Langmuir 1993,9, 2868-2818
2868
Structure of Cubic Phases in the Ternary System Didodecyldimethylammonium Bromide/Water/Hydrocarbon Paul J. Maddaford and Chris Toprakcioglu' Department of Physics, Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge CB3 OHE,U.K. Received April 13,1993. In Final Form: June 14,1993 We have studied the structure of the temary cubic phases formed by the system didodecyldimethylammonium bromide (DDAEWDzOIhydrocarbon oil by small-angle X-ray scattering (SAXS) and smallangle neutron scattering (SANS).Different oils (octane, dodecane, tetradecane, and toluene) of varying molecular size and degree of penetration into the hydrophobic tail region were used, and systematictrends were observed both in the phase behavior and structure of the cubic phase. This structure is well-described by the topology of triply periodic minimal surfaces, and either a parallel surface construction in which the surfactant bilayer decorates a minimal surface or one based on a constant mean curvature family of surfaces can be invoked to describe the data. The diffraction data reveal Bragg reflections which index to well-known cubic structures, and transitions between different cubic symmetriesare observed on changing the composition of the system. It is found that highly penetrating oils such as toluene are fully absorbed into the surfactant region, while nonpenetrating oils such as tetradecane reside largely in the middle of the bilayer, thus causing it to swell appreciably on increasing the oil content of the system. The transitions between different cubic symmetries are primarily driven by interfacial curvature and occur in a systematic manner with composition. The aqueousvolume fraction is mainly responsible for setting the mean curvature of the interface, but the interaction of the oil with the surfactant tails is also important in determining the structure through ita effect on the spontaneous curvature. The system adopts that structure which best optimizes the (generally) divergent values of the actual and preferred curvatures at the expense of alternative structures. The observed cubic structures include triply periodic ones based on the gyroid (G), diamond (D), and the Schwarz-P (P) minimal surfaces. Regions with an unresolved cubic symmetry as well as biphasic regions with two coexisting cubic symmetries are also found in the phase diagrams. The phase behavior and structure of ternary cubic phases can thus be accounted for solely on topological considerations, with the particular composition of each system merely setting the values of parameters such as curvature, lattice constant, etc.
Introduction Surfactant molecules are characterized by their ability to divide aqueous and paraffinic bulk phases into separate, finely dispersed domains. The actual geometry of these surfactant sheets that form the interface between the immiscible bulk components depends on the composition and temperature, and the resulting structures can vary from liquid crystalline to random ones. While the structure of lamellar and hexagonal lyotropic liquid crystals has long been known, it was more recently that the existence of cubic liquid crystalline phases in binary systems of surfactants and water was established.' Cubic phases, in particular, have illustrated the rich variety of microstructures which amphiphilic systems can form. The proposal that the microstructures of these phases were formed by interpenetrating bicontinuous networks of polar and nonpolar media was first established by the work of Luzzati and c o - w o r k e r ~ .These ~ ~ ~ results indicated that more complicated geometric shapes than simple Euclidean forms (e.g. micelles) are needed to describe some of the less trivial microstructures. Scriven4 was the first to postulate that the microstructure of ternary phases could be based on triply periodic minimal surfaces and thus opened the way to more complex, nonclassical geometrical descriptions of these systems."l* The intro(1) Luzzati, V.; Mariani, P.; Gulik-Krzwcki, T. In Physics of Amphiphilic Layers; Springer-Verlag: Lee Houches, France, 1987;p 131. (2) Luzzati, V.; Spegt, P. A. Nature 1967,215, 701. (3) Luzzati, V.; Gulik-Krzywicki, T.; Tardieu, A. Nature 1968, 218, 1031. (4) Scriven, L. E. Nature 1976,263,123. (5) Anderson, D. M. Ph.D. Thesis, Minnesota, 1986. (6) Charvolin, J.; Sadoc, J. F. In Physics of Amphiphilic Layers; Springer-Verlag: Les Houches, France, 1987; p 126.
duction of a third component increases the degrees of freedom of the system; the diversity of structures might therefore be expected to increase. A number of workers have shown that significant transformations in interfacial structure exist in some amphiphilic systems within regions previously assigned as being ~ne-phase."-'~ These discoveries then raise the question of the extent to which the variation in the interfacial symmetry and topology has been overlooked on primary phase determination. When investigating the interfacial geometry of amphiphilic systems small-angle X-ray scattering (SAXS)and small-angle neutron ecattering experiments (SANS)are powerful tools which can be used, in certain cases, to produce an accurate map of the surfactant interface. Although these two techniques provide a direct way of probing such systems, unique assignment of structure is not always straightforward, as the scattering profiles can often be fitted equally well by a variety of theoretical models. When small-angle scattering experiments are applied to the cubic phases, the Bragg reflections produced by the ordered orientation of the surfactant interface provide very accurate identifiers for certain structures. It is then possible to determine (7) Anderson, D. M.; Gruner, S. M.; Leibler, S. Roc. Natl. Acad. Sei.
U S A . 1988,85, 5364. (8) Hyde, S. T. J. Phys. Chem. 1989,93, 1458.
(9) Anderson,D. M.;Davis, H. T.;Scriven, L. E.; Nitsche, J. C. C. Adu. Chem. Phys. 1990, 77,337. (10)Wang, Z.-G.; Safran, S. A. Europhys. Lett. 1990, 11, 425. (11) Larsson, K. Nature 1983,304,664. (12) Hyde,S.T.:Andersson,S.;Ericsson,B.;Lareson,K.Z.Kristallogr. 1984,16& 213. (13) Hyde, 5.T.;Andersson, S.;Larsson, K. 2.Kristallogr. 1986,174, 237. (14) Radlinska, E. Z.; Hyde, S. T.; Ninham, B. W. Langmuir 1989,5, 1427.
0743-7463/93/2409-2868$04.00/0 0 1993 American Chemical Society
Structure of Cubic Phases
reliably the nature of structural transformations induced by compositional changes. The ternary system of the surfactant didodecyldimethylammonium bromide (DDAB) exhibits a cubic liquid crystalline region in its phase diagram at low oil fractions over a wide range of aqueous fractions. This region has been shown to exhibit a symmetry transition on increasing water content.’”17 The two different microstructures discovered have been successfully modeled on wellestablished triply periodic minimal surfacesa and the related constant mean curvature surface^.^?^ Work by Str6m and Andersonla on the cubic phase of the DDAB/ HzO/styrene system has suggested a further three structural transitions within the cubic region of this system in addition to the one detailed by Radiman et al.15J6 and Barois et al.17 The existence of these transitions leads to a possible total of five different structures within the one cubic region of the phase diagram. These results indicate that the cubic region, once thought monostructural, is actually formed from a series of distinct cubic structures. In this paper we report experimental data that confiim the generality of structural transformations within such ternary systems and present evidence for up to four structural transformations within a single cubic region. Systematic trends in the location of the cubic region and the actual geometry of the surfactant interface within that region as a function of composition are reported. The observed trends also indicate that the hydrocarbon moiety plays a significantrole in drivingthe structural transitions within the cubic phase. Small-angle X-ray and neutron scattering experimentson the systemsDDAB/DzO/octane, DDAB/DzO/dodecane, DDAB/DzO/tetradecane, and DDAB/DzO/toluene have been carried out to probe the structure of the cubic phases. The octane system has previously been studied by Radiman15J6 and we have extended the structural investigation of the system to higher DzO fractions. The other straight chain alkane systems were studied to investigate the effect of varying the length of the hydrocarbon chain on the cubic phase and its structure. In addition, the toluene system illustrates the effect of aromatic (or more generally, unsaturated) hydrocarbons on the interfacial structure.
Experimental Section The surfactant didodecyldimethylammonium bromide was obtained from Fluka (purity 98%). The hydrocarbons (octane, dodecane, tetradecane, and toluene) and deuterium oxide were obtained from Aldrich, 99+ % and 99.9% purity, respectively, and a l l chemicals were used as received. The samples were prepared by mixing known amounts of each component in flame-sealed glass ampules. Homogeneity of the samples was assured by heating the ampules to between 60 and 120 OC, depending on composition, with occasional agitation to ensure complete mixing of the componenta. The samples were then allowed to cool to room temperature and left to equilibrate for at least 2 weeks a t 25 OC. Cubic samples are clear, optically isotropic mixtures with a gel-like texture and exhibit the quality of ringing when struck as describedby Radh~an.’~J~ The samples were checkedfor opticalisotropy via examinationbetween crossed polars. Samples which exhibited the aforementioned criteria were tentatively assigned as being cubic. All compositionswere prepared at least twice to ensure reproducibility and samples of each composition were stored at 25 OC for a minimum of 2 months to check they had reached equilibrium. (15) Radiman, S.; Toprakcioglu,C.;Faruqi, A. R. J.Phys. (Paris)1990, 51, 1501. (16) Radiman, S.; Toprakcioglu, C.; Dai, L.;Faruqi, A. R.; Hjelm, R. P., Jr.; de Vallera, A. J. Phys. (Paris) 1990,51 (C7), 376. (17) Barois, P.; Hyde, S. T.; Ninham, B.; Dowling, T. Langmuir 1990, 6,1136-1140. (18) SWm, P.; Anderson, D. M. Langmuir 1992,8,691.
Langmuir, Vol. 9, No. 11, 1993 2869 For small-angle X-ray scattering (SAXS) the ampules were subjected to cyclicalheating and rapid coolingbefore being broken open, to reduce the formation of crystallites. The cubic phase was then placed between freshlycleaved mica sheeta and a Teflon spacer O-ring was used to maintain the sample thickness at 0.7 mm. For small-angle neutron scattering experiments (SANS) the samples were subjected to the same heating and rapid cooling cycles before being mounted between two 1-mm quartz windows and the sample thickness was again maintained at 0.7 mm by Teflon O-rings. In both types of experiments the samples were rotated at -1 rpm during the measurementa to enhance the isotropicnature of the scattering patterns by reducing the effect of any residual crystallites. Small-angleX-ray scattering experiments were carried out on two different instruments: (i) Station 8.2 on the Synchroton Radiation Source (SRS)at Daresbury Laboratory was used where the high-intensity beam of radiation (A = 0.154 nm) was point collimated and focused on a multiwire quadrant detector. The sample-detector distance varied between 2.5 and 3.0 m and the Q-rangewas calibrated using wet rat tail collagen as a reference. (ii)At the M.R.C., Addenbrookes,Cambridge,a point-collimated beam from a Cu Ka line of X = 0.154 nm from a rotating anode source was used. A two-dimensionalposition sensitivedetectorlo was used to measure the scattered intensity, with the s a m p l e detector distance set at 0.75 m. Small-angleneutron scattering experimenta were performed on two different instruments: (i) D16 at the ILL, Grenoble,with a monochromaticwavelength of 4.536 A was used. The sampledetector distance was 1m and the movable detector was mounted on an arc track to enable a large range of Q-space to be covered. The beam dimensions were restricted to 2 mm X 2 mm, by way of cadmium slits, to enable the required resolutionto be obtained. (ii) The low-Q diffractometer on the LANSCE facility at the Los Alamos National Laboratory using a pulsed source and time of flight The incident wavelength range was 0.6-13 A correspondingto an accessible momentum transfer (Q) range of O.OO3-O.5 A-1 with a sample to detector distance of 4.0 m, the detector being a two-dimensional 3He proportional counter.
Results and Discussion Phase Behavior of Various DDAB/DzO/Hydrocarbon Systems. Previous studies of the phase behavior of ternary mixtures containing water, the surfactant didodecyldimethylammonium bromide (DDAB), and various paraffinic components have concentrated on the overall pattern of phases and how their position in the phase diagram shifts on variation of the molecular structure of the hydrocarbon c o m p ~ n e n t s . ~ ”In~ ~this work more precise phase boundary determination was carried out for the cubic phases, particularly in the region located at low oil content, in four systems each with a different hydrocarbon component. The systems studied were those incorporatingoctane, dodecane, tetradecane, and toluene. This sequence of hydrocarbons was chosen in order to explore the effect of the interaction of the solvent with the paraffmic tail section of the surfactant molecules and its relation to the topology of the cubic phases. The partial phase diagrams for the four ternary systems showing the position and extent of the cubic region in each case are shown in Figure 1. The sequence of straight chain alkanes increasing in size would be expected to show a systematic trend as the more sterically hindered larger (19) Faruqi, A. R. Nucl. Znstrum. Methods Phys. Res. 1988, A273,754. (20) Hjelm, R. P., Jr. J. Appl. Crystallogr. 1988,21,618. (21) Seeger, P. A.; Hjelm, R. P., Jr.; Nutter, M. J. Mol. Cryst. Lig. Cryst. 1990,18OA, 101. (22) Chen, S. J.; Evans, D. F.;Ninham, B. W. J.Phys. Chem. 1984,88, 1631. (23) Blum, F. D.; Pickup, S.; Ninham, B.; Chen, S. J.; Evans, D. F. J. Phys. Chem. 1985,89,711. (24)F0ntell.K.: Cedie,A.:Lindman, B.: Ninham, B. Acta Chem.Scand. 1986, A40, 241. (25) Chen, S. J.; Evans, D. F.; Ninham, B. W.; Mitchell, D. J.; Blum, F. D.; Pickup, S. J. Phys. Chem. 1986,90,842.
Maddaford and Toprakcioglu
2870 Langmuir, Vol. 9, No. 11, 1993 DDAB
0
10
20
30
Hydrocarbon +
Figure 1. Partial phase diagram at 26 O C showing the position of the cubic region in four ternary systems consisting of DDAB/ DnO/toluene, DDAB/DzO/octane, DDAB/DzO/dodecane, and DDAB/D*O/tetradecane.
molecules penetrate the hydrophobic tail region of the surfactant molecules to a lesser degree thereby reducing the spontaneous curvature of the surfactant layers. It is indeed seen from the position of the cubic phase in compositional space in the tetradecane, dodecane, and octane systems that the cubic phase is stable at progressively lower aqueous volume fractions as the molecular size of the hydrocarbon component is reduced. With decreasing volume fraction of the aqueous component, the curvature of the surfactant layers must become greater toward the aqueousside of the interface,Le. more negative. The area of interface per surfactant molecule will remain essentially constant over changes in composition of this order; therefore the interaction of the hydrocarbon bulk component must be responsible for any changes in the attainable curvatures of the surfactant layer. The minimum aqueousvolume fraction present in the cubic phases increases from 0.32 in the octane system to 0.53 in the tetradecane system with an intermediary value of 0.42 for the dodecane system. This initially indicates the extent to which the nature of the paraffinic bulk component determines the configuration of the system. In all three of these systems the cubic phases become extinct at approximately the same aqueous volume fraction -0.8 with only trace amounts of hydrocarbon component (ca. 2.5%). The curvature of the surfactant layer at this composition relates to a limiting situation of minimum negative curvature, obtained within the cubic phase, when essentially only the surfactant molecules determine the curvature of the surfactant sheets. Whereas a systematic shift in the position of the cubic region on increasing the alkane chain length is to be expected, the introduction of an aromatic hydrocarbon
component may be anticipated to induce a somewhatmore pronounced shift in the location of the cubic phase. The partial phase diagram for the system DDAB/DzO/tuluene illustratingthe extent of the cubic phase is shown in Figure 1. As can be seen there is a dramatic shift in the minimum aqueous volume fraction which is tolerated by the phase (-0.13), but the phase still expires at the same maximum aqueous volume fraction as in the previous cases. There is also a marked increase in the maximum hydrocarbon fractionaccommodated (ca. 20 % ) compared with that seen in the systemscontaining aliphatic hydrophobea (ca.12?6). This observation is in line with results obtained for similar surfactants where the greater ability of the aromatic component to penetrate the surfactant paraffinictails leads to a marked shift in the phase behavior of the s y ~ t e m s . ~ F0ntell2' also noted a large increase in the size of the cubic region of DDAB systems on substituting hexane with 1-hexene and a 10-fold increase in the self-diffusion coefficients of the surfactant molecules above 60% by weight of surfactant. These observationsfurther reinforce the idea that the presence of an unsaturated hydrocarbon induces a significant alteration in the behavior of the surfactant interface, especially at high concentration of the lipophile. Structural Determinationvia Small-AngleX-ray and Neutron Scattering. The small-angle scattering patterns of cubic phases show Bragg peaks which index to a cubic structure, whose space group depends on the particular composition of the ternary mixture. Previous work by Radiman et al., on the octane system,16Js and Barois et al., on the cyclohexane system,17reported initial observations of a structural transformation within the cubic phases of these systems upon increasingthe aqueous volume fraction. They achieved a good fit to their experimental data by using bilayer structures based on Their work was Schwarz's D and P minimal restricted to the low aqueous content section of the cubic phases and did not fully explore the possibility of further transitions. The structural transition was proposed to be driven by a swelling aqueous volume forcing the surfactant bilayer into another, more favorable, configuration to minimize the deviation of the interfacial curvature from its spontaneous or preferred value and, consequently, minimize the free energy of the system. Some representative results from the present study are shown in Figure 2a,b where the SAXS patterns can be indexed to the space groupsPn3m and Im3m, respectively, and are assigned to bilayer structures decoratingthe SchwarzD and P minimal surfaces (see Figure 2c), in each case. Two main theoretical approaches have recently been reported in the study of ternary cubic phases. The geometry of the cubic structure can be described as that of a bilayer (containing the lipophile) decorating a triply periodic minimal surface in such a way that the latter bisects the bilayer.*J7 Alternatively, a triply periodic constant mean curvaturesurface can be invoked to describe the structure of the aqueous/apolar interfa~e.~.~ We begin our discussion with the latter approach, although as will be seen later both methods of analysis lead to essentially the same description of the cubic phases. It is useful when studying topological transitions in such systems to define a dimensionless area A* = A c 2 ,where A is the area of surfactant interface per unit cell and a is (26) Jada, A.; Lang,J.; h a , R. J. Phys. Chem. 1990,94, 381. (27) Fontell, K.; Jamson, M. B o g . Colloid Polym. Sci. 1988,76,169. (28) Schwan, H.A. Monatsberichte der Koniglichen Akademie der Wbsenscaften zu Berlin 1865, Jahrgang 1866, 149. (29) Schwarz, H.A. Gesammelte Mathematische Abhandlungen; Springer-Verlag: Berlin, 1890.
Structure of Cubic Phases
Langmuir, Vol. 9, No. 11,1993 2871
l " " " " " " i " " i l
a
I
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i
t
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1.OE-01
0.05
0.10
0.15
0.20
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/ 10
/ 20
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Octane +
Figure 3. Partial phase diagram (wt %) of the DDAB/D*O/ octane system at 25 f 0.5 O C showing the cubic region and the different symmetries: +, diamond symmery; #, bcc symmetry. Inset: cJQ- plot for the bcc region. The solid line represents the P family of cmc surfaces (see text).
1 A*(@)= A*(&) - ;(4 - 4,J2
(1)
where 40,A*(&), and c are symmetry-dependent constants whose values have been calculated by Anderson5for various surfaces. It can be easily shown that c,a = A*(4)/a,
Figure 2. (a) SAXS spectrum from the double diamond region in the dodecane system with composition (wt % ) 41.74/47.56/ 10.71 (DDAB/DzO/dodecane). The Bragg reflections (A, 6, 4,A,6)are consistent with the space group Fn3m. (b) SAXS spectrum from the bcc region in the octane system with composition (wt % ) 34.94/57.90/7.16(DDAB/DzO/ octane). The Bragg reflections (A, 4,4,6, fi, 6) are consistent with the space group Im3m. Note: Following the convention adopted by Luzzati, the space group of highest symmetry from all the possible ones is assigned in each case. (c) Schematic representation of the Schwarz P minimal surface and the cross section of ita unit cell showing a bilayer structure decorating the minimal surface. W denotes the aqueous regions of the system, while the oil is contained within the bilayer, i.e. in the region between the tails of the two opposing surfactant monolayers.
A,
a,
the lattice constant. By then following this parameter on changing volume fraction (4), it is possible to illustrate symmetry transitions more easily. The variation of this dimensionless area with volume fraction for a particular constant mean curvature surface is given bpi9
(2)
where a = (2a/Q,)(h2 + k2 + Z2)lI2, c, is the surfactant concentration in molecules per unit volume, Qmax is the magnitude of the scattering vector for a Bragg reflection (hlzl),and a, is the interfacial area per surfactant molecule. Therefore a plot of c$Q- against the aqueous volume fraction, 4, can reveal structural changes, since A*(4) is dependent on the symmetry and topology of a given cubic phase. In the present study, we have extended characterization of the cubic region of the octane system. The region whose structure indexes to the Im3m space group and is based on a surfactant bilayer decorating a Schwarz-P minimal surface has been found to extend to higher aqueous volume fraction (Figure 3 and Table Ia). The now extended c$ Q , plot for the cubic region of bcc structure shows good agreement between the experimental points and the theoretical curve for a P bilayer with a, = 64 f 3 A2 (see inset of Figure 3). This value is in reasonable accord with the corresponding values for the area per surfactant molecule found in both the diamond phase of the cubic
2812 Langmuir, Vol. 9, No. 11, 1993
Maddaford and Toprakcioglu
Table 1. Sample Compositions (Weight Fractions) for Each Cubic Region in the Different DDAB Systems. composition DDABIDzOloctane 48.21136.44115.34 47.73137.22115.04 44.82140.95114.23 43.84/46.12/10.03 40.10/51.70/8.20 38.18154.017.82
space group Pn3m Pn3m Pn3m Pn3m Pn3m Pn3m
composition DDABIDzOldodecane 42,49146.34111.25 40.52148.27111.21 39.97/49.52/10.51 38.77151.3019.93 37.16155.6517.19 35.71J57.3716.92 33.47J60.00J6.52 31.56162.3316.10 32.00/63.17/4.75
space IZIOUD
Pn3m Pn3m Pn3m Pn3m Pn3m Pn3m Pn3m Pn3m Pn3m
(a) DDAB/DzO/Octane lattice composition space lattice composition space lattice parameter (A) DDAB1DzOloctane group parameter (A) DDABIDzOloctane group parameter (A) 36.95157.3515.70 107 Pn3m 83 29.29/64.71/6.00 Im3m 170 36.22156.3611.42 132 Im3m 86 27.79/66.52/5.69 Im3m 184 36.22156.3611.42 92 26.44168.1515.41 Im3m Im3m 137 187 34.94151.8419.93 Im3m 140 98 24.09/70.97/4.93 Im3m 209 32.98/60.26/6.75 153 Im3m 22.13113.3314.53 Im3m 229 98 29.80/64.10/6.10 167 Im3m 99
(b)DDABlDZOlDodecane lattice composition space lattice composition space lattice parameter (A) DDABID~Oldodecane IZIOUD parameter (A) DDAB/DzO/dodecane IZIOUD parameter (A) 95 30.89164.4414.67 Pn3m 136 27.14169.4213.44 Pn3m 158 96 30.54162.8716.80 Im3m 164 26.34110.3413.32 Pn3m 161 31.37/63.14/5.49 Im3m 25.63/71.27/3.10 100 170 Pn3m 164 Im3m 102 30.71163.33J5.96 167 24.71171.9513.34 ?(C4) 109* 107 30.25163.4116.34 Im3m 167 23.12113.6513.23 ?(C4) 115. 29.84164.3815.78 Im3m 21.45/75.58/2.96 ?(C4) 127* 109 170 18.40/79.08/2.51 ?(C4) 116 29.92165.5614.52 Pn3m 137 147* 122 28.71166.9614.33 Pn3m 151 16.92J80.3812.70 ?(C4) 157* 133 28.28168.1613.56 Pn3m 156 15.68/81.30/3.02 ?(C4) 179'
~~~
composition DDABIDZOI tetradecane 35.18/58.00/6.83 34.47160.2215.31 32.27/62.70/5.03 30.64164.6014.75 31.37165.0613.56 29.44/67.18/3.38 composition DDABIDZOI toluene 64.18/15.40/20.41 63.81/17.15/19.03 62.33116.14121.52 61.98/18.30/19.71 59.98120.53119.48 58.73125.99115.27 a
space group Pn3m Pn3m Pn3m Pn3m Pn3m ?(C4)
lattice parameter (A) 114 125 131 136 134 94*
lattice space parameter group (A) Ia3d 79 Ia3d 79 Ia3d 79 Ia3d 80 Ia3d 83 Pn3m 56
(c) DDABIDzOlTetradecane composition DDABJDzOI space lattice tetradecane parameter group ?(C4) 27.37169.3312.20 102* ?(C4) 27.27169.5013.24 105* 27.04/68.73/4.24 Pn3m 158 25.56171.4113.03 ?(C4) 1091 25.19170.9413.87 Pn3m 169
(d) DDABIDzOlToluene composition lattice DDABIDZOI space parameter toluene group (A) 54.77133.36111.87 biphasic sample 51.87/39.63/8.51 biphasic sample 49.02/42.48/9.71 Im3m 91 46.46141.2116.32 Im3m 101 43.37l50.62l6.00 Im3m 108 40.00154.2515.75 Im3m 117
composition DDABIDZOI tetradecane 23.62/72.70/3.69 23.91/73.32/2.77 21.95174.6513.39 19.05J78.0212.93 17.63179.6612.70
composition DDABlD201 toluene 37.00/58.40/4.60 34.08162.2313.68 31.30/66.00/2.70 28.91/69.00/2.09 19.05l79.37l1.58
space group ?(C4) ?(C4) ?(C4) ?(C4) ?(C4)
lattice parameter (A) llS* 117* 127* 144* 1535
lattice space parameter group (A) Im3m 131 Im3m 145 Pn3m 131 biphasic sample ?(C4) 125*
In cases where the space group is uncertain, the lattice spacing (rather than the lattice parameter) is shown, as denoted by an asterisk.
regionl6J6 and the L2 microemulsion phase.5~3093~ There is however a small shift from the values determined in the adjacent lamellar phase24mainly due to hydration effects associated with differences in the aqueous content. The dodecane cubic region exhibits a similar D-bilayer to P-bilayer transition on increasing the aqueous volume fraction (Figure 4 and Table Ib). The c$Q- plot also exhibits the discontinuity related to a change in the symmetry of the structure (see insert of Figure 4). Unlike the octane system, the region of bcc structure does not extend to higher aqueous content, but on increasing the aqueous volume fraction there is a second topological transition to structures which can be indexed to the space group Pn3m. The region with a bcc structure (Im3m) is restricted to the high dodecane side of the cubic phase and spans only a limited dilution range relative to DzO. The region of structures with space group Pn3m appears to be continuous on the low dodecane content side of the cubic region (see Figure 4). From the c$Qmaxplot (see inset of Figure 4) it is seen that the D-bilayer region extends to volume fractions greater than that found for the bcc structure. This result appears to contradict the (30) Ninham, B. W.; Barnes, I. S.; Hyde, S. T.; Derian, P.-J.; Zemb,T. N. Europhys. Lett. 1987,4, 561. (31) Barnes, I. S.; Hyde, S. T.; Ninham, B. W.; Derian, P.-J.; Drifford, M.; Zemb, T. N.J . Phys. Chem. 1988,92, 2286.
idea that the swelling aqueous volume fraction is the only factor responsible for the structural transitions within the cubic region. Obviouslythe interaction of the hydrocarbon component with the surfactant tail section needs to be considered when trying to rationalize driving forces for the shift in topology within the cubic phase. The reduced ability of dodecane molecules to penetrate the paraffinic section of the surfactant layer compared to the octane molecules evidently limits the range over which it is energetically more favorable for the surfactant sheets to adopt the P-bilayer form. The fact that the D-bilayer region spans alarge aqueous volume fraction range enables a good fit to the theoretical curve for such a surface, and again a value of 64 f 3 A2 for the area of interface per surfactant molecule gives the best agreement (Figure 5). This again lends evidence toward the idea that there is a slight reduction from the value measured in the lamellar phase situated at higher water content. The distribution of experimental points, shown in Figure 5, around the theoretical curve for a single family of constant mean curvature surfaces suggests that all these samples are part of the same single phase. This weighs against the possibility of two different microstructures, which posses the same (or closely related) space group, being responsible for the extended region of samples assigned to Pn3m symmetry.
Langmuir, Vol. 9, No. 11,1993 2873
Structure of Cubic Phases t
1
6
7
+
!
h
3
+
DDAB 0.05
0.10
0.15
0.20
Q (A-1) Figure 6. SAXS spectra from the C4 region in the dodecane system with composition (wt % ) 23.12/73.65/3.23 (DDAB/DzO/
5 J
dodecane). The space group to which the Bragg reflectionsindex has yet to be resolved.
0
Dodecane
-
Figure 4. Partial phase diagram (wt %) for the DDAB/D20/ dodecane system at 25 f 0.5 O C showing the cubic phase and the different symmetries observed +, diamond symmetry; *, two coexisting cubic symmetries; #, bcc symmetry; 0 , "second" diamond symmetry; =, unresolved symmetry (C4). Inset: CJ Q- plot for the entire cubic region in the dodecane system: filled diamonds, diamond symmetry; open triangles, bcc symmetry; open diamonds, unresolved symmetry. Note that the system reverta to the D-bilayer structure on increasing the water content giving rise to an apparent *second" diamond region at high tpw.
i
c
4
1.15 to the primary Bragg reflection is distinctive and the systematic shift to lower Q values of the peaks on increasing the aqueous content discounts the possibility that a mixture of two phases might explain the appearance of the ambiguous peaks. Further evidence to support the existence of this additional structural type is given by the c$Qmar.plot (inset Figure 4) which shows a drop of -20% indicating an irrefutable topological change. Similar diffraction patterns have been reported in the 1-hexene system by Barois et aLs2 who explored the possibility of a structure based on the F-RD minimal surface, space group Fm3m, having expected reflections with ratios fi:d:fi:fi:%%:fi, but discounted this due to unfeasible values of a, required to satisfy their analysis. The spectra recorded for the dodecane system show good correlation with the Fm3m space group but are not of sufficient quality to make conclusive deductions. The next minimal surface in the theoretical sequence is that of Neovius,S3and it is possible that a structure based on this is located at the high DzO corner of the cubic phase, but better quality diffraction patterns are required to clarify the new topology. SAXS results from the tetradecane system follow the initial trends of the octane and dodecane systems with structures indexing to the space group Pn3m (Figure 7 and Table IC). No transition to the P bilayer is seen however; instead, on increasing the DzO content the structuraltransition that occurs is one to a topology whose SAXSspectra have the same Bragg spacings as those found in the high aqueous volume fraction region of the dodecane system's cubic phase (see Figure 6). This absence of a region of bcc structure further highlights the role played by the ability of the hydrocarbon to penetrate the surfactant tail section in stabilizing a structure based on a P bilayer. The higher genus of the P surface, compared to that of the D surface, requires a greater degree of negative curvature for a particular lattice parameter. The penetration of the hydrocarbon molecules into the surfactant tails is a significant factor in setting this curvature, so if this ability to penetrate the paraffinic section of the surfactant layer is reduced to a sufficiently great extent, the system may never be able to satisfy the conditions under which a P-bilayer structure is preferred over one based on a D bilayer. This factor is probably one of the main driving forces for the systematic reduction and final
5 1 0.3
0.4
0.5
0.6
Aqueous volume frachon
0.7
@w
Figure5. cJQ, plot for all the sampleswith diamond symmetry in the dodecane system. The solid line represents the theoretical curve for the D family of surfaces with the value of a, = 64 &.
The D-bilayer region exists up to -70% DzO by weight, after which SAXS experiments show a symmetrytransition to a previoualy undetected space group. A typical SAXS spectrum for this region is shown in Figure 6. It has yet to be resolved but is clearly unrelated to either of the previous structures. The presence of a peak at a ratio of
I.
(32) Barois, P.; Eidam, D.; Hyde, S. T. J. Phye. (Park) 1990,51 (Cn,
(33) Neovius, E. In Bestimmung Zweier Speciellen Periodiechen Minimalflachen; J. C . Frenckell and Sons: Helingfors, 1883.
Maddaford and Toprakcioglu
2874 Langmdr, Vol. 9, No. 11,1993
5 1
Aqueous volume fraction Q
9
Tetradecane
Figure 7. Partial phase diagram (wt % ) for the DDAB/D20/ tetradecane system at 25 & 0.5 O C showing the cubic phase and the different symmetries observed: +, diamond symmetry; =, unresolved symmetry (C4). extinction of the region of P-bilayer topology in the series of alkanes from cyclohexane to tetradecane. Structural changes within the cubic phase of the DDAEV DzO/toluene system show marked differences from the structures found for the alkane systems as might be expected from the dramatic change in phase behavior (Figure 8and Table Id). The high surfactant concentration samples exhibit reflections consistent with the distinctive Ia3d space group, i.e. at V%:h:fi (Figure :fi 9). This symmetry is consistent with a bilayer structure decorating the Gyroid (G) minimal surface." Topologies based on the gyroid have been found in pure surfactant2 and binary surfactnat/waterI2 systems, and recently Striim and Anderson presented data consistent with such a structure in the cubic region of the system water/DDAB/ styrene.18 Theoretical work predicts a transition from Gyroid surface to a Schwarz D surface,12and on increasing the aqueous volume fraction a small region exhibiting a structure with the expected Pn3m space group of the D bilayer is found. On further increasing the DzO weight fraction, a transition to the bcc structure comparable to that in all the previous systems is found. This region exists over a greater aqueous volume fraction range than in any of the other systems (-0.35-0.6) and the cJQ,plot shows a good a reement between the theoretical curve with a, = 64 f 3 ,and the experimental points (Figure loa). The enhanced ability of the toluene molecules to penetrate the surfactant layer obviously leads to the stabilization of the P bilayer over a far greater compositional range.
w
(34)Schoen, A. H.NASA Technical Note 1970, TN 0-5541.
10
;
20
30 L
Toluene 6 Figure 8. Partial phase diagram (wt %) for the DDAB/D*O/ toluene system at 25 f 0.5 O C showing the cubic region and the different symmetries: $, Ia3d (based on the gyroid structurew);
*, two coexisting symmetries; +, diamond symmetry; #, bcc symmetry; =, unresolved symmetry (C4). Inset: cJQ- plot for the entire cubic region in the toluenesystem: f i e d diamonds, diamond symmetry; open triangles, bcc symmetry; open circles, gyroid; open diamonds, unresolved symmetry.
Around an aqueous volume fraction of -0.6 there is then a transition back to the D bilayer and then a t a volume fraction of -0.7 a further transition introduces a structure as yet unidentified, but whose Bragg pattern closely resembles those found in all the other systems in this compositional range. A cJQ- plot for the two D-bilayer regions reveals that the two structures are of the same family of constant mean curvature surfaces with a theoretical curve for such a family, with as= 64 f 3 Az,showing reasonable consistence with the experimental points (Figure lob). The presence of these two regions of diamond structure which are well separated in compositional space again raises the question why the surfactant sheets revert to a previous structure on further increase of the aqueous volume fraction. It also highlights again the significant role the lipophile must play in driving the structure of the interface. The overall cJQ- plot for the toluene systems within the cubic region shows clearly the transitions between the four different structures as discontinuities (see inset of Figure 8) and provides a good illustration of the sensitivity of cJQ- versus 4 plots to such symmetry transitions. The representation of the experimental data in this form avoids having to assume any prior values for the molecular dimensions of the surfactant molecules; i.e. the plots are derived solely from experimentally measured quantities. Subsequent theoretical fita to these plots can then provide clear evidence straight from experiment, of the topology of the system.
Langmuir, Vol. 9, No. 11, 1993 2875
Structure of Cubic Phases
+
Dcdecane ("phase1") Dcdecane ("phase 2") Octane Cyclohexane
X
Tetradecane
I
0
h
8
2 -
P o
120
X A
&
I
+ +
J m
601
0
0.3
40d.2'
0.4
'
0.5
'
1
'
0.6 ,
Aqueous volume fraction $,
" 0.7
I I
8 I=
= 1 +
I
18 ++
A k+
0
0.0
0.l
0.1
0.3
Q (A')
100
Figure 9. SAXS spectra from the gyroid region in the toluene system withcomposition(wt %) 61.98/18.30/19.71 (DDAB/DzO/ toluene). The Bragg reflections (6, 4,fi,fi) are consistent with the space group Ia3d.
1
80' 0.35
X X
' 0.4
'
' 0.6 Aqueous volume fraction $, '
0.45
' 0.5
'
'
0.55
0.65
I
0.7
Figure 11. (a,top) Plot of the lattice parameter against aqueous volume fraction for a series of DDAB/DzO/oil system in the double diamond structuralregion of the cubic phases. (b,bottom) Plot of lattice parameter against aqueous volume fraction for a series of DDAB/DzO/oil systems in the bcc structural region of the cubic phases.
16
0!3
'
0.35
'
014
'
0.45
'
0:5
'
0.55
'
0:6
'
O.Q5
Aqueous volume fraction $, 12 1
6t t
4 1 " 0.1
"
0.2
"
'
I
"
0.3 0.4 0.5 0.6 Aqueous volume fraction $w
'
II
0.7
Figure 10. (a, top) CJQ- plot for the bcc region in the toluene system. The l i e representsthe theoreticalcurve for the P family of surfaces with the value of a. = 64 AZ. (b, bottom) cJQ- plot for the diamond samples in the toluene system. The h e represents the theoretical curve for the D family of surfaces with the value of a. = 64 Az.
Lattice Parameter as a Function of Aqueous Volume Fraction. A clear illustration of how the varying
molecular structure of the hydrocarbon bulk phase affecta the curvature of the surfactant interface is obtained by considering the lattice parameter as a function of aqueous volume fraction for a particular symmetry. The size of the unit cell will reflect directly the degree of curvature within the system. The smaller the unit cell for a particular aqueous volume, the greater the negative curvature of the surfactant sheets. Figure l l a shows such a plot for the double diamond structure regions (Pn3m) within all the systems. This clearly indicates how the more penetrating hydrocarbons produce structures of smaller dimensions at a constant aqueous volume fraction. It also demonstrates how the systems containing the larger hydrocarbon molecules only stabilize the cubic phase a t higher aqueous volume fraction. There is a clear correlation between the length of the hydrocarbon chain and the minimum volume fraction a t which the structural region appears. At a given aqueous volume fraction, the larger n-alkanes tend to be associated with larger lattice parameters, but the points for these straight chain alkanes generally lie fairly close to each other. In contrast, data from work by BaroiP for lattice parameters in the cyclohexane system show a shift to lower values for the size of the unit cell (- 25 % ) for a particular aqueous volume fraction (see Figure lla). A further drop is seen for the toluene system (-lo%), and so it seems that shifts in this structural region follow a systematic trend related to the size and molecular geometry of the hydrocarbon fraction of the system. Close examination of the data for the regions of bcc structure reveal similar trends relating to penetrative ability and lattice parameter at a particular aqueous volume fraction, with the more interactive hydrocarbons producing smaller structures and maintaining this type of
Maddaford and Toprakcioglu
2876 Langmuir, Vol. 9, No. 11, 1993 structure to lower aqueous volume fractions (Figure llb). The octane system exhibits the bcc region up to -0.7 D2O volume fraction but the dodecane system only retains such a structure up to -0.6 D2O volume fraction while the tetradecane system does not form a bcc structure at all. There is obviously a significant change in the interaction of the paraffinic surfactant tails and the hydrocarbon component when the length of the alkane chain becomes approximately equal to that of the surfactant chains.25 Further Observations. Another feature which highlights the change in behavior on increasing alkane chain length is the exaggerated temperature sensitivity of the cubic phase in the tetradecane system. On a rise of only - 5 “C (i.e. at 30 “C)the cubic phase expands by -50% in relation to the minimum and maximum tetradecane levels tolerated. This effect is clearly associated with the low level of interaction (or penetration) of this oil with the surfactant tails, since such a small shift in temperature is capable of increasing the compositional range over which the system can form ordered cubic structures. This rapid extension of the cubic phase on increasingthe temperature is not seen to such an extent in the other systems studied, and therefore the intrinsic ability of all the other oils to “solvate” the surfactant tails is such that a s m a l l temperature rise does not induce any major change. This type of behavior is reminiscent of solvent-monomer interactions in polymeric systems, where the solvent quality determines the solution properties of the polymer. In this context, we may say that strongly penetrating solventsare essentially “athermal”. In other words, small changes in temperature have a negligible effect on solvent quality. The surfactant tails are already fully solvated, and minor temperature shifts do not affect their state of solvation. However, with poorer, less penetrating solvents such as tetradecane, even small temperature shifts affect the phase behavior of our ternary system, since the solvating ability of the tetradecane molecules is sharply enhanced on increasing the temperature. The viscosity of the cubic phases changes significantly with composition. They are very rigid at high surfactant volume fraction and become far less viscous and more liquid-like at the other extreme of the cubic region where the aqueous fraction is high. The scattering patterns generally reveal rather subdued higher order peaks in this latter part of the region (e.g compare Figure 2a and Figure 6), and this may be due to larger fluctuations aesociated with the swollen structures formed at high aqueous content. Hyde’s Parallel Surface Approach. An alternative method for representing the experimental data for these cubic phases which gives a more direct graphical display of the two main parameters A*(&) and x, the Eul6r characteristic, that describe a particular topology was derived by Barois et al. for their description of the cubic phase in the cyclohexane ~y5tem.l~The E u l t characteristic is related to the genus, g, of the surface via the equation x=2-2g (3) This analysis proceeds from the assumption that the cubic phase consists of a bilayer decorating a minimal surface. The theoretical model developed by Hydea is based on a construction of two parallel surfaces (i.e. a parallel surface on each side of the minimal surface). The expected topologies are then described by one “master plot” equation8J7
per unit cell, and a is the normalized surface to volume ratio per unit cell (Le. A*(&) in Anderson’s approach6p9), which is defined as
(5) where S(0) is the area of the surface at the center of the bilayer, per unit cell. From eq 4 a plot of A/2a2 against 2d2/a2will generate a straight line whose slope is equal to x and the intercept yields c. The advantage of using this representation is obvious since such a plot then gives a complete description of the structure of the surfactant interface. If one could generate these plots direct from experimentally measurable quantities, this would be an ideal method of ascertaining the structure. The requirement to know the area of surfactant interface per unit cell, A, and the half width of the bilayer, I , in order to produce the points of the plot necessitates some assumptions, however, as these quantities are virtually impossible to measure within the cubic phase. These assumptions might lead to the “masterplots” being liable to inaccuracies unless the data are treated with extreme care. &rob et al.17 circumvent this problem by utilizing the values for a, and 1 derived from measurements made in the nearby lamellar phase2* and assume them to be unchanged in the cubic phase. The assumption that the bilayer half width is not altered on varying the oil content of the systemmay hold for highly penetratinghydrophobea, but it may become invalid when consideringless solvating hydrocarbons which do not penetrate to the required degree. The assumption that the area of interface per surfactant molecule remains constant over such a large range of compositions seems harder to sustain. The previous c$Q- versus 4 plots show directly from experiment that in the cubic phase there is a decrease in ae relative to its value in the lamellar phase, and this can be easily justified on hydration grounds. Though the assumptions of Barois et al.17 give a good fit to the data for the cyclohexanesystem,when Considering a range of hydrophobes care has to be taken not to “forcefit”the data to expectations, as will be shown, by taking convenient values for as and 1 which may not be truly representative of the actual structure. The cB/Qmaxversus $t plots enable a more accurate value of anto be utilized, but deriving a composition-dependentvalue of 1 proves to be particularily problematic. Stram and Andersonl8used the relation 1 = 12(1+ 240dane)A (6) when considering data from the octane ~ y s t e m where ~~J~ + a e is the volume fraction of the hydrophobe. This approximation gives a reasonable fit again, but is only really applicable for this system. In order to gain some insight into the variation of 1 with composition, a crude approximation for the value of 1 can be produced by assuming ideal mixing of the surfactant tail volumes ( V d and hydrocarbon ( V,) in the system to produce an estimate of the volume of the bilayer (vb)
(7) = nBVst+ V, where n, is the number of surfactant molecules. The value for the volume of the bare surfactant tails, Vat,is ca. 700 A3.17*s The half-width of the bilayer can also be approximated to the bilayer volume via vb
= nudl (8) where nucis the number of unit cells in the sample derived vb
(4)
where 1 is the bilayer half width, A is the head group area
(36)Evans, D. F.;Mitchell,D. J.; Ninham,B. W.J. Phys. Chem. 1986, 90,2817.
Langmuir, Vol. 9, No. 11, 1993 2877
Structure of Cubic Phases
from the densities of the three components and the lattice parameter, again assuming ideal mixing. A is the surfactant head group interfacial area per unit cell simply found from the head group area per surfactant molecule. Equation 8 is strictly valid only if the bilayer thickness is negligibly small in comparison to the mean radius of curvature of the interface averaged over the unit cell. Although this basic approach is flawed in that the mean radius of the interface is not overwhelmingly larger than 1, and it is naive to think that the ideal mixing approximation is completely justifiable, nevertheless as will be shown it does allow for some representation of the change in bilayer width with composition and demonstrates how this effect becomes more applicable for the less penetrating hydrophobes. The “master plots” were calculated for three regions of single symmetry in different systems. The plot points were generated using four different criteria: (i) both a, and 1 invariant with respect to composition and set at values determined in the nearby lamellar phase; (ii) 1 invariant with composition, as in (i) and a, determined by fits to the cs/Qmmversus 4 plots; (iii) a, set at the value determined in the lamellar phase and 1 determined by the composition (eqs 7 and 8);(iv) a, determined by fits to the c$Q, versus 4 plots and 1 determined by the composition (eqs 7 and 8). Note that in cases i and ii the oil is assumed to be fully absorbed into the bilayer region so that the thickness of the latter is taken to be constant regardless of the oil content of the system, in contrast to cases iii and iv where the oil is assumed to simply add to the volume of the bilayer thereby causing it to swell (i.e. in this latter picture virtually no solvation of the surfactant tails is postulated). Clearly, in a real system the situation will generally be intermediate between these extremes. In this way the four different plots will enable a comparison of the various assumptions and thus a better understanding of the role of the surfactant molecular geometry. The values for the linear least-squares fits to the “master plots” for the regions of Pn3m symmetry in the dodecane system and of Im3m symmetry in the octane and toluene systems are shown in Table 11. Examples of the plots are shown in parts a and b of Figure 12 for the diamond region in the dodecane system generated using criteria iv, and the bcc region in the toluene system generated using criteria i, respectively. The fact that the points produce plots with strong linear characteristics indicates that the fundamental concept of the structure of the cubic phases being based on a bilayer decorating a minimal surface is reasonably accurate. The range of values obtained for the y-intercept and the gradient indicate, however, that the plots are extremely sensitive to shifts in the basic ) x for assumptions. The expected values for A * ( ~ oand the D minimal surfaces are 1.9189 and -2.9934 As can be seen from the values in Table IIa for the dodecane system the best fit to the theoretical values is achieved with a, = 64 A2 and a composition-dependent bilayer half-width. We note that in the dodecane system the “swelling”of the bilayer amounts to some 35 9% over the value of ita thickness in the nearby lamellar phase (Le. from ca. 11 to ca. 15 A). Alternatively when considering structures based on the P minimal surface with expected values of A*(&) - 2.3455 and x = -434 in the toluene system, assumin a composition-independent half-width and a, = 64 produces the best fit (see Table IIc). These two observations indicate, that for the less penetrating hydrophobes even a crude model for the “swelling” of the bilayer gives a surprisinglyaccurate representation of the actual structure of the cubic phase, whereas highly penetrating toluene molecules are fully absorbed into the surfactant tail region without significantly altering the bilayer half-width. This
iz
Table 11. Parameters of the Linear Least-Squares Fits to Hyde ‘Master Plots” for a Series of Single-Symmetry Cubic Regions in the Dodecane, Octane, and Toluene Phase Diagrams (a) Dodecane System,Pn3m Region y intercept plot critera (a8,1) (see text) [A*(bo)l (i) 2.13 A 0.03 (ii) 2.01 0.03 (iii) 2.05 0.03 (iv) 1.97 0.03 theoretical values for the D surface 1.9189
*
(b) Octane System,Zm3m Region y intercept plot criteria (ae,1) (see text) [A* (boo)1 (i) 2.48 & 0.05 (ii) 2.34 k 0.05 (iii) 2.48 0.05 (iv) 2.36 0.05 theoretical values for the P surface 2.3455
*
~
gradient [XI
-5.03 -4.20 -2.45 -2.05 -2.00
0.60 0.53
* 0.30 * 0.26 ~~
~
gradient [XI -7.07 1.5 -6.52 k 1.5 -4.77 0.97 -3.78 0.87 -4.00
*
(c) Toluene System, Im3m Region y intercept gradient plot criteria (ae,1) (see text) [A*(ho)l [XI (i) 2.47 0.07 -4.56 h 1.00 (ii) 2.30 & 0.07 -4.26 1.00 (iii) 2.40 0.06 -3.28 0.74 (iv) 2.31 0.06 -2.85 0.66 theoretical values for the P surface 2.3455 -4.00 The four sets of fits for each system are obtained via different assumptions in generating the points for the plots (see text). ~
* *
*
point is further illustrated when consideringthe data from the octane system (seeTable IIb)whose hydrophobe might be expected to penetrate into the surfactant tails to a greater degree than dodecane but not to the extent of the toluene molecules. The crude “swelling”model gives the best fit to theory but some overcompensation for the increase in the value for 1 is made as the gradient is above -4. This follows from the fact that the half-width is one of the primary factors affecting the slope of the plot. These results clearly show the extensive degree to which the variety of hydrophobes differ in their interaction with the surfactant tails and thus produce changes in the structure of the surfactant interface. The effect of such hydrophobes on the interfacial curvature, however, proceeds via two different,but parallel mechanisms, in general. While highly penetrating oils primarily tend to reduce the preferred (or spontaneous) curvature of the interface, nonpenetrating oils such as tetradecane mainly act by reducing the actual mean curvature of the interface by residing in the middle of the bilayer and causing it to swell, i.e. forcing its half-width, 1, to increase (the mean curvature for a given bilayer volume fraction and topology s d e s , to a good approximation, with 1-’ Is). Our resulta suggest that whereas toluene affects the interface via the former mechanism due to ita high penetration, dodecane and tetradecane mainly proceed via the latter. Both mechanisms obviously tend to reduce the discrepency between the actual and preferred curvatures, thereby stabilizing the cubic phases especially at low aqueous content, but their different effects manifest themselves in the shifts seen in the compositional range and structure of the cubic phases formed by various oils. Conclusion We have shown that, in general, the ternary system consistingof the surfactant didodecyldimethylammonium bromide, Dz0,and a hydrocarbon exhibits a cubic region at low oil content made up of a series of bicontinuous
2878 Langmuir, Vol. 9, No. 11, 1993
Maddaford and Toprakcioglu
3
t 2.5
1
tt
1
t
0.02
1
0.04
0.06
0.08
0.1 0.12 2x e 2/a2
0.14 0.16 0.18
.
3t
2.5
1.5
1
i
c
1
0.51, 0.03 0.04 I
,
,
0.05
,
I
.
I
,
,
0.06 0.07 0.08 2x e '/a2
,
, 0.09
,
I
0.1
,
I
0.11
Mguw 12. (a,top) Hyde master plot for allsampleswith diflmond symmetry in the dodecane system. The bilayer half-wdth is determined via a 'swollen bilayer" concept with the value of aB = 64 A*, The dashed lines are the h e a r least-squares fits to the pointa,thedetailsofwhicharegiveninTableIIa(iv). (b, bottom) Hyde master plot for the bcc region in the toluene system. The bilayer half-width is fiied at 11.5 A and a, = 64 Az. The dashed lines are the linear least-squares fits to the points, the details of which are given in Table IIc (ii).
cubic structures. The structure of the surfactant interface has been successfully modeled on a bilayer construction developed from triply periodic minimal surfaces. The previously ~ b s e r v e d ~transition ~J' from a bilayer structure based on the Schwarz D minimal surface (space group Pn3m) to one based on the Schwarz P minimal surface (space group Im3m), on increasing the aqueous volume fraction has been confirmed. Extension of the investigation of the cubic region across a series of DDAB systems containing different hydrocarbons has resulted in two further structural transitions being revealed. In the DDAB/DzO/toluene system at low aqueous volume fraction the D-bilayer structure gives way to a structure which has been tentatively assigned as one based on the Gyroid minimal surface (space group Ia3d). At high aqueous volume fraction in all the ternary systems explored, a structural transition to a so far unassigned interfacial arrangement is observed. This new structure, termed C4, is clearly a single phase but it does not appear to conform to any of the presently known minimal surfaces. Comparison of the cubic regions across the different ternary DDAB systems reveals that the nature of the hydrocarbon component plays a significant role in determiningthe phase and structural behavior of the systems.
Highly penetrating oils such as toluene can be regarded as being fully incorporated in the surfactant tail region of the bilayer. With much less penetrating oils such as dodecane and tetradecane, however, this is no longer the case, and some of the oil, at least, remaina unaseociated with the surfactant tails and resides in the middle of the bilayer. This implies that with less penetrating oils,the bilayer will tend to swell significantlyon increasing the oil content of the cubic phase. The ability of the lipophile to penetrate the surfactant tail sections and thus affect the curvature of the interface is shown to be a primary factor in the stability of the cubic phases. The significant role the oil plays in setting the interfacial curvature modulates the structural transitions that are thought to be fundamentally driven by the swelling aqueous volume fraction. This modulation results in the position of the boundaries between different cubic structures within the cubic region being adapted appreciably. The shift in the position of the boundaries caused by the lipophile effect, from those expected purely from considering the swelling aqueous volume fraction,are great enough for the expected sequence of cubic structures to be disrupted (with the emergence of a reentrant D structure) in some of the systems studied. With thisproviso, the observed structural transitions generally seem to follow the expected overall pattern of G D P with increasing aqueous volume fraction (decreasinginterfacialcurvature). This structural transition sequence seems to be quite general and has been observed in other temary18as well as binary amphiphile% systems. It can be rationalized by simple curvature free energy theories.18*% The phase behavior and structural features of ternary cubic phases can thus be accounted for entirely on topologicalconsiderations,with the particular composition of each system merely setting the values of variables such as curvature, lattice parameter, etc. The study of the cubic region in this type of temary system has illustrated the detailed structural information that can be obtained from such phases due to the development of new theoretical models used to describe them. It has also highlighted the importance of nonEuclidean geometrical forms in the structural description of surfactant systems, as well as the rich microstructure that exists within regions once thought only to consist of one type of interfacial arrangement.
--
Acknowledgment. We thank David Anderson, Philippe Barois, Mike Cates, Margarida Cruz, Tom McLeish, and Antonio Vallera for helpful discussions. P.J.M. thanka the SERC and Shell for a CASE studentship and David Cooper and Leo Rupert for their advice and encouragement. This work benefitted from use of the SERC's Synchrotron Radiation Source at Daresbury, the LQD facility at the Manuel Lujan Jr. Neutron Scattering Center of the Loa Alamos National Laboratory, and D16 at the ILL,Grenoble. We are grateful to Wim Bras for his help at Daresbury, to Rex Hjelm and Phil Seeger for their support during the LQD measurements, and to Eva Peyroula-Pebay for her help with the experiments at D16. We also thank Wasi Faruqi for his help with some of the measurementsat the MRC-LMB. This work was partially supported by NATO. (%)Turner, D. C.; Wang, Z.; Gruner, 5. M.; Mannock, D. A.; McElhaney, R. N.J. Phys. I1 1992,2,2039.
