Controlling the Shear-Induced Structural Transition of Rodlike Micelles

cellulose (HPC) suppresses this transition, while poly(ethylene oxide) (PEO) enhances the zero-shear viscosity, with little change to the critical rat...
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Langmuir 2000, 16, 7991-7998

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Controlling the Shear-Induced Structural Transition of Rodlike Micelles Using Nonionic Polymer M. T. Truong and L. M. Walker* Department of Chemical Engineering, Center for Complex Fluids Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213 Received May 1, 2000. In Final Form: July 25, 2000 We demonstrate that nonionic polymer can be used to control the shear-induced transition observed in the cationic rodlike micellar system of cetyltrimethylammonium p-toluene sulfonate (CTAT). Hydroxypropyl cellulose (HPC) suppresses this transition, while poly(ethylene oxide) (PEO) enhances the zero-shear viscosity, with little change to the critical rates of the transition. It is proposed that the availability of hydrophobic moieties of HPC allows for its influence on the onset of the transition. This is consistent with binding, rheological, and small-angle neutron scattering (SANS) studies. Furthermore, quiescent SANS shows that both polymers affect intermicellar interactions, solvent-micelle interactions, and/or micellar length. While the onset of the shear-induced transition may be altered with polymer, polymer composition does not affect micellar flexibility and/or interactions in the aligned transitioned state.

1. Introduction Many dilute cationic surfactant systems exhibit viscoelasticity when subjected to a flow field, while at rest these systems have low viscosities and no apparent elasticity. In shear flow, this phenomenon is seen as a transition to a shear-thickened fluid. Previously observed in a number of systems, this type of behavior has been attributed to the formation of a shear-induced structure. In addition to rheological measurements,1-3 shear smallangle neutron scattering (SANS),4-7 light scattering microscopy,8,9 birefringence,3,10,11 and cryogenic temperature transmission electron microscopy (cryo-TEM)8,11,12 have been used to study the structure formed under shear. Although these investigations involved different surfactant systems, the general requirement for this transition appears to be that the micellar systems form charged, rodlike (cylindrical) micelles in dilute solution with no added electrolyte. The structure observed at rates above the critical rate is birefringent. These sheared systems have nonzero, measurable first normal stress differences indicating elasticity. Additionally, scattering studies show strong alignment in the direction of flow. To date, there are various qualitative models that attempt to explain the microscopic changes that occur in this transition. Rehage et al. proposed a model in which * Corresponding author. E-mail: [email protected]. (1) Gravsholt, S. Proc. Int. Congr. Rheol. 1980, 8, 629. (2) Rehage, H.; Hoffmann, H. Rheol. Acta 1982, 21, 561. (3) Hu, Y.; Wang, S.; Jamieson, A. J. Rheol. 1993, 37, 531. (4) Hoffmann, H.; Hofmann, S.; Rauscher, A.; Kalus, J. Prog. Colloid Polym. Sci. 1991, 84, 24. (5) Jindal, V. K.; Kalus, J.; Pilsl, H.; Hoffmann, H.; Lindner, P. J. Phys. Chem. 1990, 94, 3129. (6) Schmitt, V.; Schosseler, F.; Lequeux, F. Europhys. Lett. 1995, 30, 31. (7) Berret, J. F.; Gamez-Corrales, R.; Oberdisse, J.; Walker, L. M.; Lindner, P. Europhys. Lett. 1998, 41, 677. (8) Lu, B.; Li, X.; Scriven, L.; Davis, H.; Talmon, Y.; Zakin, J. Langmuir 1998, 14, 8. (9) Boltenhagen, P.; Hu, Y.; Matthys, E. F.; Pine, D. J. Europhys. Lett. 1997, 38, 389. (10) Rehage, H.; Wunderlich, I.; Hoffmann, H. Prog. Colloid Polym. Sci. 1986, 72, 51. (11) Oda, R.; Panizza, P.; Schmutz, M.; Lequeux, F. Langmuir 1997, 13, 6407. (12) Keller, S.; Boltenhagen, P.; Pine, D.; Zasadzinski, J. Phys. Rev. Lett. 1998, 80, 2725.

large micelles are formed when small micelles collide in shear flow and fuse together.10 More recently, Hu et al. found evidence of a secondary, more viscous phase which grew from the moving wall in a concentric cylinder geometry, indicative of a flow-induced phase transition.13 Although the exact nature of the transition is somewhat controversial, it is well established that this phenomenon is very sensitive to changes in the micelles and their environment. As the structure of the micelles is changed with temperature, salt, or cosurfactant, the magnitude of the critical shear rate is sensitive to these external parameters. As such, the transition itself is susceptible to subtle changes in micellar structure. With this knowledge, one of the goals of this work is to utilize the physicochemical properties of an added polymer to effectively control the rheology of rodlike micellar systems. By probing the effects of polymer on the shape and size of the micelles and micellar interactions (electrostatic, hydrophobic), we aim to better understand the structural changes which are key in inducing the shearinduced transition. Dilute systems of cetyltrimethylammonium p-toluenesulfonate (CTAT) and nonionic polymer are examined for these purposes. To quantify the effects of polymer on the shear-induced transition, rheological measurements are made in concentric cylinder, or Couette, geometry on mixed systems of CTAT and polymer. SANS is used to probe the structure of these systems both at rest and under shear. 2. Experimental Section Cetyltrimethylammonium p-toluenesulfonate (CTAT) is used as received from Sigma Chemical Co. The purity of CTAT is verified using surface tension measurements (no depression is observed near the critical micelle concentration (cmc)). Water is deionized and purified of organic and microbial contaminants via a Milli-Q system (20 psig) by Millipore. The surface tension of the water used at 25 °C is measured to be 71.8 ( 0.1 dyn/cm, in good agreement with literature values.14 Deuterium oxide (D2O) from Aldrich Chemical Co. is used in the scattering studies. Two polymers are used in this study: poly(ethylene oxide) (PEO) is a straight-chain polymer purchased from Acros Organics with (13) Hu, Y. T.; Boltenhagen, P.; Pine, D. J. J. Rheol. 1998, 42, 1185. (14) CRC Handbook of Chemistry and Physics, 71 ed.; Lide, D., Ed.; CRC Press: Boca Raton, Ann Arbor, Boston, 1990.

10.1021/la0006263 CCC: $19.00 © 2000 American Chemical Society Published on Web 09/22/2000

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reported molecular weight of 300 kg/mol. PEO is relatively flexible in water with reported Mark-Houwink parameters, a ) 0.72 and K ) 0.33 dL/kg.15,16 The intrinsic viscosity ([η]) of the sample used is measured to be 1.75 ( 0.1 dL/g, so the viscosity-average molecular weight (Mv) is determined to be 150 kg/mol by the Mark-Houwink-Sakurada equation.17 The entanglement concentration (c*) is defined as the concentration at which there is a rapid increase in zero-shear viscosity with concentration. For this molecular weight PEO, c*PEO is measured to be 0.5 wt % PEO/H2O at 25 °C. Hydroxypropylcellulose (Hercules Klucel HPC-L) is a relatively rigid polymer with short hydrophobic moieties (-CH2C(CH3)HO-) that extend off the backbone. The reported molecular weight is 80-100 kg/mol. By use of the measured [η] of 1.22 ( 0.1 dL/g and an empirical relation developed by Wirick and Waldman,18 the weight-average molecular weight (Mw) is calculated to be 120 kg/mol. From rheological measurements, c*HPC is 1 wt % HPC/H2O at 25 °C. On the basis of these calculations, both polymers have rather polydisperse molecular weight distributions. To prepare mixed samples, polymer and CTAT are added simultaneously to water or D2O, shaken manually, and placed in a 30 °C oven for at least 6 h. The samples are then placed in a bath or oven at 25 °C for 1 h prior to all experiments. Rheological studies are performed on a Rheometric Scientific SR5 stress-controlled rheometer with concentric cylinder (cup and bob) geometry. The bob rotates and has a radius of 13.8 mm and length of 42 mm. The gap between the cup and bob is 1.2 mm. Both the cup and bob are made of stainless steel. The temperature of the cup is controlled within (0.1 °C using a circulating fluid bath. The system is preheated to the operating temperature 30 min prior to all experiments. Stress sweep experiments are performed, and the steady shear rate is determined within 2% deviation. The reported viscosity is then just the ratio of applied stress to steady measured shear rate. Additional transient creep tests (apply a stress, measure shear rate with time) are done at various stresses to verify that steady values are reached in all stress sweeps. Even though stress is controlled in these experiments, here we report the viscosity as a function of shear rate to better compare to previous studies and to our SANS data. To probe the structural effects of polymer on CTAT both at rest and under shear, SANS is employed. These experiments are performed at the NIST facility in Gaithersburg, MD, on the 30 m SANS NG-3 beamline. By use of a neutron wavelength of 6 Å with spread of ∆λ/λ ) 0.147 Å and detector distances of 3 and 10 m, the accessible scattering vector, or q-range, is 0.0045-0.11 Å-1. A quartz Couette shear cell with a gap of 0.5 mm and outer rotating cylinder with radius of 29.5 mm designed at NIST is used for all experiments. All SANS data are corrected for background and empty cell scattering using standard techniques. With water and silica standards provided by NIST, the scattered intensity is put on an absolute scale. The scattering length density (F) of CTAT is 2.5 × 109 cm-2, assuming bulk density of 1.0 g/cm3 and based on surfactant molecular structure of C16H33N(CH3)3SO3C6H4CH3. The scattering length density of HPC and PEO are 6.8 × 109 and 5.7 × 109 cm-2, respectively, based on monomer structures and bulk densities of 1 g/cm3. In contrast to D2O (F ) 6.4 × 1010 cm-2), CTAT scatters more strongly than either of the two polymers. In addition, the number of CTAT micelles in any given mixed system is 1-25 times more than the number of polymer chains. This calculation is based on an average aggregation number (〈nagg〉) of 120 CTAT molecules per micelle at 11 mM and the reported polymer molecular weight. Although we did not measure 〈nagg〉 in this work, Carver et al. report previously that for similar systems of CTA-benzoates, 〈nagg〉 is approximately 120 at ∼10 mM.19 Furthermore, small changes in the chemistry of the (15) Ferguson, J.; Hudson, N.; Warren, B. J. Non-Newtonian Fluid Mech. 1992, 44, 37. (16) Mun, R.; Byars, J.; Boger, D. J. Non-Newtonian Fluid Mech. 1998, 74, 285. (17) Fried, J. R. Polymer Science and Technology; Prentice Hall PTR: Englewood Cliffs, NJ, 1995. (18) Wirick, M.; Waldman, M. J. Appl. Polym. Sci. 1970, 14, 579. (19) Carver, M.; Smith, T.; Gee, J.; Delichere, A.; Caponetti, E.; Magid, L. Langmuir 1996, 12, 691.

Truong and Walker counterion have little effect on 〈nagg〉 at these low concentrations. This is supported by Gamboa et al., who found similar degrees of ionization for a series of CTA-benzenesulfonates and -toluenesulfonate.20 We further assume that 〈nagg〉 is the same at 10 and 11 mM surfactant. Although increasing surfactant concentration may lead to an increase in 〈nagg〉, this value of 120 CTAT molecules per micelle is used as a basis of comparison for systems with different polymer and the assumption is reasonable. On the basis of the scattering length densities and the concentrations of polymers used, the predicted scattered intensities from PEO and HPC from Debye scattering theory are more than 2 orders of magnitude less than that of 0.5 wt % CTAT over a q-range of 0.001-0.6 Å-1. Therefore, CTAT micelles are assumed to dominate the scattered intensity and the added polymer is considered to be part of the solvent. The cmc of CTAT is 0.012 wt % (0.26 mM), as measured with electrical conductivity and surface tension. The Krafft temperature, defined as the temperature below which micelles do not form, is determined by dye solubilization to be 23 °C.21 Gamboa et al. report that the degree of dissociation of the counterion, p-toluenesulfonate or tosylate, is 0.13 by free electrophoresis.20 As a relatively large organic counterion, tosylate penetrates the surface of the micelle, through hydrophobic interaction with the core of the micelle. Due to its strong binding and penetration, a transition from spherical to rodlike micelles occurs without additional salt at 0.09 wt % CTAT. This critical rod concentration (crc) is measured with static light scattering using analysis based on the Debye equation.22 SANS measurements confirm the existence of rodlike micelles at 0.1% CTAT.23 Previous work shows that aqueous CTAT systems exhibit shear-induced transitions between 0.1 and 0.9% and 25-36 °C.7,21,23 In an aqueous solution of 0.5% CTAT, the micelles are charged and rodlike, with a polydisperse distribution in length.

3. Results 3.1. Association in CTAT-Polymer Systems. Many studies of mixed polymer and rodlike micellar systems involve specific interactions24,25 or strong hydrophobic interactions.24,26-28 Here, we aim to minimize the interactions and investigate simply the steric effects of the polymer on CTAT micelles or, at least, generate a situation as close to that as possible. Although the polymers used in this study are nonionic, they are slightly surface active, so the formation of polymer-micelle complexes via hydrophobic interactions is likely. We use three standard techniques to characterize the level of interaction between polymer and surfactant. HPC has a cloud point between approximately 35 and 45 °C in water, depending on molecular weight and degree of molar substitution. The solubility of HPC is enhanced by adding ionic surfactants that bind to HPC. This occurs through a “polyelectrolyte effect”.29 That is, through hydrophobic interaction with surfactant, the polarity of HPC is increased, improving its solubility in water. Figure 1 shows the effects of 0.5% CTAT on the cloud point of HPC. In these experiments, cloud points are assessed (20) Gamboa, C.; Rios, H.; Sepulveda, L. J. Phys. Chem. 1989, 93, 5540. (21) Thebaud, B. An examination of shear-induced micellar structures in tube flow using small angle neutron scattering. Carnegie Mellon University, 1998. (22) Imae, T.; Ikeda, S. Colloid Polym. Sci. 1987, 265, 1090-1098. (23) Gamez-Corrales, R.; Berret, J. F.; Walker, L. M.; Oberdisse, J. Langmuir 1999, 15, 6755. (24) Nagarajan, R.; Kalpakci, B. Polym. Sci. Technol. 1985, 30, 369. (25) Goddard, E.; Leung, P. Polym. Sci. Technol. 1985, 30, 407. (26) Jones, M. J. Colloid Interface Sci. 1967, 23, 36. (27) Cabane, B.; Duplessix, R. Colloids Surf. 1985, 13, 19. (28) Panmai, S.; Prud-homme, R. K.; Peiffer, D. G. Colloids Surf., A 1999, 147, 3. (29) Goddard, E. D. Colloids Surf. 1986, 19, 255.

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Figure 1. Enhancement of HPC solubility (b) in water upon addition of CTAT (open symbols). Cloud points assessed visually during increasing (0) and decreasing (4) temperature ramps.

Figure 2. Conductivity of CTAT/polymer/H2O systems at 25 °C. Data are shifted by factors given in parentheses to aid in comparison.

visually as temperature is increased and decreased. At low concentrations of HPC (0.005%), where there are more than 830 CTAT micelles per HPC chain, the cloud point is increased by close to 30 °C. At higher concentrations (0.01-0.05% HPC), the enhancement decreases to about 10 °C. These results indicate that at constant CTAT concentration, the “polyelectrolyte effect” becomes less significant as the number HPC molecules increases in comparison to surfactant concentration. This implies that at the concentrations that we use (0.05-0.8% HPC), association between CTAT and HPC exists but is very weak. The cloud point of PEO exceeds 100 °C, so the binding of CTAT cannot be probed with this method. Instead, electrical conductivity is used. These measurements are made on an ATI Orion model 162 conductivity meter. Conductivity increases linearly with ionic surfactant concentration due to the increased number of ionic species in the system. An abrupt decrease in the rate of this increase occurs at the cmc as the mobility of CTAT molecules is decreased upon micellization. In mixed systems, binding between surfactant and polymer also causes a decrease in the conductivity of the surfactant. This occurs at the critical aggregation concentration (T1). As surfactant concentration is further increased, the polymer becomes saturated with surfactant and unbound micelles form (T2). In strongly binding systems such as sodium dodecyl sulfate (SDS), an anionic surfactant, and PEO, the association leads to a deviation in the conductivity of SDS at concentrations between T1 and T2 from that of SDS systems without PEO.26,27 Figure 2 shows the conductivity of CTAT with 0.025% HPC and 0.1% PEO.

Figure 3. I1/I3 from pyrene fluorescence of CTAT/H2O (b) systems with (a) PEO, 0.07% (0) and 0.16% (4), and (b) HPC, 0.05% (0) and 0.5% (4). The critical micelles concentration (cmc) as measured by conductivity, 0.012 wt % CTAT, is shown by dash lines (- - -).

To aid in comparison, shift factors given in parentheses are used as follows; although both polymers are nonionic, 0.025% HPC increases the conductivity of water by 1.2 µS/cm and 0.1% PEO by 1.0 µS/cm. Since each set of data in Figure 2 is at constant polymer concentration, these small increases are simply subtracted from the cases with polymer and compared to the cases without polymer and are given as shift factors. Then to view all results on the same plot, the results corresponding to PEO-CTAT are shifted by 5 µS/cm, such that the total shift factor of PEOCTAT is 4 µS/cm. Correspondingly, one set of CTAT results is shifted 5 µS/cm. As shown by Figure 2, both polymers have minimal effects on the conductivity of CTAT, indicating the degree of association is very low. Finally, pyrene fluorescence spectroscopy is also used to characterize the association between CTAT and both HPC and PEO. The emission spectrum of pyrene has three monomer peaks at 370, 380-381, and 390-391 nm, which are called I1, I3, and I5, respectively. The ratio of I1/I3 has been shown previously to reflect the polarity of the solvent environment surrounding pyrene.30-32 Figure 3a shows that I1/I3 decreases near the cmc of CTAT as pyrene is solubilized by CTAT micelles. These measurements are made on a Perkin-Elmer LS-5B luminescence spectrometer. Adding PEO slightly suppresses I1/I3 below the cmc. Above the cmc, PEO has little or no effect on the polarity of the environment of pyrene. This indicates that at the higher concentration of CTAT that we use (0.5%), PEO has a negligible effect on CTAT micellization. (30) Nakajima, A. Bull. Chem. Soc. Jpn. 1971, 44, 3272. (31) Kalyanasundaram, K.; Thomas, J. K. J. Am. Chem. Soc. 1977, 99, 2039. (32) Dong, D.; Winnik, M. Photochem. Photobiol. 1982, 35, 17.

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Figure 4. Zero-shear viscosity of CTAT/H2O systems at 25 °C (b). Shear-induced transition is observed for dilute and semidilute systems as indicated by the transition zone.

On the other hand, Figure 3b shows that a high concentration of HPC has a dramatic effect on I1/I3 throughout the range of CTAT concentrations. These results indicate that HPC solubilizes pyrene; that is, the presence of HPC induces an environment that is less polar than water but more polar than the core of CTAT micelles, giving the depression of I1/I3 below the cmc and the persistent enhancement above the cmc. While the apparent association between pyrene and HPC makes the fluorescence results more complex, it is clear that at low concentrations (0.05%) HPC does not change the micellization of CTAT. When the concentration of HPC is higher (0.5%), the hydrophobic side groups do offer a sink for CTAT and other hydrophobic moieties. These characterization experiments show that a weak association exists between CTAT and both HPC and PEO. Cloud point and fluorescence measurements indicate that the interactions between CTAT and HPC are slightly stronger than those between CTAT and PEO. The association of these polymers with CTAT influences micellization close to the cmc. In this work, CTAT concentrations are more than 10 times the cmc, so the binding of polymer may have less significance. 3.2. Rheological Studies. Because of their length, rodlike micelles are effective viscosity enhancement agents. Figure 4 shows the concentration dependence of zero-shear viscosity (η0) for aqueous CTAT systems at 25 °C. Below 0.5% CTAT, η0 remains low, close to that of water. Above 0.5% CTAT, η0 increases with concentration (c) as log(η0) ∼ 7 log(c). These solutions are clearly viscoelastic when shaken. Aqueous systems of CTAT between 0.2 and 0.8%, as indicated by the transition zone in Figure 4, exhibit apparent shear-thickening transitions similar to those reported previously.7,21,23 At low rates of deformation, the viscosity is constant and the systems behave like Newtonian fluids. The transition occurs at some critical shear rate, above which the viscosity increases dramatically. Figure 5a shows that 0.5% CTAT/H2O shear-thickens at 30 s-1 at 25 °C. Increasing the temperature tends to lower η0 and increase the critical shear rate. This is consistent with previous results reported by GamezCorrales et al., where the critical shear rate (γ˘ c) in aqueous CTAT systems is related to temperature (T) by23

( )

γ˘ c(T) ∼ exp

-Ea kBT

where Ea, the activation energy, is 116 ( 4kBT. The arrows on Figure 5 indicate the shear rate at which viscosity

Figure 5. Changes in the steady-state rheology of CTAT/H2O with (a) temperature at 0.5% CTAT, (b) 25, (0) 27, and (4) 30 °C, and (b) concentration at 25 °C, (0) 0.2%, (b) 0.5%, and (4) 0.75%. Onset of Taylor instabilities for Newtonian fluids of similar η0 are indicated by arrows (f).

increases due to the onset of Taylor instabilities for Newtonian fluids of similar η0. Note that the increases in viscosity seen in this work occur at shear rates almost half a decade lower than those of the onset of Taylor instabilities for this geometry. Figure 5b shows that CTAT systems are also very sensitive to concentration; increasing concentration not only increases η0 as shown in Figure 4 but also decreases the critical shear rate. To investigate the effects of polymer on the transition, similar measurements are made on mixed aqueous systems of polymer and 0.5% CTAT (11 mM) at 25 °C. At dilute concentrations (c < c*PEO), small amounts of PEO cause a slight increase in the η0 of 0.5% CTAT/H2O as shown in Figure 6a. Increasing amounts of PEO show subsequent increases in η0. More notably, the critical shear rate remains roughly constant (22 ( 7 s-1) throughout the range of PEO concentrations. The inset to Figure 6a emphasizes this point as the critical stress (σc) is linearly related to η0. Since PEO becomes difficult to disperse in water at 25 °C at above about 3%, no measurements are made for systems with more than 2% PEO. Nonetheless, Figure 6a shows that the critical shear rate is nearly independent of the PEO concentration, while η0 increases by a decade at 2% PEO. The numbers given in parentheses are estimates of the number of micelles per polymer chain, based on 〈nagg〉 ) 120 and reported polymer molecular weight. HPC has very different effects on CTAT rheology; Figure 6b shows that at dilute concentrations, the addition of HPC to 0.5 wt % CTAT/H2O has little effect on η0 while the critical shear rate more than doubles. At c g 0.25% HPC, no apparent shear-thickening is detected within the usable range for this geometry. At higher concentrations (c g 0.5%), where there are one or more HPC chains

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high q, the scattered intensity, I(q), decreases as q-2. This is characteristic of particles of finite cross section, as given by micellar cross section. For disordered, monodisperse cylindrical objects with radius R and length L, the scattered intensity I(q) as a function of scattering vector (q) is given by33

I(q) ) 4πN(∆F)2

(

)

V2 J1(qR) qL qR

2

(1)

where N is the number density of cylinders, V is the volume of a cylinder, ∆F is the scattering length density difference between CTAT and D2O, and J1 is the first-order Bessel function. The expression can be simplified to

(

)

J1(qR) qI(q) )4 qR qI(qf0)

Figure 6. Effect of polymer on the rheology of 0.5% CTAT/ H2O: (a) PEO (c* ∼ 0.5% PEO) with inset figure of critical stress as a function of zero-shear viscosity, and (b) HPC (c* ∼ 1.0% HPC). Numbers in parentheses indicate approximate number of micelles per polymer chain.

Figure 7. Scattered intensity as a function of scattering vector for 0.5% CTAT/D2O at 25 °C (O). Heavy line indicates fit for micellar radius, R ) 20.6 Å. Other lines indicate I(q) ∼ qn, where n is -1 or -2 depending on q-range.

per micelle, increasing amounts of HPC increase η0, and again no shear-thickening is detected. The rheology is clearly arising from a composite effect of the two components. The η0 of 2% HPC is 8 cP, lower than that of 0.5% CTAT-2% HPC (11 cP). 3.3. Structural Studies. To assess the microstructural changes responsible for the drastically different effects on CTAT rheology, both quiescent and shear SANS are performed on mixed systems of 0.5% CTAT-polymer in D2O. At rest, the scattering intensity from 0.5% CTAT at 25 °C as a function of q is shown in Figure 7, typical of charged, wormlike micelles.6 The scattering vector, q, is defined as q ) (4π/λ) sin (θ/2), where θ is the scattering angle. At

2

(2)

which is shown as a solid line in Figure 7. From fitting the only parameter in eq 2, the radius of 0.5% CTAT micelles is 20.6 ( 0.5 Å. This is consistent with 21 ( 0.4 Å as reported by Gamez-Corrales et al. for 0.41% CTAT/ D2O.23 At slightly lower q, I(q) decreases as q-1, which indicates local rigid rodlike behavior in the system. For decreasing q, I(q) exhibits an interaction, or correlation, peak indicating there are electrostatic interactions present. The scattering vector qxo is defined as follows: On a Holtzer plot (qI(q) vs q), a line is fit to the power law decay of the correlation peak. The intersection of this line with the horizontal (I ∼ q-1) is defined as qxo. For uncharged systems, qxo is inversely related to micellar persistence length (lp), such that qxolp ∼ 3.2.34 In this work, electrostatic interactions cannot be ignored as shown by the correlation peak. Here qxo is characteristic of both micellar charge and flexibility. At even lower q, the intermicellar interactions are coupled to the overall length of the micelles. Although decoupling these two characteristics using solely these SANS results is not possible, various estimates for micellar length can be made. These are presented in the following section. The effect of electrostatic interactions is examined by similar experiments with added salt. Bending rod or Holtzer plots provide a demonstrative technique to separate scattering from different length scales in these systems.35,36 Figure 8 is a Holtzer plot of 0.5% CTAT with varying NaCl concentration. Added salt influences scattering at intermediate and low q (106 >106 >106

10-30 (18) 20-30 (18) 20-30 (18) 120-194 (116) 778-1167 (771) >3890

a Critical shear rates as determined by empirical fits (eq 4) are shown in parentheses.

Table 2. Empirical Parameters for 0.5% CTAT-Polymer Systems at 25 °Ca added polymer

a

b

none 0.113% PEO 0.167% PEO 0.05% HPC 0.5% HPC 0.8% HPC

10.9 10.9 10.9 214.7 1019.3 n/a

0.825 0.825 0.825 1.130 1.042 n/a

Figure 11. Characteristic scattering angle qxo as a function of increased alignment, showing that qxo tracks Af despite the polymer composition of the system: (b) no polymer, (0) 0.05% HPC, (4) 0.5% HPC, (]) 0.8% HPC, (O) 0.113% PEO, (3) 0.167% PEO, and (s) eq 5.

from rheology, showing that the onset of structural alignment coincides with the shear-thickening transition. The use of different gap sizes in rheological and SANS experiments shows that elastic instabilities cannot explain structural alignment in these systems. As found in rheological measurements, the addition of PEO to 0.5% CTAT has little effect on the critical shear rate. In the cases with HPC, increasing concentrations of HPC increase the critical shear rates. At the highest HPC concentration (0.8%), Af remains low even at very high shear rates (close to 4000 s-1). The shear rate dependence of the increase in steady-state Af can be described by the empirical relation

single relation between qxo and Af for all the systems. On comparison of these data to a more limited data set collected on systems between 0.2 and 0.7% CTAT and 25 and 35 °C,21 this trend depends weakly on temperature and strongly on surfactant concentration, but the same sort of single relation exists for a given set of conditions. From these results, there is a clear difference between the effects of polymer on CTAT systems in the aligned and isotropic states; from rheology, we found that PEO and HPC have very different effects on the onset of shearinduced transition. As shown by quiescent SANS, both polymers affect micellar interactions and/or length. Yet once the transition occurs, these interactions are independent of the polymer composition of the system. Unfortunately, our inability to relate qxo to an electrostatic or flexibility parameter makes more concrete statements about the conformation in the sheared state tenuous.

Af(γ˘ c) ) 1 - aγ˘ cb

4. Discussion

a

Values do not apply to 0.5% CTAT-0.8% HPC due high values of critical shear rate.

(4)

where γ˘ c is critical shear rate and a and b are fitted parameters given in Table 2. Note that for 0.5% CTAT0.8% HPC, these fitted parameters are not reported due to low (although nonzero) levels of alignment only at very high shear rates, near the limits of the instrument. For the 0.5% CTAT systems without polymer and with PEO, critical shear rates are consistent with those from rheological measurements. In the cases with HPC, critical shear rates are not detected within the usable range for the geometry used in rheological measurements. To relate changes in the transition state to micellar properties, qxo is examined as a function of Af. Figure 11 shows that at low levels of alignment, qxo is sensitive to the type and amount of added polymer. At higher degrees of alignment (Af g 0.2), qxo is related to Af by the empirical relation

qxo ) 0.022(1 - 0.2Af2)

(5)

regardless of the polymer composition in the system. That is, there is a universality in micellar electrostatic interactions and/or flexibility in the aligned (transition) state. For example, the values of qxo increase from 0.020 to 0.024 Å-1 upon adding 0.5% HPC to 0.5% CTAT at rest. The critical shear rate also increases. Once the system goes through its shear-induced transition, there is roughly a

The flow-induced transition found in this work has been observed previously in other shear-thickening systems.1-12 This work shows that the transition cannot be explained by inertial or a simple elastic flow instability; similar critical shear rates are acquired in the controlled stress rheometer with 1.2 mm gap (rheological measurements) and in the rate-controlled device with 0.5 mm gap (SANS). The apparent shear-thickening is also reversible. That is, similar results are obtained with increasing and decreasing stress. Thebaud found that CTAT undergoes a shearinduced transition in Poiseuille flow, showing that the transition is not attributed to the curved streamlines in Couette flow.21 Rheological measurements show that subtle changes in the architecture of an added macromolecule drastically influence the shear rate necessary for the shear-induced transition; systems of PEO, 0.167% and 0.113%, are chosen to be of the same molar (5.6 µM) and volume composition (26 vol %) as 0.05% HPC, respectively. Both polymers have similar degrees of hydrophobicity per monomer unit (based on simple chemical inventory). HPC shows more binding to CTAT than PEO, though weak by comparison to systems involving anionic surfactants. Despite this, their effects on CTAT rheology are extremely different; at low levels of deformation, HPC suppresses the critical behavior of CTAT, while PEO increases the equilibrium viscosity of the system with little effect on the apparent

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Truong and Walker

shear-thickening transition. Even though ηo and critical shear rates vary slightly in D2O as shown by comparing values in Table 1 (in D2O) and Figure 6 (in H2O), the qualitative effects of polymer are the same in both solvents. Under shear, decreasing qxo suggests that persistence length may increase with increasing alignment. This inverse relationship is established for uncharged, cylindrical particles.34,37 It is unlikely that this simple relation holds for the alignment of charged wormlike objects. Figure 8 demonstrates convincingly that it is not possible to comment on the flexibility of the micelles through a simple inverse relationship between qxo and lp, because the scattering from electrostatics interactions cannot be decoupled from either the persistence length or the overall length of the micelles. Therefore, a full model that accounts for electrostatic interactions would be necessary to quantify this relation. If we ignore electrostatics, we may use various techniques to extract a value for micellar length with models for uncharged, semiflexible, wormlike micelles. One method is to examine a Guinier-like plot of 0.5% CTAT/ D2O. By use of a model based on a Guinier approximation,38 micellar dimensions can be calculated; with 0.045 e q e 0.09 Å-1, the cross sectional radius is 20.7 Å, agreeing well our SANS result of R ) 20.6 ( 0.5 Å presented in the previous section. On the basis of 〈nagg〉 of 120, the micellar length is 160 Å. It is also possible to calculate micellar length using eq 2; when fitting for the radius, the value of qI(q) as q approaches zero is 8.4 × 106 cm-2. By use of this value in eq 1, the quantity NL is 4.0 × 1010 cm-2. The volume fraction of micelles, φ, is given by

φ ) NπR2L ) (cNa/M〈nagg〉)(πR2L)

(6)

where c is concentration of CTAT, Na is Avogadro’s number, and M is the molecular weight of CTAT. For 0.5% CTAT, φ is 0.0053 and micellar length (L) is 72 Å. With standard static light scattering techniques, the approximate static correlation length of CTAT rods is measured to be 340 ( 40 Å, which is much larger than those rendered from the argument above. The primary reason is that both models are based on intermediate and high q scattering and do not account for electrostatic interactions. Consequently, extracting micellar length based on SANS results without a full model is incorrect in this case. On the basis of evidence from characterization, rheological, and structural studies, the following hypothesis of the effects of polymer on CTAT micelles is presented. In the cases with added PEO, the polymer acts mainly to increase the solvent viscosity and quality. These changes are supported by the small deviations in CTAT conductivity and fluorescence and variations in SANS data at low q. Although the mobility of the micelles is somewhat decreased, compared to systems without PEO, similar (37) Kirste, R.; Oberthur, R. Small-angle X-ray scattering; Academic Press: New York, 1982. (38) Magid, L.; Han, Z.; Li, Z. Langmuir 2000, 16, 149.

amounts of deformation (shear rates) are required for the onset of shear-induced transition. CTAT/PEO would therefore be a model system for understanding interaction between polyelectrolyte (living or quenched) and nonionic polymer. HPC has hydrophobic side chains, which are conformationally more available as sites of hydrophobic interaction with the core of the CTAT micelles when compared to PEO. This is consistent with the variations in high q scattering. As stated earlier, the overall degree of binding remains low because the micelles greatly outnumber the polymer chains in the dilute cases of HPC. Under shear, this interaction is sufficient to hamper the mobility of the micelles. Therefore, higher levels of deformation are required to align the micelles as seen in increases in the critical shear rate. In more concentrated HPC systems, HPC is able to suppress the transition as seen in 0.5% CTAT-0.8% HPC. At high HPC concentrations, the polymer may be networking micelles, similar to the picture presented by Pfeiffer of the association of rodlike micelles and hydrophobically modified polymers.39 In the systems that exhibit shear-induced transitions, micellar interaction and flexibility are dominated by the aligned structure. The effects of either polymer are inconsequential as seen by the universality of qxo at high levels of alignment. 5. Conclusions This work demonstrates that nonionic polymer can be used to tune the rheology of cationic wormlike micelles. Low concentrations of HPC change the onset of CTAT shear-thickening transition, suppressing transition at higher concentrations. PEO affects the equilibrium viscosity with little change to the onset of the transition. The source of increases in critical shear rate with the addition of HPC may be the availability of its hydrophobic moieties, i.e., side groups. This is supported by variations in SANS spectra at high q values. SANS shows that both polymers affect micellar interactions and/or length at rest, with no change to micellar shape or radius. By use of shear SANS, micellar charge and/or flexibility are key to the onset of the transition. On the other hand, the growth of the aligned state is somewhat universal; despite their very different effects on the critical shear rate of the transition, PEO and HPC do not affect micellar flexibility and/or interactions during the evolution of the aligned state. The structure formed under shear clearly dominates these effects. Acknowledgment. This work made possible by funding from the National Science Foundation (NSF CTS9753157). SANS experiments were performed at NIST through funding from the NSF under agreement no. DMR9423101. The authors wish to thank J.-F. Berret for stimulating discussions. LA0006263 (39) Pfeiffer, D. Polymer 1990, 31, 2553.