Langmuir 1994,10, 61-67
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Rheological Study of Ternary Cubic Phases S. Radimant and C. Toprakcioglu Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge CB3 OHE,U.K.
T. McLeish' Department of Physics, University of Leeds, Leeds LS2 9JT, U.K. Received April 26, 199P We have studied the rheology of bicontinuous ternary cubic phases formed by the system didodecyldimethylammonium bromide (DDAB)/DzO/octane. The cubic samples have the appearanceand texture of optically clear, isotropic,highly viscous gels. The microstructure of these cubic phases is such that the surfactant bilayer containing the paraffinic tails and the oil may be visualized as decorating a minimal surface so that the latter constitutes the mid-surface bisecting the bilayer. Linear rheology confirms that the dissipation becomes low at high acoustic frequencies and is consistentwith the phenomenon of "ringing" in which underdamped shear modes in the gel couple to sound via the gel surface. The frequency-dependent rheology also reveals a universal scaling form at the melting transition of the cubic phase, with the dynamical scaling observed at this point reminiscent of a percolation transition. Nonlinear rheological response is consistent with the formation of dislocation or slip-planesin the cubic structure, parallel to the direction of shear. The experimental observations are related to the dynamics of the water/surfactant/oil interface, and'theoreticalideasare presented to account for the observed behavior. Our results suggest that frequencydependent rheology is a useful structural probe of the dynamics of ternary cubic phases.
Introduction The structure of bicontinuous ternary cubic phases has recently been the subject of several experimental and theoretical investigation.l-'' It has become apparent that these systems represent non-Euclidean solutions to the problem of area minization under the constraint of constant volume fraction, and their structure is described by triply periodic minimal or constant mean curvature (CMC)surfaces. These structures occur because within a certain compositional range they are capable of optimizing the curvature of the system at the expense of more conventional alternatives such as planes, cylinders, or spheres. Recently, X-ray and neutron diffraction studiess-ls clearly demonstrated the occurrence of transitions ~
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~
+ Permanent address: Department of Nuclear Science, Universiti
Kebangeaan Malaysia, 43600 Bangi, Selangor, Malaysia. * Abstract published in Aduance ACS Abstracts, November 15, 1993. (1) Luzzati, V.; Mariani, P.; Gulik-Knywicki, T. In Physics of Amphiphilic Layers; Meunier, J., Langevin, D., Boccara, N., Eds.; Springer-Verlag: Berlin, 1987. (2) Fontell, K. In Liquid Crystals and Plastic Crystals; Gray, G. W., Winaor, P., Eds.; Ellie H a r w d Chichester, 1974; Vol. 2. (3) Fontell,K.; Ceglie,A.;Lindman,B.;Ninham,B. Acta Chem.Scand. 1986, A40,247. (4) Anderson, D. M. PhD Thesis, University of Minnesota, 1986. (5) Anderdon, D. M.: Thomas, E. L. Macromolecules 1988,21,3221. (6) Strom, P.; Anderson, D. M. Langmuir 1992, 8, 691. (7) Chanolin, J.; Sadoc, J. F. In Physics of Amphiphilic Layers; Meunier, J., Langevin, D., Boccara, N., Eds.; Springer-Verlag: Berlin, 1987.
(8) Raedler, J. O.;Radiman, S.;de Vallera, A.;Toprakcioglu,C. Physica B 1989,156, 398. (9) Radiman, S. PhD Thesis, University of Cambridge, 1989. (10)Radiman.S.:ToDrakciodu. - C.:Faruai.A. R.J.Phvs. (Paris)1990. 51, 1501. (11) Radiman, S.; Toprakcioglu, C.; Faruqi, A. R.; Hjelm, R. P.; de Vallera, A. Colloq. Phys. 1990, C7, 375. (12) Barois, P.; I-lyde, S. T.; Ninham, B. W.; Dowling, T. Langmuir 1990,6, 1136. (13) Barois, P.; Eidam, D.; Hyde, S. T. Colloq. Phys. 1990, C7, 25. (14) Hyde, S. T. J. Phys. Chem. 1989,93, 1458. (15) Hyde, S. T. Colloq. Phys. 1990, C7, 209. (16) Gradzielski, M.; Hoffmann, H.; Oetter, G. Colloid Polym. Sci. 1990,268,167. (17) Oetter, G.; Gradzielski, M.; Hoffmann, H. Abstracts of Papers; 198th National Meeting of the American Chemical Society, Miami Beach, September 1989; American Chemical Society: Washington, DC, 1989.
between cubic structures of different symmetry, within the cubic region of the phase diagrams of some water/ surfactant/oil systems. In addition to their remarkable microstructure, bicontinuous cubic phases may be expected to exhibit interesting mechanical and rheological properties. As the structural features of these supramolecular assemblies have been firmly established, a detailed understanding of their dynamical and, in particular, viscoelastic behavior is now the next challenge. To some extent, these system may resemble cross-linkedpolymer networks from a rheological viewpoint, but unlike such networks cubic phases have a liquid-crystalline structure with a well-defined periodicity. Furthermore, it is presumably the energetics of the triply periodic water/oil interface that must ultimately determine the rheology. Experimentally, it has been known for some time that ternary cubic phases typically have the appearance of clear, rigid gels which often exhibit the rather interesting property of "ringing" (i.e. they ring like a bell when tapped), a feature which seems to be associated with the presence of underdamped transverse phonon modes in these systems. Some aspects of the mechanical and rheological properties of such gels have been reported by Hoffmann et al.16J7 These authors' interpretation is based on a model of concentrated hard spheres. Although this is a candidate for cubic phases consisting of close-packed individual micelles, it is not appropriate in the case of the present system, which has a well-established bicontinuous structure. In the present paper we report rheologicaldata on the cubic phase of the system water/DDAEt/octane whose microstructure has been studied extensively by X-ray and neutron diffraction.@-ll
Experimental Section Didodecyldimethylammonium bromide (DDAB)was obtained from Eastman Kodak Co., Rochester, NY. It was used without further purification. Octane (Gold Label) and deuterated water
(DzO, isotopicpurity99.8%) wasobtainedfrom AldrichChemical
Co., Dorset, England. The samples were prepared by thorough mixing of the components in sealed containers at a temperature of ca. 80-100 "C. Once cooled to room temperature, the cubic gels were delivered to the sample chamber of the rheological
0743-7463/94/2410-0061$04.50/00 1994 American Chemical Society
62 Langmuir, Vol. 10, No.1, 1994
Radiman et al.
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Figure 1. Partial phase diagram of the temary system DDAB/ D*O/octaneat 22 f 0.5 "C showing the cubic region. The points indicatethe composition (see Table I) of the cubic samples used in the present study: (star)body centered cubic (bcc)symmetry (space group Im3m); (circle) diamond symmetry (space group Pn3m). Inset: Schematic representation of the Schwarz-P minimal surface and the cross section of its 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 tailsof the two opposingsurfactantmonolayers. Note that the bilayer separates two intertwinedbut distinct and unconnectedaqueouslabyrinths. apparatuswith the aid of a spatula. The rheometer was a RMS 800 Rheometrics apparatus interfaced with an IBM-PC Taxain printer for plotting. Parallel plate measurements were initially tried, but since the samplethicknesshas to be taken into account, we chose to work with the cone and plate geometryfor simplicity. Once the sample was delivered to the base-plate, it was lightly compressed by the cone allowing a seam to form on the rim. This we found useful, since at high temperature this part forms a solid-like, impermeable "skin" due to evaporationof the volatile components of the mixture, thus preventing any further evaporationfrom the bulk of the sample. The thicknessof the sample between the baseplate and the head of the cone was kept at ca. 0.5 mm, the value recommended by the manufacturer as being optimum. Appreciable thermal expansion occurs above ca. 7080 "C but does not overload the transducer, which would be the case if the normal stress on the sample exceeds 10%. All frequencysweeps use 0.5 % strain, below the critical strain which was found to be around 1%for these systems. The small-angleX-ray diffractionmeasurementswere carried out with a point collimated beam of ca. 0.5 mm diameter from a Cu Ka line of 1.54 A wavelength. A multiwire area detector18 was used at a distance of 750 mm from the sample, which was placed between two thin mica sheets providing a path of ca. 0.7 mm, and rotated throughout the measurements at a speed of ca. 1 rpm. The samples were subjectedto several cycles of heating and rapid cooling prior to the X-ray measurementsto reduce the size of large crystallites and improve the quality of the powder diffraction spectra.10
Results and Discussion The phase diagrams of DDAB/water/hydrocaFbon systems typically exhibit a large cubic region extending over a wide range of water content. The partial phase diagram. of the system DDAB/DpO/octane is shown in Figure 1. (18) Fmqi, A. R. N u l . Instrum. Methods Phys. Res. 1988, A273,754.
Table 1. Composition (by Weight) of the Samples Used in the Rheological Measurements %DDAB %DsO %octane 8vmmetrv sample1 32.99 60.26 6.75 bcc(Im3m) 15.33 diamond (Pn3m) 48.32 36.35 sample 2
The cubic samples have the appearance and texture of clear, highly viscous gels. The properties of samples within the cubic region vary significantly with composition. Generally,the rigidity of the samples increases, while their melting point decreases with decreasing water content. The rigidity also increases with decreasing oil content at a given water/surfactant ratio. As noted previously, the samples exhibit ringing behavior (i.e. they ring like a bell when tapped gently). This is a ready guide to any variation in their rigidity, which gives rise to a proportionalvariation in the ringing frequency. The frequency depends on the size and shape of the container in which the samples are held, but if these parameters are fixed, the frequency is found to decrease with increasing aqueous content of the cubic samples. Small-angleX-ray and neutron scattering measurements from samples covering much of the cubic region in the system DDAB/DpO/octane have been described in detail elsewhere.10 These results indicate a systematic increase in the lattice parameter, and a . transition from a structure of diamond symmetry (space group Pn3m) to one of bcc symmetry (space group Im3m) as the aqueous volume fraction of the system is increased. Figure 2 shows the X-ray diffraction pattern of a sample showing diamond symmetry. The microstructure of this system is such that the surfactant bilayer containing the paraffinic tails and the oil may be visualised as decorating a Schwarz-D minimal surface in such a way that the latter constitutesthe mid-surfacebisecting the bilayer. We have carried out rheological measurements on samples both in the diamond and bcc regions of the cubic domain. We report here results from two representativesamples whose composition is given in Table 1. Strain Sweep. Figure 3showsastrainsweepforsample 2 at a frequency of 10 rad/s. The shear moduli are independent of strain up to a critical applied strain. Beyond this value, the material breaks down and the elastic modulus decreases. We have found that for most of our ternary cubic gels this limit of viscoelastic behavior is ca. 1-5 % strain. There is some frequency dependence of this limit, with the materials becoming nonlinear at smaller strains as the frequency is increased. Figure 3 also shows
Langmuir, Vol. 10, No. 1, 1994 63 IOBI
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the strain-dependent enhancement of G" which is typical of these materials. The high-strain form of both G' and G" scales with the strain X as A-l over nearly 3 decades in strain. This is also seenin Figure 3. Such behavior is most straightforwardly modeled by assuming that the network ruptures along planes parallel to the shear planes at strains X = 1and a t some critical shear stress u,, beyond which the stress increases only marginally for further strain. The nonlinear function G*(X,w) is defined so that the stress and strain are related in modulus and phase in the same way as in the linear limit. We therefore find for this model of highstrain behavior that G'(X,w)X (1) Moreover the dissipation per cycle for such a fluid is clearly =Xuc. This is related to the dissipative part of G*(X,w) so that u,
Xu, z G"(X,w)X2 (2) Thus both real and imaginary parts of the complex nonlinear modulus scale as A-' for large strains. The rise in the imaginary component occurs when this method for dissipation sets in 8s the critical stress is reached. This simple rupture model also provides us with an estimate of the energy required to rupture an element of the minimal surface (by an element we mean a locally tubular branch of the surfactant network). At strains of order 1,the energy stored elastically per unit cell is G'a3, where a is the lattice parameter of the cubic phase. We must allow the possibility of there being several (N) units separating dislocation planes, so that the energy to rupture a part of the network is not necessarily entirely local elastic energy. In this case we have the inequality
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Figure 4. Frequency sweep of (a, top) sample 1at 25 f 0.5 O C and (b, bottom) sample 2 at 27 f 0.5 O C , both at 0.5% strain. Note the maximum in G" at intermediate frequencies, and the high-frequency plateau in G', while G' G" at low frequencies, particularly for sample 2. gels exhibited interesting viscoelastic behavior. Roomtemperature plots of G'(w) and G"(o) are given in Figure 4a for the bcc gel and Figure 4b for the diamond gel. Both demonstrate a high-frequency plateau reminiscent of polymer solutions. Moreover, the dissipative modulus G"(o) has a maximum for both samples (at o- zz 1 s-1 for the bcc gel and at w- = 10 s-l for the diamond gel). The third characteristic property of viscoelastic fluids, that G" > G' a t low frequencies, is also satisfied, though the actual characteristic time scales make this clearer for the diamond gel. In this case we clearly observe the low over 3 decadesin frequency. frequencystructure (o
