7474
J. Phys. Chem. 1989, 93,1414-1418
An X-ray and M R Study of the Cubic Phase at Low Water Contents in the Dodecyltrimethylammonium Chloride/Water System 0. Siiderman,* U. Olsson, and T. C. Wongt Division of Physical Chemistry 1 , University of Lund, P . 0 . B 124, S-221 00 Lund, Sweden (Received: November 28, 1988; In Final Form: May 2, 1989)
A NMR self-diffusion and NMR relaxation study is presented on three different samples in the cubic phase found at low water concentration in the dodecyltrimethylammonium chloride/water system. The relaxation parameters were measured for the 14N nucleus at two different field strengths and as a function of temperature. The self-diffusion experiments were also performed as a function of temperature. It is shown that there is a marked dependenceupon concentration of the surfactant self-diffusion coefficients. Moreover, the spinspin relaxation rates also depend on the concentration of the surfactant and it is argued that it is the surfactant self-diffusion over the cubic unit cell that provides the dominating contribution to the NMR bandwidths. To investigate whether the observed concentration dependence in the measured parameters is caused by changes in the size of the cubic unit cell, X-ray scattering experiments were performed on these samples and no sign of changes in the unit cell was detected.
Introduction When surfactants or lipids are immersed in water, they aggregate and form a variety of phases.lV2 In the characterization of these phases, with regard to both the molecular properties of the surfactants building up the phases and the overall phase structures, various N M R methods have come to play an important role.3 One class of phases which is particularly well suited for N M R studies is constituted by the phases of cubic symmetry, sometimes called ringing gels due to the ringing sound they produce when tapped with a hard object. These phases are highly concentrated and thus the usual N M R stumbling block, namely the low sensitivity inherent in the N M R method, is seldom encountered in the case of cubic phases. Moreover, in most cases they give rise to N M R spectra in which no static effects (save for the J couplings) are present, and thus self-diffusion measurements with the pulsed field gradient N M R method are rather straightforward to apply, since the cumbersome macroscopic orientation of the samples which is necessary for anisotropic phases is not needed for cubic phase^.^^^ N M R relaxation methods are also rather straightforward to apply since the conditions for motional narrowing are fulfilled: but the results may not always lend themselves to immediate interpretations. As an example, the cationic surfactant dodecyltrimethylammonium chloride (CI2TACl),has two cubic phases6 (cf. Figure 1); one between the micellar and the hexagonal phases (termed SI,in the terminology of Winsor) and one between the hexagonal and lamellar phase (termed Vl). N M R diffusion studies clearly reveal that phase SI,consists of closed aggregate^^.^ and X-ray: NMR relaxation,8*I0as well as fluorescence quenching studies11g12 indicate that the phase is built of prolate micelles with an aspect ratio of about 1.3 (at room temperature), although recently another structure proposal for the SI,phase in C12TACl has been put forth.13 It is fair to state that a large body of N M R data and in particular frequency-dependent relaxation data have been shown to be in agreement with a phase consisting of prolate micelles. The other cubic phase in ClzTACl has been shown to be bic o n t i n u ~ u s . ~However, *~ the interpretation of N M R relaxation data from this phase and corresponding phases in other surfactant systems is not straightforward. Eriksson et ale8and Noack14 have presented N M R relaxation studies at single concentrations in V I phases. Since the concentration dependence of the relaxation parameters in these phases is of interest, we have performed a 14N N M R relaxation study for three samples with varying concentration in the V I phase in C,,TACl. The data are presented along with a discussion of the problems connected with the in-
'
On leave from Department of Chemistry, University of Missouri, Columbia, MO 6521 1.
terpretation of N M R relaxation data from the V, phases. To further investigate the relaxation behavior we have determined the self-diffusion coefficients as a function of temperature for these three samples. Finally, X-ray scattering experiments were performed for these at one temperature. The different experiments reported on here are all performed on the same samples. This is an important feature since, as will become evident from this report, slight changes in surfactant concentration may change the values of the observed experimental parameters substantially.
Experimental Section Samples. ClzTAClof 99.6% purity were obtained from Tokyo Kasei Kogyo Co., Tokyo, and purified by dissolving the surfactant in methanol. The resulting solution was treated with active charcoal, which was filtered off, and finally the methanol was evaporated. The resulting white powder gave completely transparent, clear samples when mixed with water. Three samples were made by weighing the C12TACland twice distilled water into glass ampules that were flame sealed. The samples were equilibrated through repeated centrifuging back and forth in the ampules and were finally left to equilibrate at 40 "C for 1 week prior to performing any measurements. Care was taken to treat the samples equally. Methods. The I4N N M R relaxation experiments were performed at 2.35 and 8.49 T with a Bruker MSL 100 spectrometer and a Nicolet NTC 360 spectrometer, respectively. Spin-lattice relaxation rates were performed with the standard inversion recovery method, while the spinspin relaxation rates were obtained from the bandwidths after suitable corrections for the contributions from the magnetic field inhomogeneities. The self-diffusion experiments were performed with a JEOL FX-60 spectrometer (1) Tiddy, G. J. T. Phys. Rep. 1980, 57, 1. (2) Lindman, B.; WennerstrBm, H. Phys. Rep. 1979, 52, 1. (3) Lindman, B.; SWerman, 0.;WennerstrBm, H. Surfactant Solutions. New Methods of Investigation; Zana, R., Ed.; Dekker: New York, 1987. (4) de Vries, J. J.; Berendsen, H. J. C. Nature 1969, 221, 1139. (5) Lindblom, G.; WennerstrBm, H. Biophys. Chem. 1977, 6, 167. (6) Balmbra, R. R.; Clunie, J. S.; Goodman, J. F. Nature 1%9, 222, 1159. (7) Bull, T.; Lindman, B. Mol. Cryst. Liq. Cryst. 1974, 28, 155. (8) Eriksson, P. 0.; Lindblom, G. J . Phys. Chem. 1982, 86, 387. (9) Fontell, K.; Fox, K.; Hansson, E. Mol. Cryst. Liq. Cryst. 1985, I , 9. (IO) SWerman, 0.; Walderhaug, H.; Henriksson, U.; Stilbs, P. J. Phys. Chem. 1985, 89, 3693. (11) Johansson, L. B.-A; SMerman, 0. J . Phys. Chem. 1987, 91, 5275. (12) Fletcher, P. D. I. Mol. Cryst. Liq. Cryst. 1988, 154, 323. (13) Charvolin, J.; Sadoc, J. F. J . Phys. Fr. 1988, 49, 521. (14) Ktihner, W.; Rommel, E.; Noack, F.; Meier, P. Z . Naturforsch. 1987, 42, 127.
0022-3654189/2093-1414$0~SO10 0 1989 American Chemical Society
The Journal of Physical Chemistry, Vol. 93, No. 21, 1989 7415
X-ray and N M R Study of the CIzTAC1/Water System according to published proced~res.’~In both the relaxation and self-diffusion experiments, the temperature was monitored with a calibrated thermocouple. The accuracy in the temperature is judged to be better than 1 deg. X-ray experiments were performed at 23 OC according to a procedure described in ref 16.
TABLE I: Comwsitions of Samples Studied sample wt % ClzTACl vol % CIzTAClgat 25
Theoretical Considerations
= 0.998 g ~ m - ~ .
1 2
3
82.79 84.71 86.89
“Computed with the following densities:
OC
84.02 85.88 87.87
= 0.91320and P H ~ O
PC,~TAC~
I4N has spin Z = 1 and the dominating N M R relaxation mechanism is thus provided by the quadrupole interaction with the electric field gradient at the I4N nucleus. The spin-lattice ( R , ) and spin-spin ( R 2 )relaxation rates are written” R , = (3x2/40)x2(2j(w) + 8j(2w)) R2 = (3x2/40)x2(3j(O)
+ Sj(w) + 2j(2w))
(1) (2)
In eq 1 and 2, x is the quadrupolar coupling constant (it is assumed that the asymmetry parameter of the electric field gradient is zero) while j ( w ) is the reduced spectral density function evaluated at the Larmor frequency. j ( w ) is the Fourier transform of the (aut0)correlation function for the motion of the z component of the electric field gradient tensor with respect to the static magnetic field. For ordinary micellar solutions of single-chained ionic surfactants it has been shown that the “two-step” model as derived by Wennerstrom and c o - ~ o r k e r s provides ~ * ~ ~ ~ a reasonable form for j ( w ) . The key point of the two-step model is a time-scale separation of the motions causing relaxation into internal motions occurring within the aggregates and slower motions connected with the motion of the entire aggregate and/or surfactant diffusion over the micellar surface. In this formulation j ( w ) is j ( w ) = (1
- SZ)j‘(w) + Szjyw)
C12TACI. % w
Figure 1. Phase diagram of the C12TACl/water system (after ref 6). Given in the diagram are the positions of the three samples presently studied.
(3)
In eq 3 S is the residual (quadrupolar) anisotropy, defined as S = 0.5(3(cos2 1) where the average is taken over a time that is long enough to average the fast motions. It is worth mentioning that S is analogous to the order parameter measured from quadrupolar splittings in anisotropic phases. j f ( w ) and j S ( w ) are the spectral densities of the fast and slow motions, respectively. Now for the micellar and SI, phases in CIzTACl, excellent descri tions of extensive field-dependent relaxation data are obtained if j ( w ) is assumed to be constant, i.e., the fast internal motions are in the extreme narrowing regime, and if f ( w ) is a Lorentzian spectral density;I0 i.e.
9
jS(o)=
27,”/(1
+
(UT,”)’)
(4)
where T: is the correlation time for the slow motion. The value obtained for T,” is in reasonable agreement with that expected from aggregate tumbling and surfactant diffusion over the aggregate surface. Equations 3 and 4 are thus reasonable starting points in the discussion of the relaxation data from the V, phase. It should be noted that the applicability of the two-step model to the results obtained in the V I phase only requires that the fast and slow motions are time scale separated. The choice of functional forms for f ( w ) and f ( w ) in eq 3 do however present a problem, which is discussed in the next section.
Results and Discussion The Samples. The compositions of the samples are given in Table I and the positions of the samples in the phase diagrams are given in Figure 1. The samples, which are clear as glass and of very high viscosity, were optically isotropic when viewed through (1 5) Stilbs, P.Prog. Nucl. Magn. Reson. Spectrosc. 1987, 19, 1. (16) Lindblom, G.; Larsson, K.; Johansson, L.; Fontell, K.; Forstn, S. J . Am. Chem. SOC.1979, 101, 5465. (1 7) Abragam, A. The Principles of Nuclear Magnetism; Clarendon: Oxford, 196 1. (18) Wennerstrom, H.; Lindblom, G.; Lindman, B. Chem. Scr. 1974, 6, 97. (19) Halle, B.; Wennerstrom, H. J . Chem. Phys. 1981, 75, 1928. (20) Reiss-Husson, F.; Luzzati, V. J . Phys. Chem. 1964, 68, 3504.
1 0 ~ (K-? 1 ~
Figure 2. Natural logarithm of the self-diffusion coefficients for the surfactant in the three samples plotted vs the inverse of the absolute temperature. 0, 0,A correspond to sample 1, 2, and 3, respectively. The error in D obtained when fitting the relevant equation to the raw data is typically better than f3%.
crossed polarizers. When they were tapped with a hard object they gave a ringing sound. The X-ray Data. The three samples gave identical X-ray diffractograms within the experimental uncertainty. Unfortunately, only two reflections were obtained. These were found at 3 1.6 and 27.4 A, respectively. The reflections are compatible with the space group Za3d,’I with a lattice parameter of 77 A. This appears to be the most common structure for cubic phases formed by surfactants between the hexagonal and lamellar phase.22 The structure, according to the proposal by Luzatti, consists of two interwoven, but not connected, networks of surfactant rods, connected three by three. The two networks are separated by a film of water. In conclusion, the X-ray data indicate that the change in the unit cell size is negligible in the concentration range of the samples studied here. The Self-Diffusion Study. The self-diffusion data as functions of temperature and concentration are displayed in Figure 2. The ~~
~
(21) Luzzati, V.;Tardieu, A.; Gulik-Krzywicki, T.; Rivas, E.; ReissHusson, F. Nature 1968, 220, 485. (22) Luzzati, V.;Mariani, P.; Gulik-Krzywicki, T. Physics of Amphiphilic Loyers; Meunier, J., Langevin, D., Boccara, N., Eds.; Springer: New York, 1987; p 131.
7476 The Journal of Physical Chemistry, Vol. 93, No. 21, 1989 TABLE 11: Results of the Diffusion Measurements samDle AE. kJ mol-l D,. m2 s-I 1 29.3 f 0.2' (1.3 f 0.2) X lod" 2 31.4 f 0.8 (2.2 f 0.8) X 10" 3 36.4 f 0.9 (1.2 f 0.3) x 10-5
The statistical confidence intervals correspond to an approximately 80% level. straight lines through the points have been obtained by fitting the nonlinearized equation D = Do exp(-AE/(RT)) to the data. The results of the fits are collected in Table 11. As is evident in Figure 2, the data are well described by the relation above. This is convenient, since data have not been obtained at exactly the same temperatures in the diffusion and relaxation experiments, and this procedure provides a means of comparing data at arbitrary temperatures. It is also clear from the data in Table I1 that there is a substantial dependence upon concentration for the surfactant self-diffusion in these systems. For instance, the values obtained at 30 OC (calculated from the data in Table 11) are for sample 1 D = (1.2 f 0.2) X lo-" m2 s-l, for sample 2 D = (0.8 f 0.4) X lo-" mz s-I, and finally for sample 3 D = (0.6 f 0.2) X lo-" m2 s-I, Le., a change by almost a factor of 2 from the highest to the lowest concentration. The reason for this rather marked dependence upon marginal changes in volume fraction of surfactant cannot be sought in changes in the lattice parameters. Anderson has solved the diffusion equation for the Za3d phase built of connected networks of surfactant rods and reports that a change in the volume fraction from 84 to 88% would give rise to an increase in Dsurlof approximately 4%.23 Thus it appears clear that the strong concentration dependence of D must be related to changes in the local diffusional properties within the aggregates. Considering that in the V, phase presently under study there are less than 3 water molecules per surfactant, this result may not be so surprising. When the amount of water is so small, the interactions between surfactants within and between adjacent surfactant aggregates are presumably rather dependent upon small changes in the water content. Now, values of diffusion coefficients measured in cubic phases are sometimes used in the interpretation of NMR relaxation data from isotropic solution phases to a m u n t for the relaxation caused by surfactant diffusion over a curved It is then assumed that the local aggregate diffusional properties for a given surfactant system are not dependent either upon aggregate geometries or on concentration. The present results would indicate that some care should be exercised in analyses of this kind. One word of warning should perhaps be mentioned here. The N M R self diffusion experiments measure displacements over distances equal to (x2) = 2Dt. In the present context t = 140 ms. It follows that the distance travelled by the surfactants is of the order of 1-2 pm. Now clearly the cubic structure will have defects in the crystal structure over such dimensions. At such places of defects the surfactant diffusion may be different from the diffusion over the defect-free surface and thus the number of defects may influence the measured values of D. As stated above great care was taken to treat the three samples identically in order to at least minimize the difference in defects between the samples. It should also be mentioned that the diffusion data were not collected by monotonically increasing or decreasing the temperature. Rather, the data were acquired with the temperature being randomly varied. The samples were also heated up and slowly cooled down before any diffusion measurements were performed. In conclusion, the diffusion study of the three samples shows that the diffusion is strongly dependent upon volume fraction of surfactant in the V I phase in C12TACl. The Relaxation Study. Presented in Table 111 are the results of the relaxation study. Before analyzing the data in some detail (23) Anderson, D.; Wennerstrom, H. J. Phys. Chem., in press. (24) Nery, H.; SMerman, 0.;Canet, D.; Lindman, B. J . Phys. Chem. 1986, 90, 5802. (25) S d e r m a n , 0.; Henriksson, U.; Olsson, U. J . Phys. Chem. 1987, 91, 116
Soderman et al. TABLE 111: Results of NMR Relaxation Experiments at Two Field Strengths and Varying Temperatures Bo = 2.35 T Bo = 8.49 T T,OC RI,'s-' R2,O s-' R,," s-' Rz," s-I
a. Sample 1 25.0 31.3 31.6 36.2 39.0 47.5 48.3 56.6 58.3 65.9 66.9 78.9 89.7
123
374
122
31 1
113
229
104 91.2
172 140
73.5 60.6
104 82
43.3
374
38.5
288
34.6
230
31.7 30.4
177 154
29.4
126
49.3
479
42.2
352
36.8
276
30.8
174
54.9
646
47.2
486
40.2
383
34.7 31.7
298 230
30.2
202
b. Sample 2 25.0 31.3 31.6 36.6 39.0 47.8 57.6 58.8 66.4
127
441
120
385
116
282
107 99
217 182
c. Sample 3 25.0 26.0 31.6 36.6 39.0 47.8 48.3 57.6 58.8 66.4 66.9
126
677
120
513
119
370
115 108
296 253
'The errors in the fitting of the relevant relaxation equations to the raw data are typically better than i5%. we note that Eriksson et a1.* have performed a I4N relaxation study at a single concentration in the V1 phase in CI2TAC1. The lucid account of these measurements provides an excellent background for the present work. These workers based their analysis on the assumptions that the fast motion is in extreme narrowing and the slow motion is described by a Lorentzian spectral density. It should perhaps be remarked that the validity of the latter assumption is by no means self-evident. In the case of a Lorentzian spectral density for the slow motion, the difference between R, and R, (denoted by AR in what follows) is given by AR = ( 9 ~ ' / 2 0 ) ( x S ) ~(1 ~ ; 1/(1 (UT,")') - 2/(1 + 4(UT,")')) (5) Thus AR only depends on S and 7;. As regards the assumption about extreme narrowing for the fast motion at the field strengths used here and by Eriksson et al., this is a reasonable approximation. Even if there is a frequency dependence from the fast motion, it will be slight and negligible in comparison with the values of R2 at the field strengths used in the present work. As regards the second assumption it also appears to be reasonably accurate. Extensive ZHfield-dependent relaxation data for three different Za3d phases are indeed well described with a Lorentzian spectral density (plus a constant).26 This is in contrast to the other cubic phase found in the ClzTACl/water phase at lower surfactant concentrations. This phase is not bicontinuous but consists of closed nonspherical aggregate^.^," For this phase one requires a slightly more complicated form forjS(w). As argued by Eriksson et al. it is most likely the surfactant diffusion over the cubic unit
+
+
(26) SMerman, 0.;Henriksson, U., to be published.
X-ray and N M R Study of the C12TAC1/Water System cell that is responsible for the N M R relaxation, since any second-order tensor interaction, of which the quadrupolar interaction is an example, will be averaged to zero if the surfactant can sample all the orientations in the cubic unit cell. We will return to this question below. Noack,14on the other hand, analyses IH field-cycling data from the V I phase formed in the potassium laurate/water system in terms of translational and rotational reorientations of the individual molecules and makes no reference to the structure of the cubic phase. Returning to Table 111, it is worth discussing the general features of the data before analyzing the data in a more quantitative fashion. First, R2 depends rather strongly on the concentration and the temperature. Second, for a given field strength, R , displays a very mild dependence upon temperature and concentration. We interpret these findings in the following manner. As noted above, a reasonable candidate for the slow dynamical process that causes relaxation is the surfactant lateral diffusion over the unit cell. Since the self-diffusion coefficients do indeed depend on concentration and temperature, it follows that R2 must also depend on concentration and temperature. The mild dependence of R I upon concentration would indicate that the local internal motions of the surfactant are almost independent of concentration. This follows since R , is dominated by rapid motions, described by f(i'
