16982
J. Phys. Chem. 1995,99, 16982-16990
Dynamical Behavior and Structure of Concentrated Water-in-Oil Microemulsions in the Sodium Bis(2-ethylhexy1)phosphate Systems Ken-ichi Kurumada,*?+Akihisa Shioi, and Makoto Harada Research Section of Nuclear Chemical Engineering, Institute of Atomic Energy, Kyoto University, Gokasho, Uji, Kyoto 611, Japan Received: April 25, 1995; In Final Form: September 5, I995@
Dynamical structures are elucidated by the dynamic light scattering (DLS) technique and rheological measurements for sodium bis(2-ethylhexy1)phosphate (SDEHP)/n-hexanelwaterlsodiumchloride systems in the concentrated region of the surfactant. For DLS measurements, the microstructure is deduced from the behavior of the initial relaxation and the long-time relaxation which appears when the volume fraction @.SS of the molecular aggregates exceeds 15%-20%. Both of them indicate that the network structure formed in the region @BS 2 0.15-0.20 becomes confined into a smaller size scale as @BS goes up. The long-time relaxation may reflect the spontaneous structural relaxation of the transient network like a first-order reaction independent of scattered wave number and the overall diffusive relaxation, each rate of which also shows a steep reduction in the range 0.2 I@BS I0.4with increasing @BS. Rheological measurements indicate that the relaxation time of elastic stress is shorter for more concentrated SDEHP-microemulsions. This is interpreted in terms of the formation of a more dense network structure for more concentrated systems. On the other hand, the characteristic time for recovery of the network structure from a broken state by a steady shear flow lengthens as @BS increases. The geometrical shape of the individual aggregates in the dilute region strongly influences the dynamical behavior of the microemulsion in the concentrated region.
Introduction Microemulsions1-I2have recently attracted a great deal of attention of researchers from scientific and applicative viewpoints. One of the most salient features of the system is the formation of distinctive ordered microstructures. Therefore, it is of great interest to investigate them from various viewpoints. In a surfactant dilute region, much useful information on the geometrical shape of the molecular aggregates dispersed in the solvent has been obtained mainly by means of scattering methods using light, X-rays, and neutrons, and it has been shown that the chemical species of the surfactant is one of the most crucial factors in determining the geometrical shape of molecular aggregates. For example, a microemulsion composed of sodium bis(2-ethylhexy1)sulfosuccinate (AOT), which has been examined most extensively so far, forms spherical aggregates and they behave as individual colloidal particle^.^^-'^ In the case of the microemulsion containing sodium bis(2-ethylhexy1)phosphate (SDEHP) when the volume fraction of molecular aggregates is less than 5%, rodlike aggregates are formed from the X-ray scattering pattem.18vi9 On the other hand, microstructures of the microemulsion in the concentrated region have not been understood as much as those in the dilute region due to various difficulties in direct observation represented by static scattering. In particular, since not only the form factor but also the structure factor play a dominant role in the scattering pattem in an unseparated fashion, one has to separate the pattem on the basis of proper assumptions to interpret them. The interpretation is relatively easy when the spherical shape of aggregates is kept unchanged even at a high volume fraction, as deduced for AOT-mocroemulsions.20-22Nevertheless, it is almost impossible to separate the pattem into the two types of contributions to the scattering + Present address: Department of Chemical Engineering, Faculty of Engineering, Kyoto University, Sakyo-Ku, Kyoto 606, Japan. Abstract published in Advance ACS Abstracts, November 1, 1995. @
intensity distribution when the shape or size of individual aggregates may vary with the volume fraction of surfactants as in SDEHP-microemulsions. Thus, it is quite difficult to investigate directly microstructures in a concentrated microemulsion. Therefore, we have to elucidate the microstructures through distinctive properties which the dense microemulsion exhibits in a measurable fashion. Recently, we have qualitatively deduced the static microstructures in the SDEHP-microemulsions from osmotic compressibility, viscosity, and electrical conductivity measurem e n t ~ .It~ has ~ been shown that an interconnected transient network structure is formed in the microemulsion when the volume fraction of molecular aggregates exceeds 15%-20%. As the next step of our investigation, it is interesting to examine how the microstructure behaves dynamically. Significant experimental results and microscopic models are available on flexible polymers or gigantically elongated micelle^.^^-^* For the solutions of flexible polymer, the reptation based on the ‘tube m ~ d e l ’successfully ~~,~ describes the dynamic process in a semidilute or concentrated regime, and experimental results support the model from various viewpoint^.^^-^^ Furthermore, the properties of the transient network structure composed of elongated micelles are analogous to those of polymers. For example, Candau and co-workers carried out rheological measurements on semidilute and concentrated micellar solutions containing cetyltrimethylammonium bromide (CTA13)58-60 or cetyltrimethylammonium chloride (CTAC)6i and explained the dependence of viscosity on concentration on the basis of the theory of ‘living polymers’ proposed by Cates and C a n d a ~ , ~ ~which - ~ ’ takes into account the dynamic effect of chain-breakage and chain-recombination on the reptation. For water-in-oil microemulsion systems, however, there is not as much information obtained so far on the transient network structure as that on the structure in micellar solutions, although an interconnected network structure has been deduced from
0022-3654/95/2099-16982$09.Oo/O 0 1995 American Chemical Society
Water-in-Oil Microemulsions experimental and theoretical r e s ~ l t s . ~Luisi ~ - ~and ~ co-workers pointed out that microemulsions containing soybean lecithin are quite similar to semidilute polymer solutions in the dependence of their rheological properties on the volume fraction, and they have indicated that a transient network structure is formed because soybean lecithin assembles into rodlike or wormlike molecular aggregates when the concentration is not so high.68-70 In addition, they found that a gelation phenomenon is brought about within a certain range of the mole ratio of water to lecithin, which is also related to the elongated form of molecular aggregates. Schurtenberger and Cavaco' have shown that the dynamic structure factor investigated by the dynamic light scattering (DLS) technique is quite analogous to that in the semidilute polymer solution, and they have indicated that the behavior of elongated molecular aggregates resembles that of a flexible polymer to a great extent. In the present work, we investigate SDEHP-microemulsions by DLS and rheological measurements mainly in the concentrated region wherein a transient network structure is formed. It should be noted that, in the present systems, the viscosity is much lower and the dependence of the viscosity on the concentration is weaker than that for the polymer or micellar solutions and even than that for the soybean lecithin-microemulsions. As discussed in the previous these characteristics should be ascribed to the higher rupture rates of the structures coated by SDEHP, and as a reflection of that, we should observe distinctive dynamical behavior in the system. Here, we report our experimental results and consider how such a 'fragile' system behaves dynamically when the transient network structure is extended all over the system.
Experimental Section Materials. Bis(2-ethylhexy1)phosphoric acid (DEHPA) was provided from Tokyo Kasei Co. Ltd. DEHPA was purified by the method reported previously.'8 Sodium chloride (NaCl) and n-hexane were used as supplied from Nacalai Tesque Co. Ltd. The water was purified by ion-exchange and distillation. Preparation and Analysis of Samples. The microemulsions of sodium bis(2-ethylhexy1)phosphate (SDEHP) were equilibrated in contact with an aqueous phase with a fixed concentration of sodium chloride (CN~). The method of sample preparation for the SDEHP-microemulsion was the same as that reported p r e v i o ~ s l y , ' ~where . ' ~ ~ ~the ~ solution of DEHPA in n-hexane was mixed with an aqueous solution of sodium chloride. The SDEHP-microemulsion was obtained by neutralizing the mixed solution with sodium hydroxide. To keep the salinity condition fixed at C N= ~ 4.5 and 5.0 M, the brine was exchanged two times for each sample during the preparation. The analysis of the components was carried out as previously reported.I8 To estimate the volume fraction of the i-species, denoted by ai,the following relation was used:
Here, ci and vi denote the molar concentration and the molar volume of the i-species, respectively. The value of vi used was 3.10 x m3 mol-' for SDEHP. The volume fraction Qpss of the brine taken up to the microemulsion can be set equal to that of water, because the influence of sodium chloride on the volume fraction is small enough to be neglected. The volume fraction of the molecular aggregates in the SDEHP-microemulsion phase, denoted by @BS, was obtained as @BS = @B f 0 s . Measurements. Photon correlation functions,75denoted by gl(t), were measured by dynamic light scattering (DLS) (Otsuka Denshi Co. Ltd.; DLS-700; wavelength, 1 = 632.8 nm (He-
J. Phys. Chem., Vol. 99, No. 46, 1995 16983 Ne laser beam)). The interval and the number of measuring channels were determined such that the relevant relaxation mode could be profiled. The rheological properties under both oscillatory shear flow and steady shear flow were measured using the rheological apparatus MR-300 with a Couette-typ cell (Rheology Engineering Co. Ltd.) within the range 6 = 4.04 x lo-' to 4.04 x s-' and w = 6.28 x lo-' to 6.28 x lo+' rad s-I, respectively. Here, 6 and w denote the steady shear rate and oscillatory angular velocity imposed on the samples. The sample cell was specially made in order to hinder solvent evaporation. Experiments were carried out at 298.2 K. Phase Behaviors. The phase behavior is the same as those reported in our previous article23for both salinity conditions, C N= ~ 4.5 and 5.0 M. All the samples examined in this work belong to the Winsor II state.I9 The mole ratio W Oof water to surfactant over the present experimental range for @BS is about 7 under both salinity conditions. The diameter of the cross section of rodlike aggregates is about 2.2 nm irrespective of the salinity conditions within the Winsor 11 r e g i ~ n . ' ~ , ' ~
Results and Discussion
I. Dynamic Light Scattering Measurements. General Features of the Photon Correlation Functions. The relaxation behavior of concentration fluctuations represented by a photon correlation fun~tion,'~ denoted by gl(t), is strongly influenced by the volume fraction @BS of molecular aggregates. Figure 1 shows typical photon correlation functions of SDEHP/n-hexanel brine ( C N= ~ 4.5 and 5.0 M) systems for three regions of volume fraction @BS. When @BS is small (@BS 5 0.06; Figure l a and d), a percolated structure is still not formed,23and only a relatively fast relaxation is observed. The rate ri,(lkl) of the initial relaxation is proportional to the square of the scattered wavenumber Ikl. This means that, in such a dilute region, each rodlike aggregate or assembly of them'83'9323behaves as a Brownian particle with diffusion constant rIn( (kl)/lkI2. In the middle range of @BS (0.06 5 @BS 5 0.15), the relaxation rate, which stays proportional to lkI2, shows the critical slowdown. The critical volume fraction of aggregates and the salinity condition are @BS = 0.09 and = 4.25 M, respectivelytg (Figure l b and e). Since the salinity condition C N= ~ 4.5 M is closer to this than C N = ~ 5.0 M, the more outstanding slowdown is observed in the former case. In this region, the relaxation of the concentration fluctuation is induced by the cooperative diffusion rather than by the self-diffusion. When the value of @BS exceeds the above-mentioned two regions, a distinctive long-time relaxation is observed following a much faster initial relaxation (Figure IC and f). The rate of the long-time relaxation is much slower than that of the initial relaxation, as shown in Figure lg. Each relaxation can be regarded as an exponential mode. It should be noted that a transient network structure composed of interconnected rodlike molecular aggregates is formed all over the SDEHP-microemulsion in this region (@BS 2 0.15-0.2).23 Thus, the longtime relaxation is related to the network structure which would hinder free diffusive motions, as discussed later. Another noteworthy experimental fact is that the rate of the fast initial relaxation increases, remaining proportional to lkI2 as @Bs goes up, which indicates that the cooperative diffusion becomes more rapid with the increase in @BS. Initial Relaxation. The initial relaxation rate ri,(lkl) of a photon correlation function is related to the diffusion constant Dc, which leads to the correlation length 6 of concentration fluctuations by the Stokes-Einstein formula as follows:
Kurumada et al.
16984 J. Phys. Chem., Vol. 99, No. 46, I995
-
N 3
1.1-
m
-
c
1-
I . . . . . . . i. . . ......, . i ......, . . . . . . .
102
io9
io4
105
io6
tIu =I Figure 1. Typical photon correlation functions gl(t) of the SDEHPln-hexanelbrine( C N ~= 4.5 and 5.0 M) systems for the three characteristic @BS indicated in the figures (scattering angle, 20 = 30"): (a-c) at the'salinity condition C N = ~ 4.5 M; (d-f) at the salinity condition C N= ~ 5.0 M; (g) 1 -t gl(r)*in the full range of time for an SDEHP-microemulsion in the concentrated region (Opss = 0.28, C N = ~ 4.5 M). A function g 1( t ) vanishes accompanying its complete relaxation after a sufficiently long time.
regions of
Here, k ~ T, , and rsdenote the Boltzmann constant, the absolute temperature, and the viscosity of the solvent, respectively. The dependencies of 6 and diffusion constant D, on the volume fraction @BS for the two salinity conditions CNa = 4.5 and 5.0 M are shown in Figure 2. In the dilute region (@BS I0.061, the value of 6 increases as @BS goes up, indicating the enlargement of aggregates or assemblies of them immersed in the solvent. In this region, E is a measure of the size of the aggregates which move as independent Brownian particles mutually. However, when the value of @BS is within the middle region (0.06 5 @.SS 5 0.15), E does not mean the size of independent free Brownian particles, because a percolated structure is formed in the SDEHP-microemulsion and the free Brownian motion should be hindered. In this case, 6 should be regarded as a measure of the size of concentration fluctuations. In this region, the photon correlation function gl(t) can be regarded as a single exponential, the rate of the relaxation being remarkably slow compared with that in the dilute region (@BS 5 0.06). This slowdown is due to approach to the critical point (@BS = 0.09, C N= ~ 4.25 M). Therefore, the values of 6 in this region are much larger for the salinity condition C N= ~ 4.5 M than for C N = ~ 5.0 M, as shown in Figure 2. This is visualized in terms of the size of the assembly of rodlike aggregates determined by the strength of attractive interaction between rodlike aggregates, whose effect is stronger for a
10-1 1-
"E
I
0" ~
100 10-10 "
%E.I-l Figure 2. Dependencies on
@BS of the correlation length ( of concentration fluctuations and cooperative diffusion constants D, in the SDEHPln-hexanelbrine systems obtained from the rate of the initial relaxation in the photon correlation function gl(r): ( 0 )at the salinity ~ 5.0 M. condition C N =~ 4.5 M; (0)at the salinity condition C N =
salinity condition closer to C N =~ 4.25 M. That is, when the assemblies are just stuffed up to the number density at which they are forced to be in contact with each other, the size of concentration fluctuations should be larger for larger assemblies = 4.25 M. yielded at a salinity condition closer to When our systems reach the region of @BS where the network structure is extended all over the microemulsion (@BS 2 0.150.20), 6 reduces steeply as @BS increases. This reduction of 6 is explained by the reduction of the characteristic length of the network structure with increase in @BS, as indicated by the theory of the polymer solution^.^^ A rapid relaxation of concentration fluctuations by cooperative diffusion is allowed
Water-in-Oil Microemulsions
J. Phys. Chem., Vol. 99, No. 46, 1995 16985
‘1 t
0
0.01 0.02 ! k I [nm-’1
0.03
Figure 4. Dependence of the rate rl,(lkl)of the long-time relaxation ~ 5.0 M and on lkl for the SDEHPln-hexanehrine systems for C N= @RS = 0.67: (0)experimental values; (solid curve) fitted curve for the expression Tl,(lkl) = rsp+ D,,vem~l~k~2 yielding rsp= 3.9 x IO-’ s-I and DOverall = 6.0 x lo-” m2 s-l.
lo2’ 0:1
.
0.’ 2
.
0. ’3
’
0.4 ’
’
Q, B S H
+
Figure 3. (a) Relative amplitude A,(A, A&l of the long-time relaxation versus the scattered wavenumber lkl at CNa = 4.5 M: (0)at @RS = 0.21; (0) at @BS = 0.27; (A) at @BS = 0.40; (shaded area) the region of lkl covered by the DLS-measurements. (b) Lower limit of a spatial extent b/(kho~ndarylfor which the long-time relaxation is observed against @BS at CNa = 4.5 M: (shaded area) the same as that in part a.
to occur inside a ‘mesh’ formed by molecular aggregates, and the ‘mesh’ size becomes smaller as the rodlike aggregates are stuffed more densely in the SDEHP-microemulsion. The dependency of the ‘mesh’ size on @BS is the central issue in this article and is considered in light of other experimental results in the following sections. Long-Time Relaxation. As stated above, a long-time relaxation observed in @BS 2 0.15-0.20 reflects a dynamical process retarded strongly by the existence of the network structure. The long-time relaxation which endures for 105- lo6 ,us in order of magnitude is caused by the long-lived network structure, which requires such a time scale to be renewed entirely. We qualitatively elucidate the dynamic behavior of the network structure by investigating how the long-time relaxation is influenced by the volume fraction @BS of the aggregates and the spatial extent 2n/)kl. We interpret the long-time relaxation in terms of the size over which the retardation effect becomes outstanding. Figure 3a shows the dependency of the ratios AJ(A, Af) on the scattered wavenumber lkl for three volume fractions of aggregates at C N a = 4.5 M, Af and A, being the amplitude of the faster initial relaxation mode and the slower long-time relaxation mode, respectively. The scattered wavenumber lkl is related to the scattering angle 28 as follows:
+
lkl =
4nn, sin 9
the long-time network structure is formed, because the retardation effect including the long-time relaxation should be governed by the network structure. These minimum sizes ’2dIkhundaryI may be intuitively regarded as the ‘mesh’ size of the long-lived network, too. Figure 3b shows the value of 2 d l k b u n d a r y I versus @BS for the salinity condition C N= ~ 4.5 M, which shows that the scale of the long-lived network structure reduces drastically as @BS goes up. This tendency is consistent with the dependency of l j on @BS. It should be noted that the ‘mesh’ size is larger when estimated from &/lkbundaryI than from 6 at the same @BS. This result can be understood by considering that the cooperative diffusion is considered to take place inside the longlived ‘mesh’. Therefore, we consider that the genuine ‘mesh’ size is described rather by 2 d l k b u n d a r y l than by 5‘. Further Discussion on Long-Time Relaxation. Another noteworthy feature of the long-time relaxation is pointed out in its dependence on lkl at a fixed volume fraction @RS. The longtime relaxation nearly consists of one relaxation mode with the decay rate rlf(lkl).However, the value of rI,(lkl)is not proportional to the second power of lkl, as shown in Figure 4. Therefore, the long-time relaxation cannot be ascribed to a diffusive mechanism alone. Here, we postulate that the value of rl,(lkl)depends on lkl as follows: (4) where rsp and Doverallare constants depending on CNa and a s s . As shown in Figure 4, the experimental results fit well with the curves given by eq 4. In this case, the photon correlation function gl(t) is given by
and the partial differential equation with respect to t giving eq 5 as its solution is
Thus, the inverse Fourier transformation with respect to k is given by
(3)
Here, rq)and 1 denote the refractive index of the organic solvent and the wavelength of the incident laser beam, 632.8 nm. The ratio decreases steeply as lkl increases, and A, is more dominant for higher values of @BS at the same lkl. IkboundaryI is defined as the wavenumber at which A, vanishes within the experimental range of lkl indicated by the shaded area in Figure 3. The spatial extent 2 d l k h u n d a r y I is a measure of the minimum size in which
where A(r,t) denotes the inverse Fourier transform of gl (t) with respect to k. Equation 7 means that the correlation corresponding to the long-time relaxation decays by two mechanisms. One of them is the spontaneous relaxation like a first-order reaction with rate rsp; the other should be regarded as a diffusive process characterized by the overall diffusion constant Dover;,ll.
16986 J. Phys. Chem., Vol. 99, No. 46, 1995
Kurumada et al.
' O
0
I
!
O
@,=0.40 I
0
"
'
'
'
0.5 QeSH
'
'
'
1
o [rad s-']
1
0.5 @as[-]
I nccparhbl
10'
100
o [rad s-'1
Figure 5. Dependences of (a) the rate rspof the spontaneous relaxation and (b) the overall diffusion constant Doverall on @ ~ s in the SDEHPIn~ 4.5 M; (0) hexanebrine systems: (0)at the salinity condition C N = at the salinity condition C N=~ 5.0 M.
riptrrbi I
10'
8
Figure 6. Schematic representations of the network structure in the
SDEHP-microemulsionsin the concentrated region: (solid lines) rodlike constituent parts of the network; (0)connecting structure of the rodlike constituent parts; ( x ) positions at which the constituent parts are severed. When two ruptures of aggregates take place coincidentally, the state where a part interconnected with the whole network structure becomes separable should be brought about at higher probability (a) in the more dilute system than (b) in the other. The estimated values of rsp and Doverdl are shown versus @BS in Figure 5 . A steep fall is seen, except for rspat the salinity condition C N ~= 5.0 M, as @BS increases. An intuitive interpretation is given to the decrease in rsp in light of the steep reduction of the 'mesh' size in the region. It is presumed that a connecting structure of rodlike aggregates should play an important role in the spontaneous relaxation with rsp.Figure 6 shows schematically the network structure in the concentrated SDEHP-microemulsion; when breaks of the constituent part of the network structure take place simultaneously at two points (indicated by x in the figures), the probability that the part between the two points can be removed from the whole network structure must be higher in Figure 6a (a more dilute network structure) than in Figure 6b (a denser network structure). Therefore, the elementary process of the spontaneous decay of the transient network structure should be slower for the more
Figure 7. Example of (a) the storage modulus G'(w) and (b) the loss ~ 5.0 modulus G"(o) in the SDEHPIn-hexanelbrine system for C N = M and @.SS = 0.40. For all the samples examined, the relations G'(u)
-
w2 and G"(w)
-
w
are pointed out.
concentrated microemulsion. On the basis of this idea, the dependency of rspon @BS seems to be reasonable, indicating the spontaneous decay of the network becomes slower as the system is more densely packed. The steep reduction in Doverall,which appears still more drastically than in rsp, implies that the finer 'mesh' at a higher @BS restricts more strongly translational motions of aggregates or their assemblies through it. In summary, the relaxation in photon correlation functions suggests that the network structures in the SDEHP-microemulsions become finer as @BS goes up. The stye of the concentration fluctuation is reduced as the long-lived network structure is formed into a smaller size. Such a network structure appears when Qpss 2 0.15-0.2. 11. Rheological Measurements. Viscoelastic Measurement by Oscillatory Shear Flow. Linear viscoelastic behavior under oscillatory shear flow reflects the dynamical microstructure which is responsible for the relaxation of stress. In this work, we selected sufficiently dense systems in which the network structure is entirely formed, i.e. in the region 0.37 I@BS I 0.55, and we interpret the results in terms of the relation between the characteristic time z of stress-relaxation and the 'mesh' size of the network structure. An example of the storage modulus G'(w) and of the loss modulus G"(w) is shown in Figure 7 for @BS = 0.40 and C N ~ = 5.0 M. For samples examined the following relations explain well the observed moduli: G'(o)
-
w2
-
G"(o) w
(8)
(9)
Here, the symbol ''-" signifies 'proportional to', We presume a relaxation modulus is a linear combination of exponential functions as follows:
J. Phys. Chem., Vol. 99, No. 46, 1995 16987
Water-in-Oil Microemulsions G(t) = ~ r “ ’ ” G o (exp t) TIco
10-21
1
i
i
where Go(z) is the distribution function for t dependent on @BS and CNa. Zlc0 and zuc0denote the lower cutoff and the upper cutoff o f t , respectively. Thus, the complex modulus G*(w) is given by
+ 022dz 1 + 022 (11)
iwz
G*(o) = i w L e-’”‘G(t) dt = P G o ( r ) rrc0
When otlcoI wz Iozuco
