Langmuir 1994,10, 955-961
955
Flow Behavior and Shear Induced Transition near an Isotropic/Nematic Transition in Equilibrium Polymers V. Schmitt,**+ F. Lequeux,+A. Pousse,s and D. Rouxl Laboratoire d'Ultrasons et de Dynamique des Fluides Complexes, U.R.A. 851 CNRS, Institut Le Bel, 4, rue Blaise Pascal, 67070 Strasbourg Cedex, France, Facult4 de Chimie, 1, rue Blaise Pascal 67000 Strasbourg, France, and Centre de Recherches Paul Pascal, CNRS, Avenue du Docteur Schweitzer, 33600 Pesaac, France Received September 27,1993. In Final Form: November 2 9 , 1 9 9 9 We present rheologicaland smallangle neutron scattering(SANS)measurementsunder flow of wormlike micelles solutions (CPC108 in 0.05 M NaC103) near an isotropic-nematic phase transition. Near the nematic transition, orientational correlations are put into evidence at equilibrium. The analysis of both nonlinear rheological and SANS behaviors under flow, of samples approaching the nematic phase at rest, reveals that there is an isotropic-nematic shear induced phase transition,-which differs from the shear induced alignment observed far from the isotropic-nematic transition in other similar systems.
Introduction Aqueoussolutionsof cetylpyridiniumchlorate (CPC103) in the presence of sodium chlorate (NaClOs) are known to form long cylindrical and flexible aggregates called wormlike micelles.lV2 The are characterized by their persistence length I , = 150 and their diameter d = 40-50 These labile aggregates can break and recombine continuously as a function of time; they are examples of "living polymers". We investigate the behavior of these wormlike micelles under shear using rheology and neutron scattering. Both the rheologicaland the scattering measurements are made with a Couette geometry. For the neutron scattering, the cell used is the one built by Diat and Roux314for the Laboratoire LBon Brillouin in Saclay, where the experiments have been performed. The cetylpyridinium chlorate was prepared by precipitation from an aqueous solution of cetylpyridinium chloridein a sodium chlorate brine in excess. Then it was purified by recrystallization in acetone. The effect of salt concentration has already been s t ~ d i e d The . ~ experimental results have been interpreted by a description based on a structural evolution upon increasing salt concentration from a system of entangled linear micelles to a multiconnected network.- The separation between the two structures corresponds to a maximum of the zero-shear viscosity and occurs at a NaClOs concentration equal to 0.1 M for a 10% CPC103 solution. All our samples have been prepared at a fixed salt concentration [NaC1031 = 0.05 M, so that, at any CPC103concentration it is assured that only few connections are present which do not affect the rheological properties. We focused on systems highly concentrated with surfactant content ranging from 20% to 40%. t Laboratoired'Ultrasons et de Dynamiquedes Fluidas Complexes. t Faculte de Chimie. Centre de Recherches Paul Pascal.
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(1)~ p p ej~.;,~ ~ i g n J. an J. P ~ Y S zz . iggi, I , ik47. (2)Catea, M.E.;Candau, S. J. J.Phys. Condens.Matter 1990,2,6869. (3)Diat, 0.Thesis, 1992. (4)Dmt, 0.; Roux,D.; Nallet, F. J. Phys.(Paris), in press. (5) Appell, J.; Porta,G.; Khatory, A.; Kern, F.; Candau, 5.J. J. Phys. ZZ 1992,2,1045. (6)Kbato~,A.;Kern,F.;Lequeux,F.;Appell,J.;Porte,G.;Morie,N.; Ott, A.; Urbach, W. Langmuir 1999,9,933. (7)Khatory, A.;Lequeux, F.; Kern, F.; Candau, S. J. Langmuir 1993, 9 1A.W ", (8) Candau, S. J.;Khatory, A.; Lequeux, F.; Kern, F. J.Phys.ZV 1993, 3,197.
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In a first part, we will show the existence of a phase transition toward a nematic phase as the CPClOs concentrations increases. Then, in a second part we will present the rheological behavior of the isotropic phase which exhibits two regimes: a linear and a nonlinear regime. The linear regime is detailed in a third part, the nonlinear regime is investigatedby neutron scattering and presented in a fourth part. We finally discuss all these results and suggest an interpretation in terms of shear induced phase transition. I. Static Phase Diagram
As the CPC103 concentration is increased, we observe a first-order transition from an isotropic to a birefringent phase, with a biphasic gap for different temperatures (see Figure 1). An increase of the temperature shifts this transition to higher surfactant concentration (the increase of the salt concentration gives the same effect). All the following experiments were performed at the same salt concentration [NaClOsl = 0.05 M and usually at T = 35 OC. A temperature/surfactant concentration phase diagram is represented in Figure l.
0743-7463/94/2410-0955$04.50/0 0 1994 American Chemical Society
Schmitt et al.
956 Langmuir, Vol. 10, No. 3,1994
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Figure 2. Neutron scattering spectrum of the 37% CPClO$ 0.05 M NaClOa sampleat rest at T = 35 O C . Thissample belongs to the birefringent phase. It has been oriented in the Couette cell applying a very small shear and then stopped to take the measurements. 12 [NaCIO,] 0 05M
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Figure 3. Neutron scattered intensity in high concentrated isotropicsamplesin 0.05 M NaClOSat T = 35 O C : 0,20% CPClOs; A, 31% CPclOs; 0,34% CPclOs. For neutron scattering measurementsthe sampleswere prepared with D2O rather than HzO for a better contrast. We have checked that the DzO phase diagram is the same as the H2O diagram if the surfactant concentration is calculated in volume fraction. The neutron scattered spectrum of the birefringent phase is anisotropic and exhibits a wide correlation peak, no second-order peak has been observed (Figure 2). Moreover, the scattered intensity perpendicular to the incoming neutron beam and to the orientation direction presents a peak with a large half maximum width (larger
than a Bragg peak). These observations suggest that this phase is a nematic phase. This is confirmed by the optical microscopy observations which reveal the usual structure of a nematic phase. This nematic is particular because its first Frank constant (splay term) is doubtless very strong, and a careful analysis of the texture would certainly give more information. So the observed birefringent phase was identified as a nematic phase by both neutron scattering and microscopic observations. Samplesin the isotropic phase was also investigated by neutron scattering. The isotropic spectra exhibit a welldefined peak which does not exist a t 15% of CPClOs (Figure 3). It is due to important correlations between the wormlike micelles. This peak shifts to higher values of the scattering vector q as the surfactant concentration ci, increases. The shift of the peak correspondsto the decay of the mean distance between the cylindrical micelles as ci, increases (MAat 20%, 70Aat 31%,and 66A at 34%). These strong correlationslead us to estimatethe distance between two neighbors in a simple model of hexagonal stacking of long cylinders taking the diameter to be 40A.5 The resulting distances (85A for 20%, 68 A for 3196,and 65 A for 34%) are in quite good agreement with the measured values showing a compact local structure. This indicates that the micelles are locally nearly parallel although the global structure remains isotropic. These isotropic samples were then investigated by rheology.
11. Rheological Behavior The rheological experimenta were performed on both a controlled stress rheometer (CSLlOO of Carri-med) and a strain imposed rheometer (RFSII of Rheometrics). The results obtained by the two rheometers are in good agreement. Figure 4 represents the steady-shear flow behaviors for two different surfactant concentrations: 26% and 31% In both cases, we observe a Newtonian regime where the stress varies linearly with the shear rate and a nonlinear regime where the stress stays nearly constant. We then define a critical shear rate i.cwhich corresponds to the change from linear to nonlinear behavior. In both cases the stress seems to reach a plateau value but it becomes difficult to be observed as we approach the nematic transition surfactant concentration: with the CSLlOO apparatus (stressimposed),as the plateau stress is applied
.
Langmuir, Vol. 10, No.3, 1994 957
Behavior of Wormlike Micelles under Shear [NaCIO,]= 0 05N
T
35'C
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Figure 5. Zero-shear viscosity 70 as a function of surfactant concentration, in a 0.05 M NaC108 solution, at T = 35 "C (0 samples belonging to the isotropic phase, this sample is nematic). The cross-over concentration @* is equal to 2.6 % .In the semidilute regime (2): 7 a W f o . 2 .
the shear rate increases very rapidly and exceeds the corresponding apparatus speed limit indicating that we reach a real plateau; with the RFSII apparatus, at constant shear rate, the measured stress decreases with time indicating that the equilibrium is not reached. The equilibration time increases near the transition, for instance a t 33.595, it reaches several hours. AB a consequence, with a strain imposed rheometer, we do not observe a perfect plateau but a slowly increasing stress which is overevaluated. We are also limited to high shear rate values by the "foaming-up" of the samples which reveals an aidsample surface instability. In spite of these difficulties, the experimental results clearly show a plateau of the stress for samples not too close to the concentration of the transition. However an important difference must be noticed for less concentrated than 26% samples, the change from linear to nonlinear regimes is smooth, whereas for the more concentratedsample (297% and above)this change is sharp.
111. Linear Regime In Figure 5, the plot of the zero-shear viscosity as a function of surfactant concentration at T = 35 O C shows three regimes. The first regime (1) corresponds to the dilute regime where the viscosity is low (of the order of the solvent viscosity) and varies only weakly with the surfactant concentration. The crossover concentration @* = 2.6%separates this first regime from the semidilute regime (2), where we find usual behavior for the viscosity; q a already observed in other equilibrium systems. At more concentratedsolutions (15%< Q < 34%)(3),theviscosity deviates from the previous behavior. As we increase the surfactant concentration, we get a biphasic sample (34% < CP < 36%) and then we reach the birefringent phase which has previously been identified as a nematic phase (@ > 36 % 1. Thia nematic phase has an apparent low shear viscosity lower than the concentrated isotropic phase (of the order of 3 instead of 12 Pa for */ 0.1 a-1). In fact, the low shear viscosity depends certainly on the textures (see ref 91, but as measured in the rheometer without particular care, it is smaller than the isotropic one in the
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(9) Marrucci, G.; Francesco,G . Adu. Chem. Phys. 1993,86.
whole range of measurements. We are interested here on samples of concentration just before the transition concentration. Parts b and c of Figure 6 represent the frequency dependenciesof G' and G",the real and imaginary parts of the complex shear modulus for varied concentrations: 30 % ,31%,33 % ,and 34%. At low frequencies,the C o l e Cole plot (Figure 6d) has a nearly semicircular shape, characteristic of a single exponential stress relaxation, due to a combination of the reptation and recombination processes. The reincreasing of G", at high frequencies, is the signature of the approach of high frequencyrelaxation modes due to local fluctuations.1° For concentrations lower than 31%, we observe the usual behavior for living polymers:11J2 an increase with concentration of Go,the diameter of the osculating circle of the C o l d o l e plot at the origin. In contrast, for concentrationslarger than 31 % , near the transition, we observe a decrease of Go. We also remark that in contrast to usual wormlike systems, the high frequency local relaxation process becomes slower and slower. The main part of these results are summarized in Table 1. Let us now report on the nonlinear experiments performed by neutron scattering under shear.
IV. Nonlinear Regime We investigate four samples,20 %,31%,34% ,and 37 % , by neutron scattering under shear flow. The first three samples are isotropic at rest and the fourth is nematic at rest. At low shear rates, the spectra are isotropic and equivalent to the one at rest. They become suddenly anisotropic at the shear rate */c at which the change of regime in the rheological a(+) curve arrives. For increasing shear rates, this anisotropy becomes more pronounced (Figure 7). It indicates that the micelles become more and more oriented parallel to the velocity. In Figure 8, we plot the relative anisotropy (11- 111)/11of the scattered intensities respectively perpendicular and parallel to the shear, at the q value of the peak, as a function of +,for two samples (31% and 34%). This clearly shows a threshold for the growingup of the anisotropyat the critical If the shear is switched off, the anisotropic shear rate structure quickly relaxes to the isotropic structure, this relaxation is too fast to be measured. Figure 9 represents the critical value of the ahear rate +c as a function of the surfactant Concentration. As we approach the surfactant concentration of the static transition (34 %), */c decreases abruptly. The plateau value ul of the stress has the same behavior. By comparing the nematic (Figure 2) and the sheared isotropic (Figure 7b) spectra, we can notice that these two spectra look very similar and that the two systems have the same orientation in flow. Our SANS results are comparable with the results of Jindal et a1.,'3 who have made similar experiments in a semidilute solution of wormlike micelles (C16-C8DAB), for a given shear rate and for a given concentration but in transient regime. Since our sample concentration is close to the nematic phase, we can distinguish the pure nematic effect from the usual orientational effect on the induced phase. In our opinion, the results of Jindal et al. (10) Granek, R; C a w , M . E.J. Chem. Phys. 1992, I, 4768. (11) Catea, M . E. J. Phys. 1988,49, 1693. (121Khatorv. A. Thesis. 1993. J.; Pilel, H.;Hoffmann, H.;Lindner, P.J. i13j Jiidal,v.K.; Phys. Chem. 1990,94,3129.
968 Langmuir, Vol. 10, No.3, 1994 ,
Schmitt et al.
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for eyes).
Table 1 Goa Rheo (Pa)
@=20%
@=23%
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+=29%
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are in fact equivalent to what we observe for @ (moreover their concentration is about 23 % 1.
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V. Discussion Near the transition to the nematic phase, the complex shear modulus behaves, in the function of the surfactant concentration, nearlyat the oppoeiteof that of asemidilute solution:12 the frequency difference of the fast and slow relaxation processes decreases while the surfactant concentration is increased. This slowing down of the fast relaxation process can be interpreted as a collective relaxation. We may argue that the “blob” fluctuations are replaced by orientational fluctuations due to Onsager interaction between the chains. This is confirmed by the measured mean distances by SANS between the micelles
330
that are closed to those estimated for a packed structure. The observed decay of Go is also an indication of a pretransitional effect as described by Dol and Edwards for a solution of rigid rodlike polymers14 and may also reveals orientational correlations. All these results suggest that near the transition, the cylinders are locallynearly parallel and strongly correlated with an Onsager interaction whereas the global structure remains isotropic. Hence this fluid is very different from an usual isotropic fluid and this will have consequences on the nonlinear behavior. To interpret our results we may use the theories of Doi (14) Doi, M.;Edwards, S . F.The Theory of Polymer Dynomice;Oxford Science Publication: Oxford,1986.
Langmuir, Vol. 10, No. 3, 1994 969
Behavior of Wormlike Micelles under Shear 04
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and E k l ~ a r d s and ~ ~ JCates.l8 ~ These theories predict that at high shear rates, the chains orient in the flow. Since the oriented chaine are less viscous, this leads to an instability in shear flow and, as a consequence,the stress
staysconstant with avalue related to Goby UJGO= O.67.l4l7 In their model, at high shear rates, on the plateau, the sample is divided into two zones, the isotropic phase and the oriented phase that coexist,they are s i m i i l y stressed but differently sheared, the oriented phase undergoing a
(16) h i , M.;Edwarda, 8. F.J. Chem.Soc.,Fam&y TTOns.2 1978,74, (17)Spendley,N.;Caw, M.E.;M c L e i , T.Phys. Rev. Lett. 1018,71, 1788. (16)Ca~,M.E.;McIm~,T.;MMucci,G.Europhys.Lett.,inpre~. 959.
Schmitt et al.
960 Langmuir, Vol. 10, No.3,1994 80,
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higher shear. The volume fraction of the oriented phase is proportional to 9 - i.c. Between 0 and */c, the stress first increases with i., then the slope decreases slowly and reaches zero at i.c.7 For the 26% of surfactant concentration, the experi-
mental results are compatible with this interpretation: the change from linear to nonlinear regimes is smooth; the stress reaches a plateau value that obeys to uB= 0.78G0, not too far from the predicted value; the neutron scattering spectrumis isotropic below qCand becomes more and more anisotropic above. For more concentrated solutions, the anisotropy increases and seems to saturate. For instance, the intensity 111vanishes completely for the 34% solution sheared at i. = 230 s-l. At this shear rate, the neutron scattering spectrum is very similar to the one of the nematic phase. This leads us to think that at i. = 230 s-l, the sample is nearly nematic and we interpret the increase of the anisotropy, for i. > qC,as the growing up of the nematic phase proportion in the sample. The mechanism of orientation is similar to what happens at 26%: the fact that the nematic phase is less viscous than the isotropic phase also leads to a plateau value for the stress, but the oriented phase is now replaced by a nematic phase. This idea is confirmed by the following experimental observations: the decay to zero of both the critical shear rate and the plateau stress as we approach the transition suggests that the nematic phase can be induced; the samples behave differently in the flow: the change from linear to nonlinear domains is very sharp for samplesmore concentrated than 31% and the ratio udGo deviates noticeably from the 0.67 value and vanishes at the transition (at 31 % it is equal to 0.45and at 34% it is equal to 0.01);the relaxation of the stress becomes slower, the equilibration time reaches several hours. Let us also remark that below the threshold shear rate i.c,one should observe an anisotropic spectrum, but the anisotropy in this situation is not observable (less than 1% ) and can only be detected by a more sensitive method like flow birefringence. This shear induced phase transition presents certainly a biaxiality, but our geometry prevents us from detecting it. Marrucci has also described a shear oriented nematic phase.l* The fact that this nematic phase was formed by rodlike polymers leads, for the nematic phase near the isotropic one, to tumble. In our case no phenomenon of tumbling was observed. This is probably due to the fact that the chains are stretched in flow, so rotation of the small rigid elements (of size smaller than the persistence length I,) that composethe very long chains is improbable.
Conclusion We experimentally observe a new domain of surfactant concentration in which the viscoelastic behaviors become different than those usually observed. Strong correlations and Onsager interactions between the micelles appear which lead at high concentration to a nematic phase. This nematic phase can also be induced, near the transition, by submittingthe sample to a flow. Thisfiiborder transition induced by shear is obtained by a separation into two domains differently sheared. This result is similar to the lamellar shear induced transition recently observed by Koppi et al.lD A theoretical model deacribesa similar behavior: derived from a Landau analysis, it predicts that shear can lead to an unstable situation near the isotropic-nematic transition.m Here, our experimental situation is somehow different because the nematic phase appears to be very fluid compared to the isotropic one, and the approximation (18) Marrucci, G.; Mef€ettone,P . L. Macromolecules 1989,22,4076. (19)Koppi, K.A; Well, M.;Bates, F. S. Phys. Rev. Lett. 1998, 70,
1449. (20) O h t e d ,
P.D.;Goldbart, P.Phys. Reu. A
1990, 41,4578.
Behavior of Wormlike Micelles under Shear
of a constant strain rate in the sample is no longer valid, because fluctuations of the nematic order parameter are Drobablv couded with the flow. Hence the transition b d e r shear is-probablyinfluenced by a coupling between the order parameter and the shear and, hence, between the concentration and the shear. We are now performing a model of this kind of flow induced transition where mechanical instabilities are coupled with concentration fluctuations, and we expect that it would explain some
Langmuir, Vol. 10, No. 3, 1994 961 behaviors like the long equilibration time for the stress near the shear induced transition and the break in the a(+) curves.21 Acknowledgment. We thank the Laboratoire L h n Brillouin where the Wereperformed and Noirez our contact. We also thank F, for hie help in the rheological (21)Schmitt, V.;Lequeux,F.;Marques, C. In preparation.
