Association Properties of Triblock Copolymers in Aqueous Solution

Department of Chemistry, University of Manchester, Manchester M13 9PL, U.K.. Received May 26 ..... sion of the effect of E-block length and block arch...
0 downloads 0 Views 105KB Size
Download PDF
Langmuir 2000, 16, 9645-9652

9645

Association Properties of Triblock Copolymers in Aqueous Solution: Copolymers of Ethylene Oxide and 1,2-Butylene Oxide with Long E-blocks Chiraphon Chaibundit, Shao-Min Mai, Frank Heatley, and Colin Booth* Department of Chemistry, University of Manchester, Manchester M13 9PL, U.K. Received May 26, 2000. In Final Form: August 17, 2000 Four triblock copolymers, EmB20Em, with m in the range 58-260, were prepared by sequential anionic polymerization of 1,2-butylene oxide followed by ethylene oxide. E denotes an oxyethylene repeat unit and B an oxybutylene repeat unit. The copolymers were characterized by gel permeation chromatography (for distribution width) and 13C NMR spectroscopy (for absolute molar mass and confirmation of triblock architecture). Static and dynamic light scattering were used to study the micellization and micelle properties of the copolymers in dilute aqueous solution, particularly the mass-average association number and thermodynamic and hydrodynamic radii. At a given temperature, the micelle association number decreased as the E-block length was increased while the radii increased. The gelation of relatively concentrated aqueous solutions of the copolymers was also investigated by a tube inversion method. The minimum concentration for gelation decreased in the range 9-13.3 wt % as the E-block length was increased. Comparison is made with recent results for four diblock EmBn copolymers (n ) 17-19) of similar overall chain lengths. The diblock copolymers form micelles with larger association numbers and radii, but the scaling exponents for the effects of the E-block length on association number and radius are similar for the two series of copolymers. Comparison is also made with theoretical predictions of scaling exponents. Given the cubic packing of effectively spherical micelles (bcc or fcc), the critical concentrations for gelation of the micellar solutions of the diblock copolymers could be satisfactorily predicted from the thermodynamic radii of the micelles (using the related thermodynamic expansion factor), but this was not possible for the micellar solutions of the triblock copolymers, suggestive of a more complex structure.

1. Introduction Block copolyethers may associate in dilute aqueous solution to form micelles. This property has been extensively studied for EmPnEm triblock copolymers [E denotes an oxyethylene unit, OCH2CH2, P an oxypropylene unit, OCH2CH(CH3), and m and n are block lengths in repeat units]. This work has been possible because the copolymers are available from a number of commercial sources. A number of authors have summarized recent work.1-5 Regarding the effect of E-block length, several series of copolymers based on constant P-block length are available among the EmPnEm copolymers. However, some do not micellize in dilute solution and not all that do lend themselves to investigation of micellar properties by static light scattering. Comparative studies of the micellar properties of members of the series on the basis of the P39 block have been reported: that is, E27P39E27 (coded P85), E62P39E62 (coded F87), and E97P39E97 (coded F88) by Brown, Mortensen and co-workers,6,7 using dynamic light scattering and small-angle neutron scattering (SANS). Related results for copolymer E22P39E22 (coded P84) obtained by SANS have been reported by Huang and co-workers.8 Copolymer E6P39E6 (coded L81) phase separates before micellization.7 Copolymer P85 has proved of interest (1) Wanka, G.; Hoffmann, H.; Ulbricht, W. Macromolecules 1994, 27, 4145. (2) Chu, B. Langmuir 1995, 11, 414. (3) Alexandridis, P.; Hatton, T. A. Colloids Surf., A. 1995, 96, 1. (4) Almgren, M.; Brown, W.; Hvidt, S. Colloid Polym. Sci. 1995, 273, 2. (5) Chu, B.; Zhou, Z.-K. In Nonionic Surfactants: Poly(oxyalkylene) Block Copolymers; Nace, V. M., Ed.; Marcel Dekker: New York, 1996; Chapter 3. (6) Brown, W.; Schillen, K.; Hvidt, S. J. Phys. Chem. 1992, 96, 6038. (7) Mortensen, K.; Brown, W. Macromolecules 1993, 26, 4128. (8) Liu, Y.-C.; Chen, S.-H.; Huang, J. S. Macromolecules 1998, 31, 2236.

because of the high-temperature sphere-to-rod transition of its micelles.4,9-13 A more limited comparison of the micellar properties of copolymers E31P54E31 (coded P104) and E128P54E128 (coded F108) by Hatton and co-workers14 was restricted to dynamic light scattering and fluorescence spectroscopy, though there are related measurements for P104 by SANS.8 Comparative results from static light scattering (e.g., reliable values of association numbers across a series) have not been obtained. One problem has been the formation of large particles probably caused by insoluble copolymer molecules contained within the composition distribution of the samples.6,15 For example, samples of F88 have been shown to contain two peaks in their GPC curves.16 A limited range of triblock copolymers of ethylene oxide and 1,2-butylene oxide [B ) oxybutylene, OCH2CH(C2H5)] are available from the Dow Chemical Company. The anionic polymerization of 1,2-butylene oxide is cleaner than that of propylene oxide, and study of their micellar solutions by static light scattering is more straightforward.17 Two copolymers, E13B10E13 (coded B40-1900) and (9) Glatter, O.; Scherf, G.; Schillen, K.; Brown, W. Macromolecules 1994, 27, 6046. (10) King, S. M.; Heenan, R. K.; Cloke, V. M.; Washington, C. Macromolecules 1997, 30, 6215. (11) Mortensen, K.; Pedersen, J. S. Macromolecules 1993, 26, 805. (12) Schillen, K.; Brown, W.; Johnsen, R. M. Macromolecules 1994, 27, 4825. (13) Jørgensen, E. B.; Hvidt, S.; Brown, W.; Schillen, K. Macromolecules 1997, 30, 2355. (14) Alexandridis, P.; Nivaggioli, T.; Hatton, T. A. Langmuir 1995, 11, 2874. (15) Brown, W.; Schillen, K.; Almgren, M.; Hvidt, S.; Bahadur, P. J. Phys. Chem. 1991, 95, 1850. (16) Yu, G.-E.; Altinok, H.; Nixon, S. K.; Booth, C.; Alexandridis, P.; Hatton, T. A. Eur. Polym. J. 1997, 33, 673. (17) Yu, G.-E.; Yang, Y.-W.; Yang, Z.; Attwood, D.; Booth, C.; Nace, V. M. Langmuir 1996, 12, 3404.

10.1021/la000725g CCC: $19.00 © 2000 American Chemical Society Published on Web 10/21/2000

9646

Langmuir, Vol. 16, No. 24, 2000

E33B10E33 (coded B20-3800) with identical B-block lengths are available. In water at 40 °C, it was found that their mass-average association numbers (Nw) decreased as the E-block length was increased, but their hydrodynamic radii (rh) were similar:

E13B10E13 Nw ) 23 rh ) 5.2 nm E33B10E33 Nw ) 8 rh ) 5.1 nm Unfortunately, the comparison is not as straightforward as it might appear. As pointed out by Nace et al.,18 copolymer E13B10E13 contains a substantial proportion of diblock copolymer. This is a consequence of the slow addition of ethylene oxide to a secondary B oxyanion compared to a primary E oxyanion: under the conditions used industrially, the ratio of rate constants for the two addition reactions is kE/kB > 20.18 It is known that micelles of diblock copolymers have much higher association numbers than those of triblocks with the same hydrophobe length, whether Bn or Pn,19-23 and the results for the Dow copolymers must be interpreted with this in mind. The composition distribution of copolymer E33B10E33 is less distorted by the difference in addition rate, and the effect may be ignored for EBE copolymers with E-block lengths significantly exceeding E50. The experiments described in this paper were carried out on copolymers prepared in our own laboratory to have E-blocks in the range 58-260 units. Under our laboratory conditions, which involve higher catalyst concentrations and lower polymerization temperatures than those used in industry, the effect of the difference in reaction rate is smaller, kE/kB ≈ 14.24 Since the minimum E-block length is 58 units, the present experiments allow the effect of E-block length on the properties of micelles of triblock EmBnEm copolymers to be explored with confidence. In view of the long E blocks and the need to ensure essentially complete micellization within the dilute concentration range used in light scattering studies, that is, to ensure very low critical micelle concentrations, the length of the central hydrophobe block was held at B20. The long E blocks ensured the formation of spherical micelles. We have recently reported studies on micellar solutions of diblock EmBn copolymers with long E blocks (i.e. from E96 to E398) based on a B-block length of 18 units.25-27 The present results allow for a direct comparison of micelle properties at similar overall chain lengths for the two architectures. 2. Experimental Section 2.1 Copolymers. The triblock copolymers (see Table 1 for details) were prepared by the sequential anionic polymerization of 1,2-butylene oxide followed by ethylene oxide. The methods (18) Nace, V. M.; Whitmarsh, R. H.; Edens, M. W. J. Am. Oil Chem. Soc. 1994, 71, 77. (19) Booth, C.; Attwood, D. Macromol. Rapid Commun. 2000, 21, 501. (20) Yang, Z.; Pickard, S.; Deng, N.-J.; Barlow, R. J.; Attwood, D.; Booth, C. Macromolecules 1994, 27, 2371. (21) Yang, Y.-W.; Deng, N.-J.; Yu, G.-E.; Zhou, Z.-K.; Attwood, D.; Booth, C. Langmuir 1995, 11, 4703. (22) Altinok, H.; Yu, G.-E.; Nixon, S. K.; Gorry, P. A.; Attwood, D.; Booth, C. Langmuir 1997, 13, 5837. (23) Altinok, H.; Nixon, S. K.; Gorry, P. A.; Attwood, D.; Booth, C.; Kelarakis, A.; Havredaki, V. Colloids Surf., B 1999, 16, 73. (24) Yu, G.-E.; Yang, Z.; Ameri, M.; Attwood, D.; Collett, J. H.; Price, C.; Booth, C. J. Phys. Chem. B 1997, 101, 4394. (25) Mingvanish, W.; Mai, S.-M.; Heatley, F.; Booth, C.; Attwood, D. J. Phys. Chem. B 1999, 103, 11269. (26) Hamley, I. W.; Daniel, C.; Mingvanish, W.; Mai, S.-M.; Booth, C.; Messe, L.; Ryan, A. J. Langmuir 2000, 16, 2508. (27) Kelarakis, A.; Mingvanish, W.; Daniel, C.; Li, H.; Havredaki, V.; Booth, C.; Hamley, I. W.; Ryan, A. J. Phys. Chem. Chem. Phys. 2000, 2, 2755.

Chaibundit et al. Table 1. Molecular Characteristics of the Copolymersa polymer/ copolymer B20 E58B20E58 E104B20E104 E148B20E148 E260B20E260

wt % E (NMR)

Mn, g/mol (NMR)

Mw/Mn (GPC)

Mw, g/mol

78 86 90 94

1460 6540 10 600 14 500 24 300

1.02 1.08 1.07 1.08 1.06

1490 7060 11 300 15 700 25 800

a Estimated uncertainties: (2% in wt % E; (3% in M , M /M , n w n and block lengths; (4% in Mw. Mw calculated from Mn and Mw/Mn.

used in preparation and characterization have been described previously.20,21 Vacuum line and ampule techniques were used to eliminate moisture. The difunctional initiator, 1,2-butane diol, was activated by reaction with potassium metal (mole ratio OH/K ≈ 10) and used to prepare R-hydro,ω-hydroxypoly(oxybutylene). This polymer was divided between four new ampules and subjected to prolonged evacuation to remove any accrued moisture before adding the required amount of ethylene oxide. Characterization of the homopolymer and the copolymers by gel permeation chromatography [GPC, calibrated with poly(oxyethylene) standards] served to define the widths of the chain length distributions (i.e., Mw/Mn), where Mw and Mn are the massaverage and number-average molar mass, respectively. Absolute values of Mn of the precursor polymer and the final copolymers were obtained by 13C NMR spectroscopy on the basis of the assignments of Heatley et al.28 Comparisons of integrals of the resonances of carbons associated with end groups and junction groups indicated an excess of hydroxy ends over EB junctions, this being a consequence of initiation of new chains by moisture introduced with the ethylene oxide at the second stage of the polymerization. In fact the amount of homopoly(oxyethylene) produced was small (1-3 wt %) and could be ignored. 2.2 Light Scattering. Details of the methods used and their applicability to micellar solutions of the type under investigation have been discussed previously.21,29-31 A brief description is given below. Solutions were clarified by filtering through Millipore Millex filters (Triton free, 0.22 µm, sometimes 0.1 µm) directly into the cleaned scattering cell. No differences were found for solutions treated by the two filtration techniques. Static light scattering (SLS) intensities were measured by means of a Brookhaven BI 200S instrument using vertically polarized incident light of wavelength λ ) 488 nm supplied by an argon-ion laser operated at 500 mW or less. The intensity scale was calibrated against benzene. Dynamic light scattering (DLS) measurements were made under similar conditions, using a Brookhaven BI 9000 AT digital correlator to acquire data. Experiment duration was in the range 5-20 min, and each experiment was repeated two or more times. Scattered light intensity was usually measured at an angle θ ) 90° to the incident beam. The correlation functions from DLS were analyzed by the constrained regularized CONTIN method32 to obtain distributions of decay rates (Γ), hence distributions of an apparent mutual diffusion coefficient [Dapp ) Γ/q2, q ) (4πn/λ) sin(θ/2), n ) refractive index of the solvent], and ultimately of apparent hydrodynamic radius (rh,app, radius of the hydrodynamically equivalent hard sphere corresponding to Dapp) via the StokesEinstein equation

rh,app ) kT/(6πηDapp)

(1)

where k is the Boltzmann constant, and η is the viscosity of the solvent at temperature T. In practice, intensities I(Γ) delivered by the CONTIN program at logarithmically spaced values of (28) Heatley, F.; Yu, G.-E.; Sun, W.-B.; Pywell, E. J.; Mobbs, R. H.; Booth, C. Eur. Polym. J. 1990, 26, 583. (29) Deng, N.-J.; Luo, Y.-Z.; Tanodekaew, S.; Bingham, N.; Attwood, D.; Booth, C. J. Polym. Sci., Part B: Polym. Phys. 1995, 33, 1085. (30) Yang, Y.-W.; Yang, Z.; Zhou, Z.-K.; Attwood, D.; Booth, C. Macromolecules 1996, 29, 670. (31) Yang, Z.; Yang, Y.-W.; Zhou, Z.-K.; Attwood, D.; Booth, C. J. Chem. Soc., Faraday Trans. 1996, 92, 257. (32) Provencher, S. W. Makromol. Chem. 1979, 180, 201.

Triblock Copolymer Association in Aqueous Solution

Langmuir, Vol. 16, No. 24, 2000 9647

decay rate were transformed to I(log Γ) ) I(Γ)Γ to obtain intensity distributions of log(Γ) and so of log(rh,app). Normalization of I(log rh,app) gave the intensity fraction distributions presented in section 3.3. The average values of Γ, delivered by the CONTIN program by integration over the intensity distributions, were similarly converted to intensity-average values of rh,app. 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 in eq 2), and K* is the appropriate optical constant. Values of the specific refractive index increment, dn/dc, its temperature increment, and other quantities necessary for the calculations, have been given previously.29,31,33 Values of dn/dc are very similar for poly(oxyethylene) and poly(oxybutylene), making dn/dc insensitive to exact composition of the copolymers, and making correction for refractive index difference within the copolymer unnecessary. 2.3 Gel Boundary. Samples of solution (0.5 g) were enclosed in small tubes (internal diam ∼10 mm) and observed while slowly heating the tube in a water bath within the range 0-100 °C. The heating/cooling rate was 0.5 deg min-1 or less. Additional data points in the range 0 to -14 °C were obtained by cooling the tubes in an acetone/dry ice bath, with care being taken to avoid freezing the solution at the lowest temperatures. The change from a mobile to an immobile system (or vice-versa) was determined by inverting the tube. The method served to define a mobile-gel transition temperature to (1 °C. The gels were found to be immobile in the inverted tubes over time periods of days to several months. In comparable systems, this simple method of detecting gelation, which is sensitive to the yield stress of the gel, has been shown to define the same phase boundary as rheometry and differential scanning calorimetry.34

Figure 1. Logarithm of cmc (in mol dm-3) versus B-block length for aqueous solutions of EmBnEm copolymers at 28-30 °C: (b), Results from ref 19; (9), present result. A least-squares straight line is drawn through the data points. The inset shows lightscattering intensity versus temperature for a 0.07 g dm-3 solution of copolymer E260B20E260, indicating a critical micelle temperature of 28 °C.

3. Results Copolymer solutions covering the concentration range of interest (up to 5 wt %) were tested for clouding by enclosing them in sealed tubes and heating them in a water bath to 95 °C. All the solutions remained clear. 3.1 Critical Micelle Concentration. Values of the critical micelle concentration (cmc) are available for a number of EmBnEm copolymers in solution at 30 °C, as reviewed in ref 19. Those for samples with E-block lengths of 30 units or more are reproduced in the semilogarithmic plot of cmc (molar units) against B-block length shown in Figure 1. For copolymers with lengthy B blocks, the measurement of the low cmc can be difficult: (e.g., the conventional surface tension method may require extremely lengthy equilibration times),35 while the intensity of scattered light from the dilute solutions can be very weak. Of the four copolymers of present interest, E260B20E260 is the most favorable for study by light scattering, as its high molar mass ensures a measurable signal from its molecular solutions and its long E blocks favor a relatively high cmc. The variation of the intensity of static light scattering with temperature obtained for a 0.07 g dm-3 solution of this copolymer is shown as an inset in Figure 1, and the corresponding data point on the log(cmc) plot (i.e. a cmc at 28 °C of 0.07 g dm-3, 2.9 × 10-6 mol dm-3) is shown as a square. Agreement with the data (33) 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. (34) Li, H.; Yu, G.-E.; Price, C.; Booth, C.; Hecht, E.; Hoffmann, H. Macromolecules 1997, 30, 1347. (35) Yu, G.-E.; Zhou, Z.-K.; Attwood, D.; Price, C.; Booth, C.; Griffiths, P. C.; Stilbs, P. J. Chem. Soc., Faraday Trans. 1996, 92, 5021.

Figure 2. Dynamic light scattering. Intensity fraction distributions of the logarithm of apparent hydrodynamic radius for aqueous solutions of copolymer E148B20E148 at 25 °C and the concentrations (g dm-3) indicated.

reported previously is satisfactory. Since this result indicated an upper limit of ∼0.1 g dm-3 to the cmc for the four copolymers and since 1 g dm-3 was the lowest concentration to be used in the light scattering studies, no further measurements were made. 3.2 Hydrodynamic Radius. Satisfactory results were obtained from DLS experiments on copolymer solutions at 25, 40, and 50 °C at concentrations in the range 1-50 g dm-3 for E58B20E58 to E148B20E148 and in the range 1-30 g dm-3 for E260B20E260. The lowering of the upper concentration limit accommodated the increased effect of intermicellar interaction at a long E-block length. In all cases, the intensity fraction distributions of log(rh,app) showed single peaks with maxima corresponding to rh,app ≈ 7-15 nm, indicating that only micelles formed by closed association. Examples of these distributions are shown in Figures 2 and 3. The effect of temperature (not shown) was slight. The effect of an increase in concentration was to move the peak to lower values of log(rh,app), see

9648

Langmuir, Vol. 16, No. 24, 2000

Chaibundit et al. Table 2. Properties of Micelles of EmB20Em Copolymers in Aqueous Solutiona copolymer E58B20E58 E104B20E104 E148B20E148 E260B20E260

T, °C

rh, nm

δh

Mw, 105g mol-1

Nw

δt

rt, nm

25 40 50 25 40 50 25 40 50 25 40 50

8.4 8.3 7.7 9.9 9.6 10.0 12.1 12.1 11.4 14.1 14.9 14.2

8.6 7.3 5.3 11 9.0 9.4 21 17 13 36 31 22

1.9 2.1 2.3 2.4 2.7 2.9 2.3 2.8 3.2 2.2 3.0 3.6

27 30 33 21 24 26 15 18 20 9 12 14

5.8 5.6 4.6 8.5 7.5 7.0 10.9 9.4 8.6 13.7 11.9 11.3

7.4 7.6 7.3 9.0 9.0 9.1 9.7 9.9 10.0 10.2 10.9 11.4

a The quantities listed are defined in sections 3.2 and 3.3. Estimated uncertainties are (5% in rh and rt, (10% in Mw, Nw, δh, and δt.

Figure 3. Dynamic light scattering. Intensity fraction distributions of the logarithm of apparent hydrodynamic radii for 10 g dm-3 aqueous solutions at 25 °C of the EmB20Em copolymers indicated.

The very small effect of temperature on rh for micelles of copolymer E104B20E104 is clearly seen in Figure 4. This insensitivity to temperature held for all four copolymers (see Table 2). This is usually the case for micelles of block copoly(oxyalkylene)s,5,19 and results from compensation between an increase in association number of the micelle and a decrease in swelling of the micelle fringe as temperature is increased.36 The hydrodynamic expansion factor is also listed in Table 2. This quantity is defined as

δh ) vh/va

Figure 4. Reciprocal of apparent hydrodynamic radius versus copolymer concentration for aqueous solutions of copolymer E104B20E104 at (b) 25 °C, (O) 40 °C, and (9) 50 °C. The leastsquares line through all the data points is shown.

Figure 2, which is the expected effect of intermicellar interaction (as discussed below). The effect of an increase in E-block length was to move the peak to higher values of log(rh,app), see Figure 3, consistent with an increase in micellar radius. The increase in peak width with increase in E-block length is consistent with greater intermicellar interaction for the larger micelles, and is parallel to the increase in peak width at high concentrations (Figure 2). The increase in peak width at very low concentrations reflects the response of the CONTIN analysis to weak signals. The effect of concentration on rh,app of the micelles of copolymer E104B20E104 is summarized in Figure 4. In this figure, the reciprocal of the apparent radius is equivalent to the apparent diffusion coefficient compensated for change in temperature and viscosity through eq 1. The positive slope of the plot is typical of micelles interacting as hard spheres. The data points for the three temperatures overlap: the line shown in Figure 4 is the leastsquares line through all the data points. Values of rh, obtained by extrapolating individual data sets to zero concentration, are listed in Table 2.

(3)

where vh is the average hydrodynamic volume, and va is the average anhydrous volume of the micelles, with the latter being calculated from the micellar molar mass determined by SLS (see section 3.3) and the density of the anhydrous liquid copolymer (Fa ≈ 1.11-1.06 g cm-3 according to temperature and composition).37 Parameter δh illustrates the marked effect of temperature on the “hydrodynamic” expansion of the E-block coils in the micelle fringe. 3.3 Association Number and Thermodynamic Radius. SLS experiments were performed on copolymer solutions at the temperatures described for the DLS experiments (section 3.2) but, if necessary, at lower maximum concentrations. The Debye equation (eq 2 of section 2.2) was used to analyze the data. Used for scattering at 90°, the equation assumes small particles relative to the wavelength of the light. Radii of gyration estimated as 0.775 rh (i.e., as if the micelles were uniform spheres) are 12 nm or less based on the values of rh listed in Table 2, and only a small effect from intraparticle interference is to be expected.38 Given the likely error from other sources, this effect could be ignored. Equation 2 truncated to the second term could not be used in the present experiments because micellar interaction (interparticle interference) caused significant curvature of the Debye plot, even in the low concentration range. This feature is illustrated in Figure 5, in which K*c/(I - Is) is plotted against concentration for copolymer E148B20E148 in solution at 25, 40, and 50 °C. Rather than accommodate the curvature by use of a viral expansion, introducing a number of adjustable coefficients, a method based on the Percus-Yevick theory for hard spheres as (36) Attwood, D.; Collett, J. H.; Tait, C. J. Int. J. Pharm. 1985, 26, 25. (37) Mai, S.-M.; Booth, C.; Nace, V. M. Eur. Polym. J. 1997, 33, 991. (38) Casassa, E. F. In Polymer Handbook, 3rd ed.; Brandrup, J., Immergut, E. H., Eds.; Wiley: New York, 1989; p 485. Beattie, W. H.; Booth, C. J. Phys. Chem. 1960, 64, 696.

Triblock Copolymer Association in Aqueous Solution

Langmuir, Vol. 16, No. 24, 2000 9649

Figure 5. Static light scattering. Debye plots for aqueous solutions of copolymer E148B20E148 at (b) 25 °C, (O) 40 °C, and (9) 50 °C. The curves are based on the scattering theory for hard spheres.

Figure 7. Phase diagrams. Gel boundaries for aqueous solutions of copolymers (b) E260B20E260, (O) E148B20E148, (9) E104B20E104, and (0) E58B20E58. (a) T versus c. (b) (T-T*) versus (c-c*). The value c* is the minimum concentration for gel formation (occurring at temperature T*). Figure 6. Static light scattering. Debye plots for aqueous solutions at 40 °C for copolymers (b) E260B20E260, (O) E148B20E148, (9) E104B20E104, and (0) E58B20E58. The curves are based on the scattering theory for hard spheres.

adapted by Vrij to incorporate the Carnahan-Starling equation was used to fit the data.39 This procedure is equivalent to using the viral expansion for the structure factor for hard spheres taken to its seventh term but requires only two adjustable parameters, Mw and δt. The new parameter, δt, relates to the volume excluded by one water-swollen micelle to another, that is, to the volume fraction occupied by the micelles acting as effective hard spheres. Specifically, δt is a thermodynamic expansion parameter defined by

δt ) vt/va

(4)

where vt is the thermodynamic volume (that is one-eighth of the excluded volume for a micelle acting as an effective hard sphere), and va is the anhydrous volume of the micelle, that is, va ) Mw/NAFa (NA ) Avogadro’s constant). Details of the procedure have been described many times previously: see, for example, refs 21, 25, 29, and 40. The curves shown in Figure 5 for aqueous solutions of copolymer E148B20E148 at three temperatures were obtained in this way. Corresponding plots for all four copolymers in solution at 40 °C are shown in Figure 6. Although the intercepts (i.e. the values of the micelle molar mass, Mw) are similar, the curvatures of the plots (i.e. the values of δt) differ markedly with E-block length. The values of Mw (39) Percus, J. K.; Yevick, G. J. J. Phys. Rev. 1958, 110, 1. Vrij, A. J. Chem. Phys. 1978, 69, 1742. Carnahan, N. F.; Starling, K. E. J. Chem. Phys. 1969, 51, 635.

and δt obtained for all four copolymers at the three temperatures are listed in Table 2. Given these parameters, values of the association number of the micelles were calculated from

Nw ) Mw,mic/Mw,mol

(5)

using the value of Mw listed for molecules in Table 1, values of the thermodynamic radii were calculated from the thermodynamic volume via eq 4. 3.4 Phase diagrams. Mobile-immobile boundaries determined by tube inversion (under the conditions described in section 2.3) are shown in Figure 7a. Depending on the E-block length, the minimum concentration for gel formation (c*) was in the range 9-13.5 wt %, occurring at a temperature (T*) in the range 10-35 °C: see Table 4. Plotting the data as T-T* against c-c* gave essentially a single curve for all four data sets (see Figure 7b), demonstrating the almost identical shape of the four gel boundaries. This procedure has been used previously in analyzing the phase diagrams of the series of diblock copolymers based on B18.27 4. Discussion: Effects of E-block Length and Block Architecture Combining results for the present copolymers with those published for diblock copolymers of comparable block lengths25 (E96B18, E184B18, E315B17, E398B19) allows discussion of the effect of E-block length and block architecture on micelle association numbers and radii and on gelation behavior. 4.1 Micelle Properties. Figure 8a shows a log-log plot of association number against total E-block length

9650

Langmuir, Vol. 16, No. 24, 2000

Chaibundit et al.

Table 3. Scaling Exponents for the Measured Properties of Diblock and Triblock E/B Copolymersa Slope series

E-block range

Nw

rt

rh

EmB20Em EmB17-19

m ) 58-260 m ) 96-398

-0.62 -0.61

0.24 0.25

0.40 0.37

a

Slopes are from Figure 8a and b. Table 4. Minimum Concentrations (c*) and Corresponding Temperatures (T*) for Gelation of Aqueous Solutions of EmB20Em Copolymers copolymer

c*, wt %

T*, °C

E58B20E58 E104B20E104 E148B20E148 E260B20E260

13.3 11.0 9.9 9.0

11 21 28 35

for diblock (EmBn) and triblock (EmBnEm) copolymers: that is, against log(m) for the diblocks but log(2m) for the triblocks. Plotting in this way allows direct comparison of copolymers with equivalent overall chain length and composition. The fact that the B-block lengths in the diblock series vary from 17 to 19 repeat units whereas those of the triblock copolymers are uniformly 20 repeat units long is only a minor complication: the small effect of a 10% change in B-block length can be seen in the scatter of the data for the diblock copolymers. The architectural effect is clear: the association number of a diblock copolymer greatly exceeds that of a triblock copolymer of similar overall composition and chain length. The ratio for the present copolymers is Ndi/Ntri ≈ 5. The nature of the present data means that the slopes of the lines in Figure 8a are of greater interest than their separation. These are -0.62 ( 0.07 for the triblock copolymers and -0.61 ( 0.14 for the diblock copolymers: see Table 3. Previously,19 using a slightly different treatment of the data, we obtained slopes of -0.57 for the same series of diblock copolymers and -0.67 for a related series of EmB10 diblock copolymers. We conclude that the scaling law

Nw ∼ m-0.6 adequately represents the data available for both diblock and triblock E/B copolymers. A similar exponent (m-0.51) has been derived theoretically for spherical micelles of EmPn diblock copolymers in aqueous soluion by Nagarajan and Ganesh.41 This is an equilibrium treatment based on the Flory-Huggins model in which the water/polymer interactions are introduced via known values of parameter χ for water/poly(oxyethylene) and water/poly(oxypropylene). The scaling exponent m-0.51 is system specific but depends largely on the fact that water at low temperatures is a good solvent for poly(oxyethylene). Accordingly, one might reasonably expect similar behavior for the two systems, EmPn and EmBn, which both have poly(oxyethylene) coronal blocks. Corresponding log-log plots of thermodynamic and hydrodynamic radii are shown in Figure 8b, and the slopes of the lines are collected in Table 3. Theoretically derived scaling laws for micelle radii (or the micelle corona thickness which is a large part of the micelle radius in the present systems) place the exponent of m in the range 0.5-0.8.41-46 These values are higher than those found in (40) Derici, L.; Ledger, S.; Mai, S.-M.; Booth, C.; Hamley, I. W.; Pedersen, J. S. Phys. Chem. 1999, 1, 2773. (41) Nagarajan, R.; Ganesh, K. J. Chem. Phys. 1989, 90, 5843.

Figure 8. (a) Log-log plots of mass-average association number versus total E-block length for micelles of (b) triblock and (9) diblock copolymers in aqueous solution. (b) Log-log plots of micelle radii versus total E-block length for the same copolymers. Filled symbols denote the thermodynamic radius (rt); unfilled symbols denote the hydrodynamic radius (rh). In both (a) and (b), the straight lines were obtained by least-squares calculations.

our work. However, the micelle radius of theoretical interest is the radius of gyration. The thermodynamic radius relates to the excluded volume and, consequently, theory cannot be expected to predict the observed low value of m0.25. The hydrodynamic radius is more closely related to the radius of gyration, and the higher scaling exponent (∼0.4) is closer to the range of the theoretical values. In recent work,47 Rangelov and Brown have observed that the familiar scaling law for the radius of gyration of polymer coils breaks down for linear poly(oxyethylene) in water when the chain is very long, Mw > 106 g mol-1. The effect is consistent with the coil collapsing because of the formation of intramolecular H-bonds mediated by water molecules, which increase as the chain length is increased. It could be argued that an effect of this kind is possible in the polymer-dense corona of the present micelles. However, the scaling of the hydrodynamic radius of the linear poly(oxyethylene)s with chain length was not affected,47 consistent with a compensating effect, presumably a reduction in draining of the coil, and the relevance to the present results is not obvious. 4.2 Gelation. Comparison of gel boundaries found for triblock and diblock copolymers is made in Figure 9. The (42) Zhulina, E. B.; Birshtein, T. M. Vysokomol. Soedin. 1985, 27, 511; Polym. Sci. U.S.S.R. 1986, 27, 570. (43) Halperin, A. Macromolecules 1987, 20, 2943. (44) Whitmore, M. D.; Noolandi, J. Macromolecules 1985, 18, 657. (45) Bluhm, T. L.; Whitmore, M. D. Can. J. Chem. 1985, 63, 249. (46) Wu, C.; Gao, J. Macromolecules 2000, 33, 645. (47) Rangelov, S.; Brown, W. Polymer 2000, 41, 4825.

Triblock Copolymer Association in Aqueous Solution

Langmuir, Vol. 16, No. 24, 2000 9651

Figure 10. Critical gel concentration (cgc) for copolymer solutions at 40 °C versus Fa/δt, where Fa is the density of anhydrous liquid copolymer and δt is the thermodynamic expansion factor. The data points are for (b) triblock and (9) diblock copolymers. The error bars represent an uncertainty of (10% in Fa/δt. The least-squares line through the data points for the triblock copolymers is shown as a dotted line. The full lines are predicted for bcc and fcc gels (as indicated) according to eq 7 or its fcc equivalent.

can be derived from the concentration dependence of the intensity of scattered light as the thermodynamic volume vt. The same quantity is available from other scattering techniques (e.g., small-angle neutron scattering).40 It is convenient to use the parameter δt, and write the volume fraction as Figure 9. Gel boundaries for aqueous solutions of triblock and diblock copolymers with similar E-block lengths. (a) Copolymers (9) E104B20E104, (4) E96B18 and (3) E90B10. (b) Copolymers (O) E148B20E148 and ([) E184B18. The data for copolymer E90B10 are from ref 40.

behavior of micellar solutions of three copolymers with similar E-block lengths (E90B10, E96B18, and E104B20E104) is illustrated in Figure 9a, the data being taken from previous25,40 and present work. At high temperatures, all three copolymers have similar gel boundaries, although that of E96B18 is displaced by 2-3 wt % from those of the other two copolymers. At low temperatures, the curves for E90B10 and E96B18 are significantly different: the increase in B-block length moves the gel boundary to lower concentrations and lower temperatures. The curve for E104B20E104 shows the effect of a change in architecture: the gel boundary for the triblock is intermediate between that of E90B10 (effectively the half-molecule) and that of E96B18 (a diblock with similar block lengths). Figure 9b, which involves micellar solutions of copolymers with longer E-blocks (E184B18 and E148B20E148) illustrates the same architectural effect (i.e., the shift to lower concentrations and lower temperatures). In this case the separation at high temperatures is 4-5 wt %, reflecting in part the significantly larger E-block length of the diblock copolymer. In micellar systems of the type under discussion, gelation at any temperature can be understood in terms of solvent-swollen spherical micelles filling space as effective hard spheres.1,7,11,25,29,48-50 As always, in considering packing, the important parameter is the volume fraction of effective hard spheres. As discussed in section 3.3, the effective size of micelles acting as hard spheres (48) Malmsten, M.; Lindman, B. Macromolecules 1992, 25, 5440. (49) Hvidt, S.; Jørgensen, E. B.; Brown, W.; Schillen, K. J. Phys. Chem. 1994, 98, 12320. (50) Bedells, A. D.; Arafeh, R. M.; Yang, Z.; Attwood, D.; Padget, J. C.; Price, C.; Booth, C. J. Chem. Soc., Faraday Trans. 1993, 89, 1243.

φ ) cδt/1000Fa

(6)

where c is the copolymer concentration in g dm-3, and Fa is the density of the anhydrous liquid copolymer as defined in section 3.2. In the particular case of a body-centered cubic (bcc) structure, the critical volume fraction for gelation is φc ) 0.68, and the critical concentration for gelation (cgc in g dm-3) is

cgc/(g dm-3) )

680Fa δt

(7)

For a face-centered cubic (fcc) structure, the corresponding critical volume fraction is 0.74. Both the fcc and bcc structures have been observed for the low-concentration aqueous gels of the comparable diblocks: fcc for E96B18 and E184B18, bcc for E315B17 and E398B19.26 The ratio rh/rt was recognized as a useful indicator of structure: hard spheres with rh/rt f 1 packing fcc and soft spheres with larger values of rh/rt packing bcc.26 For the present triblocks in solution at 40 °C (taking values from Table 2), the ratio rh/rt varies as follows: 1.09 (E58B20E58) and 1.07 (E104B20E104), consistent with fcc; 1.22 (E148B20E148) and 1.37 (E260B20E260), consistent with bcc. Values of the cgc obtained at 40 °C taken from Figure 7a (converted from wt % to g dm-3) are plotted against Fa/δt (δt from Table 2) in Figure 10. Data for solutions of the related diblock copolymers at 40 °C are included.25 The full lines show the predictions using eq 7 and its modification for fcc gels. The error bars ((10%) reflect the uncertainty in δt. The agreement between observation and prediction is satisfactory for the diblock copolymers, particularly if it is borne in mind that the cgc determined by the tube inversion method will be slightly overestimated because of the finite yield stress necessary to prevent flow. On the other hand, agreement between observation and prediction is poor for the triblock copolymers. A similar

9652

Langmuir, Vol. 16, No. 24, 2000

discrepancy between diblock and triblock copolymers has been noted previously51,52 but not explained. It is of interest that the slope of the dotted line through the data points for the triblocks is similar to that found previously.51 This slope is that expected for hexagonally packed cylindrical micelles, but there is no other evidence for that structure: the gels are not birefringent, and preliminary determinations of the structures of 20 wt % gels by small-angle X-ray scattering (SAXS) indicate bcc.53 It is interesting that Svensson et al.,54 in their investigation of aqueous gels of copolymer E27P61E27 (coded P104), encountered a related anomaly and assigned their bcc-like SAXS pattern to the (51) Kelarakis, A.; Havredaki, V.; Derici, L.; Yu, G.-E.; Booth, C.; Hamley, I. W. J. Chem. Soc., Faraday Trans. 1998, 94, 3639. (52) Yang, Y.-W.; Ali-Adib, Z.; McKeown, N. B.; Ryan, A. J.; Attwood, D.; Booth, C. Langmuir 1997, 13, 1860. (53) Hamley, I. W., private communication.

Chaibundit et al.

related cubic structure with eight slightly elongated micelles per cubic cell (space group Pm3n).55 Structural investigation of gels of the present copolymers over a range of concentrations is planned.53 Acknowledgment. We thank Mr. S. K. Nixon for help with the GPC experiments. The Thai Government provided financial support for C.C. The Engineering and Physical Research Council (U.K.) provided financial assistance for synthesis of block copolymers through grant GR/L22645. LA000725G (54) Svensson, B.; Alexandridis, P.; Olsson, U. J. Phys. Chem, B 1998, 102, 7541. (55) Fontell, K.; Fox, K. K.; Hansson, E. Mol. Cryst. Liq. Cryst. Lett. 1985, 1, 9. Fontell, K. Colloid Polym. Sci. 1990, 268, 264.