Micellization and Gelation of Diblock Copolymers of Ethylene Oxide

Solubilization of Docetaxel in Poly(ethylene oxide)-block-poly(butylene/styrene oxide) Micelles. Mahmoud Elsabahy, Marie-Ève Perron, Nicolas Bertrand...
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Langmuir 2002, 18, 8685-8691

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Micellization and Gelation of Diblock Copolymers of Ethylene Oxide and Styrene Oxide in Aqueous Solution Michael Crothers, David Attwood,* and John H. Collett School of Pharmacy and Pharmaceutical Sciences, University of Manchester, Manchester M13 9PL, UK

Zhuo Yang and Colin Booth Department of Chemistry, University of Manchester, Manchester M13 9PL, UK

Pablo Taboada and Victor Mosquera Department of Physics of Condensed Matter, University of Santiago de Compostela, E-15706 Santiago de Compostela, Spain

Na´gila M. P. S. Ricardo Department of Organic and Inorganic Chemistry, Federal University of Ceara´ , CX 12200 Fortaleza, Brazil

Luigi G. A. Martini GlaxoSmithKline, New Frontiers Science Park (South), Harlow, Essex CM19 5AW, UK Received June 18, 2002. In Final Form: August 21, 2002 Four diblock copolymers of styrene oxide and ethylene oxide were prepared by oxyanionic polymerization: E45S10, S15E63, S17E65, and S20E67. Surface tension measurements were used to determine critical micelle concentrations of copolymer E45S10 in aqueous solution at several temperatures and thereby its standard enthalpy of micellization. A compilation of known results for copolymers with hydrophobic blocks formed from either styrene oxide or 1,2-butylene oxide shows a discontinuity at S5 or B10 in the block length dependence of the Gibbs energy of micellization which is assigned to lengthy hydrophobic blocks being tightly coiled in the molecular state in water. Light scattering was used to determine micellar association numbers and radii, and scaling exponents were established for the dependence of these parameters on S-block length. Phase diagrams defining regions of hard and soft gel were determined by tube inversion and Couette rheometry.

1. Introduction Block copoly(oxyalkylene)s comprising a hydrophilic poly(oxyethylene) block and a second hydrophobic block have interesting properties, including micellization in dilute solution and gelation of concentrated micellar solutions.1,2 We have prepared block copolymers of ethylene oxide and styrene oxide and have investigated the aqueous solution properties of copolymers with diblock and triblock (SE and SES) architectures.3-6 We use E to denote an oxyethylene unit, OCH2CH2, and S to denote an oxyphenylethylene unit, OCH2CH(C6H5). Very recently, copolymers of this type have been released onto the market by Goldschmidt AG. (1) Booth, C.; Attwood, D. Macromol. Rapid Commun. 2000, 21, 501. (2) Chu, B.; Zhou, Z.-K. In Nonionic Surfactants, Poly(oxyalkylene) Block Copolymers; Surfactant Science Series Vol. 60; Nace, V. M., Ed.; Marcel Dekker: New York, 1996; Chapter 3. (3) Mai, S.-M.; Ludhera, S.; Heatley, F.; Attwood, D.; Booth, C. J. Chem. Soc., Faraday Trans. 1998, 94, 567. (4) Mai, S.-M.; Booth, C.; Kelarakis, A.; Havredaki, V.; Ryan, A. J. Langmuir 2000, 16, 1681. (5) 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. (6) Kelarakis, A.; Havredaki, V.; Rekatas, C. J.; Booth, C. Phys. Chem. Chem. Phys. 2001, 3, 5550.

Commercially available block copolymers of ethylene oxide with propylene oxide or 1,2-butylene oxide have provided many copolymers for academic research, and the range has been significantly extended by laboratory synthesis.1,2 A significant factor distinguishing the three types of copolymer is the hydrophobicity of the chain unit. Denoting an oxypropylene unit [OCH2CH(CH3)] by P and an oxybutylene unit [OCH2CH(C2H5)] by B, the hydrophobicities, when judged by their critical micelle concentrations, are in the ratio S:B:P ) 12:6:1.1 Indeed, the hydrophobicity of an oxyphenylethylene S unit is very similar to that of a phenylethylene unit (here denoted St) obtained by copolymerizing styrene.1 However, there are advantages in copolymerizing styrene oxide. The preparation of S-containing copolymers, like that of poly(oxyethylene), is by oxyanionic polymerization, which is more robust than the carbanion chemistry usually used for the polymerization of styrene. Also, the lower glass transition temperature of poly(styrene oxide) (Tg ≈ 40 °C) compared to that of poly(styrene) (Tg ≈ 100 °C) means that effects caused by immobility of blocks in the micelle core are less important in micellar solutions of ES copolymers. Plasticization by water associated with the ether oxygen of the S units may be a consideration. We have already shown that the cores of ES copolymer micelles

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Table 1. Molecular Characteristics of the Copolymersa copolymer

Mn/g mol-1 (NMR)

wt % S (NMR)

Mw/Mn (GPC)

Mw/g mol-1

E45S10 S15E63 S17E65 S20E67

3180 4600 4940 5300

37.7 39.7 42.1 44.4

1.04 1.04 1.04 1.05

3310 4780 5140 5570

a Estimated uncertainty: M to (3%; wt % S to (1%, M /M to n w n (0.01. Mw calculated from Mn and Mw/Mn.

have sufficient mobility at 25 °C to readily solubilize an aromatic drug,7 whereas the glassy cores of ESt copolymer micelles are immobile at 25 °C and are referred to as “frozen”.8 Our previous work on the micellization and micelle properties of diblock copolymers has involved just four copolymers of ethylene oxide and styrene oxide, E50S3.5, E50S5.1, E51S6.5, and S13E60, where the subscripts denote block lengths in chain units.4-6 In this paper we reinforce this sequence with copolymer E45S10 and extend the range with copolymers S15E63, S17E65, and S20E67. Given the E-block lengths involved (m g 45), the sequence of polymerization, indicated above by ES or SE, does not significantly affect the measured properties. 2. Experimental Section 2.1. Copolymers. Copolymers S15E63, S17E65, and S20E67 were prepared by sequential oxyanionic polymerization of styrene oxide (SO) followed by ethylene oxide (EO). The monomers were carefully dried, and a vacuum line and ampule technique was used to eliminate adventitious moisture. The initiator was 2-phenylethanol partly converted to its potassium salt (mole ratio OH/OK ≈ 9). For polymerization of SO, the temperature was gradually increased to 80 °C over a period of 8 weeks. The polymerization of EO using a similar temperature regime was over a period of 2 weeks. Copolymer E45S10 was prepared in reverse order, starting from R-methyl-ω-hydroxypoly(oxyethylene) (Mn ) 2000 g mol-1) partly converted to its potassium salt (mole ratio OH/OK ≈ 5). Samples of homopolymer taken after the first stage of polymerization and the final copolymers were characterized by gel permeation chromatography (GPC, tetrahydrofuran (25 °C) or N,N-dimethylacetamide (60 °C) eluents), matrix-assisted laser desorption ionization (MALDI) mass spectroscopy, and 13C NMR spectroscopy. Calibration of GPC was with poly(oxyethylene) samples of known molar mass. Analysis of the GPC curves gave an estimate of width of the molar mass distribution in the form of the ratio of mass-average to number-average molar mass (Mw/Mn) as if the samples were poly(oxyethylene). The GPC curves of the three SE copolymers showed a small shoulder on the low-volume side of the main narrow peak, which was attributed to initiation of homopoly(oxyethylene) by moisture introduced at the second stage of the copolymerization. NMR spectra were recorded by means of a Varian Unity 500 spectrometer operated at 125.5 MHz. Solutions were ca. 10 wt % in CDCl3, and peak assignments were taken from the report by Heatley et al.9 The integrals of resonances from backbone and end-group carbons were used to determine the S- or E-block lengths of the precursors (S15.2, S17.3, S19.6, and E45.4), and the average compositions of the copolymers then gave the other block lengths, and hence the molecular formula given in Table 1, where block lengths are rounded to the nearest whole number. The values of Mn obtained by MALDI mass spectroscopy (Micromass TOF Spec2E) were in excellent agreement with those from NMR. In analyzing the NMR spectra of the copolymers, allowance was made for the different nuclear Overhauser (7) Rekatas, C. J.; Mai, S.-M.; Crothers, M.; Quinn, M.; Collett, J. H.; Attwood, D.; Heatley, F.; Martini, L.; Booth, C. Phys. Chem. Chem. Phys. 2001, 3, 4769. (8) (a) Jada, A.; Hurtrez, G.; Siffert, B.; Riess, G. Macromol. Chem. Phys. 1996, 197, 3697. (b) Hurtrez, G.; Dumas, P.; Riess, G. Polym. Bull. (Berlin) 1998, 40, 203. (9) Heatley, F.; Yu, G.-E.; Draper, M. D.; Booth, C. Eur. Polym. J. 1991, 27, 471.

enhancements of E and S units, i.e., E/S ) 1.1. A small proportion of homopoly(oxyethylene) was confirmed by the NMR spectra which showed a small excess of E chain ends over ES junctions. Allowance was made for this homopolymer in calculating the formulas of the copolymers and also in treating the experimental results. Copolymer E45S10 was confirmed as a pure diblock copolymer. 2.2. Surface Tension. Surface tensions (γ) of dilute aqueous solutions were measured at 20, 30, and 40 °C by the Wilhelmy plate method using a Kruss K-12 instrument equipped with a processor to acquire the data automatically. The instrument was connected to a circulating water bath with a proportional temperature controller to keep the temperature constant to (0.1 °C. The plate was cleaned by washing with doubly distilled water followed by heating in an alcohol flame. A stock solution (1.0 g dm-3) was prepared with distilled water and diluted as required. In the measurements a solution was equilibrated at 20 °C, and the surface tension was recorded at 15 min intervals until a constant value was reached, a process which took 12-36 h depending on concentration. The temperature was then raised and the process repeated. The accuracy of measurement was checked by frequent determination of the surface tension of pure water. 2.3. Light Scattering. All glassware was washed with condensing acetone vapor before use. Solutions were clarified by filtering through Millipore Millex filters (Triton free, 0.22 µm porosity) directly into the cleaned scattering cell. Static light scattering (SLS) intensities were measured for solutions at temperatures in the range 25-50 °C by means of a Brookhaven BI 200 S instrument with vertically polarized incident light of wavelength λ ) 488 nm supplied by an argon ion laser (Coherent Innova 90) operated at 500 mW or less. The intensity scale was calibrated against scattering from benzene. Dynamic light scattering (DLS) measurements were made under similar conditions by means of the Brookhaven BI 200 S combined with a Brookhaven BI 9000 AT digital correlator. Measurements of scattered light were normally made at θ ) 90° to the incident beam, but with some measurements at other angles to check the angular dependence of intensity. Experiment duration was in the range 5-20 min, and each experiment was repeated two or more times. The correlation functions from DLS were analyzed by the CONTIN method to obtain distributions of decay rates (Γ).10 The decay rate distributions gave distributions of apparent diffusion coefficient (Dapp ) Γ/q2, q ) (4πns/λ) sin(θ/2), ns ) refractive index of water) and hence of apparent hydrodynamic radius (rh,app, radius of hydrodynamically equivalent hard sphere corresponding to Dapp) through the Stokes-Einstein equation

rh,app ) kT/(6πηDapp)

(1)

where k is the Boltzmann constant and η is the viscosity of water at temperature T. The basis for analysis of SLS was the Debye equation

K*c/(I - Is) ) 1/Mw + 2A2c + ...

(2)

where I is intensity of light scattering from solution relative to that from benzene, Is is the corresponding quantity for the solvent, c is the concentration (in g dm-3), Mw is the mass-average molar mass of the solute, A2 is the second virial coefficient (higher coefficients being neglected), and K* is the appropriate optical constant which includes the specific refractive index increment, ν ) dn/dc. The specific refractive index increment at 30 °C measured over a range of compositions, including other E/S copolymers,4 was calculated from

ν/(cm3 g-1) ) 0.134 + 0.067wS

(3)

where wS is the weight fraction S. The temperature derivative of v was taken to be that established previously11 for other poly(oxyethylene)-containing water-soluble block copolymers, i.e., (10) Provencher, S. W. Makromol. Chem. 1979, 180, 201. (11) Bedells, A. D.; Arafeh, R. M.; Yang, Z.; Attwood, D.; Heatley, F.; Padget, J. C.; Price, C.; Booth, C. J. Chem. Soc., Faraday Trans. 1993, 89, 1235.

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-2.3 × 10-4 cm3 g-1 K-1. As discussed previously,3,4 the effect of the different refractive indices of the blocks on the derived molar masses of copolymers of the type under consideration can be neglected. The Debye equation taken to the second term (A2 only, as in eq 2) could not be used to analyze the SLS data as micellar interaction caused curvature of the Debye plot across the concentration range investigated. The fitting procedure used for the curves was based on scattering theory for hard spheres,12 whereby the interparticle interference factor (structure factor, S) in the scattering equation

K*c/(I - Is) ) 1/SMw

(4)

was approximated by

1/S ) [(1 + 2φ)2 - φ2(4φ - φ 2)](1 - φ)-4

(5)

where φ is the volume fraction of equivalent uniform spheres. Values of φ were calculated from the volume fraction of micelles in the system by applying a thermodynamic expansion factor δt ) vt/va, where vt is the thermodynamic volume of the micelles (i.e., 1/8 of the volume, u, excluded by one micelle to another) and va is the anhydrous volume of the micelles (va ) Mw/NAFa, where NA is Avogadro’s constant and Fa is the liquid density of the copolymer solute calculated from published data assuming mass additivity of specific volumes).13,14 The parameter δt applies as an equivalent (effective) parameter for compact micelles irrespective of their exact structure. The method is equivalent to using the virial expansion for the structure factor of effective hard spheres taken to its seventh term but requires just two adjustable parameters, i.e., Mw and δt. 2.4. Rheometry. Solutions were prepared by weighing copolymer and water into small tubes and were mixed in the mobile state before being stored for a day or more at low temperature (T ≈ 5 °C). Rheological properties of the solutions were determined using a Bohlin CS50 rheometer with water bath temperature control. Couette geometry (bob, 24.5 mm diameter, 27 mm height; cup, 26.5 mm diameter, 29 mm height) was used, with 2.5 cm3 sample being added to the cup in the mobile state. A solvent trap maintained a water-saturated atmosphere around the cell, and evaporation was not significant for the temperatures and time scales investigated. Storage and loss moduli were recorded across the temperature range with the instrument in oscillatory-shear mode at a frequency of 1 Hz. The strain amplitude was maintained at a low value ( 5), implying, through eq 8, a factor of 10 in the block length dependence of ∆micG°. Both types of copolymer with x > 5 have values of ∆micH° approaching zero and, as noted in section 3.1.2, compared with shorter copolymers have their hydrophobic blocks tightly coiled in the molecular state in aqueous solution. 3.2. Hydrodynamic Radius. Intensity fraction distributions of log rh,app obtained from DLS (not illustrated) were single narrow peaks assigned to micelles and similar to those found previously for other diblock E/S copolymers.4,5 The intercepts at c ) 0 of linear plots of the reciprocal of the intensity average of rh,app against concentration (see Figure 4 for examples) gave the intrinsic values of rh listed in Table 3. Within experimental error temperature had very little effect on rh, as is usually found for block copoly(oxyalkylene)s.1,2 3.3. Association Number and Thermodynamic Radius. For the present micellar solutions, the dissymmetry (I45/I135) in SLS was shown to be 1.01 or less, which is consistent with micelles with small radii of gyration; a maximum value of rg ) 12 nm can be estimated from rg ) 0.775rh (with rh from Table 3) by treating the micelles as uniform spheres. The dissymmetry value of 1.01 corresponds to a correction factor less than 1% to the 90° scattering intensity.23 (21) Kelarakis, A.; Havredaki, V.; Booth, C.; Nace, V. M. Macromolecules 2002, 35, 5581. (22) Kelarakis, A.; Havredaki, V.; Derici, L.; Yu, G.-E.; Booth, C.; Hamley, I. W. J. Chem. Soc., Faraday Trans. 1998, 94, 3639. (23) (a) Casassa, E. F. In Polymer Handbook, 3rd ed.; Brandrup, J., Immergut, E. H., Eds.; Wiley: New York, 1989; p 485. (b) Beattie, W. H.; Booth, C. J. Phys. Chem. 1960, 64, 696.

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Table 3. Micelle Properties for E/S Diblock Copolymers in Aqueous Solutiona copolymer

T/°C

Mw/105g mol-1

Nw

δt

rt/nm

rh/nm

E45S10

25 40 50 25 30 40 50 25 30 40 50 25 30 40 50

3.4 3.6 3.9 6.7 6.9 7.0 7.3 7.7 8.0 8.5 8.6 10.5 10.5 10.7 11.3

103 109 118 140 144 146 153 150 156 165 167 189 189 192 203

2.3 2.4 2.5 4.6 4.4 4.2 3.9 4.6 4.5 4.2 4.0 4.1 4.1 3.9 3.6

6.5 6.7 7.0 10.3 10.2 10.1 10.1 10.4 10.5 10.4 10.4 11.1 11.1 11.0 10.9

10.0 9.6 8.9 11.8 11.6 11.3 11.4 12.7 12.2 12.0 12.0 15.6 15.4 14.7 14.6

S15E63

S17E65

S20E67

a

Uncertainty: Mw, Nw, and rh to (4%; δt and rt, (3%.

Figure 5. Debye plots for diblock copolymers in aqueous solution at 40 °C: (b) S15E63 and (9) S20E67. The curves were calculated using theory for hard spheres (see section 2.3).

Curvature in the Debye plots is illustrated in Figure 5, which shows data for solutions of two of the copolymers at 40 °C. The curves drawn through the data points are based on scattering theory for hard spheres, as described in section 2.3. The values of Mw and Nw obtained are listed in Table 3. Also listed are values of the thermodynamic expansion factor and the equivalent hard-sphere radius (the thermodynamic radius, rt) calculated from the thermodynamic volume of the micelles, i.e., from vt ) δtva. As usually found for micelles of block copoly(oxyalkylene)s,1,2 values of Nw increase with increase in temperature for a given copolymer and with increase in hydrophobe block length for a given temperature. Values of rt fall with increase in temperature, consistent with a reduction in exclusion by the E-blocks in the micelle corona as the solvent becomes poorer. The effect of S-block length is illustrated for diblock and triblock copolymers in solution at 40 °C by the loglog plot of Nw against n′ ) (n - ncr) in Figure 6a. Here ncr is the minimum value of n for micellization, taken to be ncr ) 1 as described previously.5 The least-squares line through all the data points has slope 1.03 ( 0.05. The effect of E-block length on the value of Nw has been explored for EB and EP diblock copolymers, and the approximate scaling relation Nw ∼ m-0.5 has been established by experiment and theory.1,24,25 Adjustment of the values of Nw to a constant E-block length of 50 units gives the plot shown in Figure 6b and a best straight line of slope 1.11 (24) Kelarakis, A.; Havredaki, V.; Viras, K.; Mingvanish, W.; Heatley, F.; Booth, C.; Mai, S.-M. J. Phys. Chem. B 2001, 105, 7384. (25) Nagarajan, R.; Ganesh, K. J. Chem. Phys. 1989, 90, 5843.

Figure 6. Dependence of association number on S-block length. Log(Nw) vs log(n′) (n′ ) n - ncr) for (b) E50S3.5, E50S5.1, and E51S6.5 (ref 4); (9) S13E60 (ref 5); (0) E45S10, S15E63, S17E65, and S20E67 (present work). (a) Association numbers from Table 3. (b) Association numbers adjusted to E-block length m ) 50 (see text).

( 0.03. Nagarajan and Ganesh have predicted Nw ∼ n1.19 for micelles of diblock EP copolymers in water.25 The loglog plots of the radii against n′ (not shown: data in Table 3) give scaling exponents of 0.48 ( 0.03 for rt and 0.34 ( 0.05 for rh, in satisfactory agreement with values obtained for other diblock copolymers.1 3.4. Hard-Gel Boundaries by Tube Inversion. Tubeinversion experiments were used to define the immobile gel region of the phase diagram. Immobility in the test (described in section 2.4) requires the gel to have a yield stress higher than 30 Pa.26 The resulting gel boundaries are shown in Figure 7. Adopting the notation used by Hvidt et al.,27,28 the immobile phase is referred to as “hard gel” . The upper limit of measurement was 95 °C, and the hard-gel boundaries cross this limit at ca. 35 wt % for S20E67, 45 wt % for S17E65, and 55 wt % for S15E63. Beyond these concentrations, the solutions were immobile at all temperatures up to the highest concentration examined (80 wt %). By contrast, the upper temperature for hard gel in the case of S10E45 was ca. 70 °C, consistent with an increase in high-T stability of the hard gel resulting from an increase in hydrophobe block length. The marked difference in critical concentration for hardgel formation (cgc) between the SnE65 copolymers on one hand and copolymer E45S10 on the other is predictable from the SLS results. Compared to micelles of E45S10, (26) Kelarakis, A.; Mingvanish, W.; Daniel, C.; Li, H.; Havredaki, V.; Heatley, F.; Booth, C.; Hamley, I. W.; Ryan, A. J. Phys. Chem. Chem. Phys. 2000, 2, 2755. (27) Hvidt, S.; Jørgensen, E. B.; Brown, W.; Schille´n, K. J. Phys. Chem. 1994, 98, 12320. (28) Almgren, M.; Brown, W.; Hvidt, S. Colloid Polym. Sci. 1995, 273, 2.

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Figure 7. Hard-gel boundaries from tube inversion for the diblock copolymers in aqueous solution: (b) S15E63, (O) S17E65, (9) S20E67, and (0) E45S10. The curves through the data points for copolymers S15E63, S20E67, and E45S10 have no theoretical significance and are intended to guide the eye. No lowtemperature boundary to the hard gel was detected within the temperature range investigated.

Figure 8. Temperature scans of the logarithm of the elastic modulus for solutions of copolymer E45S10 of concentration (4) 60, (b) 35, and (O) 31 wt %.

because of the longer E blocks in the micelle corona, those of the SnE65 copolymers exclude significantly larger volumes one to another, as can be seen in Table 3 from their larger thermodynamic radii and expansion factors. Consequently, they form packed cubic gels at lower concentrations. The determining factor is the effective hard-sphere volume fraction, which is given by

φ ≈ cδt/102Fa

(10)

where c is the copolymer concentration in wt % and Fa the anhydrous copolymer density in g cm-3, hence the factor of 100. Using the critical value of φc ) 0.74 for facecentered-cubic packing and Fa ≈ 1.13 g cm-3 at 30 °C for both S20E67 and E45S10, the values of the cgc calculated from eq 10 in the form

cgc ≈ φc102Fa/δt

(11)

are 20 wt % for S20E67 and 35 wt % for S10E45, in reasonable agreement with experiment (see Figure 7). A feature of the gelation of aqueous micellar solutions of many E/P and E/B copolymers is a low-temperature boundary to the hard gel at moderate concentrations.2,29,30 This arises from the instability of their micelles in aqueous solution at low temperature, an effect which is epitomized by a positive standard enthalpy of micellization. A low-T boundary to the hard gel is not observed for the present ES copolymer solutions (see Figure 7), nor for other ES systems investigated.4,5 Micelle stability across a wide temperature range is consistent with the low values of ∆micH° found in present and previous4,6 work on ES systems. An additional mechanism may be kinetic stabilization of the micelles by vitrification of the S-block core as T f 0 °C.7 Drug solubilization in a concentrated micellar solution at ambient followed by subcutaneous or intraperitoneal injection and consequent gelation at body temperature has been advocated as a method of controlled drug release,31 and it may be that this application is not possible using ES copolymer solutions. 3.5. Gel Boundaries by Rheology (E45S10). Temperature scans of storage and loss moduli were used to explore (29) Hamley, I. W.; Mai, S.-M.; Ryan, A. J.; Fairclough, J. P. A.; Booth, C. Phys. Chem. Chem. Phys. 2001, 3, 2972. (30) Altinok, H.; Nixon, S. K.; Gorry, P. A.; Attwood, D.; Booth, C.; Kelarakis, A.; Havredaki, V. Colloids Surf. B 1999, 16, 73. (31) Miyazaki, S.; Ohkawa, Y.; Takada, M.; Attwood, D. Chem. Pharm. Bull. 1992, 40, 2224.

Figure 9. Temperature scans of the logarithm of elastic modulus for solutions of copolymer E45S10 of concentration (1) 15.9, (3) 12.7, (2) 8.9, (O) 5.6, and (b) 2.7 wt %.

the rheological behavior of micellar solutions at concentrations above and below the critical gel concentration. Only solutions of copolymer E45S10 were investigated in this way, and because of shortage of sample, only a limited study was possible. Figure 8 shows examples of temperature scans of the logarithm of elastic modulus for solutions with concentrations in the range 31-60 wt %. The hard-gel boundary was set at G′ ≈ 103 Pa, a value which correlates with a yield stress of ca. 30 Pa for cubic micellar gels.26,32 There are transitions within the hard-gel region, possibly related to changes in structure. The modulus of the 60 wt % hard gel fell rapidly from a high value (G′ ≈ 30 kPa) through G′ ≈ 1 kPa at 55 °C to G′ < 1 Pa, the latter value being characteristic of a sol. The fall in G′ found for the hard gels of the 31 and 35 wt % solutions was less severe, and the resulting phase was a soft gel which, on further heating, formed a sol at temperatures just above 70 °C. The maximum value of G′ found for these soft gels was 1.3 kPa. The pronounced separation of the soft gel from the hard gel seen for the 31 wt % solution is similar to that found in other relatively dilute systems.5,26,28,33 Figure 9 shows examples of temperature scans of the logarithm of elastic modulus for solutions with concentra(32) 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. (33) Kelarakis, A.; Castelletto,V.; Chaibundit, C.; Fundin, J.; Havredaki, V.; Hamley, I. W.; Booth, C. Langmuir 2001, 17, 4232.

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neutron scattering for micellar solutions of EPE copolymers.36,37 There is evidence (from SAXS) that soft gels near to a cubic hard-gel boundary in diblock EB systems are defective cubic structures,26 and stress relaxation experiments on related gels of E80P30E80 (F68) point to complex relaxation functions for such materials.38 The assignment of soft gels as either percolation-induced structures or defective cubic phases differs from that made by Hvidt and co-workers for certain EPE copolymers.27,28,39 In those systems a high-temperature soft gel is formed from cylindrical (rodlike) micelles, but we have no evidence for such micelles in dilute solutions of E45S10. Figure 10. Gel boundaries from rheometry for aqueous solutions of copolymer E45S10. The curves through the data points have no theoretical significance and are intended to guide the eye.

tions in the range 2.7-15.9 wt %, i.e., below the minimum concentration for hard-gel formation. The maximum value of G′ increases with increase in concentration from 26 Pa (2.7 wt %) to 740 Pa (15.9 wt %). At the same time the lower temperature limit for soft gel falls with increase in concentration from 62 °C (2.7 wt %) to 24 °C (15.9 wt %), while the upper limit stays almost constant at ca.73 °C, the same limit as found for the soft gels which form above the hard gel at higher concentrations (see Figure 8). All these solutions had elastic moduli significantly higher than their viscous moduli. Regions of sol, soft gel, and hard gel defined by rheometry are shown on the phase diagram in Figure 10. The hard-gel boundary from rheology is similar to but not coincident with that defined by tube inversion. The lower soft-gel boundary is similar to that found for micellar solutions of many other diblock copolymers, including S13E605 as well as EB24,26,34 and EP35 copolymers. An upper boundary to the soft gel was detected for solutions of E41B8.34 Probably the high-T boundary is outside the accessible temperature range for the other systems. The dilute soft gel is thought to be a structure of weakly interacting spherical micelles formed from sol via a percolation transition.34 The transition from sol to soft gel is assumed to occur when there is sufficient structure to cause an increase in modulus and, at a suitable frequency, the dynamic storage modulus to exceed the loss modulus. There is confirmatory information from small-angle (34) Li, H.; Yu., G.-E.; Price, C.; Booth, C.; Hecht, E.; Hoffmann, H. Macromolecules 1997, 30, 1347. (35) Kelarakis, A.; Havredaki, V.; Booth, C. Macromol. Chem. Phys., in press.

4. Concluding Remarks Research on the properties of E/S copolymers in aqueous solution is at an early stage, and micellization behavior, micelle properties, and gelation require documentation. The work has urgency as micelles of ES copolymers have potential for enhanced solubilization of aromatic solutes. Moreover, related copolymers have recently been introduced to the market. The results discussed in this paper provide a broad account of the association behavior of diblock ES copolymers in aqueous solution, confirm features that are common with aqueous solutions of diblock EP and EB copolymers, and emphasize an important difference in gelation at low temperatures from these two systems. Additionally, combination of results for ES and EB copolymers has provided a sufficiently wide range of hydrophobicity to reveal, for the first time, a significant transition in the dependence of the Gibbs energy of micellization on hydrophobe block length. Acknowledgment. Mr. S. K. Nixon, Dr. C. Chaibundit, and Dr. F. Heatley helped with the characterization of the copolymers. The project was supported by the Engineering and Physical Science Research Council (UK) through Grants GR/N63727 and GR/M96742, by the Ministry of Science and Technology, Spain, through project MAT2001-2877 (P.T. and V.M.), by the Brazilian Research Council CNPq (N.M.P.S.R.), and by GlaxoSmithKline (M.C.). LA026086M (36) Lobry, L.; Micali, N.; Mallamace, M.; Liao, C.; Chen, S.-H. Phys. Rev. E 1999, 60, 7076. (37) Liu, Y.; Chen, S.-H.; Huang, J. S. Macromolecules 1998, 31, 2236. (38) Nystro¨m, B.; Walderhaug, H. J. Phys. Chem. 1996, 100, 5433. (39) Jørgensen, E. B.; Hvidt, S.; Brown, W.; Schille´n, K. Macromolecules 1997, 30, 2355.