3374
Langmuir 1996,11, 3374-3381
Counterion-DrivenSphere to Cylinder Transition in Reverse Micelles: A Small Angle X-ray Scattering and Conductometric Study E. Bardez” and Nguyen Cao Vy Laboratoire de Chimie @ndrale, CNAM, 292 rue St. Martin, 75141 Paris Cedex 03,France
Th. Zemb* Service de Chimie Moldculaire (CEA), CE Saclay, 91191 Gif sur Yvette Cedex, France Received November 2, 1994. In Final Form: June 9, 1 9 9 P SAXS and conductivity measurements are used to investigate reverse aggregates in isooctane formed by AOT in which the sodium counterion is exchangedby a trivalent counterion,the aluminum cation A13+. The corresponding surfactant is denoted by A& in contrast to NaA for AOT. The phase behavior of the system Akjlwaterlisooctane is determined in the dilute region. While NaA surfactant film in reverse micelles can be balanced toward zero spontaneous curvature close to room temperature and shows gradual transformation of spheres into a connected network upon swelling by water, A& aggregation behavior is dominated by a sphere to cylinder transition leading to liquid-gas coexistence of cylindrical aggregates. Spontaneous curvature is strongly directed toward water while the area per molecules remains constant at any water content. At water content higher than a3.5 water molecules per surfactant molecules, long and rigid cylinders are observed and produce an increase in the sample conductivity.
Previous studies ofthe effect of confiningmetallic cations in the polar core of reversed micellar aggregates were carried out using surfactants derived from the widely used Aerosol-OT (AOT, or the sodium salt of the bis(2ethylhexy1)sulfosuccinica ~ i d ) . l -These ~ surfactantswere prepared by exchanging the Na+ counterion of AOT for divalent or trivalent ions such as Ca2+,Mg2+,Zn2+,A13+, Ga3+, and In3+. The water in oil (wlo) microemulsions stabilized by such surfactants MA,, where Mn+represents the metal cation and A- the amphiphilic anion bis(2ethylhexyl)sulfosuccinate, were shown to exhibit outstanding catalytic properties which can be modulated as a function of the nature of the cation and the water content of the medium.l The reactivity displayed in the micellar core can be correlated with the properties of the water molecules belonging to the polar core of the reverse micelles, as evidenced by lH NMR measurements and FTIR spectro~copy.~ Recent studies have been focused on the microscopic aggregate structures by scattering techniques (mainly small angle neutron and small angle X-ray scattering) and have shown that the simple structural behavior of AOT (NaA) is not valid for the MA, surfactants except for c a A ~ . 4 -Spherical ~ surfactant-coated water droplets are indeed formed when reversed micelles of CaA2 in an alkane are swollen as in the case of NaA. However, the wlo systems with other bimetallic surfactants consist of spherical droplets at low water content and of ellipsoidal Abstract publishedinAdvanceACSAbstracts,August 15,1995. (1)Bardez, E.; Larrey, B.; Zhu, X. X.; Valeur, B. Chem. Phys. Lett. 1990,171,362. (2)Zhu, X.X.;Bardez, E.; Dallery, L.; Larrey, B.; Valeur, B. New J. Chem. 1992,16,973. (3)Aliotta, F.; Migliardo, P.; Donati D. I.; Turco-Liveri, V.; Bardez, E.; Larrey, B. Prog. Colloid Polym. Sci. 1992,89,1. (4)Giordano, R.; Migliardo, P.; Wanderlingh, U.; Bardez, E.; Vasi, C. J. Mol. Struct. 1993,296,265. (5)Petit, C.; Lixon, P.; Pileni, M. P. (a)Lungmuir 1991, 7,26202625.(b)Prog. Colloid Polym. Sci. 1992,89,328. (6)(a)Eastoe,J.;Fragneto G.;Robinson, B. H.; Towey, T. F.; Heenan, R. K.; Leng,,F. J. J. Chem. SOC.,Faraday Trans. 1992,88,461. (b) Eastoe, J.; Towey, T. F.; Robinson, B. H.; Williams, J.; Heenan, R. K. J. Phys. Chem. 1993,97,1459. @
or cylindrical objects at high water content. Similar conclusions could be drawn from preliminary small-angle neutron scattering (SANS) measurements performed on the Wcyclohexane ~ y s t e m In . ~ the present work, the aggregation of the A& surfactant in isooctane is further investigated by small angle X-ray scattering (SAXS) and conductivity measurements, and discussed in the light of the knowledge of the aggregation states shown by the well-known surfactant NaA.
Phase Behavior and Microstructures Previously Described in Systems Formed from NaA(A0T) AOT (denoted NaA in the present paper) is a widely used anionic surfactant in particular for reactivity studies in reversed micellar aggregates.7 Thorough structural studies concerning this surfactant have been reported, and a precise ternary phase diagram has been determined in 1970 by Ekwall,8 Chen: and co-workers. The small globular micelles observed in pure water have a very limited growth, aggregation numbers varying linearly from 15 to 30 with concentration, according to the socalled “ladder” model.g In water, by addition of the order of 0.1 M of salt, a disordered open connected lamellar structure (=“sponge” or symmetric L3 or “random molten bilayer”) is obtained.lOJ1 The exact location of phase domains in salt-temperature diagrams is largely dependent on the impurities and residual salt content. As shown by Shinoda, with 10% weight NaA content, the maximum ofwater in the reverse micelle is decreased from 70%when NaA is used with impurities (single chains resulting from partial hydrolysis, salt remaining from synthesis), to less than 40% with purified surfactant. The former value of (7)Structure and reactivity in reverse micelles; Pileni, M. P., Ed.; Elsevier: Amsterdam, 1989. (8)Ekwall, P.; Mandell, L.; Fontell, K. J. Colloid Interface Sci. 1970, 33,215. (9)Sheu, E.Y.;Chen, S. H.; Huang, J. S. J. Phys. Chem. 1987,91, 3306. (10)Skouri, M.; Marignan, J.; Appell, J.; Porte, G. J. Phys. II 1991, 1121. (11)Balinov, B.; Olsson, U.; Soderman, 0.J.Phys. Chem. 1991,95, 5931.
0743-746319512411-3374$09.00/00 1995 American Chemical Society
Reversed Micellar Aggregates swelling in hexane can be restored by adding salt as a “controlled impurity”.12 Moreover a practical problem in phase diagram determination is self-catalysis of the hydrolysis of the surfactant.13 In the reverse micellar (oil-rich)region, the maximum amount of water solubilized can also be controlled by the nature of oil and by temperature.14J5 However, the structure in the middle of the phase diagram has remained a mystery: the conductivity depends on temperature at given volume fractions. It has first been determined as being alocally lamellar structure in heptane16and claimed to be made of close packed spherical droplets in decane by Kotlarchyk et al.” Three different phase transitions from reverse micelles to di- and triphasic samples have been described yet with NaA surfactant: A. Coexistence of a concentrated and a diluted reverse micellar phase (oil in excess or Winsor I system), induced by long range attractions between micelles. For instance, this type of phase separation has been observed in dodecane at 25 O C . l 8 B. Coexistence of a lamellar phase with reverse micelles, described by Kunieda and Shinoda in isooctane at 15 O C 1 2 and by Assih et al. in decane at 25 O C . 1 9 C. Phase separation with water in excess, corresponding to Winsor I1 regime. This regime is observed with a highly connected water in oil structure: excess water is expelled. In this regime, maximum of water included in the connected network of micellar cores as well as conductivity is quantitatively predicted by the DOC model.20 This model uses the three basic constraints in this regime: volume fraction is fixed by the waterfoil ratio; surface is fixed by the amount of surfactant; spontaneous curvature is either a parameter or can be determined from the phase diagram for stiff interfaces (bending constant larger than KT). To our knowledge, the DOC model proposed 5 years ago is still the single model of microemulsion allowing prediction of scattering peak position and conductivity percolation from composition alone.20 Phase separation processes of types A and C have been rationalized and shown to be induced or hindered by penetration of the hydrocarbon, medium chain alcohol addition, salinity and temperature.21s22 The aim of this paper is to investigate what are the features remaining valid in the presence of a trivalent counterion: aluminum cation, A13+,and hence to answer the following questions: (12)Kunieda, H.; Shinoda, K. J.ColloidInterface Sci. 1979,70,577. (13)Fletcher P. D. I.; Perrins, N. M.; Robinson, B. H.; Toprakcioglu, C. In Reverse Micelles; Luisi, P. L., Straub, B. E., Eds.; Plenum Press: New York, 1984;p 69. (14)(a)Chen, S.H.; Chang, S.L.; Strey,R.J.Phys. Chem. 1990,93, 1907-1918. (b) Chen, S. H.; Chang, S. L.; Strey, R.;Samseth, J.; Mortensen, K. J. Phys. Chem. 1991,95,7427. (15)Pileni, M. P.; Zemb, Th.;Petit, C. Chem. Phys. Lett. 1986,118, 414. (16)Cabos, C.; Delord, P.; Marignan, J. Phys. Rev.B 1988,37,9796. (17)Kotlarchyk, M.; Chen, S. H.; Huang, J. S.; Kim M. W. (a)Phys. Reu. Lett. 1984,53, 941.(b)Phys. Rev.A 1984,29,2054. (18)North, A. N.;Dore, J. C.; Katsikides, A,; McDonald, J. A.; Robinson, B. H. Chem. Phys. Lett. 1988,132,541. (19)Assih T.;Delord, P.; Larch& F. C. In Surfactants in Solutions; Mittal, K. L., Lindman, B., Eds.; Plenum Press: New York, 1984;Vol. 3,p 1821. (20)Zemb, T.N.; Barnes, I. S.; Derian, P. J.; Ninham, B. W. Prog. Colloid Polym. Sci. 1990,81, 20. (21)Hou, M.J.; Shah, D. 0. Langmuir 1987,3, 1086. (22)Jada, A.;Lang, J.; Zana, R.J. Phys. Chem. 1990,94,381. (23)Barnes, I. S.;Derian, P. J.; Hyde, S. T.; Ninham, B. W.; Zemb, T. N. J. Phys. (Paris) 1990, 2605. (24)De Gennes, P.G.; Taupin, C. J. Phys. Chem. 1982,86,2294. (25)Milner, S.T.; Safran, S.A.; Andelman, D.; Cates, M. E.; Roux, D. J. Phys. (Paris) 1988,49,1065. (26)Israelachvili,J. N.;Mitchell, D. J.;Ninham, B. W. J. Chem. SOC. Faraday Trans. 2 1976,72, 1525. (27)A short program written in BASIC is available from the authors for testing.
Langmuir, Vol. 11, No. 9, 1995 3375 (i) What are the phases observed with excess water? (ii) What is the structure of the wlo microemulsions, with A13+as a counterion? What are the driving forces toward this structure? (iii) What is the conductometric behavior of these microemulsions?
Materials and Methods 1. Materiala The surfactant aluminum bis(2-ethylhexy1)sulfosuccinate (A&)was obtained by the methathesis reaction of methanolic solution of NaA (AOT) and aqueous aluminum chloride. Details of the preparation have already been reported elsewhere.l92*4AOT was obtained from Sigma and used without further purification. Sudan IV and Eosin Y were purchased by Aldrich. Potassium chloride used for the determination of the cell constant in conductivity measurements was from Merck and of Suprapur grade. Isooctane (2,2,4-trimethylpentane) of spectroscopic grade was purchased by Prolabo. Millipore filtered C2-l.cm-l at 25 “C) was employed to water (conductivity < prepare the microemulsions. 2. M e t h o d s The study dealing with A& microemulsions in isooctane is carried out as a function of the total amount of solubilized water, which is the sum ofthe residual water and the added water. The water content W can be expressed by either the molar ratio WMof water to aluminum ion or the molar ratio WAof water to the surfactant anion A- (WA = wM/3). Moreover, in the presence of aluminum cation, the residual water amount in the surfactant cannot be lowered below the hydration requirement of the A13+ cation, Le. 6 HzO molecules per A13+, because of the strong affinity of aluminum for oxygen. This is peculiar to the aluminum derivative, because we are used to drying all the other metallic surfactants below the hydration requirement of the cation, but A&. Phase separation studies were performed at room temperature. Water was added dropwise and slowly under stirring in samples of 2-4 cm3 of surfactant solutions. The water solubility is considered to be the maximum value of W for which no turbidity occurs. The overall error on the value ofthe solubilityis estimated to be &1 on the WM scale. Various surfactant concentrations from 0.025 to 0.1 M (Le. [A-I ranging from 0.075 to 0.3 M) were investigated. At water content larger than the water solubility, the systems are diphasic. To determine the nature of the phases in equilibrium beyond the phase separation, water was added in quantities 4 or 5 times larger than the solubility and the samples were allowed to equilibrate for at least 60 h. Then dyes were added to the systems to identify the nature of the phases in equilibrium: either oil-soluble dye Sudan IV or water-soluble dye Eosin Y. Phase behavior could then be observed by visual inspection. For each experiment, a reference sample was systematically kept without dye addition in order to ascertain that the presence of the dye does not modify the respective volumes of the phases in equilibrium. The SAXS experiments have been carried out by use of a pinhole collimation Huxley-Holmes SAXS camera. This type of SAXS camera is well suited for studying diluted samples of small micelles: flux is high (more than lo7photons through the sample), the measurable q-range lies between 0.01 and 0.4 A-1, and the background is very low, about 10 times lower than a 1.5 mm scattering of water due to its compressibility a t room temperature. The LUPOLEN (by BASF) sample was used as a reference standard (scattering at maximum, 6 cm-l). Typical counting time on a 2D gas detector or an “image plate” system is 4 h with a 15 kW, 8 kV source. Data reduction was done according to a procedure developed in the laboratory.28 Since the image of the source in the detector plane is a point, no desmearing procedure due to geometrical effects is needed to obtain the results shown in Figures 2-4. Data reduction and radial average scattering intensities are expressed in cm-l (according to the formalism introduced by StuhrmannZ91. The (28)Le Flanchec, V.;Gazeau, D.; Taboury, J.; Zemb, Th. J. Appl.
Crystallogr., in press.
(29)Stuhrmann,H.B.; Miller, A. J.Appl. Crystallogr. 1978,11,325.
3376 Langmuir, Vol. 11, No. 9, 1995
Bardez et al.
3
2.5
2 1.5 1
0.5
, 6
1 1
8
10
12
14
16
AIA,, wt%
Figure 1. Phase diagram for the ternary system Al&/isooctaneJ water. Dashed lines are guidelines for eyes. Top: Two phaseseparated systems w/o microemulsions.Area 1: no experimental points in this area because the presence of residual water in &does not allow one to obtain microemulsions with WMlower than 6. Area 2: spherical-shape droplets. Area 3: cylindershape droplets. plots are divided by the invariant,
therefore, the scattering powers are expressed in absolute units and can be compared when divided by volume fraction and contrast (square of the electronic density f l u c t ~ a t i o n ) . ~ ~ In the simulations of the scattered intensity, we have used two different expressions of the intensity:
for simulation of spherical structures:
for simulation of cylinders:
I
0.1
1
q (A-'1
Figure 2. (a)Variation ofthe normalized scattered intensities with q for & microemulsions at three different water WM= 10;( x ) WM = 12. [&I = 0.1 contents: (0)WM= 6;(0) M. (b) Variation of the normalized scattered intensities with q for & microemulsions at three different surfactant = 0.1 M; (0)[&I = 0.05 M; ( x ) concentrations: (0)[&I [&I = 0.025 M. WM = 10.
kHz and a conductivity cell from Tacussel. The cell constant (0.77 f 0.10 cm) was determined using aqueous solutions of KCl of standard concentrations. The reproducibility of every conductivity curve was checked by repeated experiments. is the where is the volume fraction of the polar core, contrast (the square ofthe difference in scattering length density), and R the radius of the object. As can be seen in Table 1, the maximum polar core volume fraction is 4.3%. However, the dispersed phasevolume fraction &, includingthe chains, which is important for interaction between aggregates, is 5 13%. In eq 2, Jl(x)is the first Bessel's function, and Jl(qR)/(qR)may be written as
Due to the small values of the observed radii, it was not necessary to introduce two different scattering length densities for the micelles. Electronic density differences between the oil and the surfactant chains have been neglected. Constant background due to scattering of the solvent has been subtracted by extrapolation to a pure Porod (q-4)behavior. No interparticle interaction effects were included in the modeling and theoretical curves represent the structures of independent micelles. Conductivity measurements were carried out at 25 "C using a Wayne-Kerr bridge type 4225 operating a t 100 Hz, lkHz or 10 (30)Small Angles Scatterings of X-rays; Guinier, A., Fournet, G., Eds.; Wiley and Sons: New York, 1955.
Results Phase Behavior of A& in Isooctane. The phase behavior of the W w a t e r l i s o o c t a n e system w a s investigated for three surfactant concentrations [&I = 0.025, 0.05, and 0.1 M, as described in the Experimental Section. The m a i n results are displayed in Figure 1. Region 1 beyond the lowest dashed line corresponds to microemulsions which cannot be experimentally obtained, because t h e correspondingw a t e r content should be WM< 6, a value lower than the amount ofresidual w a t e r in t h e surfactant. Indeed, the hydration requirement of aluminum cation is 6 HzO per A13+(see Methods). Regions 2 and 3 correspond microemulsions in to the monophasic domain of the isoctane. Spherical-shape aggregates will be shown to occur in region 2 a n d cylinder-shape aggregates in region 3. The w a t e r solubility is estimated t o be WM= 13 (i.e. W A e 4.5) and does not depend on whether the surfactant concentration is 0.025, 0.05, or 0 . 1 M. Hence region 4 (above the solid line) is a diphasic region. "he identification of the two phases with the dyes Eosin Y a n d S u d a n IV shows that a very diluted oil phase is in equilibrium with a concentrated inverted micellar p h a s e (Winsor I type demixtion). None of t h e two coexisting liquids is birefringent. Moreover, no flow birefringence could be
Langmuir, Vol. 11, No. 9, 1995 3377
Reversed Micellar Aggregates
lozo
r
-.
1024 1 0.01
I
I
0.1
I
.
, ,
. ,,
1024 I 0.01
1
lr . . .
0.1
9 (A’)
, . ,
s(A-’)
Figure 3. Normalized scattered intensity versus q for A& microemulsions, [A&]= 0.05 M, WM= 6.Solid line is best fit for monodisperse spheres. Dashed line is best fit for cylinders.
detected between crossed polarizers. Note that the points represented on the phase diagram indicate positions of the samples investigated by SAXS experiments. SAXS Results. Figure 2a shows the scattered intensity, normalized by the invariant, for three different water contents, i.e. WM= 6,10,and 12,respectively. The increase at low angle may be interpreted either in terms of an attraction and/or a shape transformation of spheres to cylinders upon swelling with water. Note that the slope of this log-log plot at low q and high water content is close to -1: the interaction potential V ( R ) between spherical micelles could probably be adjusted in order to force S(q) to be close to a q-l decay. However this pathologic potential should have a very unreasonable distance dependence. On the opposite, this power-law dependence is expected for a stiff cylinder. Figure 2b shows, in the same units, a concentration scan with a constant water to surfactant ratio (WM = 10). This experiment shows that the sphere to cylinder transition can be induced either by increasing the water to surfactant ratio or by dilution. This evolution, an increase of the scattering divided by concentration, is the proof that any type of structure factor due to an attractive interaction cannot explain the measurement: ifattractive interactions would play a role in the scattering in this system, the opposite evolution of the scattering versus volume fraction would be observed. To ascertain whether a transition from a sphere to cylinder is possible, we tried to fit the observed scattering to the relevant expression of the scattering, eqs 1 and 2. Results shown on Figure 3 demonstrate that a dispersion of independent spheres is an excellent model at lowest water content WM= 6. For that sample, where [AM31 = 0.05 M,the volume fractions of the polar core and the dispersed phase calculated from molecular volumes are @I, = 1.6% and = 6.2%,respectively. The scattering curve obtained is proof that the attractive interaction between micelles has negligible effects, i.e. S(q)= 1 at the
Figure 4. Normalized scattered intensity versus q for A&
microemulsions, [A&]= 0.1M,WM = 12. Solid line is best fit
for monodisperse spheres. Dashed line is best fit for cylinders.
precision of the experiment. Moreover, experiment and modeling with spheres are done on absolute scale of scattering cross section, normalized by the invariant. The same modeling with spherical objects could be done for the two other concentrations of surfactant, [AM31 = 0.1 and 0.025 M at the lowest water content WM= 6, and the resulting values of the radius of the spheres are displayed on Table 1. These values appear to be independent of the surfactant concentration and lie in the range R RZ 12-13
A.
Figure 4 shows that infinite cylinder is the best representation of the data a t the highest water content considered here. Adjustment is made to find the best value of the radius, that is 10 A at WM= 12 and [AM31= 0.1 M. Since radius of the cylinder is the single parameter and the simulated curve on absolute scale of scattering crosssection scales like the square of the radius, this method of estimation of the radius has a good precision. Note that there is no cut-off of the slope of the scattering at lowg: this means that the length of these stiff cylinders is larger than 50 nm. Similar simulations were done for the other surfactant concentrations at WMvalues larger than 10 because, in this water content range, the best fit ofthe data is obtained by modeling the shape of the objects with cylinders. The results in Table 1 show that the R values remain in the range 10-12 A. Another method to determine the radius of cylinders, independent of the absolute scale of the scattering, is the ln(q I ( q ) )versus q2 plot: the slope of this Guinier plot of the cross section allows direct determination of the radius of the homogeneous cylinder. Results consistent with the previous determination via curve fitting, are also reported in Table 1. Radii could not be directly measured from a Porod plot: the radii of the objects are too small to allow direct observation of the asymptotic behavior in accessible q-range. Due to the high curvature, the asymptotic scattering regime which allows area determinations is
Table 1. Results at All Water Contents and Concentrations from SAXS Measurements [AlAd. M WM
-
WA
M e, x l V 1 cm-2 rii3+1,
(6e)2, x
cm-4
@polar
@dis* Q*exp,
x
cmV4
fit spheres R,A u, A 2
fit cylinders R, A u,A2 lntl(q)l = f(q2) R , A
0.1
0.1
6
10
2 9.2 1.93 1.58 0.033 0.12 5.18 12 1 46 -
3.3 5.5 1.76 1.17 0.039 0.13 5.05 10 iz 1 44 11
-
1
0.1 12 4 4.6 1.70 1.05 0.043 0.133 4.84
-
-
lo* 1 47 12
0.05 6 2 9.2 1.93 1.58 0.016 0.062 2.71 13 f 1 42 -
0.05 10 3.3 5.5 1.76 1.16 0.02 0.065 2.94 lo& 1 42 11
0.05 11 3.7 5.1 1.72 1.08 0.021 0.066 2.01
-
12 f 1 37 12
0.25 6 2 9.2 1.93 1.58 0.008 0.031 1.25 13 iz 1 42
-
0.25 10 3.3 5.5 1.76 1.16 0.01 0.033 1.09 12 37 11
Bardez et al.
3378 Langmuir, Vol. 11, No. 9, 1995 not even reached at 0.5 k1 with enough precision to allow direct determination of the area per surfactant. Results at all water contents and concentrations are summarizedin Table 1,including the area per headgroup. This area is calculated from the volume to surface ratio of the cylinder and spheres. It can be observed that a reduction of the area per molecule in comparison to the NaA surfactant, where 0.6 nm2 per surfactant head, has been obtained.15 In Table 1, concentration of aluminum counterions in the core of the micelles, [A13+l,(whatever the ions are free or associated to the polar heads), is compared to the overall surfactant concentration in isooctane, [A&].The internal concentration ofaluminum is in the range of 4.6-9.2 M. This high local aluminum concentration may be the cause of the lowering of the headgroup area as will be seen in the discussion. The result of these measurements is the observation of a sphere to cylinder transition. Regions of the phase diagram where the reverse aggregates may be considered to be either spheres or cylinders are specified in Figure 1. This transition upon addition of water should have two consequences: (a) The apparition of a diluted cylinderlconcentrated cylinder coexistence. This consequenceis indeed observed. This coexistencemay be due to an Onsager-type transition and/or the presence of strong attractive interactions. Determination of the leading mechanism would require light scattering studies as well as difficult titrations of the very low concentration of cylinders in the upper (diluted) phase and we have not clarified this point. (b)The enhancement of the conductivity of the solution in the region where cylinders are detected by scattering (videinfra). Scattering alone does not allow determination of whether the cylinders are connected or not. Electrical Conductivity of the Microemulsions. The electrical conductivity of 0.05 M A & solutions in isooctane is studied as a function of the swelling of the microemulsion with water from WM = 6 (residual water of the surfactant) to WM % 13 when phase separation occurs. The corresponding volume fractions of the dispersed phase @dispremain low, varying from 0.062 to 0.069. Figure 5a shows that the conductivity K increases rapidly from (1-2) x lo-@to 1.5 x lo-’ 8 - k m - l upon increasing W M up to ca. 9. Then a slight decrease of K is observed between WM 9 and 11, followed by a sharp increase above WM% 11. At WM 13, the conductivity reaches nearly 4 x lo-’ W1.cm-l. The interpretation of these results requires a comparison with the behavior of NaA microemulsions in isooctane because they constitute in a way the reference system. The conductivity of NaA solutions in isooctane at 25 “C has been measured again in the present work as a function of W (in the case of NaA, WA = WM = W = [H20ll[NaAl). The NaA concentration is 0.15 M so that the surfactant anion concentration is the same as in the measurements with 0.05 MA& solutions, i.e. [A-I = 0.15 M. The results shown in Figure 6a are in agreement to those obtained by Jada et al.31and Eicke et al.,32respectively. A maximum of conductivity is observed at low W values (W % 15), whereas this maximum occurs at W x 10 with n-octane or n-decane as oil phases, and at W FZ 17 with n-heptane, re~pectively.~~ Moreover,when our values of K are divided by the volume fraction of the dispersed phase @disp in order used by Eicke to calculate the “specificconductivity” et al.,32we obtain, within experimental error, the same ~~sW ~ as those found by numerical values of K I @versus these authors, with a maxlmum of K/&isp displayed at W RZ 8. Remembering that a similar maximum is shown on (31)Jada, A.; Lang, J.; Zana, R. J. Phys. Chem. 1989,93,10. (32)Eicke, H. F.;Borkovec, M.; Das-Gupta, B. J. Phys. Chem. 1989, 93, 314.
lo6
i
++ t +
+ +
lo6 1 0 6
++
+
+
t
+
i
t
**
E
10B6 2
+ +
’ *+ *
**
6
7 2.3
8 2.7
9 3
10 3.3
11 3.7
12 4
13 4.3
14 W, 4.7 W,
Figure 5. (a) Dependence of the conductivity of 0.05 M A& in isooctane on the water content expressed as W Mat 25 “C. (b) Dependence of the product K W Aon ~ either W Mor WA, from the
experimental values plotted in (a).
the A& conductivity curve at WMw 9 (Figure 6a), further attention on the meaning of this maximum will be paid in the Discussion.
Discussion The electrical conductivity of a wlo microemulsion far from phase boundary is known to be of the order of lo-@S2-lcm-l while the conductivity of the solvent phase is typically 10-18-10-14 9-km-l. When either thevolume fraction @disPofthe dispersed phase (surfactant and water) at constant temperature or temperature at constant @ is increased, the percolation transition may be observed and is shown by a large and steep increase in conductivity of 3-4 orders o f m a g n i t ~ d e . ~ l In j ~the ~ - ~present study, the increase in conductivity above WM 11is interrupted by phase separation and the value of the conductivity reached in the A& microemulsion at the maximum amount of solubilized water ( ~ x4 S2-l.cm-l) is far from the (33)Bhattacharya, S.;Stokes, J. P.; Kim, M. W.; Huang, J. S. Phys. Rev. Lett. 1986,55, 1884. (34)Geiger, S.;Eicke, H. F. J. Colloid Interface Sci. 1986,110,181. (35)Eicke, H. F.;Hilfiker, R.; Holz, M. Helv. Chim. Acta 1984,67, 361. (36)Borkovec, M.; Eicke, H. F.; Hammerich, H.; Das-Gupta, B. J. Phvs. Chem. 1988.92.206. 137) Van Dijk, M. A.;Casteleijn, G.; Joosten, J. G. H.; Levine, Y. K. J. Chem. Phys. 1986,85,626. (38)Dutkiewicz, E.; Robinson, B. H. J. Electroanal. Chem. 1988, _2.51 _ _ 11
(39cMathew, C.; Patanjali, P. K.; Nabi, A.; Maitra, A. Colloids Surf: l988,30,253. (40)Kahlweit, M.; Busse, G.; Winkler, J. J. Chem. Phys. 1993,99, 5605. (41)Both static and dynamics percolation models have been proposed; the former is consistent with micelle coalescence in a precursor t o a bicontinuous phase, the latter puts forward percolation clusters associated with “sticky encounters” due to attractive interactions. (42)Jada, A.;Lang, J.; Candau, S. J.; Zana, R. Colloids Surf 1989, 38,251. (43)Eastoe, J.; Robinson, B. H.; Steytler, D. C.; Thorn-Leeson, D. Adv. Colloid Interface Sci. 1991, 36, 1.
Langmuir, Vol. 11, No. 9, 1995 3379
Reversed Micellar Aggregates
on the average, electrically neutral, they can carry instantaneous positive or negative excess charges due to spontaneous charge fluctuations resulting from material exchange between droplets according to
. . lo8
b
1'0
20
30
40
50
+
neutral droplet neutral droplet - positive droplet negative droplet a .
60
70
w
(b)
107
The conductivity results then from the migration of the charged droplets in the applied electric field. It should be noted that no conductivity due to free ions in the external solvent phase is to be considered because it is essentially negligible: the appearance of ions in an apolar medium is in fact extremely unlikely. In particular, the monomeric ionic surfactant, dispersed in the apolar solvent in the form of contact ion pairs, is not expected to contribute to conductivity. Charge fluctuations for a given droplet relax on the time scale of the mean time of exchange of material between micelles, typically of the order of 0.1-1 The measurements being usually performed at frequencies of 300 Hz to 5 kHz, an average conductivity is measured, independent of how charge fluctuations are created. Thus, the following expression of the conductivity K of a monodisperse solution of spherical rigid objects carrying an excess charge z is generally considered as the basic relationship for all the theoretical K
10'7
= (Ce2/6n7r,) (z2)
(3)
In this expression, C denotes the droplet concentration (number in unit volume), e is the proton charge, 7 is the viscosity of the medium, and q,is the hydrodynamic radius ofthe droplets. The mean-square charge of a droplet was shown to be conveniently approximated by the simple expres~ion:~~
I* e
i
'0' 0
+
10
20
30
40
50
60
(z2)= 4n~,,,r,&T/e~
(4)
70 W
Figure 6. (a) Dependence of the conductivity of 0.15 M NaA in isooctane on the water content expressed as W at 25 "C. (b) Dependence of the product KW on W, from the experimental values plotted in (a). ( c ) Dependence of the product K Won~W, from the experimental vqlues plotted in (a). values usually obtained when a percolation phenomenon is shown to occur; moreover, the corresponding volume fraction of the micelles is quite low (0.069). Further interpretation of this experimental behavior requires consideration of the conductometric curve on the whole. Hence the physical phenomena leading to the conductivity of a microemulsion in the Lg phase are now to be recalled. As far as we are aware, the only experimental investigations of wlo microemulsions far below the percolation threshold were carried out either in water-n-alkaneAOT(NFA)~~,~~ or water-chlorobenzene-alkylbenzyldimethylammonium chlorides31systems where spherical droplets are to be expected. The data obtained in waterisooctane-NaA micro emulsion^^^ were interpreted in terms of droplet charge fluctuations, in several successive theoretical models assuming that the water droplets coated by the surfactant molecules are spherical i n shape and monodisperse i n size.32,44-51Although such droplets are, (44) Hall, D. G. J. Phys. Chem. 1990,94, 429. (45) Kallay, N.; Chittofrati, A. J.Phys. Chem. 1990,94,4755. (46) Halle, B. Prog. Colloid Polym. Sci. 1990,82, 211. (47)Pan, H.-Y. Chem. Phys. Lett. 1991,185, 344. (48) Bratko, D.; Woodward, C. E.; Luzar, A. J.Chem. Phys. 1991,95, 5318. (49) Kallay, N.; Tomic, M.; Chittofrati, A. Colloid PoZym. Sci. 1992, 270, 194.
(where E , denotes the permittivity of the oil medium, rc the water core radius, k the Boltzmann constant, and T the thermodynamic temperature), provided that the degree of counterion binding to the surfactant polar head is not higher than 99%. This expression means that is determined by the ratio of the thermal and Coulomb energies of the charged droplets.32 The point is now to interpret the variations of K when the volume fraction of the droplets is increased, especially upon swelling with water. The case of the NaA microemulsions where a maximum of conductivity was shown to occur will be considered first. This maximum could not be accounted for by the theoretical treatment presented by E i ~ k ebut , ~more ~ refined alternative treatments aimed at predicting its existence and at fitting the experimental data were p r o p ~ s e d . ~A~physical -~~ origin of this maximum is given by Halle as follows.46 For small droplets the electrostaticwork for charging noninteracting droplets and separating the ionic pair consisting of close positive and negative droplets, is much larger than the thermal energy. Consequently,nearly all droplets are neutral and the conductivity is small. As the size of the droplets increases upon addition of water, this work becomes less prohibitive because of the increasing distance between the centers of two droplets in each pair, and the conductivity rises sharply. Concurrently, the concentration of the droplets decreases, which reduces the number of charge carriers and then the conductivity. As a result of these two antagonistic effects, the conductivity passes (50) Tomic, M.; Kallay, N. J. Phys. Chem. 1992,96,3874. (51) Molski, A,; Dutkiewicz, E. Colloid Polym. Sci. 1993,271,1177.
Bardez et al.
3380 Langmuir, Vol. 11, No. 9, 1995 through a maximum. For the sake of better legibility of the experimental data, the contribution of the droplet size increase can be eliminated by a simple treatment which is now applied to our results. In eq 3, the concentration C ofdroplets can be expressed as a function of the aggregated surfactant concentration [surf],,
C = [surflaggN/N ([surf], denotes the concentration in the molar scale, N the Avogadro number, and N the aggregation number). The aggregated surfactant concentration is the difference between the total surfactant concentration ([surf]) and the critical micellar concentration (cmc). In the case of M. NaA, the cmc value is known to be below 2 x Considering that in the present work measurements were performed in 0.15 M solutions, the cmc can be neglected and [surf]aggx [surf]. The NaAconductivity appears then to be proportional to the quantity [surf] Ir$V K
= ( [surfI(z2)/r8
(5)
Moreover,it is noteworthy from eq 4 that a linear variation of with rc is to be expected. The water core radius rcitself is proportional to Wprovided that the area occupied by a surfactant head group at the micellar interface, A,, can be considered constant
rc = (3vwW)/A,
(6)
where uw represents the volume of a water molecule (30 x cm3). Similarly, the aggregation number N is related to W through the expression52
N = (36mw2w)/A,3
As for the hydrodynamic radius Q, it is the sum of the thickness of the surfactant shell ( 1 ) and the radius of the water core (rc). Using the limiting value ofA, = 55 x cm2 for the NaA polar head,53eq 6 leads to r, Inm = 0.16W. With 1 estimated to be 0.6 nm, the following expression for r h may be used:34
r&m = 0.16W
+ 0.6
(7)
From these considerations, one can conclude that is proportional to W, N proportional to W , and rh a linear function of W, provided that A, can be considered constant and that the counterion is not very strongly associated with the anionic polar head. Consequently, eq 5 becomes K
[surfI/(Wrh)
or KWrh = [surf] = constant
(8)
The variation of the product KWQ versus W (calculated using eq 7 for rh) is displayed in Figure 6b for NaA microemulsions. This calculation procedure effectively smooths out the conductivity maximum, and at Wvalues larger than ca. 30, eq 8 is satisfied. However, a t Wvalues lower than ca. 30, a marked increase in KWQwith W is always shown. In this range of water contents, several assumptions ofthe model are no longervalid. For instance below W x 30, the polar head area A, is not constant but (52) Karpe, P.; Ruckenstein, E. J. Colloid Interface Sci. 1990,137, 408. (53) Eicke, H.F.;Kvita, P. InReuerse Micelles; Luisi, P. L., Straub, B. E., Eds.; Plenum: New York, 1984; p 21.
shows a progressive increase with W.53 Moreover, in the same W range, a gradual lowering of the counterion binding upon addition of water is also observed.52 Nevertheless, the type of calculation and representation used here allows one to get rid of the effect of the variations of conductivity due to the parameter r, and to check the validity of the different equations given above for W 2 30, that is for droplets larger than 5 nm. Note that another representation in which the entirely experimental quantity KW is studied as a function of W gives, on the logarithmic scale, a curve similar toKWrhversus W(Figure 6c). KWseems then to be a reasonable approximation for K W ~which , means that 1 can be neglected with respect to r, in the rh value used in eq 8. These results show then which kind of variation for KW as a function of W is to be expected when spherical objects are supposed to migrate in the electric field. They are now to be compared to the results obtained in the water-isooctane-A& microemulsions. The dependence of KWon W for the latter system is presented in Figure 6b. The Wvalue used in this calculation is WA,that is the third of WM,because the W value expressed in the previous equations for spherical droplets, for example in eq 6, is relative to one polar head. The main qualitative difference between the curves corresponding to & and NaA microemulsions respectively (Figures 5b and 6c) is the sharp increase of KWbeyond WMx 11(Le. WA 3.6) for the former surfactant. Below this Wvalue, the shapes of the curves are analogous which allows us to conclude that spherical droplets are then expected for A&. On the contrary, the rise in conductivity observed from WM% 11 up to the demixtion, which does not occur for NaA microemulsions, indicates a specific behavior of the A L 4 3 microemulsion. We now face the question as to whether the beginning of a percolation-like process may account for this experimental feature despite the aforementioned low values of both conductivity and volume fraction of the dispersed phase. Complementary experiment^^^ where performed on A& microemulsions formed in cyclohexane which accommodate up to WM% 17-18 water molecules per aluminum cation: surprisingly the conductometric Q-km-l curve displays a larger increase in K from 5 x at WMFZ 13-14 to 5 x Q-l*cm-' at WMx 17-18. The shape of the curve is similar to the typical sigmoid shape observed for the percolation process. This observation supports the hypothesis that the end ofthe conductometric curve obtained with the A& microemulsion in isooctane may be interpreted by the beginning of a percolation-like process induced by the strong attraction between the objects, in spite of the low volume fraction of the dispersed phase. Then aggregation of sticking droplets in elongated objects of increasing lifetimes is expected. Obviously, in such a case, the different parameters and equations introduced with the assumption of spherical micelles become unadapted, and the quantity KW is of course deprived of any physical meaning in the corresponding W range, i.e. from WM 11 to 13.5. Nevertheless, this qualitative interpretation of the conductivity measurements is consistent with the proposal of a change in the shape ofthe colloidal aggregates, from spheres to elongated structures, put forward to account for the SAXS study. The convergence of the conclusions from the two techniques is quite good. It is worth noting that similar shape changes were already observed in the case of microemulsions formed from derivatives ofAOTwith divalent metallic counterions as reported in the Introduction?-6 The presence of a trivalent counterion does not modify this observation. As regards the area per headgroup, it has been measured at room temperature in decane for different sodium salt (54) Bardez, E.; Nguyen Cao, V. To be sumitted for publication.
Langmuir, Vol. 11, No. 9, 1995 3381
Reversed Micellar Aggregates counterion concentrations:14it varies smoothly from u = 85 A2/molecule at 0.2 M monovalent salt to a = 62 A2/ molecule at 1M monovalent salt. Our result with 3 M trivalent counterion concentration is u = 42 f 5 AZI molecule, constant in the whole monophasic reverse micellar domain, that is close to the geometric minimum compatible with double chain structure: the headgroup expansion is totally screened by the trivalent counterion, holding together three headgroups each. Here we notice the main feature ofreverse micelles with trivalent counterions: the low area per molecule is independent of micelle concentration, water content and even shape of the aggregate in the region where micelles exist in a monophasic sample. As can be see on Table 1,the average curvature is not constant for all the samples. Let us turn now to the phase separation observed with A& microemulsions. With NaA samples, two demixtion regimes have been observed:22(i) Excess oil, i.e. Winsor I type demixtions when attractive interactions become important. Liquid-gas demixtion is a peculiar case of Winsor I type of demixtion, since the “oil”may always be considered as an extremely diluted micellar phase. (ii) Excess water which has often been interpreted as associated to a sharp increase of curvature energy, due to a large difference between spontaneous curvature and curvature imposed by compositions. In the case of fluid interfaces, bending energy may always be compensated by flexibility. In the case of rigid interfaces, the three constraints (volume, area and curvature) can only be satisfied together by a continuousvariation of the topology of the interface, from lamellae to cylinders and spheres. We have shown in the first figure that isolated spheres and connected spheres exist in the case of NaA: At low temperature, a Winsor I1 type demixtion defines the limit where the micelle is in equilibrium with excess water. At high temperature, a conducting, connected structure is present until a liquid-gas transition occurs with excess oil. With the trivalent counterion (A& surfactant), the situation at room temperature is the same as that for NaA at high temperature. But the area per molecule is reduced by almost 30% from 0.6 to 0.45 nm2. Therefore, we have to admit an increase of the thickness of the interfacial film, leading to an increase of the stiffness. The consequence of stiffness of the interface is a phase limit insensitive to temperature. By using quaternary ammonium counterions, larger ions than the Na+ cation, Eastoe et al.55have gone the
oppositeway: with larger counterions,curvatures toward oil as well as Winsor I1 equilibria with excess water are favored. For low water content and the largest counterion studied (tetrapropylammonium), the necessity for the counterion to be embedded in the micellar core induced a sphere to cylinder transition associated to excess water. Since we have observed a sphere to cylinder transition with excess oil, the conclusion is that morphology transitions can be induced either via an increase of the counterion volume or a decrease of the interfacial area per headgroup. The results with A& can be compared with another ternary systemwhich has been studied in the dilute regime with excesswater: the DDAEVwatedoil system. A gradual transition from spheres to cylinders for constant curvature has been m e a s ~ r e d . In ~ ~the , ~diluted ~ region, an increase of the water to surfactant ratio produces a rod to sphere transition due to constant curvature. In the case of A& observed here, we have under the same conditionsa sphere to rod transition at constant area per molecule, while the curvature varies.
Conclusion We have shown that trivalent counterions reduce the area per headgroup to the lowest possible value compatible with chain packing. This strong constraint of lowest possibleheadgroup area per chain induces a smooth sphere to cylinder transition in the reverse micelle region: in the whole reverse micellar domain, the area remains constant. The maximum amount of water solubilized is limited and conductivity increases near the phase boundary. However, no electric percolation is observed: the stiff c linders of persistence length of the order of at least 600 i fare not connected. Acknowledgment. Pr Bernard Valeur (CNAM,Paris), Dr. Jacques Lang (Institut Charles Sadron, Strasbourg), R. Strey (Gijttingen), and Ch. Petit (Paris) are thanked for extremely useful discussions. We are grateful to Bernadette Larrey (CNAM) for preparation of the A& surfactant. LA940861J ( 5 5 ) Eastoe, J.; Robinson, B. H.; Heenan, R. K. Langmuir 1993,9, 2820. Eastoe, J.;Chatfield, S.; Heenan, R. K. Langmuir 1994,10,1650. (56)Eastoe, J. Langmuir 1992,8,1503.
