J . Phys. Chem. 1993,97, 4535-4539
4535
Cylinders and Bilayers in a Ternary Nonionic Surfactant System Ulf OIsson,*J Ulrich Wiirz,$ and Reinhard Streyt Physical Chemistry 1 , Chemical Center, Lund University, P.O.B. 124, S-221 00 Lund, Sweden, and Max- Planck-Institut fur Biophysikalische Chemie, Postjach 2841, 0-3400 Giittingen, Germany Received: December 23, 1992
We have investigated a section through the composition-temperature phase prism of a ternary nonionic surfactantw a t e r 4 1 system defined by a constant surfactant to water ratio. The structural sequence normal cylindersmultiply connected bilayer-planar bilayer-reverse monolayer structure is obtained when increasing the temperature. This sequence corresponds to a gradual reversal of the mean curvature of the polar-apolar interface as the temperature is increased as has been observed previously in the corresponding microemulsion systems. The cylinders can incorporate (swell with) moderate amounts of oil. In addition to the bicontinuous cubic phase present in the binary water-surfactant system the ternary system contains a bicontinuous cubic phase with simultaneously high contents of water and oil. Upon dilution with oil, this phase undergoes an order4isorder transition to a liquid "sponge phase" (L4)retaining the multiply connected bilayer structure. A lamellar phase swells with large amounts of oil. From the variation of the periodicity with oil content we obtain the solubility of the nonionic surfactant in the oil.
1. Introduction Nonionic surfactants have an interesting and rich phase behavior in binary mixtures with showing, for example, dilute L3 (sponge phase) and lamellar phases.2 They are also capable of forming balanced microemulsions in ternary Due to the richness in phase behavior, obtained with a minimum of components, the nonionic surfactant systems are suitable model systems for structured liquids and liquid crystals in the absence of long-range electrostatic interactions. The temperature dependence of the phase behavior arises from the fact that water changes from a good to a bad solvent for the oligo(ethy1ene oxide) (EO) polar "tail" of the surfactant, within an accessible temperature range.l0.I1As a consequence, the local water concentration in the EO layer regulates the curvature of the film. In some cases it is useful to express this property in terms of a spontaneous or preferred curvature of the surfactant film.12 At lower temperatures the film has a spontaneous curvature toward oil, while the opposite holds at higher temperatures. At an intermediate temperature the spontaneous curvature is zero and a lamellar phase or a balanced microemulsion is stable. In this paper we extend the investigation4x8of ternary mixtures with nonionic surfactant to include concentrated and lowtemperature phases. We start with a concentrated sample in the binary penta(ethy1ene glycol dodecyl ether) (CI2E5)-watersystem that for the given surfactant-to-water ratio shows a hexagonal-bicontinuous cubic-lamellar phase sequence with increasing temperature. We then dilute this sample, gradually, with tetradecane and follow the swelling of the structures and the structural transitions that occur. 2. Experimental Section
Materials. Penta(ethy1ene glycol dodecyl ether) (C12E5) was purchased from Nikko Ltd. Tokyo, Japan, and tetradecane from BDH Chemicals Ltd., Poole, England. The water was millipore filtered. SAXS. The SAXS instrument has been used in previous and is described in detail elsewhere.l3 Samples for the SAXS experiments were left to equilibrate at temperatures
* To whom correspondence should be addressed. +
f
Lund University. Max-Planck-Institut fur Biophysikalische Chemie
corresponding to the lamellar phase (-45 OC, see the phase diagram below) before they were rapidly transferred to the capillaries. Self-Diffusion. The self-diffusion experiments were carried out on a modified JEOL FX-60 NMR spectrometer operating at 60 MHz (IH), equipped with an external ZHfield frequency lock, and using the Fourier-transform pulse gradient spin-echo (FTPGSE) technique.I4 Density Measurements. The density of pure C12Es was determined as a function of temperature between 25 and 50 OC by using a Paar DMA60 density meter (Paar, Graz). 3. Geometrical Considerations When calculating structural length scales we divide space into polar and apolar domains. The surfactant molecule consists of a polar oligo(ethy1eneoxide) (EO) part and an apolar alkyl part, essentially representing a short AB block copolymer. For ClzEs the alkyl chain makes up roughly one-half of the volume of the molecule and we define a hydrocarbon (hc) volume fraction given by
ahc= a. + a,/2
(1) where 'Po and 'P, are the volume fractions of oil and surfactant, respectively. At this polar-apolar interface we evaluate the area occupied by a surfactant molecule, a,, or, equivalently, the surfactant length, defined as I, ys/as,where v, = 702 A3 is the volume of the C12E5molecule based on the density ps = 0.9603 g/cm3 at 25 "C. In order not to complicate the calculations we assume the volume fractions to be temperature independent. A correction could be made by using the relation p, = 0.9791 0.0007551 T (g/cm3), where T is the temperature in degrees Celsius. 4. Phase Behavior
We investigatehere a cut through the composition-temperature phase prism in the ternary system CI2E5-water-tetradecane as illustrated in Figure 1. This cut is defined by a constant surfactant-tc+water weight ratio Ws/ W, = 1.5, where W,and W, are the weight fractions of surfactant and water, respectively. A cut through the phase prism, excluding the specifications of the multiphase regions, is presented in Figure 2 as temperature versus the weight fraction of tetradecane. To illustrate further the evolution of the phase equilibria in the full ternary system
0022-365419312097-4535$04.00/0 0 1993 American Chemical Society
4536 The Journal of Physical Chemistry, Vol. 97, No. 17, 1993
Olsson et al.
0.1
0.05
,
0
0
0
0
0
W
Figure 1. Illustration of the section through the phase prism defined by
20
30
40
50
60
70
T I "C Figure 4. Variation of the first-order Bragg peak with temperature in the lamellar phase for various oil contents. The different oil volume fractions are 9,= 0 (o), 0, = 0.124 ( O ) , 9, = 0.301 (A), 9,= 0.482 ( O ) , aC= 0.658 (m), and 9, = 0.751 (A).
a constant surfactant-twwater ratio.
T/
t
0 0
I 8
t
8
"
a
LO
20
HzO/CizEs L0/60
'
"
60
80
100
C,H,/wt%
Figure 2. Partial phase diagram of the section defined by a constant surfactant-twwater weight ratio: W,/ W, = 1.5.
present microstructure. Starting from lower temperatures we find first a region of cylinders with a normal hexagonal phase. Above the region of cylinders comes a region of a multiply connected bilayer structure. This structure may exist in either an ordered form in cubic phases15-19 or a disordered form in a liquid sponge In the present system we find two cubic phase regions and at higher oil content a sponge phase, which we here denote L4, in order to distinguish this phase from the more commonly observed water-rich analogue, often referred to as an L3 phase. Increasing the temperature further, we find a lamellar phase with bilayers of planar topology. This lamellar phase extends over a very large dilution range, from the binary water-surfactant system up to 9,= 0.95. At temperatures above the lamellar phase a microemulsion phase, with a reversed monolayer structure, is stable. The microemulsion phase of this ternary system has been studied previ~usly~-~ and we focus here on the liquid crystalline mesophases and the liquid L4 phase of the present system. 5. The Lamellar Phase The lamellar phase can swell with large amounts of oil if the temperature is properly choosen. The repeat distance was studied as a function of temperature and 9,. Only a weak temperature dependencewas found as is seen in Figure 4 where we have plotted the position of the first-order,ql, peak as a function of temperature for some different compositions in the lamellar phase. The periodicityof a lamellar phase is given by the bilayer area per unit volume and the position of the first-order Bragg peak corresponds to
H2O
L,+H,+ O
011
Figure 3. Schematic phase diagrams at three different temperatures, TI
< T2 < T3, illustrating the evolution of the phase equilibria of a ternary
nonionic surfactant-water-oil system with increasing temperatures. For the present system the different temperatures correspond approximately to T I = 5 O C , T2 = 25 O C , and T3 = 48 "C. At 48 O C the three-phase triangle is approximately~ymmetric,~ and in the phase diagram at T3 we have captured the basic features of the phase diagram of Kunieda and Shin~da.~
with temperature, we have drawn in Figure 3 a sequence of schematicisothermal phase phase diagrams from within the phase prism. (For an extensive study of the phase behavior at some selected temperatures in the range 35-60 "C,see Kunieda and Shinoda.3) The phase diagram of the section Ws/ W, = 1.5 (Figure 2) can be divided into different temperature regions with respect to the
In Figure 5 we have plotted q1 as a function of 9,corresponding to an oil dilution line at 48 OC. As is seen, a linear dependence is obtained, but the data points do not extrapolate to the origin. Instead, the intercept is negative. Nonionic surfactants of the oligo(ethy1ene oxide) type are completely miscible with oil, where they do not aggregate in the absence of water.25 In the structural ternary mixtures the oil domains contain significant amounts of molecularly dispersed surfactant. This may be accounted for by a simple model where we assume that the local concentration of surfactant in the oil is constant, i.e. %,o
= k@o
(3)
where a,, is the volume fraction of surfactant solubilized in the
Ternary Nonionic Surfactant System
The Journal of Physical Chemistry, Vol. 97, No. 17, 1993 4537 10'9
* r"3 #
O.O50 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
QS
Figure 5. Variation of the first-order Bragg peak with asin the lamellar phase at 48 O C . The solid line results from a linear least-squares fit of eq 4 to the data, yielding I, = 14.2 A and k = 0.0294.
oil and k is a constant. Replacing 9, in eq 1 with 0,- 9's.o and using 0,= 1 - 0,- 9, we obtain q1
=e[*,( + 1
k( 1 +?))-k]
(4)
From a linear fit of the data in Figure 5 we obtain k = 0.029 and I, = 14.2 A. There are to our knowledge no data in the literature from direct measurements on surfactant monomer concentration in the oil, with which we could compare our k value. However, the k value is in reasonable agreement with cmc data,9-26,27which would extrapolate to k = 0.01 5 at 48 OC. The value of l,, which corresponds to a, = 49 A2,is very similar to the value found in the lamellar phase of the binary CIzES-water system. This result is also consistent with the as= 43 A of the previous investigation of Lichterfeld et a1.,8 who neglected the effect of monomeric solubility of the surfactant in the oil. We have neglected the effect of area renormalization,28which, based on measurements in the binary system,2we expect to be small relative to the solubility effect. 6. The Cubic and Ld Phases
The present cut through the phase prism shows two cubic phase regions. The cubic phase in the binary surfactant-water system (90= 0) is located between the hexagonal and lamellar phasesl.2 and can thereforeI6 be expected to have a bicontinuous microstructure. From a self-diffusion experiment on a sample containing 59.9 wt % CIzE5at 20 OC weobtaineda surfactantdiffusion coeffcientD,= 1.6OX m2s-'andawaterdiffusioncoefficient D, = 5.19 X itio mz s-I. The measured D, value is consistent with a lateral diffusion constantz9of about Diat = 3 X 10-1' mz s-I and confirms the biocontinuity of the microstructure (we may compare with the data of Nilsson et aL30who found D, < 5 X l0-l3 m2s-I in the micellar cubic phase of the binary water-ClzEs system). As seen in the phase diagram of Figure 2, this structure can incorporate only very minor amounts of oil, at the present surfactant-twwater ratio. There are very few reports on cubic phases containing simultaneouslylarge amounts of water and oil, which makes the second cubic region, which appears at Bo = 0.4-0.5, particularly interesting. The cubic phase in the present system is possibly related to the cubic phases found in the potassium oleats-waterdecanol, the octyl ammonium-water-decanol, and the C12Elr water-oleic acid systems.31However, in these systems the longchain alcohol and acid respectively act as both a hydrophobic solvent and a cosurfactant, which complicates the situation. It is in general very difficult to obtain powder diffraction data from cubic phases due to very large microcrystallites. This was also a problem in the present system. In spite of several attempts, we were not able to obtain a powder diffraction pattern. We therefore
I
I
I
I
water .............
t
P
surfactant
+...........-..----a L4
"I I
10'"
0.40
0.45
I
0.50
I
I
0.55
0.60
0.65
a0 Figure 6. Self-diffusion constants of water ( 0 , m), oil (A, A), and surfactant (O,.) in thecubicandL4phases. Theopensymbolscorrespond to samples in the cubic phase and the filled symbols correspond to a sample in the L4 phase. The measurements were done at the following temperatures: In the cubic phase at a, = 0.41 and 0.44, T = 20 O C . In the cubic phase at a0 = 0.48, T = 23 O C . In the Lq phase at 0,= 0.61, T = 25 O C . The lines are only guides to the eye.
have to leave the question regarding the space group of this cubic phase open. We note, however, that the possibly related cubic phase in the ClzElrwater-oleic acid system, which is found between a lamellar and a reverse hexagonal phase and is expected to have a reverse bilayer structure (mean curvature toward water), is r e ~ r t e d 3to~have a face-centered cubic structure. In contrast to the one-dimensionally ordered lamellar phase, the two- and three-dimensionally ordered phases, such as the hexagonal and cubic phases, cannot swell by undulations while retaining the symmetry of the phase. The hexagonal phase transforms to a liquid phase of disordered cylindrical micelles and the cubic phase transforms to a liquid L4 phase upon dilution. The latter case is illustrated in the present phase diagram. The cubic to L4 transition with oil dilution can be seen as an orderdisorder transition, where the long-range periodic order is lost while the topology of the multiply connected bilayer remains essentiallyconstant. In the AOT-brine system, a similar situation is observed and the topology invariant transition was recently confirmed by self-diffusion measurements.19 In the present system, we performed self-diffusion measurements on three samples in the cubic phase and on an additional sample in the L4 phase close to the cubic-Ld transition. The results are presented in Figure 6. Minor adjustments of the temperature had to be done. The measurements in the cubic phase were performed at 20 OC for the two lowest values of 0, (ao= 0.41 and a0= 0.44, respectively), while for a0= 0.48 the temperature was 23 OC. For the sample in the L4 phase (90= 0.61) the measurements were performed at 25 OC. In the cubic phase, the simultaneouslyhigh diffusion constants of water, oil, and surfactant demonstrate that the microstructure is continuous for all three components. The diffusion constants of all three components in the L4 phase are very similar to the corresponding values in the cubic phase, demonstrating that the microstructuresin the two phases are topologically closely related. Our findings are similar to those found in the AOT-brine s y ~ t e and m ~confirm ~ ~ ~ the ~ order4isorder character of the cubic to sponge phase transition. 7. The Hexagonal Phase
In the hexagonal phase the Bragg reflections correspond to 47r(hz
+ k2 + hk)'/'
(5) a3II2 where a is the lattice parameter (nearest-neighbor distance). The first three reflections corresponds to (h,k) = (l,O), (l,l), and (2,O) and give the characteristic pattern 1:31/2:41/z. qhk
=
4530 The Journal of Physical Chemistry, Vol. 97, No. 17, 1993 0.11
Olsson et al. 120 100
0.1 80
r(
4
0.09
60
0
w-
40
0.08
0
20 0.07
0
0.6
0.8
1
1.2
1.4
1.6
1.8
0
0.1
3 (Qo+@s/2)/2 x ) ' ~ ' ~
0.2
0.3
0.4
0.5
@O
Figure 7. Variation of the measured position of the first-order Bragg peak, 410, in the hexagonal phase with the quantity @s(3'/2(% + @ S ) / ~ T ) - ' ' ~(see eq 8). The solid line is a least-squares fit o f 3 8 to the four data points at lowest oil contents, yielding 1, = 15.3 A.
Figure 8. Variation of a (A) and Rhc (O), calculated from the measured first-order bragg peak, 4'0, by using eqs 5 and 6, with @,, in the hexagonal phase at 5 O C . The lines are calculated from eqs 6 and 7, respectively, using 1, = 15.3 A.
For cylinders of cross-sectionradius Rcylon a hexagonal lattice the relation between Rcyland a is
Rcyl= a(
g@c,,,)"2
where acylis the volume fraction of cylinders. With cylindrical hydrocarbon domains, containing the oil and the hydrocarbon tails of the surfactant, the radius evaluated at the polar-apolar interface is given by Rhc
= 2zs@hc/@s
(7)
Identifying Rcyl = Rhc and acyl= @hc, eq 6 in eq 5 gives
+ + hk)'I2 as
(h2 k2
For the given surfactant-twwater ratio, the hexagonal phase can solubilize roughly 20 wt % of oil. We followed the swelling ofthecylindersat o c , beyondthe limit ofswelling,by measuring the repeat spacing as a function of the oil concentration. A characteristic 1 :31 /2:4l/2 diffraction pattern was observed and the measured positions of the first-order Bragg peak, q,o, are plotted as a function of d , ( d 3 ( 9 , + 9 , ) / 2 ~ ) - l /(see ~ eq 8) in Figure 7. The lattice parameter increases with increasing oil content up to about 9, = 0.25, above which it levels off at a constant value. The samples at 5 OC were prepared by cooling from the Laphase at higher temperatures. Above 9, = 0.25 the samples were turbid and birefringent at 5 O C , while the samples were transparent and birefringent at lower oil contents. From this observation together with the measurement of a constant lattice parameter at higher oil contents, we conclude that the hexagonal phase at the limit of oil swelling at this temperature is in equilibrium with almost pure oil. The result of a leastsquares fit to the four data points at lower oil contents is shown in Figure 7 as a solid line and from the fit we obtain 1, = 15.3
A. In Figure 8 we have replotted the variation of the lattice parameter, a, together with Rhc as a function of 9,within the homogeneous hexagonal phase region. Also shown are the calculated variations of these parameters, using eqs 6 and 7 with 1, = 15.3 A. Due to the relatively low oil content, the solubility of surfactant monomers in the oil has a negligible effect on the results presented. The value of I,, measured in this hexagonal phase, is very close to the value found in the lamellar phase at higher temperatures. The relative area of two parallel surfaces depends on the distance between them and the mean and Gaussian curvatures.33 Hence, the present result indicates that the interfacial area where we evaluated 1, is the invariant area when curving the surfactant
',
,'
Figureh Drawing of a triangular section of the hexagonal phase structure illustrating the various lengths discussed in the text.
monolayer. A similar IS value has also been found in a reverse hexagonal phase formed in a related system?4 which supports the present finding of an area-invariant dividing surface. In the hexagonal phase the repulsive intercylindrical interaction results from the overlap of the Eo+b%terpallisade layers of two adjacent cylinders, similar to sterically stabilized colloidal particles. Hence, a relevant length is the distance
b = a - 2Rhc
(9) which is the shortest distance between nearest-neighbor polarapolar interfaces corresponding to the smallest thickness of two overlapping EO layers. Another important length is associated with the sizeof the triangular interstices. This size we characterize by the length c, which can be written
and corresonds to the normal distance from the polar-apolar interface to the center of the triangular interstice. The various lengths involved are illustrated in Figure 9, where we have drawn a triangular section of the hexagonal structure. In Figure 10we show the variations of the lengths b and c with a,, calculated by means of eqs 9 and 10, respectively,and assuming a constant 1, = 15.3 A. Shown are also the values of b and c calculated from the scattering data. From these calculations we may find a possible explanation for the limited oil swelling of the hexagonal phaseand we have therefore extended the plot to higher 9,. The length b varies only weakly with 9,. The length c, on the other hand, increases monotonically with 9,. Hence, the fraction of water within the triangular interstices, which is unaccesable for the EO chains, increases with 9,,which means that the ethylene oxide chains become gradually dehydrated and the packing of EO chains in the overlapping region between
The Journal of Physical Chemistry, Vol. 97, No. 17, 1993 4539
Ternary Nonionic Surfactant System
40
w
Acknowledgment. This work was supported by the Swedish Natural Science Research Council (NFR). U.W. and R.S. are indebted to Prof. M.Kahlweit for support. References and Notes
2o 15
t
b
I
I
I
I
I
1
0
0.1
0.2
0.3
0.4
0.5
I
QLl
Figure 10. Variation of the lengths b (A)and c (O),calculated from the measured first-order bragg peak, ql0, by using e q s 5, 6,9, and 10, with a0in the hexagonal phase at 5 OC. The lines are calculated from eqs 7, 9, and 10, using I, = 15.3 A.
nearest-neighbor cylinders becomes denser. One way to decrease this "frustration" would be to increase the area per surfactant molecule (decreasing I,). This, however, does not occur. Instead, beyond a certain upper limit, further additions of oil result in an excess oil phase.
8. Concluding Remarks We have investigated a section, defined by a constant surfactant-tewater ratio, through the phase prism of a ternary, nonionic surfactant system. As a function of increasing temperature we find a sequence of phases composed of normal cylinders, multiply connected bilayer, planar bilayer,and reversely curved monolayers. From comparing SAXS data from the hexagonal and lamellar phases we have found that the area per surfactant molecule, if evaluated at the dividing surface separating the ethylene oxide from the hydrocarbon chains of the surfactant, is roughly constant when curving the monolayer. The observed phase sequence corresponds to a gradual reversal of the mean curvature of the surfactant film, from curvature toward oil at lower temperatures, to curvature toward water at higher temperatures. Analogous temperature-dependent structural transitions have been observed at lower surfactant concentrations, where balanced microemulsions may be formed. Of particular interest is also the observation of a bicontinuous cubic phase at simultaneously high contents of water and oil. This phase undergoes an order-disorder transition to an oil-rich L4phase upon diluting with oil, retaining its multiply connected bilayer structure.
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