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Giant Micellar Worms under Shear: A Rheological Study Using SANS Vania Croce,* Terence Cosgrove,* and Ce´cile A. Dreiss School of Chemistry, University of Bristol, Cantock’s Close, Bristol BS8 1TS, United Kingdom
Stephen King ISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot OX11 0QX, United Kingdom
Geoff Maitland and Trevor Hughes Schlumberger Cambridge Research, High Cross, Madingley Road, Cambridge CB3 0EL, United Kingdom Received August 18, 2004. In Final Form: May 10, 2005 Flow-SANS experiments were performed on viscoelastic aqueous solutions of erucyl bis(hydroxyethyl) methylammonium chloride in the presence of potassium chloride. This cationic surfactant has the ability to form very long and flexible wormlike micelles upon addition of salt. The effects of the key-parameterss shear rate, temperature, surfactant and salt concentrationson the ability of the micelles to align in the flow-field were investigated. The scattering data were analyzed in terms of an anisotropy factor (Af). It was found that the wormlike micelles aligned in the direction of the applied shear rate and that the anisotropy factor increased with shear rate. In addition, an increase in temperature caused a decrease of the anisotropy factor (Af) due to the formation of shorter worms. Furthermore, the branching of the micelles at high ionic strength caused the anisotropy factor to decrease in comparison with the values obtained from linear wormlike micelles, hence revealing that the formation of 3-way junctions restricts the alignment of the micelles in the shear-flow. Furthermore, the total surfactant concentration was found to affect the shear-induced patterns significantly, and different behaviors were observed depending on the ionic strength.
Introduction Wormlike micelles are self-assembly structures formed by surfactant molecules under specific thermodynamic conditions controlled by surfactant concentration, salinity, temperature, type of counterion, etc. In the semidilute regime, these wormlike chains form entangled viscoelastic networks, and their properties are analogous to those observed in solutions of flexible polymers. However, unlike ordinary polymers, wormlike micelles can break and recombine within a characteristic time (breaking time) and their micellar length obeys an exponential distribution.1-3 As a result of the scission-recombination process and the polydispersity, the flow properties of these living * To whom correspondence should be addressed. E-mail:
[email protected] (V.C.); terence.cosgrove@ bristol.ac.uk (T.C.). (1) Croce, V.; Cosgrove, T.; Maitland, G.; Hughes, T.; Karlsson, G. Langmuir 2003, 19, 8536. (2) Raghavan, S. R.; Kaler, E. W. Langmuir 2001, 17, 300. (3) Cates, M. E. Macromolecules 1987, 20, 2289. (4) Cates, M. E.; Candau, S. J. J. Phys. Condens. Matter 1990, 2, 6869. (5) Berret, J. F.; Gamez-Corrales, R.; Oberdisse, J.; Walker, L. M.; Lindner, P. Europhys. Lett 1998, 41, 677. (6) Hu, Y. T.; Boltenhagen, P.; Pine J. D. J. Rheol. 1998, 42, 1185. (7) Gamez-Corrales, R.; Berret, J. F.; Walker, M. L.; Oberdisse, J. Langmuir 1999, 15, 6755. (8) Nowak, M. Rheol. Acta 1998, 37, 336. (9) Bautista, F.; Soltero, J. A. F.; Macias, E. R.; Puig, J. E.; Manero, O. J. Phys. Chem. B 2002, 106, 13018. (10) Berret, J. F.; Roux, D. C.; Lindner, P. Eur. Phys. J. B 1998, 5, 67. (11) Penfold, J.; Staples, E.; Cummins, P. Adv. Colloid Interface Sci. 1991, 34, 451. (12) Hayter, J.; Penfold, J. J. Phys. Chem. 1984, 88, 4589. (13) Cummins, P.; Staples, E.; Hayter, J. B.; Penfold, J. J. Chem. Soc., Faraday Trans. 1 1987, 83, 2773.
polymers show a characteristic behavior. For example, if the scission-recombination process is rapid enough, the rheological response of the system is well approximated by a Maxwell model, with a single relaxation time.4 Solutions of wormlike micelles are extremely versatile systems as small variations of the physicochemical conditions can alter significantly their contour length, flexibility, structure, and interactions. Due to their viscoelastic properties, these systems have found numerous applications as thickeners, drag-reduction agents in heating systems and more significantly in oil-recovery uses. To optimize these processes, a clear understanding of the relation between the microstructure and the macroscopic flow properties is paramount. The wide variety of shear-induced phenomena encountered in wormlike micellar systems has been studied by many authors. The shear-thickening behavior observed in dilute wormlike micellar solutions has been interpreted in terms of the growth of shear-induced structures (SIS).5-8 Some authors have attributed the stress plateau found in the rheology of wormlike micellar systems as evidence of (14) Thurn, H.; Kalus, J.; and Hoffmann, H. J. Phys. Chem. 1984, 80, 3440. (15) Cummins, P.; Staples, E.; Penfold, J.; Heenan, R. K. Langmuir 1989, 5, 1195. (16) Schubert, B.; Wagner, N.; Kaler, E. Langmuir 2004, 20, 3564. (17) Richtering, W. Curr. Opin. Colloid Interface Sci. 2001, 6, 446. (18) Cummins, P.; Staples, E.; Penfold, J. Meas. Sci. Technol 1990, 1, 179. (19) www.isis.rl.ac.uk. (20) Hartmann, V.; Cressely, R. Rheol. Acta 1998, 37, 115. (21) Magid, L. J. Phys. Chem. 1998, 102, 4064. (22) Cappelaere, E.; Cressely, R. Colloid Polym. Sci, 1998, 276, 1050. (23) Koehler, R.; Raghavan, S. R.; Kaler, E. W. J. Chem. Phys. B 2000, 104, 11035.
10.1021/la0479410 CCC: $30.25 © 2005 American Chemical Society Published on Web 06/23/2005
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a shear-banded flow, which corresponds to the coexistence of regions of different shear rate within the sample.9 Others have interpreted this stress plateau in terms of a transition between an isotropic state and a shear-induced nematic state.10 An important technique used to characterize different types of flow behavior in wormlike micellar systems is small-angle neutron scattering under shear or flow-SANS. The ability of neutrons to penetrate through both the sample and flow cell allows the investigation of changes in micelle structure and orientation under shear. If the applied shear gradient exceeds the rotational diffusion coefficient of the micelles then they will align along the flow direction (usually horizontal). The whole sample then acts like a “molecular diffraction grating”. In other words, the scattering intensity is enhanced in one direction, perpendicular to the flow, and depressed in the other direction, parallel to the flow. Along the vorticity direction, information across the diameter of the micelles is obtained, and along the flow direction, information on the length of the worms can be obtained. Penfold 11-13 and Hoffmann14 pioneered the application of the flow-SANS technique to study the shear-induced alignment of rodlike micelles. Penfold et al.11-13 proposed a model to fit the scattering curves for aligned monodisperse and noninteracting rodlike micelles. In particular, they presented the effect of polydispersity, turbulence, flexibility, and hindered rotation on the scattering patterns. One of the systems they studied was rodlike micelles of poly(oxyethylene) nonionic surfactants.15 They found that with an increase in temperature the micellar rod length first increased and then decreased. This evolution of the micellar rod length was accompanied by subtle changes in rod flexibility and was attributed to a modification in the intra-micelle ethylene oxide (EO)-ethylene oxide interactions. Schubert et al.16 have studied the shear-induced turbidity and phase-separation of solutions of wormlike micelles formed by erucyl bis(hydroxyethyl) methylammonium chloride (EHAC) with two different salts (NaCl and NaSal). They found that this phenomenon occurred for systems in which long-range concentration fluctuations were present and which contained predominantly branched micelles. The results of a combination of flow-SANS and small-angle light scattering under flow (flow-SALS) suggested that the turbidity is due to a shear-induced growth of concentration fluctuations, which manifests as large anisotropic domains oriented along the vorticity axis. In this work, we report a flow-SANS study on viscoelastic solutions of EHAC in the presence of KCl. Unlike the work of Schubert et al.,16 which focused on a section of the phase diagram close to the phase-separation boundary, corresponding to the decreasing part of the low-shear viscosity vs salt concentration plot, this study explores a wider region of the phase-diagram and completes our rheological study of the system reported in an earlier publication.1 Solutions of EHAC wormlike micelles display extremely high viscosities, due to the giant size of the micelles and for this reason they are an attractive option for use in rheological control.17 Due to the diversity of rheological behaviors displayed by this system, a comprehensive study of the key parameters is necessary. The present contribution aims at gaining a better understanding of the viscosity behavior of EHAC micellar solutions, by investigating systematically the effect of shear rate, temperature, added salt, and surfactant concentration. The scattering patterns are analyzed by comparing the intensity scattered in the vorticity and flow directions. From these, an anisotropy factor is derived, which is an indication of the degree of alignment of the wormlike micelles. It is in turn related
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to the rheology of the system, to elucidate the connection between the viscosity and the orientation of the selfassembly structures in the field-flow. Experimental Section Materials. The chemical structure of the viscoelastic surfactant erucyl bis(hydroxyethyl) methylammonium chloride (EHAC) is shown below.2 It was obtained as a gift from Schlumberger Cambridge Research Limited and was thoroughly purified to remove any isopropyl alcohol present.
Potassium chloride (KCl) was purchased from Aldrich with a purity of 99+ wt %. Deuterium oxide (D2O, 99.9 atom weight %D) was purchased from GOSS Scientific Instruments Ltd. Samples were prepared by weighting the appropriated amounts of a 9.0 wt % surfactant stock solution, deuterium oxide, and salt (as a solid) in this order of addition. After mixing, the samples were heated to 60 °C in order to remove any trapped air bubbles. Steady-State Rheology. Steady-state rheological measurements were carried out on a controlled stress Bohlin Instrument (CVO). The shear stress was varied between 0.06 and 80 Pa to obtain shear rates between 0.0003 and 1000 s-1. The shear stress dependence was monitored as a function of increasing and decreasing shear stress (up/ down ramp). No effects of hysteresis were observed. A Couette geometry with cup 27.5 mm diameter, bob 25 mm diameter, and height 37.5 mm was used for the high viscosity samples. Steady-state measurements were performed at 40 °C and given a delay time of 30 s and an integration time of 200 s for each shear stress. A solvent trap was used to minimize changes in composition due to water evaporation. Two surfactant concentrations were used: 1.5 and 4.5 wt % (respectively 35 and 105 mM) and the salt concentration was varied from 2.0 to 12 wt % (or from 270 to 1610 mM). Small-Angle Neutron Scattering under Shear. Neutron scattering experiments under shear were performed at the ISIS facility, Rutherford Appleton Laboratory, U.K. The LOQ instrument at ISIS uses incident wavelengths between 2.2 and 10 Å sorted by time-of-flight with a sample detector distance of 4.1 m. This gives a Q-range between 0.006 and 0.24 Å-1. The samples were placed in a quartz Couette shear cell consisting of an outer rotating cylinder and a fixed inner spigot, with a cylindrical gap of 0.50 mm, which gives a total optical path length of 1.0 mm. A constant shear gradient along the gap is achieved since d , r (where d is the gap width and r is the Couette diameter). The shear rate applied was varied between zero and 100 s-1. An important feature is the rotating seal, which prevents solvent loss due to evaporation, sample rejection, and foaming. More details about the shear cell used at ISIS can be found elsewhere.18,19 The neutron beam was incident perpendicular to the flow direction and the two-dimensional scattering pattern was collected in the flow-vorticity plane. It was verified that the viscoelastic gels maintained a constant viscosity at a single shear rate by means of steady-state rheological measurements. The experiments were performed at three different temperatures 25, 40, and 60 °C and controlled within (0.1 °C. The scattering length densities of the
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Figure 1. Rheograms obtained at 40 ° C for two concentrations of EHAC at a fixed salt concentration of 6 wt %. (0) 4.5 wt % EHAC and (]) 1.5 wt % EHAC.
surfactant and D2O are 6.07 × 10-9 Å-2 (including the counterion) and 6.38 × 10-6 Å-2, respectively. The raw scattering spectra were corrected for background radiation, detector efficiency, empty cell scattering, transmission, and electronic noise by the standard procedures. Results and Discussions Steady-State Rheology. Figure 1 shows the rheological response of aqueous solutions of EHAC for two surfactant concentrations (4.5 and 1.5 wt %) at a fixed salt concentration of 6.0 wt % and a temperature of 40 °C. The main features in Figure 1 are the high viscosity plateau, where the samples display a Newtonian behavior, followed by a shear-thinning region occurring above a critical shear rate. The shear-thinning region has been explained in terms of the alignment of the micellar aggregates in the direction of the flow. However, it was noticed that, within a specific range of shear rates, these viscoelastic gels could not reach the steady-state condition and a drop in viscosity was recorded in the rheograms, leading to a stress plateau.1 In addition, the decrease in low-shear viscosity observed at lower surfactant concentrations is due to the formation of wormlike micelles with shorter contour lengths. The solid lines represent fits to the Carreau model as mentioned in a previous publication.1 Figure 2 shows the low-shear viscosity as a function of salt concentration at a fixed temperature of 40 °C and for the two surfactant concentrations studied here. The lowshear viscosity increases with salt concentration, reaching a broad maximum, and then decreases at high ionic strength. This behavior has been observed for other surfactant systems.2,20-22 The increase in viscosity at low salt concentration is a consequence of micellar growth. The addition of the electrolyte screens the interaction between the headgroups and promotes an increase in micellar length, which further gives rise to an entangled network of wormlike micelles at intermediate salt concentrations.23-25 The decrease in the low-shear viscosity at high salt concentration is the result of the formation of branched wormlike micelles, as observed from the presence of 3-way connections on the Cryo-TEM images1 and also reported by other authors.21,24,26 Unlike polymers, these branching points are not chemically fixed; they are created by the fusion of two wormlike chains formed by (24) Hassan, P.; Candau, S.; Kern, F.; Manohar, C. Langmuir 1998, 14, 6025. (25) Cappelaere, E.; Cressely, R. Rheol. Acta 2000, 39, 346.
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Figure 2. Low-shear viscosity (ηo) as a function of salt content (KCl) at a fixed temperature of 40 °C for two surfactant concentrations: (O) 4.5 wt % EHAC and (3) 1.5 wt % EHAC.
surfactant molecules that are in equilibrium with each other and with the surrounding media. These junctions can slide along the cylindrical body and serve as stress release points, resulting in lower viscosities.27 Hence, the maximum in viscosity observed upon addition of salt corresponds to a shift from linear wormlike micelles to a dynamic network of branched wormlike micelles. In addition, there is a decrease in the low-shear viscosity as the surfactant concentration is lowered, as seen in Figure 1. Small-Angle Neutron Scattering under Shear. (A) Effect of Shear Rate. Flow-SANS is a powerful technique that helps elucidate the rheological response of surfactant solutions as one can monitor structural changes occurring while shearing the sample. Contour plots of a sample containing 4.5 wt % EHAC with 6.0 wt % KCl at 40 °C and varying shear rates are shown in Figure 3. At zero shear rate, the scattering pattern is isotropic, indicating that the wormlike micelles are randomly oriented in the solution. As the shear rate is increased, this pattern becomes elongated in the vorticity direction, assuming a two-lobed shape at a shear rate of 50 s-1. The appearance of this anisotropy reveals the alignment of the wormlike micelles in the flow direction with increasing shear rate. These patterns are characteristic of solutions of anisometric micelles and have been observed by other authors.11,14,16,28 Hence, the shear thinning behavior experienced by these viscoelastic gels is a consequence of their alignment in the flow direction. The scattering patterns, such as those in Figure 3, contain information about the degree of alignment of the wormlike micelles. To perform a simple quantitative analysis of these experimental data, it is convenient to consider the intensity in the two orthogonal directions, Q-parallel (Q|) and Q-perpendicular (Q⊥). Q-parallel corresponds to the flow direction and Q-perpendicular to the vorticity direction. The scattering intensities in the two orthogonal directions were averaged over sectors of 60°: -30 to +30° for Q| and 60-120° for Q⊥. These angles were chosen in order to cover the scattering pattern in the region of interest. The scattering intensity curves for Q| and Q⊥ obtained for one of the contour plot shown in Figure 3 (shear rate of 50 s-1) are (26) Khatory, A.; Lequeux, F.; Kern, F.; Candau, S. J. Langmuir 1993, 9, 1456. (27) Drye, T. J.; Cates, M. E. J. Chem. Phys. 1992, 96, 1367. (28) Fo¨rster S, Konrad M, Lindner P, Phys. Rev. Lett. 2005, 94, 017803.
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Figure 3. Contour plots of a solution of 4.5 wt % EHAC with 6.0 wt % KCl at 40 °C at various increasing shear rates. Table 1. Anisotropy Factor Values Obtained for the Contour Plots Showed in Figure 3 for a Sample Containing 4.5 wt % EHAC and 6 wt % KCl at 40 °C
Figure 4. Scattering intensity curves in the two orthogonal direction: Q-perpendicular (Q⊥) (b) and Q-parallel (Q|) (O) for a solution of 4.5 wt % EHAC and 6.0 wt % KCl at 40 °C and a fixed shear rate of 50 s-1. Insert: Anisotropy factor as a function of the scattering vector for three different shear rates: (]) 5.0 s-1, (0) 10 s-1 and (4) 50 s-1. The solid lines represent the average value of Af plotted over the Q-range of interest.
shown in Figure 4. Clearly, the scattering intensity in the perpendicular direction is much higher than in the parallel direction. This anisotropy observed in the flow-SANS patterns can be quantified, through an anisotropy factor (Af) defined by16
Af )
(I(Q)⊥ - I(Q)|) I(Q)⊥
(1)
shear rate (s-1)
Af
0 5 10 50
0.00 0.20 ( 0.01 0.30 ( 0.02 0.72 ( 0.02
where I(Q)⊥ and I(Q)| are the scattering intensities defined above. The anisotropy factor was calculated for each data point at each shear rate as shown in the insert of Figure 4. In the high Q-region, above Q g 0.10 Å-1, the determination of a reliable anisotropy factor was difficult, as the magnitudes of the two scattering curves are similar in this region. Therefore, the anisotropy factor was averaged over a Q-range between 0.02 and 0.06 Å-1. At rest, when there is no alignment, Af ) 0, and when the micelles are perfectly aligned, Af ) 1. The values obtained for the anisotropy factor from the contour plots shown in Figure 3 are presented in Table 1. As expected, the anisotropy factor increases with an increase in shear rate, confirming the effect of shear rate on the alignment of these macrostructures in the flow-field. (B) Effect of Salt and Surfactant Concentration. The salt concentration has a visible effect on the alignment of the wormlike micelles, as shown in Figure 5 for a solution of 4.5 wt % EHAC. The values of the alignment factor are shown in Table 3 for the various KCl concentrations used. An interesting behavior is observed: as the salt concentration is increased, the scattering pattern does no longer correspond to that of aligned wormlike micelles; the twolobed shape is lost. This is shown quantitatively through
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Figure 5. Contour plots and anisotropy factor (Af) at a and fixed shear rate of 10 s-1 for a sample containing 4.5 wt % EHAC and varying KCl concentration at 40 °C.
the anisotropy factor, which decreases upon addition of KCl. This behavior can be explained by structural modifications of the sample occurring upon addition of salt. As salt is added, branching of the micelles takes place, resulting in the formation of a three-dimensional network with no preferential orientation. With the formation of branching points (6.0 wt % KCl), the anisotropic pattern is smoothed out, suggesting that the branched wormlike micelles no longer align in the flow-field and that it is even harder to orient a saturated network of such micelles (12.0 wt % KCl), in comparison with linear wormlike micelles (2.0 wt % KCl). In fact, rheological measurements29 of the three systems presented in Figure 5 show an increasing viscosity with increasing salt concentration, at a shear rate of 10 s-1 (different from the zero-shear viscosity, which is shown in Figure 2). This suggests that the differences observed in the viscosity in the shearthinning region could be related to the ability of these structures to align in the flow-field. Schubert et al.16 studied a higher salt/EHAC ratio (hence with a higher number of connections) and were able to observe an elongation of the anisotropic pattern leading to a “needlelike shape” when increasing the shear rates up to 2000 s-1. This indicates that a highly branched micellar network can be aligned by the shear-flow if a high enough shear rate is applied. However, their surfactant concentration was less than half the one used here, and this points to an effect of the total surfactant concentration, which is discussed below. In our system, higher shear rates could not be applied due to foaming of the samples. (29) Croce, V. unpublished measurements (First Year Report).
Figure 6. Anisotropy factor (Af) as a function of shear rate for two concentrations of EHAC at 40 °C and for a salt concentration of 6.0 wt % KCl. (O) 1.5 wt % EHAC and (4) 4.5 wt % EHAC. The solid lines are guide lines to the eye.
Figure 6 shows the anisotropy factor (Af) as a function of shear rate for two concentrations of EHAC at a fixed temperature of 40 °C and a salt concentration of 6.0 wt %. As observed above, the anisotropy factor increases with increasing shear rate, indicating that the wormlike micelles are becoming more oriented in the direction of the flow. The effect is stronger at low shear rates. In addition, the anisotropy factor is higher for the 1.5 wt % solution of EHAC than for the 4.5 wt % solution, over the entire range of shear rates studied. However, when
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Table 2. Anisotropy Factor (Af) at 40 °C for EHAC Solutions at Two Surfactant Concentrations with 2.0 wt % KCl and for a Shear Rate of 10 s-1 [EHAC] (wt %)
Af
4.5 1.5
0.88 ( 0.01 0.34 ( 0.02
considering the viscosity curve shown in Figure 2, it appears that the composition of both samples corresponds to the occurrence of branching (maximum of the viscosity). This is also confirmed by Cryo-TEM images.1 Hence the difference observed in the ability of these structures to align is linked to the difference in surfactant concentration. At a higher surfactant concentration, it is likely that the branched micellar network is more highly connected and denser, and it could also be more entangled, due to the larger size of the worms; hence, it makes it more difficult to orient in the flow-field. In contrast, the trend is different when lower salt concentrations are used. The anisotropy factors for the same surfactant concentrations but with 2 wt % KCl are presented in Table 2. The composition of these samples now corresponds to the left-hand side of the viscosity peak shown in Figure 2, where linear wormlike micelles are present at both surfactant concentrations. At this low salt content and for a constant shear rate of 10 s-1, the opposite behavior in observed: the anisotropy factor is higher for the 4.5 wt % EHAC solution than for the 1.5 wt % solution. It is important to note that at this salt concentration the charges are already screened and adding salt imparts more flexibility to the system. In this case, where only linear wormlike micelles are formed, their contour length plays
an important role in the alignment: the longer the wormlike micelles, the easier their alignment. At 2.0 wt % added KCl, longer wormlike micelles are formed at higher surfactant concentration;1 therefore, the anisotropy factor is higher. (C) Effect of Temperature. The influence of temperature on the two-dimensional scattering patterns of a solution of 1.5 wt % EHAC and 6.0 wt % KCl at a fixed shear rate (10 s-1) is shown in Figure 7. In addition, the values of the alignment factor are shown in Table 4 at different temperatures used: 25, 40, and 60 °C. It can be seen that with an increase in temperature the anisotropic two-lobed shape pattern disappears and at 60 °C the scattering corresponds to an isotropic scattering pattern. This is reflected in the values obtained for the anisotropy factor, which decrease as shown in Table 4. This tendency is in good agreement with the rheology data, where the low-shear viscosity was seen to decrease with an increase in temperature.1 This trend is clearly a consequence of the decrease in contour length of the wormlike micelles with an increase in temperature.21,22 As the wormlike micelles decrease in length, their alignment is more difficult to achieve. In addition, the Brownian motion of the shorter worms is stronger, which tends to randomize the orientations. Hence, much higher shear rates are needed to cause a strong orientational state at higher temperatures. (D) Local Structure: The Micellar Cross-Section. In the concentration range studied here, EHAC wormlike micelles are extremely long, flexible, and well above the overlap concentration. Furthermore, the micellar length falls outside the Q-region accessible to neutrons.1 As a
Figure 7. Contour plots and anisotropy factor (Af) of a sample containing 1.5 wt % EHAC with 6.0 wt % KCl at a fixed shear rate of 10 s-1 and varying temperature.
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consequence, there is no useful model to fit the whole scattering curve. The wormlike chain form factor for semiflexible chains with excluded volume effects derived by Pedersen and Schurtenberger30 could only be applied to the most dilute solutions. However, we were able to obtain quantitative information on the size of the crosssection of the wormlike micelles in the high Q-regime, by fitting the data to the Kratky-Porod wormlike chain model.31 The cross-sectional radius of gyration (Rg,xs) and the mass per unit length (ML) of the wormlike micelles obtained are 19.6 ( 0.2 Å and (3.0 ( 0.2) × 10-13 g/cm, respectively. They are in the range of values reported for other micellar systems.32-34 It is interesting to note that these values were not significantly influenced by an increase in shear rate, temperature, salt, and surfactant concentration; in other words, varying the conditions used in this study does not alter the local structure of the micelles. Rg,xs is related to the micellar cross-section radius (rxs) by23
rxs ) x2Rg,xs
(2)
It was found that the cross-sectional radius of the wormlike micelles formed by EHAC is approximately 27.8 ( 0.3 Å. This value is similar to the one reported in our previous publication1 within the experimental error and by Raghavan et al.2 Conclusions The effect of shear rate, surfactant concentration, temperature, and salt on aqueous solutions of erucyl bis(hydroxyethyl) methylammonium chloride (EHAC) was investigated by means of small-angle neutron scattering under shear (flow-SANS) and steady-state rheology. Rheological measurements showed a strong dependence of the low-shear viscosity on the salt concentration. A broad maximum in the viscosity curve against KCl concentration was observed and explained in terms of a transition from (30) Pedersen, J. S.; Schurtenberger, P. Macromolecules 1996, 29, 7602. (31) King, S. M. In Modern Techniques for Polymer Characterization; Pethrick, Dawkins, Eds.; John Wiley & Sons Ltd.: New York, 1999. (32) Magid, L. J.; Li, Z.; Butler, P. D. Langmuir 2000, 16, 10028. (33) Garamus, V. M.; Pedersen, J.; Kaeasaki, H.; Maeda, H. Langmuir 2000, 16, 6431. (34) Maillet, J. B.; Lachet, V.; Coveney, V. Phys. Chem. Phys. 1999, 1, 5277.
linear wormlike micelles to branched wormlike micelles. The results of flow-SANS experiments were analyzed by calculating an anisotropy factor (Af) from the ratio of the scattered intensity in the two orthogonal directions. Af was found to increase with increasing shear rate as the two-lobed shape scattering pattern became increasingly elongated in the vorticity direction, which is characteristic of wormlike micelles aligning in the flow direction. In addition, the anisotropy factor at a fixed shear rate decreased with increasing temperature, due to the formation of shorter wormlike micelles, which are more difficult to align. The formation of branches was found to play a critical role on the alignment of the wormlike micelles. The results suggest that solutions of linear wormlike micelles, present at low KCl concentration (
