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Solution Properties of Micelle Networks Formed by Nonionic Surfactant Moieties Covalently Bound to a Polyelectrolyte: Salt Effects on Rheological Behavior Tetsuya Noda, Akihito Hashidzume, and Yotaro Morishima* Department of Macromolecular Science, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan Received December 8, 1999. In Final Form: March 21, 2000 Rheological properties of aqueous solutions of micelle networks formed by a copolymer of sodium 2-(acrylamido)-2-methylpropanesulfonate (AMPS) and an associative macromonomer, methacrylate substituted with HO(CH2CH2O)25C12H25 (C12E25) (20 mol % content in the copolymer), were investigated as a function of the polymer concentration (Cp), added salt concentration ([NaCl]), and shear stress. The polymer-bound C12E25 surfactant moieties form micelles via intra- and interpolymer association. These polymer-bound micelles are bridged by polymer chains and hence form a network structure. The solution viscosity of this micelle network increases markedly with increasing Cp near 10 g/L (at [NaCl] ) 0.10 M) and beyond this Cp the number of micelle bridges greatly increases with increasing Cp. The extent of the micelle bridging depends on [NaCl]. When Cp is sufficiently high, where interpolymer associations are favorable, steady-state viscosity measured at a low-shear rate increases with increasing [NaCl], exhibiting a maximum value at [NaCl] ≈ 0.13 M (at Cp ) 25.0 g/L), and then decreases as [NaCl] is further increased. The micelle network solutions exhibit shear-dependent viscosity behavior, i.e., Newtonian behavior at low shear rates (200 s-1). Furthermore, the solutions behave as a viscoelastic fluid at low polymer concentrations (Cp e 25.0 g/L) but they show significant elastic properties with increasing Cp, both storage and loss moduli increasing greatly with increasing Cp and the two moduli becoming close to each other. When Cp is increased to ca. 100 g/L or higher, the micelle network system exhibits gel-like behavior with a plateau modulus (G0) increasing markedly with increasing Cp whereas a terminal relaxation time (λ) remaining practically the same (ca. 10 ms). The value of G0 increases with increasing [NaCl], passing through a maximum at [NaCl] ≈ 0.13 M (at Cp ) 25 g/L), and then decreases with further increasing [NaCl]. Thus, the viscosity is virtually governed by G0 but not by λ. The micelle bridge is dynamic in nature, which makes the disruption and re-formation of the micelle bridge occur reversibly in response to external stimuli.
Introduction There has been increasing interest, in recent years, in a class of hydrophobically modified polymers that undergo spontaneous structural organization in water mainly derived from hydrophobic associations to form various types of micellelike nanostructures.1-3 Amphiphilic polyelectrolytes are among such polymers that have been extensively studied in the past decade.4-11 Considerable interest has been directed toward amphiphilic random copolymers of electrolyte monomers and hydrophobic comonomers possessing a hydrophobe in the side chain because of their ease of synthesis and a wide range of monomer selections as compared to the case of block (1) McCormick, C. L.; Bock, J.; Schulz, D. N. Water-Soluble Polymers. In Encyclopedia of Polymer Science and Engineering, 2nd ed.; Kroschwitz, J. I., Ed.; John Wiley: New York, 1989; Vol. 11. (2) Laschewsky, A. Adv. Polym. Sci. 1995, 124, 1. (3) Morishima, Y. In Solvents and Self-Organization of Polymers; Webber, S. E., Tuzar, D., Munk, P., Eds.; Kluwer Academic Publishers: Dordrecht, The Netherlands, 1996; p 331 and references therein. (4) McCormick, C. L.; Armentrout, R. S.; Cannon, G. C.; Martin, G. G. In Molecular Interactions and Time-Space Organization in Macromolecular Systems; Morishima, Y., Norisuye, T., Tashiro, K., Eds.; Springer-Verlag: Berlin, 1999; p 125 and references therein. (5) Webber, S. E. J. Phys. Chem. B 1998, 102, 2618 and references therein. (6) McCormick, C. L.; Chang, Y. Macromolecules 1994, 27, 2151. (7) Chang, Y.; McCormick, C. L. Macromolecules 1993, 26, 6121. (8) McCormick, C. L.; Salazar, L. C. Polymer 1992, 23, 4617. (9) Zhang, L.; Shen, H.; Eisenberg, A. Macromolecules 1997, 30, 1001. (10) Zhang, L.; Eisenberg, A. Science 1995, 268, 1728. (11) Astafieva, I.; Zhong, Z. F.; Eisenberg, A. Macromolecules 1993, 26, 7339.
copolymers.3,4,6-8 It has been well-documented that associative properties of hydrophobically modified polyelectrolytes strongly depends on macromolecular architectures in the case of such amphiphilic random copolymers. Among various structural parameters that influence associative properties,12-20 a spacer bond between hydrophobes and the polymer backbone is an important structural factor that controls the associative behavior of polymer-bound hydrophobes.18-20 This is due to the fact that in the process of the self-association of polymer-bound hydrophobes, polymer chains impose steric constraints to the hydrophobes and thus affect the motional and hence geometrical freedom of the hydrophobes. In our earlier work, we synthesized random copolymers of sodium 2-(acrylamido)-2-methylpropanesulfonate (AMPS) and a methacrylate substituted with a nonionic surfactant moiety HO(CH2CH2O)25C12H25 (C12E25), the (12) Kramer, M. C.; Welch, C. G.; Steger, J. R.; McCormick, C. L. Macromolecules 1995, 28, 5248. (13) Hu, Y.; Kramer, M. C.; Boudreaux, C. J.; McCormick, C. L. Macromolecules 1995, 28, 7100. (14) Branham, K. D.; Snowden, H. S.; McCormick, C. L. Macromolecules 1996, 29, 254. (15) Kramer, M. C.; Steger, J. R.; Hu, Y.; McCormick, C. L. Macromolecules 1996, 29, 1992. (16) Hu. Y.; Smith, G. L.; Richardson, M. F.; McCormick, C. L. Macromolecules 1997, 30, 3526. (17) Hu. Y.; Armentrout, R. S.; McCormick, C. L. Macromolecules 1997, 30, 3538. (18) Morishima, Y.; Nomura, S.; Ikeda, T.; Seki, M.; Kamachi, M. Macromolecules 1995, 28, 2874. (19) Yusa, S.; Kamachi, M.; Morishima, Y. Langmuir 1998, 14, 6059. (20) Noda, T.; Morishima, Y. Macromolecules 1999, 32, 4631.
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content of the methacrylate-end-capped C12E25 macromonomer (DE25MA) unit (fDE25) ranging from 10 to 30 mol %.21 These polymers can be visualized as a “polymeric” surfactant system in which numbers of surfactant fragments are linked to a polyelectrolyte backbone. It is expected that, since the (CH2CH2O)25 spacer is a flexible chain, dodecyl groups at an end of the spacer chain can move freely and therefore they can easily associate with other hydrophobes on the same polymer chain as well as on different polymer chains. Furthermore, the polyAMPS backbone and the (CH2CH2O)25 spacer chain are highly hydrated in water and thus the terminal dodecyl groups at an end of the spacer should be microscopically phaseseparated by being excluded from the hydrophilic macromolecular environment. In such a situation, dodecyl groups would preferably associate with one another. A similar type of polymers, known as associating thickening (AT) polymers, has been extensively studied.22-33 Some of these AT polymers and their model polymers reported so far include copolymers of acrylamide or (meth)acrylic acid with associative comonomers containing a (CH2CH2O)n chain as a spacer between a polymerizable moiety at one end and a terminal hydrophobe at the other end.22-28 The contents of associative comonomers in AT copolymers are usually very low, i.e., ∼5 mol % at the highest (normally, lower than 2 mol %). In general, these polymers are designed, from a practical point of view, such that a largest extent of interpolymer association can be achieved with a smallest amount of hydrophobes incorporated in a water-soluble polymer. A major difference between these AT polymers and the polymer in the present study is the amount of associative macromonomers incorporated in a polymer chain. This work focuses on self-organization of the polymer derived from micellization of polymer-bound surfactant moieties rather than on thickening efficiency arising from interpolymer hydrophobic associations. Therefore, we incorporated a much larger number of surfactant comonomer units into a polyelectrolyte chain. To this end, we employed AMPS, a strong electrolyte monomer, to render the copolymer water soluble up to a high loading amount of the associative macromonomer unit. We previously investigated the association behavior of the polyAMPS-bound C12E25 moieties in 0.1 M NaCl aqueous solutions using fluorescence (using pyrene as a probe) and quasielastic light scattering (QELS) techniques.21 Characterization results indicated that the polymer-bound C12E25 moieties form micelles that are somewhat similar in aggregation number to those formed by discrete C12E25 molecules. The polymer-bound micelle
consists of the C12E25 moieties mostly on the same polymer chain, but some surfactant groups on different polymer chains occupy the same micelle and hence the polymerbound micelles are interconnected with polymer chains, forming a network structure. The polymer-bound C12E25 micelles have a mean aggregation number (Nagg) of the terminal dodecyl groups ranging from 50 to 70 depending on fDE25. These values are not much different from that found for discrete C12E25 micelles (Nagg ≈ 40) under the same conditions. In this paper, we report on aqueous solution properties of this copolymer in dilute, semidilute, and concentrated regimes with a focus on the effect of added salt on rheological properties.
(21) Noda, T.; Hashidzume, A.; Morishima, Y. Macromolecules, in press. (22) Hwang, F. S.; Hogen-Esch, T. E. Macromolecules 1995, 28, 3328. (23) Schultz, D. N.; Kaladas, J. J.; Maurer, J. J.; Bock, J.; Pace, S. J.; Schultz, W. W. Polymer 1987, 28, 2110. (24) Kumacheva, E.; Rharbi, Y.; Winnik, M. A.; Guo, L.; Tam, K. C.; Jenkins, R. D. Langmuir 1997, 13, 182. (25) Horiuchi, K.; Rharbi, Y.; Spiro, J. G.; Yekta, A.; Winnik, M. A.; Jenkins, R. D.; Bassett, D. R. Langmuir 1999, 15, 1644. (26) Tirtaatmadja, V.; Tam, K. C.; Jenkins, R. D. Macromolecules 1997, 30, 1426. (27) Tirtaatmadja, V.; Tam, K. C.; Jenkins, R. D. Macromolecules 1997, 30, 3271. (28) Tam, K. C.; Farmer, M. L.; Jenkins, R. D.; Bassett, D. R. J. Polym. Sci., Part B: Polym. Phys. 1998, 36, 2275. (29) McCormick, C. L.; Nonaka, T.; Johnson, C. B. Polymer 1988, 29, 731. (30) Biggs, S.; Selb, J.; Candau, F. Polymer 1993, 34, 580. (31) Volpert, E.; Selb, J.; Candau, F. Macromolecules 1996, 29, 1452. (32) Klucker, R.; Candau, F.; Schosseler, F. Macromolecules 1995, 28, 6416. (33) Branham, K. D.; Davis, D. L.; Middleton, J. C.; McCormick, C. L. Polymer 1994, 35, 4429.
where I(t) and I(0) are the fluorescence intensities at time t and 0 following laser-pulse excitation, respectively, kQ is the pseudofirst-order rate constant for quenching of excited pyrene, k0 ()τ0-1) is the fluorescence decay rate constant for pyrene inside the micelle without excimer formation, [Q]m is the molar concentration of quencher inside micelle, and [M] is the molar concentration of micelles. Because the quenching of monomeric pyrene fluorescence is due to the excimer formation of pyrene in this study, [Q]m corresponds to the concentration of pyrene. The [Q]m/[M] ratio was determined from the best fit. Values of Nagg were calculated from the [Q]m/[M] ratios. Details of the experimental procedures have been reported elsewhere.20,21
Experimental Section Materials. Poly(ethylene oxide) mono-n-dodecyl ether of a number average degree of polymerization of 25 (DE25OH) (TCI Co.) and AMPS (Wako Pure Chemical Co.) were used without further purification. N,N-Dimethylformamide (DMF) were distilled under reduced pressure over calcium hydride. 2,2′Azobisisobutyronitrile (AIBN) was recrystallized from ethanol. Pyrene was recrystallized twice from ethanol. Water was purified with a Millipore Milli-Q System. Other reagents were used as received. A methacrylate-end-capped nonionic surfactant macromonomer (DE25MA) was prepared according to the procedure reported previously.21 A copolymer of AMPS and DE25MA with a DE25MA content of 20 mol % was prepared by AIBN-initiated free radical copolymerization in a homogeneous solution in DMF.21 The composition of the copolymer determined by 1H NMR spectroscopy was the same as that in the monomer feed. Measurements. (a) Specific Viscosity. Specific viscosity measurements were performed with polymer solutions in 0.1 M NaCl using a modified Ubbelohde type viscometer at 25.0 °C. Reduced viscosity was plotted against polymer concentration to estimate the intrinsic viscosity. (b) Aggregation Number. Aggregation numbers (Nagg) of polymer-bound C12E25 surfactants were determined by a timeresolved fluorescence technique using pyrene as a probe. Pyrene was solubilized in polymer hydrophobic microdomains at its concentration high enough for excimer to be formed within the hydrophobic microdomain. Sample solutions were prepared by adding a small amount of a concentrated pyrene solution in acetone to aqueous solutions of the polymer and heated at 50 °C for 12 h. All sample solutions were filtered with a 0.20 µm membrane filter prior to measurement. The quenching of monomeric pyrene fluorescence, resulting from excimer formation, was used to determine Nagg by fitting monomeric pyrene fluorescence decay data to the Infelta-Tachiya equation20,21,34-36
ln[I(t)/I(0)] ) ([Q]m/[M])[exp(-kQt) - 1] - k0t
(1)
(34) (a) Infelta, P. P.; Gra¨tzel, M.; Thomas, J. K. J. Phys. Chem. 1974, 78, 190. (b) Tachiya, M. Chem. Phys. Lett. 1975, 33, 289. (c) Infelta, P. P. Chem. Phys. Lett. 1979, 61, 88. (35) Tachiya, M. In Kinetics of Nonhomogeneous Processes; Freeman, G. R., Ed.; John Wiley & Sons: New York, 1987; Chapter 11, pp 575650. (36) Yekta, A.; Aikawa, M.; Turro, N. J. Chem. Phys. Lett. 1979, 63, 543.
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Chart 1. AMPS-DE25MA Copolymer
(c) Quasielastic Light Scattering (QELS). QELS data were obtained at 25 ( 0.1 °C with an Otsuka Electronics Photal DLS7000 light scattering spectrometer equipped with an Ar laser (60 mW at λ ) 488 nm) and an ALV-5000 multi-τ digital time correlator. Sample solutions were filtered with a 0.45 µm membrane filter prior to measurement. The diffusion coefficient, D, and the apparent hydrodynamic radius, Rh, were calculated as reported previously.20,21 (d) Rheometric Analysis. The rheological properties of the copolymers were measured on a DynAlyser 100 stress-control rheometer (RheoLogica) equipped with a cone and plate at 25 °C. The radius of the cone is 40 mm, and the angle between the cone and plate is 4.0°. Steady shear and oscillatory flow measurements were conducted to obtain the steady shear viscosity and dynamic viscoelastic properties of polymer solutions.
Figure 1. Reduced viscosity in 0.1 M NaCl (at 25 °C) as a function of polymer concentration.
Results and Discussion Characteristics of the Copolymer. Copolymerizations of water-soluble monomers and surfactant macromonomers can be carried out in either aqueous or organic media in the presence or absence of nonpolymerizable surfactants.37,38 In “micelle” or “emulsion” polymerization in aqueous media, copolymers with a blocky distribution of the surfactant comonomer are likely to be formed,37 whereas in solution polymerization in organic media, copolymers with a random distribution are formed. To obtain a copolymer with a random distribution of AMPS and DE25MA units along the polymer chain, we employed a solution polymerization method using DMF as a solvent. Both the monomers and copolymer yielded are soluble in DMF, and therefore the copolymerization proceeds in a homogeneous solution. Apparent number- and weightaverage molecular weights of the AMPS-DE25MA copolymer employed in this study (Chart 1) were roughly estimated to be Mn ) 3 × 104 and Mw ) 8 × 104, respectively, from gel permeation chromatography (GPC) data obtained by using methanol (containing 0.10 M LiClO4) for an eluent and standard poly(ethylene oxide) samples for calibration. From the copolymer composition (fDE25 ) 20 mol %) and Mn, the number of the surfactant units per polymer chain is roughly calculated to be ca. 15. The polymer-bound C12E25 surfactant moieties associate in both intra- and interpolymer fashions and form C12E25 micelles that are bound to the polymer backbone.21 The interpolymer hydrophobic association commences to occur at a relatively well-defined polymer concentration of ca. 0.021 g/L, which corresponds to 9.1 × 10-6 M of the residual concentration of the C12E25 units.21 This apparent critical micelle concentration (cmc) was estimated from fluorescence excitation spectra of solubilized pyrene probes using a method reported by Wilhelm et al.39 and found to be ca. 30 times lower than that for discrete C12E25 surfactants. (37) (a) Ezzell, S. A.; Hoyle, C. E.; Greed, D.; McCormick, C. L. Macromolecules 1992, 25, 1887. (b) Hill, A.; Candau, F.; Selb, J. Macromolecules 1993, 26, 4521. (c) Dowling, K. C.; Thomas, J. K. Macromolecules 1990, 23, 1059. (38) (a) Ito, K.; Tanaka, K.; Tanaka, H.; Imai, G.; Kawaguchi, S.; Itsuno, S. Macromolecules 1991, 24, 2348. (b) Ito, K.; Kobayashi, H. Polym. J. 1992, 24, 199.
Figure 2. Plots of the aggregation numbers as a function of polymer concentration at varying concentrations of added salt.
Viscosity of Dilute Solutions. Reduced viscosity data obtained with a capillary viscometer at 25 °C for the copolymer in 0.1 M NaCl aqueous solutions are presented in Figure 1. The plot of the reduced viscosity as a function of the polymer concentration (Cp) can be approximately fitted to a linear line. An apparent intrinsic viscosity ([η]) value was estimated to be [η] ) 0.15 dL/g by extrapolating the reduced viscosity plot to zero concentration of the polymer. The polymer shows an unusually large Huggins constant (KH) of 12.6. This large KH value would suggest the presence of interpolymer interactions in the Cp regime investigated. Similar behavior has been reported for copolymers of acrylamide and surfactant macromonomers23 and also for model polymers of hydrophobically modified alkali swellable/soluble emulsions (HASE).28 As will be discussed in the following subsections, the polymerbound C12E25 surfactant groups associate not only on the same polymer chain but also on different polymer chains in the Cp range for the viscosity measurements. Therefore, the reduced viscosity in Figure 1 is not for a single polymer chain but for polymer aggregates. Aggregation Number of Polymer-Bound C12E25 Surfactant Moieties. Figure 2 shows Nagg (i.e., the average number of dodecyl groups per micelle core) plotted against the polymer concentration at varying concentrations of added salt ([NaCl]). These Nagg values were obtained by a time-dependent fluorescence method based on the excimer formation of pyrene probes solubilized in the micelle core.20,21,34-36,40-42 For the calculation of Nagg, (39) Wilhelm, M.; Zhao, C.-L.; Wang, Y.; Xu, R.; Winnik, M. A.; Mura, J.-L.; Riess, G.; Croucher, M. D. Macromolecules 1991, 24, 1033. (40) Yekta, A.; Xu, B.; Duhamel, J.; Adiwidjaja, H.; Winnik, M. A. Macromolecules 1995, 28, 956.
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Figure 3. Dependence of the aggregation number on the concentration of added salt at Cp ) 12.5 g/L.
pyrene monomeric fluorescence decay data were fitted to eq 1 (see Experimental Section). Equation 1 assumes that all pyrene probes are randomly distributed over the micelles according to a Poisson distribution and that distributions of fluorophores and quenchers over the micelles are frozen on the time scale of the fluorescence lifetime. As can be seen in Figure 2, the value of Nagg is dependent on [NaCl] whereas it is independent of Cp in the whole range of Cp studied. Thus, it can be concluded that polymer-bound micelle cores conserve their size over a significant range of Cp (e12.5 g/L) at a constant [NaCl] (e0.40 M). With increasing concentration of added salt, the size of the polymer-bound micelle increases at all polymer concentrations studied. In Figure 3, the Nagg value at Cp ) 12.5 g/L is plotted against the concentration of added salt. The Nagg value increases gradually with increasing [NaCl] when [NaCl] e 0.15 M, but it increases more significantly at higher salt concentrations. Hydrodynamic Size of Micelles Bridged by Polymer Chains. To clarify the effects of the concentrations of the polymer and added salt on the hydrodynamic size of the polymers cross-linked by the C12E25 micelles, we measured QELS at varying concentrations of the polymer and NaCl. Figure 4 compares relaxation time distributions in QELS at varying polymer concentrations in 0.1 M NaCl aqueous solutions observed at a scattering angle of 90°. When Cp e 18.8 g/L, the QELS relaxation time distributions are bimodal with a slow relaxation mode as a major component and a fast relaxation mode as a minor component. The slow-mode component is attributed to assemblies of C12E25 micelles bridged by polymer chains, and the fast-mode component may be attributed to a “unimeric” micelle (a micelle formed by a single polymer chain) or an “oligomeric” micelle (a micelle formed by a small number of polymer chains). At Cp g 25.0 g/L, the relaxation time distributions are unimodal and the distribution peak shows a tendency to shift toward longer relaxation times with increasing polymer concentration. It is to be noted that the width of the distribution peak becomes broader on going from Cp ) 25.0 to 50.0 g/L. To assess apparent hydrodynamic radii (Rh) for the bridged micelles, we measured QELS at several different scattering angles. At Cp e 18.8 g/L, plots of the relaxation rates (Γ) (i.e., the reciprocal of the relaxation time) against the square of the scattering vector (q2) were found to yield straight lines going through the origin (data not shown). (41) Xu, B.; Li, L.; Yekta, A.; Masoumi, Z.; Kanagalingam, S.; Winnik, M. A.; Zhang, K.; Macdonald, P. M.; Menchen, S. Langmuir 1997, 13, 2447. (42) Xu, B.; Zhang, K.; Macdonald, P. M.; Winnik, M. A.; Jenkins, R. D.; Bassett, D. R.; Wolf, D.; Nuyken, O. Langmuir 1997, 13, 6896.
Figure 4. Relaxation time distributions in QELS observed at a scattering angle of 90° at varying concentrations of the polymer in 0.1 M NaCl.
Figure 5. Relationship between Rh and the polymer concentration in 0.1 M NaCl.
From the slope of the Γ-q2 plot, we estimated apparent diffusion coefficients from which Rh values were calculated using the Einstein-Stokes relation. At higher polymer concentrations (Cp g 25.0 g/L), the Γ-q2 plots were found to deviate from the linear relationship particularly in a region of large q2 values. However, as a rough estimate of the hydrodynamic size, we roughly estimated Rh values from the slope of the Γ-q2 plot within a narrow range of small q2 values. In Figure 5, Rh values thus estimated are plotted as a function of the polymer concentration over a wide Cp range of 0.195-37.5 g/L. In a low Cp region (Cp
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Figure 6. Dependence of the apparent hydrodynamic radius on the concentration of added salt for varying concentrations of the polymer.
Figure 7. Dependence of the low-shear viscosity on the polymer concentration. Shear rate applied for the measurement is 0.1 s-1 at 25 °C.
e 18.8 g/L) where the relaxation time distributions are bimodal, Rh values for the slow relaxation mode are plotted in Figure 5. In a low Cp region, Rh increases from ca. 80 to 120 nm when Cp is increased from ca. 0.2 to 7.0 g/L. In the higher Cp region (Cp g 25.0 g/L), Rh values are only rough estimates but it is clear that Rh increases markedly with increasing polymer concentration. Although the polymer-bound C12E25 micelle cores conserve their size over a significant range of polymer concentrations (Figure 2), the hydrodynamic size of the polymer increases significantly with increasing polymer concentration. This means that the extent of micelle bridging by polymer chains increases with increasing polymer concentration whereas the size of the polymerbound C12E25 micelle (i.e., Nagg) remains unchanged. This micelle bridging occurs when some C12E25 moieties on different polymer chains occupy the same micelle. The sharp increase in Rh at Cp near 20 g/L (Figure 5) is indicative of the formation of a larger network structure made up of an increased number of bridged micelles with increasing Cp. An observation to be noted here is that at high polymer concentrations, Rh values are much larger than the pore size of the membrane filter (450 nm) used to filter sample solutions prior to QELS measurement. For example, a solution of Cp ) 37.5 g/L passes through the filter by applying a small pressure with an ordinary glass syringe. The sample solution filtered repeatedly with the same type of new filters resulted in the identical QELS data regardless of the repeating number of the filtration. This observation suggests that the bridged polymer micelles are sheared into entities with a smaller size when they are forced to pass through pores of the filter and after passing through the pore they associate back to the bridged micelles of the original size. This will be discussed more in detail in the following subsection. Values of Rh were estimated at varying concentrations of added salt at Cp ranging from 1.0 to 18.8 g/L (Figure 6). The hydrodynamic size decreases progressively with increasing salt concentration over an [NaCl] range of 0.020.4 M. This trend is in contrast to that for the aggregation number; Nagg increases with increasing [NaCl] (Figure 3). These observations indicate that with increasing salt concentration, the extent of micelle bridging decreases whereas the core size of the polymer-bound C12E25 micelle increases. The extent of micelle bridging is governed by the number of polymer chains that participate in the formation of the same micelle. As the salt concentration is increased, the micelle tends to be formed by a decreased number of polymer chains although Nagg increases.
Therefore, it is concluded that the tendency for the intrapolymer association of polymer-bound surfactants increases as the salt concentration is increased. Steady Shear Viscosities of Semidilute and Concentrated Solutions. Low-shear viscosities of polymer solutions measured at a shear rate of 0.1 s-1 are presented in Figure 7 as a function of the polymer concentration at [NaCl] ) 0.10 and 0.35 M. The solutions are Newtonian at this low shear rate (see later subsection), and thus the viscosities are regarded as zero shear viscosities. At [NaCl] ) 0.10 M, the viscosity increases gradually with increasing polymer concentration in the low Cp region ( ca. 0.1 M, and the extent of the shear thickening increases as the salt concentration is increased. When the shear rate is further increased beyond 200 s-1, a large decrease in the viscosity (i.e., shear thinning) is observed. Given that shear thickening can be derived from a shearinduced increase in the density of mechanically active chains, a plausible explanation for the observed shear thickening is a shear-induced increase in micelle bridging.40,43 When shear stress is applied to the micelles bridged by polymer chains beyond the shear rates in the Newtonian region, some of the polymer-bound surfactant moieties may be “pulled out” of the micelle and become available for associations with other surfactant moieties in different polymer chains. Such a rearrangement of polymer-bound micelles may lead to an increase in the number of bridging polymer chains and hence a viscosity increase. A further increase in the shear rate may cause the interpolymer network bridges to fragment, resulting in a decrease in the network structure in size and hence a decrease in the viscosity. An observation to be noted is that the viscosity restored instantly when applied shear stress was removed. This means that the shear-induced disruption and re-formation of the micelle bridge are reversible, which is a characteristic of reversible transient networks, as conceptually illustrated in Figure 10. When the network is sheared at a high shear rate, the micelle bridges are destroyed at a faster rate than the rate of their re-formation. This leads to a decrease in the bridge density and hence a drop in the steady shear viscosity. Viscoelastic Behavior of Polymer-Bound Micelle Networks. Figure 11 shows plots of storage modulus (G′(ω)) and loss modulus (G′′(ω)) as a function of angular frequency (ω) at varying polymer concentrations observed at [NaCl] ) 0.1 M. We confirmed that at Cp e 25.0 g/L, the polymer-bound micelle solutions behave as a viscoelastic liquid; G′′(ω) is proportional to ω while G′(ω) is proportional to ω2, which is typical of the second-order fluid behavior. With increasing polymer concentration, (43) Tam, K. C.; Jenkins, R. D.; Winnik, M. A.; Bassett, D. R. Macromolecules 1998, 31, 4149.
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Figure 10. Hypothetical model for polymer-bound micelles reversibly bridged by polymer chains.
properties in the concentrated regime arise from a larger number of bridging polymer chains that are mechanically active. Both the G′(ω) and G′′(ω) data at Cp ) 25.0 g/L in Figure 11 can be best-fitted to the simple single-element Maxwell model: 45
Figure 11. Plots of storage (G′(ω)) and loss (G′′(ω)) moduli as a function of angular frequency (ω) in 0.1 M NaCl. Closed and open symbols represent G′(ω) and G′′(ω), respectively. Shear stress applied is 1.0 Pa at 25 °C.
both G′(ω) and G′′(ω) values increase and the two values become close to each other. At Cp ) 150 g/L, G′(ω) and G′′(ω) values are of the same order of magnitude and they are nearly parallel at low and intermediate frequencies, the solutions exhibiting significant elastic properties. According to a simple theory of rubber elasticity extended to transient networks or reversible physical bonds,44 the magnitude of G′(ω) at a moderate ω value is related to the density of mechanically active junctions. Thus, the increase in G′(ω) indicates an increase in the number of micelle bridges arising from increased interpolymer associations. On the other hand, the increase in G′′(ω) indicates an increase in the effective volume occupied by the network structure in solution. At Cp ) 150 g/L, the slope of the G′(ω) plot is rather flat over the ω range from 0.3 to 300 rad/s (Figure 11), exhibiting gel-like behavior.45 Examining carefully G′(ω) and G′′(ω) data at varying polymer concentrations, we conclude that when Cp > ca. 100 g/L, polymer-bound micelle solutions exhibit dominantly elastic behavior, whereas at Cp < ca. 40 g/L the viscous behavior is dominant. The dominant elastic (44) Green, M. S.; Tobolsky, A. V. J. Chem. Phys. 1940, 14, 80. (45) Ferry, J. D. Viscoelastic Properties of Polymers, 3rd ed.; Wiley: New York, 1980.
G′(ω) ) Goω2λ2/(1 + ω2λ2)
(2)
G′′(ω) ) Goωλ/(1 + ω2λ2)
(3)
The Maxwell model, a two-parameter model consisting of a single elastic component connected in series with a viscous element, describes G′(ω) and G′′(ω) with a plateau modulus (G0) and a terminal relaxation time (λ) at all ω values. We measured G′(ω) and G′′(ω) values at varying concentrations of added salt as a function of ω at varying polymer concentrations. The G′(ω) and G′′(ω) data obtained for Cp e 25.0 g/L (Figure 11) were able to be fitted well to eqs 2 and 3, respectively. The good fits of the data to the Maxwell model indicate that the relaxation process of the solution under shear is dominated by a single terminal relaxation time. From the fits, we estimated values of G0 and λ at all salt concentrations studied. On the other hand, for higher Cp (Cp > 50.0 g/L), values of G0 and λ were roughly assessed from the intersection of the extrapolated lines for G′(ω) and G′′(ω) plots as a function of ω. Values of G0 and λ thus estimated for Cp ) 9.38, 25.0, and 75.0 g/L are plotted as a function of the salt concentration in panels a, b, and c of Figure 12, respectively. The value of G0 increases markedly with increasing polymer concentration whereas the value of λ remains more or less the same (ca. 10 ms) independent of the salt concentration over the polymer concentrations investigated. At Cp ) 9.38 g/L, G0 decreases gradually with increasing salt concentration in the region [NaCl] < 0.1 M and then it starts to decrease more significantly near 0.1 M NaCl showing a tendency to slow in the decreasing trend at a salt concentration near 0.2 M (Figure 12a). At Cp ) 25.0 g/L, in contrast, G0 increases with increasing the salt concentration passing through a maximum at a salt concentration near 0.13 M and then decreases (Figure 12b). A similar tendency is observed for Cp ) 75.0 g/L, but
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Figure 12. Dependence of plateau modulus (G0) and terminal relaxation time (λ) on the concentration of added salt at Cp ) 9.38 (a), 25.0 (b), and 75.0 (c) g/L.
Figure 13. Zero shear viscosity calculated from G0 and λ values plotted as a function of [NaCl] for Cp ) 9.38 (a), 25.0 (b), and 75.0 (c) g/L.
the maximum shifts toward higher salt concentrations ([NaCl] ≈ 0.2 M) (Figure 12c). Given the zero shear viscosity can be expressed as η0 ) G0λ, zero shear viscosity values thus calculated from the results in Figure 12 are plotted against the salt concentration in Figure 13. The profile of the calculated zero shear viscosity as a function of the salt concentration appears to be quite similar to that of the observed lowshear viscosity (Figure 8). Furthermore, the calculated viscosity values at varying salt concentrations are in fair agreement with the experimental values, at least on the same order of magnitude, over the salt concentrations investigated. Therefore, we can conclude that the viscosity is practically governed by G0 but not by λ. The simple theory for transient networks44 suggests that the magnitude of G0 is proportional to the number density of mechanically active chains in the network. The micelle bridges (or cross-linking points) behave as transient junctions for a network structure, the junctions being in equilibrium of disruption and re-formation (Figure 10). The lifetime of the micelle bridge depends on the residence time for a hydrophobe that constitutes a micelle core (i.e., the reciprocal of the exit rate of the hydrophobe from the bridged micelle). The Maxwell terminal relaxation time obtained from the best fits can be regarded as the lifetime of the micelle bridge and hence the residence time of the hydrophobe in the bridged micelle under shear conditions.
Consequently, the results in Figures 8 and 12 indicate that when the polymer concentrations are sufficiently high for a macroscopic network structure to be formed (i.e., Cp g 25.0 g/L), the number of micelle bridges increases with increasing salt concentration in the low [NaCl] range (e.g., [NaCl] < ca. 0.13 M for Cp ) 25.0 g/L). However, when the salt concentration is further increased beyond a certain level, the number of micelle bridges decreases with increasing salt concentration. Moreover, the lifetime of the transient network (i.e., micelle bridging) remains virtually the same independent of the polymer concentration over the salt concentrations examined. Conclusions Rheological behavior in aqueous solutions of a random copolymer of AMPS and a methacrylate substituted with C12E25 with a 20 mol % content of the surfactant macromonomer in the copolymer was investigated. The polymer-bound C12E25 surfactant moieties form micelles via intra- and interpolymer associations, and these polymer-bound micelles are bridged by polymer chains, forming a network structure. The extent of the micelle bridging strongly depends on Cp, ionic strength, and shear stress. The steady shear viscosity in a high Cp region increases with an increase in [NaCl], reaching a maximum value at a certain [NaCl] dependent on Cp, and decreases with a further increase in [NaCl]. Viscoelastic measurements at varying Cp and [NaCl] revealed that, although
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solutions exhibit viscoelastic behavior in a semidilute regime (6.25 < Cp < 20 g/L), elastic properties become dominant at higher Cp. Analysis of G′ and G′′ data for varying Cp at varying [NaCl] indicates that the viscosity is practically governed by G0 but not by λ. The micelle bridging is dynamic in nature, and thus the disruption and re-formation of the micelle bridge occur reversibly in response to a change in external conditions.
Noda et al.
Acknowledgment. The authors are indebted to Dr. T. Shikata for discussions. This work was supported in part by a Grant-in-Aid for Scientific Research No. 10450354 from the Ministry of Education, Science, Sports, and Culture, Japan. LA9916070
