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Langmuir 2000, 16, 1042-1049
Phase Behavior and Phase Structure of a Cationic Fluorosurfactant in Water Ke Wang,† Greger Ora¨dd,‡ Mats Almgren,*,† Tsuyoshi Asakawa,§ and Bjo¨rn Bergenståhl| Department of Physical Chemistry, Uppsala University, P.O. Box 532, S-751 21, Uppsala, Sweden, Department of Physical Chemistry, Umeå University, S-90187, Umeå, Sweden, Department of Chemistry and Chemical Engineering, Kanazawa University, Kanazawa 920, Japan, and Department of Food Technology, Lund University, P.O. Box 124, S-221 00, Lund, Sweden Received July 20, 1999. In Final Form: September 27, 1999 The phase behavior of the cationic fluorocarbon surfactant 1,1,2,2-tetrahydroperfluorodecylpyridinium chloride in water has been studied using small-angle X-ray and 2H NMR spectroscopy as the main techniques. The following phase sequence was found: micellar (L1), hexagonal (HI), centered rectangular (R; spacegroup c2mm) and centered trigonal (T, spacegroup R3 h m) with increasing surfactant concentration. At higher concentrations evidence for random mesh phase and a lamellar phase was found, at high temperatures a bicontinuous cubic phase was found. Compared to a cationic hydrocarbon surfactant of similar hydrophobicity, the occurrence of the intermediate phases is more extensive in the phase diagram, and the fluorocarbon surfactant prefers to form intermediate phases instead of a cubic phase. The surface curvature of the aggregates changes from highly curved cylindrical structures of the hexagonal phase to the planar bilayer structure of the lamellar phase over a sequence of geometries that allow the average of the mean curvature to change gradually as water content is decreased.
Introduction The phase behavior of normal hydrocarbon surfactants has been fairly well studied.1-3 Most hydrocarbon surfactant-water mixtures form a micellar (L1) phase at low concentrations and several lytropic liquid crystal phases at higher concentrations. The most common and best characterized are the hexagonal (HI) and lamellar (LR) phases. The hexagonal phase consists of rod-shaped micelles of indefinite length packed in a hexagonal array, whereas the lamellar phase consists of infinite continuous bilayers separated by water layers. In some systems a variety of phases have been reported to exist between the hexagonal and lamellar phases,4 such as bicontionous cubic and the so-called intermediate phases.5 The intermediate phases between the hexagonal and lamellar phase have structures that fill the gap between the rather strong spontaneous curvature giving the cylindrical structure of the hexagonal phase and the zero curvature of the bilayers in the lamellar phase. The intermediate phases are anisotropic and birefringent and exhibit nonuniform interfacial curvature. They are more probable to occur with long or rigid alkyl chains. The different structures proposed for the intermediate phases in surfactant-water mixtures were reviewed by Holmes.5 Rectangular and mesh intermediate phases with a variety of symmetries have been identified in a number of systems. Fluorocarbon surfactants have many properties in * To whom correspondence should be addressed. † Uppsala University. ‡ Umeå University. § Kanazawa University. | Lund University. (1) Luzzati, V. In Biological Membranes; Chapman, D., Ed.; Academic Press: London, 1968; Chapter 3. (2) Ekwall, P. In Advances in Liquid Crystals; Brown, G. H., Ed.; Academic Press: London, 1971; Vol. 1, Chapter 1, p 1. (3) Tiddy, G. J. T. Phys. Rep. 1980, 57, 1. (4) Fontell, K. Adv. Colloid Interface Sci. 1992, 41, 127. (5) Holmes, M. C. J. Curr. Opin. Colloid Interface Sci. 1998, 3, 485.
common with their hydrocarbon analogues. Like normal hydrocarbon surfactants, they can self-assemble into various surfactant aggregates, depending on conditions such as water content, temperature, electrolyte concentration, etc. They form micelles in dilute water solution, and liquid crystalline phases at higher concentrations. A review of the self-assembly in fluorocarbon surfactant systems was recently presented by Monduzzi.6 The same sequence of phases is often found as in a hydrocarbon surfactant-water mixture: L1, HI, possibly intermediate phases, and LR.7-14 In early work, Tiddy and co-workers7-10 found hexagonal, lamellar, and intermediate phases in ammonium and lithium perfluorooctanoate. Fontell and Lindman11 presented a family of phase diagrams for perfluorononanoate with different counterions. It is striking that the lamellar phase is dominant in many of the systems and often appears as the first liquid crystalline phase, at rather high water content. Boden and coworkers12-14 studied the phase diagram of cesium perfluorooctanoate, where a nematic phase was found. Compared to normal hydrocarbon surfactants, fluorocarbon surfactants prefer to form structures with less curvature. Recently we made a study of the aggregation behavior of fluorocarbon surfactants in aqueous solutions.15 It was found that the growth of long micelles starts (6) Monduzzi, M. J. Curr. Opin. Colloid Interface Sci. 1998, 3, 467. (7) Tiddy, G. J. T. Symp. Faraday Soc. 1971, 5, 150. (8) Tiddy, G. J. T. Trans. Faraday Soc. 1972, 68, 653. (9) Tiddy, G. J. T.; Wheeler, B. A. J. Colloid Interface Sci. 1974, 47, 59. (10) Everiss, E.; Tiddy, G. J. T.; Wheeler, B. A. J. Chem. Soc., Faraday Trans. 1976, 72, 1747. (11) Fontell, K.; Lindman, B. J. Phys. Chem. 1983, 87, 3289. (12) Boden, N. In Micelles, Membranes, Microemulsions, and Monolayers; Gelbart, W. M., BenShaul, A., Eds.; Springer: New York, 1994. (13) Boden, N.; Jackson, P. H.; McMullen, K.; Holmes, M. C. Chem. Phys. Lett. 1979, 65, 476. (14) Holmes, M. C.; Reynolds, D. J.; Boden, N. J. Phys. Chem. 1987, 91, 5257. (15) Wang, K.; Karlsson, G.; Almgren, M.; Asakawa, T. J. Phys. Chem. 1999, 103, 9237.
10.1021/la9909603 CCC: $19.00 © 2000 American Chemical Society Published on Web 11/11/1999
Fluorosurfactant in Water
at lower concentrations of surfactant and salt than for the corresponding hydrocarbon surfactants. Among the lyotropic liquid crystalline phases, fluorocarbon surfactants often seem to prefer formation of intermediate phases instead of a cubic phase between the hexagonal and lamellar phase. The reasons for this preference is not fully understood. Tiddy and coworkers16-18 concluded that it depends on the balance between interfacial curvature and the conformational restrictions of the hydrophobic chain. The fluorocarbon chain is stiffer with less conformational freedom than the hydrocarbon chain due to the larger energy difference between gauche and trans conformations.16 Most of the earlier work on the phase behavior of fluorosurfactants was connected with anionic surfactants. Due to difficulties in synthesis, much less is known about the cationic fluorosurfactants. The phase behavior of the cationic fluorosurfactant 1,1,2,2-tetrahydroperfluorodecylpyridinium chloride (HFDePC) which was synthesized and studied earlier,15,19-21 is the subject of the present investigation. The phase diagram was determined by visual inspection using crossed polaroids, small-angle X-ray scattering (SAXS), and 2H NMR spectroscopy. The phase diagram shows that a number of intermediate phases occur over a broad range of compositions and temperatures. The detailed structural information was provided by SAXS, with NMR as a complementary technique to characterize the different phases. Originally, our aim was to investigate the phase behavior of a mixture of a fluorocarbon and a hydrocarbon cationic surfactant, i.e., the system C16TAC(cetyl trimethylammonium chloride)-HFDePC-water, and in particular look for effects from demixing in the lyotropic liquid crystalline phases, as a counterpart to the demixing found in the micellar phase.20,21 The complexity of the two-component system was not anticipated, and so far most of our efforts have been devoted to this system. Experimental Section Samples. The cationic fluorocarbon surfactant 1,1,2,2-tetrahydroperfluorodecylpyridinium chloride (HFDePC) was synthesized as described earlier.19 The purity of the synthesized surfactants was checked with high-performance liquid chromatography. The chromatograms gave no indication of impurities. Deuterated water of 99.9% purity was obtained from Aldrich. Samples of HFDePC/H2O mixtures used in the crossed polaroids experiments were prepared by carefully weighing appropriate amounts of surfactant and H2O into 5 mm glass vials, which were then flame sealed. The samples were centrifuged back and forth, until phase equilibrium was assumed to be attained after 1 week of periodical mixing. After that, the samples were stored at 25 °C for at least 4 weeks. Samples of HFDePC/D2O used in the SAXS and NMR measurements were prepared into 5 mm NMR tubes, in the same way as described above. Optical Birefringence. Samples of HFDePC/H2O mixtures were examined without and between crossed polaroids by the naked eye, for homogeneity and birefringency at different temperatures up to 210 °C. The observations were made in a thermally controlled chamber. In the temperature range 25150 °C, visual observations of birefringency were made on samples (16) Tiddy, G. J. T. In Modern Trends of Colloids Science in Chemistry and Biology, Eicke, H. F., Ed.; Birkhauser Verlag: Basel, Switzerland, 1985; p 158. (17) Hall, C.; Tiddy, G. J. T, In Surfactants in Solutions; Mittal, K. L., Ed.; New York, 1989; Vol. 8, p 9. (18) Kekicheff, P.; Tiddy, G. J. T. J. Phys. Chem. 1989, 93, 2520. (19) Asakawa, T.; Hisamatsu, H.; Miyagishi, S. Langmuir 1995, 11, 478. (20) Asakawa, T.; Hisamatsu, H.; Miyagishi, S. Langmuir 1996, 12, 1204. (21) Almgren, M.; Wang, K.; Asakawa, T. Langmuir 1997, 13, 4535.
Langmuir, Vol. 16, No. 3, 2000 1043 in glass vials. In the temperature range 150-210 °C, the observations were made on very small samples in thin capillaries. SAXS. Small-angle X-ray diffraction experiments were performed on Station 8.2 of the Daresbury Laboratory, England, using a monochromatic beam of wavelength 1.54 Å. The camera length was 1.5 m. The samples were transferred to a 1 mm thick sample holder with thin mica windows which was mounted on the heating element of a modified THM 600 thermally controlled microscope stage. Sample temperature was initially held at 25 °C for 2 min and was then raised to 65 °C at a rate of 5 °C/min. It was then kept at 65 °C for 2 min before returning to 25 °C at a rate of 10 °C/min, where it was again held for a couple of minutes. All measurements were monitored by a thermocouple embedded in the sample adjacent to the beam. No changes in the diffraction patterns were observed during the constant temperature periods. Furthermore, the observed phase transitions were centered at the same temperature on both the heating and the cooling scans, indicating that the samples were close to thermal equilibrium at all times. Calculations of Aggregate Dimensions. Calculations of the aggregate dimensions were made using relations between the volume fraction of HFDePC and the lattice parameters of the hexagonal and rectangular phase, obtained from SAXS. The volume fraction φ of HFDePC was calculated by using 1.4217 g/cm3 as the density of the surfactant. The density was estimated by performing density measurements in aqueous micellar solutions. Since only the hydrophobic chain of HFDePC was assigned as being part of the hydrophobic core while the headgroup was considered to belong to the hydrophilic domain of the hexagonal and rectangular phase, the volume fraction φ′ of the alkyl chain of the surfactant (CF3(CF2)7CH2CH2) was used in the calculations of the aggregate dimensions. The volume of the tail was estimated as 425 Å3 by summing the molecular group volumes,15,22 whereas 656 Å3 was used for the molecular volume of HFDePC. NMR. 2H measurements on 2H2O were performed on a wideband probe on a Varian CMX-400 Infinity system using a quadrupole echo23 sequence with a 900 pulse length of 30 ms and pulse separation time 100 µs. Temperature was held within 1 °C by a heated air stream passing the sample. Measurements were made at 25-75 °C in 10 degree steps with a waiting time of 20 min at each temperature. Analysis of Deuterium NMR Spectra. Detailed theoretical analysis of the static quadrupole line shapes for lyotropic liquid crystalline systems are abundant in the literature (see for example refs 24-27). Here only a brief introduction of the topic will be given. The deuterium line shape is governed by three parameters, namely, the motionally averaged quadrupole coupling constant, 〈χ〉, the asymmetry parameter, η, and the angular distribution function, f(θ,φ), of the polar and azimuthal angles that specify the orientation of the principal axis system with respect to the main magnetic field. The quadrupolar frequency is defined as27
νq(θ,φ) )
3 〈χ〉(3 cos2 θ - 1 + η sin2 θ cos 2φ) 8
For cylindrically symmetric geometries η ) 0, and if the angular distribution is random, one gets the well-known “powder pattern” line shape featuring a pair of “peaks” at (3〈χ〉/4 (θ ) 90°) and a pair of “shoulders” at (3〈χ〉/2 (θ ) 0°) from which 〈χ〉 can be obtained directly. If the orientation of the molecules is not random but is peaked around some preferred value, the intensities of the powder pattern line shape will be modified. If, for example, the θ-distribution is weighted toward the 0° orientation, the intensity of the shoulders will be enhanced. (22) Tanford, C. The hydrophobic effect: Formation of micelles and biological membranes; Wiley: New York, 1973. (23) Davis, J. H.; Jeffrey, K. R.; Bloom, M.; Valic, M. I.; Higgs, T. P. Chem. Phys. Lett. 1976, 44, 390. (24) Wennerstto¨m, H.; Lindblom G.; Lindman, B. Chem. Scr. 1974, 6, 97. (25) Chidichimo, G.; Vaz, N. A. P.; Yaniv, Z.; Doane, J. W. Phys. Rev. Lett. 1982, 49, 1950. (26) Quist, P.-O.; Halle, B. Mol. Phys. 1988, 65, 547. (27) Davis, J. H. Biochim. Biophys. Acta 1983, 737, 117.
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Wang et al.
Figure 2. Partial phase diagram for the HFDePC/D2O system. Nomenclature: L1, isotropic micellar solution phase; HI, hexagonal phase; R, centered rectangular phase; T, centered trigonal phase (rhombohedral).
Phase Behavior. A rough composition-temperature partial phase diagram of the HFDePC/H2O system, constructed by visual inspection of the samples, is shown in Figure 1, where we can locate regions of isotropic and anisotropic phases. The upper boundary marks the temperature at which the birefringence of the liquid crystalline phases disappears on heating. At 25 °C samples containing up to 45% (w/w) HFDePC were fluid and optically isotropic solutions of the L1 phase. Earlier transmission electron microscopy at cryogenic temperature (cryo-TEM) investigations15 showed that the L1 phase comprises globular micelles at low surfactant concentrations and rodlike micelles at high surfactant concentrations (11% (w/w)). Samples containing 45% (w/w) or more HFDePC were nonfluid and birefringent liquid crystalline phases. The demarcation line between fluid isotropic and nonfluid anisotropic phase regions is shown in Figure 1 for the temperature range 25-150 °C. A nonfluid and nonbirefringent phase, found in a narrow region at elevated temperature, is indicated as a hatched region in the diagram. At high temperatures the most concentrated samples were fluid and birefringent; this region is indicated as the dotted area in Figure 1. The observations above 150 °C were made in a complementary experiment. To save material, very small samples were prepared in
capillaries, and it was impossible to determine whether the samples were fluid or not. For all observations above 150 °C (dotted line) we have only observed the disappearance of birefringence and have no direct evidence of melting or a change of fluidity. A more detailed partial phase diagram for the system HFDePC/2H2O over a limited range of temperature, 2565 °C, is shown in Figure 2, based on data from SAXS and 2 H NMR. The following sequence of phases is found with increasing concentration: micellar (L1), hexagonal (HI), and two intermediate phases: centered rectangular (R) and centered trigonal (Rhombohedral) (T). With increasing temperature, the hexagonal to rectangular phase transition moved to higher concentrations, while the rectangular to trigonal phase transition was almost unchanged. The phase boundaries as determined by SAXS are in good agreement with the results from NMR. At higher concentration a random mesh phase and a lamellar phase were indicated as discussed below. SAXS. SAXS investigations were performed in the concentration range 47-86% (w/w) surfactant and in the temperature range 25-65 °C in the HFDePC/D2O system. Three separate diffraction patterns could be observed and were indexed to a hexagonal (HI), a centered rectangular (R, space group c2mm), and a centered trigonal phase (T, space group R3 h m) (also referred to as rhombohedral phase), respectively.30 Typically, 2 to 4 reflections were observed from the hexagonal phase, 7 to 9 reflections from the rectangular, and 10 to 12 reflections from the trigonal phase. The phases are characterized by the unit cell dimensions (a, hexagonal), (a,b, rectangular), and (a,c, trigonal). Figure 3 shows typical examples of different diffraction patterns from three samples in HI, R, and T phases, respectively, together with the calculated positions of the expected peaks. Table 1 shows the observed and calculated repeat distances, d, for the three samples together with the hkl indexation. At 25 °C the samples with 47-61% (w/w) HFDePC formed hexagonal phases. With increasing surfactant concentration the hexagonal phase transformed into intermediate phases; the samples containing 61-77% (w/ w) HFDePC formed rectangular phases while samples containing 77-86% (w/w) HFDePC formed trigonal phases. The H-R transition was accompanied by the disapperance of sharp diffraction peaks before new sharp peaks were formed, indicating large disorder in the sample upon the transformation. The sample with 64.1% (w/w) surfactant is believed to be very close to the phase transition line, and this caused hysteresis and equilibrium problems. At 65 °C the occurrence of micellar, hexagonal, rectangular, and trigonal phases was also found with increasing surfactant concentration. The samples with 4569% (w/w) HFDePC formed hexagonal phases. For HFDePC concentrations between 69 and 76% the rectangular phase was formed, while samples containing 7685% (w/w) HFDePC formed trigonal phases. A two-phase
(28) Gustafsson, S.; Quist, P.-O.; Halle, B. Liq. Cryst. 1995, 18, 545. (29) Persson, N.-O.; Lindman, B. J. Phys. Chem. 1975, 79, 1410.
(30) Hahn, T. International Tables For Crystallography, 4th ed.; Kluwer Academic: Dordrecht, 1995.
Figure 1. A rough partial phase diagram for the HFDePC/ H2O system. Boundaries are marked by a solid line to locate the regions between isotropic and anisotropic phases. Temperature region 25-150 °C: L1, fluid isotropic phase; LC, nonfluid anisotropic liquid crystal phases. The hatched area indicates a nonfluid isotropic phase. The dotted area indicates a fluid anisotropic phase. For samples with biaxial symmetry the powder pattern will generally consist of three potential singularities corresponding to the angles (θ ) 90°, φ ) 0°), (θ ) 90°, φ ) 90°) and (θ ) 0°). An isotropic orientation gives one peak (θ ) 90°, φ ) 0°) and two shoulders (θ ) 90°, φ ) 90°) and (θ ) 0°). From the position of these one can get 〈χ〉 and η, but often orientation effects blur the line shape so that only a simulation of the lines can give the wanted parameters.28 The NMR quadrupole splittings of 2H2O are generally rather narrow due to fast exchange between bound sites and isotropically “free” water.29 This exchange will scale down 〈χ〉, thus giving small quadrupole splittings that can be difficult to resolve. Therefore it is advantageous to use deuterated surfactants where the splitting is typically tenths of kilohertz for line shape analyses. In this work, NMR on deuterated water only will be presented; therefore no attempts have been made to simulate the line shapes, instead a rather qualitative description of the NMR data will be given in the Discussion. More detailed discussions, together with results from measurements on samples prepared with deuterated surfactant, will be reported elsewhere.
Results
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Langmuir, Vol. 16, No. 3, 2000 1045
Figure 3. Small-angle X-ray scattering at 25 °C from samples at (a) 60.6% (w/w) HFDePC/D2O in the hexagonal phase, a ) 51.2 Å; (b) 72.9% (w/w) HFDePC/D2O in the rectangular phase, a ) 38.9 Å, b ) 101.0 Å; (c) 79.7% (w/w) HFDePC/D2O in the trigonal phase, a ) 61.0 Å, c ) 105.0 Å. Table 1. Observed and Calculated Repeat Distances, d, for the Three Samples in HI, R, and T Phases, Respectively, Together with hkl Indexation hexagonal, a ) 51.2 Å
rectangular, c2mm, trigonal, R3 h m, a ) 38.9 Å, b ) 101.0 Å a ) 61.0 Å, c ) 105.0 Å
dobs hkl dcalc
dobs
hk
dcalc
dobs
hkl
dcalc
44.2 10 44.3 25.6 21 25.6 22.2 20 22.2
50.5 36.3 25.5
02 11 13 04 20 22 15 06
50.5 36.3 25.5 25.2 19.4 18.2 17.9 16.8
47.3 37.4 35.0
101 102 003
47.2 37.2 35.0
30.7 25.8
110 201
30.5 25.6
23.6
202 104 113 211 105 212 204 300 006
23.6 23.5 23.0 19.6 19.5 18.7 18.6 17.6 17.5
19.4 18.1 16.9 16.8
23.1 19.6 18.7 17.5
behavior could be observed in the sample with 76.4% (w/ w) surfactant. Two distinct diffraction patterns, superposed on each other, could be observed at higher temperatures and they could be indexed to the rectangular and the trigonal phase, respectively. The transition to trigonal phase was only partial at 65 °C, with peaks belonging to both phases present in the diffractogram. On returning to 25 °C the peaks assigned to the T phase gradually disappeared again. For the most concentrated sample with 85.7% (w/w) HFDePC, the diffractogram at 65 °C only gives two sharp peaks at distances 33 and 16.5 Å, together with a broad reflection centered at 44 Å. This is characteristic for the so-called random mesh structure, Mh(0), which consists of stacked bilayers that are pierced
Figure 4. Unit cell parameters for different phases at (a) 25 °C, (b) 65 °C. H, hexagonal phase; R, centered rectangular phase; T, centered trigonal phase. Mh(0), random mesh lamellar phase.
with water-filled defects randomly organized in the bilayers.31-33 As this phase was only observed at one temperature for the most concentrated sample, we refrain from any further discussion of this proposed random mesh phase, but it can be mentioned that cross-polarized microscopy also indicates another intermediate phase in the system and in addition a lamellar phase.34 A concentrated sample (92.8% (w/w)) was investigated with SAXS. Only one peak, corresponding to d ) 34.0 Å at 25 °C and d ) 33.2 Å at 65 °C, was obtained in the d-range accessible in this measurement (d ) 125-25 Å). Since no broad reflection was present, this sample most probably represents a lamellar phase. To summarize the results at both temperatures, Figure 4 shows the unit cell parameters from all samples: for the hexagonal (a), the rectangular (a, b), and the trigonal (a, c) phases. The letter symbols indicate the observed phases. The spectra of two-phase samples appear as the superposition of the individual phase spectra; therefore the parameters for both phases have been plotted in the figures. As the temperature was raised, the hexagonal to rectangular phase transition moved to higher concentrations while the rectangular to trigonal phase transition was almost unchanged. The phase transition temperatures for all the samples from 25 to 65 °C were obtained with SAXS and indicated in Figure 2. NMR. No distinct assignments of the different phases can be made from the deuterium line shape of the (31) Gustafsson, J.; Ora¨dd, G.; Almgren, M. Langmuir 1997, 13, 6956. (32) Kekicheff, P.; Cabane, B.; Rawiso, M. J. Phys. Lett. 1984, 45, 813. (33) Fairhurst, C. E.; Holmes, M. C.; Leaver, M. S. Langmuir 1997, 13, 4964. (34) Tiddy, G. J. T. Private communication.
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Figure 5. 2H NMR spectra from the same samples as in Figure 3. The arrows in the figure indicate from left to right the three singularities (θ ) 0°), (θ ) 90°, φ ) 90°), and (θ ) 90°, φ ) 0°) of the biaxial line shape.
deuterated water alone. Combined with the SAXS assignments, it is however possible to observe several characteristics of the line shapes. Figure 5 shows NMR spectra from three samples in the hexagonal, rectangular, and trigonal phases at 25 °C, the same samples as in Figure 3. The hexagonal phase (top) is characterized by a pair of sharp peaks. The rectangular phase (middle) has broader line shapes featuring one pair of peaks plus a second, poorly resolved, pair of peaks closer to the center of the line shape, indicating a biaxial symmetry. There are also indications of the shoulders in the line shape. Finally, the line shape from the trigonal phase (bottom) shows one sharp pair and one broad pair of peaks. None of the observed line shapes are compatible with the powder pattern associated with randomly oriented microdomains. Instead, these line shapes indicate a nonrandom orientational distribution centered around θ ) 90° for the hexagonal and around θ ) 0° for the trigonal phase. The rectangular line shape shows biaxial character, at least for the higher concentrated samples. In Figure 6 the residual quadrupole coupling constant, 〈χ〉, defined in eq 1 is plotted as a function of the molar ratio of surfactant to water at 25 and 65 °C. (For the calculation of 〈χ〉, see Discussion.) The data from the hexagonal and rectangular phases fall on a single line passing the origin, while this strict proportionality is missing for the data from the trigonal phase. Note that some of the values of 〈χ〉 for the rectangular phase are only estimates based on the assumption of constant η as discussed in the next section. Discussion SAXS. The hexagonal phase consists of infinitely long cylinder-like aggregates packed in a hexagonal array and separated by a continuous water region. In this region
Wang et al.
Figure 6. Residual quadrupole coupling constant 〈χ〉 as a function of surfactant to water molar ratio at (a) 25 °C, (b) 65 °C.
the X-ray diffraction patterns clearly identified the phase as a classical hexagonal structure, there being two to four reflections with d-values in the ratio 1:x3:x4:x7. The hexagonal lattice parameter a, which represents the distance from the center of one cylinder to another, including the total diameter of the cylinder and the thickness of the water layer, can be calculated from the first-order Bragg spacing d in accordance with the expression:1
a ) 2d/x3
(1a)
The radii, r, of the cylinders in the hexagonal phase were estimated from:
r)a
( ) x3 φ′ 2
1/2
(1b)
The distance between the cylinders, dw, is given by the relation:
dw ) a - 2r
(1c)
The results for each sample in the hexagonal phase at both 25 and 65 °C are presented in Table 2 and Figure 7. The volume fraction, φ′, of the alkyl chain part of the surfactant is used in the calculations, and hence the values for the aggregate dimensions refer to the hydrophobic core of the aggregates. Parts a and b of Figure 7 show how these geometrical parameters extracted from the first-
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Langmuir, Vol. 16, No. 3, 2000 1047
Table 2. Parameters Obtained for the Hexagonal Phase at 25 and 65 °Ca a (Å)
r (Å)
Table 3. Parameters Obtained for the Rectangular Phase at 25 and 65 °C
d (Å)
% w/w
φ′
25 °C
65 °C
25 °C
65 °C
25 °C
65 °C
47.0 49.6 51.3 54.4 57.7 60.6 64.1 67.2 69.2
0.265 0.281 0.292 0.312 0.334 0.353 0.377 0.398 0.412
58.9 57.0 55.7 54.2 52.7 51.2 R/H R R
54.3 52.6 51.4 50.2 48.3 47.1 45.5 44.4 44.0
15.91 15.88 15.81 15.91 15.99 15.97 R/H R R
14.67 14.65 14.59 14.73 14.65 14.70 14.67 14.72 14.97
27.08 25.24 24.08 22.38 20.72 19.26 R/H R R
24.96 23.30 22.22 20.74 18.99 17.70 16.16 14.97 14.46
a The weight fraction of surfactant % w/w, the hydrophobic volume fraction φ′, the lattice parameter a, the radius of the cylinder r, and the thickness of the water layer dw. R/H, a two-phase sample of rectangular and hexagonal phase. R, the samples that are in the rectangular phase at 25 °C.
a (Å) % (w/w)
φ′
25 °C
67.2 69.2 72.9 76.4
0.398 0.412 0.439 0.464
41.2 40.4 38.9 37.7
65 °C
b (Å) 25 °C
H 100.0 H 99.4 38.3 101.0 R/T 102.8
A (Å2)
b/a 65 °C
25 °C
65 °C
25 °C
65 °C
H H 87.2 R/T
2.43 2.46 2.60 2.73
H H 2.28 R/T
820 827 862 899
H H 733 R/T
a The weight fraction of surfactant % (w/w), the hydrophobic volume fraction φ′, the lattice parameters a and b, the ratio b/a and the cross sectional area of the ribbon (A). H, the samples that are in the hexagonal phase at 65 °C (see Table 1). R/T, a two-phase sample of rectangular and trigonal phase.
Table 4. Parameters Obtained for the Trigonal Phase at 25 and 65 °Ca a (Å)
c (Å)
% (w/w)
φ′
25 °C
65 °C
25 °C
65 °C
79.7 82.6 85.7
0.488 0.510 0.534
61.0 59.2 60.0
56.5 55.0 Mh(0)
105.0 102.9 102.0
101.7 99.9 Mh(0)
a The weight fraction of surfactant % (w/w), the hydrophobic volume fraction φ′, the lattice parameters a and c. Mh(0), a random meshlike lamellar phase.
separated by a continuous water region. The lattice parameters a and b of the rectangular unit cell determined by SAXS are presented in Table 3. The results at 25 °C show that the short dimension of the unit cell decreases and the long dimension increases somewhat with increasing surfactant concentration. With the lattice parameters of the unit cell determined, the cross sectional area of the ribbons in the rectangular phase can be calculated according to36
A ) 1/2φ′ab
Figure 7. Dimensions of the aggregates in the hexagonal phase of the HFDePC/D2O system at (a) 25 °C, (b) 65 °C as a function of the volume fraction (φ) of surfactant. The representative symbols are as follows: lattice parameter (a, x; the diameter of the cylinder, •; and the water layer thickness (dw), O.
order Bragg spacing depend on the volume fraction in the system at 25 and 65 °C, respectively. The results indicate that the radius of the rods is constant and that the thickness of the continuous water layer is decreasing with increasing surfactant concentration. The mean radius of the cylinder r ) 15.9 Å is comparable to the all-trans chain length 16.1 Å, as calculated from the expression L/nm ) 0.306 + 0.130n, where n is the number of carbons in the tail.35 With increasing surfactant concentration the hexagonal phase transforms into a rectangular phase. The rectangular phase consists of infinitely long cylinder-like surfactant aggregates (ribbons) of noncircular cross section arranged on a two-dimensional rectangular lattice and (35) Boden, N.; Harding, R.; Gelbart, W. M.; Ohara, P.; Jolley, K. W.; Heerdegen, A. P.; Parbhu, A. N. J. Chem. Phys. 1995, 103, 5712.
where φ′ is the volume fraction of the hydrophobic alkyl chain part of the surfactant in the sample and the factor of 1/2 compensates for the two ribbons in each unit cell. The results are collected in Table 3 and show that the cross sectional area of the ribbon increases with increasing surfactant concentration and is larger than the cross sectional area of the circular cylindrical rods in the hexagonal phase, 794 Å2. Assuming the ribbon to have an elliptical cross section, with the short axis fixed by the radius from the HI phase, the ratio of the cross sectional areas in R and HI is equal to the ratio of the long and short axis of the ellipse. The ratio increases from 1.03 to 1.13 over the surfactant concentrations investigated. The small axial ratio is in accord with NMR results discussed below. With further increase of the surfactant concentration, the rectangular phase transformed into a trigonal phase. It can be described as bilayers pierced by water-filled pores forming a hexagonal mesh with the holes in one layer positioned over the nodes in the one below in an ABCA stacking, as discussed by Holmes and co-workers.5,37 This structure can also be described by a primitive rhombohedral unit cell, but this description is more difficult to visualize. The lattice parameters corresponding to the triple obverse trigonal cell [a ()b), c] were determined and are presented in Table 4 for 25 and 65 °C. In the (36) Gustafsson, S.; Quist, P.-O. J. Colloid Interface Sci. 1996, 180, 564. (37) Burgoyne, J.; Holmes, M. C.; Tiddy, G. J. T. J. Phys. Chem. 1995, 99, 6054.
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primitive rhombohedral cell this corresponds to the lattice parameters:
a′ ) b′ ) c′ )
1 x3a2 + c2 3
[ ]
c2 3 a2 2 R′ ) β′ ) γ′ ) arccos 2 c +3 a2
For further details, see section 2.1 in ref 27. Note that the c value corresponds to the distance over three bilyers, i.e., the distance between two “A” layers in the ABCA stack. Thus, the separation between the center of two adjacent bilayers is c/3. NMR. The NMR spectra from the hexagonal phase are not in the form of powder patterns. Instead, the 90° peaks have enhanced intensity, indicating that the hexagonal rods preferentially orient with their axis perpendicular to the main magnetic field. The residual quadrupole constant, 〈χ〉, can be calculated as 4∆νq/3 in the hexagonal phase, where ∆νq is the frequency difference between the two 90° peaks. On going into the rectangular phase the line shapes still show evidence of a preferred orientation perpendicular to the main magnetic field and now also show evidence of a nonzero η. This is manifested in a second pair of peaks closer to the center of the line shape. The outer and inner pair of peaks correspond to (θ ) 90°, φ ) 90°) and (θ ) 90°, φ ) 0°), respectively and 〈χ〉 and η can be calculated according to
2 〈χ〉 ) (∆νq(90,90) + ∆νq(90,0)) 3 η)
2 (∆νq(90,90) - ∆νq(90,0)) 3〈χ〉
Due to difficulties of resolving the inner splitting, 〈χ〉 and η could only be calculated for the two most concentrated samples in the rectangular phase, where the splittings were (barely) resolved. However, it was observed that η was constant for these two samples so, to make a rough estimation of 〈χ〉 for the two more diluted samples it was assumed that η would remain constant (approximately 0.5) over the whole rectangular phase. This would correspond to a constant axial ratio of the ribbons, something that has been found to be true in other systems.36 Under this assumption, 〈χ〉 can be calculated from the (θ ) 90°, φ ) 90°) peaks as
〈χ〉 )
4∆νq(90,90) 3(1 + η)
In the trigonal phase, the spectra again indicate cylindrical symmetry with orientation effects. In contrast to the hexagonal phase, the preferred direction of orientation is now parallel to the main magnetic field (θ ) 0), giving rise to enhanced intensity of the shoulders. 〈χ〉 can still be calculated from the inner splitting in the same way as for the hexagonal phase. The proportionality between 〈χ〉 and the surfactant/ water molar ratio indicated in Figure 6 is expected for the two-site fast exchange of water between bound and free sites, provided that the number of bound water molecules per surfactant and the motional averaging at the bound site is constant in the observed concentration range. The
Wang et al.
increase of 〈χ〉 can then be explained by the increasing weight of the bound water as water concentration is decreased. These requirements seem to apply to both the hexagonal and the rectangular phase, indicating that the microstructures of the two phases are quite similar. This implies that the axial ratio of the cylinders in the rectangular phase is close to unity, in accord with SAXS data. The data from the trigonal phase deviates from the line in Figure 6. For a transition from a hexagonal to a lamellar phase, one would expect 〈χ〉 to increase by a factor of 2 as a consequence of the loss of motional averaging given by fast rotation around the curved cylinders.38,39 This relation is no longer true for bilayers including structural defects. The occurrence of defects in the bilayer will enhance the motional averaging of the quadrupole interaction compared to a defect-free bilayer, resulting in a smaller 〈χ〉.31,40 The disproportionality between 〈χ〉 and the surfactant to water molar ratio for the trigonal phase can be rationalized if the number of bound water per surfactant changes with water content, something that has been observed in other systems at low water content.41 The Phase Diagram. Figures 1 and 2 summarizes the main features of the phase behavior as found in this study. Besides the hexagonal phase and the two intermediate phases firmly established, there is also some evidence for one more intermediate phase and, at high concentrations, a lamellar phase. A preliminary check by penetration polarization microscopy found evidence for an intermediate phase and a lamellar phase. The intermediate phase could be what we found from the SAXS data and tentatively assumed to be a random mesh phase. We must be rather cautious on this point, however, since it appears somewhat surprising that a random mesh phase follows a trigonal phase when the water content is decreased on the way toward the lamellar phase. One would rather expect ordering and interbilayer correlation to build up when the interactions between the bilayers increase with decreasing separation distance. A possible explanation would be that, starting with bilayers in the normal lamellar phase, there is at first a formation of only few hole defects and that the ordering in the trigonal mesophase is caused by the interactions between the holes when they become more numerous within the bilayer. The hatched and dotted areas in Figure 1 indicate an isotropic nonfluid and a anisotropic, rather fluid phase, respectively. It is tempting to assign the dotted area to the lamellar phase and the hatched area to a cubic bicontinuous phase (note that the cut off at 150 °C is not a phase border but indicates that the fluidity was not assessed above this temperature). From a comparison with the phase diagrams of C16TAC42 and C12TAC43 in H2O this makes sense. In the former system two intermediate phases were identified between the hexagonal and the lamellar phase. At higher temperature, and with the shorter chain length, the intermediate phases were replaced by a bicontinuous cubic phase, VI, and at high temperature and concentration by a lamellar phase. The phase transitions are seemingly displaced to high concentrations of surfactant in the fluorinated system. (38) Wennerstro¨m, H.; Lindblom, G.; Lindman, B. Chem. Scr. 1974, 6, 97. (39) Quist, P.-O.; Halle, B. Mol. Phys. 1988, 65, 547. (40) Gustafsson, J.; Ora¨dd, G.; Lindblom, G.; Olsson, U.; Almgren, M. Langmuir 1997, 13, 852. (41) Carvell, M.; Hall, D. G.; Lyle, I. G.; Tiddy, G. J. Chem. Soc. 1986, 81, 1. (42) Henriksson, U.; Blackmore, E. S.; Tiddy, G. J. T.; So¨derman, O. J. Phys. Chem. 1992, 96, 3894. (43) So¨derman, O.; Walderhaug, H.; Henriksson, U.; Stilbs, P. J. Phys. Chem. 1985, 89, 3693.
Fluorosurfactant in Water
This is partly due to the high density of the fluorocarbon, and a better comparison may be obtained using volume fractions. Using the volume fraction, φ′, of the hydrophobic tails we find the following: for C12TAC in water, L1 0.31, II 0.40, HI 0.60, VI 0.65 LR; for C16TAC in water, L1 0.35, HI 0.59, Int1 0.63, Int2 0.65 LR. The corresponding limits for the system with HFDePC are L1 0.26, HI 0.40, R 0.48, T 0.54, Int3 0.58 LR. It is now obvious that the hexagonal, intermediate, and lamellar phases all require higher surfactant volume fractions with C12TAC and C16TAC than with the fluorosurfactant. The effect may be somewhat exaggerated, since the pyridinium headgroup of the fluorosurfactant is larger than the trimethylammonium group of CnTAC, so that the interaction distances between the structures are more equal than what the volume fractions suggest, but the transition to a less curved structure still seems to occur at a lower volume fraction in the fluorinated case. This is in accord with the larger surfactant parameter and the general preference for less curved structures which we have discussed previously.15 In their studies of the phase behavior and the structure of the lyotropic liquid crystals in a number of cationic hydrocarbon surfactant-water systems, Blackmore and Tiddy44 demonstrated that a cubic bicontinuous phase between the hexagonal and lamellar phases was replaced (44) Blackmore, E. S.; Tiddy, G. J. T. J. Chem. Soc. Faraday Trans. 2 1988, 84, 1115.
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by intermediate phases at an alkyl chain length of 16, for both CnTAC and CnPC and the cubic phase also appears at higher temperature. A survey of the phase behavior of the fluorocarbon surfactants showed that intermediate phases are formed even at the shortest chain length (C7). Tiddy and co-workers suggested that a balance between the preferred interfacial curvature and the conformational restrictions of the surfactant is what determines whether cubic or intermediate phases will develop in the series of cationic hydrocarbon surfactants they studied. The behavior of the fluorinated surfactants, with their stiff fluorocarbon tail, fits well into this pattern. The stiffness of the tail, maybe in combination with the increased hydrophobicity, seems to impose rather severe packing constraints on the fluorosurfactants, so that they are less ready to accept deviations from the spontaneous curvature than are hydrocarbon surfactants and therefore seek to satisfy the demands, on average, by forming intermediate phases. Acknowledgment. Michael Holmes and Gordon Tiddy are thanked for helpful discussions and comments. TFR, the Swedish Research Council for Engineering Sciences, and NFR, the Swedish Natural Science Research Council gave financial support. LA9909603
