Langmuir 1995,11, 1392-1395
1392
Effect of Shear on Dilute Sponge Phase 0. Diat* and D.Roux Centre de recherche Paul-Pascal, CNRS, Av. Dr Schweitzer 33600 Pessac, France Received July 26, 1994. I n Final Form: October 17, 1994@ Although lyotropic sponge phases are isotropic multiconnected membrane systems, these phases present
a strong flow birefringence upon shaking them. In this brief report we investigate this effect and present data allowing determination of a characteristic frequency which seems to be related to the fusion time of the membranes.
1. Introduction Surfactants in solution lead to a rich variety of selfassembly systems.lg2 In such cases, the surfactant aggregates to form an isotropic structure, where the basic unit is a bilayer (or a membrane) which is randomly connected at large scale. This phase is called the sponge phase (or L3 phase) and is a bicontinuous system where the membrane divides the space into two identical regi~ns.~-ll Several models (microscopic or Landau-Ginzburg model) describe t h e structure and the thermodynamics of this phase and many experiments confirm these theories. On t h e other hand, the dynamical properties have been less studied, especially far from One of the most striking properties of the sponge phase is the flow b i r e f r i n g e n ~ e . ~Indeed, J~ when we gently shake a very dilute sponge phase, a transient flow birefringence occurs which relaxes with a characteristic time of a few seconds u p to a few hours, depending on the system and its dilution. This paper presents a set of results giving some quantitative insight to this phenomena.
2. Experiments 2.1. Couette Cell. To study the effect ofthe flow on a sponge phase, two home-made Couette cells were built: one designed for small angle neutron scattering experiments which were performed at the PAXY beam line of the LBon Brillouin Laboratory (CEA Saclay, France) and the other one was used at
* Present address: ESRF, BP 220, 38043 Grenoble, France. @Abstractpublished in Advance ACS Abstracts, December 1, 1994.
(UEkwall, P. Advances in Liquid Crystals; Brown, G. M., Ed.; Academic Press: New York, 1975. (2)Tanford, C. In TheHydrophibicEffct,2nd ed.; Wiley: New York, 1980. (3)Porte,G.; Appel, J.;Bassereau, P.; Marignan, J.J . Phys.Fr. 1989, 50,1335. (4)Strey,P.; Schomaker,R.; Roux,D.; Nallet, F.; Olsson,U. J. Chem. SOC.Faraday Trans. 86,1990,2253. ( 5 ) Gazeau, D.; Bellocq, A-M.; Roux, D.; Zemb, T. Europhys. Lett. 1989,9,447. (6)Bellocq, A.-M.; R o n , D. In Microemulsions. Structure and Dynamics; Friberg, S . E., Bothorel, P., Eds.; CRC Press: Boca Raton, FL., 1987;p 33. Thanic, (7)Miller, C. A.;Gradzielski,M.; Hoffmann, H.; Kramer, U.; C. Progr. Colloid Polym. Sei. 1991,84,243. (8) Cates, M. E., Roux, D., Andelman, D., Milner, S. T.; Safran, S. A. Europhys. Lett. 1988,5,733;Europhys. Lett. 1988,7,94. (9) Roux, D.; Coulon, C.; Cates, M. E. J . Phys. Chem. 1992,96,4174. (10)Huse, D.; Leibler, S. J . Phys. France 1988,49,605. (11)Roux, D.; Cates,M. E.; Olsson, U.; Ball, R. C.; Nallet,F.;Bellocq, A.-M. Europhys. Lett. 1990,11, 229. (12)Milner, S.T.; Cates, M. E.; Roux, D. J . Phys. Fr. ISSO,51,2629. (13)Pleiner, H.; Brand, H. R. Europhys. Lett. 1991, 15,393. (14)Onuki, A.; Kawasaki, K. Europhys. Lett. 1992,18,729. (15)Snabre, P.; Porte, G. Europhys. Lett. 1990,13,642. (16)Porte, G.; Delsanti, M.; Billard, I.; Skouri, M.; Appell, J.; Marignan, J.; Debauvais, F. J. Phys. Fr. 1991,1, 1101. (17)Waton, G.; Porte, G. J . Phys. I I F r . 1993,3,515. (18)Gazeau, D.ThBse, 1987.
Couette cell
detector
U laser beam
screen
polarizers Figure 1. Schematic setup for light scattering and SANS measurement (on the PAXY line at LLB) with the main axis representation. The beam can be either a laser beam or a neutron beam which goes through the cell along the gradient velocity direction (radial direction). The 2 axis is the vertical and rotation axis for the rotor. We can choose a gap of 0.5,1, or 2 mm between the rotor and the stator and this allows achievement of shear rates between 0 and lo5 s-l. the Centre de Recherche Paul Pascal for either light diffraction or birefringence measurements. Both cells consist of two concentric cylinders (a fixed inner one, the stator, and a rotating one, the rotor), leaving an annular gap of 0.5-1 or 2 mm, depending of the stator diameter, this gap being filled by the liquid sample. The two cylinders are enclosed in a transparent and temperature-controlled sealed oven. The details ofthe design are given in a previous paper.19 Figure 1 shows the geometry of the experimental setup: the neutron beam goes through the cylinders in the radial direction (TV axis) and allows collection of information on the membrane distribution in the reciprocal plane space which is thus restricted to the neutralhelocity (see Figure 1). We have chosen the neutron wavelength and the position of the detector to cover a scattering vector q range between 5*10-3and 6 ~ 1 0 A-1 - ~ (q = 2 ~ d Lsin(N2) where 19is the scattering angle). In the case of the “light” experiments the intensity of the linearly polarized transmitted beam was measured using a photodiode in the beam axis, and a vertical screen placed after the cell allows observationofthe light scattering from the sheared sample. 2.2. Studied Sample. The studied sample is a quaternary system consisting of a mixture of surfactant (sodium dodecyl sulfate or SDS),pentanol, dodecane, and pure water. The phase diagram is given in Figure 2.’ We investigated several samples obtained by a dilution process which consists of adding some solvent (94.5%dodecane and 5.5% pentanol in weight) to an initial concentrated sponge phase (14.43% SDS, 10.38% pentanol, 57.88% dodecane, 17.31% water in weight). The dilution process permits a variation of the volume fraction of membrane (4) from
(m
(19)Diat, 0.; R o w , D.; Nallet, F. J . Phys. I1 Fr. 1993,3,1427;J . Phys W ,1993,coll.C8,3,193.Diat, O., thesis no. 833 from University Bordeaux I, France, 1992.
0743-746319512411-1392$09.00/00 1995 American Chemical Society
Effect of Shear on Dilute Sponge Phase
Langmuir, Vol. 11,No. 4,1995 1393
PENT AN 0L
10'
A
e o
A
\
WATERISDS = 1.2
slope =3
t
10' lof
DODECANE
Figure 2. Phase diagram of the quaternary mixture of dodecane, water, SDS, and pentanol drawn in the restricted plane water/SDS = 1.2. L1 is a micellar phase, Lais the lamellar phase, H is the hexagonal phase, and S is the sponge phase.
Iflo
0.06
-
8 0 0
97.48***
.
r6-1) Figure 3. Variation ofthe transmitted polarized beam through three sponge phases versus the shear rate; y* corresponds to the critical shear rate. 30% to 1.6%,which corresponds to a variation of the correlation distance (5) between the membrane from 100 to 1900 A. For neutron experiments, water has been replaced by heavy water in order to increase the scattering contrast between membrane and solvent. This substitution changes only very slightly the limits of the phase diagram. 2.3. Birefringence Measurements. A linearly polarized laser beam goes through the Couette cell filled with the sample and the transmitted intensityis detected via a photodiode. This measurement is carried out between crossed polarizers. The signal ( I )is normalized, dividingz by the sum of the transmitted intensities between crossed and parallel polarizers ( l o ) which is constant whatever the shear rates. The ratios IN0 are plotted in Figure 3, versus the shear rate for three different volume fractions of membrane. We observe two distinct regimes around a shear rate value (p*) which depends on the membrane volume fraction. At rest, for y = 0, the intensity between crossed polarizers is zero because the system is isotropic (we measured actually a residual intensity due to the weak birefringence of the glass cylinder ofthe cell, but this can be easily compensated for). When we increase the shear rates up to the threshold y*, the intensity remains constant and equal to zero. Above the value p*, the transmitted intensity starts to increase. The transition is continuous within the accuracy of the measurements (A(Z/Zo) about In the plane, the shear rate p* corresponds to a threshold frequency between an isotropic structure at low shear rates and a birefringent structure at higher shear rates. This birefringence is due to an orientation of the membrane under shear which is at rest randomly distributed in space.8 We also noticed that the threshold p* varies with respect to the amount of dilution. Indeed, the more diluted the sponge phase, the lower the threshold occurs. In Figure 4 the lower curve corresponds to the variation in p* versus the membrane volume fraction (9) in a In-ln plot. The straight line is only an indication of a 43 scale law for this y* variation. It is important to note that the observed and measured birefringence (by means of the transmitted intensity20) do not correspond to what we usually call the linear flow birefringence.
(z@
1
/
cridcal shear rate diffusion frequency
I
10'
9
1 oo
Figure 4. (lower curve) +-Dependence of the critical shear rate y*, (upper curve) @-dependenceof the diffusion frequency OD at qo = 2x4. The straight lines with the slope 3 is just a guide for the eyes. Indeed the flow birefringence is a linear effect which (i) is plane and (ii) corresponds to currently measured in the (fi? a second-order effect in the plane too low to be detected within the accuracy of our detection instruments. Consequently, the observed effect above the critical shear rate is a nonlinear effectthat we can correlate with neutron scattering experiments. 2.4. Neutron Scattering. The same system has been investigated by neutron scattering, replacing water with deuterated water. Figure 5 shows the evolution of the coherent scattering in the plane from a dilute sponge phase (@= 2.9%),for four shear rates. It should be noted that for dilute sponge phases at rest only the intensity profile decreasing as 1/q2can be observed (where ?jis the scattering vector in the reciprocal space), without the correlation bump, characteristic of the organization of the membra ne^.^.^ Below p* (see Figure 5a,b),we observe anisotropic scattering (like at rest) related to an isotropic distribution of the membranes in the real space. When the shear rate is further increased ( y > y* see Figure 5c,d),the scattering profile becomes anisotropic while the total scattered intensity decreases (without any change on the shape of the intensity profile). The anisotropy can be characterized by a contrast coefficient (C) which is defined as follows:
(m
(z@
where I, and I , are the maximum intensities in the 2 and p directions, respective; C = 0 means that the system is isotropic (or that all the membranes are oriented parallel to the surfaces of the cylinders) and C = 1 means that there are no bilayers oriented with their normal parallel to the velocity direction. The contrast curves for three dilute sponge phases (@ = 2.1%, = 2.9%, @ = 3.5%) are plotted in Figure 6. The curves behavior is quite similar to that ofthe transmitted intensity versus the shear rate. Although there is a lack of experimental points around the threshold shear rate, we can easily verify that the corresponding y* values which can be estimated from the last curves are of the same order of magnitude of whose determined by light measurements. Thus, we can relate the occurrence of this anisotropy t o the occurrence of the birefringence which comes from an alignment of the membranes along the flow direction above p*. Moreover, above y*, we measured a continuous decreasing of the total scattered intensity in the 2 and pdirections (as similar with what we observe for the orientation state 3 for lamellar phases under shear, in the same plane'g). Considering that for the sponge phase the scattered intensity is isotropic in the 4n angular range (due to an isotropic distribution ofthe membranes) this decreasing might indicate a progressive orientation of the membrane parallel to the surface of the cylinders.
+
(20) The transmitted intensity between crossed poladzers is simply a sinusoidal function of the birefringence (AnJ in the (ZVI plane: Ill0 = sin2(2d;.AneJ where e is the sample thickness and i. the wavelength.
Diat and Roux
1394 Langmuir, Vol. 11, No. 4, 1995
1
1 $ t
t
E (m
Figure 5. Evolution of the neutron diffraction plane from the sponge phase &,9 for different shear rates [the first two patterns below y* and the other two above y*: (a) 3 = 0 s-l, (b) p = 18 s-l, (c) y = 720 s-l, and (d) y = 2880 s-ll.
4000
i
0
0.41
-
/
Qe+O
2e-6
4e-6
* 2 qO n 0
6e-6
8e-6
q 2 ('4-2)
1000
3000
2000
'y
6-9
Figure 6. Variation of the contrast with the shear rate for three different sponge phases: (0)&.I, (0)A.9,and (*I h.5.The inset represents the contrast variation at low shear rates and allows observation of a first regime where the contrast is zero and then, at higher shear rates, becomes nonzero. 3. Analysis We noted in the previous paragraph that the shear rate (p*) which can be assimilated to a characteristic frequency follows a cubic power law in 4. As the free energy of a dilute sponge phase is only a function of the topology (characterized by the handles density), it has been demonstrated that the variation of the free energy density follows a scaling law with regard to the membrane volume f r a ~ t i o nthus, : ~ all the thermodynamical quantities which ensue from it also follow a #-scaling law. In particular the hydrodynamic relaxation frequencies decrease with #3.12,16
In order to relate the frequencies to thsdynamics of the sponge phase, we have measured the diffusion frequency of the membrane in its solvent using the dynamic light scattering method. In Figure 7 we plot WD versus the square of the scatteringvector q for several sponge phases
Figure7. q-Dependence of the diffision frequency for different sponge phases along a dilution line. along the dilution line mentioned previously. From the slopes of these curves, we deduced the hydrodynamic diffision coefficient, D:
wD = Dq 2
(2)
with
(3) where ?I is the viscosity of the solvent and E;H the hydrodynamic length, which is twice the correlation length ( 5 ) of the sponge phase.21 In order to compare the diffision frequency with y*, we plotted the characteristic frequency W D (at qo= 2n4)versus # (upper curve) on the same graph as for p* versus # (lower curve, see Figure 4). There is evidence of two different frequencies separated by a factor of order 100. (21)The correlationlength is calculated from the static law 4 = 1.56/
5, where 6 is the thickness of the membrane.
Effect of Shear on Dilute Sponge Phase STRANGLING
Langmuir, Vol. 11, No. 4, 1995 1395
FUSION
Figure 8. Schematic representation of strangling and fusion of the membrane.I6
Bearing in mind the theoretical work of Milner et a1.,12 one would expect to have two regimes for the dynamics of a sponge phase. Because of the thermal fluctuations the flexible membrane undulates, some connections break and disappear and some other handles are created by the proximity and even fusion of two parts of the membrane. In other words, the density of handles fluctuates over a long time, which corresponds to a topology relaxation time of l / o F , which is much longer than the diffusion time, l/wD. This process can be deemed as a two-step process (see Figure 8):12J6 The first step corresponds to the strangling of a passage via the diffusion of the membrane over a distance ( with a characteristic frequency, OD. The second step corresponds to the fusion of the membrane through a n activation barrier, E,, of a few kBT. The associated frequency, OF, reads
(4) For the sponge phase under shear flow, when the shear rate is above y * , the deformation rate is too high to permit a relaxation of the structure with the consequent fusion of the membrane, along the flow direction; thus, the structure becomes anisotropic above y * . Taking into account a n activation barrier (E,) of about 3-4 kBT, then OF and y* occur to be comparable. This energy is lower than that estimated by Milner or Porte, but it strongly depends on the system and especially on the surfactant-over-cosurfactant ratio.
The question about the transition of the sponge phase under shear toward a lamellar phase22still remains a n open issue. Although it might seem that the orientation of the membrane changes continuously toward a configuration where the normal to the layers is mainly parallel to the velocity gradient (which corresponds to the orientation of a dilute lamellar phase under shearlg),there is no real evidence for the transition. One of the drawbacks comes from the fact that no correlation or Bragg peaks for the dilute sponge and lamellar phases, respectively, are visible on the scattering spectra. 4. Conclusion
The series of experiments performed show that the sponge phase -an isotropic phase of membrane-becomes birefringent above a certain shear rate (?*) which seems to be directly related to the fusion frequency of the membrane. Practically, for a very dilute system, the birefringence measured in Couette cell above a welldetermined shear rate (?*) corresponds to the birefringence observed between crossed polarizers when one gently shakes a transparent cell filled with the same sponge phase. Also, for the concentrated sponge phase, y* is too high to observe the transient birefringence just by shaking. These first experiments can be deemed as a n encouraging starting point for future investigation aiming to get a deeper insight into different systems. By studying the behavior of the sponge phases above y* and a t higher shear rate, one should be able to observe a dynamic transition toward a lamellar phase.
Acknowledgment. The authors would like to thank M. E. Cates, F. Nallet, and G. Porte for very useful discussions. LA9405962 (22) Cates, M.
E.;Milner, S.T.Phys. Rev. Lett. 1989,62, 16,1856.
