Gelation of Concentrated Micellar Solutions of a Triblock Copolymer of

Apr 14, 2004 - Dharmista Mistry, Tom Annable, Xue-Feng Yuan, and Colin Booth ... Chiraphon Chaibundit, Zhuo Yang, David Attwood, and Colin Booth...
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Gelation of Concentrated Micellar Solutions of a Triblock Copolymer of Ethylene Oxide and Styrene Oxide, S5E45S5 Na´gila M. P. S. Ricardo,† Sara B. Honorato,† Zhuo Yang,‡ Valeria Castelletto,§ Ian W. Hamley,§ Xue-Feng Yuan,| David Attwood,*,⊥ and Colin Booth‡ Department of Organic and Inorganic Chemistry, Federal University of Ceara´ , CX 12200 Fortaleza, Brazil, and Department of Chemistry and School of Pharmacy and Pharmaceutical Sciences, University of Manchester, Manchester M13 9PL, School of Chemistry, University of Leeds, Leeds LS2 9JT, and Department of Mechanical Engineering, King’s College London, Strand, London WC2R 2LS, U.K. Received January 27, 2004 Triblock copolymer S5E45S5 was synthesized by oxyanionic polymerization of styrene oxide initiated by a preformed difunctional polyethylene glycol. Here E denotes OCH2CH2, S denotes OCH2CH(C6H5), and the subscripts denote number-average block lengths in repeat units. Previous work on the closely related copolymer S4E45S4 indicated that micelles would form in aqueous solutions of copolymer S5E45S5, and that they would undergo transient intermicellar bridging. Dynamic light scattering was used to confirm this. Rheometry and small-angle X-ray scattering were used to explore gel boundaries, structures, and properties. At moderate copolymer concentrations (14 and 20 wt %) measurements of the dynamic shear moduli indicated the formation of low-modulus soft gels attributed to spherical micelles forming transient networks. A region of low storage modulus at c ≈ 30 wt % preceded a change to hard gel. A 40 wt % hard gel was disordered, while at higher concentrations (49 and 60 wt %) the micelles packed into hexagonal structures with high values of the storage modulus (G′ ≈ 10 kPa at 25 °C and 1 Hz).

1. Introduction Aqueous solutions of triblock copolymers of ethylene oxide and styrene oxide may micellize in dilute aqueous solution, and their concentrated micellar solutions may gel. In recent years we have investigated the aqueous solution properties of diblock copolymers and triblock copolymers (type EmSnEm) in some detail.1 We use E to denote an oxyethylene unit, OCH2CH2, S to denote an oxyphenylethylene unit, OCH2CH(C6H5), and n and m to denote number-average block lengths in repeat units. By comparison, the corresponding triblock copolymers of type SnEmSn have been somewhat neglected, with just one paper exploring the dilute solution properties of S4E45S4.2 Block copolymers with terminal hydrophobic blocks are of interest because transient molecular bridging between micelles causes intermicellar attraction, which can modify the solution properties when compared with copolymers of other block architectures. Of the class of block copoly(oxyalkylene)s, those of ethylene oxide with 1,2-butylene oxide, BnEmBn [B denotes oxybutylene, OCH2(C2H5)], have †

Federal University of Ceara´. Department of Chemistry, University of Manchester. University of Leeds. | King’s College London. ⊥ School of Pharmacy and Pharmaceutical Sciences, University of Manchester. ‡ §

(1) (a) Mai, S.-M.; Booth, C.; Kelarakis, A.; Havredaki, V.; Ryan, A. J. Langmuir 2000, 16, 1681. (b) Kelarakis, A.; Havredaki, V.; Rekatas, C. J.; Mai, S.-M.; Attwood, D.; Booth, C.; Ryan, A. J.; Hamley, I. W.; Martini, L. Macromol. Chem. Phys. 2001, 202, 1345. (c) Kelarakis, A.; Havredaki, V.; Rekatas, C. J.; Booth, C. Phys. Chem. Chem. Phys. 2001, 3, 5550. (d) Crothers, M.; Attwood, D.; Collett, J. H.; Yang, Z.; Booth, C.; Taboada, P.; Mosquera, V.; Ricardo, N. M. P. S.; Martini, L. Langmuir 2002, 18, 8685. (e) Yang, Z.; Crothers, M.; Ricardo, N. M. P. S.; Chaibundit, C.; Taboada, P.; Mosquera, V.; Kelarakis, A.; Havredaki, V.; Martini, L.; Valder, C.; Collett, J. H.; Attwood, D.; Heatley, F.; Booth, C. Langmuir 2003, 19, 943. (f) Yang, Z.; Crothers, M.; Attwood, D.; Collett, J. H.; Ricardo, N. M. P. S.; Martini, L.; Booth, C. J. Colloid Interface Sci. 2003, 263, 312. (2) Mai, S.-M.; Ludhera, S.; Heatley, F.; Attwood, D.; Booth, C. J. Chem. Soc., Faraday Trans. 1998, 94, 567.

been studied most frequently, particularly to detect molecular bridging of micelles in dilute solution by light scattering,3,4 but also to characterize the gelation of more concentrated solutions by tube inversion5 and rheometry.6 There are related investigations of copolymers of ethylene oxide and propylene oxide, PnEmPn [P denotes oxypropylene, OCH2(CH3)],7 including an interesting study by light scattering, small-angle neutron scattering, and rheology of solutions of copolymer P15E156P15 over a wide concentration range covering molecular and micellar networks and packed-micellar gels.8 Because of their commercial importance as associative thickeners, poly(oxyethylene)s with urethane-linked n alkyl end blocks have been extensively studied.9 Considering the corresponding model diethers CnEmCn [C denotes methylene or methyl], light scattering methods have been used to (3) (a) Yang, Z.; Pickard, S.; Deng, N.-J.; Barlow, R. J.; Attwood, D.; Booth, C. Macromolecules 1994, 27, 2371. (b) Yang, Y.-W.; Yang, Z.; Zhou, Z.-K.; Attwood, D.; Booth, C. Macromolecules 1996, 29, 670. (c) Yang, Z.; Yang, Y.-W.; Zhou, Z.-K.; Attwood, D.; Booth, C. J. Chem. Soc., Faraday Trans. 1996, 92, 257. (4) (a) Zhou, Z.-K.; Chu, B.; Nace, V. M.; Yang, Y.-W.; Booth, C. Macromolecules 1996, 29, 3663. (b) Zhou, Z.-K.; Yang, Y.-W.; Booth, C.; Chu, B. Macromolecules 1996, 29, 8357. (c) Zhou, Z.-K.; Chu, B.; Nace, V. M. Langmuir 1996, 12, 5016. (d) Liu, T.-B.; Zhou, Z.-K.; Wu, C.-H.; Chu, B.; Schneider, D. K.; Nace, V. M. J. Phys. Chem. B 1997, 101, 8808. (e) Chu, B.; Liu, T.-B.; Wu, C.-H.; Zhou, Z.-K.; Nace, V. M. Macromol. Symp. 1997, 118, 221. (f) Liu, T.-B.; Zhou, Z.-K.; Wu, C.-H.; Nace, V. M.; Chu, B. J. Phys. Chem. B 1998, 102, 2875. (5) Yang, Y.-W.; Ali-Adib, Z.; McKeown, N. B.; Ryan, A. J.; Attwood, D.; Booth, C. Langmuir 1997, 13, 1860. (6) (a) Kelarakis, A.; Yuan, X.-F.; Mai, S.-M.; Yang, Y.-W.; Booth, C. Phys. Chem. Chem. Phys. 2003, 5, 2628. (b) Kelarakis, A.; Havredaki, V.; Yuan, X.-F.; Yang, Y.-W.; Booth, C. J. Mater. Chem. 2003, 13, 2779. (7) (a) Zhou, Z.-K.; Chu, B. Macromolecules 1994, 27, 2025. (b) Altinok, H.; Yu, G.-E.; Nixon, S. K.; Gorry, P. A.; Attwood, D.; Booth, C. Langmuir 1997, 13, 5837. (8) Mortensen, K.; Brown, W.; Jørgensen, E. Macromolecules 1994, 27, 5654. (9) See, for example, Annable, T.; Buscall, R.; Ettelaie, R. In Amphiphilic Block Copolymers: Self-assembly and Applications; Alexandridis, P., Lindman, B., Eds.; Elsevier: Amsterdam, 2000; Chapter 12.

10.1021/la049758c CCC: $27.50 © 2004 American Chemical Society Published on Web 04/14/2004

Gelation of Micellar Solutions of S5E45S5

demonstrate molecular bridging between micelles,10 and their gelation and clouding behavior has also been reported.11 For the four types of hydrophobic units, an approximate assessment of their hydrophobicity, based on values of the critical micelle concentration (cmc; in molar units) for a range of copolymers, gives P:C:B:S ) 1:5:6:12.1d,12 The use of C and B blocks, and particularly S blocks, means that equivalent effects can be obtained with much shorter block lengths than is possible using P blocks. Our previous study of copolymer S4E45S4 was focused on light scattering from dilute aqueous solutions.2 The second virial coefficients from static and dynamic light scattering were both negative, thus confirming that copolymer S4E45S4 in aqueous micellar solution formed transient intermicellar bridges, i.e., that the micellemicelle interaction was attractive. Here we describe an investigation of the formation, structure, and rheology of aqueous gels of copolymer S5E45S5, which was newly synthesized to reproduce the properties of S4E45S4. Although there is a difference in composition, it can be safely assumed that the new copolymer would also form intermicellar bridges, as the effect has been shown to be present across a range of hydrophobic block lengths in aqueous solutions of related BnEmBn and CnEmCn copolymers.3,4,10 However, it was thought desirable to use dynamic light scattering from dilute solutions of copolymer S5E45S5 to confirm the effect. A copolymer based on the same E45 central block but with longer S blocks, S7E45S7, was also synthesized, but proved to be insoluble in water at all accessible temperatures. 2. Experimental Section 2.1. Copolymer. Copolymer S5E45S5 was prepared by oxyanionic polymerization using a vacuum line and ampule technique. A mixture of polyethylene glycol (number-average molar mass Mn ) 2000 g mol-1, ratio of mass-average to number-average molar mass Mw/Mn ) 1.03) and KOH (85%) was heated and stirred under vacuum (70 °C, 0.1 mmHg, 100 h) to remove water and to partly convert the glycol to its potassium salt (mole ratio OH/ OK ) 5). Styrene oxide was distilled and dried over type 4A molecular sieves, added to the ampule by syringe under anhydrous conditions, and polymerized at 80 °C over a period of six weeks. Characterization of the copolymer by gel permeation chromatography gave Mw/Mn ) 1.03 on the basis of poly(oxyethylene) standards excluding a small peak at high elution volume attributed to a small fraction of poly(styrene oxide). This was partly removed by fractional precipitation from dichloromethane by addition of hexane, the residue being ignored in subsequent work. Comparison of the integrals of the 13C NMR resonances from backbone, junction, and end-group carbons confirmed the triblock architecture of the copolymer and the overall composition, which, together with related information for the original glycol, gave the molecular formula, and corresponding values of Mn ) 3200 g mol-1, Mw ) 3300, and a mass fraction of S, wS, of 0.38. 2.2. Clouding and Gelation. Clear aqueous solutions were prepared at room temperature and stored for several days at 5 °C before use. If equilibration of concentrated solutions was slow, a small magnetic stirrer was used to gently agitate the solution. Clouding and gelation temperatures were determined by enclosing samples of the aqueous solutions (0.3 g) in small tubes (internal diameter ca. 5 mm) and observing them while slowly (10) See, for example, (a) Alami, E.; Almgren, M.; Brown, W.; Franc¸ ois, J. Macromolecules 1996, 29, 2229. (b) Chassenieux, C.; Nicolai, T.; Durand, D. Macromolecules 1997, 30, 4952. (c) Lafle`che, E.; Durand, D.; Nicolai, T. Macromolecules 2003, 36, 1331. (11) (a) Franc¸ ois, J.; Maıˆtre, S.; Rawiso, M.; Sarazin, D.; Beinert, G.; Isel, F. Colloids Surf., A 1996, 112, 251. (b) Franc¸ ois, J.; Beaudoin, E.; Borisov, O. Langmuir 2003, 19, 10011. (12) Booth, C.; Attwood, D. Macromol. Rapid Commun. 2000, 21, 501.

Langmuir, Vol. 20, No. 10, 2004 4273 heating the tube in a water bath through the temperature range 5-85 °C. Gelation was detected during this process by immobility of the solution when the temperature was held constant and the tube was inverted. 2.3. Dynamic Light Scattering (DLS). DLS intensities were measured using well-filtered dilute solutions and a Brookhaven BI200S instrument equipped with a BI9000AT digital correlator and vertically polarized incident light of wavelength λ ) 488 nm supplied by an argon ion laser operated at 500 mW. The scattering angle was 90° to the incident beam. The CONTIN procedure13 was used to provide intensities at logarithmically spaced values of the decay rate (G), and thereby corresponding distributions of the apparent mutual diffusion coefficient (Dapp) and, through the Stokes-Einstein equation

rh,app ) kT/(6πηDapp)

(1)

where k is the Boltzmann constant and η is the viscosity of the solvent at temperature T, distributions of the apparent hydrodynamic radius (rh,app). 2.4. Rheometry. Aqueous solutions were prepared as described in section 2.2. Fresh solutions were used for each set of measurements. A Bohlin CS50 rheometer (Couette geometry) in oscillatory-shear mode was used at frequency f ) 1 Hz to determine storage (G′) and loss (G′′) moduli as the samples were heated at 1 °C min-1 in the range 5-90 °C. The strain amplitude was held at a low value (ca. 0.5%) by means of the autostress facility of the Bohlin software, thus ensuring that measurements of G′ and G′′ were in the linear viscoelastic region. Frequency scans were obtained at selected temperatures under the same low-strain conditions. Details of these procedures can be found elsewhere.1b 2.5. Small-Angle X-ray Scattering (SAXS). SAXS experiments were conducted on beamline 16.1 at the Synchrotron Radiation Source, Daresbury Laboratory, U.K., details of which have been provided elsewhere.14 Samples were loaded into 1 mm thick brass cells, with an inner spacer ring to hold the liquids sealed between mica windows. The cells were heated from 25 °C to the clouding temperature or beyond. SAXS profiles were recorded using a quadrant multiwire detector that provided the scattered intensity on a linear scale. The q scale (q ) 4π(sin θ)/λ, where λ ) 1.41 Å and 2θ is the scattering angle) was calibrated using a specimen of wet collagen (rat tail tendon). 2.6. Polarized Light Microscopy (PLM). An Olympus BX51 polarizing microscope was used, with 0.5 mm films of the samples held in the optical window of a Linkam CSS450 optical shearing system. The temperature of the cell was controlled by a silver heater utilizing platinum resistors and a water cooling bath, and was heated from 3 to 50 °C at 1 °C min-1. The temperature was held at a specific value as required.

3. Results and Discussion 3.1. Clouding and Gelation. The cloud-point curve obtained for aqueous solutions of copolymer S5E45S5 is illustrated in Figure 1. In the same experiment tube inversion served to define the immobile/fluid boundary. Following Hvidt and co-workers,15 this immobile gel is denoted as hard. Note that the hard gel boundary at low temperatures lies between 32 wt % copolymer (hard gel) and 30 wt % (fluid). As described below, rheometry was used to confirm the hard gel boundary and to investigate the state of more dilute solutions. In those experiments values of the moduli were recorded at f ) 1 Hz from 5 °C to within a few degrees of the cloud point. The cloudy solutions were not studied. 3.2. Dynamic Light Scattering. As examples of the results obtained, Figure 2 shows distributions of log(rh,app) (13) Provencher, S. W. Makromol. Chem. 1979, 180, 201. (14) Bliss, N.; Bordas, J.; Fell, B. D.; Harris, N. W.; Helsby, W. I.; Mant, G. R.; Smith, W.; Towns-Andrews, E. Rev. Sci. Instrum. 1995, 66, 1311. (15) (a) Hvidt, S.; Jørgensen, E. B.; Schille´n, K.; Brown, W. J. Phys. Chem. 1994, 98, 12320. (b) Almgren, M.; Brown, W.; Hvidt, S. Colloid Polym. Sci. 1995, 273, 2.

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Figure 1. Phase diagram determined for aqueous solutions of copolymer S5E45S5: cloud-point curve (dashed curve and 0); hard gel boundary (solid curve) determined by (O) tube inversion and (b) rheology; soft gel boundary (dotted curve) determined by (9) rheology. The soft gel boundary is drawn schematically; the other boundaries are known to (3 °C.

Figure 3. Temperature dependence of the modulus (frequency 1 Hz, strain amplitude 0.5%) for aqueous solutions of copolymer S5E45S5: (a) storage modulus at the concentrations indicated; (b) storage (filled symbols) and loss (unfilled symbols) modulus at the concentrations indicated. Figure 2. Intensity fraction distributions of the logarithm of the apparent hydrodynamic radius for micellar solutions at 10 °C of copolymer S5E45S5.

found for 2 and 4 wt % solutions of copolymer S5E45S5 at 10 °C, i.e., well below the clouding temperature. The peaks at rh,app ) 4-5 nm are assigned to micelles, and the peak at ca. 15 nm in the distribution for the 4 wt % solution is assigned to a small mass fraction of micelle clusters. Similar distributions have been reported for aqueous solutions of related BnEmBn copolymers, and the movement of the micelle peak to a higher value of rh,app at the higher copolymer concentration is consistent with intermicellar attraction.3c,4f The results shown in Figure 2 confirm the formation of micelles and micelle clusters, while the absence of a measurable signal at rh,app ≈ 1 nm, which would be expected for unassociated molecules, is consistent with a low cmc. A value of 0.002 wt % was reported for aqueous solutions of copolymer S4E45S4 at 15 °C.2 3.3. Soft Gel. The temperature dependence of the modulus was determined for solutions of concentrations 14, 20, and 30 wt %. All three solutions were mobile fluids in the tube-inversion test. The 14 and 20 wt % solutions at low temperatures had significant values of G′ (see Figure 3a; G′ > 200 Pa at 10 °C), and as illustrated in Figure 3b for the 14 wt % solution, values of the storage modulus exceeded those of the loss modulus over the high modulus range. To distinguish these solutions from sols, we refer to them as soft gels, so defining a soft gel solely by the rheology of the system. Insofar as we can locate it from the results available, the soft gel region is shown schematically in Figure 1, the actual measured soft gel/ sol transition temperatures being shown as filled squares. The 30 wt % solution had low values of the storage modulus throughout the range investigated (see Figure 3b). The scatter in log(G′) of this solution was caused by using the autostress facility of the Bohlin rheometer near the limit of its applicability. Values of the loss modulus exceeded those of the storage modulus by a factor of 10 or more. We refer to this fluid, and others of the type, as sols.

Figure 4. Phase diagram of the hard and soft gels reported for aqueous solutions of copolymer E45S10. Adapted from ref 1d.

It has been established that a yield stress of at least σy ≈ 30 Pa is required to stop flow under the conditions of the inverted-tube test described in section 2.2.16,17 Also it is known that σy/G′ ≈ 0.3 (G′ measured at f ) 1 Hz) for body- or face-centered cubic gels formed from spherical micelles, whereas the corresponding relationship for hexagonal gels formed from cylindrical micelles is σy/G′ ≈ 0.1.16,17 Considering the maximum values of G′ recorded at 1 Hz for the 20 wt % soft gel (see Figure 2, 700 Pa at 5 °C), the mobility of the system indicates that the soft gel phase is formed from spherical micelles. In Figure 4 we show the phase diagram established1d for aqueous solutions of diblock copolymer E45S10, which corresponds in overall composition to S5E45S5. Solutions of this copolymer do not cloud in the accessible temperature range. The micelles of E45S10 are nonbridging and, effectively, have the solution properties of hard spheres. (16) (a) Kelarakis, A.; Havredaki, V.; Mingvanish, W.; Li, H.; Booth, C.; Daniel, C.; Hamley, I. W.; Ryan, A. J. Phys. Chem. Chem. Phys. 2000, 2, 2755. (b) Mingvanish, W.; Kelarakis, A.; Mai, S.-M.; Daniel, C.; Yang, Z.; Havredaki, V.; Hamley, I. W.; Ryan, A. J.; Booth, C. J. Phys. Chem. B 2000, 104, 9788. (17) (a) Li, H.; Yu, G.-E.; Price, C.; Booth, C.; Fairclough, J. P. A.; Ryan, A. J.; Mortensen, K. Langmuir 2003, 19, 1075. (b) Li, H.; Yu, G.-E.; Price, C.; Booth, C.; Hecht, E.; Hoffmann, H. Macromolecules 1997, 30, 1347.

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Figure 6. Frequency dependence of the modulus (strain amplitude 0.5%) for a 20 wt % aqueous solution of copolymer S5E45S5 at 30 °C. Filled symbols denote G′ and unfilled symbols G′′. The curves correspond to two Maxwell elements with G∞ ) 370 Pa and τ ) 0.005 s (fast process) and G∞ ) 1 Pa and τ ) 0.4 s (slow process).

Figure 5. (a) Frequency dependence of the modulus (strain amplitude 0.5%) for a 14 wt % aqueous solution of copolymer S5E45S5. (b) Scaled moduli plotted against scaled frequency. Quantities a and b are scaling factors. Solution temperatures were (9, 0) 10 °C, ([, ]) 15 °C, and (b, O) 20 °C. Filled symbols denote G′ and unfilled symbols G′′.

Solutions of E45S10 at concentrations below 20 wt % form soft gels with storage moduli as high as 700 Pa (f ) 1 Hz), but only at relatively high temperatures, i.e., maximum values of G′ at T ≈ 50-60 °C. Indeed, the soft gels of nonbridging diblock and triblock copolymers found for a range of compositions are typically formed on heating solutions with concentration below the minimum for a hard gel: see, e.g., refs 17 and 18. The soft gels of EB and EBE copolymers have been attributed to spherical micelles being weakly attractive in a poor solvent (water at high temperature) and forming loose structures through a percolation transition.17 The finding that aqueous micellar solutions of copolymer S5E45S5 form soft gels at low temperatures indicates intermicellar attraction in a good solvent, and this most probably originates from intermicellar bridging. We note that aqueous solutions of copolymer B10E114B10 with concentrations around 15 wt % also show regions of raised modulus at low temperatures (5-25 °C).6a 3.3.1. Frequency Dependence of the Modulus. As discussed previously,17a soft gels defined solely by rheometry at a fixed frequency can have a range of disordered structures. Knowledge of the frequency dependence of the modulus allows a more informed discussion. The frequency dependence of the modulus found for the 14 wt % solution is shown in Figure 5a. The solution at 10 °C is in the soft gel phase (see Figure 1), and that at 20 °C is in the clear fluid phase above the soft gel boundary. Corresponding plots found for the solution at 5 and 15 °C were similar in shape to that illustrated for the solution at 10 °C, although the level of the moduli differed, as shown in Figure 3. With the Bohlin instrument working under the restriction of 0.5% strain amplitude, the moduli for the solution at 20 °C were too low to measure at frequencies (18) Hamley, I. W.; Mai, S.-M.; Ryan, A. J.; Fairclough, J. P. A.; Booth, C. Phys. Chem. Chem. Phys. 2001, 3, 2972.

less than 0.1 Hz. Overall, Figure 5a illustrates well the arbitrary nature of the choice of f ) 1 Hz to define the soft gel region. Previously we have shown that it is possible to scale the frequency and moduli of micellar solutions of BnEmBn copolymers to obtain a single master curve covering the range from fluid to gel.6a The treatment followed that used by Trappe and Weitz for weakly attractive colloidal particles.19a The parallel effect in block copolymer solutions is weak attraction generated by transient bridging between spherical micelles. Scaling of this type applied to 14 wt % solutions of S5E45S5 at 10, 15, and 20 °C is illustrated in Figure 5b, the data for 5 °C being omitted for clarity. The curve generated is characteristic of behavior at the transition from a fluid with G′′(f) tending to unit slope at high scaled frequency to a gel with G′(f) tending to zero slope at low scaled frequency.6a,19a At low scaled frequency, the scaled modulus approaches the form expected for a mesophase of packed spherical micelles, i.e., a weak dependence of G′ on frequency and a shallow minimum in G′′.19b Taken together, the evidence from the frequency sweeps points to the low-temperature soft gel being comprised of attractive spherical micelles with local cubic order. Because of clouding, it was not desirable to raise the temperature of the 14 wt % solution further. However, the opportunity was taken to record the frequency dependence of the modulus for a 20 wt % solution at 30 °C, immediately below its clouding temperature; see Figure 6. The low storage moduli of this solution (ca. 1 Pa at 1 Hz) mark it out as a sol. Consideration was given to modeling the viscoelasticity of the solution with parallel Maxwell elements, i.e.

G′ ) (G∞τ2ω2)/(1 + τ2ω2) G′′ ) (G∞τω)/(1 + τ2ω2) (2) where G∞ is the plateau value of G′ at high frequency, τ is the relaxation time, and ω ) 2πf (f ) frequency in hertz). A good fit required the sum of several such elements, but as illustrated in Figure 6, the essential physics of the system could be reproduced using two elements, one representing a fast process characteristic of a mobile fluid and the other a slow process which we assign to an effect of intermicellar bridging. 3.4. Hard Gel. The hard gel boundary determined by tube inversion was confirmed by determining the temperature dependence of the storage modulus (frequency (19) (a) Trappe, V.; Weitz, D. A. Phys. Rev. Lett. 2000, 85, 449. (b) Mason, T. G.; Weitz, D. A. Phys. Rev. Lett. 1995, 75, 2770.

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Figure 9. Frequency dependence of the modulus (strain amplitude 0.5%) for a 50 wt % aqueous solution of copolymer S5E45S5 at the temperatures indicated. Filled symbols denote G′ and unfilled symbols G′′. The curves through the data points for the solutions at 40 °C correspond to two Maxwell elements with G∞ ) 1000 Pa and τ ) 0.003 s (fast process) and G∞ ) 1 Pa and τ ) 0.4 s (slow process).

Figure 7. Temperature dependence of the dynamic moduli of aqueous solutions of copolymer S5E45S5 (frequency 1 Hz, strain amplitude 0.5%): (a) storage modulus at the concentrations indicated; (b) (b) storage and (O) loss moduli for the 50 wt % solution.

Figure 8. SAXS pattern obtained for the 60 wt % gel of copolymer S5E45S5 at 25 °C. Intensity is plotted against q/q*, where q* is the value of q at the first-order maximum. The arrows point to the measured reflections.

1 Hz) of 30, 38, and 50 wt % solutions; see Figure 7a. The storage moduli measured for the 30 wt % solution taken from Figure 3b are reproduced in Figure 7a to emphasize the observation that a fluid of very low modulus (sol) occurs between the soft gel and hard gel phases. The filled circles in Figure 1 correspond to the temperatures at which values of the storage modulus fall below a value (ca. 1 kPa) typical of hard gels (see Figure 7). As indicated in Figure 7b for the 50 wt % gel, the storage modulus exceeded the loss modulus in the hard gel region. Hard gels of concentrations 40, 49, and 60 wt % were examined by SAXS. Scattering patterns were recorded at 30 s intervals as the temperature was raised at 2 °C min-1 from 25 °C into the cloudy phase. As an example, the SAXS pattern obtained for the 60 wt % gel at 25 °C is shown in Figure 8. Intensity is plotted against q/q*, where q* is the value of q at the first-order maximum. The reflections in the sequence q/q* ) 1, x3, and x4 provide evidence of a hexagonal structure formed from packed cylindrical micelles. We note that packing depends on the exclusion properties of the micelles, and that it occurs irrespective of micelle bridging, when the volume fraction of micelles exceeds a critical value dependent on the micelle

shape. The hexagonal structure was found at temperatures up to 32-33 °C, with a single broad peak at higher temperatures characteristic of a disordered phase. Similar patterns were found for the 49 wt % gel, indicating a hexagonal structure at temperatures up to 36-37 °C which disorders at higher temperatures. The order-disorder transition temperatures are in fair agreement with the hard gel boundary derived from tube inversion and rheometry shown in Figure 1. The 40 wt % solution is a hard gel (see Figure 1), but the SAXS pattern showed no evidence of the structure. The immobility of this gel under tube inversion implies a high yield strength, and so a high storage modulus, which we attribute to extensive bridging in an incompletely ordered phase, the high extent of bridging being a consequence of the small intermicellar core-core distance in the concentrated micellar solution. The structure of the hard gels at low temperatures was not investigated by SAXS. However, corresponding gels were examined from 3 to 50 °C by PLM. Gels of concentrations 49 and 60 wt % were birefringent from 3 to 34 °C and isotropic at higher temperatures, in satisfactory agreement with the results from SAXS, and indicating that the anisotropic structure extended to low temperatures. A 38 wt % gel was isotropic at all temperatures examined. There is evidence in the G′(T) curves of a transition centered on T ≈ 10 °C for the 38 wt % gel and an indication of one below 5 °C for the 50 wt % gel (see Figure 7). It is possible that these low-T high-modulus gels are cubic structures of packed spherical micelles. Cubic/hexagonal transitions on heating have been reported for aqueous solutions of other poly(oxyalkylene) block copolymer systems, e.g., for E/B copolymers with various architectures,5,18 particularly relevant to the present work being the results for copolymer B7E40B7, which are described in section 3.5. Unfortunately, our PLM was limited to T g 3 °C, putting a possible isotropic/birefringent transition for the 49 wt % gel out of range. 3.4.1. Frequency Dependence of the Modulus. The frequency dependence of the modulus was measured for a 50 wt % solution; see Figure 9. This solution at 10 °C is well within the hard gel region (see Figure 1a), and a corresponding plot obtained for the solution at 20 °C (not shown) was very similar. The 50 wt % solution at 30 °C is near the high-T limit of the hard gel, and that at 40 °C is within the clear fluid phase. Straight lines drawn through the data points for the 50 wt % gel at 10 °C indicate an approximate scaling law of G ≈ f0.3 for both moduli, much as expected for cylindrical micelles in a hexagonal

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Figure 10. Frequency dependence of the modulus (strain amplitude 0.5%) for a 38 wt % aqueous solution of copolymer S5E45S5 at the temperatures indicated. Filled symbols denote G′ and unfilled symbols G′′.

gel. As noted for the 20 wt % fluid at 30 °C (see section 3.3.1), the data points for the 50 wt % solution at 40 °C could also be fitted approximately by two Maxwell elements in parallel modeling fast and slow processes. The frequency dependence of the modulus was also recorded for 38 wt % aqueous hard gels of S5E45S5; see Figure 10. The structure of the hard gel at this concentration is uncertain, as we obtained no helpful information from SAXS and PLM (see section 3.4). In agreement with the temperature scans of the modulus, the frequency scans show G′ > 103 Pa at f ) 1 Hz, as expected for hard gels, but the frequency dependence of the modulus is very different from that expected for gels formed from spherical micelles with cubic packing, for which G′ should be insensitive to frequency and G′′ should show a minimum. This rheological behavior was approached by the 14 wt % soft gel at low frequency and low temperature, as illustrated in Figure 5b. We speculate that the sol at or about 30 wt % copolymer, which intervenes between the soft and hard gel phases (see Figure 1), marks a transition from spherical to elongated micelles, and that the elongation of micelles formed immediately above the transition (c ≈ 31-40 wt %) is insufficient to force the transiently linked micelles into a well-structured packed phase. 3.5. Comparison with Other Systems. It is of interest to compare the gelation of the present copolymer with that of comparable BEB, CEC, and PEP copolymers. As the association properties of copolymers of this type are known to be sensitive to block length and composition,4f,10,11 we have looked for copolymers with similar E-block lengths and with end blocks of similar hydrophobicity. Considering the relative hydrophobicities of the various chain units noted in the Introduction, i.e., P:C:B:S ≈ 1:5:6:12, ideally we look for information on the gelation of copolymers with a central block of 45 E units and with B10, C12, and P60 end blocks. In fact no such PEP copolymer is available, but we can compare results for copolymers B7E40B75 and, in our notation, C12E45C12;11a see Figure 11. For copolymer B7E40B7, visual observation was used to detect clouding, tube inversion to obtain the hard gel boundary, and PLM to locate approximately the regions of isotropic, hexagonal, and lamellar hard gel. The results for C12E45C12 were obtained mainly by SAXS aided by visual observation, DSC, and PLM. As might be expected, the phase diagram for copolymer B7E40B7 shows features similar to those found for copolymer S5E45S5. The clouding curves are similar, and a hard gel with hexagonal structure is common to both. Considering 50 wt % hard gels, a difference is that an isotropic hard gel was detected by PLM for solutions of copolymer B7E40B7 at moderate temperatures but not for solutions of copolymer S5E45S5, even at the lowest temperatures

Figure 11. Phase diagrams reported for aqueous solutions of B7E40B7 and C12E45C12, as indicated. Phase boundaries within the hard gel region of the solutions of B7E40B7 were not defined. The diagrams were adapted from refs 5 and 11a, and use the present notation.

within the range of our experiments, as discussed in section 3.4. SAXS was not used to identify the structures of the gels of copolymer B7E40B7, and it could be that its 40 wt % isotropic gel is disordered like that of copolymer S5E45S5. Also, rheometry was not used to investigate solutions of B7E40B7, so there is no information regarding the soft gel for that system. One further difference of detail is that the hard gel region of solutions of copolymer B7E40B7 in the concentration range 37-40 wt % can be entered by heating from the fluid phase. This feature of the gelation of block copoly(oxyalkylene)s is of interest in the development of micelle-based drug delivery systems.20 Our experiments show that this is not possible for solutions of S5E45S5. In this respect the hard gel of copolymer S5E45S5 resembles that of its nonbridging diblock (ES) and triblock (ESE) counterparts, none of which, when they do gel, show a low-T boundary.1 The phase diagram for copolymer C12E45C12 has very different features compared to those for S5E45S5 and B7E40B7. Principally we note the cloudy region below 20 wt % at low T but extending to ca. 50 wt % at high T and, particularly, the cubic (bcc) gel phase at or above room temperature extending from ca. 25 to 75 wt %. There is no evidence of a hexagonal gel. It has been shown that aqueous micellar solutions of CE diblock copolymers form cubic gels with bcc structures up to high copolymer concentrations, e.g., for C11E40 from 25 to 75 wt % or more at T < 50 °C.21 In comparison gels of E41B8, a copolymer of similar E-block length and hydrophobicity, in the same T range undergo a cubic (bcc) to hexagonal transition at or about 50 wt % copolymer concentration.17a,22 As expected for diblock copolymers with similar E-block length and hydrophobicity, the association numbers of their micelles are similar; N ≈ 20-30 at T ≈ 30 °C. In principle it should be possible to construct a universal phase diagram in terms of the Flory interaction parameters and the lengths of the blocks. However, the marked difference in the gelation (20) Miyazaki, S.; Tobiyama, T.; Takada, M.; Attwood, D. J. Pharm. Pharmacol. 1995, 47, 455. (21) (a) Ameri, M.; Attwood, D.; Collett, J. H.; Booth, C. J. Chem. Soc., Faraday Trans. 1997, 93, 3545. (b) Hamley, I. W.; Pople, J. A.; Ameri, M.; Attwood, D.; Booth, C.; Ryan, A. J. Macromol. Chem. Phys. 1998, 199, 1753. (22) Fairclough, J. P. A.; Ryan, A. J.; Hamley, I. W.; Li, H.; Yu, G.-E.; Booth, C. Macromolecules 1999, 32, 2058.

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behavior of solutions of copolymer C12E45C12 compared to that of copolymers S5E45S5 and B7E40B7 may well relate in part to differences in the uniformity of the hydrophobic blocks and the incorporation of water and E blocks into the micelle cores, features which have yet to be examined in a systematic way. 4. Conclusions Because of transient micellar bridging, micelles of copolymer S5E45S5 in dilute solution are weakly attractive. In moderately concentrated solutions, 14 and 20 wt %, this attraction leads to the formation of soft gels at low temperatures, the rheology of which is characteristic of spherical micelles clustering with local cubic order. Hard gels are formed at concentrations of 32 wt % or greater. At high concentrations, 50 and 60 wt %, the gels are birefringent and SAXS indicates cylindrical micelles

Ricardo et al.

packed in a hexagonal structure. At 38-40 wt % the hard gel is isotropic and yields just one broad SAXS peak. This gel is thought to comprise transiently linked but poorly packed elongated micelles. The sol at or about 30 wt % copolymer, which separates the regions of soft and hard gel, is related to the transition from spherical to elongated micelles. Acknowledgment. We thank Dr. Frank Heatley and Mr. Keith Nixon for help with the characterization of the copolymer. The Engineering and Physical Science Research Council (U.K.) supported the work through Grants GR/N63727, GR/N22052, and GR/N35373. The Brazilian Research Council CNPq provided financial support for N.M.P.S.R. LA049758C