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SYSTEMS OF SURFACTANT DDAB, WATER AND OIL
P. Barois, D. Eidam, S. Hyde
To cite this version:
P. Barois, D. Eidam, S. Hyde. X-RAY STUDY OF CUBIC PHASES IN TERNARY SYSTEMS OF
SURFACTANT DDAB, WATER AND OIL. Journal de Physique Colloques, 1990, 51 (C7), pp.C7-
25-C7-34. �10.1051/jphyscol:1990703�. �jpa-00231102�
COLLOQUE DE PHYSIQUE
Colloque C7, suppl6ment au n023, Tome 51, ler dkcembre 1990
X-RAY STUDY OF CUBIC PHASES IN TERNARY SYSTEMS OF SURFACTANT DDAB, WATER AND OIL
P. BAROIS, D. EIDAM and S.T. HYDE*
Centre de Recherche Paul Pascal, Avenue A. Schweitzer, F-33600 Pessac,
;ranee
Department of Applied Mathematics, Australian National University, Canberra ACT 2601, Australia
RCsumC: Nous prksentons des rksultats de diffraction des rayons X par des phases cubiques obtenues dans des systhmes ternaires: tensioactif (Bromure de Didodecyl Dimethyl Ammonium), eau et huile (cyclohexane et l-hexhe). Dans les deux cas, une transition de premier ordre entre deux phases cubiques de sym6trie diffhnte est observke.
Nous montrons que la topologie et l'aire norrnaliske de l'interface formCe par le tensioactif peuvent se d6duire simplement des variations du paramttre de maille avec la concentration en eau. Ces rksultats sont tout ti fait en accord avec une structure formCe par une bicouche de tensioactif dkorant deux types de surfaces minimales infiniment pCriodiques: les surfaces D et P de Schwartz.
Abstract: We report experimental studies of diffraction of X-rays by crystalline cubic phases in ternary systems of surfactant (Didodecyl Dimethyl Ammonium Bromide), water and oil (Cyclohexane and 1- Hexene). In both cases, a fmt order transition between two different cubic symmemes is found.
We show that the topology and the normalized surface to volume ratio of the surfactant interface can be simply obtained from measurements of lattice parameter variations with water content. Our results strongly support the existence of a bilayer of surfactant lying on infinitely periodic minimal surfaces:
Schwartz' D and P surfaces.
INTRODUCTION:
The pioneering work of Luzzatti [l], Tardieu [2], Fontell [3] and Larsson [4] on cubic phases in surfactant-water systems added a new dimension to the world of self assembly. They showed that the supramolecular structure of surfactant aggregates could be more complex than spheres (micelles in microemulsions), cylinders (hexagonal liquid crystals) or planes (lamellar phases).
The existence of crystalline phases with cubic symmetry is now clearly established in a wide variety of chemical (lyotropic and therrnotropic) and biological systems [1,5].
In the case of surfactant-water systems, a bicontinuous microstructure formed by a mono- or bilayer of surfactant molecules lining an infinitely periodic minimal surface (IPMS) has often been proposed [6,7]. Strong theoretical arguments of symmetry such as the minimization of the bending energy of the symmetric bilayer indeed support this picture.
On an experimental point of view, many data are consistent with the P M S description (cubic symmetry, bicontinuous structure from NMR data, acceptable volume fractions) but it must be emphasized that direct proofs of this microstructure such as freeze-fracture experiments associated with electron microscopy are not often available.
On the other hand, X-Ray diffraction data are not always conclusive: due to the generally small number of reflections, an accurate reconstruction of an electronic density map of the cubic unit cell is often impossible.
The aim of this paper is to provide simple experimental evidences that support (or may rule out!) the IPMS description of the microstructure.
We have chosen the ternary systems didodecyldimethyl ammonium bromide (DDAB), water, cyclohexane and DDAB, water, l-hexene. Phase diagrams of the DDAB, water and allcane, allcene solutions indicate that a cubic phase can exist over a large range of water contents [g], for example from -30% to 65%
W/W water to in the DDAB/water/cyclohexane system. Thus, this systems provide an optimal field in which to explore the possibility of new microstructures within crystalline phases of surfactant mixtures.
Out X-Ray data [9] clearly demonstrate that:
-i- the microstructure of the cubic phase changes with composition: a first order phase transition is found between two cubic phases of different symmetries.
-ii- the relationship between the cubic lattice parameter and the volume fraction of surfactant shows that the area of the surfactant bilayer scales like the simplest IPMS's of lowest genus and appropriate symmetxies (Schwartz' P an D surfaces).
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1990703
-1- CYCLOHEXANE SYSTEM:
EXPERIMENTAL SECTION,
We have made two series of ternary mixtures: DDAB, water, cyclohexane, all of which fall within the cubic phase region of the phase triangles determined by Fontell and Jansson [g] fig. 1. All samples were prepared with commercial DDAB (from SOGO Pharmaceutical, Tokyo, Japan) analytical grade cyclohexane (Merck, Darmstadt FRG) and twice distilled water. The three components were added to a glass ampule to give total weight of about 3 g, with all component weights measured to a relative accuracy of about 0.2%. The sealed ampules were heated to 90°C for 1 h to accelerate mixing of the components, followed by centrifugation to eliminate air bubbles from the gel. All ampules were left at room temperature for an average period of three weeks (with intermittent heating and cooling from 22OC to 90°C) after which the macroscopic appearance of the mixtures did not change for any of the samples.
In order to measure the X-Ray scattering patterns of these cubic phases, the ampules were opened and samples were injected into lmm diameter Lindemann capillaries.
Water DDAB
Single-phase regions of the ternary DDAB/cyclohexane/water system from reference 5. The cubic phase region is investigated in detail in this paper. Also marked are the two lamellar phases and the microemulsion L2.
The dotted triangle indicates the axes of the magnified region of the phase triangle shown in figure 3.
All spectra were obtained with the Small Angle X-ray Scattering (SAXS) Huxley-Holmes camera in the Research School of Chemistry, Australian National University. This camera admits measurements down to momentum transfers of 1.5~10-2 A-l, with spatial resolution of about 2x10-3 A-l (full width half maximum). We have used Cu K a i radiation selected by use of a bent quartz crystal from X-rays produced by a rotating anod generator. The slitted cross section of the beam was quasi-Smear and horizontal at the sample (6 mm X 1 mm), focused to a vertical strip 0.4 mm wide at a horizontal linear gas detector. The sample-detector region (905 mm length) was evacuated in order to reduce absorption and parasitic scattering. The temperature was set to 22OC
+
1°C.
The capillary tubes were mounted horizontally and slowly rotated about their long axis. The X-ray transmission varied between 16% and 23%, and data were typically collected for 12-24 h. Scattering spectra were stored every 2 h in order to ensure that the microstructure did not change during data collection. No dynamic behaviour was detected for properly sealed capillaries.
The crystallite orientation within the capillaries was checked by mounting a film plate on the detector to one side of the main beam. The diffraction rings recorded on the films were usually slightly spotty, although invariably continuous, indicative of many small crystallites with no preferred orientation.
RESULTS:
Some samples clearly showed one two phase region within the cubic phase region of the ternary phase diagram. The existence of two phases was macroscopically visible: interfaces were seen of variable slope from horizontal to vertical, indicating a variation in the relative densities of the two phases.
The existence of two separate phases was confmed by SAXS measurements which indicated that the mixtures self-assembled to form crystals of cubic symmetry: both body-centered and primitive lattices. Three classes of mixtures were detected (fig. 3).
Table I. Sample compositions (water/cyclohexane/DDAB)
Weight fraction; W, o and s refer to the weight fraction of water, cyclohexane and DDAB respectively. The space group symmemes and relative peak intensities are determined from SAXS spectra. Peak intensities are given for the f m t three peaks only (S = strong, m = medium, W = weak).
lattice
Sample composition symmetry spacing,
A
intensities peak1 61.0/6.0/33.0 Im3m 155.9 s,m,m
2 60.2fl.2132.6 Im3m 155.3 s,m,m
3 (bottom) 59.616.8133.7 Pn3m 124.7
13 14 15 16 (bottom) 16 (top)
17
I I " " I " "
-
lm3m
-
49.0/9.3/41.7
'L
-l ~ ~ ~ ~ ~ ' ~ ~ ~ ~ ' * ' ' L
Fie. 2: (a) Small-angle X-ray scattering pattern for a ternary mixture (wlw composition marked in the figure) within the cubic phase region. The peaks can be indexed on a primitive cubic lattice of space group symmetry Pn3m.(b) Scattering pattern for a mixture forming a single cubic phase of body-centered cubic symmetry. The most symeaic space group conforming to these peak positions is Im3m.
The low water samples within the cubic phase region formed single phases, whose scattering spectra contained six to eight discernible peaks. These peaks were in the ratio
fi: 45: 16: 46: 4% 45: 4% .\IE
(Table I, fig. 2a). The consistent absence of thefi
reflection is consistent with a primitive cubic symmetry, space groups Pn3m or Pn3.At high water contents within the cubic phase region of the ternary phase diagram, single phases were
- - -
also spontaneously formed. The SAXS spectra (fig. 2b) can be indexed
a: .I& 6: d a :
412: 414: 416 spacing ratios, characteristic of body-centered cubic symmetry (maximal symmetry space group I d m ) . Within this high water region, X-ray spectra fell into three groups, with varying relative intensities of the first three visible reflections between these groups Cable I).At intermediate water contents, two coexisting phases were usually formed. In nearly all cases, analysis of these phases indicated that they belonged to the primitive and body-centered cubic syrnrnetries detected within the single-phase regions.
Fig. 3: Magnified view of the cubic phase region of the ternary phase mangle (dotted triangle in figure 1). The mixtures investigated in this paper are indicated by a symbol which denotes the spectral type recorded. Three distinct spectra were found within the body-centered phases; these are denoted s,m,m
-
m,s,m and s,w,m in legend according to the relative intensities of the three peaks recorded at lower q values (S = strong, m = medium,W = weak). We refrain ourselves from giving more accurate values of the intensities since they were not perfectly constant all over the diffracted rings.
DISCUSSION:
The measurements presented in the previous section indicate that the microstructure is certainly not fixed throughout the cubic "single phase" region. First of all, it is clear that there are two distinct symmemes within the cubic phase.
In general, it is a difficult issue to resolve the actual geometry of the surfactant interface, which is characteristized by the interfacial topology per unit cell (related to the number of tunnels per unit cell), as well as symmetry. We proceed to determine the microstructure as follows.
Analyses of the microemulsion region of DDAB/cyclohexane/water within the ternary phase diagram indicate that the cyclohexane molecule appears to be taken up between the DDAB hydrophobic chains, thereby swelling the hydrophobic region of the surfactant molecules until the surfactant parameter vlal (v is the total volume of the surfactant chains plus any absorbed oil between the chains, a is the surfactant head-group area and l is the surfactant tail length [6]) exceeds -1.6 [10]. Assuming reasonable chain lengths of about 10-13
A
and a head-group area of 68A2
for the DDAB molecules [ l 1,121, all the cyclohexane within the cubic phase mixture should be taken up by the DDAB chains, since the volume of oil is very low and not sufficient to give an effective surfactant parameter of 1.6 (it is found to be slightiy- larger than one [6]). Therefore, if the surfactant forms bilayers-
which appears to be the case for bicontinuous cubic phases-
these are normal (as opposed to reversed), and the channels are water filled, while the end methyl groups of the DDAB chains lie on a 3-d periodic surface of cubic symmetry.If these arguments are accepted, one can ask whether these surfaces are Infinitely Periodic Minimal Surfaces (IPMS) or not. We will show that our experimental data, analysed with simple arguments of scaling can help answering this question.
I-WP s u r f a c e
surface
2x12/a2
Fig. 4: (a) Master plot indicating two distinct structures within the cubic phase region. The axes of this plot are a function of the head group-area per unit cell (A), the lattice parameter (a), and the bilayer half-thickness (l). The slope of the data is a measure of the topology of the bilayer per unit cell, and the intercept is equal to the surface area of the minimal surface at the center of the bilayer for a unit cell of edge length unity. (b) Magnification of the master plot for the primitive cubic samples. The theoretical line for the diamond D-surface is shown. (c) Master plot of the body-centered samples, together with theoretical lines for two periodic minimal surfaces of symetry Im3m, the P-surface and the I-WP surface.
In the case of the primitive cubic symmetry (Pn3m), the D-surface (also known as the F-surface), which separates two interpenetrating diamond labyrinths of equal volume, is a suitable IPMS. This structure was tirst proposed by Tardieu as a model S-ture for bicontinuous lyotropic crystalline phases [2]. It has been observed in monoglyceride solutions [13,14] and tetraether lipids 1151.
Let S(0) be the interfacial area per unit cell at the center of the bilayer and V= a 3 the volume of the unit cell ( a is the lattice parameter). A useful parameter characteristic of a surface structure is the normalized surface to volume ratio per unit cell o:
If the structure is preserved upon swelling with water, CT will remain constant. The size of the unit cell a is directly measured from X-ray diffraction and S(0) can be simply related to the composition and the topology.
Let A be the head-group area per unit cell:
where d(> is the surface-averaged value of the Gaussian curvature at the center of the bilayer and I is the chain length of the surfactant. The Gaussian curvature is related to the topology per unit cell (defined by the Euler- Poincar6 characteristic, X) by
(eq 12 of ref 6). Insemon of eq 2 and 3 into 1 and rearrangement give
This "master plot" equation turns out to be a very useful expression for deriving the interfacial structure of cubic phases: from equation 4, if A12cr2 is plotted against 2a121a2, the resulting slope is equal to the interfacial topology
X,
and the intercept yields the value of the normalized surface to volume ratio C.In practice, the head-group area of the surfactant molecule a, the lattice parameter a , the molecular volumes and the composition set the interfacial area per unit cell A. We assume ideal mixing, densities of 0.985 [12], 0.777 and 1.000 g cm-3 for DDAB, cyclohexane and water respectively.We have taken the head group area a to be 68
A2,
the volume of bare DDAB chains v to be eq 704 A3 and the tail length to be l lA
[12].The data are plotted according to equation 4 and are shown in figure 5. This master plot clearly reveals the existence of more than one interfacial structure within the cubic phase region of the ternary phase diagram, as expected from the symmetry analyses of the SAXS data. The linear character of the plots strongly supports the proposal that the bilayer decorates a surface that scales like the size of the unit cell.
The straight line corresponding to a symmetrical bilayer decorating a D-surface (intercept o = 1.9193 and slope
X
= -2, [16,17] fits well the experimental points obtained in the Pn3m region which indicates that the real interface scales like the D-surface upon swelling.The master plot of the body-centered cubic data also exhibits linear character and the experimental points fall particularly well on the straight line corresponding to the genus three IPMS of Im3m symmetry: the P- surface. The intercept of the master plot is in agreement with the normalized surface to volume ratio of the P- surface (2.3451) [18].
On the basis of these data, we suggest that the surfactant forms a bilayer lying on two IPMS: the D- surface at low water content and the P-surfaces at higher water content.
-2- 1-=NE SYSTEM:
The l-hexene system was chosen because of the large extension of the cubic phase region [g] fig. 5. Very high weight fractions of water are accessible to experiment.
The ternary mixtures of DDAB, l-hexene and water were prepared and thermally cycled like in the cyclohexane system except that the ampules were frozen in liquid nitrogen before sealing to prevent evaporation of the extremely volatile l-hexene.
A stable interface separating two clear cubic phases was found again in one of the samples at intermediate water content ( sample no 6, Table D). Samples of lower water content looked very stiff whereas diluted samples (weight fraction of water higher than 55%) flowed under gentle shaking. These macroscopic observation again suggest that at least two different structures are present.
Water DDAB
Fig. 5: Single phase regions of the ternary DDAB/l-hexendwater system from reference 5.
X-ray diffraction experiments were canied out likewise on l-mm-diameter Lindernann glass capillaries at CRPP on the high resolution X-ray diffraction apparatus. Samples were mounted on a four-circle goniometer and illuminated by a Cu Ka d t i o n selected by a flat graphite monochmator. Coarse resolution of about 1OP2
k1
was achieved by a series of slits. The cross section of the beam at the sample was 0.8 mm X 3 mm and the intensity about 5 X 107 photonds. The scattered intensity was collected by a scintillation counter on the 2-theta arm of the goniometer.
Table 11. Sample compositions (waterll-hexene1DDAB)
Weight fraction; W, o and s refer to the weight fraction of water, l-hexene and DDAB respectively.
Question marks (?) denote samples of unknown symmetry.
lattice Sample composition symmetry spacing,A
1 36.111 1.7152.2 Pn3m 73.3
2 39.9/11.0149.1 Pn3m 79.4
3 40.911 1.3147.8 Pn3m 77.8
4 44.211 0.3145.5 Pn3m 82.5
S 44.7/8.1/47.2 Pn3m 81.2
6 47.819.6142.6 coexistence
7 48,218.0143.8 Pn3m 85.4
8 53.0/7.0/40.0 Pn3m 100.5
9 57.216-3136.5 Fm3m 130.9
10 62.8/4.3/32.9
(3
11 65.416.4l28.2
(2
12 66.515.Ol28.5 Fm3m 180.7
I3 70.415.51'24.1
(2
14 7 1 Sl4.3l24.2 (?)
15 75.314.6l20.1
(3
The crystaUite orientation within the capillaries was checked with the phi and chi angles of the goniometer. The crystalline samples were found to be neither good powders nor good single crystals so that Bragg reflections had to be searched for very carefully in three dimensions in reciprocal space. The spectra were collected as follows: a first 2-theta scm showed two or three sharp peaks that could generally be indexed with simple ratios. Careful phi and chi scans of the samples were then carried out at each 2-theta position where a reflection could be expected. Short 2-theta scans were finally run with phi and chi angles optimized for each particular hkl reflection.The difbction patterns presented on figure 6 are collections of these runs.
Like in the cyclohexane system, X-ray diffraction data clearly show the existence of two separate phases of different symmetries (fig. 7).
The low water samples withim the cubic phase region (zone 1) displayed at least 6 discernible peaks in the ratio
G: 6% d& 46 d& d!?
(fig. 6a). We claim that the symmetry is primitive cubic, space group Pn3m like in the cyclohexane system.At high water content, the data are not so clear and several different behaviours are observed upon increasing the amount of water. We checked that the samples always appeared mamscopicaIIy like cubic phases ( i.e. soft, clear, non-biuefringent gels).
Close to the Pn3m boundary (zone 2), two samples exhibit 6 peaks in the ratio
d?: 441- 6g: Jii: dz: 416
(fig. 6b) consistent with a face-centered cubic symmetry, space p u p Fm3m (or F432, F43m, Fm3 or F23).
As far as we know, this symmetry has never been observed in lyotmpic systems and the absence of the fireflection is of particular importance. If a peak can be detected at the
47
position, all the sums h2+
k2+
12- - - W
have to be doubledand the newsequence
G: -6 6fi:
616: 622: 424: 432 is then consistent with the commonly observed Ia3d symmetry (with however unobserved allowed reflectionsa, 4%
and 4%). We looked very carefully for this reflection atfi
position with phi and chi scans and we never found it. Unfortunately, this limited number of samples (two) is not sufficient to rule out a fortuitous extinction due to a minimum of the form factor in coincidence with the67
reflection. We therefore conclude that the symmetry is either Fm3m or Ia3d with additional extinctions. Although very little is known on the form factor of these cubic phases, other data we obtained with dodecane (Ia3d symmetry, unpublished) clearly show a I d d symmetry with a sharp K 4 reflection which suggests that a Fm3m symmetry may be right.Further increase of the volume fraction of water leads to scattering patterns with only one or two sharp peaks (zone 3). The peaks are resolution limited, which implies a correlation length of the crystalline order of at least 600
A.
Although a clear, sharp interface was present within the ampules after very gentle shaking, no stable coexistence of two cubic phases was found between zones 2 and 3. No dependence on phi or chi angle of the peaks could be detected, which suggests an isotropic dismbution of the crystallites.At last, more sharp peaks (4) were observed at very high water content (zone 4) but sensible cubic indexation turned out to be impossible: the ratios of the wavector of these peaks could not fall into any simple series of hkl indices.
As already pointed out by Fontell and Jansson [g], a very slow kinetics towards equilibrium can be invoked to explain the observations in zones 3 and 4. One may also think of other possibilities such as a coexistence with a third cubic structure or a quasi-crystalline ordering.
In the low water region (zone 1, Pn3m symmetry) the master plot technique can be used to test the existence of a minimal surface. Figure 8 shows that the experimental points are consistent with the cyclohexane case and therefore with a D surface provided the head-group area is taken equal to 71.5 A2.
In zone 2, simple face-centered cubic structures of micelles (normal or reversed) are inconsistent with the calculated volume fractions. On the other hand, a structure formed by a bilayer lying on a F-RD minimal surface (Fm3m symmetry, genus 6 per unit cell [6]) would require a too high head-group area (> 100 A2). Our data are therefore not conclusive in this region and more experimental work is clearly needed on the l-hexene system.
100
=P=
loao 1
CPS .
100
-
s Pn3m
A Fm3m 2 phases
+ (?) l peak simple cubic
0 (?) indexation is not possible a m.
=.
&Magnified view of the cubic phase region in the l-hexene system. The symmetry of the samples is unknown at high water content.
10 7
I 1
10
. . . I . . . . , . . . , - . . . 7 1
0.00 0.05 0.10 5 Q 0.20 0.00 0.05 0.10 0.15 020 035
Fie. 6: (a) X-ray scattering profiles for a ternary mixture (wlw waterll-hexenePDAB = 53.01 7.0140.0). The peaks can be indexed on a primitive cubic lattice of space group symmetry P d m . (b) X-ray spectrum for a ternary mixture in zone 2 (see text). The weight fractions of waterll-hexene/DDAB are 57.216.3136.5, The observed Bragg's reflections at positions h2+k2+12 = 3,4,8,11,12 and 16 are consistent with a simple face- centered cubic symmetry, space group Fm3m.
2.4
-
A/2a2 '
2.0
-
1.6
-
1.2 -l
0.06 0.10 0.14 0.18 21c12/a2
Fig. 8: Master plot within the cubic phase region of the ternary system with l-hexene ( P d m symmetry).
The experimenal points obtained with the Pn3m phase of cyclohexane are also reported (open circles). The all fit well the straight line calcu1ated for the D-surface. 7'he head goup area of DDAB in 1-hexene is then 71.5
h.
CONCLUSION;
These studies have established unequivocally that the microstructure within the cubic phase of a ternary surfactant solution can vary throughout the "single phase" region. Indeed, it appears possible that the topology as well as the c~ystal symmetry changes upon water dilution. This behaviour reported here in the cyclohexane and l-hexene systems seems to be very general: similar observations are reported in the DDAB/water/octane [l91 and dodecane (C. Toprakcioglu, private communication) systems.
The measurements of lattice parameter variation with water content reported here (master plot technique) lead to virtual clues as to the geometry and topology of the surfactant interface.We suggest this technique as a general one to study the microstructure of ordered phases.
In the cubic phases of the cyclohexane system and of the low water region of the l-hexene system, our results clearly demonstrate that the molecules of surfactant lie on a surface that scales l i e the minimal surfaces of appropriate symmetry and lowest genus (D- and P-surfaces) upon dilution with water (i.e. the values of the topologies and of the normalized surface to volume ratios are consistent with these two IPMS). We therefore suggest that the microstructures of the cubic phases observed in DDAB/water/cyclohexane and DDAB/water/l- hexene mixtures m an example of natural infiniely periodic minimal surfaces formed in chemical systems.
The value of the head-group area within the cubic phase can also be obtained from the master plot; 68 1$2 is consistent with earlier SAXS data on cyclohexane whereas we propose a value of 71.5 A2 for the l-hexene system.
Acknowledgment. We thank D. Anderson, I. Bames, V. Luzzati, C. Topragcioglu for fruitful discussions, and T. Dowling and R. Bernon for their help on the X-ray apparatus. Last but not least, it is a pleasure to thank E. Dubois-Violette and B. Pansu for the great organization of this workshop.
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