Polyoxyalkylene Block Copolymers in Formamide−Water Mixed Solvents

consisting of water and formamide (a nonaqueous polar solvent). ... Upon an increase of the formamide-water ratio, the enthalpy and entropy of micelli...
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Langmuir 2000, 16, 4819-4829

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Polyoxyalkylene Block Copolymers in Formamide-Water Mixed Solvents: Micelle Formation and Structure Studied by Small-Angle Neutron Scattering Lin Yang and Paschalis Alexandridis* Department of Chemical Engineering, University at Buffalo, The State University of New York, Buffalo, New York 14260-4200 Received September 22, 1999. In Final Form: February 21, 2000 We investigated the solution properties of an amphiphilic poly(ethylene oxide)-poly(propylene oxide)poly(ethylene oxide) (PEO-PPO-PEO) block copolymer (Pluronic P105: EO37PO58EO37) in mixed solvents consisting of water and formamide (a nonaqueous polar solvent). The critical micellization concentration and temperature, the thermodynamic parameters of micellization, and the micelle structural parameters were obtained from small-angle neutron scattering (SANS) as a function of the formamide-water ratio, solution temperature, and block copolymer concentration. PEO-PPO-PEO block copolymers self-assemble in formamide-water mixed solvents with increasing temperature, indicating an endothermic micellization. Upon an increase of the formamide-water ratio, the enthalpy and entropy of micellization become smaller than the respective quantities in water. The micelle core and corona radii, the hard-sphere interaction distance of the micelles, the micelle association number, as well as the polymer volume fraction in the core and corona were obtained by fitting a core-corona form factor and a hard-sphere interaction structure factor to the SANS scattering patterns. The micelle radii and association numbers decrease with increasing formamide-water ratio in the mixed solvents. The polymer volume fractions in both the micelle core and corona also decrease with increasing formamide-water ratio. These indicate that the addition of formamide into water affects the micellization process by increasing the solvation of the micelle core and corona, thereby favoring smaller micelles. An increase of temperature results in larger micelle association numbers and a lower degree of solvation in the micelle core and corona in the formamide-water mixed solvents.

Introduction Poly(ethylene oxide)-block-poly(propylene oxide)-blockpoly(ethylene oxide) (PEO-PPO-PEO) amphiphilic block copolymers (commercially available as Poloxamers or Pluronics1) find many applications (industrial,2 as well as pharmaceutical, e.g., drug solubilization3 and controlled release4-6) which emanate from their unique ability to self-assemble in aqueous solutions and to modify interfacial properties.7,8 The self-assembly properties of PEOPPO-PEO block copolymers can be modulated by a variation (during synthesis) of their molecular characteristics, e.g., the hydrophilic (PEO) to hydrophobic (PPO) ratio and the molecular weight. For a block copolymer of fixed PEO/PPO ratio and molecular weight, the selfassembly properties can be further modulated by the solvent conditions (e.g., solvent quality, temperature, presence of cosolvents and/or cosolutes).7,9,10 Block copolymers dissolved in selective solvents (solvents which are good for one block type, but bad for the * To whom correspondence should be addressed. Fax: (716) 6453822. E-mail: [email protected]. (1) Pluronic and Tetronic Surfactants. Technical Brochure, BASF Corp.: Parsippany, NJ, 1989. (2) Edens, M. W. Surfactant Sci. Ser. 1996, 60, 185-210. (3) Hurter, P. N.; Alexandridis, P.; Hatton, T. A. Surfactant Sci. Ser. 1995, 55, 191-235. (4) Johnston, T. P.; Punjabi, M. A.; Froelich, C. J. Pharm. Res. 1992, 9, 425-434. (5) Bhardwaj, R.; Blanchard, J. J. Pharm. Sci. 1996, 85, 915-919. (6) Yang, L.; Alexandridis, P. ACS Symp. Ser. 2000, 752, in press. (7) Alexandridis, P.; Hatton, T. A. Colloids Surf. A 1995, 96, 1-46. (8) Alexandridis, P. Curr. Opin. Colloid Interface Sci. 1997, 2, 478489. (9) Alexandridis, P.; Nivaggioli, T.; Hatton, T. A. Langmuir 1995, 11, 1468-1476. (10) Alexandridis, P.; Holzwarth, J. F. Langmuir 1997, 13, 60746082.

other) can spontaneously associate to form micelles, with the solvent-insoluble block localized in the micelle core and the solvent-soluble block forming a corona (shell) around the core.11,12 The solvent quality is a controlling factor in the self-assembly of block copolymers.12,13 Water, the solvent most commonly used in applications of PEOPPO-PEO block copolymers, is a good solvent for PEO and relatively (above a certain temperature) bad solvent for PPO. The solubility in water of both PEO and PPO decreases with increasing temperature.14 This is the origin of the reverse thermal gelation, one of most unique and useful properties of PEO-PPO-PEO block copolymers.1,2 The addition of cosolvents or cosolutes to water can alter its solvent quality toward the PEO and PPO blocks and thus affect the micellization properties as well as the structure of the block copolymer self-assemblies, thereby providing an extra degree of freedom in tailoring the PEOPPO-PEO solution properties for specified applications.10,12,15-17 We recently examined the self-assembly of a PEOPPO-PEO block copolymer in formamide (instead of water) as selective solvent.18,19 Formamide is the most (11) Alexandridis, P.; Hatton, T. A. In Polymeric Materials Encyclopedia, Salamone, J. C., Ed.; CRC Press: Boca Raton, FL, 1996; pp 743-754. (12) Alexandridis, P.; Spontak, R. J. Curr. Opin. Colloid Interface Sci. 1999, 4, 130-139. (13) Holmqvist, P.; Alexandridis, P.; Lindman, B. J. Phys. Chem. B 1998, 102, 1149-1158. (14) Alexandridis, P.; Holzwarth, J. F.; Hatton, T. A. Macromolecules 1994, 27, 2414-2425. (15) Cheng, Y.; Jolicoeur, C. Macromolecules 1995, 28, 2665-2672. (16) Armstrong, J.; Chowdhry, B.; Mitchel, J.; Beezer, A.; Leharne, S. J. Phys. Chem. 1996, 100, 1738-1745. (17) Alexandridis, P.; Ivanova, R.; Lindman, B. Langmuir 2000, 16, in press. (18) Alexandridis, P. Macromolecules 1998, 31, 6935-6942. (19) Alexandridis, P.; Yang, L. Macromolecules 2000, 33, in press.

10.1021/la991262l CCC: $19.00 © 2000 American Chemical Society Published on Web 04/09/2000

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studied nonaqueous polar solvent. Such solvents are of fundamental (e.g., elucidation of “hydrophobic effect”20-22) and practical (e.g., in applications where it is desirable to replace water by a nonaqueous solvent22) interest in surfactant self-assembly. We note, however, that the number of published reports on amphiphiles in nonaqueous solvents is rather limited, especially those concerning the variation of the micelle structure under various solvent conditions.20-25 Earlier studies on the micellization of lowmolecular weight oligo(ethylene oxide) alkyl ethers in formamide indicated that, compared with water, the critical micellization concentrations (cmc) are much higher, while the micelle association number and enthalpy of micellization are smaller. A differential scanning calorimetry study found the addition of 40% formamide in aqueous solutions of Pluronic F87 to increase the cmc 3-fold.16 Our recent studies demonstrated that PEOPPO-PEO block copolymers can form in formamide micelles (in solution) as well as lyotropic liquid crystalline “gels” with a variety of morphologies.18,19 The concentration-temperature range where these micelles and “gels” form suggests that formamide is a better solvent than water for the PEO-PPO-PEO block copolymers. To further probe the effects of solvent quality on the block copolymer self-assembly, we examine here the PEOPPO-PEO micelle formation and structure in mixed solvents consisting of water and formamide (at varying mixing ratios, covering the whole range from 100% water to 100% formamide). We employed small-angle neutron scattering (SANS) as the principal means of characterization. SANS is a very powerful tool for the study of polymers26 and has been useful in the structural characterization of aqueous PEO-PPO-PEO block copolymer solutions.27-32 Our results are presented in two parts: in the first part we examine the conditions under which micelles form, and from these we deduce the thermodynamic parameters of micellization in the mixed solvents; in the second part we propose an appropriate model to fit the SANS scattering patterns, and from these fits we obtain the micelle structural parameters, such as micelle core and corona radii, association number, and polymer volume fraction in the micelle core and corona. We thus provide a comprehensive picture of how the addition of formamide, as a representative nonaqueous polar cosolvent, affects the self-assembly of PEO-PPO-PEO block copolymers in aqueous solutions. (20) Evans, D. F. Langmuir 1988, 4, 3-12. (21) Wa¨rnheim, T. Curr. Opin. Colloid Interface Sci. 1997, 2, 472477. (22) Sjo¨berg, M.; Wa¨rnheim, T. Surfactant Sci. Ser. 1997, 67, 179205. (23) Jonstro¨mer, M.; Sjo¨berg, M.; Wa¨rnheim, T. J. Phys. Chem. 1990, 94, 7449-7555. (24) Perche, T.; Auvray, X.; Petipas, C.; Anthore, R.; Rico-Lattes, I.; Lattes, A. Langmuir 1997, 13, 1475-1480. (25) Penfold, J.; Staples, E.; Tucker, I.; Cummins, P. J. Colloid Interface Sci. 1997, 185, 424-431. (26) Higgins, J. S.; Benoit, H. C. Polymers and Neutron Scattering; Oxford University Press: New York, 1996. (27) Mortensen, K.; Pedersen, J. S. Macromolecules 1993, 26, 805812. (28) Wu, G.; Chu, B.; Schneider, D. K. J. Phys. Chem. 1995, 99, 50945101. (29) Goldmints, I.; von Gottberg, F. K.; Smith, K. A.; Hatton, T. A. Langmuir 1997, 13, 3659-3664. (30) Liu, Y.; Chen, S.-H.; Huang, J. S. Macromolecules 1998, 31, 2236-2244. (31) Jian, N. J.; Aswal, V. K.; Goyal, P. S.; Bahadur, P. J. Phys. Chem. B 1998, 102, 8452-8458. (32) Yang, L.; Slawecki, T. M.; Alexandridis, P. Macromolecules submitted.

Yang and Alexandridis

Materials and Methods Materials. The Pluronic P105 poly(ethylene oxide)-block-poly(propylene oxide)-block-poly(ethylene oxide) copolymer was obtained as a gift from BASF Corp. and was used as received. On the basis of its nominal molecular weight of 6500 and 50% PEO content, Pluronic P105 can be represented by the formula EO37PO58EO37. Deuterated formamide (DCOND2) and deuterated water were purchased from Cambridge Isotope Laboratories. Care was taken to avoid exposure of formamide to atmospheric humidity. Note the disclaimer that identification of certain commercial materials and equipment does not imply recommendation by the National Institute of Standards and Technology. Small-Angle Neutron Scattering. SANS measurements were performed at the National Institute of Standards and Technology (NIST) Center for Neutron Research (NCNR), on the NG3 beam line. The sample-to-detector distance was 260.0 cm. The neutron wavelength used was λ ) 0.6 nm, and the wavelength resolution was ∆λ/λ ≈ 0.15. The angular distribution of the scattered neutrons was recorded in a two-dimensional detector. For a given scattering vector value, q*, the scattering intensity was obtained by averaging the intensity of all the points the 2-D detector space whose distance from the central point is q*. This circular average scattering intensity was used for data analysis. Scattering intensities from the block copolymer solutions were corrected for detector background, empty cell scattering, and sample transmission, following established procedures. The Pluronic P105 solutions (block copolymer concentration: 1 and 8 wt %) in formamide-water mixed solvent (where the formamide content in the mixed solvent was 0, 20, 40, 60, 80, or 100 vol %) were placed in stoppered 1 mm path-length banjo quartz cells. Scattering intensity data were recorded at different temperatures in the range 10-60 °C. Adequate time for thermal and kinetic33 equilibration was allotted.

Block Copolymer Micelle Formation in Mixed Solvents Temperature Dependence of Scattering Patterns. The evolution with temperature (in the range 10-60 °C) of the SANS scattering patterns for Pluronic P105 block copolymer in formamide-water mixed solvent is presented in Figure 1. Two different regimes are evident for both block copolymer concentrations and solvent-cosolvent ratios shown in Figure 1. (i) At low temperatures (e.g., 10 °C), the scattering intensity is low and the scattering function shows very weak q-dependence, indicating that scattering originates from unassociated block copolymer chains, denoted here as unimers. (ii) At higher temperatures, the scattering intensity increases dramatically at low q values (q < 0.1 Å-1), which indicates the association of unimers into micelles with well defined spherical shape. In the 8 wt % block copolymer solutions (Figure 1, bottom row), the scattering functions become increasingly dominated by a correlation peak, revealing significant intermicellar interactions. As seen in Figure 1, the scattering intensity at high q values does not vary much with temperature. The similar scattering function at large q values observed in unimers and micelles is attributed to the presence of polymers dissolved in the solvent region even when well-defined micelles are present. In fact, a closer look at the high q region of Figure 1 reveals a slight decrease of the scattering intensity with increasing temperature for a given block copolymer concentration, suggesting that the concentration of polymer chains in the solvent decreases as the unimer-to-micelle equilibrium is shifted to favor micelles. From scattering patterns such as shown in Figure 1 we extract information about the unimer and micelle structure, as well as about the onset of micellization. Below, (33) Kositza, M.; Bohne, C.; Alexandridis, P.; Hatton, T. A.; Holzwarth, J. F. Macromolecules 1999, 32, 5539-5551.

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Figure 1. Representative SANS scattering patterns from Pluronic P105 (EO37PO58EO37) solutions in formamide (DCOND2)water (D2O) mixed solvent as a function of temperature (10, 20, 30, 40, 50, and 60 °C). The block copolymer concentration is 1 wt % (top row) and 8 wt % (bottom row), and the formamide content in the mixed solvent is 20 vol % (left column) and 80 vol % (right column). The error bars for the SANS intensities are smaller than the symbols.

we first analyze the micelle formation and then continue with the micelle structure. Temperature-ConcentrationMicellizationBoundary. The formation of micelles is often reflected in a dramatic change of a number of solution properties such as scattering intensity or surface tension.9,34 The unimerto-micelle transition can thus be identified by monitoring the change of properties related to micelle formation. Most often in surfactant solutions such changes take place at varying surfactant concentrations. In the case of PEOPPO-PEO block copolymers in aqueous solutions, temperature is an important parameter which affects the micellization through a change in the solvent quality for the PPO and PEO blocks. The sensitivity of the PEOPPO-PEO micellization to temperature allows the determination of cmt, the temperature where micelles start forming at a given block copolymer concentration. The determination of cmt at a given concentration is equivalent to the determination of cmc at different temperatures.14 Figure 2 shows the normalized scattering intensity (I/c) at a constant q value (0.021 Å-1 for 1 wt % P105 solution, and 0.041 Å-1 for 8 wt % P105 solution) as a function of temperature for Pluronic P105-formamide (DCOND2)-water (D2O) solutions with different formamide contents (0-100 vol %) in the mixed solvent. At low temperatures, e.g., 10 °C, the scattering intensity I/c remains constant for both block copolymer concentrations and does not vary with formamide content in the mixed solvent. This low-temperature region, with similar scat(34) Alexandridis, P.; Athanassiou, V.; Fukuda, S.; Hatton, T. A. Langmuir 1994, 10, 2604-2612.

tering intensities for different formamide-water ratios and for different block copolymer concentrations, corresponds to unimers. Figure 2 also points to a characteristic temperature, after which a further temperature increase will lead to a significant increase of the scattering intensity, indicating the formation of micelles. We can then define the cmt from the intercept of the horizontal line passing though the temperature-independent I/c data points and the tangent of the I/c vs temperature curve in the region of increasing I/c. The cmt values thus extracted are plotted in Figure 3 as a function of the block copolymer concentration, for formamide-water mixed solvents with varying formamide content (the error bars in Figure 3 reflect the uncertainty of determining the cmt’s from Figure 2). Also plotted in Figure 3 are cmt data from the micellization of Pluronic P105 in one-component solvents, for both water and formamide.19 The line connecting the cmt-cmc points can be viewed as a micellization boundary within the onephase solution region. At temperatures and concentrations below the micellization boundary (low temperature-low concentration corner), the block copolymers exist in the solution as unimers. At the region above the micellization boundary (high temperature-high concentration corner), the block copolymers begin to self-assemble into micelles, which coexist in equilibrium with unimers (the concentration of unimer in equilibrium with micelles decreases rapidly with increasing temperature, and eventually becomes vanishingly small10). From a comparison of the micellization boundary of Pluronic P105 in mixed solvents of different formamide-

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Figure 3. Micellization boundary for Pluronic P105 dissolved in formamide-water mixed solvents of varying formamide contents in the mixed solvent (0, 20, 40, 60, 80, and 100 vol %). The micellization boundary represents cmt and cmc data. At temperatures and concentrations below the micellization boundary, the block copolymers do not associate (unimers). At temperatures and concentrations above the micellization boundary, micelles are formed which coexist in equilibrium with unimers.

where R is the ideal gas constant, T is the absolute temperature, and Xcmc is the critical micelle concentration, expressed in mole fraction units, at temperature T (cmc values at different temperatures can be obtained from the micellization boundaries of Figure 3). ∆G° is expressed in terms of the standard enthalpy of micellization, ∆H°, and the standard entropy of micellization per mole of surfactant, ∆S°, as: Figure 2. Scattering intensity (I/c) normalized with respect to the block copolymer concentration (top: 1 wt % at q ) 0.021 Å-1; bottom: 8 wt % at q ) 0.041 Å-1), plotted as a function of temperature for Pluronic P105 dissolved in different formamide-water mixed solvents (the formamide content in the mixed solvent is 0, 20, 40, 60, 80, and 100 vol %). Note that at low temperature, I/c is the same for all mixed solvents examined. The increase of I/c with increasing temperature is indicative of the formation of micelles. The error bars for the SANS intensities are smaller than the symbols.

water ratios, we find that the micellization boundary shifts gradually to higher temperatures and concentrations with an increase of the formamide content in the mixed solvent. For a given temperature, the concentration at which Pluronic P105 forms micelles increases with the increase of the formamide content in the mixed solvent, indicating that, upon adding formamide, the formamide-water mixed solvent becomes a better solvent for the PEOPPO-PEO copolymer. The slope of the micellization boundary changes gradually with the increase of formamide content, suggesting that adding formamide will affect the thermodynamic parameters of the micellization. Thermodynamics of Block Copolymer Micellization in Formamide-Water Mixed Solvents. The cmccmt data for the Pluronic P105 solution in the mixed solvent can be further used to generate information on the thermodynamic parameters of the amphiphile micellization.14 The standard free energy change for the transfer of 1 mole of amphiphile from solution to the micellar phase (free energy of micellization), ∆G°, assuming an equilibrium between unimers and micelles, is given by:

∆G° ) RT ln(Xcmc)

(1)

∆G° ) ∆H° - T ∆S°

(2)

The micellization free energy values, ∆G°, are negative since thermodynamically stable micelles are formed spontaneously. Furthermore, ∆G° becomes more negative at higher temperatures, suggesting a larger driving force for micellization. From a comparison of the ∆G° vs T data plotted in Figure 4 for Pluronic P105 dissolved in formamide-water mixed solvents, we note that at a given temperature ∆G° becomes less negative as the amount of formamide in the solvent increases. Moreover, the ∆G° vs T slope becomes smaller with increasing formamide content. These data indicate that the addition of formamide to water decreases the driving force for micellization. The standard enthalpy of micellization, ∆H°, can be obtained from the intercept of the ∆G° vs T curves (Figure 4 top), according to eq 2 and assuming ∆H° to be independent of temperature. The ∆H° values thus calculated are plotted in Figure 4 (bottom) vs the formamide content in the mixed solvent. The ∆H° values are positive in all formamide-water ratios, indicating that the transfer of the block copolymer molecules from unimers to micelles is an enthalpically disfavored endothermic process. With the change of the solvent quality, the ∆H° value for Pluronic P105 solution decreases by a factor of 1/3, from 330 kJ/mol in pure water to 110 kJ/mol in pure formamide. At low formamide content (up to 40 vol %) ∆H° remains close to the corresponding value in water, while a decrease of the ∆H° value occurs at higher formamide content. Since the enthalpy of micellization is positive, a positive entropy contribution (∆S° > 0) must be the driving force for the micellization to be spontaneous (∆G° < 0). The association of the block copolymers results in an increase of their order and thereby the entropy of the individual block copolymer chains decreases. The increase in the

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a factor of 1/3 with a further increase in the formamide amount in the mixed solvent. This indicates that formamide reduces the enthalpic barrier to the PEO-PPOPEO micellization. At the same time, however, formamide also reduces the entropic driving force responsible for micelle formation. Note that in a study14 of the micellization of 12 different PEO-PPO-PEO block copolymers in aqueous solutions, the lowest ∆H° and ∆S° values were observed for Pluronic F88, which has a higher PEO content (80%), and is thus more hydrophilic in water, than Pluronic P105 which we study here. Thereby the overall impact of formamide in the PEO-PPO-PEO micellization is to render the block copolymer more solvophilic (less solvophobic), compared to the case of pure water solvent. This is also reflected in the micelle structure (as discussed in detail in the following section). Block Copolymer Micelle Structure in Mixed Solvents Unimer Structure. At low temperatures and concentrations, the PEO-PPO-PEO block copolymers are present in solution as unassociated polymer chains (unimers). Within experimental error, the scattering functions of these unimers are in very good agreement to those of polymers obeying a Gaussian conformation (Debye function for the form factor of random coils, Fcoil):35,36

Fcoil(q) ) x-2 [exp(-x) + x - 1]

Figure 4. (Top) Free energy of micelle formation, ∆G°, plotted as a function of temperature for Pluronic P105-formamidewater systems of varying formamide content. (Bottom) Micellization enthalpy ∆H° and entropy ∆S° plotted as function of the formamide vol % content in the mixed solvent. The estimation of the enthalpy ∆H° and entropy ∆S° of micellization comes from the linear fits of ∆G° vs temperature. The error bars for ∆G° and ∆H° are smaller than the symbols.

overall solution entropy observed during the micellization of PEO-PPO-PEO block copolymers can be related to an entropy gain by the solvent molecules when the block copolymers associate, and/or to a decrease in the polarity of the PEO and PPO segments with increasing temperature.7,14 As indicated in Figure 4, ∆S° is positive for all formamide-water ratios; the presence of more than 60 vol % formamide results in much lower ∆S° values compared to the ∆S° in pure water solvent. The entropy of Pluronic P105 micellization in pure formamide is 0.4 kJ/mol K, while that in pure water is 1.2 kJ/mol K, 3 times higher. We wish to note here that, while the specific ∆H° and ∆S° values discussed above were obtained from a limited block copolymer concentration data set and under the assumption of ∆H° and ∆S° being independent of temperature, the observed trends are unambiguous and valid even within the possible error associated with the ∆H° and ∆S° evaluation. In summary, the addition of formamide to water leads to less negative values of the micellization free energy (∆G°), indicating that micelle formation becomes less favorable in the mixed solvents. However, the addition of formamide does not affect the fundamental mechanism (entropic driving force) responsible for the PEO-PPOPEO block copolymer micellization. The solvent properties are dramatically changed when the formamide amount in the mixed solvent is more than 40 vol %: the magnitudes of both enthalpy (∆H°) and entropy (∆S°) are reduced by

(3)

where x ) (qRg)2, and Rg is the radius of gyration of the polymer chain. The radii of gyration (Rg) that result from the best fitting of eq 3 to the SANS data, are plotted in Figure 5 as a function of the formamide content in the mixed formamide-water solvent at 10 and 20 °C. The unimer Rg values remain almost constant at 30 Å throughout the range of conditions examined here. Although the thermodynamic parameters for micellization presented in the previous section suggest that formamide is a better solvent than water at the temperatureconcentration region where micelles form, the constant values of Rg obtained at different formamide-water ratios indicate that at the conditions where the block copolymer chains exist as unimers, the addition of formamide to water does not change the polymer conformation to a noticeable extent. Development of a Model for Spherical Micelles to be Used in the SANS Data Analysis. Upon a further increase of temperature, the solvent quality becomes progressively worse and the unimers start to self-assemble into micelles. It is well accepted that the PEO-PPOPEO block copolymer micelles are composed of a core dominated by the hydrophobic PPO blocks and surrounded by a corona of solvated hydrophilic PEO blocks. This corecorona structure can be explored using the SANS scattering pattern, due to the different content of the deuterated solvent in the solvent phase, in the solvated PEO corona, and in the relatively “dry” PPO core.26 If we assume the micelle solution to be a monodisperse system, then the SANS scattering intensity can be expressed as a product of the form factor, F(q), and the structure factor, S(q), as indicated in eq 4. The form factor F(q) describes the structure of the micelle particle, while the structure factor describes the interaction between the micelle particles.35,36

I(q) ) N (∆F)2 F(q) S(q)

(4)

(35) Mortensen, K. J. Phys.: Condens. Matter 1996, 8, A103-A124. (36) Pedersen, J. S. Adv. Colloid Interface Sci. 1997, 70, 171-210.

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Figure 6. Schematics of (a) block copolymer solution with high micelle concentration; (b) dilute micelle solution. R1 and R2 are the radii of micelle core and core-plus-corona, respectively. Rhs is the hard-sphere interaction distance. When the micelle concentration is high, Rhs ≈ R2, as indicated in (a). When the micelle concentration is relatively low as in (b) micelles are well separated and Rhs > R2.

Figure 5. (Top) Representative example of the best fit (solid line) of the Debye function to SANS scattering intensity data (empty circles), used to extract the unimer radius of gyration for a 1 wt % Pluronic P105 solution in formamide-water mixed solvent with 60 vol % formamide content at 10 °C. (Bottom) Radius of gyration of Pluronic P105 (1 wt %) unimers in formamide-water mixed solvents at 10 and 20 °C plotted as a function of the formamide vol % content. The error bars are smaller than the symbols.

where N is the number density of the micelles, and ∆F is the scattering length density contrast between the micelle particles and the solvent. Hard Sphere Model Form Factor. The hard sphere model describes the form factor of a dense spherical particle with sharp interfaces. For a hard sphere with radius R,

Fc(q,R) ) {3 y-3 [sin(y) - y cos(y)]}2

(5)

where y ) qR. The hard sphere model has only one parameter to fit in the form factor, and in many cases can give good fits to the scattering intensity curves.27 In the evaluation of the micelle radius using the hard sphere model, it is assumed that there is no solvent in the core and corona, thus the radius R obtained from eq 5 is the radius of the micelle. The assumption about solvent-free core and corona is generally not valid for the PEO-PPOPEO micelles. However, as indicated in Figure 6a, in block copolymer solutions where the micelle concentration is adequately high so that the micelle coronas start to “touch” each other, the hard sphere model can describe the scattering generated from the contrast between the dry core and the solvated corona (which occupies the rest of the solution volume). In the case depicted in Figure 6a,

the R obtained from eq 5 corresponds to the micelle core radius, if there is a sharp boundary between the core and corona. The disadvantages of the hard sphere model are the following. (i) There is a certain concentration (usually difficult to know and dependent on the solvent conditions) below which the micelles remain independent in the solvent (as shown in Figure 6b), and the radius R evaluated from eq 5 has a value intermediate between the core radius and that of the micelle (core-plus-corona). Equation 5 usually fits well the scattering data but it is not certain that we are in the proper region. (ii) The hard-sphere model provides little information about the solvent content in the micelle core and corona. In the case of PEO-PPOPEO block copolymers, it is known that the solubility in water of both PEO and PPO changes with increasing temperature.38 Micelles should thus undergo a progressive solvent loss in both the corona and the core when the temperature increases from the cmt to a higher value. Typically, when the hard-sphere model is used to evaluate the temperature evolution of the PEO-PPO-PEO micelle structure, the micelle core is assumed to be solvent-free. Core-Corona Model Form Factor. The core-corona model for the form factor, which has been developed29 as an alternative to the hard sphere model, allows the presence of solvent (e.g., water) in both the micelle core and corona, and can be applied to the dilute micelle solution (see Figure 6b):

F(q) (∆F)2 ) {(4πR13/3)(F1 - F2)[3J1(y1)/y1] + (4πR23/3)(F2 - Fs)[3J1(y2)/y2]} (6) where R1 and R2 are the radii of the micelle core and coreplus-corona, respectively (see Figure 6), F1, F2, and Fs are the scattering length densities (SLD) of the micelle core, micelle corona, and the solvent, respectively, y1 ) qR1 and (37) Goldmints, I.; Yu, G.; Booth, C.; Smith, K. A.; Hatton, T. A. Langmuir 1999, 15, 1651-1656. (38) Svensson, M.; Alexandridis, P.; Linse, P. Macromolecules 1999, 32, 637-645.

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y2 ) qR2. J1(y) is the first-order spherical Bessel function:

J1(y) ) [sin(y) - y cos(y)]/y2

(7)

The form factor given in eq 6 describes the scattering due to the contrast between the micelle core and corona, which have different solvent contents, and the scattering due to the contrast between the micelle corona and the solvent phase (i.e., the solvent with the polymer dissolved in it). Under the assumption that only PPO (and all the PPO) is present in the core and only PEO (and not PPO) is present in the corona (solvent is also present in the micelle core and corona), the SLD of the core, F1, and the corona, F2, are a function of the average (over the core radius) volume fraction of PPO in the core (R1) and of the average volume fraction of PEO in the corona (R2), respectively:

F1 ) R1 FPPO + (1 - R1) Fs F2 ) R2 FPEO + (1 - R2) Fs

(8)

where FPPO (0.325 × 1010 cm-2) and FPEO (0.547 × 1010 cm-2) are the SLD of PPO and PEO, respectively, and Fs is the SLD of solvent, consisting of deuterated formamide and water at different proportions (FD-formamide ) 6.38 × 1010 cm-2 and FD2O ) 6.48 × 1010 cm-2).26 The volume fraction of PPO in the core (R1) and the volume fraction of PEO in the corona (R2) can be expressed in terms of core and core-plus-corona radii (R1 and R2) and the micelle association number, Nassociation, i.e., the number of block copolymer molecules which (on the average) participate in one micelle:

R1 ) R2 )

3 Nassociation VPPO 4πR13 3 Nassociation VPEO 4π(R23 - R13)

(9)

where VPPO is the volume of the PPO block (VPPO ) 5530 Å3) and VPEO is the volume of the PEO blocks (VPEO ) 5410 Å3) of one pluronic P105 PEO-PPO-PEO block copolymer. In summary, the core-corona form factor model has three fitting parameters: the micelle core and core-pluscorona radii, R1 and R2, and the micelle association number, Nassociation. On the basis of these three fitting parameters, the volume fraction of the polymer blocks in the micelle core and corona can be calculated according to eq 9. Hard-Sphere Interaction Structure Factor. As seen in Figure 1, a strong correlation peak develops with increasing temperature in the neutron scattering patterns of 8 wt % Pluronic P105 solution. The appearance of this correlation peak indicates that the interaction between micelles becomes significant. We thus need to take into account the structure factor, S(q), in eq 4 in order to describe the intermicellar interaction. If we view micelles as spherical particles interacting with a hard-sphere distance, Rhs, then the hard-sphere structure factor can be expressed as:36

S(q) )

1 1+24Φ G(qRhs)/(2qRhs)

(see Figure 6a), and G is a trigonometric function of A ) 2qRhs and Φ:

(10)

where Φ is the micellar volume fraction (Φ ) C4πRhs3/ 3Nassociation, with C being the wt % block copolymer concentration), Rhs is the hard-sphere interaction distance

G(A, Φ) ) R(sinA - A cosA)/A2 + β[2A sinA + (2 - A2)cosA - 2]/A3 + γ{-A4cosA + 4[(3A2 - 6)cosA + (A3 - 6A)sinA + 6]}/A5 (11) where R, β, and γ are:

R ) (1 + 2Φ)2/(1 - Φ)4 β ) -6Φ (1 + Φ/2)2/(1 - Φ)4 γ ) (Φ/2)(1 + 2Φ)2/(1 - Φ)4 Note that Φ is a function of the block copolymer concentration (C) and the polymer volume fraction in the micelle core (R1) and corona (R2), which, in turn, are functions of the form factor fitting parameters, R1, R2, and Nassociation (as shown in eq 9):

Φ)

C (VPPO/R1 + VPEO/R2) VPPO + VPEO

(12)

In an attempt to reduce the number of fitting parameters, the assumption was made in some cases, e.g., for 5% Pluronic P85 aqueous solution,29 that the hard-sphere interaction radius, Rhs, is equal to the core-plus-corona radius, R2. This is a reasonable assumption provided the block copolymer concentration is high enough so that the micelles begin to touch each other with their solvated PEO corona parts (Figure 6a). In a case of a very dilute (1%) PEO-PPO-PEO solution, the structure factor was neglected (S(q) ) 1) due to the fact that the micelles could not feel each other.37 Under these low polymer concentration conditions, very weak interparticle interactions will lead to a structure factor close to 1. At an intermediate block copolymer concentration, however, the micelles may be well separated but the interactions among micelles still exist. In other words, the micelles do not touch each other, but could feel each other. In this case the structure factor is significant and we would expect the Rhs and R2 values to be quite different. A sharp boundary between the micelle core and corona is implicit in the definitions of the core and corona SLD (F1 and F2) and polymer volume fraction (R1 and R2) used above. We also assumed that only PPO segments are present in the core and only PEO segments in the corona. Since it is more realistic that PPO and PEO mix to a certain extent at the micelle core-corona boundary, the sharp boundary assumption may seem severe. However, the calculation of the polymer volume fraction in the micelle core and corona is still valid even if there is some PEO in the core and some PPO in the corona, as long as the amount of PPO present in the corona is comparable to the amount of PEO present in the core. Note that the SLD of PPO and of PEO are very close to each other compared with the SLD of deuterated solvent, as shown in Figure 7. Thereby, the calculation of the SLD of the core and corona will not change much even if PEO and PPO were mixed at the core-corona boundary. Another assumption used in the calculation of the solvent SLD is that of homogeneous mixing of formamide and water throughout the solution. This may not be the case if these two solvents exhibited different affinity to the PPO and PEO blocks.17 Again, as indicated by Figure 7, the SLD of formamide and water are very similar, and therefore the possibly uneven distribution of the formamide and water will not affect

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Figure 7. Comparison between the scattering length densities (SLD) of the hydrogenated PEO and PPO blocks and those of the deuterated solvents: D2O and D-formamide (DCOND2).

the results of the SANS fitting. Last, the assumption of monodisperse micelles may affect to a small extent the absolute values of the micelle structural parameters, but should not affect the resulting trends (presented in the following section). SANS Data Analysis: Micelle Structure. As discussed in the Micelle Formation Section the shift of the micellization boundary to higher temperatures and concentrations, and the less negative micellization free energy (∆G°), reveal that the addition of formamide to water enhances the solvation of the PEO-PPO-PEO block copolymer. Such improved solvation may lead to the micelle core and corona swelling to a higher extent when formamide is present. We fitted the scattering data to the core-corona form factor described by eqs 6-9, to directly extract the information on the micelle core and core-pluscorona radii (R1 and R2) and the micelle association number (Nassociation). The solvation conditions in both core and corona are reflected in the calculated (from eq 9) PPO volume fraction in the core (R1) and PEO volume fraction in the corona (R2). The structure factor described in eqs 10-12 is used to account for the intermicellar interactions. We treat the hard-sphere interaction distance (Rhs) as an independent parameter to examine how close to each other the micelles remain in the solution. Representative fittings of the above-described model to 1 and 8 wt % Pluronic P105 in formamide-water mixed solvent with 40 vol % formamide, in the temperature range 30-60 °C, are shown in Figure 8. The parameters (R1, R2, Nassociation, and Rhs) obtained from the fitting of eqs 6-12 to the scattering function of Pluronic P105 in formamide-water mixed solvents at 60 °C are listed in Table 1. The calculated polymer volume fractions in the micelle core and corona (R1 and R2) are also given there. At 60 °C, both 1% and 8% Pluronic P105 solutions are located well into the micelle region of the diagram of Figure 3, and far away from the unimer/micelle transition boundary in the mixed formamide-water solvents. Therefore we can consider the block copolymer micelles at 60 °C to be well defined and to accommodate the majority of the block copolymer present in solution. From a comparison of the data for the 1 and 8 wt % block copolymer solutions, we find that the micelle core and core-plus-corona radii as well as the micelle association number have similar values in both block copolymer concentrations and for all formamide-water compositions examined. The independence of micelle size and association number on the PEO-PPO-PEO concentration observed here is consistent with the behavior observed previously in aqueous Pluronic F127 solutions (in the concentration range of 1-5%).35 However, the hard-sphere

Figure 8. Representative examples of fits of the core-corona model (discussed in the text) to the SANS scattering intensities, used to extract information on the micelle core and core-pluscorona radii (R1 and R2), hard-sphere interaction distance (Rhs) and micelle association number (Nassociation). Data are shown for (top) 1 wt % and (bottom) 8 wt % Pluronic P105 in formamidewater mixed solvent with 40 vol % formamide, in the temperature range of 30-60 °C. The error bars for the SANS intensities are smaller than the symbols.

interaction distances (Rhs) obtained in 1 wt % Pluronic P105 solutions are much higher than the corresponding values in 8 wt % solutions. In fact, Rhs in the 1% solution is about 80% higher than the micelle corona radius (R2), whereas in the 8% solution, Rhs is not more than 10% higher than R2. Thus the micelles are well separated in the 1 wt % block copolymer solution. This leads to a very weak interparticle interaction (see Figure 9 for a plot of the structure factor) and thereby a scattering function without any obvious peak at low q values (Figure 1, top row). In the 8 wt % block copolymer solutions, however, the micelles are much closer to each other. The resulting stronger interaction (see Figure 9) gives rise to a scattering peak at low q values for all the 8 wt % Pluronic P105 samples (Figure 1, bottom row). The difference between Rhs and R2 is not negligible in both block copolymer concentrations, and Rhs remains an important fitting parameter. It is also notable in the data of Table 1 that the polymer (PPO in the core and PEO in the corona) volume fractions in both the micelle core and corona are generally higher in the 8 wt % block copolymer solution compared to the 1 wt % solution, for all formamide contents examined. This coincides with our observations of 8-20 wt % Pluronic P105 micelles in solutions of pure formamide19 and indicates that in formamide-water mixed solvent, a lower

PEO-PPO Block Copolymers in Mixed Solvents

Langmuir, Vol. 16, No. 11, 2000 4827

Table 1. Micelle Structural Parameters Obtained from Fitting Eqs 4-11 to the SANS Scattering Intensities Obtained for 1 and 8 wt % Pluronic P105 Solutions in Formamide-Water Mixed Solvents (of Varying Formamide Content) at 60 °C Pluronic P105 concentration (wt %)

formamide content in mixed solvent (vol %)

R1 (Å) (0.5

R2 (Å) (1

Rhs (Å)

Nassoc (1

R1 (0.02

R2 (0.02

1 1 1 1 1 1 8 8 8 8 8 8

100 80 60 40 20 0 100 80 60 40 20 0

39.5 42.0 43.5 44.5 46.0 47.0 39.0 41.0 43.0 44.0 45.5 46.5

68 73 75 77 79 82 68 70 72 74 77 80

100 ( 5 105 ( 5 135 ( 5 130 ( 5 130 ( 5 140 ( 5 65 ( 2 79 ( 2 83 ( 2 86 ( 2 85 ( 2 85 ( 2

41 51 57 63 70 76 40 48 58 63 71 78

0.88 0.91 0.92 0.94 0.95 0.97 0.89 0.93 0.96 0.96 1.00 1.00

0.21 0.21 0.22 0.23 0.23 0.22 0.20 0.23 0.26 0.26 0.25 0.25

Figure 9. Structure factor, S(q), obtained for 1 and 8 wt % Pluronic P105 in formamide-water mixed solvent with 40 vol % formamide at 60 °C

PEO-PPO-PEO block copolymer concentration results in a looser micelle structure. With an increase of the formamide content in the mixed solvent, the micelle radii and association numbers decrease, accompanied by a small decrease of the polymer volume fraction in both micelle core and corona, as shown in Figure 10. The formation in nonaqueous polar solvents of smaller micelles compared to pure water is generally observed in surfactant systems.23,24 Small micelles, with a large part of the surfactant hydrophobic chain in contact with the solvent, are unfavorable in water because the interfacial tension between water and the hydrophobic chain is high. However, the presence of a nonaqueous polar solvent such as formamide reduces the interfacial tension between the solvent and the hydrophobic chain and allows the formation of smaller micelles.22 The change of micelle radii not only reflects a change of the micelle association number, but also indicates a change of solvation in the micelle corona and core with varying solvent quality. As presented in Figure 10b, the polymer volume fraction in the micelle core and corona progressively decreases with increasing amount of formamide in the mixed solvent, indicating a larger amount of solvent present in the micelle structure. From Table 1 we can see that formamide has the ability to swell the PEO blocks of the PEO-PPO-PEO block copolymers 10-20% more than water, and the PPO blocks 10% more. These observations can be related to a higher solubility of both PEO and PPO in formamide compared to water.18 An enhanced solvation of the PEO-PPO-PEO block copolymer in formamide is also reflected in the micellization diagram of Figure 3. In conjunction with the information from the micellization diagram and corre-

Figure 10. Structural information obtained from SANS in 8 wt % Pluronic P105 solution at 60 °C, plotted as a function of the formamide content in the mixed solvent: (top) micelle core and core-plus-corona radius (R1 and R2) and micelle association number (Nassociation); (bottom) polymer volume fraction in core and corona (R1 and R2). The error bars are indicated in Table 1.

sponding to thermodynamic parameters, the parameters obtained from fitting the SANS scattering intensities provide direct evidence that the addition of formamide to water enhances the swelling of the micelle core and corona. In addition to the effects on the PEO-PPO-PEO micelle structure of varying the solvent composition presented above, the effects of temperature are of significance. The evolution of the micelle structure with temperature for 8 wt % Pluronic P105 solution in pure water and in formamide-water mixed solvents (with 20 and 40 vol % formamide) is recorded in Table 2. Representative structural data for 40 vol % formamide are also plotted in Figure 11 as a function of temperature. Very similar temperature-

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Table 2. Evolution with Temperature of the Micelle Structure in 8 wt % Pluronic P105 in Pure Water and Formamide-Water Mixed Solvents with 20 and 40 vol % Formamide formamide content (vol %)

temperature (°C)

R1 (Å) (0.5

R2 (Å) (1

Rhs (Å) (2

Nassoc (1

R1 (0.02

R2 (0.02

40 40 40 40 20 20 20 20 0 (pure water) 0 (pure water) 0 (pure water) 0 (pure water)

30 40 50 60 30 40 50 60 30 40 50 60

40.0 42.5 43.0 44.0 41.0 42.5 44.0 45.5 40.0 41.5 44.0 46.5

69 73 73 74 71 74 77 77 71 74 77 80

81 84 84 86 83 85 83 85 84 86 84 85

46 56 58 63 50 57 64 71 50 57 67 78

0.94 0.96 0.96 0.96 0.96 0.98 0.99 0.99 1.00 1.00 1.00 1.00

0.22 0.23 0.24 0.25 0.22 0.22 0.22 0.25 0.22 0.22 0.23 0.25

with increasing temperature of the solvent conditions for PPO in water leads to the onset of PEO-PPO-PEO micellization (microphase separation).14 With a further increase of temperature, the solubility of PEO in water is also reduced, as reflected in the 12% increase of the PEO volume fraction in the corona from 30 to 60 °C (Table 2). Since formamide is a better solvent for both PPO and PPO, its addition to water results in a solvated (wet) core and a lower micelle association number compared with pure water solvent. However, the temperature dependence of the PPO and PEO solubility remains unchanged in formamide-water mixed solvent compared to that in aqueous solvent. As shown in Table 2, the PPO volume fraction in the core increases about 6% from 30 to 60 °C in formamide-water mixed solvent with 40% formamide, indicating that the solvent is driven out of the core upon temperature increase; the PEO volume fraction in the corona increases by 12% over the same temperature range. Summary

Figure 11. Structure information obtained from SANS in 8 wt % Pluronic P105 solution in formamide-water mixed solvent with 40 vol % formamide, plotted as a function of temperature: (top) micelle core and core-plus-corona radius (R1 and R2) and micelle association number (Nassociation); (bottom) polymer volume fraction in core and corona (R1 and R2). The error bars are indicated in Table 2.

dependent behavior is observed in pure water and in formamide-water mixed solvents: R1, R2, and Nassociation increase with temperature. In the formamide-water mixed solvent with 40 vol % formamide, R1 ranges from 40 Å at 30 °C to 44 Å at 60 °C, an increase of approximately 10%, while R2 goes from 69 to 74 Å, an 8% increase. Nassociation increases from 46 to 63 (by about 40%) in the same temperature interval. The data presented in Table 2 and Figure 11b also indicate an increase of the PEO volume fraction in the micelle corona (for water and for mixed solvents) and an increase of the PPO volume fraction in the core (for the formamide-water mixed solvents, but not for water) with increasing temperature. It is accepted that the worsening

The micelle formation and structure of a representative poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) amphiphilic block copolymer (Pluronic P105: EO37PO58EO37) in formamide-water mixed solvents was investigated as a function of formamide content, block copolymer concentration, and temperature using smallangle neutron scattering. The micellization of PEO-PPOPEO block copolymers in formamide-water mixed solvents is an endothermic entropy-driven process. The propensity of Pluronic P105 to form micelles becomes smaller with increasing formamide content in the mixed solvent, as evidenced from an increase in the critical micellization temperature and concentration and a decrease in the corresponding micellization free energy. Upon an increase of the formamide content, the enthalpy and entropy of micellization become smaller (by up to a factor of 1/3) than the respective quantities in water. Therefore, the PEO-PPO-PEO block copolymers become more solvophilic in formamide-water mixed solvent compared with that in pure water. In the low temperature-low concentration region where the block copolymers exist as unimers, the SANS scattering patterns were fitted to a Gaussian conformation form factor. The resulting unimer radii of gyration were found to be independent of the formamide-water ratio in the mixed solvent. A model which includes a core-corona form factor and a hard-sphere interaction structure factor was used to fit the SANS data in the high temperaturehigh concentration region where micelles are present. Information on the micelle core and core-plus-corona radii (R1 and R2), intermicellar distance (Rhs) and micelle association number (Nassociation) was extracted from the fits. From the above parameters, and under the assumption that all PPO is localized in the micelle core and all PEO

PEO-PPO Block Copolymers in Mixed Solvents

in the micelle corona, we estimated the volume fraction of the PPO and PEO polymer blocks in the core and corona, respectively. The addition of formamide to water results in a reduction of the micelle radii and association number. The polymer volume fractions in both the micelle core and corona also decrease with increasing formamidewater ratio. These effects indicate that the addition of formamide to water affects the micellization process by increasing the solvation of the micelle core and corona, thereby favoring smaller micelles, and are in agreement with the cmc and cmt observations and micellization thermodynamic analysis. An increase of temperature results in higher micelle association numbers, smaller micelle radii, and a lower degree of solvation in the micelle core and corona in the formamide/water mixed solvents. Therefore, the formamide-water mixed solvent become progressively worse for the PEO-PPO-PEO block copolymer with increasing temperature. The micelle radii are found to be independent of the block copolymer concentration, but the hard-sphere

Langmuir, Vol. 16, No. 11, 2000 4829

interaction distance (Rhs) is larger in the more dilute systems. The above temperature effects are in agreement with published observations in aqueous solutions of PEOPPO-PEO block copolymers. Acknowledgment. P.A. acknowledges the National Science Foundation (CTS-9875848) and the donors of the Petroleum Research Fund, administered by the American Chemical Society (ACS-PRF# 33408-G7) for partial support of this research. We also acknowledge the support of the National Institute of Standards and Technology (NIST), U. S. Department of Commerce, in providing the neutron research facilities used in this work; this material is based upon activities supported by the National Science Foundation under Agreement No. DMR-9423101. We thank Dr. Paul D. Butler at NIST for valuable assistance with the SANS data acquisition. LA991262L