Langmuir 1994,10,2177-2187
2177
Divalent Surfactants. Experimental Results and Theoretical Modeling of Surfactant/WaterPhase Equilibria HBkan Hagslatt,* Olle Soderman, and Ben& Jonsson Division of Physical Chemistry 1, Chemical Center, Lund University, P.O. Box 124, S-22100 Lund, Sweden Received January 10, 1994. In Final Form: April 22, 1994@ The influence of the headgroup charge on the phase behavior of SurfactantJwater systems has been investigated. T w o binary phase diagrams with divalent surfactant and water are presented together with a ternary phase diagram for a system comprising a divalent (anionic)surfactant, a monovalent (anionic) surfactant and water (at 50 “C). The studied surfactants are dodecylpentamethyl-1,3-propylenebis(ammonium chloride) [DoPPDAC, CH3(CH2)11Nf(CH3)z(CH2)3N’(CH3)3 2C1-I, dipotassium dodecylmalonate W o M , C&(CHZ)&H(COO-K+)I and potassium tetradecanoate [KTD, C&(CHZ)~~CHZCOO-K+I. The absolute value of the average surfactant charge ( z )varies between 1and 2 for these systems. 2HNMR, crossed polarizing microscopy, and small angle X-ray scattering are the main techniques used in order to determine the phase diagrams. The isotropic phase region with micellar solution and discontinuouscubic phases is followed by a hexagonal phase. A lamellar phase is obtained only for low values of z, on account of the fact that the solubility temperature increases when z increases. T w o intermediate phases are obtained for z = 1.5,or less. One of these is a “ribbon phase,” presumably a centered rectangular phase, while the other may be an orthorhombic phase. The formation of the discontinuous cubic phase, which most likely is constituted by slightly prolate-shaped micelles, is strongly promoted by high z-values. Moreover,the presence oftwo different discontinuous cubic phases in the KzDoWwater system is indicated. Hence, the studied systems show the same succession of phases when the total surfactant concentration increases (although the number of phases varies between the systems), but they differ in that the phase transitions are shifted towards higher surfactant concentrations when z increases. These observations are in accord with theoretical predictions, as demonstrated by a phase diagram, which has been calculated by use ofthe Poisson-Boltzmann cell model. In addition, there is a marked decreasein the free amphiphile concentration when the total surfactant concentration increases above the critical micelle concentration for the case of the investigated divalent surfactants. This observation is also accounted for by PoissonBoltzmann cell-model calculations.
+
1. Introduction Surfactants are used in a great number of technical applications. Naturally, a detailed theoretical understanding on a molecular level is of great importance when designing surfactants so that they have special physical properties which make them useful for whatever application in which they are intended to be used. The interpretation of phase diagrams is one important source to gain such an understanding.lS2 Hence it would seem worthwhile to investigate to what extent the phase appearance is affected by the charge of the surfactant headgroup. Divalent surfactants have not been investigated in this respect until a few years ago, when we initiated such a project. In our first communication on this tropic we dealt primarily with different aspects of the micellar solution phase of the dodecyl-1,3-propylenebis(ammoniumchloride) (DoPDAC)/water system3 (the abbreviations used for the surfactants in this study are given in Table l),and the critical micelle concentration (cmc), the micellar aggregation number, the amphiphile self-diffusion coefficients, the monomer distribution outside the micelles and the pH in the solution were investigated. Comparisons were made with predictions of the models, based on the Poisson-Boltzmann cell-model, which have been developed by Jonsson and co-~orkers.*-~ This approach
* To whom correspondence should be addressed. @
Abstract published in Advance ACS Abstracts, June 15,1994.
(1)Ekwall, P.In Advances in Liquid Crystals; Brown, G. H., Ed.; Academic Press: New York, 1975;pp 1-142.
(2)Tiddy, G.J. T. Phys. Rep. 1980,57, 1-46. (3)Hagslatt, H.; Soderman, 0.; Jonsson, B.; Johansson, L. B.-A. J. Phys. Chem. 1991,95,1703-1710. (4)Jansson, B., Thesis, Lund University, 1981.
Table 1. Abbreviations and Molecular Structure of Some Different Surfactants DoPDA dodecyl-1,3-propylenebis(amine)
DoPDAC DoPPDAC DoTAC
K~DoM KTD
KzDoP KHDoP
CH~(CH~)~INH(CH~)~NH~ dodecyl-1,3-propylenebis(ammoniumchloride) CH~(CHZ)~~N+HZ(CH~)~N+H~ 2C1dodecylpentamethyl-1,3-propylenebis-
+
(ammonium chloride) CH~(CH~)~~N+(CH~)Z(CHZ)~N+(CH~)~ + 2C1dodecyltrimethylammoniumchloride C H ~ ( C H ~ ) I I N + ( C HC1~)~
+
dipotassium dodecylmalonate CH3(CHz)llCH(C00-K+)z potassium tetradecanoate CH3(CHz)llCHzC00- K+
dipotassium dodecylphosphate CH3(CH2)l10P032-2K+ potassium hydrogen dodecylphosphate CH3(CH2)1iOPH03-K+
has been successful in describing several features of monovalent surfactant/water systems. Also the observations made for the isotropic phase region of the divalent surfactant case (DoPDAC/water) could be accounted for by this model.3 The temperature-composition phase diagram for the binary DoPDACID20 system was also presented in that paper,3 while ternary phase diagrams for the DoPDACDoPDA (dodecyl-l,3-propylenebis(amine))l DzO system (at 25,37,50,and 60 “C)were demonstrated in a later publication.8 In this communication, we present the phase diagrams with water for two additional divalent surfactants, dodecylpentamethyl-l,3-propylenebis(5)Jonsson, B.;Wennerstrom, H. J. Colloid Interface Sci. 1981,80, 482-496. (6)Jonsson, B.;Wennerstrom,H. J.Phys. Chem. 1987,91,338-352. (7)Landgren, M.,Thesis, Lund University (1990). (8) Hagsliitt, H.; Fontell, K. J. Colloid Interface Sci., in press.
0743-7463/94/2410-2177$04.50/00 1994 American Chemical Society
Hagslatt et al.
2178 Langmuir, Vol. 10,No. 7,1994 (ammonium chloride) (DoPPDAC) and dipotassium dodecylmalonate (KzDoM), respectively, together with a ternary system with a divalent surfactant, a monovalent surfactant and water, KzDoM/KTD (potassium tetradecanoate)/D~O. These phase diagrams have been investigated primarily by means of crossed polarizers,heavy and small-angle water nuclear magnetic resonance (NMR), X-ray scattering (SAXS) measurements. Phase diagrams for a number of different systems with single-chain,monovalent ionic surfactants have previously been calculated by use of the above-mentioned PoissonBoltzmann cell-model procedure. These show the correct trends of the phase behaviour as compared to the experimentally obtained one^.^^^ Consequently, we will provide a theoretical phase diagram for a divalent surfactantlmonovalent surfactantlwater system, as calculated with this model. On the basis of these experimental and theoretical phase diagrams, we will state some conclusionsregarding the general effects ofthe headgroup charge on the aggregate shape and phase behavior of single-chain surfactants. In addition, the free surfactant concentrations above the cmc have been obtained by 'H NMR self-diffision measurements for DoPPDAC and KzDoM, and these are compared with the theoretically predicted values as obtained from the Poisson-Boltzmann cell model approach. The outline of this paper is as follows. We start by presenting the experimentally determined phase diagrams for the DoPPDAC/water,K~DoM/water,and K2DoM/KTD/ water systems. Then the 'H NMR self-diffision data for DoPPDAC/water and K~DohUwatersystems and the derived free surfactant concentrations are presented. Subsequently, the Poisson-Boltzmann cell model is introduced, and its prediction in the form of a phase diagram and free surfactant concentrations above the cmc are shown. Finally, we draw some general conclusions concerning the effect of headgroup charge on the aggregational process for single-chain, ionic surfactants. 2. Experimental Section 2.1. Materials. Dodecylmalonic acid, with a melting point of 118-120 "C (to be compared with the value 121-121.5 "C given by Shinodag), was obtained from Synthelec AB, Lund, Sweden. A potassium hydroxiddwater solution was gradually added to a dodecylmalonic acidhexandwater system until pH = 10 was reached for the water phase. The potassium content of the subsequently freeze dried crystals was determined by atomic absorption spectroscopyto 22.7f 0.4w t %, to be compared with the theoretical value of 22.4 wt %. Potassium tetradecanoate was a kind gift from Dr. Krister Fontell. The DoPPDAC was prepared by Synthelec AB, starting with the same batch of DoPDA as was usedin previous A batch ofDoPPDACd15, i.e., DoPPDAC with deuterium labeled N-CHs groups was also prepared by Synthelec AB. The chloride contents were 18.4w t % (DoPPDAC) and 17.7 wt % (DoPPDACd15), respectively, as determined by elemental analysis. These numbers equal the theoretical values for these compounds. The 2Hz0 (99.7%) was obtained from Norsk Hydro. 2.2. Sample preparation. Samples were prepared by adding the components directly to glass-tubes which were then flame sealed. The samples were homogenized by repeated heating and centrifugation back and forth, and they were then left for at least 1 month at mom temperaturebefore being studied by means of crossed polarizing microscopy, N M R and small-angle X-ray scattering. The composition of the samples is characterized by the total surfactant concentration, C,(in wt %), and the absolute value of the average surfactant charge, z z =IpPiI
(1)
where X,is the mole fraction of surfactant i with net charge 2,. (9) Shinoda, K. J . Phys. Chem. 19BB,59, 432-435.
2.3. Conductivity. The conductivityof a DoPPDAC solution that was gradually diluted with water was measured by a Metrohm 660 conductometer in order to obtain the critical micellar concentration (cmc). The conductivity of the pure HzO was approximately 1 x h - l . 2.4. IfI NMR Self-Diffusion Measurements. The lH Fourier transform pulsed-gradient spin-echo (FT-PGSE)NMR techniquelowas used on highly modified JEOL FXlOO and Varian XZllOO spectrometers in order to obtain the self-diffision coefficients of the different components in the samples at 26 f 1 "C with DzO as solvent. The diffusioncoefficients(0) were evaluated by fitting the equationlo
to the echo amplitudes, A, as obtained for different lengths, 6, of the gradient pulse. A0 is the echo amplitude in the absence of a gradient pulse, y is the magnetogyric constant, G is the strength ofthe gradient pulse, and A is the time interval between the gradient pulses. A nonlinear least-squares fitting procedure was used to obtain the self-diffusion coefficients. The experimental conditions, were as recommended by Stilbs.lo The diffusion coefficients of the micellar aggregates were obtained by adding a hydrophobic probe, hexamethyl disilane (HNDS), to the samples. The HMDS to amphiphile molar ratios were in all cases smaller than 1/65. 2.5. aB: N M R Measurements. A Bruker MSL-100spectrometer operating at 15.371 MHz was used for the 2HNMR measurements. The quadrupole echo technique was used, and standard phase cycling procedures were performed to reduce the influences from imperfections of the radio frequency pulses. 2.6. Small-AngleX-ray Scattering. The liquid crystalline structure of the different phases were identified by small-angle X-ray scattering measurements performed at 25 "C. A camera with pinhole collimationafter Kiessigll and nickel-filteredcopper Ka radiation was used, and the sample to film distance was 0.2085m. The values of the Miller indices for the actual space group12were f i s t assigned to the Bragg spacings obtained from the iilms when evaluating the diffractograms. The best values of the unit cell dimensions were then obtained by minimizing the s u m ofthe squared differences between the observed and the calculated Bragg spacings.
3. Heavy Water NMR The 2H N M R method is a powerful tool when determining phase diagrams of surfactantiwater systems, the main advantage being that no separation of multiphase samples is necessary. The spectra are in general different for different phases, and for multiphase samples the obtained spectrum are simply the sum of the individual spectra for each phase, weighted by the fraction of the studied species in the phases. Moreover, the band shape of the quadrupole spectra achieved from heavy water NMR measurements are dependent on the structure of the hydrophilid hydrophobic interface of the aggregates. Therefore the shape of these can be used in order to gain information of the aggregate structure of the phase. The appearance of the NMR bands have been analyzed in this respect in the literature, and refs 13-18 constitute some examples where such analyses can be found. Singlepeak spectra are obtained for the isotropic phases, while two 2HNMR absorption bands are obtained for (10) Stilbs, P. Prog. Nucl. Magn. Reson. Spectrosc. 1987,19, 1-45. (11) Kiessig, H. Kolloid 2.1942, 98, 213-221. (12) International Tables for X-ray Crystallography; The Kynoch Press: Birmingham, 1952; Vol. 1. (13) Wennerstriim, H.; Lindblom, G.; Lindman, B. Chem. Scr. 1974, 6, 97-103. (14) Davis, J. H. Biochim. Biophys. Acta 1983, 737, 117-171. (15) Chidichimo,G.;Vaz, N. A. P.;Yaniv,2.;Doane, J. W.Phys.Rev. Lett. 1982,49, 1950-1954. (16) Khan, A.; Fontell, IC;Lindblom, G.; Lindman, B. J.Phys. Chem. 1982,86,4266-4271. (17) Anderson, D. M. J. Phys., Colloq. 1990, C7, 1-18. (18) Quist, P.-0.; Halle, B. Mol. Phys. 1988, 65, 547-562.
Langmuir, Vol. 10,No. 7,1994 2179
Divalent Surfactants anisotropic liquid crystals. The energy connected with the separation ofthe absorption bands, i.e. the quadrupolar splitting, has a magnitude, A, which depends on the angle between the symmetry axis of the aggregate and the direction of the static magnetic field, 8 (among several other parameters). All values of 8 are present for a powder sample, and the resulting powder band shape is termed a Pake pattern. Pake patterns with asymmetry parameter, 11 = 0, are obtained for phases with a 3-fold (at least) symmetry axis, while Pake patterns with 0 < 7 5 1are obtained otherwise. The hexagonal and lamellar phases are examples of phases which belong to the former class while centered rectangular phases, with noncircular surfactant cylindersbelong to the latter (cf. Figure 3, where some spectra are presented). For heavy water NMR the values of 2A (where 2A is defined as the separation between the two outer edges of the spectrum, where 8 = 0) depend on the location of the water molecules with respect to the aggregate surfaces, but since the deuterium nuclei generally exchange rapidly between the different sites of the system, single Pake patterns are obtained. Therefore,the observed quadrupole splittings are inversely proportional to the water content of the system according to A = (nJn,)K
(3)
where n, and n, are the total number of surfactant molecules and water molecules in the system. In this definition, the asymmetry parameter is 11 = 1 - Ape&lA, where Ape& is the separation between the central peaks (cf. Figure 3). The value ofKis for most cases independent of n$n, for a certain phase, as long as there are “free” water molecules, i.e., water molecules with no rotational restrictions, present in the system. As mentioned above, information about the phase and aggregate structure can be obtained by analyzing the appearance of the obtained NMR spectra. Let us consider the normal type of anisotropic liquid crystalline phases (i.e. phases for which the hydrophobidhydrophilicinterface is curved toward the hydrocarbon-richpart) of hexagonal (hex), rectangular (rect), rhombohedral (rhom), orthorhombic (ortho), tetragonal (tet), and linear (lam) (i.e., lamellar phase) symmetries. The rectangular, rhombohedral, orthorhombic, and tetragonal phases are all examples of phases which are classified as intermediate phases, i.e., phases that form in the region between the hexagonal and lamellar phases. 19,20 The rectangular phases possess a two-dimensional symmetry while the other intermediate phases possess three-dimensional symmetries. The aggregates of the classical hexagonal and lamellar phases are circular cylinders and bilayers respectively, while the aggregates of the rectangular phases are long, noncircular ~ y l i n d e r s . ’ ~ JThere ~ - ~ ~ are indications that anisotropic, three-dimensional intermediate phases exist in several systems, see e.g. refs 23-36. (19)Luzzati, V.;Mustacchi, H.; Skoulios, A. E.; Husson, F. Acta Crystallogr. 1960,13,660-667. (20)Husson, F.; Mustacchi, H.; Luzzati, V. Acta Crystallogr. 1980, 13,668-677. (21)Hagslatt, H.; Soderman, 0.; Jonsson, B. Liq. Cryst. 1992,12, 667-688. (22)Hagslgtt, H.; Soderman, 0.; Jonsson, B. Liq. Cryst., in press. (23)Madelmont, C.;Perron, R. Colloid Polym. Sci. 1976,254,581595. (24)Rendall, K.;Tiddy, G. J. T.; Trevethan, M. A. J. Chem. Soc., Faraday Trans. 1 1983,79,637-649. (25)Kbkicheff, P.; Cabane, B. J.Phys. (Les ulis, Fr.) 1987,48,15711583. (26)Kbkicheff, P.; Cabane, B. Acta Crystallogr. 1988,44,395-406. (27)Kilpatrick, P. K; Bogard, M. A. Langmuir 1988,4,790-796. (28)Blackmore, E. S.;Tiddy, G. J . T. J . Chem. Soc., Faraday Trans. 2 1988,84,1115-1127.
Aggregates of two-dimensional as well as three-dimensional surfactant networks have been proposed for the tetragonal phase structure, while three-dimensional surfactant networks have been proposed for the rhombohedral and orthorhombic phase structures. In case of threedimensional networks, the structures of these phases and the structures of the isotropic, three-dimensional intermediate phases, i.e. the bicontinuous cubic p h a s e ~ , ~ ~ ~ ~ ~ differ mainly in that the networks have anisotropic extensions for the former class of phases. It is theoretically predicted that the constant K (cf. eq 3) for these different phase structures (under certain conditions, for example that “free”water molecules are present in the system) of a specific system are related according to13-18*21,33
Here it is assumed that the aggregate networks of the rhombohedral, orthorhombic, and tetragonal phases are formed by interconnected rods. For the case of the rectangular phase it is further assumed that the axial ratio of the aggregates normal sections are small, so that the “small deformation regime” a p p l i e ~ , ~ ~ J ~ * ~ ~ which appears to be the general situation for these phases.15,21,22,33,34,36,3g,40 The asymmetry parameters of these phases are13,15J7,33 qhex, h m , Vrhom, r t e t
=
(5)
0 < ~ o f i o , Prect
1
(6)
and 5
As pointed out above, for multiphase samples, the spectrum is the sum of the individual spectra for each phase. Subsequently, the type of phasdphases present may then be distinguished by comparing the band shapes of the obtained 2HNMR spectra. 4. Experimental Results We start this section by presenting the experimentally obtained phase diagrams, as the appearance of these will make the presentation of the experimental results (2H NMR spectra and SAX3 data), which then follow, clearer. We terminate the section by presenting some conductivity data and lH NMR self-diffusion data obtained in the isotropic phase region of the DoPPDACIwater and the KzDoWwater systems. 4.1. Phase Diagrams. Composition phase diagrams for the DoPPDACAI20 and the K2DoM/D20 systems at 25 “C are presented in Figure 1. The two systems show ~~~
(29)mkicheff, P.;Grabielle-Madelmont, C.; Ollivon, M. J. Colloid Interface Sci. 1989,131,112-132. (30)Kbkicheff, P. Colloid Interface Sci. 1989,131,133-152. (31)Kbkicheff, P.; Tiddy, G. J. T. J.Phys. Chem. 1989,93,25202526. (32)Auvray, X.;Perche, T.; Anthore, R.; Petipas, C.; Rico, I.; Lattes, A.Lungmuir 1991,7,2385-2393. (33)Henriksson, U.; Blackmore, E. S.; Tiddy, G. J. T.; Soderman, 0. J.Phys. Chem. 1992,96,3894-3902. (34)Kang, C.;SiAerman, 0.;Eriksson, P. 0.;Stael von Holstein, J . Liq. Cryst. 1992,6, 71-81. (35)Kilpatrick, P. K.;Blackburn,J. C.; Walter, T. A. Langmuir 1992, 8,2192-2199. (36)Blackburn, J.C.;Kilpatrick, P. K. J.Colloid Interface Sci. 1993, 157,88-99. (37)Lindblom, G.; Rilfors, L.Biochim. Biophys.Acta 1989,988,221256. (38)Fontell, K. Colloid Polym. Sci. 1990,268,264-285. (39)Chidichimo, G.;Golemme, A.; Doane, J . W.; Westerman, P. W. J . Chem. Phys. 1986,82, 536-540. (40)Blackburn, J. C.; Kilpatrick, P. K. J . Colloid Interface Sci. 1992, 149,450-471.
Hagslatt et al.
2180 Langmuir, Vol. 10, No. 7,1994 K2DoM
I
DoPPDAC
I
t
Ll
I
LI
,
'I
J'Ejl
I.C+C ._
11
1;Eq
LC+C .
Table 2. SAXS Results As Obtained from the Hexagonal Phases of the KfloM/D20 and the DoPPDACdldHzO Systems da(exp)/ da(calc)/
0I
:
:
20
:
'
40
:
:
60
:
: 80
:
&
1 )
wt% surfactant
Figure 1. Composition phase diagram for the DoPPDACPH20 and the K2DoWH20 systems at 25 "C. The micellar solution phase is denoted L1, I1 denotesdiscontinuouscubic phases, and E is a hexagonal phase, accordingto Ekwalls' notation. LC+C denotes regions with liquid crystalline phases plus hydrated surfactant crystals. No two-phase regions are included in the phase diagram. The resolution of the phase boundaries isbetter than 32.5 wt %.
samde 70wt%K2DoM
dn
A
A
dl d3
32.7 19.1 16.4
32.8 18.9 16.4
a/ &e
~~~~~
d4
37.9 0.517 14.3 70wt%DoPPDAC dl
d3
36.8 21.1
d4 d7
13.9
36.7 21.2 18.4 13.9 42.4 0.372 13.6
4.2. SAXS Measurements. SAXS measurements have been performed at 25 "C in order to determine the liquid crystalline structure of the K2DoM/D20 and DoPPDAC/D20 systems. Samples of the hexagonal phase are identified by two or three Bragg reflections, for which the corresponding relative Bragg spacings followthe sequence 1:1/43:1/d4:1/d7... etc.12 The Bragg spacings for a twodimensional hexagonal lattice and the unit cell dimension, a,are related through12
+
d, = 74 3( h 2 k2 - hk)-*2
*
wt% K ~ D o M
Figure 2. Composition phase diagram for the KzDoM/KTD/ 2H20 system at 50 "C. The distance between two ticks represents 10 w t %. R denotes a "ribbon" phase (presumably of centred rectangular (cmm)symmetry),D is a lamellarphase, and IN" is an intermediate phase, possibly an orthorhombic phase. Remainingnotationsare as defined in Figure 1. Shaded regions are multiphase regions, and the hatched lines of these are approximate tie-lines. About 130 samples have been investigated when determining the phase diagram.
essentially the same phase behavior. The micellar solution phase is succeeded by a discontinuous cubic phase, which in turn is followed by a hexagonal phase when the surfactant concentration increases. The surfactant concentrations at the phase transitions are also about the same for both surfactants, and this feature is true also if the surfactant concentrations are expressed in mollkg of solvent, since the molar masses of K2DoM (348.6 gmol-l) and DoPPDAC (385.5 gmol-l) differ only slightly. The effect of temperature on the phase behavior for the divalent surfactantiwater systems has not been extensively investigated. However, the phase boundaries are only slightly affected by the temperature (up to about 150 "C or so) for similar systems.1p2.8 Moreover, there are indications in favor of the presence of two different discontinuous cubic phases in the KzDoWwater system. The ternary phase diagram with K~DoM,KTD, and D20 at 50 "C is presented in Figure 2. As can be seen, the cubic phase is not present for low average surfactant charges. Furthermore, the temperature of 50 "C is sufficiently high to exceed the solubility temperature for the lamellar phase only at low average surfactant charges. Intermediate phases, i.e., phases that form in the region between the hexagonal and lamellar phase^,^^^^^ are obtained for z < 1.5. One of these phases is identified as a "ribbon phase" (cf. below) presumably with centered rectangular symmetry. The experimental 2H NMR data and SAXS-data underlying the phase diagrams of Figures 1 and 2 are presented in the following sections.
(7)
where the Miller indices, h and k , take all integer values. The experimentally obtained Bragg spacings are presented in Table 2, together with the unit cell dimensions, and corresponding Bragg spacings as obtained by minimizing the sum of the squared differences between the observed and calculated Bragg spacings. The radius, r,, of the assumed circular cylindrical aggregates, evaluated according to
are also given in Table 2. The hydrocarbon volume fraction (see ref 21) is used in the calculations, and hence the values for the aggregate dimensions given in Table 2 are for the hydrocarbon core of the aggregates. The micellar solution phase and the discontinuous cubic phase of the presently investigated systems are conveniently distinguished by their difference in viscosity (the cubic phase is highly viscous). The SAXS data obtained in the cubic phase region indicate a primitive cubic symmetry, but the quality of the data is not sufficient to determine the cubic space group or the unit cell lattice parameter. However, interesting to note is that, according to optical-microscope penetration investigations performed by Tiddy,4' two different discontinuous cubic phases are present at temperatures between 0 and 90 "C for the K2DoM/D20 system. 4.3. Water 2HNMR Splittings. For the binary, divalent surfactantiwater systems only one anisotropic liquid crystalline phase (a hexagonal phase) is obtained at temperatures below 50 "C. However, for low average surfactant charges of the K2DoM/KTD/watersystem, the situation is different. Therefore we have investigated this region of the phase diagram by means of 2H heavy water NMR band shape measurements. Spectra of four different anisotropic liquid crystalline phases were obtained by this method. Moreover, the spectra obtained in these phases have been analysed by taking into consideration the relations for the band shape of different phases given in eqs 3-6. Further aid in the process of identifjlng the (41) Tiddy, G. J. T. Unpublished results, 1981.
Divalent Surfactants
Langmuir, Vol. 10, No. 7, 1994 2181 1600 \
I \
M
0“ 0
0.05
0.1
0.15
0.2
I
0.25
%Inw
I\ Figure 3. Heavy water NMR spectra obtained for KTD/water samples at 50 “C, for (a) C, = 40 wt %, (c) C, = 55 wt % and (e) C, = 62 wt % surfactant. Corresponding simulated quadrupole NMR spectra, and the parameters used in the simulations are given in parts b, d, and f, respectively(LBis the applied Lorentzian line broadening). The total spectral width is 5000 Hz for all cases.
structure of the different phases is provided by the knowledge one has of the general succession of phases in similar single chain ionic surfactanvwater systems. As an example, consider the sodium dodecyl sulfate/water system, which displays a rich phase behavior. The phase sequence with increasing surfactant concentration for this system is24225330932 micellar solution phase-hexagonal phase-centered rectangular phase (cf., ref 21)-rhombohedral or orthorhombic phase-bicontinuous cubic phasetetragonal phase-lamellar phase. Similar systems follow the same succession of phases,lB2but not all of the phases are always present, and in addition discontinuous cubic phases are obtained at surfactant concentrations intermediate between those ofthe micellar solution phase and the hexagonal phase for some systems.38 Moreover, the KTD/water system has been investigated previously, and a micellar solution phase, a hexagonal phase, and a lamellar phase was identified in this system when the surfactant concentration was increased.42 In addition, there is a bicontinuous cubic phase at surfactant concentrations intermediate between those of the hexagonal and the lamellar phase (59-66 wt %) at 100 0C,19,20,43 No intermediate phases have, to the best of our knowledge, been reported at 86 oC.44However, the existence of two anisotropic intermediate phases has been indicated by the optical-microscope penetration technique.24 Some obtained 2HNMR spectra for the pure KTD/water system are reproduced in Figure 3 and the observed quadrupole splittings as a function of n$n, are represented in Figure 4. Pake patterns with 7 = 0 are obtained for the anisotropic phase region, which via a two-phase region follows the isotropic phase regions when the surfactant concentration increases. The location of this phase in the phase diagram and the band shape of the obtained 2H NMR spectra show that this phase has a hexagonal (42) McBain, J. W.; Sierichs, W . C. J.Am. Oil Chem. SOC.1948,25, 221-225. (43) Luzzati, V.; Tardieu, A.; Gulik-Krzywicki,T.; Rivas, E.; ReissHusson, F. Nature 1968,220, 485-488.
Figure 4. Quadrupole splittings for the for KTD/water system the hexagonal phase, ( 0 )the “ribbon”phase, (W) at 50 “C in (0) the INT phase, and (+)the lamellar phase. The solid line that starts at the origin does not represent a fit to the data, but is drawn only to facilitate the reading of the data. structure, in agreement with previous results.19,20,24,42,44 The value of K (cf. eq 3) within this phase is approximately constant along lines for which z is constant (Kx 9000 Hz for z = 1). For z .e 1.5 Pake patterns with 7 f 0 are obtained at surfactant concentrations around 60 wt %. K = 9000 Hz for these samples, which is about the same value as obtained for the hexagonal phase. These two observations strongly indicate (cf. eqs 4-6) that this phase belongs to the class of “ribbon phases”.45 Ribbon phases consist on noncircular, surfactant cylinder^,'^^^^-^^ which are packed on two-dimensional lattices possessing 2-fold symmetry axes only. At still higher surfactant concentrations, Pake patterns with 7 = 0 are again obtained, strongly indicating the existence of a lamellar phase (see also refs 19,20,24,42, 44). Kdoes not take its predicted values KI- = =hex (cf., eq 41, which may be caused by the low water content (less than six water molecules per surfactant) of the lamellar phase samples. A second intermediate phase is obtained a t a concentration of 62 wt % KTD, since a powder pattern with 7 = 0.3 and A = 600 Hz (corresponding to K x 5000 Hz)was obtained a t this concentration. The K value is considerably lower than the values of Khex and ICrea,and together with the fact that 7 t 0, this suggests that the phase has an orthorhombic structure, according to eqs 4-6. Similar spectra have been obtained for the Int-2 phase of the hexadecyltrimethylammonium chloriddwater system,33and an orthorhombic structure was tentatively assigned to this phase. This phase was reported to transform to a cubic phase with time (at least in its most concentrated regions). There is no indication that this would also be the case for the intermediate, possibly orthorhombic phase of the K2DoM/KTD/water system; however, the extension of this phase is quite limited with respect to the total surfactant concentration, and no single phase sample has been obtained for z > 1. For the sake of completeness, we note that three-dimensional structures with lower symmetries than the orthorhombic symmetry, i.e. the monoclinic and the triclinic symmetries would also be consistent with the NMR spectra obtained for the sample with 62 wt % KTD. Hence these symmetries cannot be ruled out as candidates for the structure of this intermediate phase. Monoclinic and triclinic phases have not yet been reported for lyotropic liquid crystalline systems (leaving aside the fact that ribbon phases with oblique symmetries have been discussed in the literature in terms of two-dimensional monoclinic). (44) Gallot, B.; Skoulios, A. Kolloid Z . 2.Polym. 1969,208, 37-43. (45) Balmbra, R. R.; Bucknall, D. A. B.; Clunie, J. S. Mol. Cryst. Liq. Cryst. 1970,11, 173-186.
Hagslatt et al.
2182 Langmuir, Vol. 10, No. 7, 1994 We have used the 2H NMR method to obtain the tielines of the two-phase region that separates the cubic and hexagonal phases for the KzDoM/KTD/water system. Tentative tie-lines for this biphase region, drawn on the basis that Ahex is approximately constant for the samples along the lines, are given in Figure 2. Finally, we note that the phase boundaries in Figure 2 are unchanged if the samples are leR for 1year. 4.4. Surfactant2H Splittings. The anisotropicliquid crystalline phase that follows the discontinuous cubic phase when C,is increased (cf., Figures 2 and 31, in both the binary and ternary systems, possesses a hexagonal structure. This is in accord with the general trend for single chain ionic surfactants. In order to investigate the state of the polar headgroup in the DoPPDACaldwater system, we have performed surfactant 2H NMR measurements for a sample with 70 wt % DoPPDACdl5 in H2O. A Pake pattern consisting of two superimposed 2Hbands, both with q = 0, is obtained at 25 "C. The splittings are Aout = 1.78kHz and Ain = 4.70 kHz,respectively,where Aoutrefers to the splittings of the outer -CD3 groups and Ain from the inner -CD3 groups. For a hexagonal phase the order parameter, S,ofthe C-D bond with respect to the aggregate symmetry axis is given by13
Using the value 167 kHz14 for the quadrupole coupling constant, x,Sout = 0.028 and Si,,= 0.075 are obtained. The value of S contains information about the motional restrictions the C-D bonds experience due to the presence of the hydrophobicfhydrophilic interface. To put the obtained values into perspective, it is interesting to compare them with the corresponding value of the analogous monovalent surfactant, i.e. to dodecyltrimethylammonium chloride (DoTAC) with the -CH3 groups in the headgroup replaced with -CD3 groups. The 2H quadrupole splittings for this molecule have been obtained in the hexagonal phase and the value is A ~ T A C = 1.95 x lo3 Hz a t 25 0C34(the value does not vary over the concentration interval of 76-82 wt % DoTAC of the hexagonal phase at this temperature). This yields an order parameter of SD~TAC = 0.031,i.e., a value which is close to that obtained for the outer -CD3 groups in DoPPDAC, while the value of S for the inner -CD3 groups is considerably larger (more than 3 times larger). Thus it would appear that the ordering of the outer -CD3 groups resembles that of DoTAC, while the two inner CD3 groups in DoPPDAC experience higher degree of restrictions in their motions. This implies that the N-C-C-C-N fragment is oriented with its axis normal to the aggregate surface (an interpretation which for electrostatic reasons seems reasonable) and furthermore is constrained in its motional freedom and does not perform large-amplitude motions. In view of the fact that available area for the outer trimethylammonium group of DoPPDAC is quite large for such a headgroup configuration (around 75 k assuming that the N-C-C-C-N fragment has a length of 5 A),it may appear surprising that the N-C-C-C-N fragment is so restricted in its motion. However, it is an experimental observation for many binary surfactantl water systems that the order parameter is only slightly affected by changes of the curvature of the hydrophobic/ hydrophilic interface and the value of the area that each polar headgroup occupies on (46) M61y, B.; Charvolin, J.;Keller, P. Chem. Phys. Lipids 1975,15,
161.
0.020
- 0.018 0
E 0.016
3
& .
0.014
< 0.012 0.010
I
1
I
I
I
-
-
I 1
2
4 6 cl/Z / moll/?.m - 3 1 2
8
10
Figure 6. Molar conductivity (A) of DoPPDAC solutions at 25 "C.
We end this section by noting that the quadrupolar splitting of deuterated choline-methyl groups in the lamellar liquid crystalline phase of dipalmitoyl-3-snphosphatidylcholine (DPPC)is around 1~ H Z The. order ~ parameter of the C-D bond with respect to the aggregate symmetry axis is for this case13
and therefore the order parameter is SDP~C = 0.008, which is considerably less than Soutfor DoPPDAC. This observationindicates tha theP-O-C-C-Nfiagment ofDPPC, if oriented with itg axis parallel to the director of the aggregate,experiences a notably higher degree of motional freedom than the N-C-C-C-N fragment of DoPPDAC does. An alternatively, perhaps more likely explanation, is that the zwitterionic group of DPPC has a bent structure with its positively charged trimethylammonium group in the vicinity of its negatively charged phosphate as proposed by Gally et al. 4.5. Critical Micelle Concentration. The cmc for M by DoPPDAC was determined to (4.8 f 0.2) x conductivity measurements at 25 "C, as presented in Figure 5. Published cmc-values for KzDoM at 25 "C are 4.8 x M and (4.7 f 0.2) x M obtained by M conductivity m e a s u r e m e n t ~and ~ ~ (5.5 ~ ~ f 0.2) x obtained by pH-mea~urements.~~ 4.6. Self-DiffusionStudy of the Isotropic Phase Regions. The aggregation process in the micellar solution phase and the cubic phase of the K2DoWwater and the DoPPDAC/water systems have been investigated by means of determining the self-diffision coefficientsof the surfactant, Dad and the micelles, Dfic. The FT-PGSE 'H NMR techniquelo was used in order to obtain these selfdiffision coefficients. The micellar self-diffusion coefficients were assumed to be equal to the diffusion coefficientsobtained for the HMDS molecules. The results for the DoPPDAC and -OM systemsare shown in Figure 6. The error in the diffusion coefficients,as obtained from fitting eq 2 to the raw PGSE echo data is typically smaller than f 2 % for Dad and f 5 % for DdC. No difference is noted for Dsd between the samples containing HMDS and the corresponding samples that do not contain HMDS, and it is therefore assumed that the aggregation number of the micelles is only slightly affected by the addition of this small amount of HMDS. The diffusion experiment (47) Sodeman, 0.; Henriksson, U. J. Chem. Soc., Faraday Trans.1 1987,83,1515-1529. (48)Gally, H.-U.; Neiderberger, W.; Seelig, J. Biochemistry 1976, 14, 3647-3652. (49) Brackman, J. C.; Engberts, J. B. F. N. Langmuir 1991, 7,4650.
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Langmuir, Vol. 10, No. 7, 1994 2183
10'~
c
50
Ll
g
n 10-12
10'3
L
0
10
I,
I
Q
P
W 0 0 0
i 50
60
I
20
30
40
wt% DoPPDAC
0
.
b 30 3
:20 5
10
0
0.2 0.4
0.6 0.8 1 C,,, / molal
1.2
1.4
1.6
Figure7. Free surfactant concentrationsas a function of total
(0) DoPPDAC and (0)&DoM concentrationrespectively, at 26 "C. The solid line represents the values as obtained from
Poisson-Boltzmann calculations. The parameters which are used in the calculations are given in the text.
0
5
10
15
20
25
30
35
40
wt% K,DoM Figure 6. Self-diffusioncoefficientsas a functionof surfactant concentration at 26 "C for (a, top) DoPPDAC and (b, bottom)
K~DoM,respectively. The total surfactant diffusion (U) and the HMDS/micellar diffusion (0)are marked. could not be carried out for the cubic phase samples of the K2DoM/D20 systems, due to rapid 'H transverse relaxation rate for these samples. The free amphiphile concentrations are evaluated by use of the equation60
where Pb is the fraction of micelle-bound surfactant and
Dh is the monomer diffusion coefficient, which is assumed to be equal to Dad as obtained below the cmc. The result is presented in Figure 7 where it can be seen that the surfactant monomer concentration decreases rapidly when the surfactant concentration increases above the critical micellar concentration. The effect of the surfactant headgroup charge on the investigated properties could be discussed qualitatively in terms of electrostatic contributions; however, we find it worthwhile also to make a more quantitative analysis of the data by comparing these with predictions made from the Poisson-Boltzmann cell model. This model and its prediction of the phase appearance and the micellar aggregation process for divalent surfactants are presented in the next section. 6. Thermodynamic Modeling of the Phase
Diagram In what follows we present a theoretical investigation of the influence of headgroup charge on the phase behavior of surfactant water systems. The theoretical framework used is the Poisson-Boltzmann cell model approach as ~
~~
~~~~~
developedby one ofthe authors and c ~ - w o r k e r s . ~These -~,~~ models predict phase diagrams with ionic, single-tailed surfactant and water nearly quantitatively. We have calculated the phase diagram for a system with water, a divalent surfactant, and a monovalent surfactant, for which both surfactant molecules have the same sign of the charge. The transition from the micellar solution phase to the hexagonal phase, as well as the transition from the hexagonal phase to the lamellar phase, is investigated in the calculations. The aggregates of the micellar solution phase are approximated by spheres with radius, r, the value of which is smaller than, or equal to, a certain length, r,,, and the aggregates of the hexagonal phase are assumed to be circular cylinders with r 5 r,,, while the bilayers are assumed to be flat and of infinite extension in two dimensions. The half-thickness of the bilayers is r Ir,,. The interior of the aggregates are modelled as a pure liquid hydrocarbon and the headgroups of the amphiphilic molecules are confined at the surface ofthe aggregates. Moreover, the aggregates are assumed to be monodisperse in shape and size. In the following two sections the basic assumptions pertaining to the Poisson-Boltzmann cell model are presented. For a more detailed analysis refs 4-6,51 should be consulted. 6.1. The Thermodynamic Model. The electrostatic interactions between the ions provide important contributions to the free energy of ionic surfactant systems, and these w i l l be described by the Poisson-Boltzmann equation. The electrostatic energy ofthe system is conveniently divided into one energy term
and one entropy term which describes the entropy of mixing of the ions in the water region
-TS-
= NAkTJci(ln(5)
- 1)dV
CO
Here, e is the charge density, CP the electrostatic potential, EO the permittivity in vacuum, cr the dielectric constant of water, T the temperature, N A Avogadro's number, k Boltzmann's constant, and ci the local concentration of ion i, and CO, finally, is the water concentration. The entropy of mixing the different amphiphilic molecules in the aggregates also contribute significantly to
~~
(50) Lindman,B.;Puyal,M.-C.;Kamenka,N.;Brun,B.;Gunnarsson, (61)Gunnarsson,G.; Jhsson,B.;WennersWm, H.J. Phys. Chem. 1980,84, 3114-3121. G.J. Phys. Chem. 1982,86,1702-1711.
2184 Langmuir, Vol. 10, No. 7, 1994
Hagslatt et al.
the free energy of the system. This entropy will be approximated by the expression for ideal mixing
-TSagg= kT
C n , In Xa
where n, and X, are the number and the number fraction of the different amphiphile molecules respectively. The interfacial energy contribution, which is assumed to be proportional to the area,A,,, that each surfactant molecule exposes towards the water, is given by
The interfacial energy of lamellar phases in many different surfactant systems4 have experimentally been shown to follow this expression, with the proportionality constant y 1.8 x J*m-2. The value of y may vary slightly m t h the curvature of the aggregate surfaces and with Asp. However, since our interest is focused on describing the general trends of the phase diagrams and not on for all specific details, we have used y = 1.8 x lov2J*mV2 aggregate geometries in the calculations. As mentioned above there is no intrinsic aggregate entropy included in the calculations, i.e., the aggregates are considered to be stiff and of monodisperse size distribution. However, in case of the spherical aggregate symmetry there is an additional contribution to the free energy of the system due to the entropy of mixing the micelles. In the simplest model the micelles are assumed to mix ideally with the water, and a=
GEL = KTN,, (InX,,
-
1)
where N m i c and Xmieare the number and the mole fraction of micelles, respectively. The repulsive force (sometimes called “the hydration force”) between the aggregates a t short interaggregate distances (the decay length of this force is about 2-4 &5233 is not included in the calculations. This repulsive force contributes significantly to the free energy of systems at high surfactant concentrations (>50 wt %), and it should be kept in mind that this force is not included in the calculations when consideringthe obtained results. When the phase boundaries are determined as described above, all surfactant molecules of the system are assumed to be aggregate bound; this is not the case when the aim is to calculate the free surfactant concentration above the cmc. The chemical potential for the different componentsare calculated by direct differentiation of the free energy expressions. These have been derived for the three presently investigated aggregate symmetries, in refs 4-6. Important to note is that there are no fitting parameters in the presented model. 5.2. The Computational Procedure. The phase diagram and the aggregate dimensions are calculated according to the following procedure: (i) The optimum aggregate radius and the chemical potentials for all components are calculated for the cylindrical symmetric system with specified composition and temperature. (ii) The chemical potentials of the components for a lamellar system, which has the same chemical potential ofthe water as that obtained for the cylindrical system, is calculated. The lamellar thickness and the composition of the system for which the free energy is a t minimum is determined. (iii) The most stable phase is identified. Points in the phase diagram, for which the chemical potential of all (52)Rand, R. P.Annu. Rev. Biophys. Bioeng. 1981,10, 277-314. (53)Jonsson, B.;Wennerstrom, H. J . Chem. Soc., Faraday Trans. 2 1983,79,19-35.
I
I
I
I
I
-
I
I
wt% Surfactant (z=2)
Figure8. Theoretically calculated phase diagram for a divalent surfactantlmonovalentsurfactantPHz0 system. The distance between two ticks represents 10 wt %. Precipitated surfactant crystals and surfactants in spherical, circular cylindrical, and planar aggregates have been considered in the calculations. Single phase regions are white, two-phase regions are shaded, and three-phase regions are black. The dotted lines are tielines between the different phases. The parameters which are used in the calculations are given in the text.
components have the same values for the cylindrical region as for the lamellar region, are endpoints of the tie-lines of the two-phase region that separates these regions. (iv) The boundary between the spherical and cylindrical symmetries is obtained by the same procedure. The free surfactant concentration for which the micellarbound surfactants and the monomeric surfactants is in equilibrium a t a given micelle concentration is obtained by following the computational procedure described in ref 51. For this case the micellar size is fixed (66 amphiphiles per micelle in our calculations). The free surfactant concentration in the micellar solution phase is obtained after integrating the surfactant concentration profile over the whole water volume. 5.3. Theoretical Results-Phase Diagram. The calculated phase diagram for a surfactant(z = 2)/surfactant(z = 1 ) / D 2 0 system is presented in Figure 8. The aggregate growth is suppressed when z increases, and consequently the phase boundaries are then shifted to higher C,. The spherical, circular cylindrical and bilayer aggregate symmetries have been considered in the calculations. The parameters used are chosen so that comparisons can be made with the experimentally obtained phase diagram for the K2DoM/KTD/D20 system at 50 “C. Thus the surfactant molecular volumes are Vz=2 = 450 A3 and Vz=l = 420 A3 and the surfactant molar masses are Mz=2= 349 gmol-l and Mz,l = 266 gmol-l for the divalent surfactant (z = 2) and the monovalent surfactant (z = l),respectively. The molar mass, density and dielectric constant of the water are M , = 20 gmol-l, Qw = 1.10g ~ m and - ~cr= 69.5,respectively. The maximum length of the smallest dimension of the aggregates is r,, J*m-2. = 19 A and y = 1.8 x The question if the spherical micelles form a micellar solution phase or a discontinuous cubic phase is not considered in the calculations. However it is an experimental fact that the aggregate size and shape is about the same for the discontinuous cubic phase and the micellar solution phase. Therefore the spherical region of the theoretically determined phase diagram would correspond to the whole isotropic phase region as obtained experi-
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Langmuir, Vol. 10, No. 7, 1994 2185
mentally, i.e., the region with both cubic and micellar solution phases. Similarly, the circular cylindrical and bilayer regions of the theoretically predicted phase diagram would correspond to the hexagonal phase region and lamellar phase region ofthe experimentally obtained phase diagram, respectively. Keeping this identification of the different regions in mind, the calculated phase diagram given in Figure 8 and the experimentallyobtained phase diagram of Figure 2 show a good agreement. As discussed above, there is no "hydration force" included in the theoretical model. The introduction of such a repulsive force would shift all phase boundaries toward higher water contents of the phase diagram. The effect would be more pronounced the lower the water content of the system is. For example, the spherical/ cylindrical boundary would hardly be affected for z = 1, but would for z = 2 be shifted to the leR of the phase diagram on account of the fact that the water content of the system is then smaller. Thus, the appearance of the calculated phase diagram would match the experimentally obtained one even better if hydration forceswere included in the model. Nevertheless, we have preferred not to include hydration forces in the model, and this is mainly for two reasons. The first is that the calculated phase diagram as presented in Figure 8 shows the correct trends for how the succession of phases is affected by the headgroup charge. Since our purpose is to investigate these effects in general and not any specified system in detail, this is quite satisfactory. The second reason concerns the fact that there are weaknesses in the description of the hydration forces, both from experimental and theoretical points of view. As a consequence the introduction of hydration forces in the model would in essence amount to the introduction of a fitting parameter by which perfect agreement to the experimentally determined phase diagram could be obtained, a procedure which leads to little additional understanding of the system presently investigated. 6.4. Theoretical Results--The Free Surfactant Concentration. The predicted values of the free surfactant concentrations above the cmc for a divalent surfactant is reproduced in Figure 7 and agrees well with the experimentallyobtained results. The parameters used in the calculations are cmc = 5 x m,the micellar aggregation number is 66, Mz=2= (295 2 x 38) g-mol-l, Vz=2= (540 2 x 30) A3,V, = 30 A3, T = 298 K, Qw = 1.10 g - ~ m - and ~ , er = 76.2.
+
+
Table 3. Cmc Values for Some Monovalent and Divalent Surfactants cmc(z = 1)/ cmdz = 2)/ surfactant(z = 1) M M surfactant(z = 2) DoAC DoTAC
KTD IMDoP
0.0146O 0.203O 0.0063a 0.0094d
0.033b 0.048 m0.05c 0.063e
DoPDAC DoPPDAC &DoM K~DoP
a From ref 54 at 25 "C. From ref 3 at 25 "C. From refs 9 and 49 at 25 "C. From ref 57 at 55 "C. e From ref 57 at 25 "C.
and is rationalized by the difference in electrostatic repulsion between the polar headgroups. Higher counterion concentration is required in order to reduce the electrostatic potential of the micellar surface when the surfactant charge increases, resulting in higher values of the cmc. The cmc values for DoTAC and KTD differ considerably, while they are approximately the same for DoPPDAC and K2DoM. This observation indicates that nonelectrostatic effects are of less importance for the value of the cmc the higher the average surfactant charge is. However, any specific interactions between the counterions and the micelle surface, which tend to decrease the electrostatics of the system, become increasingly important the higher the average surfactant charge is, since the counterion concentration outside the micellar surface then increases as well. The low cmc values for the alkylammonium chloride surfactants DoPDAC (cmc = 3.3 x M) and DoAC (dodecylammoniumchloride, cmc = 1.48 x M) as compared to the corresponding values for their analogues with quaternary ammonium groups may be due to such specific interactions. 6.2. Free Surfactant Concentrations. It is often assumed that the monomer concentration is constant as the surfactant concentration increases above the cmc. This is generally a good assumption for nonionic and zwitterionic surfactant^,^^ but for ionic, single-tail surfactants, a decrease of Ck,, is noted above the cmc.60-62This is especially true for divalent surfactants, as we have shown in previous communication^.^^^^ The decrease of C h above the cmc is of electrostatic origin, and is quantitatively described by the Poisson-Boltzmann cell-model both for monovalent51and divalent ~urfactants.~ That this is the case also for the DoPPDAC/water and the KzDoWwater systems is clearly demonstrated in Figure 7. One can rationalize the decrease of Ck,, above the cmc by considering the heterogeneous distribution of counterions outside the micelle^.^^^^^ Consider an ionic surfactant for which micelles form already at infinite dilution. Outside the highly charged micellar surface the counterions are distributed according to the Poisson-Boltzmann equation. This nonhomogeneous distribution of counterions is entropically unfavorable. When the surfactant concentration increases,the water volume confined to each micelle decreases,while the number of counterions that belong to each micelle remains constant (assuming that the micellar aggregation number is constant). The
6. Discussion This section begins with a discussion concerning the aggregational process in the isotropic phase region for the systems containing divalent surfactants, with emphasis on the cmc values and the free surfactant concentrations above the cmc. We then proceed by summarizing the results pertaining to the structures of the liquid crystalline phases of these systems. Finally, we discuss the z-dependence of the succession of phases when the surfactant concentration varies. The experimentally and theoretically phase diagrams presented above are con(55)Cooper, R. S.J.Am. Oil Chemists Soc. 1963,40,642-645. sidered in this discussion. (56)Tahara, T.; Satake, I.; Matuura, R. Bull. Chem. Soc. Jpn. 1969, 8.1. Cmc Values. The cmc values are 4.8 x M 42,1201-1205. forDoPPDAC and(4.7-5.5) x 10-2MforKzDoM,9p49which (57)Arakawa, J.; Pethica, B. A. J. Colloid Interface Sci. 1980,75, 441-450. is considerably higher than those for corresponding (58)Chevalier, Y.;Belloni, L.; Hayter, J. B.; Zemb, T. J.Phys. fLes monovalent surfactant analogues. As comparisons, the Ulis,FrJ 1986,46,749-759. M for DoTAC and 6.3 x cmc values are 2.0 x (59)Faucompr6, B.;Lindman, B. J.Phys. Chem. 1987,91,383-389. (60)Cutler, S. G.;Meares, P.; Hall, D. G. J. Chem. Soc., Faraday M for KTD" (see also Table 3). This effect ofthe surfactant Tiam. 1 1978,74, 1758-1767. charge on the cmc has been demonstrated p r e v i o ~ s l y 3 ~ ~ , ~ ~ -(61) ~ Stilbs, P.;Lindman, B. J.Phys. Chem. 1981,85,2587-2589. (62)Lindman, B.;Puyal, M.-C.; Kamenka, N.; RymdBn, R.; Stilbs,
(54)Mukerjee, P.; Mysels, K. J. Natl. Stand. Ref. Data Ser., Natl. Bur. Stand. 1971,No. 36, 1.
P. J. Phys. Chem.1984,88,5048-5057. (63)Hagsliitt, H., Thesis, Lund University, 1994.
Hagslatt et al.
2186 Langmuir, Vol. 10,No. 7, 1994 counterion concentrationat the surface of the micelle stays approximately constant, while the corresponding concentration in the bulk increases. Therefore the counterion distribution becomes more homogeneous the higher the micelle concentration, with a reduction of the negative counterion entropy as a consequence. For an actual ionic surfactanvwater system micelles start to form at a finite surfactant concentration. The negative counterion entropy is then reduced by the added salt, i.e., the monomeric surfactants with counterions. However, as for the case discussed above when cmc % 0, the negative counterion entropy is reduced when the surfactant concentration increases above the cmc also for the case when the cmc takes a finite value. Hence, the micellar-bound state for the surfactants is stabilized when the surfactant concentration increases. Less additional salt is accordingly needed, with a reduction of the free surfactant concentration as a consequence. The decrease of C,,, is more rapid for the divalent surfactant case than for its monovalent surfactant analogues, and this is for two reason^.^!^^ The first can be traced back to the high cmc values for divalent surfactants, which imparts a high starting value of Cfiee. The second reason is that each surfactant molecule contributes two counterions, and hence the nonuniform counterion distribution levels off more rapidly for this case. 6.3. The Discontinuous Cubic Phases. Cubic phases of the K2DoM/D20, K2DoM/KTD/D20, and DoPPDAC/DzO systems are obtained intermediate between the micellar solution phases and the hexagonal phases. Surfactant self-diffusion data and time-resolved fluorescence quenching data obtained for this kind of cubic phase for several different systems show that this phase is comprised of closed aggregate^.^^,^^*^ Therefore, the location of the presently studied cubic phases strongly indicates that they are of the discontinuous type. Direct information that this is actually the case is provided by the slow surfactant self-diffusionof the cubic phase of the DoPPDAC/water system (DsUfi< 1 x 10-l2 m2*s-'). For the KzDoWwater cubic phase the surfactant self-diffision could not be measured due to the rapid 'H transverse relaxation rate of the surfactant molecule. The cubic phases of the K2DohUD20 and the DoPPDAC/ D2O systems extend over large regions of concentration (about 30 wt % surfactant). Hence they are, as far as we are aware of, the discontinuous cubic phases with the largest extension in the phase diagrams found so far (cf., ref 38). The cubic phases of the DoPDAC/D20 system, which was presented in a previous communication,3also extend over a rather large region. One can therefore conclude that the formation of large discontinuous cubic phases is a general property for divalent surfactant'water systems. The reason underlying this observation is that the micellar growth when the surfactant concentration increases is suppressed when the surfactant headgroup charge increases. Quadrupole NMR band shape and relaxation measurements and fluorescence data have demonstrated that the micelles of the discontinuous cubic phases of several systems have nonspherical shapes,47s65-67 and Fontell et al. have proposed that this type of cubic phase, considering its location in the phase diagram, consists of slightly ~
(64)Bull, T.;Lindman, B. Mol. Cryst. Liq. Cryst. 1974,28,155-160. (65)Soderman, 0.; Walderhaug, H.; Henriksson, U.; Stilbs, P. J . Phys. Chem. 1985,89,3693-3701. (66)Eriksson, P.0.; Lindblom, G.; Arvidsson, G . J . Phys. Chem. 1985,89,1050-1053. (67)Johansson, L. B.-A; Soderman, 0.J.Phys. Chem. 1987,91,52755278.
prolatelike micelle^.^^^^^ Luzzati et al. have previously advocated an alternative structure, of a partially bicontinuous nature.69 However, recently these workers have rejected this proposal70and now favor a structure which is similar to the one proposed by Fontell, but where the micelles have disklike shapes. However, the fact that strong electrostatic headgroup repulsion favors the formation of prolate-shaped micelles over discoidal-shaped micelles,6together with the results presented above, that high values of z promotes the formation of discontinuous cubic phases, constitutes strong evidencein favor of prolate micelles of these cubic phases (see also ref 63). SAXS data obtained for this type of cubic phase for several different systems are consistent with the Pm3n of the fact that slightly s t r u c t ~ r e . ~ ~ fOn ' ~ ~account ~~ prolatelike micelles act as quadrupoles, Fontell et al. have proposed a cubic structure, in which the micelles are arranged similar to the arrangement of y-02 and @-F2at 50 KS8 In this structure, which is consistent with space group Pm3n, each unit cell contains eight micelles, six of which are pairwise oriented in a T-wise,or crossed manner (due to their possession of quadrupole moments), while two micelles are freely rotating or statistically disordered among several orientations.38@ Micellar axial ratios of about 1.4:1, assuming the above presented cubic structure,3*38,47,65,67 for the discontinuous cubic phases in the DoTAC/water and the DoPDAC/water systems are obtained from fluorescencequenching data, NMR relaxation as well as from SAXS data. It is likely that the structure proposed by Fontell et al. is applicable also to the cubic phases of the presently investigated systems, for two reason^.^ The first is the fact that the aggregational growth is suppressed in the divalent surfactant cases, while the second reason is that the micelles may act as stronger quadrupoles when z increases. However, other cubic structures are also possible, as indicated by the fact that two different cubic phases appear to be present in the KzDoWwater system, as well as in other systems.72 Interesting to note is that, according to the tie-lines of the two-phase region separating the cubic phase and the hexagonal phase of the K2DoM/KTD/D20 system the total surfactant concentrations are essentially the same for the two phases for C, > 50 w t %. The surfactant molecules segregates into one KzDoM-rich cubic phase and one KTDrich hexagonal phase. Apparently, the cubic phase can solve a very small amount of KTD when C, > 50 wt %. Whether this observation is connected to the observation of two different cubic phases for the KzDoWwater system remains to be seen. 6.4. The Anisotropic Liquid CrystallinePhases. Hexagonal phases follow the isotropic phase region when the surfactant concentration increases. The radius of the hydrocarbon core of the aggregates are about 80% of the all-trans conformation of the hydrocarbon chain for the 0 % surfactant) of both the hexagonal phase (at ~ 7 wt K2DoM/Dz0 and D o P P D A C , . J ~ ~systems. ~O For the systems with z > 1.5, no further liquid crystalline phases are obtained, for reasons of solubility. However, for z < 1.5, both a lamellar phase and intermediate phases are obtained. The first intermediate phase is a ribbon phase. (68) Fontell, K.; Fox, K. K.; Hansson, E. Mol. Cryst. Liq. Cryst. 1985, 1 , 9-17. (69)Tardieu, A,; Luzzati, V. Biochim. Biophys. Acta 1970,219,ll-
17. (70)Vargas, R.;Mariani, P.; Gulik, A.; Luzzati, V. J.Mol. Biol. 1992, 225, 137-145. (71)Balmbra, R.R.;Clunie, J. S.; Goodman, J. F. Nature 1969,222, 1159- 1160. (72)Jahns, E.;Finkelmann, H. ColloidPolymer Sci. 1987,265,304311.
Divalent Surfactants Four different symmetries have been proposed for ribbon phases, but out of these only one, namely the centred rectangular space group (cmm), appears to be well established,consideringpreviously obtained SAXS-results for this type of phases.21 Presumably the ribbon phase of the presently investigated system possess a centred rectangular symmetry (cmm) as well. A second intermediate phase, possibly an orthorhombic phase (but monoclinic and triclinic structures are also possible), is identified intermediate between the ribbon phase and the lamellar phase. The observation ofthese two intermediate phases at 50 "C are in accord with the findings of Rendall et al.24 An intermediate, cubic phase has been reported previously, at 100 "C and 59-66 wt % surfactant for the binary KTD/H20 ~ y s t e m . This ~ ~ , cubic ~ ~ phase has been reported at 86 OC,& and there is no indication in favor of the existence of such a phase in our study at 50 "C either. However, anisotropic intermediate phases have previously been observed to disappear when the temperature increases for similar systems.8~24~30*31~33~34~36*40 6.6. General Aspects on the Phase Diagrams. It is a fact that high aggregate electrostaticsurface potentials favor aggregate shapes with high interfacial curvature (toward the hydrocarbon).6 The surface energy however, promotes the formation of large, disklike aggregates.'j Therefore, (for single-chain, ionic surfactantiwater systems) spherical micelles are obtained at low C,, when the counterion concentration is low, while bilayers are obtained at high C,. For the same reasons, an increase of z leads to an increased value of the cmc (see Table 3), and to a suppressed aggregational growth. ks a consequence, all phase transitions are shifted to higher C, when z increases (Figures 1 and 2). These effects are well accounted for by the Poisson-Boltzmann cell model, as shown in Figure 8 (consult also the discussion in section 5, concerning the hydration forces). Above, it was concluded that the geometrical appearance of the headgroup (which,for example, determines the steric repulsion between the headgroups of the aggregate bound surfactants) has less effect on the aggregational process and the phase appearance the higher the headgroup charge is. This is since the electrostatic headgroup repulsion then becomes increasingly important. Specific counterion binding to the aggregate-bound surfactants, which tends to lower the phase transition concentrations,has increasing importance the higher the valence of the surfactant ion is, which is due to the fact that the counterion concentration at the surface of the aggregates increases when the headgroup charge increases. In contradiction to the case of systems for which 0 Iz I 1,1,2,8 the succession of phases is on the whole independent of the average surfactant charge for z 1 1. The main exception to this rule is the formation of the discontinuous cubic phase, which is promoted by high z-values. However, the structure ofthis phase differs from the micellar solution phase only with respect to the
Langmuir, Vol. 10, No. 7, 1994 2187 ordering of the micelles, which is more complete for the cubic phase. The micellar shape and size, for instance, are essentially the same for the two phases. 7. Conclusions The purpose of this study has been to investigate the influence of the surfactant charge on the phase behavior for surfactantiwater system. Comparisons are made with predictions by Poisson-Boltzmann cell model calculations. For 1 I z I 2 the following main results have been obtained. (i)For single-chain, monovalent surfactantiwater systems, one obtains when increasing the surfactant concentration an isotropicphase region (micellarsolution and cubic phases), a hexagonal phase region, an intermediate phase region, and a lamellar phase region.lp2 Increasing the headgroup charge does not alter this general phase behavior. (ii) The phase transitions shiR to higher surfactant concentrations when z increases. This follows since the growth of the aggregates is suppressed when the aggregate surface charge density increases. (iii) The general trends of the phase behavior are correctly described by the Poisson-Boltzmann cell model, which consequently has validity also for high surfactant charges. (iv)As for the monovalent surfactant case, the surfactant monomer distribution outside the micelles is accurately described by the Poisson-Boltzmann cell model for divalent surfactant systems. (VI High z-values promote the formation of the discontinuous cubic phase. This fact support the proposal that the micelles of these phases are prolatelike and, further, is consistent with the structure as proposed by Fontell et for this kind of cubic phase. (vi)The geometrical appearance of the headgroup (Le,, its size and shape) has less effect on the aggregational process and the phase appearance the higher the headgroup charge is. (vii) Possible specific counterion binding to the aggregate-bound surfactants, which tend to lower the phase transition concentrations is increasingly important the higher the valence of the surfactant ion is. This is due to the fact that the counterion concentration at the surface of the aggregates increases when the headgroup charge increases.
Acknowledgment. Dr. Krister Fontell, Frederik Nilsson, and Cecilia Strom are greatly acknowledged for performing the SAXS measurements, for the sample preparation and for performing the conductivity measurements. We thank Gordon J. T. Tiddy for providing the results from optical penetration investigations on the KzDoWwater system, and the Swedish National Science Research Council is thanked for financial support.
