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Self-Assembly of Mixed Amphiphilic Triblock Copolymers in Aqueous Solution Tianbo Liu,† Vaughn M. Nace,‡ and Benjamin Chu*,†,§ Department of Chemistry, State University of New York at Stony Brook, Stony Brook, New York 11794-3400, The Dow Chemical Company, Freeport, Texas, 77541, and Department of Materials Sciences and Engineering, State University of New York at Stony Brook, Stony Brook, New York 11794-2275 Received September 15, 1998. In Final Form: February 17, 1999 A 1:1 (weight ratio) mixture of two commercial amphiphilic triblock copolymers, F127 (E99P69E99) and B20-5000 (E45B14E45) in aqueous solution, was studied by using static light-scattering and dynamic lightscattering techniques. E, P, and B are oxyethylene, oxypropylene, and oxybutylene, respectively, with the subscript denoting the number of segment units in the block. Both triblock copolymers tend to self-assemble into starlike micellar structures in aqueous solution because of the poorer solubility of their middle blocks at room temperature. Due to the difference in their thermodynamic parameters of the micellization process and in their micellar sizes, the mixed block copolymer system provides a suitable model for studying the self-assembly behavior of mixed, miscible triblock copolymers in aqueous solution. At temperatures below 27 °C, the E45B14E45 block copolymer has a much lower cmc than that of E99P69E99. Therefore, the micelle formation of the mixed polymer solution was determined by the cmc of E45B14E45. E99P69E99 chains gradually joined into the micelles at higher polymer concentrations. At temperatures above 33 °C, E99P69E99 had lower cmc values. Therefore, it micellized first, and then E45B14E45 chains gradually joined to form mixed micelles. At temperatures in between, where the two kinds of copolymers had similar cmc values, both unimers contributed to the cmc value in the mixed solution. In a special case, at the temperature where the two kinds of polymers had the same cmc value, mixed micelles comprised 50 wt % of each kind of polymer chains, with a cmc value equal to the sum of half of each of the two cmc values in its own pure polymer solution. The cmc value of the mixed polymer solution is the same as the cmc value of either of the two copolymer solutions. Other basic parameters of the mixed micelles, for example, association number (nw) and hydrodynamic radius (Rh), were also measured. The results are discussed in the text.
Introduction Block copolymers can self-assemble in selective solvents and have many applications as surfactants,1 separation media,2 or synthetic matrixes.3 The association behavior of oxyalkylene triblock copolymers in aqueous solution has been extensively studied during the past few years, especially for EnPmEn, PnEmPn, EnBmEn, and BnEmBn type block copolymers, where E, P, and B represent, respectively, oxyethylene, oxypropylene, and oxybutylene segment units with the subscript denoting the number of segment units in the block. The solubility of the E block in water is much better than that of the P (or B) block. The difference in the temperature-dependent solubility of the P (or B) block makes these triblock copolymers particularly useful, as the micellization process is thermally reversible. Several in-depth reviews on the micellization behavior of such block copolymers in solution have appeared recently.4-6 * To whom correspondence should be addressed. † Department of Chemistry, State University of New York at Stony Brook. ‡ The Dow Chemical Company. § Department of Materials Sciences and Engineering, State University of New York at Stony Brook. (1) Pluronic & Tetronic Surfactants, BASF Corporation, New Jersey, 1989. (2) Wu, C.; Liu, T.; Chu, B. Electrophoresis 1998, 19, 231. (3) Zhao, D.; Feng, J.; Huo, Q.; Melosh, N.; Fredrickson, G. H.; Chmelka, B. F.; Stucky, G. D. Science 1998, 279, 548. (4) Tuzar, K.; Kratochvil, P. In Surface and Colloid Science; Matijevic, E., Ed.; Plenum Press: New York, 1993; Vol. 15. (5) Chu, B.; Zhou, Z. In Nonionic Surfactants: Polyoxyalkylene Block Copolymers; Nace, V. M., Ed.; Marcel Dekker: New York, 1996; Chapter 3. (6) Chu, B. Langmuir 1995, 11, 414.
The closed association mechanism yields core-shell, starlike micelles for XYX type triblock copolymers in solvents selectively good for the terminal X blocks. However, for YXY type triblock copolymers in the same solvents selective for the middle X block, there are several possible self-assembly structures: flower-like micelles, a branched structure at low concentrations, or a gel-like network at high concentrations and the intermediate situation that some of the coronal middle blocks show a looping geometry, while some other middle blocks may have one of the end blocks dangling in solution.7-11 The micellization of triblock copolymers under more complicated conditions is also a topic of continuous attention. Wu et al. first studied the micellization of L64 (E13P30E13) in aqueous solution in the presence of o-xylene and water-induced micellization in o-xylene.12-14 Adding an additional solvent that was immiscible with the solventdispersing medium but was a solvent for the P block would induce the association process, whereby a smaller critical micelle concentration (cmc) and a much larger association number (nw) could be expected, suggesting that the micellization process had become much more favorable. (7) Balsara, N. P.; Tirrell, M.; Lodge, T. P. Macromolecules 1991, 24, 1975. (8) Raspaud, E.; Lairez, D.; Adam, M.; Carton, J.-P. Macromolecules 1994, 27, 2956. (9) Nguyen-Misra, M.; Misra, S.; Wang, Y.; Rodrigues, K.; Mattice, W. L. Prog. Colloid Polym. Sci. 1997, 103, 1138. (10) Zhou, Z.; Chu, B.; Nace, V. M. Langmuir 1996, 12, 5016. (11) Yang, Y.-W.; Yang, Z.; Zhou, Z.; Attwood, D.; Booth, C. Macromolecules 1996, 29, 670. (12) Wu, G.; Zhou, Z.; Chu, B. Macromolecules 1993, 26, 2117. (13) Wu, G.; Chu, B. Macromolecules 1994, 27, 1766. (14) Wu, G.; Zhou, Z.; Chu, B. J. Polym. Sci., Part B: Polym. Phys. 1993, 31, 2035.
10.1021/la9812525 CCC: $18.00 © 1999 American Chemical Society Published on Web 04/02/1999
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Katime and co-workers have done a large amount of work on the micellization of polystyrene-block-poly(ethylene/ propylene) in different solvents, as well as in the presence of polystyrene homopolymers.15-18 The addition of polystyrene homopolymer was similar to adding another solvent that was good for polystyrene but was immiscible with the solvent-dispersing medium. The polystyrene homopolymer, with chain length essentially shorter than the length of the polystyrene block in the block copolymer, would reside inside the micellar cores and promote the micellization process. A more complicated case is to study the micellization of mixed block copolymers with different chain lengths or different chemical compositions. In the presence of another kind of block copolymer which can also self-associate, the micellization behavior can be very interesting because of mutual interactions among different polymer chains. Some meaningful exploration has been done by Booth and coworkers.19 They reported the formation of mixed B8E41 and B12E260B12 micelles; the latter one was a very hydrophobic material and could not be dissolved in water even at room temperature (cloud-point temperature ) 12 °C for 1 wt % B12E76B12 solution). Adding B8E41 into the solution increased the solubility of B12E76B12, and mixed micelles were formed. B8E41 had a cmc of 0.9 mg/mL at 25 °C. The presence of B12E76B12 decreased this value. However, they also reported that the association number (nw) of the mixed micelles seemed to be determined mainly by B8E41 (around 60 at 25 °C) and was not affected by the presence of B12E76B12 even though B12E76B12 was responsible for the very low cmc value. This conclusion is a little different from the general understanding for a micellization process; that is, the cmc and the nw are intercorrelated and are determined mainly by the more solventphobic block. More importantly, the cmc of B12E76B12 was always much smaller than that of B8E41 and even too small to be precisely measured.20 As the individual micelles formed by the two copolymers had similar hydrodynamic radii (Rh), light scattering was too insensitive to monitor certain important aspects of mixed copolymer systems. In this paper, we report the self-assembly behavior of a mixture (1:1 weight ratio) of two triblock copolymers (E45B14E45 and E99P69E99) in aqueous solution. This mixed copolymer system is very suitable as a model to provide a deeper understanding on the nature of the self-assembly behavior in mixed block copolymers because the temperature-dependent micellar parameters of E45B14E45 and of E99P69E99 in aqueous solution are different. Due to the difference in ∆H° (enthalpy of micellization) in aqueous solution, three different conditions can be found in the mixture over a temperature range of just 10-15 °C: (1) one cmc is much higher than the other, (2) vice versa, and (3) both have similar individual cmc’s. The magnitudes of the cmc and of the nw of both the individual and the mixed micelles are just in the range that can be measured easily by static light scattering (SLS). Moreover, there exists a large difference in the magnitude of Rh of the two kinds of individual micelles (about 6.0 and 12.0 nm for E45B14E45 and E99P69E99 micelles, respectively). Therefore, dynamic (15) Quintana, J. R.; Villacampa, M.; Munoz, M.; Andrio, A.; Katime, I. A. Macromolecules 1992, 25, 3125, 3129. (16) Quintana, J. R.; Janez, M. D.; Villacampa, M.; Katime, I. A. Macromolecules 1995, 28, 4139, 4144. (17) Quintana, J. R.; Salazar, R. A.; Villacampa, M.; Katime, I. A. Makromol. Chem. 1993, 194, 2497. (18) Quintana, J. R.; Salazar, R. A.; Katime, I. A. Makromol. Chem. Phys. 1995, 196, 1625. (19) Yang, Z.; Yang, Y.-W.; Zhou, Z.; Attwood, D.; Booth, C. J. Chem. Soc., Faraday Trans. 1996, 92 (2), 257. (20) Zhou, Z.; Yang, Y.-W.; Booth, C.; Chu, B. Macromolecules 1996, 29, 8357.
Liu et al.
light scattering (DLS) can be employed successfully to provide information on the micellization process of mixed copolymers. To our knowledge, this is the first time that systematic studies on this kind of mixed block copolymer micelle in aqueous solution have been carried out. A 1:1 weight ratio (instead of molar ratio) was used for our study; the reason for this was that usually the cmc values of micelles were expressed with the concentration unit (g/mL, not mol/L) in the literature. By using the weight ratio, the results can be compared more easily with those of other works. The molecular weights of E45B14E45 and E99P69E99 single chains are 5000 and 12 600 Da, respectively. The mixed copolymer solution with a 1:1 weight ratio is equivalent to the mixed solution of E45B14E45 and E99P69E99 with a molar ratio of about 2.5:1. Experimental Section Sample Preparation. The commercial triblock copolymers F127 (E69P99E69) and B20-5000 (E45B14E45) were obtained as gifts from BASF Corp., New Jersey, and the Dow Chemical Company, Texas, respectively. Both samples were purified with hexane to remove the very hydrophobic impurities that were present in the samples during synthesis. The detailed procedure has been described earlier.21,22 Copolymer samples were dissolved into water to obtain a 20 mg/mL stock solution. For the mixed copolymer solutions, the two block copolymers were dissolved simultaneously in cold water near 0 °C, at which temperature the P (or B) block was soluble, to ensure equilibration of the systems, with long-time stirring, making sure that the solution was homogeneous. Then, lower concentration solutions of mixed copolymers were prepared by further dilution. Equilibration was checked by measuring the scattered intensity before and after cooling the diluted solution to near 0 °C. Static Light Scattering (SLS) and Dynamic Light Scattering (DLS). SLS and DLS were used to characterize the formation and the structures of block copolymer micelles in aqueous solution. We used a standard laboratory-built lightscattering spectrometer23 that was capable of both SLS and DLS measurements over the angular range 15-140°. The spectrometer was equipped with a Coherent Radiation 200 mW diode-pumped solid-state (DPSS) laser (Model 532) operating at 532 nm and a Brookhaven Instruments (BI 9000) correlator. The sample chamber was thermostated and could be controlled to within (0.02 °C. The intensity-intensity time correlation functions were analyzed by the CONTIN method.24 The basis for data analysis of SLS is the Rayleigh-GansDebye equation, valid for small, interacting particles, in the form25
Hc/R90 ) 1/Mw + 2A2c
(1)
where H ≡ 4π2n02(dn/dc)2/NAλ4 is an optical parameter with n0 being the solvent refractive index, NA, Avogadro’s constant, λ, the laser wavelength (532 nm), Mw the weight-average molecular weight, A2 the second virial coefficient, and dn/dc the refractive index increment. For the mixed copolymer solution, dn/dc ) 0.132 ( 0.002 cm3 g-1 at 25 °C. R90 is the excess Rayleigh ratio of the copolymer solution at 90°, and it is equal to RBz,90(I - I0)/IBz(n2/nBz2), where RBz,90 is the Rayleigh ratio of benzene at 90°, with a value of 2.0 × 10-5/cm at 532 nm,26 I, I0, and IBz are the scattered intensities of the solution, the solvent, and benzene, respectively, and nBz is the refractive index of benzene. From static light-scattering measurements, only Mw and A2 can be (21) Liu, T.; Zhou, Z.; Wu, C.; Chu, B.; Schneider, D. K.; Nace, V. M. J. Phys. Chem. B 1997, 101, 8808. (22) Liu, T.; Nace, V. M.; Chu, B. J. Phys. Chem. B 1997, 101, 8084. (23) Chu, B.; Onclin, M.; Ford, J. R. J. Phys. Chem. 1984, 88, 6566. (24) Provencher, S. W. Makromol. Chem. 1979, 180, 201; Comput. Phys. Commun. 1982, 27, 213, 229. (25) Hiemenz, P. Z. Principle of Colloid and Interface Chemistry; Marcel Dekker Inc.: New York, 1985. (26) Chu, B. Laser Light Scattering; Academic Press Inc.: New York, 1990.
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determined, as the radius of gyration (Rg) of the micelles is too small to be measured by SLS. Dynamic light scattering (DLS) measures the intensityintensity time correlation function G(2)(Γ) by means of a multichannel digital correlator.26
G(2)(Γ) ) A(1 + b|g(1)(τ)|2)
(2)
where A, b, and |g(1)(τ)| are respectively the background, a coherence factor, and the normalized electric field time correlation function. The field correlation function was analyzed by the constrained regularized CONTIN24 method, to yield information on the distribution of the characteristic line width (Γ) from
|g(1)(τ)| )
∫G(Γ)e
-Γτ
dΓ
(3)
The normalized distribution function of the characteristic line width G(Γ) so obtained can be used to determine an average apparent diffusion coefficient
Dapp ) Γ/q
2
(4)
where q ≡ [(4πn/λ2) sin(θ/2)] is the magnitude of the scattering wave vector. The apparent hydrodynamic radius Rh,app is related to Dapp via the Stokes-Einstein equation
Dapp ) kT/6πηRh,app
Figure 1. Plots of excess scattered intensity as a function of polymer concentration at 25, 30, and 35 °C for the determination of the critical micelle concentration (cmc) of the E45B14E45 triblock copolymer in aqueous solution by using the SLS technique.
(5)
where k is the Boltzmann constant and η is the viscosity of water at temperature T. From DLS measurements, we can obtain the particle-size distribution in solution from a plot of ΓG(Γ) versus Rh,app, with ΓiG(Γi) being proportional to the scattered intensity of all the i particles having an apparent hydrodynamic radius Rh,i. The subscript app is used to denote DLS measurements performed at finite concentrations when interparticle interactions have been neglected. During all the SLS and DLS experiments, the experimental error in the total scattered intensity and the apparent Rh is about (2-3%.
Results and Discussion 1. Self-Assembly of E45B14E45 Triblock Copolymer in Aqueous Solution. Detailed studies on the micellization behaviors of individual triblock copolymers in aqueous solution represent the required reference points for work on the mixed system. The characterization of triblock copolymers in a solvent that is good for the end blocks has become routine because such a kind of micellization process has been reported in detail.4,5 The closed association process can be represented by the relation
nA T An
(6)
Figure 1 shows a determination of the cmc of E45B14E45 triblock copolymer in aqueous solution at different temperatures by using SLS. The scattered intensity experiences a great increase with increasing polymer concentration, suggesting the formation of some large structures, for example, micelles. The cmc can be defined as the polymer concentration at which the micelle formation begins; above the cmc, the static light-scattering intensity departs significantly from a baseline value established for the calculated scattered intensity due to the single triblock copolymer molecules, as shown in Figure 1 (the dotted line, also in Figures 6, 8, and 11). Figure 1 indicates that, for E45B14E45 in aqueous solution, the cmc becomes lower at higher temperatures (from 0.66 mg/mL at 25 °C to 0.28 mg/mL at 35 °C), which is due to the unique hydrogen-bond-breaking process by the E and B blocks in aqueous solution. A positive enthalpy change of micellization was observed. However, when compared with the
Figure 2. Weight-average association number (nw) of the E45B14E45 triblock copolymer micelles in aqueous solution at different temperatures by using the SLS technique.
cases for some other polyoxyalkylene triblock copolymers, the temperature dependence of the cmc values of E45B14E45 individual micelles was quite weak.21 The nw of micelles can be calculated from the modified Debye equation11
H(c - ccmc)/[RBz(I - Icmc)n2/(IBznBz2)] ) 1/nwMw,uni + 2A2(c - ccmc) (7) where Icmc represents the scattered intensity at the cmc and Mw,uni is the weight-average molecular weight of the unimers (or single-chain block copolymers). In eq 7, the contribution by the unimers to the total excess scattered intensity and the unimer concentration are removed so that only the information on micelles remains. Equation 7 can be utilized under the assumptions that nw is a constant at a fixed temperature and that the concentration of unimers does not increase above its value at the cmc. Both of these two premises are met when the copolymer concentrations are only several times larger than the cmc. The calculation of nw at different temperatures is shown in Figure 2. Similar to the cmc, the nw value also increases with increasing temperature. However, the increment is also quite small (from 7 at 25 °C to 14 at 35 °C) when compared with that for EPE type triblock copolymers.
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Figure 3. Calculation of the enthalpy change of micellization ∆H° of the E45B14E45 triblock copolymer in aqueous solution from its cmc values (eq 8).
Figure 5. Polymer concentration dependence of apparent Rh values of pure E45B14E45 micelles (25 °C) and micelles in the mixed E45B14E45 and E99P69E99 triblock copolymer solution (1:1 weight ratio at 23.5 and 25 °C).
E45B14E45 triblock copolymer micelles as a function of copolymer concentration at 25 °C, and the dashed line is used for guiding the eyes. The diffusion coefficient of the micellar solution D0 can be calculated from11
D0 ) Dapp/(1 + kcc)
Figure 4. CONTIN analysis of DLS results on 5.0 mg/mL E45B14E45 triblock copolymer micelles at 25 °C (open squares) and 5.0 mg/mL E99P69E99 triblock copolymer micelles at 35 °C (filled circles).
The thermodynamic parameters of micellization can be calculated by
∆H° ) R[d ln(cmc)/d(1/T)]
(8)
with cmc in units of mol/L. A positive ∆H° for the micellization process in aqueous solution suggests an entropy-driven process due to the breakage of hydrogen bonds between water molecules and polymer chains. Figure 3 shows that, for E45B14E45 triblock copolymers, ∆H° is only about 1.0 kJ/mol, which is much smaller than those of BnEmBn and EnPmEn triblock copolymers with similar chemical compositions (about 70-80 kJ/mol).10,21 DLS was used to measure the micellar size in aqueous solution. Figure 4 shows the CONTIN analysis of DLS results on the 5.0 mg/mL E45B14E45 triblock copolymer micelles at 25 °C (open squares). The average apparent hydrodynamic radius (Rh), calculated from eqs 4 and 5, is around 6.0-6.1 nm. We have concluded that the Rh value of micelles is mainly determined by the soluble blocks which form the micellar shells and usually shows a very weak concentration and temperature dependence, although the nw value may have changed drastically with temperature.27 The Rh values of E45B14E45 triblock copolymer micelles follow the same rules. In Figure 5, the filled circles represent the average apparent Rh values of
(9)
where kc is a constant, denoting the interaction between polymer chains. For starlike micelles, kc usually has a small, positive value, suggesting that micelles have weak, repulsive interactions. On the contrary, for a triblock copolymer in a solvent selectively good for the middle block, they form flower-like micelles with some of the end blocks dangling in solution. Therefore, the nature of the interaction among polymer chains becomes attractive, and a negative, comparatively large kc value can be expected. 2. Self-Assembly of F127 (E99P69E99) Triblock Copolymer in Aqueous Solution. The characterization of E99P69E99 in water and in other biological buffers has been widely reported (including our group)28-33 because this triblock copolymer has been found to be effective as a separation medium for DNA capillary electrophoresis.2 Here we omit the detailed description on the characterization procedure, since it is quite similar to that of E45B14E45. The major results, including the cmc and nw at different temperatures and ∆H°, are listed in Table 1 to make a comparison with E45B14E45. Several remarks can be made from the results in Table 1 and Figure 4: (1) The micellizations of E45B14E45 and E99P69E99 are quite similar; in both cases. starlike micelles will form, obeying the closed-association process. The micellization abilities of both copolymers increase with increasing temperature. (27) Liu, T.; Zhou, Z.; Wu, C.; Nace, V. M.; Chu, B. J. Phys. Chem. B 1998, 102, 2875. (28) Wu, C.; Liu, T.; Chu, B.; Schneider, D. K.; Graziano, V. Macromolecules 1997, 30, 4574. (29) Wanka, G.; Hoffmann, H.; Ulbricht, W. Colloid Polym. Sci. 1990, 268, 101. (30) Wanka, G.; Hoffmann, H.; Ulbricht, W. Macromolecules 1994, 27, 4145. (31) Yu, G.; Deng, Y.; Dalton, S.; Wang, Q.; Attwood, D.; Price, C.; Booth, C. J. Chem. Soc., Faraday Trans. 1992, 88, 2537. (32) Lenaerts, V.; Triqueneaux, C.; Quarton, M.; Rieg-Falson, F.; Couvreur, P. Int. J. Pharm. 1987, 39, 121. (33) Prud’homme, R. K.; Wu, G.; Schneider, D. K. Langmuir 1996, 12, 4651.
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Table 1. Critical Micelle Concentrations (cmcs) of E45B14E45 and E99P69E99 Individual Micelles, as Well as the Mixed Triblock Copolymer Micelles (1:1 Weight Ratio) in Aqueous Solution at Different Temperatures (error < (3%) cmc (E45B14E45) temp (°C) mg/mL mol/L 20.0 23.5 25.0 27.0 28.0 29.0 30.0 32.0 33.0 35.0 37.0 40.0 a
1.11a 0.82 0.66 0.55a 0.50a 0.45a 0.41 0.35a 0.32a 0.28 0.25a 0.18a
cmc (E99P69E99) mg/mL
2.2 × 10-4 53 1.6 × 10-4 10.3a 1.3 × 10-4 6.1 1.1 × 10-4 1.72a 1.0 × 10-4 1.04a 9.0 × 10-5 0.63a 8.2 × 10-5 0.40 7.0 × 10-5 0.14a 6.4 × 10-5 0.09a 5.6 × 10-5 0.03 5.0 × 10-5 0.01a 3.6 × 10-5 ≈0.003
mol/L
cmc (mixture) mg/mL
4.2 × 10-3 8.2 × 10-4 4.8 × 10-4 1.4 × 10-4 8.3 × 10-5 5.0 × 10-5 3.2 × 10-5 1.1 × 10-5 7.1 × 10-6 2.4 × 10-6 7.9 × 10-7 2.4 × 10-7
1.1 0.82 0.66 0.50 0.39 0.24 0.19 0.09 0.07 0.03 0.01 ≈0.003
Calculated data from linear regression.
(2) E99P69E99 has a much higher value (380 kJ/mol) of the enthalpy change of micellization ∆H° when compared with that of E45B14E45 (1 kJ/mol). This difference also affects the temperature dependence of their cmc values: at 25 °C, E45B14E45 triblock copolymer chains associate first at a lower copolymer concentration; at 35 °C, E99P69E99 chains associate first; and at around 30 °C, they associate into micelles at similar copolymer concentrations (in units of mg/mL). (3) The average Rh of E99P69E99 (12.0 nm, Figure 4, filled circles) is much higher than that of E45B14E45 (6.0 nm, Figure 4, open squares), since the Rh is mainly determined by the hydrophilic E block. The Rh of E99P69E99 micelles also shows little temperature and copolymer concentration dependence, which will be shown in the following section. 3. Formation of E45B14E45 and E99P69E99 Mixed Micelles in Aqueous Solution. To study the micellization behavior of mixed triblock copolymers, a series of E45B14E45 and E99P69E99 mixtures with 1:1 weight ratio and at different concentrations were prepared and studied by SLS and DLS. As an example in the text, we used the notation “1 mg/mL mixed solution” to represent the solution which contains 1 mg of E45B14E45 and 1 mg of E99P69E99 in a total volume of 1 mL. From Table 1 we can find that there are several different temperature regions for the mixed copolymer solution. (1) In the comparatively low-temperature region (T e 27 °C), the cmc of E45B14E45 is lower than that of E99P69E99. (2) In the high-temperature region (T g 33 °C), the cmc of E45B14E45 becomes higher than that of E99P69E99. (3) At temperatures in between, the cmc values of the two individual copolymers become comparable. It should be noted that we separated the three regions on the basis of the mixed copolymer solution with a 1:1 weight ratio (E45B14E45 to E99P69E99 molar ratio is 2.5:1). If mixed copolymer solutions with different weight (or molar) ratios were studied, the boundaries of these regions should shift to other temperatures. However, the principle presented in the text should remain valid. The current three regions are discussed separately as follows. A. Low-Temperature Region (T e 27 °C). In this region, the cmc of E45B14E45 is much smaller than that of E99P69E99. Figure 6 shows the SLS data that suggest apparent cmc’s of 0.66 and 0.82 mg/mL, at temperatures of 25 and 23.5 °C for mixed solutions, respectively. By comparing these data with those in Table 1, it is noted that these cmc values are about the same as those of the pure E45B14E45 aqueous solution and much smaller than those of the E99P69E99 copolymer solution. As the micellization ability of E45B14E45
Figure 6. Plots of excess scattered intensity as a function of polymer concentration at 23.5 and 25 °C for the determination of the critical micelle concentration (cmc) of the mixed E45B14E45 and E99P69E99 triblock copolymers (1:1 weight ratio) in aqueous solution.
is much higher than that of E99P69E99 in this temperature range, it is quite safe to conclude that it is the E45B14E45 that controls the micelle formation because the E99P69E99 copolymer is being solubilized by the E45B14E45 copolymer to form the mixed micelles. DLS results on the apparent Rh of micelles can be used to support the above conclusion. In Figure 5, the apparent Rh values of micelles in 1:1 mixed copolymer solutions at two different temperatures are plotted versus copolymer concentration. The filled circles with the dotted line, representing Rh data points of pure E45B14E45 micelles, are presented for comparison. At 23.5 and 25 °C, the apparent Rh values of 5.9-6.3 nm were found for the micelles in the mixed copolymer solution at concentrations just above the cmc (see Figure 6) of the mixed micelles. These Rh values were similar to those of E45B14E45 micelles but much lower than those of the pure E99P69E99 micelles with Rh ) 12.0 nm, suggesting that the micelles in the mixed solution were comprised of essentially E45B14E45 copolymer chains, that is, with the E45B14E45 micelles just able to form micelles by themselves. They were not able to solubilize the E99P69E99 copolymers that still exist as unimers. However, it is clear from Figure 5 that the two curves start to separate from each other with increasing copolymer concentration. As discussed earlier, for starlike micelles, their apparent Rh values should have a very weak concentration dependence and should become a little smaller at higher micellar concentrations, as shown by the curve for pure E45B14E45 micelles in Figure 5. The change in apparent micellar size in the mixed solution could be attributed to the change in the composition of the micelles; that is, some E99P69E99 copolymer chains had been solubilized by the E45B14E45 micelles. The E99P69E99 copolymer chains have longer E end blocks than E45B14E45. Therefore, it should have the effect of making the mixed micelles larger. With increasing copolymer concentration, the self-assembly tendency of the E99P69E99 block copolymer is increased. E99P69E99 pure copolymer chains have the cmc values 10.3 and 6.1 mg/mL at 23.5 and 25 °C in the aqueous solution, respectively. The E45B14E45 micellar cores provide hydrophobic environments in solution, and this obviously triggers the solubilization of E99P69E99 copolymer chains into the E45B14E45 micelles at copolymer concentrations lower than the cmc of E99P69E99. The Rh curve of the mixed micelles started to deviate from that of the pure E45B14E45 micelles at copolymer concentrations
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Figure 8. Critical micelle concentration (cmc) measurements of the mixed E45B14E45 and E99P69E99 triblock copolymer solution at 32, 33 and 35 °C, respectively.
Figure 7. CONTIN analysis of DLS results on the mixed E45B14E45 and E99P69E99 triblock copolymer micelles at (a) 2.0 and 12.0 mg/mL at 25 °C and (b) 0.3 and 12.0 mg/mL at 35 °C.
much lower (about 3.0 and 1.5 mg/mL at 23.5 and 25 °C, respectively) than the cmc of E99P69E99. The apparent Rh value of mixed micelles increases with increasing copolymer concentration, suggesting that more and more E99P69E99 copolymer chains had been incorporated into the micelles at higher copolymer concentrations. At a copolymer concentration of 12 mg/mL, the apparent Rh values were 7.1 and 7.7 nm at temperatures of 23.5 and 25 °C, respectively. It is important to show that mixed micelles, instead of two kinds of individual micelles, have been formed in the mixed triblock copolymer solution. Evidences can be found in both SLS and DLS measurements. In SLS measurements, the sudden increase in the scattered intensity denotes formation of micelles in solution, as shown in Figures 1 and 6. If E99P69E99 copolymer chains associate individually at higher copolymer concentrations, another sudden increase in the total scattered intensity should be observed at that copolymer concentration, since more micelles of a different type of block copolymer were being formed. However, we did not find any such kind of “secondtransition” in the total scattered intensity in our experiments. An example is shown in Figure 6. From DLS measurements, the two different kinds of micelles should in principle give two separated peaks in the CONTIN analysis, centered around the two apparent Rh values of around 6.0 nm (E45B14E45) and 12.0 nm (E99P69E99). Unfortunately, the Rh values differed by only a factor of 2; with the limited experimental resolution of DLS in combination with the CONTIN analysis, the two peaks could not be resolved. However, a combination of the two peaks should result in a much broader peak. From Figures 4 and 7, the peak widths for micelles in the pure copolymer solution, in the mixed copolymer solution with only
E45B14E45-forming micelles, and with both copolymer chains participating in the micellar formation, the size distributions were quite similar and no obvious peakbroadening effect could be detected. A quantitative h )2, comparison can be made by using the parameter (µ2/Γ which is derived from the cumulants analysis and is an h )2 indication of peak width with Γ h ) ∫G(Γ)Γ dΓ. The (µ2/Γ values of the micelles at different copolymer concentrations (lower and above the E99P69E99 cmc value) in the mixed copolymer solutions, as well as the pure E45B14E45 and E99P69E99 micelles, have been found to be very similar, with values of around 0.10-0.12. Therefore, we could conclude that the mixed micelles were the association products containing both triblock copolymers in aqueous solution. In the current temperature region, E45B14E45 copolymer chains first associate, and then the E99P69E99 copolymer chains gradually join into micelles with increasing copolymer concentration. B. High-Temperature Region (T g 33 °C). From Table 1, it is noted that, in this temperature region, the cmc of E99P69E99 has become much smaller than that of E45B14E45; that is, the P blocks in E99P69E99 copolymer chains have become more hydrophobic and associate at lower copolymer concentrations. Similar to the low-temperature case, SLS and DLS measurements were employed to study the mixed copolymer solutions. Figure 8 shows the cmc measurements of the mixed copolymer solution at 32, 33, and 35 °C, respectively. Other data are collected in Table 1. Figure 8 and Table 1 show that the values of cmc for the mixed copolymer solution are about the same as those of E99P69E99. At the same time, DLS measurements (Figures 7b and 9) indicate that, at copolymer concentrations slightly above the cmc, the apparent Rh values of the micelles (11.9-12.0 nm) in the mixed solutions are about the same as the Rh values for pure E99P69E99 micelles in aqueous solution (represented by a dotted line in Figure 9). At higher copolymer concentrations, the apparent Rh value of micelles in the mixed solution decreased and departed away from that of pure E99P69E99 micelles, until it finally reached the value 7.7 nm. Therefore, similar conclusions to those for the low-temperature case can be made that E99P69E99 copolymer chains form micelles first, and then E45B14E45 copolymer chains gradually join into the micelles. It is interesting to note that, in both the high- and the low-temperature regions, the apparent Rh of micelles finally reached the same value of 7.7 nm when the copolymer concentrations became sufficiently high, that is, when the mixed micellar composition approached
Self-Assembly of Mixed Amphiphilic Triblock Copolymers
Figure 9. Polymer concentration dependence of apparent Rh values of individual E99P69E99 micelles (25 °C) and micelles in the mixed E45B14E45 and E99P69E99 triblock copolymer solution (at 32 and 35 °C).
Figure 10. Plots of the cmc values of pure E45B14E45 and E99P69E99 triblock copolymers versus 1/T(K) to determine the coassociation point. The open squares represent the cmc values of the mixed E45B14E45 and E99P69E99 triblock copolymer solution.
a 1:1 weight ratio. The only exception was in the case of T ) 23.5 °C, where the apparent Rh reached only a value of 7.1 nm at the copolymer concentration of 12 mg/mL for each copolymer. This difference in the Rh value could be due to the very high cmc (10.3 mg/mL) of E99P69E99 at 23.5 °C. Therefore, a large percentage of the E99P69E99 copolymer chains were still free single chains in the mixed solution even at the copolymer concentration of 12 mg/ mL for each copolymer. This behavior led to a larger weight fraction of E45B14E45 copolymer chains in the mixed micelles, implying a smaller apparent Rh value. C. Intermediate Region (27 °C e T e 33 °C). A more complicated case can be expected in the temperature region between 27 and 33 °C because at these temperatures the cmc of E45B14E45 and that of E99P69E99 in aqueous solution are comparable (in units of mg/mL). On the basis of eq 8, there exists a linear relationship between the logarithmic values of the cmc (in units of mg/mL) and 1/T (K). Figure 10 was plotted by using the cmc values of the two individual triblock copolymers versus 1/T(K) to determine the temperature at which the two kinds of copolymers had the same cmc. From the plot it is easy to locate 30 °C, the intersection of the two straight lines, as that point. At lower temperatures, E45B14E45 copolymer chains associate into micelles first; at higher temperatures, E99P69E99 has a lower cmc.
Langmuir, Vol. 15, No. 9, 1999 3115
Figure 11. Critical micelle concentration (cmc) measurement of the mixed E45B14E45 and E99P69E99 triblock copolymer in aqueous solution at 30 °C by using the SLS technique.
SLS measurements were performed to determine the cmc values of the mixed copolymer solutions at different temperatures around 30 °C. The results are shown in Figure 11 and Table 1. It should be noted that for cases where the cmc of polymer A is much smaller than that of polymer B, as discussed in parts A and B, the cmc of the mixed polymer system (A + B) is about the same as that of polymer A. However, this quantitative rule becomes ambiguous when the two polymers have similar cmc values. Table 1 shows that at each temperature between 27 and 33 °C, the cmc of the mixed copolymer solution is smaller than the cmc of either individual polymer; that is, in the mixed solution, the polymer with the lower cmc (we assign it as polymer A) tends to associate into micelles at even lower polymer concentrations. In Figure 10, the cmc data points in this temperature region shifted lower from the two straight lines that represent the cmc values of the two pure copolymers. The explanation is that because another polymer (we call it polymer B) has a similar cmc, due to the polydispersity of polymers, some of the B polymer chains may be similar to some of the A single chains in hydrophobicity, so that they can also make some contributions to the micellization process. As micellization is a thermodynamic process that is controlled by temperature, the cmc of polymer A should have a fixed value at a certain temperature. In the current case, the combination of polymer A chains and some of the polymer B chains maintains the apparent cmc value to be about the same as that in pure polymer A solutions. The cmc value of the mixed polymer solution in Table 1 becomes lower because it only counts the concentration of the polymer having the lower cmc (which we have arbitrarily defined as polymer A). It should be noted that, in Figure 11, the cmc for the mixed solution is denoted as 0.19 mg/ mL at 30 °C but it actually contains 0.19 mg/mL each of E45B14E45 and E99P69E99. Thus, in Figure 10, the coincidence of the two points at A signifies that E45B14E45 controls the cmc of the mixed solution while that of the points at B signifies that E99P69E99 does so, as discussed in parts A and B. Another approach may be used to quantitatively analyze the contribution of the two kinds of triblock copolymer chains to the cmc of the mixed micelles: take the apparent cmc value (mg/mL) of the mixed copolymer solution divided by the lower cmc (mg/mL) of the two pure copolymers, as shown in Figure 12. This coefficient, defined as β ) cmc(mix.)/cmc(small/pure), denotes the average weight percentage of copolymer A chains in the mixed micelles at
3116 Langmuir, Vol. 15, No. 9, 1999
Figure 12. Temperature dependence of β of the mixed E45B14E45 and E99P69E99 triblock copolymer solutions. The coassociation point is the point where β reaches its minimum value (0.5).
the cmc, or it can be considered as the effect of copolymer B on the cmc of the mixed copolymer solution. Figure 12 was plotted by using the coefficient β versus temperature. In low- and high-temperature regions (corresponding to parts A and B in the text), β ) 1, indicating that the micellization of the mixed copolymer solution was determined essentially by one type of block copolymer. At 27 °C, the value of β started to decrease, suggesting that the other block copolymer also contributed toward the cmc value. At 30 °C, the two copolymers had the same cmc (about 0.4 mg/mL), while the measured cmc of the mixed copolymer solution was 0.19 mg/mL for each copolymer (1.5 × 10-5 mol/L E99P69E99 and 3.8 × 10-5 mol/L E45B14E45, respectively), just about half the value of the pure one, and the total copolymer concentration in the solution had about the same value as the pure cmc. This result confirms that, at this temperature, these two triblock copolymers have about the same ability to associate. We define this point as the “coassociation point”. At this special point, the two types of copolymer chains are equivalent and β should reach its minimum value (0.5), since the two types of copolymers are equal in weight in the aqueous solution. From Figure 12, it is clear that the experimental results have adequately confirmed the above supposition. In an ideal case, if the copolymer samples were perfectly monodisperse, the curve in Figure 12 should be a δ function, with β ) 0.5 at the coassociation temperature and β ) 1 at other temperatures. However, the polydispersity of the copolymers, that cannot be avoided, has broadened this δ function with the widths of the peaks on both sides denoting the degrees of polydispersity of the two block copolymers, respectively. DLS measurements at 30 °C were very important because, at this temperature, the mixed micelles at every copolymer concentration should be composed of 50 wt % of each kind of triblock copolymer chain. The concentration dependence of the apparent micellar Rh values is plotted in Figure 13, showing the curves at different temperatures as well as those for the two for pure copolymer micelles. At 30 °C, the Rh value decreased from 8.8 to 7.7 nm with increasing copolymer concentration. This decrease is reasonable for a starlike micellar system. In Figure 13 the apparent Rh values became the same (7.7 nm) at high enough copolymer concentrations for all the curves of mixed micelles (except the one at 23.5 °C, as discussed earlier), suggesting that the weight ratio of E99P69E99 and E45B14E45 in the mixed micelles approaches a 1:1 weight ratio with increasing copolymer concentration. For tem-
Liu et al.
Figure 13. Polymer concentration dependence of the apparent Rh values of the mixed E45B14E45 and E99P69E99 triblock copolymer micelles at different temperatures. Curves for pure E45B14E45 and pure E99P69E99 micelles were plotted for comparison.
peratures close to 30 °C, the Rh values approach the 7.7 nm magnitude at lower copolymer concentrations. On the other hand, by examining the Rh values at low copolymer concentrations, it is noted that the Rh value increases with increasing temperature, indicating that more E99P69E99 copolymer chains participate in the micelle formation with increasing temperature. This observation coincides with the fact that the hydrophobicity of the E99P69E99 chains changes much more drastically than that of E45B14E45 chains with increasing temperature. Another interesting curve in Figure 13 is the one at 28 °C. At this temperature, the Rh value of the mixed micelles shows first an increase and then a decrease with increasing copolymer concentration. This curve actually contains two different regions that show the effect of competition between the intermicellar interactions and the change in micellar composition. At copolymer concentrations lower than 2.0 mg/mL, the apparent Rh value increased from 6.0 to 8.6 nm with increasing copolymer concentration, suggesting that E45B14E45 triblock copolymer chains associated first and then more and more E99P69E99 triblock copolymer chains joined into the micelles to make them bigger. In this region, the participation of E99P69E99 copolymer chains into micelles was the dominant effect on the change in the micellar size. At copolymer concentrations higher than 2.0 mg/mL, the apparent Rh value of micelles decreased from 8.6 to 7.7 nm with increasing copolymer concentration. It suggests that the intermicellar interactions, which are repulsive for starlike micelles and make the apparent Rh value smaller at higher copolymer concentrations, have become the major effect on determining the change in the micellar size although the weight percentage of E99P69E99 copolymer chains in the micelles is still increasing gradually with copolymer concentration. 4. Association Number (nw) of Mixed Micelles. The nw of mixed micelles can also be calculated from SLS measurements. However, it becomes meaningful only in the case that the weight percentage of the two copolymers in the micelles can be determined. At low temperatures (e25 °C), because of the very high cmc of E99P69E99, a large fraction of E99P69E99 copolymer chains are single chains in the studied copolymer concentration region. As this fraction changes with copolymer concentration, the weight-average association number cannot be accurately determined. At the coassociation point (30 °C), the weight ratio of two copolymers in the micelles is 1:1 at all copolymer
Self-Assembly of Mixed Amphiphilic Triblock Copolymers
Langmuir, Vol. 15, No. 9, 1999 3117 Table 2. Weight-average Association Number (nw) of E45B14E45 and E99P69E99 Individual Micelles, as Well as the Mixed Triblock Copolymer Micelles in Aqueous Solution at Different Temperatures mixed micelles
Figure 14. Determination of the weight-average association number (nw) of the mixed E45B14E45 and E99P69E99 triblock copolymer micelles in aqueous solution at 30 °C (coassociation point) by using the SLS technique (eq 7).
concentrations. Figure 14 shows that from SLS measurements the nw at this temperature is about 16, by realizing the fact that the weight-average molecular weight of one single chain in the mixed micelles Mw,mix can be calculated by the expression
Mw,mix ) (cEBEMw,EBE + cEPEMw,EPE)/(cEBE + cEPE) (10) with cEBE and cEPE being the copolymer concentrations of E45B14E45 and E99P69E99 in units of mg/mL and Mw,EBE and Mw,EPE being the weight-average molecular weights of E45B14E45 (5000 g/mol) and E99P69E99 (12 600 g/mol) single chains, respectively. For a E45B14E45 and E99P69E99 mixed copolymer solution with a 1:1 weight ratio, eq 10 can be simplified as
Mw,mix ) (Mw,EBE + Mw,EPE)/2
(11)
The nw values of E45B14E45 and E99P69E99 pure micelles are 10 and 23, respectively. It is interesting to find that nw,mix is just about the middle value of the nw,EBE and nw,EPE values, suggesting that the association ability of the mixed triblock copolymer solution is about the average of those of the two individual triblock copolymers. As discussed earlier in the text, at 30 °C the mixed micelles contain two block copolymers with equal weight over all the copolymer concentrations. With the molar ratio of E45B14E45 and E99P69E99 being 2.5:1, it is easy to calculate that on average every mixed micelle contains 11-12 E45B14E45 copolymer chains and 4-5 E99P69E99 copolymer chains at 30 °C. At the temperatures above the coassociation point, the weight percentage of E99P69E99 copolymer chains in the mixed micelles will gradually increase. However, because of the very low cmc values at these temperatures for both pure triblock copolymers when compared with the copolymer concentrations we have studied, we still can estimate the nw without introducing large errors by assuming a 1:1 copolymer weight ratio in the mixed micelles. The calculated nw values at different temperatures for the mixed micelles and for the two pure micelles, as well as the number of each kind of copolymer chain in the mixed micelles, are listed in Table 2 for comparison.
temp (°C)
nw (E45B14E45)
nw (E99P69E99)
30 32 35
10 12 14
23 27 33
nw
no. of E99P69E99 chains
no. of E99P69E99 chains
16 19 24
4-5 5-6 6-7
11-12 13-14 17-18
It is quite obvious that, for the mixed micelles, the nw value also increases with increasing temperature, similar to the case for the individual micelles. At each temperature, the nw,mix value is about the average value of the nw values of the two kinds of individual triblock copolymer micelles. Conclusions A mixed aqueous solution of two triblock copolymers, E14B45E14 and E99P69E99, was studied by using static and dynamic laser light-scattering techniques as a model to understand the self-assembly behaviors of mixed amphiphilic triblock copolymers in solution. Several conclusions can be made through this study: (1) For two miscible block copolymers in a selective solvent, mixed micelles, instead of the coexistence of two kinds of individual micelles, are generally the products of the self-assembly process. (2) If the cmc of one block copolymer (A) is much lower than that of the other one (B) at a certain temperature, the cmc of the mixed copolymer solution is mainly determined by copolymer A. Copolymer A chains first associate into micelles at the same cmc as that for the pure A solution while copolymer B chains gradually participate in the micellization process with increasing copolymer concentration. The weight percentage of B copolymer chains in the mixed micelles increases with increasing copolymer concentration, until it approaches the weight percentage of B copolymer chains in the total copolymer concentration at high enough copolymer concentrations. (3) If the cmc of copolymer B is only slightly higher than that of copolymer A, some of the B chains can take part in the micellization process with A chains even below the cmc of pure A chains due to the polydispersity effect of block copolymers. For a special case, if the two polymers have the same cmc (coassociation point), they will associate at the same time to form mixed micelles with a 1:1 weight ratio for a 50 wt %/50 wt % A-B mixed solution. The cmc value remains the same as that in the individual A or B polymer solution. The weight-average association number nw and the hydrodynamic radius Rh of the mixed micelles are found to be between the nw and the Rh values of the two kinds of pure micelles, respectively. The copolymer having a higher percentage in the mixed micelles has a larger effect on determining nw and Rh. Acknowledgment. B.C. gratefully acknowledges the support of this work by the National Institutes of Health (Grant 2R01HG0138604) and the National Science Foundation (Grant DMR9612386). LA9812525
