Didodecyldimethylammonium Bromide Vesicles and Lamellar Liquid

09124 Cagliari, Italy. Received November 21, 1995. In Final Form: March 28, 1996X. Didodecyldimethylammonium bromide (DDAB) in water has been reported...
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Langmuir 1996, 12, 3548-3556

Didodecyldimethylammonium Bromide Vesicles and Lamellar Liquid Crystals. A Multinuclear NMR and Optical Microscopy Study Francesca Caboi and Maura Monduzzi* Dipartimento di Scienze Chimiche, Universita` di Cagliari, Via Ospedale 72, 09124 Cagliari, Italy Received November 21, 1995. In Final Form: March 28, 1996X

Didodecyldimethylammonium bromide (DDAB) in water has been reported to form two coexisting lamellar phases. Here, the phase diagrams of DDAB in H2O and in D2O are reinvestigated focusing on the isotopic effect, on the coexistence of two different types of surfactant bilayers at room temperature, and on the structural transition from vesicles to lamellar liquid crystals, observed at low surfactant concentration with increasing temperature. Only at high temperature DDAB forms a monophasic lamellar liquid crystalline structure in the whole range of composition, with critical points located around 84 °C in D2O and 74 °C in H2O. The higher energy (zero-point stretching) associated with the O-D‚‚‚O bond not only increases the transition temperature but also causes the formation of a regular lamellar phase, at room temperature, at a slightly higher surfactant/water molar ratio than in H2O. 2H NMR data for the DDABD2O system evidentiate the temperature dependent structural transition from a LR1 phase, where lamellar liquid crystals coexist with multilayer vesicles, to a more ordered and apparently homogeneous LR2 lamellar phase. At 85 °C the water molecules, close to the interface, appear to be significantly affected by the surfactant interface, thus displaying a much higher order parameter than at 25 °C. The analysis of 81Br and 14N NMR data reveals details related to this structural transition which should occur through two main steps. In the range of temperature 30-50 °C bromine dissociation plays a crucial role in unsettling the vesicle arrangement whereas in the range 60-85 °C the charged bilayers evolve toward a regular lamellar packing. The significant increase of the 14N quadrupolar splittings with increasing surfactant concentration is interpreted in terms of an increased order of the nitrogen nuclei, which reflects the tendency of the surfactant molecules to assume a more symmetric conformation with respect to the aggregate surface, thus allowing for a higher chain compressibility. The existence of two different stable microstructures, at room temperature, implies that two minima of the self-association energy occur for two different compositions, which, in turn, satisfy two packing requirements, namely, 0.5 < v/al < 1 (for vesicles) and v/al ≈ 1 (for lamellae).

Introduction Didodecyldimethylammonium bromide (DDAB) is a double chain surfactant belonging to an important class of molecules which have a great scientific interest and also industiral applications in the field of bactericides, immunosuppressing drugs, and wetting and antistatic agents.1,2 Many investigations were carried out on DDAB multicomponent systems since the DDAB molecule has peculiar geometric features and it was chosen as a model molecule to investigate phase behavior.3-13 Particularly the large regions of water-in-oil microemulsions formed by DDAB, water, and a suitable oil have caused wide interest. The microstructure of these microemulsions has * Author to whom correspondence should be addressed: Fax, (39)-70-669272; e-mail, [email protected]. X Abstract published in Advance ACS Abstracts, May 15, 1996. (1) Jungerman, E. Cationic Surfactants; Marcel Dekker: New York, 1970. (2) Kunieda, H.; Shinoda, K. J. Phys. Chem. 1978, 82, 1710. (3) Chen, S. J.; Evans, D. F.; Ninham, B. W.; Mitchell, D. J.; Blum, F. D.; Pickup, S. J. Phys. Chem. 1986, 90, 842. (4) Evans, D. F.; Ninham, B. W. J. Phys. Chem. 1986, 90, 226. (5) Fontell, K.; Ceglie, A.; Lindman, B.; Ninham, B. W. Acta Chem. Scand. 1986, A40, 247. (6) Warr, G. G.; Sen, R.; Evans, D. F.; Trend, J. E. J. Phys. Chem. 1988, 92, 774. (7) Hyde, S. T. J. Phys. Chem. 1989, 93, 1458. (8) Dubois, M.; Zemb, T. Langmuir 1991, 7, 1352. (9) Dubois, M.; Gulik-Krzywicki, T.; Cabane, B. Langmuir 1993, 9, 673. (10) Kang, C.; Khan, A. J. Colloid Interface Sci. 1993, 156, 218. (11) Khan, A.; Kang, C. Prog. Colloid Polym. Sci. 1993, 93, 146. (12) Zemb, T.; Belloni, L.; Dubois, M.; Marcelja, S. Prog. Colloid Polym. Sci. 1992, 89, 33. (13) Zemb, T.; Gazeau, D.; Dubois, M.; Gulik-Krzywicki, T. Europhys. Lett. 1993, 21, 759.

S0743-7463(95)01057-2 CCC: $12.00

been clearly outlined and models have been produced to rationalize the structural variations observed when adding water to surfactant-oil mixtures.7 DDAB is rather insoluble either in water or oil (any type of oil, from decane to benzene); thus it resides at the polar-apolar interface. Microstructure, in terms of mean curvature of the interface, has been related to the effective packing features of the surfactant and to the modifications induced by the oil penetration among the surfactant chains. As other double chain surfactants, and because of a packing parameter, ‘v/al’ (as defined by Ninham et al.14,15), close to unity, DDAB has the tendency to display a mean curvature close to zero in the presence of water molecules. In terms of microstructure, this means that a lamellar packing is favored. A number of papers reported the phase diagram of the binary system DDAB/water, where the occurrence of multilayer vesicles was ascertained at very low surfactant concentration and two different lamellar phases,5,8,12,13 hereafter named LR1 and LR2, were clearly identified at low and at high surfactant concentration, respectively. Particularly, the two lamellar phases have been characterized in D2O by significantly different deuteron NMR quadrupolar splittings.5,10,16 However, different phase boundaries have been reported by the various authors. In a recent paper Zemb et al.13 investigated the two lamellar phases of the binary system DDAB/water by (14) Mitchell, J. D.; Ninham, B. W. J. Chem. Soc., Faraday Trans. 2 1981, 77, 601. (15) Israelachvili, J. Intermolecular and Surface Forces, 2nd ed.; Academic Press: San Diego, CA, 1991; and references therein. (16) Fontell, K.; Jansson, M. Prog. Colloid Polym. Sci. 1988, 76, 169.

© 1996 American Chemical Society

DDAB Lamellar Phases

means of a detailed SAXS and SANS study. The swollen LR1 and the collapsed LR2 lamellar regions are characterized by a bilayer thickness of always 24 Å but by different periodicity, being the spacing ∼110 Å for the LR1 and ∼32 Å for the LR2 phase. These two lamellar phases are separated by a gap of immiscibility where the two phases coexist and whose width decreases with increasing temperature up to reaching a critical point, located at 62.2 wt % of DDAB and at the critical temperature Tc ≈ 74 °C. Above this temperature only one large monophasic lamellar region is found to be stable up to above 100 °C. The phase boundaries and the critical temperature are modified by replacing D2O for H2O, as pointed out qualitatively by several authors.8,9 Thus here the phase diagram of DDAB either in H2O or D2O was reinvestigated by means of NMR techniques and optical microscopy, to clarify the phase behavior and to highlight the dynamic processes involved, at a molecular level, in the structural transition from the swollen LR1 to the collapsed LR2 lamellar phase. Experimental Section Materials. Didodecyldimethylammonium bromide (DDAB) was from Sigma and used as received. Few samples prepared with recrystallized DDAB (from ethyl acetate) did not show appreciable differences of phase behavior. D2O, 99% enriched, was from Carlo Erba-Pharmacia. Sample Preparation. Samples differing by 3-5% were prepared by weighing the components into 7 mm o.d. glass ampules that were centifuged, frozen for 12 h, flame-sealed, and homogenized by repeated centrifuging back and forth. To obtain the homogeneous monophasic LR2 region, which is stable in the whole range of composition only at high temperature, the samples were allowed to slowly flow back and forth at 85 °C for several days. Methods. The approximate two-component phase diagrams were mapped out by visual inspection of the samples located in a transparent thermostat, by decreasing the temperature 5 °C every 12 h, from 85 to 25 °C. The LR1 and LR2 phases, when coexisting, can be easily identified, because of their different densities. The homogeneous liquid crystalline phases were then observed by optical microscopy (Zeiss Universal II) in polarized light, at 25 °C, in comparison with the typical textures of other surfactants. The homogeneous samples (at 85 °C) for NMR studies were stored for 12 h at the temperature selected for the experiment, heated for 1 h at a temperature 5 °C higher, and then left for 1 h in the magnetic field to reach again the selected temperature prior to starting the measurements. 2H, 14N, and 81Br NMR measurements were performed by a Varian VXR-300 (7.05 T) spectrometer at the operating frequencies of 46.05, 21.67, and 81.02 MHz, respectively. Deuterium NMR spectra were recorded without lock. A standard variabletemperature control unity, with an accuracy of (0.5 °C, was used in the NMR experiments. The 14N and 81Br NMR spin-lattice relaxation experiments were performed by means of the usual inversion recovery pulse sequence (PD - 180° - τ - 90° - AC). The spin-lattice relaxation rates, R1, were obtained by a three-parameter nonlinear fit of the partially relaxed NMR signal intensities obtained at 10 to 14 different τ values.

I(t) ) A - Be(-τR1) The error in the obtained value of R1 from the fitting procedure is lower than (2%. The spin-spin relaxation rates R2 were deduced from 14N NMR spectra recorded with a 90° pulse angle. R2 values were calculated from the bandwidths taken at half height, ∆ν1/2.

NMR Background The interaction of the electric quadrupole moment (of nuclei with a spin quantum number I ) 1, such as 2H and

Langmuir, Vol. 12, No. 15, 1996 3549 14 N, or I ) 3/2 for 81Br nucleus) with nonzero electric field gradients (due to anisotropic orientation) produces 2I resonance peaks whose separation ∆νq, in a lamellar phase, is given by17

3 ∆νq ) Pbχ Sb 4

(1)

where Pb is the fraction of the observed nucleus in the bound state, χ is the quadrupolar coupling constant (QCC), and

Sb ) 1/2(3 cos2 ϑD - 1)

(2)

is the order parameter relating the time averaged orientation (ϑD) of the nucleus with respect to the surfactant chain axis. Extensive literature citations are available on the investigation of water binding at the polar-apolar interface in surfactant-water systems by NMR of quadrupolar nuclei.18-22 For water molecules, Pb is linearly dependent on the surfactant/water (S/W) molar ratio, thus eq 1 can be written as

∆νq )

S 3 n χ Sb 4 bW

(3)

where nb is the number of bound water molecules per polar head. The straight line of eq 3 would pass through the origin at low surfactant concentration while, with increasing surfactant concentration, the line should reach a maximum ∆νq splitting at the concentration occurring at18,19

nb )

(WS + 1)

(4)

Only the nuclei at a close distance from the oriented interface experience the anisotropic motion and the observed quadrupolar splittings are reduced by the exchange with the unbound species. If the interface region is considered as a general binding site while neglecting the real sites where the water molecules can be localized, we can also assume that a rapid exchange, on the NMR time scale, between bound and free species occurs, thus, as a first approximation, eqs 1 and 3 hold. In the case of 81Br, we made only a qualitative use of the NMR results; thus no details concerning the I ) 3/2 nuclei exponential behavior will be here included. Here, for 14N nucleus (spin I ) 1), the quadrupolar splitting is given by eq 1, with Pb ) 1, while the quadrupolar mechanism determines both the longitudinal (R1) and the transverse (R2) NMR relaxation rates, which are given by23 (17) Wennerstrom, H.; Lindblom, G.; Lindman, B. Chem. Scr. 1974, 6, 97. (18) Rendall, K.; Tiddy, G. J. T. J. Chem. Soc., Faraday Trans. 1 1984, 80, 3339. (19) Carvell, M.; Hall, D. G.; Lyle, I. G.; Tiddy, G. J. T. Faraday Discuss. Chem. Soc. 1986, 81, 223. (20) Blackmore, E. S.; Tiddy, G. J. T. Liq. Cryst. 1990, 8, 131. (21) Bleasdale, T. A.; Tiddy, G. J. T. In Organized Solutions Friberg, S. E., Lindman, B., Ed.; Marcel Dekker: New York, 1992; Vol. 44; p 125 and references therein. (22) Boden, N.; Jolley, K. W.; Smith, M. H. J. Phys. Chem. 1993, 97, 7678. (23) Abragam, A. The principles of Nuclear Magnetism; Clarendon: Oxford, 1961.

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[ ] [ ]

3π2χ2 [2J(ωN) + 8J(2ωN)] 40

(5)

3π2χ2 [3J(0) + 5J(ωN) + 2J(2ωN)] 40

(6)

R1 ) R2 )

Caboi and Monduzzi

where the various J(ωN) are the reduced spectral density functions and ωN is the 14N Larmor frequency. The relaxation data of surfactant systems have been successfully described in terms of the so-called two-step model.24 Within this model, the fast motion, in the extreme narrowing regime, is related to the internal motions of the surfactant molecules, while the slow motion is related to the whole aggregate tumbling. The spectral densities in eqs 5 and 6 are given25 by

(

J(ωN) ) 1 +

)

η2 - S2b Jf(0) + S2b Js(ωN) 3

(7)

where Jf(0) is the frequency independent spectral density function of the fast motion and Js(ωN) is the spectral density function associated with the slow motion, η is the asymmetry parameter of the electric field gradient tensor (EFG), while Sb is the order parameter, as defined above. The difference between eq 6 and eq 5, and by introducing eq 7, gives the following relation:

R2 - R1 )

[ ]

9π2 (Sbχ)2(Js(0) + Js(ωN) - 2Js(2ωN)) (8) 40

The various Ji(ω) are expressed as

Ji(ω) )

2τi 1 + (ωτi)2

(9)

where τi is the appropriate correlation time of the fast (f) and slow (s) motion. Results and Discussion Phase Diagram. Figure 1 shows the phase diagrams of DDAB/H2O and DDAB/D2O, in terms of surfactant/ water (S/W) molar ratio vs temperature (T °C). The accuracy of the phase boundaries is within (2 wt % in the composition and (2 °C in the temperature. The phase boundaries of the DDAB/H2O system correspond to those reported by Zemb.13 In the H2O system a critical point was found at 62.2 wt % DDAB (S/W ) 0.064), whereas in the D2O system the occurrence of two different 2H quadrupolar splittings in the samples containing 64.8 and 68.4 wt % of DDAB (S/W ) 0.079 and 0.093, respectively) at T slightly lower than 85 °C suggests the existence of a critical point located between 65 and 68 wt % of DDAB and a critical temperature Tc ≈ 84 °C. At 85 °C all the samples are homogeneous and display an ordered LR2-type lamellar microstructure (see below 2H NMR). The samples in the range 90-95 wt % of DDAB, either in H2O or D2O, are homogeneous transparent, and birefringent only at 85 °C. Upon decreasing the temperature, they become less transparent, slightly milky, although homogeneous, and birefringent. A clear white solid phase appears only below 25 °C, thus it is difficult to establish whether a real phase separation occurs in these samples. In fact, the marked decrease of the 2H quadrupolar splittings in these samples, at first, might (24) Wennersto¨m, H.; Lindman, B.; So¨derman, O.; Drakenberg, T.; Rosenholm, J. B. J. Am. Chem. Soc. 1984, 101, 6860. (25) Halle, B.; Wennerstrom, H. J. Chem. Phys. 1981, 75, 1928.

Figure 1. Phase diagram of DDAB/H2O (2) and DDAB/D2O (0) in terms of surfactant/water molar ratio (S/W) vs T (°C).

suggest the occurrence of a solid phase. Upon considering that this behavior is found at all the temperatures (see Figure 3), that is simply due to a W/S molar ratio lower than 4, which determines the collapse of the DDAB bilayers toward an almost crystal lattice.19 As to the H2O and D2O systems, the largest differences in the boundaries of the immiscibility gap between the two lamellar phases are observed at high S/W ratio. What is more, however, is the relevant effect of the temperature. This behavior can be mainly related to the different energies of zero-point stretching, associated to the hydrogen bonds OH‚‚‚O and OD‚‚‚O, which amounts to ∆(hν°/2) ∼ 1.3 kcal/mol, and which determines the higher density, viscosity, and heat of vaporization of D2O.26 In practice the OD‚‚‚O bond is stronger than the OH‚‚‚O bond; thus hydrophobic interactions are reinforced in D2O and generally lower critical micelle concentrations are observed.27 In addition, apart from F-, the heat of solution is smaller in D2O than in H2O. In particular, it has been shown that a charged N+ center, whose accessibility to solvent molecules is settled by the symmetry of the bonded alkyl groups, exhibits a relatively large decrease of accessibility to D2O solvent, with respect to H2O.28 From a macroscopic point of view, it can be stressed that the increase of the critical temperature from Tc ≈ 74 °C in H2O to Tc ≈ 84 °C in D2O mainly reflects a viscosity effect (η[D2O]/η[H2O] ≈ 1.2). Optical Microscopy. Figure 2 reports some examples of optical micrographs at 25 °C, where the very different textures of the two lamellar phases can be easily assigned.29 In the swollen LR1 region, large multilayer vesicles (Figure 2a) occur up to 30 wt % of DDAB. Samples in the two-phase regions (Figure 2b,c) display either the maltese crosses (typical of vesicles) or the mosaic texture (typical of pure lamellar liquid crystals). In the region of existence of the pure LR2, the mosaic texture dominates but the presence of some maltese crosses can be still revealed, although their sizes decrease with increasing surfactant concentration (Figure 2d). Generally spontaneous vesicles are reported to form only in very diluted surfactant systems; here the very low relative viscosity of the LR1 phase allows the coexistence of vesicles and lamellar liquid crystals. (26) Conway, B. E. Ionic Hydration in Chemistry and Biophysics; Elsevier Science Publishers Co.: Amsterdam, 1981. (27) Pashley, R. M.; McGuiggan, P.; Ninham, B. W.; Evans, D. F. Science 1985, 229, 1088. (28) Philip, P. R.; Desnoyers, J. E. J. Solut. Chem. 1972, 1, 353. (29) Rosevear, F. B. J. Am. Chem. Soc. 1954, 31, 628.

DDAB Lamellar Phases

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Figure 2. Optical micrographs at 25 °C for the DDAB/H2O system (scale: 2 cm ≡ 100 µm): (a) vesicles in the LR1 region (DDAB wt % 20); (b) vesicles in the LR1 region (DDAB wt % 30), the definition of the micrograph in the diluted region was very poor because of the high fluidity of the samples; (c) “onion-like” texture typical of multilayer vesicles (DDAB wt % 40); (d) small maltese crosses in the two-phase region (DDAB wt % 70); (e) mosaic texture in the lamellar phase LR2 (DDAB wt % 80); (f) mosaic texture in the lamellar phase LR2 (DDAB wt % 90). 2 H NMR. The samples in D2O were examined for the quadrupolar splittings of water to clarify a few details of the phase diagram as mentioned above, but especially to

highlight the hydration and the degree of order of the two lamellar microstructures. Figure 3a shows the 2H ∆νq observed at 25 °C. It is

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Figure 3. 2H ∆νq vs S/W for the D2O system at (a) 25 °C, where the splittings are overlapped the two lamellar phases coexist, and (b) 85 °C.

clear that two different anisotropic phases occur in the system, and their 2H quadrupolar splittings overlap in a large gap where both coexist, as earlier qualitatively described.5 The range of composition, over which both the quadrupolar splittings can be observed, is obviously smaller than that reported in Figure 1 since a significant amount of each phase must occur to be revealed in the NMR spectrum. The two phases display very different quadrupolar splittings which, following the theory (eq 3), can be interpreted in terms of a very different fraction of water molecules (nbS/W) affected by the presence of the bilayer and in terms of a different degree of order (Sb), if a constant value of the QCC χ may be assumed. In fact it has been demonstrated, by experimental methods and by ab initio calculations,30-33 that the QCC is almost insensitive to temperature and to ion concentration. The χ value in pure D2O varies from 256 kHz at 300 K to 262 kHz at 359 K. When D2O is in the first hydration shell of ions, χ decreases about 15%, but it keeps almost constant with varying salt concentration.33 Thus in the range of temperature here examined, we can reasonably assume χ ) 217 kHz and 222 kHz at 25 and 85 °C, respectively. Let us examine the 2H data at 25 °C in terms of eqs 1-4. The maximum for the LR1 phase cannot be identified, while for the LR2 phase it is located around S/W ) 0.25. Then, assuming that nb ) 5 is always valid, we calculate, with χ ) 217 kHz, Sb ) 0.002 for the LR1 phase and Sb ) 0.011 for the LR2 phase. If Sb ) 0.011 is a typical order parameter for a well-structured lamellar phase,21 as well as (30) Eggenberger, R.; Gerber, S.; Huber, H.; Searles, D.; Welker, M. J. Chem. Phys. 1992, 97, 5898. (31) Eggenberger, R.; Gerber, S.; Huber, H.; Searles, D.; Welker, M. J. Comp. Chem. 1993, 14, 1553. (32) Furo`, I.; Halle, B. Phys. Rev. E 1995, 51, 466. (33) Struis, R. P. W. J.; deBleijser, J.; Leyte, J. C. J. Phys. Chem. 1987, 91, 1639.

Caboi and Monduzzi

nb ) 5 is a reasonable number of water hydration molecules, in the case of the LR1 phase, the order parameter is too small for the existence of a lamellar bilayer. The latter observations may be better accounted for by the occurrence of large multilayer vesicles together with lamellar liquid crystals in all the range of existence of the LR1 monophasic region, as indicated by optical microscopy. With increasing temperature, the range of the two-phase region decreases, and at 85 °C a single 2H ∆νq is detected in all samples. The data, shown in Figure 3b, lay on a straight line, nicely crossing through zero, with the maximum occurring around S/W ) 0.2. From eqs 1-4 we obtain nb ) 6 and Sb ) 0.024 by introducing χ ) 222 kHz. These data confirm the existence of only one LR2-type lamellar phase in the range 5-95 wt % DDAB in D2O, in agreement with the observation of Zemb for the DDABH2O system that, above 74 °C, gives a monophasic lamellar phase. In practice, in the DDAB-water system, with increasing temperature, we observe a transition from a “disordered” LR1 to a “more structured” LR2 phase with a significant increase of the water order parameter. Obviously, the increase of T causes the decrease of the water viscosity, of the hydrogen bond strength, and of the hydration forces, while favoring the chain mobility. However, the dissociation of Br- counterions, induced by the increase of the temperature, is likely to play the crucial role in the structural transition observed at low surfactant concentration. Actually DDAB molecules in water, at low T, are 90% undissociated and almost unsoluble.4,5 This fact reduces the electrostatic repulsion among the polar heads and, because of a surfactant packing parameter v/al ≈ 0.82,4 multilayer vesicles can easily form in a metastable equilibrium with a lamellar mesophase. The transition observed with increasing temperature must imply that a v/al closer to 1 is brought about either by a decrease of the optimal area (dissociation is expected to increase the polar head area, but here, the significant decrease of the hydration strength would produce the opposite effect) or by an increase of the chain volume (increase of configurational entropy). Phenomenologically speaking, the transition induced by the temperature can be regarded in terms of a different balance between repulsion and attractive force. On the basis of an interbilayer potential proposed by Wennerstrom,34 Tiddy et al. suggested that a short-range attractive force, due to a specific counterion/head group association, is responsible of the coexistence of two lamellar phases in the binary system sodium dodecyl-5-p-benzensulfonate/water.35 Here, at low temperature, the high degree of counterion binding brings about an analogous effect, while the increase of the temperature is likely to play the same role as the addition of salt to nonionic surfactants sytems:36,37 the spontaneous curvature of the interface decreases, while the water structure becomes less effective thus a more ordered bilayer is allowed to form. We might try to play with several current theories which rely either on the earlier van der Waals picture of liquids (which focuses on the differing roles of the short-ranged repulsive intermolecular forces and the long-ranged attractions38) or on the various type of repulsive steric (34) Wennerstrom, H. Langmuir 1990, 6, 834. (35) Ockelford, J.; Timini, B. A.; Narayan, K. S.; Tiddy, G. J. T. J. Phys. Chem. 1993, 97, 6767. (36) Piculell, L.; Nilsson, S. Prog. Colloid Polym. Sci. 1990, 82, 198. (37) Kabalnov, A.; Olsson, U.; Wennerstrom, H. J. Phys. Chem. 1995, 99, 6220. (38) Chandler, D.; Weeks, J. D.; Andersen, H. C. Science 1983, 220, 787.

DDAB Lamellar Phases Table 1.

solv.

DDAB, wt %

H2O D2O a

81Br

No

26 80 26 80 81Br

Langmuir, Vol. 12, No. 15, 1996 3553

Relaxation Rates R1 and Band Widths at 50 and 85 °C 50 °C R1 (s-1) ∆ν1/2 (Hz)

25063 ( 685 30581 ( 7285 27701 ( 3062 a

6800 15000 7879 a

85 °C R1 (s-1) ∆ν1/2 (Hz) 8621 ( 464 78868 ( 3072 10121 ( 337 22173 ( 1883

3000 6667 3400 8000

NMR signal is detected in this sample.

forces (undulation, peristaltic, protrusion, and head group overlap forces15,39), but the problem of clarifying the interplay of hydrophobic-hydrophilic interactions in relation with the dissociation of the counterions and with the water structure and the hydration is actually far from being resolved. We tried instead to add some pieces of information, at a molecular level, to this complicated puzzle. 81 Br NMR. Two samples containing 26 and 80 wt % of DDAB in H2O (S/W ) 0.014 and 0.016) and D2O (S/W ) 0.015 and 0.017) were investigated for 81Br NMR. 81Br is a quadrupolar nucleus with I ) 3/2; thus in a lamellar phase it is expected to give a central peak and two satellites separated by the ∆νq given by eq 1. Here, because of the very large broadening of the NMR signals (the very short T2 is due to the high counterion binding), only the central line was detected even at 85 °C where NMR bands shrink significantly. The 81Br NMR signals, however, could be easily detected only at T g 50 °C, with the exception of the sample S/W ) 0.017 in D2O for which a higher temperature is needed (cf. phase diagram). This means that at 50 °C the counterion dissociation becomes appreciable. Table 1 reports R1 and ∆ν1/2 (the bandwidth at half height is related to the spin-spin relaxation rate by the approximate relation: R2 ≈ π∆1/2, which is valid if a Lorentian shape is observed) at 50 and 85 °C. These values, especially those at 50 °C and in D2O, all suffer large errors since they are so short and fall in the limit of the instrumental “dead time” (100-200 µs), thus only qualitative guesses can be deduced. The main information is that at 50 °C a significant amount of Br- ions should be dissociated and in a hydrated form, but only at 85 °C do the differences in the hydration forces between H2O and D2O systems play a minor role. In fact the viscosity effect, which is mainly responsible for the large differences in the ∆ν1/2 (but not in the R1 values) at 50 °C, almost vanishes at 85 °C, while the broadening due to the deuterons quadrupolar coupling is obviously present for the D2O samples. 14 N NMR. (i) Phase Diagram. 14N NMR spectra were easily detected at T g 30 °C for the LR1 and T g 40 °C for the LR2 phases. Figure 4a reports the 14N ∆νq at 50 °C as a function of S/W. In the range 0.05 < S/W < 0.25 the 14N ∆νq splittings increase with increasing the S/W molar ratio, without substantial differences between the H2O and the D2O samples. It is noteworthy that the trend of the 14N R1 relaxation rates closely reflects the 14N ∆νq splittings, as shown in Figure 4b. At S/W > 0.25 the 14N ∆νq splittings and the R1 values become constant, whereas at S/W < 0.05 we observe fluctuations, which might be casual and perhaps within the experimental error, but, as shown in Figure 4c, they are present either in the H2O or in the D2O samples. If the increase of the 14N ∆νq splittings below 85 °C (or 74 °C for the samples in H2O) might be due to the occurrence of two different phases, the same justification cannot hold at 85 °C. Figure 5a reports 14N ∆νq splittings at 85 °C. In principle there should not be any reason for (39) Helfrich, W. Z. Naturforsch. 1978, 33a, 305.

Figure 4. 14N NMR data: (a) 14N ∆νq vs S/W at 50 °C (H2O (2) and D2O (0); (b) relaxation rates (R1) vs S/W at 50 °C; (c) expansion of (b).

observing variations of the 14N ∆νq splittings if only one type of lamellar microstructure, or in other words of interfacial curvature, is present. On the other hand, no variations of the 14N QCC are likely to occur. The possible justification is solely an increase of the 14N order parameter Sb. The whole range of the 14N ∆νq values, here observed, can be reproduced by introducing in eq 1, Pb ) 1, χ ) 24 kHz, and by considering fluctuations of ϑD between 15° and 40° (eq 2), as shown in Figure 5b. Hence, with increasing surfactant concentration, the order parameter Sb increases while the ϑD angle (which is the angle formed between the nitrogen symmetry axis and the direction of the planar surface) is forced to decrease because of the compression of the flat bilayer. (ii) LR1-LR2 Structural Transition. The fluctuations observed at low surfactant concentration were not seen in the 2H data, since water, although in the vicinity of the

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Langmuir, Vol. 12, No. 15, 1996

Figure 5. (a) 14N ∆νq vs S/W at 85 °C for samples in H2O (2) and D2O (0). (b) Calculated 14N ∆νq vs the ϑD angle obtained from eq 1 by introducing χ ) 24 kHz, Pb ) 1, and eq 2.

interface, is not likely to experience, within the average NMR observation time, any significant modifications, whereas the nitrogen nuclei, which are the active part of the polar head, experience more closely the fluctuations due to the steric and the hydration forces. Actually, these forces should be particularly effective in the diluted regime and are expected to vary significantly if polydisperse multilayer vesicles occur. Support for this idea can be extracted from observing the trend of the 14N ∆νq as a function of the temperature in a few selected samples at low and high S/W. These data, which are shown in Figure 6, seem to confirm that some important processes, i.e. variations of the mean curvature of the surfactant interface, must occur at low S/W to determine a nonmonotonic dependence on the temperature: it should not be a “first order transition”, whichever it is. It is almost commonplace that the ∆νq of a quadrupolar nucleus in a magnetically anisotropic environment decreases with increasing temperature. Occasionally, it has been observed that if the nucleus is part of a surfactant molecule, the ∆νq shows a slight increase with increasing temperature as a consequence of the increase of the term χSb, in eq 1, especially at high surfactant concentration. This can affect the temperature dependence of the splitting, as is the case of our systems at high S/W (cf. Figure 6b). Indeed anomalous behavior can be claimed for the trend of the 14N ∆νq at low S/W (see Figure 6a). With increasing T, they at first increase slightly and then decrease, being the inversion of tendency observed between 40 and 50 °C. Above 50 °C, the trends, although nonlinear, look more usual. This brought us to indicate the temperature of 50 °C as a somehow critical point in the transition from the

Caboi and Monduzzi

Figure 6. 14N ∆νq as a function of temperature for the DDAB/ water samples (H2O (2) and D2O (0) at (a) S/W ) 0.012 and (b) S/W ) 0.15.

LR1 to a dominant LR2 microstructure, either for the H2O or for the D2O system. Once we accept the idea that the most significant variations of the microstructure occur around 50 °C, at low S/W, we will try to extract some quantitative information on the dynamics of the interface. Before discussing the 14N NMR relaxation data, the use of a “two-step” motional model for describing dynamics of surfactant aggregates in lamellar liquid crystals should be clarified. The two-step model by Wennestrom et al.,24 mentioned above, is rigorously valid for a micellar solution, but it has been successfully adopted to describe dynamics features in other systems, such as the bicontinuous cubic structure of the cetylpyridinium salicylate/water system.40 In that case an isotropic long range order of the microstructure occurred; however, a similar two-step motional model was used by Brown et al. to rationalize the frequency dependence of the 2H R1 of deuterated surfactants in the lamellar phase.41 The choice of this model can be here justified by the single exponential decay of R1 relaxation, by the Lorentzian shape of the 14N NMR signals, and by the fact that a single orientation of the sample (90°) is always observed. These experimental observations represent the necessary qualifications for the following theoretical considerations. As to the calculation of R2 from the line width of the 14N NMR doublet, the approximation is valid if the time scale over which the quadrupolar frequency is averaged by molecular motions is much shorter than the inverse of the frequency spreading (related to the orientational disorder). (40) Monduzzi, M.; Olsson, U.; Soderman, O. Langmuir 1993, 9, 2914. (41) Williams, G. D.; Beach, J. M.; Dodd, S. W.; Brown, M. F. J. Am. Chem. Soc. 1985, 107, 6868.

DDAB Lamellar Phases

Langmuir, Vol. 12, No. 15, 1996 3555

Table 2. 14N Quadrupolar Splittings and Relaxation Parameters of DDAB/D2O at S/W ) 0.012 as a Function of Temperature T (°C)

R1 (s-1)

R2a (s-1)

∆νqb (Hz)

R2m - R1 (s-1)

τs (µs)

τfA (ns)

30 40 50 60 70 85

17.54 ( 1.40 12.05 ( 0.84 9.34 ( 0.63 6.91 ( 0.45 5.96 ( 0.42 4.45 ( 0.31

637 714 668 615 592 624

8897 8904 8841 8768 8604 8240

624 630 633 635 636 638

1.00 1.01 1.03 1.05 1.10 1.19

8.31 5.67 4.43 3.31 2.95 2.38

a R ) π∆ν . The experimental ∆ν 2 1/2 1/2 values are affected by an average error, which increases with decreasing temperature, of about (35 Hz. Thus the R2 variations with T cannot be considered significant and the average value R2m ) 642 (s-1) is taken for the “R2 - R1” calculation. b Estimated errors on ∆νq values are (30 Hz.

Hence, the quadrupolar splitting is reduced but the satellites are symmetric and their width is determined by R2.42 As to the terms of the autocorrelation function of eq 7, Halle et al.43 demonstrated that for a quadrupolar nucleus (such as 14N, or 2H) in most mesophases, fluctuations over three time scales must be considered: (1) the fast fluctuations (