J. Phys. Chem. 1992, 96, 8640-8646
8640
Microstructure near the Oil Corner of a Ternary Microemulsion Roald Skurtveitt.tand Ulf Ohson*-+ Physical Chemistry 1, Chemical Center, Lund University, P.O. Box 124, S-221 00 Lund, Sweden, and Department of Chemistry, University of Bergen, N-5007 Bergen, Norway (Received: January 29, 1992; In Final Form: July 18, 1992)
The microstructure in the oil-rich part of the microemulsion phase in the DDAB-water-dodecane system was investigated at 20 "C.Surfactant I4N NMR relaxation and water self-diffusion experiments were performed as a function of oil dilution for three different surfactant-to-water ratios, sfw. At high volume fractions, CP, of surfactant and water, the microstructure is bicontinuous. Upon dilution with oil, there is a gradual transition to a discrete particle structure. The average size of the particles decreases with dilution, to become spherical, with a radius dictated by sfw, at infinite dilution. At constant CP, the particle size increases with increasing sfw. The volume fraction, a*, which marks the onset for the formation of a connected microstructure, decreases with increasing sfw. Outside the phase boundary at high water content, there is a concentrated and dilute microemulsion coexistence, with a critical point. This system does not have an oil dilution line of invariant spherical reverse micelles.
1. Introduction Microemulsions are thermodynamically stable liquid mixtures comprising surfactant, water, and oil. While being macroscopically homogeneous, these solutions are structured on a microscopic length scale (10-103 A) into polar and apolar microdomains separated by a surfactant-richfilm. Depending on the conditions, the surfactant film may enclose a finite volume, as in the case of micellar or reverse micellar structures, or form a 3D continuous dividing surface of multiply connected topology in a bicontinuous microstructure. Ternary systems with the double-chained surfactant didodecyldimethylammoniumbromide (DDAB) show a large liquid solution phase (microemulsion phase) for a variety of different The microstructures of these microemulsion phases have been the subject of several studies in recent years, involving small-angle scattering$-* condu~tivity,~,~ self-diffusion,2v'0*' I dielectric,12 and fl~orescence'~ spectroscopies. Most experimental studies on these systems have been performed at relatively high surfactant and water content. The observation1.2*e"of a transition from a bicontinuous to a particle structure with increasing water content is indicative of a constraint of roughly constant mean curvature of the surfactant film toward water. In terms of an elastic model for the surfactant film, this is consistent with a high elastic bending modulus constraining the mean curvature of the film to be close to its spontaneous value. This property is not unique but has, for example, also been found for nonionic surfactants, in microem~1sions'~J~ as well as in L3 phases.16 The objective of this study has been to investigate the microstructure in the dilute regime of the microemulsion phase of the DDAB-water-dodecane system. The knowledge of the microstructure is of fundamental importance for understanding microemulsions. While most experimental efforts have been directed toward the concentrated solutions, very little is known about the variation in microstructure as one approaches the oil corner. Here we have used a combination of two techniques: (1) The first is water self-diffusion, which can discriminate between closed and when water is micellar and bicontinuous confined to discrete reverse micelles, a hydrodynamic radius can be obtained from the diffusion constants in dilute solutions. (2) The second is surfactant I4N NMR relaxation, which gives structural information through the isotropic reorientation dynamics of the surfactant moleculesZoand is therefore sensitive to small changes in aggregate size. A combination of these two techniques is often advantageous,21and they are not complicated by the *To whom correspondence should be addressed. Lund University. *University of Bergen.
0022-3654/92/2096-8640$03.00/0
presence of critical fluctuations. The experiments were performed on three different oil dilution lines. Particular care was taken to identify the phase boundary on the water-rich side of the phase, in order to find the minimum surfactant-to-water ratio that can be diluted infinitely with oil. We also present some additional information on the phase behavior of the system.
2. Experimental Section MpteMls. DDAB (purum) was obtained from Fluka A.G. It was additionally purified by recrystallization from dry ethyl acetate and an acetone/ether mixture as described pre~iowly.~ Mecane (puriss) was obtained from Fluka A.G. and used as received. The water was distilled and ion exchanged. Sampk Reparation. Samples were prepared by weighing them into glass ampules that were flame sealed. When samples were prepared on a dilution line, a concentrated stock solution was diluted with oil. The samples for NMR experiments were transformed to NMR tubes shortly before measurements. The samples were equilibrated at 20 OC for seveal days. In the studies of phase equilibria, the samples were centrifuged at 20 OC for several days to observe macToBcopic phase separation. The critical point was determined by measuring the relative volumes of s e p arated phases in the two-phase region. We estimate the accuracy in the composition of the critical points to be better than 10%. Self-DiffusionExperiments. Self-diffusion experiments were performed on a modified JEOL FX-60 spectrometer using the Fourier transform pulsed-gradient spin-echo (FTPGSE)22,23 technique. 'Hwas observed at 60 MHz, and an external *Hfield frequency lock was used. The temperature was kept at 20 f 0.3 OC for all measurements. 14NNMR. Measurements of 14Nlongitudinal ( R , )and transverse (R,) relaxation rates were performed on a Bruker XL-400 NMR spectrometer operating at 28.91 MHz. R I was measured by inversion recovery using composite pulses.24 R2 was measured from Lorentzian fits of the frequency spectrum. The effect of magntic field inhomogeneity was checked by also performing spin-echo experiments on selected samples. Contributions from field inhomogeneity were always found to be negligible. The temperature was kept at 20 f 0.3 OC. The samples containing lamellar or reversed hexagonal phases were prepared by weighing into glass tubes that were flame sealed. After homogenizing, the samples were kept at 20 OC for several weeks before the measurements. The glass tubes were inserted in 1 0 " NMR tubes, and the spectra were obtained by recording the free induction decay after a 7r/2 pulse. 3. PbaseBehsvior The isothermal phase behavior of the DDAB-watedodecane system at 20 OC has previously been investigated by Fontell et al.* and more recently by Skurtveit et We have performed 0 1992 American Chemical Society
Microstructure near the Oil Corner of a Microemulsion Dodecane
The Journal of Physical Chemistry, Vol. 96, No. 21, 1992 8641 TABLE I: Compositioas a d Geometrical a d Mffusion Properties of tbe Three Investigated Dilution Lines SIW %I@* Rs.H, A D,,ho,m2 s-' 0.37 2.61 112 1.3 X lo-" 0.41 2.35 103 1.4 X lo-" 0.50 1.93 88 1.6 X lo-" ' s / w is the weight ratio of surfactant to water. b @ w / @ s is the volume fraction ratio of water to surfactant. RS,"is the radius calculated from eq 1 using 1, = 11.7 A and adding 15 A for the surfactant tales. d D s p t is the diffusion coefficient calculated from eq 4 which corresponds to a hydrodynamic radius given by Rs,H.
Water
DDAB
Figure 1. (a, top) Isothermal phase diagram of the DDAB-water-dodecane system at 20 O C . DI and D2are lamellar phases, F is a reverse hexagonal phase, I is a region containing one or several cubic phases, and L2 is a fluid (microemulsion) phase. In the water corner, there is an additional, here very small, fluid phase, normally denoted L,,and the pure surfactant is crystalline. The crystalline and LIphases are not shown. The two points ( 0 )located on the phase boundary of the microcmulsion phase correspond to the locations of two critical points. (b, bottom) Enlargement of the oil corner of the phase diagram showing the region 2 50 wt 96 dodecane. The three dashed-lotted lines inside the microemulsion phase indicate the different dilution lines investigated by "N NMR relaxation and water self-diffusion measurements.
here some additional studies of the phase behavior, in particular at lower surfactant-to-water ratios ( s / w ) . The phase diagram resulting from the present and p r e v i o u ~studies ~ ~ ~ is ~ presented in Figure 1. The modifications of the phase diagram relative to previously published version^^^^^ include mainly the estimated locations of two critical points, the phase boundary on the water-rich side of the L2 phase and the extension of the reverse hexagonal phase. The phase equilibria involving the cubic and surfactant-rich lamellar phase are taken from the original work of Fontell et Figure l a shows the full phase diagram, while the oil-rich part (150 wt % dodecane) is presented separately in Figure 1b. Here, our fm is on the large solution phase L2which has been subject to a number of investigations in recent years. On the phase boundary, there are two critical points. One is on the water-poor side, and one is on the water-rich side of the phase. Their approximate locations were determined by comparing the relative volumes of macroscopically phase-separated samples in the twophase region: L21-L;. The locations of the critical points are indicated in Figure 1 (the estimated uncertainty is 10% with respect to the oil content). The existence of the critical point on the water-rich side (cf. Figure 1) has not previously been reported. The phase boundary on this side has been assumed to be a straight line at constant surfactant-tewater ratio and to correspond to the optimum size of spherical reverse micelles.6.26Such a phase boundary has been analyzed by Safran,27-30who referred to it as the emulsification failure, which implies coexistence with excess water, However, we observe an L;-Lz'' coexistence, which implies that the phase
boundary is, at least slightly, of a different character. Self-diffusion and I4N NMR relaxation experiments were performed as described below along three dilution lines connected to the oil corner. These dilution lines are indicated as dasheddotted lines in Figure lb. 4. Geometrical Parameters The size of the stoichiometric spherical reverse micelle is given by the water-tesurfactant ratio and the average area, a,, occupied by a surfactant molecule at the water-oil interface. An often quoted number for the DDAB headgroup area is a, = 68 A2. This value was obtained in the binary DDAB-water lamellar phase at higher water contente2The same value has also been reported from analyzing the asymptotic small-angle X-ray scattering (Porod's law), on an absolute scale, in L2 phases with various oils.6 The literature, however, contains some confusion regarding the headgroup area. Different values for the interfacial area per unit volume and corresponding headgroup areas have been reported from S A X S studies on the same compositions in the DDABwater-cyclohexane system?+ According to the authorsY3'the latest reported values? which are consistent with a, = 68 A, are the most correct. For curved interfaces, it is necessary to explicitly define where the surface area is evaluated. The metria of two parallel surfaces are related by the distance between them and the mean and Gaussian curvatures. Porod's limit measures the surface area per unit volume at the interface of scattering contrast. In the case of SAXS experiments on DDAB, this is thought6 to correspond to a dividing surface separating the surfactant headgroups from the tails. Recent studies6 have shown that the headgroup area evaluated for different compositions and with different oils is constant, indicating that this interfacial area appears to be the invariant to variations in the average mean and Gaussian curvatures. Following the authors in ref 6,we define an "interior" consisting of water, Br- ions, and the surfactant headgroups (N+(CH3)2)having a volume fraction aINT = 9, 0.15CpS. The surfactant headgroup and Br- ions constitute approximately 15% of the total surfactant volume of us = 797 A3. The stoichiometric spherical radius of the interior is then given by
+
RINT=
3l,(Cpw
+ 0.159,) 9,
(1)
1, is the surfactant length defined as 1, = u,/a, with a, evaluated at the interface separating the surfactant headgroups from the tails. To obtain a hydrodyamic radius, RS,+of the stoichiometric sphere, we have to add a contribution from the solvated surfactant tails. In Table I, we give the calculated values of RS,.,for the different dilution lines using 15 for the surfactant tails. 5. Water Self-Diffusion
The water self-diffusion constant, D,, was measured along the three oil dilution lines, corresponding to s / w = 0.37, 0.41, and 0.50, respectively, where s / w is the weight ratio of surfactant to water. The dilution lines are indicated in Figure lb. We made an effort to have a dilution line as close as possible to the low s/w phase boundary. For example, it was found that s/w = 0.32 could only be diluted to about 95 wt % oil. The results of the self-diffusion experiments are presented in Figure 2 where we have plotted D , as a function of the total
Skurtveit and Olsson
8642 The Journal of Physical Chemistry, Vol. 96, No. 21, 1992 20
6
,,.,l,,,,l..,,l,,I,l.,,,l.,,,l,,,,
L
5
1 1
-1
A
h
4
7w
"E
1
-
3
Q*
1 0
0.2
0.1
0.0
0
0.3
50
100
Figure 2. Variation of the water self-diffusion constant with the total volume fraction of surfactant and water, @ = + The different symbols correspond to the different dilution lines: s / w = 0.37 (O),s / w = 0.41 (A),and s / w = 0.50 (U).
volume fraction of surfactant and water, as+ 9, = 9.The results from the three dilution lines show qualitatively the same general behavior. At low 9,D, decreases with increasing 9.After passing a minimum, D, then increases as 9 increases. Quantitatively, however, the behavior is different. The minimum in D, becomes sharper and shifts toward lower 9 with increasing s / w . Correction for Water Solubilized in the Oil. At lower 9,the information on the microstructure is masked by the contribution to D, from the finite fraction of water solubilized in the continuous apolar solvent medium. To obtain the desired information on the microstructure, one can analyze the diffusion constants in terms of a two-site model with free and micellar water, respectively. If the lifetimes of a water molecule in the two sites are short compared to the experimental observation time (eO.1 s) and the lifetime in a reverse micelle is long relative to the diffusion time inside the micelle (=%h2/D = lO-' s), the experimentally observed diffusion constant, D,, is a population weighted average of the diffusion constants in the two sites. Hence, we can write that QW.0
Dw = -(Dw,o 9,
- Dw.aq) + D w . a q
200
150
@PW
@
Figure 3. Variation of the water self-diffusionconstant with a,,/@,. The solid line corresponds to an estimated linear dependence at high dilution (see text). The different symbols correspond to the different dilution lines: s /w = 0.37 (O),s / w = 0.41 (A), and s / w = 0.50 (0). The error bars correspond to an estimated relative uncertainty of 5%. 20
"E --
h
" " 1 , , , , 1 , " , 1 , , , , 1 , , , , , , , , , 1 , , , ,
15
m
10
5
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0.2
0.1
0.3
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, , , ,
1
,
1
,
1
,
,
1
1
I
.
.
,
,
,
,
(2)
Here, 9w,o is the volume fraction of water in the oil, and we have assumed > Dw,aq.Hence, in the case where DwIaq is constant or Dw,aq> R , . To illustrate how AR varies with particle shape and size, we comparej,(O) for a prolate or oblate particle with that of a sphere. To reduce the number of independent variables, we again introduce the constraint of a constant ratio of surface area to enclosed volume of the particles. This allows us to calculate how js(0)varies with the axial ratio, r. In Figure 7, we have plotted the ratiojs,pr(0)/js,sph(O) as a function of the axial ratio r for different values of D,,,and for two different radii of the sphere under the constraint of a constant surface area t o enclosed volume. The corresponding ratio, js,ob(0)/jsr,,,,(O),for the case of oblates is plotted vs r in Figure 8. The curves were t o the theory of Halle39 and calculated n ~ m e r i c a l l yaccording ~~
Microstructure near the Oil Corner of a Microemulsion
ha
The Journal of Physical Chemistry, Vol. 96, No. 21, 1992 8645 in which the surfactant film contains saddlelike regions. The rate of surfactant reorientation by lateral diffusion depends on the principle curvatures, and saddlelike regions can have high magnitudes of the principle curvatures, while the mean curvature is low. Similar maxima have been observed at the particle-to-bicontinuous transition in ternary nonionic2’and quinaryIs (ionic surfactant-cosurfactant-salt-water-oil) systems.
2.0
1.0 0.00
3.0
,
, ,
0.05
0.10
0.15
0.05
0.10
0.15
,
-
2.5
0.00
Figure 9. Variation of the particle axial ratio, as determined from the 14N relaxation data, with the total volume fraction of surfactant and water, @ = 0, aW.a (top) shows the results of an analysis in terms of a prolate ellipsoidal particle shape, while b (bottom) shows the correswndinn results in terms of an oblate ellimoidal Darticle sham. . . . r -
+
serves to illustrate the sensitivity of AR to small deviations from spherical shape. The sensitivity is particular evident at higher Dlatvalues. Hence, while the self-diffusion experiment is not particularly sensitive to detect minor variations in the particle size, it is clear that it is possible to obtain such information from a NMR relaxation experiment. Particle Size Determination from Relaxation Data. For a quantitative analysis of the relaxation data, we need to determine Dlat,which can be obtained from the data if the size and shape of the aggregates are known. On the basis of entropy arguments (vide infra), we assume that the particles are spherical at infinite dilution. There, we obtain by extrapolation ARo = 120 s-I for s / w = 0.50, ARo = 180 s-’ for s / w = 0.41, and ARo * 200 s-’ for s / w = 0.37. By analyzing these values in terms of spherical reverse micelles, we use a radius calculated from eq 4 and lxAl from the quadrupolar splitting in the reverse hexagonal phase and calculate 4,.A similar value of Qat = 3 X mz s-I is obtained for the different dilution lines, which also is similar to the values found for other double-chained surfactants$I supporting the assumption of a spherical shape. On the basis of the assumption of spheres at infinite dilution, we may then quantitatively analyze the aggregate growth with 9 in terms of monodisperse prolate and oblate spheroidal aggregates. To estimate a functional form for the experimentally determined particle axial ratios as a function of 9,we have fitted the variation of AR with 9 to simple functions. For s / w = 0.37 and 0.41, AJ? varies roughly linearly with 9,and we obtained AR/ARo= 1 + 8.6@ and AR/ARo = 1 + 11.49,.respectively, while for s / w = 0.50 a good fit was obtained with a power dependence plus an offset: AR/ARo = l + 14.29°.64. ARo is the extrapolated value at infinite dilution. The resulting functions, r ( 9 ) ,are presented in Figure 9. In the case of prolates, r reaches a value of 2-3 at 9*for the three dilution lines. In terms of oblates, the r values are slightly smaller. For the s / w dilution line, we observe a maximum in AR at Q = 0.2, above which it decreases with increasing 9.This can be understood as an effect of the bicontinuity of the microstructure
7. General Discussion We have investigated the variation of the microstructurealong three oil dilution lines in the microemulsion phase of the DDAB-water-dodecane system. At sufficiently high dilution, only discrete reverse micelles are present, the average size of which decreases with decreasing concentration. Extradated to infinite dilution, the relaxation ciata are consistent with’spherical reverse micelles having radii as dictated by s / w . The aggregates grow in size both with increasing 9 and with increasing s/w. At higher 9,there is a crossover to a bicontinuous microstructure. The onset volume fraction for formation of the connected structure decreases strongly with increasing s / w . s / w = 0.37 is very close to the minimum value of s / w that can be diluted infinitely with oil. Since for thii dilution line we observe a particle growth and, furthermore, a crossover to a connected microstructure, we conclude that the present system does not contain an oil dilution line of invariant spherical reverse micelles. Likewise, the phase boundary on the higher water content side does not form a straight line of constant s/w. Similar conclusions regarding the microstructure, however slightly different in detail, were reached by Samseth et a1.8 from recent SANS and viscosity studies in the dilute regime of the DDAB-water-hexane system. The structural properties of dilute microemulsions evolving under the Of a curvature free energy have been by Safran et a1.27-30The fluid surfactant monolayer is described as an incompressible elastic surface characterized by a given spontaneous mean curvature, Hha bending rigidity, K , and a saddle splay constant, FZ. In an expansion to secondorder, the curvature free-energy area density is often written as42
fJA = K(H- H0)’ + RK
+
H = (cl c2)/2 is the mean and K = cIc2is the Gaussian curvature, where cI and c2 are the two principal curvatures. The transition from a bicontinuous ((K) < 0) to a particle structure ( ( K ) > 0) observed in the present system under water dilution demonstratesthat the system seeks to minimize its mean curvature free energy. Neglecting the Gaussian curvature term for simplicity, we can understand the observed particle growth with increasing s / w at constant 9 as a mean curvature effect. Since we observe nonspherical shapes together with a transition to a bicontinuous structure, even for our smallest value of s / w = 0.37, it is clear that the stoichiometry of the optimum sphere with a radius RmT = & = l/Hocorresponds to s/w < 0.37. With increasing s / w , RlNT deviates more and more from Ro, and elongated shapes, having a lower area averaged mean curvature, are favored. In order to understand the 9 dependence of the microstructure at constant s / w , we have to consider the entropy of mixing contribution to the free energy. Restricting oneselves to particles, this is often taken as an ideal mixing. Such a term, which favors smaller particles, becomes increasingly important when 9 decreases, resulting in a decrease of the average particle size upon dilution. Neglecting polydispersity, the smallest possible particle is the stoichiometric sphere, which then should be the limiting case at infinite dilution. The free-energy expression discussed above predicts an emulsification failure which is not observed. Instead, the phase boundary contain a critical point with a dilute and concentrated microemulsion coexistence. Neither does the L2’-L2’’-D1 three-phase triangle correspond to a Winsor 111 type eq~ilibrium~~ (here with a dilute DI phase replacing a dilute aqueous solution). The composition of the concentrated microemulsion (91NT= would in this case imply that the microstructure of this phase is bicontinuous, with an almost zero average mean curvature.
8646 The Journal of Physical Chemistry, Vol. 96, No. 21, 1992 However, experiments show that the microstructure here is very close to that of discrete reverse micelles.’.* Since the microstructure forms under the constraint H = H,, it is striking that the system does not show an emulsification failure with spherical reverse micelles. Recall that emulsification failure phase boundaries are present in, for example, ternary systems with nonionic ~ u r f a c t a n t sboth , ~ ~ with ~ ~ excess oil and with excess water. One possible explanation for the difference in phase behavior is the additional contribution to the free energy arising from the entropy of mixing of the ions in the ionic microemulsions. This entropic contribution suppresses phase sepration with excess water due to the entropy loss associated with the electroneutrality requirement that forces the counterions to the surfactant-rich phase. This entropy is found to be an important factor in the phase behavior of aqueous polymer-polyelectrolyte and polyelectrolytepolyelectrolyte Additions of salt offer an additional degree of freedom to regulate the electroneutrality requirement, which relaxes the constraint. In the polymer syst e m as~well ~ as~in the ~ present ~ surfactant-wateroil small additions of salt have dramatic effects on the phase behavior, decreasing the stability of the solution phase.
Acknowledgment. We are grateful to Bertil Halle for sharing with us a computer program for spectral density calculations, to Keiichi Fukuda for his help with some of the self-diffusion measurements, to Hdkan Wennerstrbm and Ilias Iliopoulos for stimulating discussions, and to Michael Brown for his comments on the manuscript. This work was supported by the Swedish Natural Science Research Council (NFR). R.S. thansk the Norwegian Council for Science and the Humanities (NAVF) and Nordiska Ministerrddet for financial support. Registry No. DDAB,3282-73-3; dodecane, 112-40-3.
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