J. Phys. Chem. 1983, 8 7 , 3991-3999
399 1
Anisotropic Aggregates of Amphiphillc Molecules in Lyotropic Nematic Phases Y . Hendrlkx,’ J. Charvolin, M. Rawfso,t L. LlObert, and M. C. Holmes’ Laboratoire de Physique des SolMes, I n Flnal form: May 31, 1983)
at.510, Universl Paris-Sud, 91405 Orsay, France (Received: December 28, 1982;
Lyotropic nematic phases of amphiphilic compounds are homogeneous fluid solutions of anisotropic micellar aggregates organized with some orientational order but without translational order. Recent X-ray studies have shown that the aggregates are either oblate or prolate spheroids depending on composition and temperature. We present neutron-scatteringstudies, complementing the previous X-ray studies, which make possible a more quantitative description of the shape and dimensions of the aggregates. We have focused our attention on two systems, (I) sodium decyl sulfate/l-decanol/water and (11) potassium laurate/l-decanol/water, which present nematic phases in the room temperature range. The phase diagrams were determined by studying the orientational properties of the samples, their textures, and their orientations in a magnetic field. The evolution of the aggregates was followed with X-ray and neutron-scattering techniques within the nematic domain, when their shapes change from that of oblate to prolate spheroids. For both systems, in the concentration and temperature ranges studied here, the oblate aggregates have a rather constant shape with a low anisotropy (e.g., diameter-to-width ratios < 3) and their polydispersity is weak; when the aggregates become prolate in the potassium laurate/l-decanol/water system, they have still a rather constant shape with a low anisotropy (e.g., length-to-width ratio 1.75), while in the sodium decyl sulfate/ 1-decanol/watersystem their polydispersity increases significantly and only a lower bound for their anisotropy (-2.3) can be given.
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Introduction Lyotropic nematic phases of amphiphilic compounds appear as anisotropic fluids with many properties (e.g., textures and spontaneous orientation in a magnetic field) similar to those of thermotropic nematics. They were observed for the first time in 1967 in the system sodium decyl sulfate (SdS)/1-decanol/water/sodium sulfate in a region of the phase diagram located between the fluid isotropic micellar phase and the viscous anisotropic mesophases, at high content of amphiphiles (-45% by weight).’ Since then many other aqueous solutions of amphiphilic compounds have been shown to exhibit these properties.2 They fall into two classes which were first distinguished according to their orientation in a magnetic field: they have either positive or negative anisotropy of the diamagnetic susceptibility, Ax. In the same system a concentration change, or a temperature change, may change the sign of Ax. Recently, the structures of these phases were studied with small-angle X-ray scattering in the system SdS/ 1-decanol/water/sodium sulfate.3 It was shown that the amphiphilic molecules assemble in anisotropic aggregates which are arranged with long-range orientational order but without long-range translational order. This is a lyotropic state which is intermediate between the totally ordered (e.g., lamellar, cubic, and hexagonal) phases and the totally disordered (isotropic micellar) phase^.^ For the system presented above the nematic phase with A x > 0 was shown to contain elongated aggregates, and that with A x < 0 was shown to contain flattened aggregate^.^ Following ref 6, we called the first nematic phase “calamitic” (from xaXap0u: reed), or Nc and the second phase “discotic” (from 6iuX0& quoit), or Nd.14 (These terms have been chosen because they do not imply a particular shape, circular or otherwise, for the section of the aggregate normal to its axis.) In order to specify some of our notations, we have chosen to represent the most general aggregate, in a very schematic way, as an I.L.L. 156 X, 38042 Grenoble Cedex, France. *Division of Physics and Astronomy, Preston Polytechnic, Preston PRI 2TQ, England. On Sabbatical leave. Laboratoire associ6 au C.N.R.S. (LA No. 2). 0022-3654/83/2087-399 1$01.50/0
ellipsoid with three axes as shown in Figure L7 One point of interest of these systems concerns the nematic ordering of their aggregates. Another involves their relevance to our knowledge of micellar systems in general. Indeed the description of micellar shapes and their departure from spherical has been approached up to now in isotropic solutions only. This is an unfavorable situation for studying anisotropic aggregates because we have access to radial information only. The situation is in principle much better in anisotropic solutions where orientational information makes possible a clear-cut characterization of the anisotropy of the aggregates. This should encourage the study of nematic phases. There is, however, a drawback associated with the fact that the solution is spontaneously anisotropic for high concentrations only; accordingly we are dealing with strongly interacting-rather than isolated-aggregates. These aspects will be approached by investigating the structures of two nematic systems with X-ray and neutron-scattering techniques. The first system will be the original one, sodium decyl sulfate (SdS)/l-decanol/water; the second will be a more recently studied mixture, potassium laurate ~_______
(1) Lawson, K. D.; Flautt T. J. J . Am. Chem. SOC. 1967, 89, 5489. (2) Forrest, B. J.; Reeves, L. W. Chem. Reu. 1981, 81, 1. (3) Charvolin, J.; Samulski, E.; Levelut, A. M. J.Phys. Lett. 1979,40, L-587. (4) See the review articles by: Fontell, K. Mol. Cryst. Liq. Cryst. 1981, 63,59. Charvolin, J.; Tardieu, A. Solid State Phys. 1978,209, Suppl. 14. Luzzati, V. In “Biological Membranes”; Chapman, D., Ed.; Academic Press: London, 1968; p 209. (5) It must be emphasized here that this relation between the sign of Ax and the shape of the aggregates is not general. Other chemicals may lead to the opposite situation. See Boden, N.; McMullen, K. J.; Holmes, M. C.; Tiddy, G. J. T. In “Liquid Crystals of One- and Two-Dimensional Order”;Helfrich, W.; Hepke, C., Ed.;Springer Series in Chemical Physics, Springer Verlag: Berlin, 1980; p 299. And more recently Boden, N.; Radley, K.; Holmes, M. C. Mol. Phys. 1981, 42, 493. Forrest, B. J.; Reeves, L. W.; Robinson, C. J. J . Phys. Chem. 1981,85, 3244. (6) Billard, J. In “LiquidCrystals of One- and Two-dimensional order”; Helfrich, W.; Hepke, G., Ed.; Sptinger series in Chemical Physics, Springer Verlag: Berlin, 1980; p 383. (7) This representation is not the only one possible. However, it visualizes our description of the shape of the aggregate in a simple way. A more accurate representation would require systematic contrast variation experiments and form factor calculations which are not yet feasible at this stage.
0 1983 American Chemical Society
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x3
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Figure 1. A schematic representationof the most general aggregate. I, > I, the phase is discotic (Nd), when I , > I, I, the phase is calamitic (Nc). The distances between the aggregates along the three axes are d , , d,, and d,.
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The three axes have length I,, I,, and I,. When I ,
(KL)/ 1-decanol/water, which has the particular interest of exhibiting a biaxial nematic phase.8 In addition to the structural aspects quoted above, this article aims at clearing up a methodological point. Our first X-ray spectra demonstrated clearly the anisotropic shapes of the aggregates. At that time we tried also to determine the characteristic micellar dimensions. However, in such systems, with a high amphiphilic content (-45% by weight), the dimensions of the aggregates and their separations are of the same order of magnitude; consequently the intra- and interaggregate interferences may contribute to the scattering in the same range of scattering vectors and the two contributions cannot be directly distinguished (see note 12 of ref 3). At the time of this first publication, we assumed that the interaggregate interferences were dominant in determining the peak values of the scattered intensity. By comparing X-ray and neutron-scattered intensities, we present here a test of the validity of this in the case of concentrated systems and then proceed with a more accurate analysis. Experimental Section Samples. Potassium laurate was prepared in the laboratory from commercial lauric acid (Fluka p.p.a. 99% and CEN Saclay). The samples were prepared in sealed glass tubes by weighing the appropriate quantities of the compounds and homogenizing them through ultrasonication and centrifugation. All samples were made of protonated amphiphilic aggregates in DzO. Microscopic Observations. The mesophases were first identified by observing their textures in polarized light. Samples were introduced either between glass plates separated by Teflon spacers of 50 pm, or in flat capillaries of thickness 200 pm, and studied under a polarizing microscope (Leitz orthoplan Pol) equipped with a heating stage (Mettler FP 52) and a temperature regulator (Mettler FP 5). As we found in certain cases that the texture change was not always evident at the transition between several phases, we complemented the optical observations by NMR determination of the sign of the anisotropy of magnetic susceptibility, AX. Nuclear Magnetic Resonance. This method was used to determine the sign of the anistropy of the magnetic (8) Yu, L. J.; Saupe, A. Phys. Rev. Lett. 1980, 45, 1000. (9) Strzelecki, L.; Germain, C. according the synthesis of Radley, K.; Reeves, L. W.; Tracey, A. S. J. Phys. Chem. 1976, 80, 174.
Hendrikx et al.
susceptibility, A x , which contains information about the structure of the samples (see above and ref 5). The method, which consists of observing the evolution of the DzO quadrupolar splitting when the sample aligns in the magnetic field, has been described We recall here briefly only the essentials. The D 2 0 splitting Av for a uniaxial nematic phase which is aligned parallel to the magnetic field ( A x > 0) changes to -1/2Av when the sample is rotated through 90°. On the other hand, the D20 splitting Av for a uniaxial nematic phase which is aligned perpendicular to the field ( A x < 0) does not change under rotation. The D20 spectra were obtained at 13 MHz with a Bruker CXP 100 spectrometer. Scattering Methods. The structures of the samples were determined from X-ray and neutron scattering; owing to the expected sizes of the aggregates (i.e., several tens of A), small angle scattering equipments is required. The samples were oriented by a magnetic field, and the scattered intensities plotted as functions of the scattering vector ij = 2 d = 4~ sin 8/X, where X is the wavelength and 28 the angle between the scattered and incident beams. 1. X-rays. The experimental arrangement was described in ref 3: it consists of a photographic Laue camera with point collimation, X = 1.54 A, and sample-to-film distance of 8 cm. The camera was equipped with a movable 12-kG permanent magnet with horizontal field parallel to the equator. The samples were in glass capillaries of diameter 1.5 mm, held perpendicular to the X-ray beam. Therefore the director was parallel to the equator for calamitic samples ( A x >O) and perpendicular to the equator for discotic samples ( A x < 0). 2. Neutrons. The experiments were performed at the Institut Laue Langevin in Grenoble, France, on the instrument D 17. This spectrometer is equipped with a planar square multidetector; the distance between the sample and the detector was 81 or 140 cm, the wavelength of the incident neutron beam X = 8 or 12.1 A, and the wavelength spread AX/X = 10%. A large range of scattering vectors, i j , has been explored (1.5 X lo-* < 4‘ < 3 X 10-1A-*) giving access to distances in the samples from 400 to 21 k. The samples, contained in quartz cells 2 or 1 mm thick, were prepared in homotropic or planar configurations by applying a 12.5-kG magnetic field before placing them in the sample holder of the spectrometer. (The duration of the experiment, -15 min, was short enough so that no relaxation of the sample configurations was detected). The spectra were recorded for different orientations of the scattering vector ij in the (xl,x 2 , x 3 ) system of axes (Figure 1). The scattered intensity, which depends on the difference between the average scattering length density of the aggregate, p , and that of the solvent, ps, is maximum for samples of protonated amphiphilic aggregates in D20.13 All data were treated according to standard I.L.L. procedures for small angle anisotropic scattering. The data were normalized for unit incident beam flux. The spectra were corrected for background, absorption, and normalized for detector efficiency by using a similarly corrected HzO spectrum. As the scattering curves recorded for the same sample in 1-and 2-mm cells (10) Khetrapal, C. L.; Kunwar, A. C.; Tracey, A. S.; Diehl, P. “Lyotropic Liquid Crystals” in “NMR Basic Principles and Progress”; Diehl, P.; Fluck, E.; Kosfeld, R., Ed.; Springer Verlag: Berlin, 1975; Vol. 9. (11) Fujiwara, F.; Reeves, W.; Suzuki, M.; Vanin, J. A. “Proceedings of the National Colloid Symposium”, Knoxville, June 1978; Mittal, K.. Ed., Plenum Press: New York, 1979. (12) Charvolin, J.; Hendrikx, Y. In ‘Liquid Crystals of One- and Two-dimensional Order”; Helfrich, W.; Hepke, G. Ed.; Springer Series in Chemical Physics, Springer Verlag: Berlin, 1980; p 265. (13) Jacrot, B. R e p . Prog. Phys. 1976, 39, 911.
The Journal of Physical Chemistry, Vol. 87, No. 20, 1983
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Flgwe 2. Region of the SdS/decanol/water phase diagram where the lyotropic nematic phases and their adjacent phases (ordered lamellar, ordered cylindrical, and disordered micellar) are located. The hatched area represents biphasic and triphasic domains. The llmits are only indicative. Concentrations in weight percent. The structure of the phases were determined through an X-ray diffraction study.
Figure 4. Schematic representation of the contrast profiles of a spherical SdS/decanol micelle in D,O: p x , electron density profile of the aggregate relevant to the X-ray experiment; pn, scattering length density profile of the aggregate relevant to the neutron experiment.
Figure 3. Temperature phase diagram of the nematic phases along line C of Figure 2. Concentrations in weight percent. SdS/decanol 5.45 (I, isotropic phase; Nd, discotic phase; Nc, calamitic phase; M, ordered cylindridical phase or middle phase). The phases were identified by optical study of the textures.
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were quite similar, multiple scattering could be neglected. Sodium Decyl Sulfate/l-DecanoVWater System Phase Diagrams. The phase diagram of the SdS/1decanol/water ternary system at room temperature was investigated previously in the region of the nematic domain.14 It is shown in Figure 2. In Figure 3 we show an additional temperature study along line C of the first diagram; the sequence of the phase transitions agrees with that observed by Yu and Saupe15 (a slight discrepancy between the transition temperatures may be due to slightly different alcohol contents). Scattering Experiments. As already pointed out in the introduction, the amphiphile concentration of our systems is so high that not only the interferences associated with the scattering originating in a single aggregate will be recorded but also those associated with the scatterings of neighborings aggregates. This may be illuritrated by considering the formalism established for spherical particles in solution. (We use it here, although our aggregates are anisotropic, as a basis for discussion. The scattered intensity may be written as16
I({)
[email protected](Q)
(1)
where N is the mean aggregate number in the irradiated (14)Hendrikx, Y.; Charvolin, J. J.Phys. 1981, 42,1427. (15)Yu, L.J.; Saupe, A. J. Am. Chem. SOC.1980, 102, 4879. (16)Cotton, J. P.'Introduction B la spectrometric neutronique, Diffusion aux petits angles"; Cours donn6s au CEN-Saclay, 1974.
volume. The factor F(Q) corresponds to the scattering by a single aggregate,it is the Fourier transform of the density of scattering centers within the aggregate. The term S({) takes account of the scattering originating from the distribution of the aggregates in the solution: S(q') = 1 + ( C / m ) . f [ g ( r-) l1e-q #where g(r) is the radial distribution function, C is the mass concentration, and m is the mass of one aggregate. Thus (1)shows that the contributions from the aggregates and their distribution are intermingled in the scattered intensity I({). In order to determine the structure of the system it is necessary to know F ( { ) and S(q') separately. This can be done in the case of rigid particles by varying the concentration C and then extrapolating to C = 0. But this method is not applicable here since size and shape of the aggregates,and hence F({), changes with the concentration. Therefore one must keep the concentration constant and find another way to distinguish between the two contributions. One might think of making F(q') independent of q' so that I(Q)would directly give access to the packing of the aggregates, and therefore to their mean distances from which the dimensions could be estimated through a model. In principle this might be done with X-rays by labeling the aggregate with a solute molecule bearing a heavy atom so that the aggregate would be seen as a point. However, as solutes may induce structural modifications which we cannot control, we preferred to work with another method, one which takes advantage of the change of scattering centers associated with a change of radiation (i.e., X-ray neutron). 1. Comparison between Scattered Spectra Obtained from X-ray and Neutron Scatterings. The two radiations do not see the aggregate as the same object: X-rays see the aggregate as a hollow shell of polar heads, neutrons see the aggregate in D 2 0 as a bulky paraffinic core because H and D scatter neutrons in very different ways. Therefore, moving from X-rays to neutrons, F ( { ) changes but not S({). This provides a way to separate the two contributions. It is straightforward if the X-ray and neutron
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Hendrikx et al.
. .
0
0 0 0
41)
.
1 *
O
.
0 .
0
O0
.'
1
..sa..
.
2
3
'.
.4 ' *
. a x 105(A-')
,(a)
Flgure 5. Calculated intensities scattered by an isolated spherical SdS/decanol micelle in D,O: (1) X-ray diffraction, (2) neutron dtfraction. The values px, pn, R,,,, and R , are as in Figure 4.
spectra are similar because we can say that the scattering is controlled by the constant S(tj), Le., the interferences between aggregates. It requires more complex modeling if the spectra are appreciably different. This procedure will be discussed in the context of Figure 4 where the contrast profiles of a spherical SdS-decanol micelle in D20 are schematically represented. The aggregate exhibits three electron density levels (p,) as well as three scattering length densities (p,) which are pPm, ppol, and pw, the densities of the paraffinic region, the interfacial region, and the water region, respectively. The values of p x are those reported in ref 14 and the values of pn were calculated from the coherent scattering lengths given in ref 17. In the case of neutron scattering, the scattering length density of the interfacial region and the water region are very close, Le., Ppol
= PW.
The relevant F(q')curves for an isolated micelle are shown in Figure 5. They have been calculated following ref 18:
F(G)= [Vparbpar
- ppoJ@(qf&ar)
+
vpOl(~pO1-pw)@(qRpoJ12
(2)
where Rp, and RP1 are respectively the radius of the paraffinic core and that of the micelle. (Their values are those reported in ref 14). @(qR) = 3(sin qR - qR cos qR)/(qR)3 is the scattering function of a sphere, Vp, and V,, are respectively the volume of the paraffinic core and that of the micelle. Clearly the intensity scattered by one aggregate drastically changes with the radiation used: the rather regular and rapid decrease of F(q')observed with neutrons contrasts with the slower oscillatory decrease of F({) observed with X-rays. We present in Figure 6 X-ray and neutron spectra obtained with the same calamitic sample for scattering vectors normal to the director of the phase. Obviously the spectra are very close; in particular, their maxima have similar positions. Moreover, in both cases, the intensity is weak at q' 0. Therefore we have a situation where the interferences between aggregates are dominant. We shall use these spectra to estimate the mean distances d,, d2, d3 between the aggregates along their different axes, as we did in our first X-ray e~periments.~ This treatment is only a fiist approximation because it does not take into account
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(17) Bacon, G. E.Acta Crystallogr., Sect A 1972, 28, 357.
(18) Reiss-Husson, F. These d'Etat de L'Universit6 de Straabourg, 1963.
Flgure 6. Scattered intensity obtained with a calamitic sample for scattering vectors perpendicular to the director of the phase (G J: (1) X-ray diffraction (microdensitometer analysis of the X-ray pattern); (2) neutron diffraction. The sample composition was as follows: SdS, 38.1%; decanol, 6.8%; D,O, 55.1%; temperature 23 O C . The values of I ( a ) are in arbitrary units.
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-equator
1
2
3 I ,
Flgure 7. Density map of the scattered intensities provided by the XY detector for an oriented discotic sample. The neutron beam is perpendicular to the director of the phase. The intensity levels are 10, 15, 20, 22, 24, 50,and 60 in arbitrary units. The sample composition was as follows: SdS, 36.32%; decanol, 6.63%; D,O, 57.06%; tem23 OC. The black spot in the center is the shadow of the perature beam-stop.
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slight differences between the spectra. 2. Neutron Spectra. We have followed the evolution of the Z(q') spectra moving from a discotic to a calamitic phase either by increasing the amphiphile concentration at room temperature (line C in the phase diagram of Figure 3) or by increasing the temperature while keeping the amphiphile concentration constant (line T in the phase diagram Figure 3). All data reported here were recorded with the neutron beam perpendicular to the director, Z, of the phases. The XY detector provides density maps of scattered intensities for all q' vectors in a plane containing the director. An example of such spectra is given in Figure 7 for a discotic sample: the anisotropy of the aggregates is evident. We have made several attempts to identify a biaxial phase in the vicinity of the Nd-Nc transition8 which should originate from the biaxiality of the aggregates. In that case the aggregates should exhibit different dimensions along their three axes xl, x 2 , and x3 (Figure 1). To this end the samples were repeatedly rotated around an axis perpendicular to the magnetic field so that a complete alignment of the aggregates with their largest dimension parallel to the field and their shortest dimension parallel to the rotation axis was achieved. The I ( @ curves were recorded with the neutron beam parallel to the director of the phase, Le., ij was along the x1 and the x 2 axes in the discotic phase
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T A B L E I: Volume, Dimensions, and Mean Aggregation Number of the Aggregates in Discotic ( N d ) and Calamitic ( N c ) Phases of the SdS/1-Decanol/Water System
Nd
Nc Nd
phase
Nc
vc
volume available t o one aggregate volume of one aggregate hypothesis
= (n/4)di2dI/ va= (n/4)dlZdll@= ( 7 7 / 4 ) ~ i 2 1where ~ ~ , @ is the volume fraction of amphiphiles Ill 20 A , the thickness of a lamella I1 26 A , the diameter o f a cylinder
estimation mean aggregation number
in a L, phase the diameter of the disk I 1 n - 145
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or along the x 2 and x 3 axes in the calamitic phase. We were unable to detect any differences between the intensity curves recorded along these axes. As at this stage the aggregates appear uniaxial, we shall discuss only sections along ii(GIl) or perpendicular to ii(QL) of the density maps. Figure 8a shows the intensity curves recorded at room temperature for a discotic phase. The I(G) curve along the director ii shows a sharp maximum at qI1= 1.5 X lo-' A-1, Le., at s,, = q I 1 / 2 a= [41.9 A]-', while the I(+) curve perpendicular to ii shows a smooth but unambiguous maximum at q L = 1.05 X lo-' A-', Le., at sI = q I / 2 a = [59.8 A]-'. The intensity along GI, is large compared with that along GI for all the explored range. Also the line width at mid-height (Aq N 0.7 X 10-1 A-') is smaller along the A-1). direction qll than along the direction G, (1 X When T > 26 OC,this phase becomes a calamitic phase. In this Nc phase the scattered intensity was recorded at 30 OC and the corresponding I(G) curves are shown in Figure 8b. The I(G)curve along the director ii is very broad and no clear maximum appears, while the I(G) curve perpendicular to ii shows a sharp maximum at q1 = 1.5 X lo-' A-1, i.e., at s, = q L / 2 a = [41.9 A]-'. The intensity along G, is large compared with the intensity along Gl1for all the explored G range. The line width along GL, Aq, is -0.5 X lo-' k';we have no access to Aq along GI,. A similar behavior is observed when the calamitic phase is obtained from the discotic phase by increasing the concentration of amphiphilic molecules and Figure 9 shows the intensity curves recorded at room temperature for such a Nc phase. Here the I(q') curve along the director of the phase ii is infinitely broad and shows no maximum while the I(G) curve perpendicular to 6 shows again a sharp maximum at Gl = 1.48 X lo-' A-1, Le., at sI. = q 1 / 2 a = [42.3 A]-'. Here also the intensity along GI is large compared with that along GI1for all the explored 4' range, and the line width along can be estimated: Aq -0.62 X lo-'
a,
A-1.
Data Analysis. As the curve of scattered intensities I@) are very similar whatever the radiation used, and as they show no scattering for 4' 0, we conclude that the scattering is dominated by the interferences between the aggregates. We therefore have access to the distribution of the aggregates in the solution and we may estimate from the maxima of the I(G) curves the mean distances between the centers of the aggregates along the direction parallel to the direction ii, d,,,or perpendicular to it, d,. Following Table I, we may calculate the volume available to one aggregate in the solution, V,, and the volume of one ag-
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- 57 A
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in a H a phase the length of the cylinder Ill 2 60 A n > 90
I (au) 30
2o
lo
I I
I
t 1
0
1
2 (b)
J
3 x 10( b,-' 1
Figure 8. Typical neutron scattering curves of oriented nematic phases with G vectors along n' or perpendicular to n'. The neutron beam is perpendicular to the director of the phase. (a) Discotic phase (Nd)with the following composition: SdS, 36.32 % ; decanoi, 6.63 % ; D,O, 57.06% at 23 O C [0,I(+) along the director n'; X, I ( i ) perpendicular to n']. (b) Calamitic phase (Nc) with the same composition as (a) but at 30 O C [0,I ( ? ) along the director 6;X , I ( ? ) perpendicular to The values of I ( i ) are in arbitrary units.
z].
gregate, V,, if @ the volume fraction of amphiphilic molecules is known. We can also estimate the dimensions of the aggregates, even though the dimensions 1, and l,, are not known independently. A reasonable assumption is to in the discotic phase the value measured for the give Ill thickness of a cl0 bilayer in an ordered lamellar phase, 20
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The Journal of Physical Chemistry, Vol. 87, No. 20, 1983
Iiauif
30
t
I
I
,
I I
S I
1
l a
l . l I b
I .
I
1
250 252 254 256 250 260 262 2 6 4 Potassium laurate (weight per cent) Figure 9. Neutron scattering curves for an oriented nematic cahmltic phase (Nc) of the following composition: SdS,38.1 % ; decanol, 6.8 % ; D,O, 55.1% at 23 OC [0, I ( G ) along the director ?; X, I ( ? ) perperpendicular to ;]. The values of I ( G ) are in arbitrary units.
to give 1, in the calamitic phase the value measured for the diameter of a cl0 cylinder in an ordered hexagonal phase, -26 A.1g Of course I,, in the discotic phase and 1, in the calamitic phase may differ from these values by a few percent but that will not affect in an appreciable way the calculated dimensions I , and Ill, respectively. Along the lines of the phase diagram we have followed, the size of the aggregates in the discotic phase does not change significantly. They are disks, or oblate spheroids, whose average dimensions are small: thickness (Ill)20 A and diameter (I,) 57 A, so that their anisotropy defined as the ratio of their largest to their shortest dimension is rather weak, about 2.8. In the calamitic phase the aggregates are cylinders, or prolate spheroids, and their polydispersity increases when we move away from the discotic-calamitic transition. Just after the discotic-calamitic transition we estimate the length of the cylinders (Ii,) to be -60 A, so their anisotropy is about 2.3 (diameter I, 26 A). The polydispersity of the aggregates manifests itself by a broadening of the scattering line; very rapidly, in the calamitic phase, it becomes such that we loose information about the length I,, of the cylinders, concluding only that lIi>, 60 A at higher concentrations. Finally, from the angular distribution of the intensity along an arc of circle centered a t ij = 0, and passing through the maximum of intensity (cf. the density map in Figure 7 ) ,we have access to a coarse estimation of the orientational fluctuation of the axis of each aggregates, a', relative to the nematic axis or director of the phase, fi. This estimate of the order parameter S can be only a lower limit because of possible local disorientations induced by the sample cell. The analysis leads to a limit of 0.7 in both calamitic and discotic phases. At this stage we must compare our experimental data with those obtained by other authors20,21 for a Nd phase in the SdS/l-decanol/water/Na2S04 system. Their data differ considerably from ours; they conclude that the sizes of the aggregates are much larger. In particular, they see an additional band at q 6.28 X lo-* A-1, Le., at s = q/21r
Flgure 10. Phase diagram of the nematic phases in the KL/ldecanol/water system as a function of the KL concentration at constant decanol content = 6.27% against the temperature: I, isotropic phase; Nd, discotic phase: Nc, cahmitic phase: hatched area, biphasic domain. Concentrations in weight percent.
A,19 and
4
'Y
Y
-
X
X
d
eouotor
-
-
-
-
(19)In a lamellar phase (SdS = 39.65%, decanol = 10.23%; D20= 50.03%) the lattice parameter, which is the distance between two lamallae, corresponds to s = q/Zn = (37.3A)-1;moreover in a hexagonal phase (SdS = 49.87;D20= 50.13%), the lattice parameter (distance between the cylinders) corresponds to s = q/2n = (36.5A)-'. See ref 14. (20)Amaral, L.Q . ;Tavares, M. R.; Vanin, J. A. J. Chem. Phys. 1979, 71, 2980. (21)Amaral, L.Q.; Tavares, M. R. Mol. Liq. Cryst. Lett. 1980,56, 203.
Figure 11. Typical density maps of the scattered intensities provided by the XY detector for oriented nematic samples at -22.5 OC. The neutron beam is perpendicular to the director of the phase. (a) Calamitic phase. The intensity levels are 7, 8, 9, 10, 20, 30, 40, 50, and 52 in arbitrary units. The sample composition was as follows: KL, 26.34%; decanol, 6.28%; D,O 67.38%. (b) Discotic phase. The intensity levels are 7, 10, 15, 19, 20, and 22 in arbitrary units. The sample composition was as follows: KL, 25.26%; decanol, 6.28%; D,O, 68.47%. The black spot in the center is the shadow of the beam-stop.
--
-
[lo0 A]-', along the same direction as the band at qll 1.5 X lo-' A-l, i.e., at sli = q1,/27r [42 A]-', and the relative intensities of the two bands depend on the nature of the sample cell and its thickness. We were unable to observe such a band whatever the configuration of the experiment.
Potassium Laurate/l-Decanol/Water System Phase Diagram. The phase diagram is represented in Figure 10. The hatched area is a biphasic region. When compared with the phase diagram in ref 8 the boundary of the calamitic phase is a little shifted toward lower KL concentrations. Scattering Experiments. The shape and sizes of the aggregates in the nematic domain were investigated by following the evolution of the I(q') spectra along line C and along line T of the phase diagram shown in Figure 10. The measurements along line C were carried out at room temperature, 22.5 "C. Most of the data were recorded with the neutron beam perpendicular to the director fi of the phases. Thus the XY detector provides density maps of scattered intensities for each tj vector in the plane containing the director 5. Density maps of samples charac-
-
Anisotropic Aggregates of Amphiphilic Molecules
The Journal of Physical Chemistty, Vol. 87,
I (au)
No. 20, 1983 3997
I(au1 3c
20
20 e
10
P
9
10
P
D
.e
P P
.............
$%?.
0 1
2
3 qx100
Figure 12. Neutron scattering curves for an isotropic phase of composition KL = 25.25%, decanol = 6.28%, D,O = 66.47% at 14.7 OC [0, I ( ? ) along the axis perpendicularto the equatorial plane; X , I(+) along the axis parallel to the equatorbl plane]. The values of I(G) are in arbitrary units.
teristic of each nematic phase are shown in Figure 11 (a, Ax > 0; b, Ax C 0). They are anisotropic in both phases, therefore the aggregates are anisotropic, and these maps are very similar to those obtained for the nematic phases of the SdS/ 1-decanolfwater system. Therefore the phase with Ax > 0 contains elongated aggregates or prolate spheroids, and we shall call it as before a nematic calamitic phase (Nc); the phase with A x C 0 contains flattened aggregates or oblate spheroids, and we shall call it a nematic discotic phase (Nd). (It was pointed out that the relation between the sign of Ax and the shape of the aggregates is not general,5i.e., it may change with the nature of the chemicals; however, in the present system the same relation holds as in SdS). In the isotropic phase the recorded intensities along two axes, parallel and perpendicular to the equator, are shown in Figure 12. The I(q') curves along both directions are identical. In the nematic domain several attempts were made, without success, to identify a biaxial phase from the biaxiality of the aggregate in the vicinity of the Nd-Nc transition. We proceed then in the same way as described before for the SdS/l-decanol/water/system, i.e., we discuss only sections along Z or perpendicular to Z of the density maps for different Samples. The I(q') spectra were recorded along line C (phase diagram, Figure 10). They fall into two classes, one representative of the discotic phases, the other representative of the calamitic phases. Figure 13a shows the neutron scattered intensity curves characteristic of a discotic phase (Nd). The I(3) curve along the director ii of the phase shows a sharp maximum at qll = 1.155 X lo-' A-', i.e., at sIl = qll/2rr= [54.37 A]-'; the maximum in the I(;) curve perpendicular to 6 is also sharp and occurs at q, = 0.885 X lo-' A-1, i.e., at s, = q,/2?r = [70.96 A]-'. The intensities along ill and q', are of the same order of magnitude. The line width along the director of the phase (ill), A,, is -0.72 X lo-' A-'; along lj, it is -0 .80 X lo-' .kl.Figure 13b shows the neutron scattered intensities characteristic of a calamitic phase (Nc). The I(Q) curve along the director ii of the phase shows a smooth but unambiguous maximum at qlI = 0.720 X lo-' A-', Le., at SI, = qll/2rr= [87.22 A]-'; the I(q')curve perpendicular to Z shows a sharp maximum at q, = 1.185 X lo-' %.-I, Le., at s, = q,/2rr = [53 AI-'. The intensity along 4' is large compared with the intensity along gll. The line width along q',, Aq, is -0.50 X lo-' A-'; along ill the Aq value cannot easily be estimated. Similar spectra for discotic and calamitic phases were recorded along time T (phase diagram, Figure 10).
X .
O O
r o :.;Do
0 1
................. 2
3 ?fxlOlA-')
(a)
I f
(b) Figure 13. Typical neutron scattering curves for oriented nematic phases with G vectors along ? or perpendicular to 5 at -22.5 "C. The neutron beam is perpendicular to the director of the phase. (a) Discotic phase (Nd) with the following composition: KL, 25.25 % ; decanol, 6.28%; D,O, 68.47% [0, I ( + ) along the director 5; X , I @ ) perpendicular to 51. (b) Calamitic phase (Nc) with the following composition: KL, 26.34%; decanol, 6.28%; D,O, 67.38% [0, I ( G ) along the director 5; X , I(G) perpendicular to 61. The values of I ( G ) are in arbitrary units.
Data Analysis. As already quoted in the preceding section (data analysis in the SdS/l-decanolfwater system) we may estimate from the maxima of the I(q') curves the mean distances between the centers of the aggregates along the directions parallel to the director 6, d,,,or perpendicular to it, d,. Figure 14a shows the evolution of d,land d , in the nematic domain along line C, i.e., with KL concentration of the samples. Figure 14b shows the evolution of dlland d, in the nematic phases along line T, i.e., with temperature when the KL concentration was kept constant. It is not yet clear whether the isotropic phase results from the disappearance of the orientational order of the aggregates or from a change to isotropic aggregatesz2 The phase boundaries, i.e., the phase transitions associated with the variation of the KL concentration and of the tem(22) It was shown the aggregates are still anisotropic in the concentrated micellar phases of the SdS/l-decanol/water system. See ref 14.
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The Journal of Physical Chemistry, Voi. 87,
No. 20, 1983
Hendrikx et ai.
T A B L E 11: Dimensions and Mean Aggregation Number of the Aggregates in Discotic ( N d ) and Calamitic (Nc) Phases of the KL/l-Decanol/Water System Nd
phase
- 23 A , t h e thickness of a lamella in a L,
hypothesis
I,i
estimation mean aggregation number
t h e diameter of t h e disk l l n 215
-
-
Nc
H,
36 A , the diameter oE a cylinder in a phase the length of t h e cvlinder 60 A < Ill < 66 A 175 < % < 195
11
phase
64 A
loot
N
pr3ses
25
Discotic c r Nd phases
26
Caiamitic or Nc phases
26
25
Potassium iaurate ( weight percent)
Potassium laurate (weight percent)
(a1
(a)
e, I
,.
-
---A-
4u
I
20
25
Temperature (
O
30
C I
(b) Flgure 14. Evolution of the mean distances, dlland d , , between the centers of the aggregates in the oriented nematic phases: (a) along line C (phase diagram, Figure 10) Le., with the KL concentration of the samples at 22.5 OC;(b) along line T (phase diagram, Figure 10) Le., with the temperature at KL = 25.25%.
perature, see parts l a and b of Figure 14) are in agreement with those identified by our optical observations and NMR determination of Ax. From these data we may calculate the volume available to one aggregate in the solution, V,, and the volume of one aggregate, V,, if the volume fraction of amphiphiiic molecules is known, and then estimate the dimensions of the aggregates following Table I. In this calculation the dimensions 1, and l,, are again not known independently and we propose once more that a reasonable assumption is to give l,, in the discotic phase the value of the thickness of a bilayer in an ordered lamellar phase and 1, in the calamitic phase the value of the diameter of cylinders in an ordered hexagonal phase. This assumption could easily be used for the SdS/ 1-decanol/water system, because the chain lengths of the amphiphilic molecules (SdS and decanol) were the same and the amphiphile concentrations of the nematic phases involved were comparable to those of neighboring lamellar and hexagonal phases.14J9 In the present system the chain lengths of the two amphiphilic molecules differ; furthermore the laurate concentration is rather low compared to those of the closest known lamellar and hexagonal phases of potassium laurate. To calculate the dimensions of the aggregates we assumed that their thickness in the Nd phase (1 J is e 2 3 8, and their diameter
14
Discotic or Nd phases
.
e1
1
Cjl.imitic or Nc phase,
25
20
.-.-.
- -
30
Temperature ( O C )
ib) Figure 15. Evolution of the average dimensions, I l l and I , , of the aggregates in the oriented nematic phases: (a) along line C (phase diagram, Figure 10) i.e., with the KL concentration of the sample at -22.5 O C ; (b) along line T (phase diagram, Figure 10) Le., with the temperature at KL = 25.25%.
in the Nc phase (II) is -36 A; these correspond to values of the thickness of lamellae in lamellar phases and the diameter of cylinder in hexagonal phases made of KL with small amounts of several long chain alcohols given in ref 23. The evolution of the dimensions of the aggregates, I,, and l,, with the KL concentration and with the temperature are respectively shown in parts a and b of Figure 15. The size of the aggregates does not change appreciably in either the discotic region or in the calamitic region. The average dimensions are given in Table II.24 They are rather small and the anisotropy of the aggregates is weak, about 2.8 for disks and about 1.75 for cylindres. From our results it appears that when the temperature is varied with the amphiphile concentration kept constant the volume of the aggregates decreases at the Nd-Nc transition but the area to volume ratio of the aggregates does not change. Since the scattering curve which gives access to the length of the cylinders in the Nc phase is sufficiently narrow at all (23) Fraqois, J.; Gilg, B.; Spegt, P. A.; Skoulios, A. E. J . Colloid Interface Sci. 1966, 21, 293. (24) A calamitic nematic phase made of KL/potassium chloride/water was recently investigated through X-ray diffraction by Figueiredo, A. M.; Amaral, L. Q.Mol. Cryst. Liq. Cryst. 1981, 74, 109. Their diffraction patterns differ from ours. A similar disagreement was pointed out in the case of a Nd phase in the SdS/decanol/Na2S04/water system.
The Journal of Physical Chemistry, Vol. 87, No. 20, 1983
Anisotropic Aggregates of Amphiphilic Molecules
concentrations studied (though not as sharp as the scattering curve which gives access to the diameter of the disks in the Nd phase), we are able to deduce that the cylinder length varies between 60 and 66 A. As with the SdS/l-decanol/water nematic phases, an analysis of the density maps provides a coarse lower limit for the order parameter S which is about 0.7.
Conclusion In this paper we have presented X-ray and neutron scattering studies of concentrated solutions of amphiphilic molecules which assemble in anisotropic aggregates and form nematic phases. We have studied two ternary systems: sodium decyl sulfate/l-decanol/water and potassium laurate/ 1-decanol/water. We moved in the phase diagrams (Figures 3 and 10) along two lines crossing a transition between nematic phases with opposite anisotropies of magnetic susceptibility. Along line C the amphiphile concentration increases while the temperature is kept constant; along line T the temperature increases while the concentration is constant. The phases in the nematic domains of these ternary systems have very similar properties. In the regions of highest water content, the phase is an uniaxial discotic nematic or Nd phase with A x < 0. The aggregates are small disks or oblate spheroids, randomly distributed in the solution but with axes nearly parallel to each other, their average orientation defining the director, 5, of the phase. The average dimensions of the disks are small (thickness -20 8,and diameter -57 A in the first system, thickness -23 A and diameter -64 A in the second system) so that their anisotropy is rather weak, about 2.8. Within this discotic phase the dimensions of the aggregates appear independent of the amphiphile concentration. At higher amphiphile concentration the discotic phase transform into a calamitic or Nc phase with A x > 0. Here the aggregates are cylinders or prolate spheroids, which are again randomly distributed in the solution but with their axes nearly parallel to each other, their average orientation defining the director 5 of the phase. Just after the Nd-Nc transition we estimate the diameter of the cylinders to be -26 A and their length 60 A in the SDS/l-decanol/water system. The cylinders in the Nc phase appear more polydisperse than the disks in the Nd phase and, very rapidly, when the water content decreases the length and the polydispersity of the cylinders increase so that no average value for the length of the aggregates in the concentrated Nc phases can be given. This should be connected to recent theoretical analyses of isotropic phases in which an increase in concentration is shown to give a crossover from monodisperse disks to polydisperse rods.25 On the other hand, the cylinders in the calamitic domain of the KL/ 1-decanol/water system appear more uniform in size. Assuming their diameter is 36 A, we found that their length lies between 60 and 66 A (so that their anisotropy is coarsely -1.75).
-
(25)McMullen, W. E.; Ben-Shaul, A.; Gelbart, W. M., manuscript in preparation.
3999
It has been shown in other studies8 that the transformation from one uniaxial nematic phase to the other is not direct, being separated by a biaxial nematic phase. It is natural to ask then whether the biaxial phase results from biaxial aggregates or from the coexistence of uniaxial aggregates with different (e.g., rod and disk) shapes. We failed to detect this phase and to answer this question with our techniques but this may well be due to insufficient intrumental resolution. Indeed we would not expect a large effect considering the weak value of the anisotropy of the aggregates around the transition. We must emphasize that, in any case, ours is only a first approach: a better resolution and the use of the contrast variation method in neutron scattering should help us to refine our experiments. To finish with the description of our results we must recall (as already pointed out in ref 14 of ref 3) that the diffraction data are ambiguous with respect to the topology of the structure, paraffin in water or vice versa. In particular, in the SdS/l-decanol/water system, as the volume fraction of water and amphiphilc molecules are of the same order of magnitude, the water medium as well the paraffinic medium may be thought to be the continuous medium. Bearing in mind that the nematic phases are located between cylindrical and micellar phases (phase diagram in Figure 2) we decide in favor of a structure with a continuous aqueous medium. This study, which concerns rather large varations of concentration and temperature within the nematic domains of two ternary systems, confirms the structural description we proposed earlier on the basis of our preliminary s t ~ d y Our . ~ efforts to be more quantitative have of course provided a better description and have raised new questions concerning the structure of the aggregates and their ordering in the nematic phases. As for the structure of the aggregates, we have always described them as static objects. However, in the vicinity of the transition, their lateral dimensions and distances are so close that their shape might exhibit dynamical fluctuation phenomena; further experiments will be necessary to pursue these aspects. As for the ordering of the aggregates two points are to be raised. First, we have always said that there is no long-range translational order, but of course this does not imply that there is no short-range order, for instance, along the direction of shortest packing as suggested by the rather small line width of the scattering along this direction (compared to that along the perpendicular direction). Second, our estimate of the orientational order parameter suggests a lower bound value of 0.7. This is rather high, considering the weak anisotropy of these aggregates, and further experimental and theoretical exploration is clearly required.
Acknowledgment. We are indebted to Mr. W. M. Gelbart for his helpful criticisms on the redaction of the manuscript. M. C. Holmes thanks the Royal Society, London, for a European Fellowship. Registry No. Sodium decyl sulfate, 151-21-3; potassium laurate, 10124-65-9; 1-decanol, 112-30-1.
