoate, 1-decanol, and water has been most extensively investigated and found to exhibit three mesophases: the hexagonal (E), lamellar (D), and reversed hexagonal (F) phases.1-3 The phase diagram shown in Figure 1 indicates that only the E phase is formed without 1-decanol; addition of 1-decanol leads to the formation of the D phase over a large area and the F phase in a narrow range of 1-decanol concentration. The shapes of the molecular aggregates have often been discussed from the thermodynamic point of view and characterized in terms of the surface area per head and the volume and length of the hydrocarbon tail of the amphiphile.4,5 The hydrocarbon chains have mostly been assumed to be as flexible as in the liquid state. In the present study we have attempted to elucidate the conformational characteristics of octanoate and 1decanol incorporated in the hexagonal, lamellar, and reversed hexagonal aggregates of the ternary system by analyzing 2H NMR quadrupolar splittings observed from * To whom correspondence may be addressed. E-mail address: [email protected] FAX number: +81 43 290 3395. (1) Ekwall, P.; Mandell, L.; Fontell, K.; Leihtinen, H. Acta Polytech. Scand. 1968, 74, I-III. (2) Tiddy, G. J. T. J. Chem. Soc., Faraday Trans. 1972, 68, 369. (3) Lindblom, G.; Lindman, B.; Tiddy, G. J. T. J. Am. Chem. Soc. 1978, 100, 2299. (4) Israelachvili, J. N. Intermolecular and Surface Forces With Applications to Colloidal and Biological Systems; Academic: New York, 1985; Chapter 16. (5) Israelachvili, J. N.; Mitchell, D. J.; Ninham, B. W. J. Chem. Soc., Faraday Trans. 1 1976, 72, 1525.

Figure 1. Phase diagram of the sodium octanoate/1-decanol/ water system at 20 °C.1-3 Compositions of samples used in this study are indicated by their numbers. The concentration was in wt %.

their deuterides. Our approach is based on the rotational isomeric state (RIS) scheme,6 which has been developed mostly for unperturbed polymeric chains. This study is an attempt to extend the RIS scheme to systems dominated by intermolecular interactions. Previously we carried out the conformational analysis of the two amphiphiles.7 Compared with the former work, this study has undergone siginificant improvements: (1) For the unambiguous (6) Flory, P. J. Statistical Mechanics of Chain Molecules; Interscience: New York, 1969. (7) Sasanuma, Y.; Nakamura, M.; Abe, A. J. Phys. Chem. 1993, 97, 5155.

10.1021/la991115n CCC: $19.00 © 2000 American Chemical Society Published on Web 06/23/2000

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assignment of 2H NMR splittings from 1-decanol, not only the randomly but also partially (1-decanol-1,1-d2, 1-decanol-2,2-d2, and 1-decanol-3,3-d2) deuterated compounds have been prepared. (2) The Fourier transform (FT) based on the maximum entropy (MaxEnt) method8,9 has been employed to obtain well-resolved spectra. (3) The geometrical parameters required for the analysis have been determined by ab initio molecular orbital (MO) calculations at the HF/6-31G* level. (4) For the reliable analysis, the RIS scheme has been combined with the MaxEnt method.10,11 (5) The molecular-axis system has been defined with respect to the headgroup structure using the Eulerian angles, φ, θ, and ψ,12 which are treated as adjustable parameters. (6) The conformational free energies of model compounds for octanoate and 1-decanol have been evaluated from ab initio MO calculations at the MP2/ 6-31+G*//HF/6-31G* level to reveal their intrinsic conformational preferences. With these refinements we have reexamined the conformational and orientational characteristics of the two amphiphiles forming the molecular aggregates. In this article our methodology is described in detail, and the results thereby obtained are reported and discussed. 2. Materials and Methods 2.1. Randomly Deuterated Octanoic Acid. This compound was prepared according to Zimmermann’s review.13 The deuteriation grade was estimated by 1H NMR to be 69%. 2.2. Randomly Deuterated 1-Decanol (1-Decanol-d21). A mixture of sodium decanoate (16.2 g, 83.2 mmol), sodium hydroxide (1.6 g, 40 mmol), platinum on activated carbon (Pt 5%, 4.0 g), and deuterium oxide (99 atom % D, 80 mL) was sealed up in a 300-mL autoclave and heated at 210 °C for 100 h. After being allowed to cool to room temperature, the reaction mixture was filtrated, neutralized with sulfuric acid, and extracted with ether. After being dried over sodium sulfate, the organic extract was distilled under reduced pressure, and randomly deuterated 1-decanoic acid (8.95 g) was obtained. The product was dissolved in tetrahydrofuran (THF, 30 mL) and added into a mixture of THF (200 mL) and lithium aluminum deuteride (98 atom % D, 5.12 g, 122 mmol). The solution was refluxed for 2 h under nitrogen, and neutralized with hydrochloric acid (pH 3). Extraction, drying, and distillation were carried out in the same manner as above, and randomly deuterated 1-decanol (7.42 g, 82 atom % D) was obtained. 2.3. 1-Decanol-1,1-d2. This compound was prepared from decanoic acid by the same method as in the second step of section 2.2. The deuteriation grade was 92%. 2.4. 1-Decanol-2,2-d2. A mixture of sodium decanoate (9.39 g, 48 mmol), sodium hydroxide (0.61 g, 15 mmol), and deuterium oxide (99 atom% D, 40 mL) was sealed up in the autoclave and heated at 210 °C for 60 h to yield a crude product of decanoic acid-2,2-d2. 1-Decanol-2,2-d2 was prepared by almost the same procedure as that used in section 2.2, using LiAlH4 instead of LiAlD4. The yield was 4.47 g (91.0%, 87 atom % D). 2.5. 1-Decanol-3,3-d2 (6). This compound was prepared as shown in Scheme 1. 2.5.1. 1-Octanol-1,1-d2 (2). Octanoic acid 1 (30.0 g, 208 mmol) was added dropwise to a mixture of THF (50 mL) and LiAlD4 (15.2 g, 363 mmol), and the mixture was refluxed for 2 h under nitrogen. After being cooled to room temperature, the reaction mixture was neutralized with hydrochloric acid and extracted with ether. The organic extract was dried over sodium sulfate. (8) Sibisi, S. Nature 1983, 301, 134. (9) Sibisi, S.; Skilling, J.; Brereton, R. G.; Laue, E. D.; Staunton, J. Nature 1984, 311, 446. (10) Levine, R. D., Tribus, M., Eds. The Maximum Entropy Formalism; MIT Press: Cambridge, MA, 1979. (11) Buck, B., Macaulay, V. A., Eds. Maximum Entropy in Action; Oxford University Press: New York, 1991. (12) See, e.g.: Rose, M. E. Elementary Theory of Angular Momentum; Wiley & Sons: New York, 1957; Chapter 4. (13) Zimmermann, H. Liq. Cryst. 1989, 6, 591.

Suzuki et al. Scheme 1

After removal of ether, a crude product of 2 was obtained and used in the next step without further purification. 2.5.2. 1-Bromooctane-1,1-d2 (3). The crude product (36.8 g) was refluxed for 5 h with hydrobromic acid (47%, 59.9 g, 350 mmol) and sulfuric acid (39.2 mL). The reaction mixture was extracted with petroleum ether, and the ethereal solution was washed successively with sulfuric acid, water, sodium hydrogen carbonate, and water, dried over sodium sulfate, and distilled under reduced pressure to give 3 (47.0 g, 86.6%). 2.5.3. 2-(Nonyl-2,2-d2)-4,4-dimethyl-2-oxazoline (4). 2,4,4Trimethyl-2-oxazoline (11.3 g, 100 mmol), prepared according to Allen and Ginos,14 was dissolved in THF (40 mL) and cooled to -78 °C under nitrogen. To the solution n-butyllithium (1.54 M in hexane, 65 mL) and 3 (19.5 g, 100 mmol, in THF) were added dropwise. After being warmed to room temperature, the reaction mixture was poured into water (100 mL) and acidified to pH 3 with hydrochloric acid. The aqueous layer was neutralized with sodium hydroxide and extracted with ether. The organic extract was dried over magnesium sulfate and concentrated to yield 4 (17.1 g, 76.0%). 2.5.4. Decanoic Acid-2,2-d2 (5). The product 4 (17.1 g) was dissolved in hydrochloric acid (6 N, 150 mL) and refluxed for 2 h. After being cooled to room temperature, the reaction mixture was extracted with ether. The ethereal solution was dried over sodium sulfate and distilled under reduced pressure to give 5 (6.34 g, 48%). In a manner similar to that presented in section 2.2, the product 5 was reduced with LiAlH4 to give 6 (3.5 g, 60%, 88 atom % D). The total yield was 29%. 2.6. Sample Preparation for 2 H NMR Measurements. Sodium octanoate powder was weighed in an NMR glass tube of 5 mm o.d. After addition of required amounts of 1-decanol and water, the sample tube was sealed, heated at 160 °C for 4 h to achieve visual homogeneity, and further annealed at 120 °C for 12 h. Then ultrapure water, prepared by a Toray Toraypure LV10T, was used. After being cooled slowly to room temperature, the sample was kept in a Haake K20 thermostat at 20 °C for a week to form a homogeneous liquid crystalline phase. The compositions of the individual samples (sodium octanote/1decanol/water in mole %) are as follows: sample no. 1 (the E phase), 9.6:0.9:89.5; sample no. 2 (the D phase), 8.6:11.2:80.2; sample no. 3 (the F phase), 11.4:28.7:59.9. The molecular weights of randomly deuterated octanoate and randomly and partially deuterated 1-decanols were estimated from the individual deuteriation grades. Samples used in the NMR measurements were prepared on the basis of the molecular weights. 2.7. 2H NMR Measurements. Deuterium NMR spectra were recorded at 76.65 MHz under complete proton decoupling on a JEOL GSX-500 spectrometer equipped with a variable-temperature controller. During the measurement the probe temperature was maintained at 20 °C within a (0.1 °C fluctuation. The free induction decay (FID) signals were accumulated ca. 200-1400 (14) Allen, P.; Ginos, J. J. Org. Chem. 1963, 28, 2759.

Conformations of Amphiphilic Molecules times by using a single pulse excitation scheme. The π/2 pulse width (t1) ranged from 2.4 to 9.0 µs. The sweep width (∆w) and block size were, ca. 30 kHz and 16K for the E and F phases or ca. 60 kHz and 32K for the D phase, respectively. These parameters, adjusted for each sample to obtain a well-defined spectrum, did not always satisfy the recommended relation t1 < 1/4π∆w.15 The recycle delay was set equal to 1.5 s, being much larger than the spin-lattice relaxation time of ordinary soap/ water systems.15 The FID data underwent the FT using the software included with the spectrometer. Then the apodization using an exponential function was carried out. The broadening factor was within the range of 5-10 Hz. Only the FID signal from 1-decanol-d21 in the F phase was subjected to the FT based on the MaxEnt method. The broadening factor was 15 Hz. 2.8. Molecular Orbital Calculations. Ab initio MO calculations were carried out using the Gaussian94 program16 installed on the Cray CS6400 or the Hitachi S-3800/160 in the Information Processing Center, Chiba University. Because octanoate and 1-decanol are too large to be objects of ab initio MO calculations, pentanoate and 1-butanol were employed as models for the head portions of octanoate and 1-decanol, respectively. The geometries were fully optimized by the MO calculations at the HF/6-31G* level. Then default criteria for convergence were used for all the optimizations. By use of the geometries thus determined, the electronic correlation effects were calculated at the MP2/6-31+G* level. Vibrational frequencies for the equilibrium geometries were evaluated at the HF/6-31G* level and scaled by 0.8929, and the zero-point energies were scaled by 0.9135 to correct for the overestimation.17 The entropy change from 0 to 298.15 K was concomitantly computed. With these thermodynamic quantities, the conformational free energies for the individual conformations at 298.15 K were evaluated.

Langmuir, Vol. 16, No. 15, 2000 6319 Table 1. Geometrical Parameters Used for Octanoate and 1-Decanola Octanoate Bond Length, Å OOC-C1 Ci-Ci+1 (i g 1)

1.558 1.530

Bond Angle, deg ∠CCD of methylene group ∠CCD of methyl group

108.7 111.3

C-D C-O

1.088 1.234

∠OCO ∠OCC ∠CCC

129.5 114.2 113.3

bond 2

Dihedral Angle for Gauche State, deg (111.4 bond n (n g 3)

(112.8

1-Decanol Bond Length, Å C1-C2 Ci-Ci+1 (i g 2)

1.519 1.528

Bond Angle, deg ∠CCD of methylene group ∠CCD of methyl group

108.4 111.2

C-D C-O

1.088 1.404

∠OCD ∠OCC ∠CCC

109.7 108.2 112.8

bond 2

Dihedral Angle for Gauche State, deg (116.5 bond n (n g 3)

(112.8

a

Determined by the geometrical optimization using ab initio MO calculations at the HF/6-31G* level for pentanoate and 1-butanol.

3. Results of Experiments and MO Calculations 3.1. Geometrical Parameters. The geometrical parameters obtained by the MO calculations are listed in Table 1. The two oxygen atoms of octanoate are located on the same plane as the C0-C1 bond (for the carbon numbers, see Figure 2). We searched for the potential minima in the rotation about the C0-C1 bond of octanoate; the geometrical optimization for 1-butanol was attempted by setting the initial dihedral angle at 0° (where one C0-O and the other C0-O bonds are, respectively, in the antiperiplanar and eclipsed positions with respect to the C1-C2 bond), 30°, 60°, 90°, or 120°. Irrespective of the initial value, the optimization always gave the C0-O/C1C2 antiperiplanar (eclipsed) form. Thus the analysis described below was carried out with the torsional angle fixed at 0°. 3.2. Observed 2H NMR Data. Shown in Figure 3 are 2 H NMR spectra observed from randomly deuterated octanoate incorporated in the E (sample no. 1), D (no. 2), and F (no. 3) phases. In the three spectra well-defined peaks are observed. According to the previous studies,18-21 (15) Davis, J. H. Biochim. Biophys. Acta 1983, 737, 117. (16) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.; Johnson, B. G.; Robb, M. A.; Cheeseman, J. R.; Keith, T.; Petersson, G. A.; Montgomery, J. A.; Raghavachari, K.; Al-Laham, M. A.; Zakrzewski, V. G.; Ortiz, J. V.; Foresman, J. B.; Cioslowski, J.; Stefanov, B. B.; Nanayakkara, A.; Challacombe, M.; Peng, C. Y.; Ayala, P. Y.; Chen, W.; Wong, M. W.; Andres, J. L.; Replogle, E. S.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Binkley, J. S.; Defrees, D. J.; Baker, J.; Stewart, J. P.; Head-Gordon, M.; Gonzalez, C.; Pople, J. A. Gaussian 94, Revision E.2; Gaussian, Inc.: Pittsburgh, PA, 1995. (17) Pople, J. A.; Scott, A. P.; Wong, M. W.; Radom, L. Isr. J. Chem. 1993, 33, 345. (18) Klasson, T.; Henriksson, U. In Solution Behavior of Surfactants: Theoretical and Applied Aspects; Mittal, K. L., Fendler, E. J., Eds.; Plenum Publishing: New York, 1982; Vol. 1, p 417. (19) Klasson, T. Ph.D. Thesis, The Royal Institute of Technology, 1983. (20) Charvolin, J.; Hendrikx, Y. In Nuclear Magnetic Resonance of Liquid Crystals; Emsley, J. W., Ed.; Reidel: Dordrecht, 1985; Chapter 20.

Figure 2. Schematic representation of (a) octanoate, (b) 1-decanol, (c) pentanoate, and (d) 1-butanol in thier all-trans conformations. As indicated, the skeletal bonds and atomic groups (carbon atoms) are numbered.

the quadrupolar splitting ∆vi was so assigned to each Ci-D bond as to decrease with increasing carbon number i. In the E and D phases, the ∆vi value decreases considerably between the carbons 1 and 2. Such tendencies have been observed for, e.g., potassium laurate-d23 in the lamellar and hexagonal phases.21 For the F phase, however, the change in ∆vi is comparatively small. In Figure 3, parts a and b, the peaks from the first methylene unit are (21) Thurmond, R. L.; Lindblom, G.; Brown, M. F. Biochemistry 1993, 32, 5394.

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Figure 3. 2H NMR spectra observed from randomly deuterated octanoate: (a) sample no. 1 (E phase); (b) sample no. 2 (D phase); (c) sample no. 3 (F phase). The probe temperature was 20 °C. As numbered, the peaks were assigned to the individual atomic groups. For the atomic-group numbers, see Figure 2. Note that the frequency scale in (b) is twice that in (a) and (c).

subdivided into two. This is due to the dipolar coupling between the deuterium atoms at the C1 site. For the unambiguous assignment of the less wellresolved large quadrupolar splittings from 1-decanol, we

Suzuki et al.

prepared 1-decanol-1,1-d2, 1-decanol-2,2-d2, and 1-decanol3,3-d2, as well as 1-decanol-d21. Figure 4 shows 2H NMR spectra from (a) 1-decanol-d21, (b) 1-decanol-1,1-d2 + 1-decanol-d21, (c) 1-decanol-2,2-d2 + 1-decanol-d21, and (d) 1-decanol-3,3-d2 + 1-decanol-d21 in the E, D, and F phases, respectively. The spectra observed from the mixed samples were used for determining the relative peak positions. Intense outer peaks found in Figure 4, parts b, c, and d, can be evidently assigned to the first, second, and third methylene units from the OH group, respectively. However, the assignment is partly inconsistent with that in the previous study,7 where 1-decanol-d21, 1-decanol-1,1d2, and 1-decanol-2,2-d2 separately underwent the NMR measurements. Thus a slight fluctuation in concentration might cause the experimental error. In the present study, the three partially deuterated compounds were individually mixed with 1-decanol-d21 and subjected to the NMR measurements. Accordingly, the present assignment should be more reliable. The other quadrupolar splittings (4 e i e 10) are assigned so that the ∆vi value decreases with increasing carbon number. In the spectrum from 1-decanol-d21 in sample no. 3, four quadrupolar splittings from the CiD2 groups (1 e i e 4) overlap to form the broad outermost peaks. To improve the resolution, we applied the FT based on the MaxEnt method8,9 to the FID data under different processing conditions. In Figure 5, the best spectrum is compared with that obtained from the fast FT installed in the spectrometer. In the MaxEnt spectrum, all the methylene signals are observed as the doublets due to the 2H-2H dipolar coupling. From the spectrum, the ∆v values i were determined. The experimental quadrupolar splittings from octanoate and 1-decanol in the three samples are listed in Table 2.

Figure 4. 2H NMR spectra observed from (a) randomly deuterated 1-decanol (1-decanol-d21), (b) 1-decanol-1,1-d2 + 1-decanol-d21, (c) 1-decanol-2,2-d2 + 1-decanol-d21, and (d) 1-decanol-3,3-d2 + 1-decanol-d21. The probe temperature was 20 °C. As numbered, the peaks were assigned to the individual atomic groups. For the atomic-group numbers, see Figure 2.

Conformations of Amphiphilic Molecules

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reversed hexagonal aggregates the director is parallel to the cylinder axis. Accordingly, the order parameter SNi with respect to the normal of the interface can be related to Si by

Si ) SNi for the D phase

(2)

Si ) -SNi/2 for the E and F phases

(3)

and

Figure 5. 2H NMR spectra of 1-decanol-d21 in sample no. 3 (F phase), obtained from the Fourier transform (FT) using the maximum entropy method (above) and ordinary fast FT (below). The probe temperature was 20 °C. As numbered, the peaks were assigned to the individual atomic groups. Table 2. Observed and Calculated Values of 2H NMR Quadrupolar Splittings of Octanoate and 1-Decanol no. 1 (E phase)

no. 2 (D phase)

no. 3 (F phase)

obsd

calcd

obsd

calcd

obsd

calcd

1 2 3 4 5 6 7

16.45 11.68 11.68 10.83 9.61 7.23 2.80

Octanoatec 16.45 34.62 11.68 30.98 11.68 30.10 10.83 29.38 9.61 27.07 7.23 21.39 2.80 8.09

34.62 30.55 30.54 29.38 27.07 21.40 8.09

15.43 14.91 14.11 13.57 12.39 9.46 3.35

15.43 14.91 14.11 13.57 12.39 9.46 3.35

1 2 3 4 5 6 7 8 9 10

13.42 13.69 14.45 12.30 11.29 9.10 8.21 6.14 4.11 0.90

1-Decanold 13.69 26.91 13.94 27.86 14.93 30.04 12.30 28.48 11.29 26.46 9.10 24.95 8.20 21.16 6.14 16.19 4.11 11.85 0.90 2.51

26.06 26.85 31.53 27.56 27.49 23.59 22.11 14.91 12.86 4.35

10.85 11.11 11.42 10.64 10.24 8.81 7.42 5.78 4.22 1.03

10.85 11.11 11.42 10.64 10.24 8.81 7.42 5.78 4.22 1.03

a For the atomic group numbers, see Figure 2. b In kHz. c The quadrupolar splittings from the second and third methylene units of octanoate in the E phase were not resolved. d The |∆vi| values of 1-decanol in the F phase were determined by the Fourier transform using the MaxEnt method (see Figure 5).

4. Analysis 2H

NMR Splittings. The deuterium quadrupolar 4.1. splitting ∆vi observed from the Ci-D bond is given by20,22

∆vi )

3 e2qQ Si 4 h

[ 〈

SNi ) SZZ

|∆vi|b atomic group no.a

In related work,24,25 lipid dynamics have been studied by pulsed 1H and 2H NMR of unoriented and macroscopically aligned bilayer membranes over a wide temperature range. These studies have indicated that three kinds of molecular motions exist in the liquid crystalline phases: the trans-gauche isomerization of the aliphatic chains (correlation time 10-12 to 2 × 10-10), the phospholipid long axis rotation and fluctuation (10-10-10-8), and the collective lipid motions (∼10-6). These three motions have sufficiently different correlation times as to be considered decoupled with each other. Since the molecular motions may be assumed to be similar in the mesophases treated here, we have

(1)

where e2qQ/h is the quadrupolar coupling constant ()163 kHz)23 and Si is the orientational order parameter of the Ci-D bond with respect to the director of the molecular aggregate. In the lamella the director coincides with the normal of the interface, while in the hexagonal and (22) Seelig, J. Q. Rev. Biophys. 1977, 10, 353. (23) Greenfield, M. S.; Vold, R. L.; Vold, R. R. J. Chem. Phys. 1985, 83, 1440.

〉 〈

3 cos2 θZ,i,k - 1 + 2 cos2 θX,i,k - cos2 θY,i,k (SXX - SYY) 2

〉]

(4)

where the X, Y, and Z axes are the principal axes of the order matrix, and, e.g., θX,i,k is the angle between the X axis and the Ci-D bond of the kth conformer. The angular brackets represent the average over all the possible conformations of the hydrocarbon chain. The orientational order parameters, SZZ and SXX - SYY, reflecting the rotation and fluctuation of the molecular axes, are assumed to be independent of the conformation, thus being placed outside the angular brackets (the single-ordering-matrix approximation). 4.2. Molecular-Axis System. The molecular axes may be defined with respect to the headgroup structure. In this study the origin of the molecular axes has been located around the methylene carbon that exhibits the largest quadrupolar splitting, because the C-D bond has the largest order parameter, i.e., the smallest fluctuation. For octanoate (1-decanol), the origin is placed on the C0 (C2) atom, the initial axes, X0, Y0, and Z0,are set as shown in Figure 6, the Z0 axis is parallel to the C0-C1 (C2-C3) bond, the X0 axis is located on the C0C1C2 (C1C2C3) plane and perpendicular to the Z0 axis, and the Y0 axis is normal to both X0 and Z0 axes. Here the symbols in parentheses are related to 1-decanol. In the simulation the directions of the axes are adjusted using the Eulerian angles, φ, θ, and ψ: the φ rotation around the Z0 axis, the θ tilting around the Y1 axis, and the ψ rotation around the Z axis.12 The X, Y, and Z thus obtained are considered the molecular axes. 4.3. Statistical Weight Matrixes. The conformations of chain molecules in the free state may be represented only in terms of the short-range intramolecular interactions. The RIS scheme is based on this hypothesis.6 The weights of all possible conformations of an n-alkyl chain (24) Rommel, E.; Noack, F.; Meier, P.; Kothe, G. J. Phys. Chem. 1988, 92, 2981. (25) Kothe, G.; Mayer, C. In The Molecular Dynamics of Liquid Crystals; Luckhurst, G. R., Veracini, C. A., Eds.; Kluwer Academic Publishers: Dordrecht, 1994; Chapter 21.

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where σn′ and ωn′ represent the weight parameters including the effects of the anisotropic field. This modified RIS scheme has some advantages: (1) All possible molecular symmetries are taken into account. (2) No a priori assumptions on the conformational energies and the potential function of the anisotropic field are required. (3) The formulas established in the conventional RIS scheme are, in principle, valid. For example, the fractional population fξηζ... of a conformation ξηζ ... (ξ, η, ζ ) t, g+, or g-) can be calculated from

fξηζ... )

J*[U2′(ξ)U3′(ξη)U4′(ηζ)...]J N-1

J*[

(9)

∏ Un′]J

n′)2

Figure 6. Molecular-axis system for (a) octanoate and (b) 1-decanol. For the details, see text.

can be evaluated from the statistical weight matrixes, Un (n, bond number), assigned to the skeletal bonds. When the intramolecular interactions up to the second-order interactions (between groups separated by four bonds) are taken into account, the relative weights of all the conformations may be expressed as a function of only two parameters, σ and ω. These parameters are defined as the Boltzmann factors of the corresponding conformational energies; e.g., σ ) exp(-Eσ/RT), where R is the gas constant and T is the absolute temperature. The Un matrixes are given by6,26

[ ]

and

1 σ σ U2 ) 0 0 0 0 0 0

(5)

[

(6)

]

1 σ σ Un ) 1 σ σω (n g 3) 1 σω σ

Here the rows and columns of these matrixes are indexed to rotational states for the preceding and current bonds. If the n-alkyl chain is placed in an anisotropic field, the conformation must be perturbed from the free state. By a minor revision, however, the RIS scheme may be fitted for evaluation of conformer populations of such perturbed molecules. The C-C bonds are expected to have different degrees of the rotational freedom. Thus the statistical weights of the individual C-C bonds must be distinguished:

[

1 σ2′ σ2′ U2 ) 0 0 0 0 0 0 and

[

]

(7)

]

(8)

σn′ 1 σn′ σn′ωn′ (n g 3) Un ) 1 σn′ 1 σn′ωn′ σn′

(26) Abe, A.; Jernigan, R. L.; Flory, P. J. J. Am. Chem. Soc. 1966, 88, 631.

where J* ) [100], J is the 3 × 1 column matrix of which elements are unity, and N is the number of skeletal bonds. The U2′(ξ) matrix can be obtained by filling the columns of the U2 matrix other than that corresponding to the ξ state with zero and the U3′(ξη) matrix by filling the elements of the U3 matrix other than that corresponding to the ξη conformation with zero, etc. The trans fraction pt;n of the nth bond can also be calculated from

pt;n )

J*[U2‚‚‚Un-1Un′(t)Un+1‚‚‚UN-1]J N-1

J*[

(10)

∏ Un′]J

n′)2

Here the Un′(t) matrix can be obtained by filling the columns corresponding to the g( states of Un with zero. 4.4. Maximum Entropy Method. The MaxEnt method is known as a powerful simulation technique. Even in the case where the parameters outnumber the data, the MaxEnt method can derive the most probable conclusion.10,11 The conformer probability of the solute must satisfy the reproducibility of the experimental observations. It may be monitored by 2

χ )

∑i

(∆vi,calc - ∆vi,obsd)2

(11)

i2

where ∆vi,calc and ∆vi,obsd are, respectively, calculated and observed quadrupolar splittings and i is the corresponding experimental error. The entropy concerning the conformer probability fk (k, conformer) is defined as27 K

S(fk) )

(

fk

∑ fk - mk - fk ln m k)1

)

(12)

k

where mk is the initial model of fk and K is the number of conformers. In the MaxEnt method it is hypothesized that the most probable solution of fk maximizes the S value. Accordingly, the solution may be found at the maximum of

Q ) RS -

χ2 2

(13)

(27) Skilling, J. In Maximum Entropy and Bayesian Methods; Erickson, G. J., Smith, C. R., Eds.; Kluwer: Dordrecht, 1988; p 45.

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where R is the regularization constant, which counterbalances the two requirements: maximizing of entropy and reproduction of experiment. Because the entropy S is convex and χ2 is concave, Q always reaches a unique maximum. The MaxEnt simulation is carried out under the restriction of the RIS scheme. So far, the MaxEnt method has been incorporated into mean-field theories for anisotropic fields and applied to the conformational analysis of flexible molecules dissolved in nematic solvents.28-30 Recently, the methodology has been modified for the simultaneous analysis of different types of experimental data from the flexible solutes.31 However, our approach is based on the RIS scheme, and the MaxEnt method has been adopted as a technique for the parameter optimization to acquire the most probable solution from a restricted number of observations. 4.5. Procedure for Simulation. In our simulation, the second-order statistical weight parameters, ωn′, were assumed to be null. This hypothesis may be justified from the fact that the alkyl chain can hardly have the g(gconformational sequences (the pentane effect6) even in the free state (Eω ) 2.0-3.0 kcal mol-1).6,26 In the anisotropic field, these conformations must occur more rarely. For octanoate, there were 10 adjustable parameters, SZZ, SXX - SYY, φ, θ, ψ, and σn′ (n ) 2-6), and seven ∆vi values. For 1-decanol, the 10 experimental data, ∆vi (i ) 1-10), were simulated using 13 variables, SZZ, SXX - SYY, φ, θ, ψ, and σn′ (n ) 2-9). As the initial model mk, the conformer probabilities obtained from the Simplex fitting7 were employed. Then the adjustable parameters were SZZ, SXX - SYY, θ, and σn′; that is, φ and ψ were set equal to zero. The conformer fractions were calculated from eq 9 using the initial σn′ parameters obtained. The entropy S on the conformer fractions was estimated according to eq 12 using the mk values. The 2H quadrupolar splittings were calculated from eq 1 and compared with the experimental data to yield the χ2 value. Iterative computations were carried out using a new set of variables which were determined so as to increase the Q value efficiently, until the Q function was maximized within a given allowance. For the simulation, the MemSys5 package32 was altered to be combined with the RIS scheme. The adjustment of the regulation constant R, the calculations of the Q and S values, and the noise scaling are based on the original algorithm of MemSys5.33 4.6. Results of Simulation. In Table 2, the calculated ∆vi values for octanoate and 1-decanol are compared with the corresponding experimental data. The reproducibility of the experiment can be checked by the R factor

R(%) )

[

]

∑i (∆vi,calcd - ∆vi,obsd)2 ∑i

∆vi,obsd2

× 100

(14)

(28) Berardi, R.; Spinozzi, F.; Zannoni, C. J. Chem. Soc., Faraday Trans. 1992, 88, 1863. (29) Emsley, J. W.; Wallington, I. D.; Catalano, D.; Veracini, C. A.; Celebre, G.; Longeri, M. J. Phys. Chem. 1993, 97, 6518. (30) Berardi, A.; Spinozzi, F.; Zannoni, C. Chem. Phys. Lett. 1996, 260, 633. (31) Berardi, A.; Spinozzi, F.; Zannoni, C. J. Chem. Phys. 1998, 109, 3742. (32) Gull, S. F.; Charter, M.; Skilling, J. MemSys5 Ver. 1.20; Maximum Entropy Data Consultants Ltd.: Cambridge, England, 1990, 1991. (33) For the details, see: Gull, S. F.; Skilling, J. Quantified Maximum Entropy MemSys5 User’s Manual; Maximum Entropy Data Consultants Ltd.: Cambridge, England, 1991.

Table 3. Optimized Parameters and the First Derivatives of the R Factora with Respect to the Parameters no. 1 (E phase)

no. 2 (D phase)

no. 3 (F phase)

SZZ SXX - SYY φb θb ψb σ2′ σ3 ′ σ4 ′ σ5 ′ σ6 ′ |∂R/∂SZZ| |∂R/∂(SXX - SYY)| |∂R/∂φ| |∂R/∂θ| |∂R/∂ψ| |∂R/∂σ2′| |∂R/∂σ3′| |∂R/∂σ4′| |∂R/∂σ5′| |∂R/∂σ6′|

Octanoate 0.558 0.577 0.000 0.000 0.060 -0.033 -22.45 -25.75 0.000 0.000 1.56 × 10-1 5.83 × 10-2 1.90 × 10-4 2.79 × 10-4 3.82 × 10-2 1.91 × 10-2 9.29 × 10-2 6.10 × 10-2 1.41 × 10-1 1.18 × 10-1 13.3 7.05 1.99 1.57 2.23 × 10-4 2.42 × 10-4 8.89 × 10-2 2.69 × 10-2 0 0 10.3 3.69 2.17 × 10-1 4.85 × 10-1 1.50 1.79 6.49 × 10-1 6.99 × 10-1 2.37 1.20

0.507 0.000 -0.015 -29.41 0.000 1.77 × 10-2 3.49 × 10-2 2.01 × 10-2 6.72 × 10-2 1.40 × 10-1 36.0 1.81 2.91 × 10-4 9.46 × 10-3 0 3.64 1.87 1.40 4.83 × 10-1 3.54

SZZ SXX - SYY φb θb ψb σ2′ σ3 ′ σ4 ′ σ5 ′ σ6 ′ σ7 ′ σ8 ′ σ9 ′ |∂R/∂SZZ| |∂R/∂(SXX - SYY)| |∂R/∂φ| |∂R/∂θ| |∂R/∂ψ| |∂R/∂σ2′| |∂R/∂σ3′| |∂R/∂σ4′| |∂R/∂σ5′| |∂R/∂σ6′| |∂R/∂σ7′| |∂R/∂σ8′| |∂R/∂σ9′|

1-Decanol 0.481 0.636 0.000 -0.079 0.000 0.005 -20.17 -11.40 0.000 0.023 1.33 × 10-2 4.62 × 1012 2.98 × 10-5 1.58 5.31 × 10-2 6.09 × 10-2 8.22 × 10-2 2.86 × 10-3 9.52 × 10-2 5.40 × 10-2 1.07 × 10-1 1.75 × 10-1 1.60 × 10-1 2.08 × 10-1 6.81 × 10-1 1.59 8.06 16.8 2.92 × 10-1 2.58 1.22 × 10-4 6.81 × 10-5 3.28 × 10-2 7.58 × 10-2 0 1.01 × 10-5 7.70 × 10-1 0.00 6.64 × 10-1 1.76 × 10-2 8.40 5.47 1.91 2.19 × 10-1 7.53 4.57 6.75 × 10-1 1.02 × 10-1 2.06 2.47 2.84 × 10-2 2.17 × 10-3

0.398 0.000 0.000 -19.09 0.000 1.60 × 10-2 2.80 × 10-2 2.86 × 10-2 3.70 × 10-2 6.78 × 10-2 2.03 × 10-1 1.36 × 10-1 7.72 × 10-1 64.5 4.19 9.80 × 10-5 2.65 × 10-2 0 4.10 × 10-1 3.22 × 10-1 3.58 3.23 × 10-1 1.48 3.32 × 10-1 1.39 9.95 × 10-3

a

Defined in eq 14. In percent. b In degrees.

For 1-decanol in sample no. 2 (the D phase), an R value of 0.27% was obtained, while in other cases the calculated values exactly agree with the observations within the significant figures (R ) 0.00%). In Table 3 the optimum variables and the first derivatives of the R factor with respect to the individual parameters are listed. The latter quantity represents the effect of each variable on the reproducibility of the experiment. For both octanoate and 1-decanol, of all the adjustable parameters, SZZ is shown to be, in principle, most effective on the R value, and each SXX - SYY term can be seen to have a comparatively large derivative. However, except for 1-decanol in sample no. 2, the SXX SYY term was evaluated to be virtually null. The transformation of the molecular-axis system is indicated to be less effective; however, the θ tilting is comparatively contributory to the change in the R value. These results may be due to the fact that SZZ is much larger than SXX - SYY. Here we do not examine values of the statistical

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Table 4. Free Energies Relative to the tt State, Evaluated by ab Initio MO Calculations at the MP2/ 6-31+G*//HF/6-31G* Level conformation pentanoate

1-butanol

bond no. 2a

bond no. 3a

free energy (kcal mol-1)

t g( t g( g( t g( t g( g(

t t g( g( gt t g( g( g-

0.00 -0.09 0.82 0.73 b 0.00 -0.27 1.47 0.42 1.25

a For the bond numbers, see Figure 2. b Owing to a steric repulsion between the carbonyl and methyl groups, these states were indicated to be essentially absent.

Figure 7. Intramolecular (C-H)‚‚‚O interaction in the g+g+ conformation of 1-butanol. By ab initio molecular orbital claculations at the MP2/6-31+G*//HF/6-31G* level, the stabilization energy was estimated to be -0.78 kcal mol-1.

weight parameters but will later discuss the bond conformations therefrom calculated. 5. Discussion 5.1. Conformational Energies of the Free State. Listed in Table 4 are the conformational free energies of pentanoate and 1-butanol (Figure 2), which may be regarded as the model compounds for the bonds 2 and 3 of octanoate and 1-decanol, respectively. Bond 2 of pentanoate is suggested to prefer the gauche state to the trans one by only 0.09 kcal mol-1, while bond 3 exhibits a moderate trans preference (0.82 kcal mol-1). The free energy (0.73 kcal mol-1) of the g(g( state exactly corresponds to that estimated by the additivity of the conformational energies (-0.09 + 0.82 kcal mol-1). For bond 2 of 1-butanol, the gauche state has a lower free energy by 0.27 kcal mol-1 than the trans one. On the other hand, the conformational energy of the gauche state of bond 3 was estimated to be as much as 1.47 kcal mol-1. The g(g( conformation has a free energy of 0.42 kcal mol-1, which is smaller by as much as 0.78 kcal mol-1 than that suggested by the additivity (-0.27 + 1.47 kcal mol-1). We investigated the optimized geometry of the g+g+ state of 1-butanol. As illustrated in Figure 7, the distance between the oxygen atom and one of the hydrogen atoms of the third methylene group was evaluated as 2.622 Å, being slightly smaller than the sum (2.72 Å) of van der Waals radii of oxygen and hydrogen.34 Then the oxygen and hydrogen atoms have partial charges of -0.777 and +0.221, respectively. Thus an electrostatic interaction such as the (C-H)‚‚‚O attraction found in ethers35-37 is (34) Bondi, A. J. Phys. Chem. 1964, 68, 441. (35) Sasanuma, Y. Macromolecules 1995, 28, 8629. (36) Law, R. V.; Sasanuma, Y. J. Chem. Soc., Faraday Trans. 1996, 92, 4885. (37) Law, R. V.; Sasanuma, Y. Macromolecules 1998, 31, 2335.

suggested to exist in such alcohols and to stabilize these conformations. The g(g- states have a free energy of 1.25 kcal mol-1, which is close to the sum of -0.27 (g(t) and 1.47 (tg() kcal mol-1. Thus, neither extra attraction nor repulsion may not be present in the g(g- states. 5.2. Crystal Structures of Fatty Acids and Alcohols. Saturated fatty acids are known to have some crystal forms. For example, stearic acid shows the B (stable at low temperatures), C (stable at high temperatures), and E forms.38-40 In the B form the second C-C bond from the headgroup is found in the gauche conformation. In the C form, however, the molecular chain takes the all-trans conformation. Long saturated alcohols tend to assemble themselves into lamellar structures by inter- and intralamellar hydrogen bonds and exhibit complicated polymorphism.41,42 Although not all reports on the polymorphism are consistent with each other, it seems certain that two (R and β) crystal structures are present. The R form is stable at high temperatures and has a hexagonal unit cell in which the molecules are arranged so as to be normal to the lamellar surface. The β form appears at low temperatures, the molecular axis is almost perpendicular to the lamellar surface, and the C-C bond adjacent to the OH group takes the gauche conformation. From the above reports and our MO calculations, it seems reasonable to conclude that the C-C bond adjacent to the headgroup of both fatty acids and alcohols tends to accept the gauche conformation. 5.3. Conformations and Dimensions of Amphiphiles and Aggregate Shapes. 5.3.1. Free State. The trans fractions of the individual C-C bonds of octanoate and 1-decanol are shown in Figure 8. The bond conformations for the free states, calculated using the free energies in Table 4 for the bonds 2 and 3 and the conformational energies (Eσ ) 0.5 and Eω ) 2.0 kcal mol-1) of n-alkanes26 for the higher bonds (n g 4), are shown in Figure 8d. As expected from the above discussion, in the free state, both octanoate and 1-decanol have small trans fractions at bond 2. The trans fraction of bond 3 of 1-decanol was estimated to be 0.82; the moderate free energy (0.42 kcal mol-1) of the g(g( states (in the bonds 2 and 3) may compensate the high energies of the tg( (1.47 kcal mol-1) and g(g- (1.25 kcal mol-1) states. 5.3.2. E Phase. In the E phase the octanoate chain can be found to be much more rigid than that in the free state. Bond 2 has a comparatively low trans fraction. This is probably because the large area at the interface of the cylindrical aggregate can then be filled effectively, and the contact between the hydrocarbon chain and water is avoidable. The trans fraction of 1-decanol tends to decrease toward the methyl terminal. The longer 1-decanol chain compared to octanoate can be incorporated in the cylindrical aggregate, with its C-C bonds near the methyl end forced into the gauche state. The E phase appears only in the region of low decanol concentration. 5.3.3. D Phase. In the D phase the octanoate molecule seems almost fully extended. On the other hand, the 1-decanol chain shows peculiar conformational features; bond 2 is fixed in the gauche state, and bonds 3 and 9 have high gauche probabilities. In Figure 9 three highly populated conformers of 1-decanol are depicted together (38) Vand, V.; Morley, W. H.; Lomer, T. R. Acta Crystallogr. 1951, 4, 324. (39) Holland, R. F.; Nielsen, J. R. J. Mol. Spectrosc. 1962, 9, 436. (40) Goto, M.; Asada, E. Bull. Chem. Soc. Jpn. 1978, 51, 2456. (41) Tanaka, K.; Seto, T.; Hayashida, T. Mem. Coll. Sci., Univ. Kyoto 1957, 35, 123. (42) Seto, T. Mem. Coll. Sci., Univ. Kyoto, Ser. A 1962, 30, 89.

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Langmuir, Vol. 16, No. 15, 2000 6325

Figure 10. (a) Schematic illustration of the cone model. The lipid molecule is assumed to move freely within a cone angle βmax around the normal to the interaface. β is the angle between the molecular Z axis and the normal. (b) Distribution function g(β) of the cone model.

Figure 8. Bond conformations (trans fractions) of the individual C-C bonds of octanoate and 1-decanol: (a) sample no. 1 (E phase); (b) sample no. 2 (D phase); (c) sample no. 3 (F phase); (d) free state. For the bond numbers, see Figure 2.

behaviors of the amphiphiles on the basis of the cone model.43-45 In the model it is assumed that the lipid molecules can freely move within a cone angle βmax around the normal of the interface (see Figure 10a). Figure 10b shows the distribution function g(β), where β is the angle between the Z axis and the normal. Then the orientational order parameter SZZ is given as

1 SZZ ) (cos2 βmax + cos βmax) 2

(15)

The average tilting angle 〈β〉 can be estimated from

(

〈β〉 ) cos-1 cos2

Figure 9. Highly populated conformers of octanoate and 1-decanol in sample no. 2 (D phase): (a) all-trans octanoate; (b) g(g(tttttg( (or g(g(tttttg-) conformer of 1-decanol (probability, 5.9% × 4); (c) g(ttttttg( (or g(ttttttg-) conformer of 1-decanol (3.7% × 4); (d) g(g(tttttt conformer of 1-decanol (3.7% × 2). The hydrogen atom of the hydroxy group of 1-decanol is omitted.

with the all- trans octanoate. From the illustration, it can be seen that lengths of the 1-decanol conformers are close to that of the extended octanoate; both hydrophilic and hydrophobic surfaces of the lamella become flat. As the MO calculations suggest, the gauche preference of the bond 2 of 1-decanol seems intrinsic. If bond 2 takes the gauche state, it may not be difficult for bond 3 to accept the gauche conformation owing to the intramolecular (C-H)‚‚‚O attraction. 5.3.4. F Phase. In the F phase, the octanoate chain diverges from the aqueous core where its polar heads are anchored, being wobbled and perturbed around the normal of the interface. Thus we have analyzed the wobbling

1 β 2 max

)

(16)

From these equations, the βmax and 〈β〉 values of octanoate in sample no. 3 were evaluated to be 51.4° and 35.7°, respectively. The Eulerian angle θ of the octanoate chain was determined as -29.41°, being almost equal to the angle (ca. -29°) between the C0-C1 bond and the longest principal axis of inertia of its all-trans conformation. The extended chain must wobble synchronously with the neighboring molecules. For 1-decanol, the following results were obtained: βmax ) 58.5° and 〈β〉 ) 40.4°. In the inner part of the reversed hexagonal aggregate, the hydrocarbon chains are so densely packed that the bonds 2-6 of 1-decanol have high trans fractions (see Figure 8). On the other hand, bond 9, which would be located outside the hydrophobic terminal of octanoate, shows a low trans fraction owing to the oppression by the neighboring aggregates. 5.4. Alcohol Effects. Phase behaviors of a number of ternary systems of saturated single-chain soap, alcohol, and water have been investigated.46,47 From these studies, the effects of alcohols on the phase behaviors may be (43) Petersen, N. O.; Chan, S. I. Biochemistry 1977, 16, 2657. (44) Kinoshita, K.; Kawato, S.; Ikegami, A. Biophys. J. 1977, 20, 289. (45) Kawato, S.; Kinoshita, K.; Ikegami, A. Biochemistry 1977, 16, 2319. (46) Ekwall, P. Composition, Properties and Structures of Liquid Crystalline Phases in Systems of Amphiphilic Compounds. In Advances in Liquid Crystals; Brown, G. H., Ed.; Academic: New York, 1975; Vol. 1.

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summarized as follows. (1) Without alcohol, no mesophase but E is formed. (2) If an alcohol either longer or shorter than the soap exists, the D phase is apt to be formed. (3) Only when an alcohol is longer than the soap dissolved, the F phase possibly appears in a narrow concentration range. On the basis of the results obtained here, these phenomena may be interpreted as follows. In the lamella, the alcohol chain takes the gauche state for the C-C bond(s) near the OH group, enhancing the area per head, and it may form a hydrogen bond. Therefore, even short alcohols such as 1-butanol cooperate with the soap to build the lamellar structure.48 However, in the sodium octanoate/1-butanol/water system, the D phase appears only within a small area. Alcohols much longer than the soap, being difficult to form flat lamellar surfaces with the soap, would destabilize the layer structure. It may not be fortuitous that the D phase has been mostly found in the ternary systems including alcohols longer than the soap by up to three methylene units. Since, in the F phase, the extended alcohol chain requires only a small area per head, the alcohol can be effectively packed in the aggregate. If both amphiphilic chains had the same length, the uniform hydrophobic cylinder with a curvature should be formed and vacancies would be made between the aggregates. The amphiphiles having different chain lengths avoid the vacancy formation and stabilize the reversed hexagonal phase. However, the F phase appears merely in an extremely narrow range of decanol composition. For the sodium octanoate/1-nonanol/ water system,49 the F area in the phase diagram is much smaller than that of the present system. Thus the stability of this mesophase can be seen to be sensitive to differences in chain length and composition. In Figure 11, a 2H NMR spectrum observed from randomly deuterated 1-decanol dissolved in a thermotropic liquid crystal 4′-methoxybenzylidene-4-n-butylaniline (MBBA) is shown and compared with that from perdeuterated n-decane in MBBA. For n-decane, the quadrupolar splittings can be assigned so as to decrease gradually from the central methylene to the methyl groups. For 1-decanol, as shown in Figure 11, four pairs of peaks could be assigned to the first, second, and third methylene and methyl units by comparison with spectra from 1-decanol-1,1-d2, 1-decanol-2,2-d2, and 1-decanol-3,3-d2 dissolved separately in MBBA. It is especially noteworthy that the first methylene unit of 1-decanol exhibits an extremely small splitting. This fact suggests that the gauche defect exists at the C-C bond nearest the OH group at a high probability. The conformational analysis of alcohols dissolved in the nematic solvent is currently in progress in our laboratory. 6. Concluding Remarks Deuterium NMR quadrupolar splittings observed from deuterated amphiphilic molecules incorporated in the hexagonal, lamellar, reversed hexagonal phases exhibited by the ternary system of sodium octanoate/1-decanol/water (47) Laughlin, R. G. The Aqueous Phase Behavior of Surfactants; Academic: London, 1994. (48) Ekwall, P.; Mandell, L.; Fontell, K. J. Colloid Interface Sci. 1969, 31, 508. (49) Ekwall, P.; Mandell, L.; Fontell, K. Mol. Cryst. Liq. Cryst. 1969, 8, 157.

Suzuki et al.

Figure 11. 2H NMR spectra observed from (a) n-decane-d22 (2.0 mol %) dissolved in 4′-methoxybenzylidene-4-n-butylaniline (MBBA) at 27 °C and (b) 1-decanol-d21 (2.0 mol %) in MBBA at 25 °C. The measurements were carried out under a nonspinning mode. As numbered, the peaks were assigned to the individual atomic groups. For 1-decanol, see Figure 2.

have been analyzed by using the single ordering matrix, the molecular-axis system related by the Eulerian angles to the headgroup structure, and the RIS scheme combined with the MaxEnt method. Our analysis has indicated that the octanoate chain is, in general, extended in the three phases. On the other hand, 1-decanol has been shown to take different conformations in the individual phases. In particular, it is noteworthy that the C-C bond adjacent to the OH group was indicated to be fixed in the gauche state in the D phase. By the ab initio MO calculations, this tendency has been suggested to be intrinsic to saturated alcohols. As shown above, the RIS-MaxEnt simulation has given a detailed interpretation on the phase behaviors of the lyotropic system in terms of orientations and conformations of the amphiphiles. Acknowledgment. We wish to thank Professor Abe of Tokyo Institute of Polytechnics for valuable advice at the early stage of this study, Professor Akutsu and Mrs. Inoki of Chiba University for hearty encouragement, Dr. Kasashima of Keio University for help in the autoclave operation, Dr. Seki of Chiba University for helpful advice on the NMR measurements, Dr. Okudaira of Chiba University for providing the ultrapure water, and JEOL Datum Co. Ltd. for providing information on ALICE2 for Windows95. This work was supported in part by Grantin-Aid for Scientific Research (C) (No. 11650920) of the Japan Society for the Promotion of Science. LA991115N