Micellization and Phase Separation for Triblock Copolymer 17R4 in

Department of Physics, The College of Wooster, Wooster, Ohio 44691, United States. ‡ Department of Chemistry and Biochemistry. § Department of Chem...
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Micellization and Phase Separation for Triblock Copolymer 17R4 in H2O and in D2O )

Alison Huff,† Kelly Patton,† Hosanna Odhner,† Donald T. Jacobs,† Bryna C. Clover,‡ and Sandra C. Greer*,‡,§,

)

† Department of Physics, The College of Wooster, Wooster, Ohio 44691, United States, ‡Department of Chemistry and Biochemistry, and §Department of Chemical and Biomolecular Engineering, The University of Maryland, College Park, College Park, Maryland 20742, United States. Current address: Office of the Provost, Mills College, Oakland, CA 94613.

Received October 30, 2010. Revised Manuscript Received December 11, 2010 The reverse Pluronic triblock copolymer 17R4 is formed from poly(propylene oxide) (PPO) and poly(ethylene oxide) (PEO): PPO14-PEO24-PPO14, where the subscripts denote the number of monomers in each block. In water, 17R4 shows both a transition to aggregated micellar species at lower temperatures and a separation into copolymer-rich and copolymer-poor liquid phases at higher temperatures. For 17R4 in H2O and in D2O, we have determined (1) the phase boundaries corresponding to the micellization line, (2) the cloud point curves marking the onset of phase separation at various compositions, and (3) the coexistence curves for the phase separation (the compositions of coexisting phases). In both H2O and in D2O, 17R4 exhibits coexistence curves with lower consolute temperatures and compositions that differ from the minima in the cloud point curves; we take this as an indication of the polydispersity of the micellar species. The coexistence curves for compositions near the critical composition are described well by an Ising model. For 17R4 in both H2O and D2O, the critical composition is 0.22 ( 0.01 in volume fraction. The critical temperatures differ: 44.8 °C in H2O and 43.6 °C in D2O. The cloud point curve for the 17R4/D2O is as much as 9 °C lower than in H2O.

Introduction The triblock copolymer 17R4 has a structure PPO14-PEO24PPO14, where PPO is poly(propylene oxide) and PEO is poly(ethylene oxide), with the subscripts denoting the number of monomers in each block. In H2O, 17R4 shows both micellization at lower temperatures and separation into coexisting liquid phases at higher temperatures.1 We present here new data for the micellization and phase separation of 17R4 in both H2O and D2O, as functions of temperature and composition. Micellization. A key point in our analysis of the behavior of these solutions will be the importance of the polydispersity of the assembled structures. There are two sources of polydispersity in a micellar system: (1) the original, fixed polydispersity of the copolymer itself, and (2) the polydispersity of the resulting micellar aggregates. Most theories and simulations have considered only monodisperse copolymers that then form polydisperse micelles. Using mean-field lattice theory, Linse2 found that the copolymer polydispersity affects the critical micelle concentration (CMC) and the micelle size.3 The assembled micelles are, in turn, polydisperse species. For a monodisperse starting copolymer, Tanford4 showed that the distribution of aggregation numbers (or micelle masses) will be h i lnðγn xn Þ ¼ - ðn=RTÞ μ°mic, n - μ°S þ n lnðγs xs Þ þ ln n ð1Þ where xn is the mole fraction of copolymers in micelles of aggregation number n, xs is the mole fraction of copolymers in the solvent, γs is the activity coefficient of the copolymer in the *Author to whom correspondence should be addressed. E-mail: [email protected]. (1) Zhou, Z.; Chu, B. Macromolecules 1994, 27, 2025–2033. (2) Linse, P. Macromolecules 1994, 27, 6404–6417. (3) Linse, P. Macromolecules 1994, 27, 2685–2693. (4) Tanford, C. The Hydrophobic Effect: Formation of Micelles and Biological Membranes; John Wiley & Sons: New York, 1980.

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solvent, and γn is the activity coefficient of the copolymer in a micelle of size n. Here, μ°mic,n is the standard chemical potential of the copolymer in a micelle of aggregation number n, and μ°s is the standard chemical potential of the copolymer in the solvent. Equation 1 includes the nonideality of the copolymers in the solvent (γs) and in the micelles (γn), whereas Tanford set γn =1. ° , the standard free energy change of a The term [μ°mic,n-μ°s] is ΔGmic copolymer molecule due to micellization. ° , and the Equation 1 then leads to a means of determining ΔGmic ° and ΔSmic ° . The assumpchanges in enthalpy and entropy, ΔHmic tions of a large, temperature-independent5,6 n and of ideal solutions (γn =γs =1) give1,7 ΔG°mic ¼ RT lnðCMCÞ

ð2Þ

so that lnðCMCÞ ¼

° ΔG°mic ΔHmic ΔS° ¼ - mic RT RT R

ð3Þ

If ΔHmic ° and ΔSmic ° are fairly constant over a range of temperature, then eq 3 gives a straight line when ln(CMC) is plotted versus 1/T, where the slope determines ΔH°mic and the intercept ΔS°mic . Then, ΔG°mic is calculated from ΔG°mic = ° - TΔSmic ° . However, we note that ΔHmic (1) (2)

The aggregation number n is not large near the micellization line and does change with temperature.8 “Significant interactions between amphiphiles in aqueous solution occur already at very low solute concentrations.”4

(5) Taboada, P.; Mosquera, V.; Attwood, D.; Yang, Z.; Booth, C. Phys. Chem. Chem. Phys. 2004, 5, 2625–2627. (6) Kelarakis, A.; Havredaki, V.; Rekatas, C. J.; Booth, C. Phys. Chem. Chem. Phys. 2001, 5550–5552. (7) Lindman, B.; Wennerstrom, H. Top. Curr. Chem. 1980, 87, 1–83. (8) Holtzer, A.; Holtzer, M. F. J. Phys. Chem. 1974, 78, 1442–1443.

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(3) The quantities obtained may describe the CMC data, but they are not necessarily accurate values ° , ΔHmic ° , and ΔSmic ° .9 for ΔGmic (4) ΔGmic ° , ΔHmic ° , and ΔSmic ° refer to the standard state, and are not equal to ΔGmic, ΔHmic, and ΔSmic at some other state. ΔH°mic = ΔHmic can be a good approximation, but this is not the case for ΔGmic or ΔSmic.10 Because of all these caveats, thermodynamic parameters obtained by using eqs 2 and 3 can be referred to as “apparent” values.11 In summary, polydispersity occurs in the (fixed) structure of the starting copolymer and in the (variable) aggregation numbers of the assembled micelles. The separation of these two effects is not simple; indeed, the first affects the second. In the work presented here, we start with a copolymer of low fixed polydispersity, but we must assume that both types of polydispersity matter for the phenomena measured. Phase Separation. In addition to the micellization, 17R4 in aqueous solution exhibits a macroscopic separation into two liquid phases.1 We note that cloud points are measured by preparing several compositions and then slowly changing the temperature until phase separation is observed for each composition. Coexistence curves are measured by preparing one composition (usually the critical concentration) and measuring the concentration in each phase as a function of temperature. For 17R4/H2O, Zhou and Chu1 measured an inverted cloud point curve, corresponding to the lower critical solution temperature (LCST), with the cloud point curve intersecting the micellization line. We will present both cloud points and coexistence curves for 17R4 in H2O and in D2O. It is important to note that, for polydisperse micelles that form coexisting liquid phases, the cloud points and the coexistence curves do not coincide. Koningsveld12,13 has shown that for polydisperse systems: “As a rule, it is not allowed to identify a cloud-point curve with a bimodal (coexistence curve), nor the maximum in a cloud-point curve with a critical point.”12 This differs from a monodisperse system such as methanol and cyclohexane14 or even from a polymer of narrow polydispersity in a solvent,15 where the onset of phase separation;the “cloud point”, where the system is opalescent as a second phase forms; coincides with the coexistence curve. For monodisperse systems with an upper critical solution temperature (UCST) [or a lower critical solution point (LCST)], the maximum of the cloud point curve is also the maximum [or minimum] of the coexistence curve and is the critical point.16 Polydisperse systems show a cloud point curve (the temperature of phase separation for a given composition) and a “shadow” curve (the composition of the smaller incipient “daughter” phase at that temperature) with a different shape than the cloud point curve.17 The critical point is below the maximum in the cloud point (9) Kresheck, G. C. J. Phys. Chem. B 1998, 102, 6596–6600. (10) McGlashan, M. L. Chemical Thermodynamics; Academic Press: New York, 1979. (11) Kelarakis, A.; Mai, S.-M.; Havredaki, V.; Brett, A.; Booth, C. J. Colloid Interface Sci. 2004, 275, 439–444. (12) Koningsveld, R. Discuss. Faraday Soc. 1970, 49, 144–161. (13) Koningsveld, R.; Stockmayer, W. H.; Nies, E. Polymer Phase Diagrams; Oxford University Press: Oxford, 2001. (14) Jacobs, D. T.; Anthony, D. J.; Mockler, R. C.; O’Sullivan, W. J. Chem. Phys. 1977, 20, 219–226. (15) Jacobs, D. T.; Braganza, C. I.; Brinck, A. P.; Cohen, A. B.; Lightfoot, M. A.; Locke, C. J.; Suddendorf, S. J.; Timmers, H. R.; Triplett, A. L.; Venkataraman, N. L.; Wellons, M. T. J. Chem. Phys. 2007, 127, 124905 (10 pages). (16) Wilding, N. B.; Sollich, P.; Fassolo, M.; Buzzacchi, M. J. Chem. Phys. 2006, 125, 014908 (12 pages). (17) Sollich, P. J. Phys.: Condens. Matter 2002, 14, R79–R117.

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Figure 1. The cloud point curve (solid line) and the shadow curve (dashed line) for a polydisperse system.12,13 Their intersection is the critical point, shown for an LCST. A particular prepared composition will phase separate at the cloud point curve: one phase with a larger volume and the other phase with a smaller volume. The phase with the smaller volume has an initial composition on the shadow curve. A different coexistence curve (symbols) will result for each prepared composition.

curve for an UCST system, above the minimum for an LCST, and marks the intersection of the cloud and shadow curves.16 Moreover, for a set of different prepared compositions of a polydisperse system, there will be a set of coexistence curves, each one starting at the cloud and shadow curves (see Figure 1).17 Only when the prepared composition matches the critical composition will the critical point be the extremum of the coexistence curve.13 Critical Phenomena. The 17R4/H2O or D2O phase diagram shows a lower critical solution point. Phenomena near liquidliquid critical points can be described by power laws in the reduced temperature (t = |Tc - T|/Tc) with universal Ising exponents.18-20 The shape of the coexistence curve is described by   ð4Þ jju - jl j ¼ B t β 1 þ B1 t Δ þ B2 t2Δ þ 3 3 3 where ju and jl are the volume fractions in the upper and lower phases. The Ising critical exponents are β = 0.326 and Δ = 0.52.18,21,22 The amplitudes B, B1, and so forth, and the locations of the critical point in temperature and composition (Tc and jc) are not universal and depend on the system. The coexistence curve is described both by its shape (eq 4) and by its asymmetry, which is given by the diameter of the coexistence curve. Cerdeirina et al.23,24 have argued that any nonlinearity, or asymmetry, in the diameter can be described using a “complete scaling” approach developed by Fisher and co-workers.24,25 The diameter then has the form23,24   jju þ jl j ¼ 2jc 1 þ D1 t2β þ D2 t ð1 - RÞ þ D0 t þ 3 3 3 ð5Þ where D1 is related to the square of the coexistence curve amplitude B2; D2 is proportional to Ao , the leading amplitude (18) Sengers, J. V.; Shanks, J. G. J. Stat. Phys. 2009, 137, 857–877. (19) Greer, S. C.; Moldover, M. R. Annu. Rev. Phys. Chem. 1981, 32, 233–265. (20) Kumar, A.; Krishnamurty, H. R.; Gopal, E. S. R. Phys. Rep. 1983, 98, 57–143. (21) Compostrini, M.; Pelissetto, A.; Rossi, P.; Vicari, E. Phys. Rev. E 2002, 65, 066127 (19 pages). (22) Pelissetto, A.; Vicari, E. Phys. Rep. 2002, 368, 549–727. (23) Cerdeirina, C. A.; Anisimov, M. A.; Sengers, J. V. Chem. Phys. Lett. 2006, 424, 414–419. (24) Wang, J. T.; Cerdeirina, C. A.; Anisimov, M. A.; Sengers, J. V. Phys. Rev. E 2008, 77, 031127 (12 pages). (25) Kim, Y. C.; Fisher, M. E.; Orkoulas, G. Phys. Rev. E 2003, 67, 061506 (21 pages).

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-R of the heat capacity in the two-phase region: CpµAo t ; and R = 18,21,22 For nitrobenzene in n-alkane mixtures, Cerdeirna 0.110. et al.23,24 found the t2β term to dominate, while the higher-order terms made negligible contributions to the diameter. We also found the t2β term to dominate for an eight-armed star polystyrene in methylcyclohexane.15 The t(1-R) term will generally be negligible in polymer systems, where universal amplitude rela15 tions imply small Ao values and thus negligible D2 amplitudes. The work by Eckert et al.26 on mixtures of the two polydisperse polymers poly(ethylene glycol) and poly(propylene glycol) is of interest for comparison. They found a different coexistence curve for each prepared composition, a cloud point curve with a maximum well away from the critical point, a critical exponent β close to the Ising value,18 and coexistence curve diameters that remain similar for all the coexistence curves. Deuteration Effects. H2O and D2O are often taken to be interchangeable as solvents. However, the hydrogen bonding strengths in H2O and D2O differ,27 resulting in distinct differences28,29 in physical properties such as density, viscosity, and heat capacity. Because deuterium atoms are heavier than hydrogen atoms, the amplitudes of the atomic vibrations are smaller, and a deuterium bond in D2O is stronger than a hydrogen bond in H2O. If a copolymer can engage in hydrogen bonding with the solvent, then these hydrogen bonds will be stronger in D2O than in H2O. Studies have suggested that hydrophobic interactions are greater in D2O than in H2O,28,30,31 due to both the structure of the solvation cage around the hydrophobe and the structure of the bulk D2O.28,31 The self-aggregation of many hydrophobic bodies does occur at lower temperatures and lower copolymer concentrations in D2O than in H2O.28,30,31 A study of several Pluronic copolymers has shown micellization at lower temperatures in D2O than in H2O.32 Phase separation behavior on changing from H2O to D2O is harder to predict. For example, poly(vinyl methyl ether) (PVME) and poly(N-isopropyl acrylamide) (PNIPAM) have higher LCSTs in D2O than in H2O.33,34 Poly(ethylene glycol) (PEG) and Pluronic 10R5 (PPO22PEO8PPO22) have lower LCSTs in D2O than in H2O.34 PVME and PNIPAM have electronegative atoms protruding into solution, allowing ready formation of hydrogen bonds to the copolymer. Conversely, in PEG and 10R5, the electronegative oxygens are within the polymer backbone, making hydrogen bonding to the copolymer more difficult. The structure of 17R4 is like those of PEG and 10R5, so we expect that the exchange of D2O for H2O will lower cloud points and LCST values, as is the case.

Experimental Methods Materials. The 17R4 sample, PPO14-PEO24-PPO14, was a gift from BASF Chemical Company. BASF reported that the sample had an average molecular mass of 2650 g/mol, a density of 1.048 g/mL, and a 0.09 wt % water content. Size exclusion chromatography (SEC) was performed in tetrahydrofuran at 35 °C by Polymer Source, Inc., using poly(ethylene glycol) standards (26) Eckert, S.; Meier, G.; Alig, I. Phys. Chem. Chem. Phys. 2002, 4, 3743–3749. (27) Engdahl, A.; Nelander, B. J. Chem. Phys. 1987, 86, 1819–1823. (28) Luan, C. H.; Urry, D. W. J. Phys. Chem. 1991, 95, 7896–7900. (29) Mukerjee, P.; Kapauan, P.; Meyer, H. G. J. Phys. Chem. 1966, 70, 783–786. (30) Chang, N. J.; Kaler, E. W. J. Phys. Chem. 1985, 89, 2996–3000. (31) Emerson, M. F.; Holtzer, A. J. Phys. Chem. 1967, 71, 3320–3330. (32) Shvartzman-Cohen, R.; Ren, C.; Szleifer, I.; Yeruhalmi-Rozen, R. Soft Matter 2009, 5, 5003–5011. (33) Shirota, H.; Kuwabara, N.; Ohkawa, K.; Horie, K. J. Phys. Chem. B 1999, 103, 10400–10408. (34) Bergbreiter, D.; Fu, H. J. Polym. Sci., Part A: Polym. Chem. 2008, 46, 186–193.

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for calibration. The SEC results showed a single peak, indicating the sample to be free of PPO or PEO monomers or diblock copolymers. The number average molecular mass was found to be 2670 g/mol, very close to that reported from BASF, and the polydispersity index of the sample was 1.06. An 1H NMR analysis of 17R4 in deuterated chloroform by Polymer Source, Inc., indicated the PEO/PPO block ratio to be 0.98; thus, there were slightly fewer PEO blocks than PPO blocks in the copolymer. The copolymer contained about 5% unsaturated end groups, as opposed to the hydroxyl groups expected. The H2O used was from a Barnstead NANOpure system, with resistivity greater than 18 MΩ-cm. The D2O was purchased from Aldrich (99.98%) or Cambridge Isotope (99.9%) and used without further purification. Each copolymer solution was prepared by massing the desired amount of copolymer into a glass vial and adding the solvent until the total desired mass was achieved. All samples were immediately sealed so that measurements could be taken over a period of several weeks. All samples were vigorously shaken to ensure complete mixing. Mass fractions were converted to volume fractions by using the densities of H2O, D2O, and 17R4 and by assuming no change of volume on mixing. Micellization and Cloud Point Measurements. Several vials with different compositions were immersed in a water bath with temperature measured to an accuracy of 0.2 K and a precision of 0.01 K.35 The temperature of the water bath was lowered in steps while the samples were observed by eye. Samples were allowed to sit for 30 min at each temperature to come to thermal equilibrium with the bath, after which the samples were stirred vigorously and allowed equilibrate for 1-3 h. Each CMT value is reported as the midpoint between the last temperature at which a solution was cloudy (free copolymer region) and the first temperature at which the solution was transparent (micellar region). Each cloud point temperature is given as the temperature at which a second phase began to form. At high concentrations, the second phase was difficult to see, and the onset of opacity was taken as the point of phase separation. For the phase at lower temperatures and concentrations in 17R4/H2O, Zhou and Chu1 reported that free copolymers were present and that an “anomalous micellization” due to “composition heterogeneity of the block copolymer” and other hydrophobic impurities such as PPO homopolymers36 caused a cloudiness that could be eliminated by filtering. However, Ho et al.37 found that, for PEO/H2O, aggregates could be broken by filtration, but then reformed within 24 h. We filtered some mixtures, but filtering did not prevent the cloudiness in the free copolymer region. Coexistence Curve Measurements. The coexistence curves were determined by measuring the compositions (volume fractions) of the coexisting phases as a function of temperature. The volume fractions were determined from measurements of the refractive index using a prism-shaped cell.15 The volume of sample was about 6.5 mL with an air bubble of 0.5 mL to maintain a pressure of one atmosphere. The cell was surrounded by two concentric temperature-controlled cylinders with air between them.15 The cell temperature was monitored with a calibrated thermistor.15 The precision in cell temperature was better than 0.1 mK, and the accuracy was 20 mK. Since the temperature of the cell itself was not actively controlled, there was a long equilibration time (about 6 h) after a temperature change and before we mixed the solution with a magnetic stirrer. The solutions were then left for at least another 2 h and sometimes 8 h (when in the two-phase region) to come to thermal equilibrium before the refractive index in each phase was measured. (35) Greer, S. C. Measurement and Control of Temperature. In Building Scientific Apparatus: A Practical Guide to Design and Construction, 4th ed.; Moore, J. H.; Davis, C. C.; Coplan, M. A., Eds.; Cambridge University Press: New York, 2009; pp 617-619. (36) Zhou, Z.; Chu, B. Macromolecules 1988, 21, 2548–2554. (37) Ho, D.; Hammouda, B.; Kline, S. J. Polym. Sci. Polym. Phys. Ed. 2003, 41, 135–138.

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The refractive index was determined by measuring the minimum deviated angle for He-Ne laser light (λo=632.8 nm) passing through each phase, by means of a Gaertner spectrometer with a precision of 20 arcsec. The resulting refractive indices (relative to air) had a resolution of 0.000 15. The volume fraction j of copolymer in the mixture was determined from a set of calibration measurements in which we measured the refractive index n as a function of temperature in the one-phase (clear) region for several known mass fractions of copolymer in H2O and in D2O. Mass fractions were converted to volume fractions by using the known densities and by assuming no change of volume on mixing. Only the choice of copolymer, the choice of solvent, and the concentration of copolymer in solvent are important in determining the refractive index; neither branching nor aggregation matters.38,39 From a weighted least-squares fit to the calibration data, we determined the following equations that give the volume fraction of 17R4 in solution to a precision of (0.0025 from the measured refractive index n(T) j ¼ - 7:8133 - 0:04157 T þ 5:847n þ 0:03205Tn in H2 O

ð6Þ

j ¼ - 7:7751 - 0:04117 T þ 5:848n þ 0:03157Tn in D2 O

ð7Þ

with T in °C.

Figure 2. Cloud point curves and micellization (CMT) lines for 17R4 in H2O (black symbols and solid lines) and in D2O (red symbols and dashed lines). Lab A refers to The College of Wooster and lab B to the University of Maryland, College Park. Open circles and squares are data from Zhou and Chu.1 All lines are guides to the eye and divide the space into regions I (copolymers), II (micellar aggregates), and III (two phases).

Results and Discussion We consider the behavior of the copolymer solutions in three regions:1 Region I, where a cloudy network of free copolymers makes the mixture opaque; Region II, where micelles coexist with free copolymers and the mixture is transparent with some opalescence near the micellization line or near the cloud point; and Region III where two liquid phases coexist. Recall that cloud point and micellization point measurements have uncertainties determined from the midpoint between two temperatures and are considered to be 99% uncertainties. Uncertainties from leastsquares fits are given as one standard deviation. Micellization Lines. The micellization lines for 17R4/D2O and 17R4/H2O are shown in Figures 2 and 4, and the data are given in Table 1 of the Supporting Information. The micellization lines show the CMT to decrease with increasing concentration, but in a different way for each of the two solvents. For 17R4/H2O, the micellization line is concave upward and can be described well by eq 2, as indicated by the straight line in Figure 3. These new micellization data for the 17R4/H2O system are quite consistent with the data of Zhou and Chu.1 The fit to eq 2 for the combined data sets for the 17R4/H2O system yields ΔH°mic = 125 ( 5 kJ/mol, ΔS°mic = 461 ( 17 J/ (mol K), and thus ΔG°mic = -20 ( 11 kJ/mol. These values are consistent with those determined by Zhou and Chu (115 ( 6, 400, and -9, respectively),1 with the caveats listed above under eq 3. For the 17R4/D2O, the micellization line is concave downward (Figure 2). This behavior indicates a nonconstant ΔH°mic, as shown by the curved line in Figure 3. The micellization line for the 17R4/D2O system at the lower concentrations is quite close to that for 17R4/H2O, yielding comparable values for ΔG°mic, ΔHmic°, and ΔS°mic over that region. At higher concentrations (upper right in Figure 3, last four points), the 17R4/D2O micelliza° and ΔSmic ° becoming smaller tion line corresponds to both ΔHmic but still yielding a negative value of ΔG°mic (rough values being 20 ( 5 kJ/mol, 111 ( 17 J/(mol K), and -15 ( 10 kJ/mol, (38) Zhou, C.-S.; An, X.-Q.; Xia, K.-Q.; Yin, X.-L.; Shen, W.-G. J. Chem. Phys. 2002, 117, 4557–4563. (39) Xia, K.-Q.; An, X.-Q.; Shen, W.-G. J. Chem. Phys. 1996, 105, 6018–6025.

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Figure 3. Micellization line data (critical micelle concentration, CMC, and inverse temperature, 1/T). The CMC is given as the mole fraction of 17R4. Equation 3 indicates that the data will fall on a straight line if ΔHmic ° is constant. The 17R4/H2O data do fall on a straight line that gives the thermodynamic quantities as described in the text. The micellization data for 17R4/H2O do not extend to concentrations as high as those for 17R4/D2O. The 17R4/D2O data do not fall on a straight line (dashed curve is a guide for the eye) and indicate that ΔHmic ° changes from a negative value toward zero.

respectively). This point will be discussed further in under Discussion and Conclusions. Cloud Point Curves. Cloud point curves for 17R4/D2O and 17R4/H2O are compared in Figure 2 and shown in Figure 4, and the data are given in Table 2 of the Supporting Information. Our cloud point curve for 17R4/H2O is at slightly lower temperatures than that of Zhou and Chu,1 which could indicate small differences in the 17R4 samples. The cloud point curve for 17R4/D2O is lower in temperature than that for H2O by as much as 9 °C. Coexistence Curves and Critical Phenomena. Coexistence curves were measured for seven concentrations of 17R4 in H2O Langmuir 2011, 27(5), 1707–1712

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Figure 5. Difference in volume fraction, Δj, between the lower and upper phases as a function of reduced temperature (t = |Tc T|/Tc) for the coexistence curve data shown in Figure 4. See eq 4, Table 4, and text. The blue line represents the fit to the H2O data.

Figure 4. Measured coexistence curves, with cloud point curves and micellization lines from Figure 2. CP marks the critical points. Regions I, II, and III are as in Figure 2. Prepared compositions are indicated by arrows along the composition axes and are listed in the legends. There is a specific coexistence curve associated with each prepared composition. D2O is more dense than 17R4, but H2O is less dense than 17R4; thus, the upper phase is 17R4-rich when the solvent is D2O, and the lower phase is 17R4-rich when the solvent is H2O.

and for three concentrations of 17R4 in D2O, as shown in Figure 4 and listed in Table 3 of the Supporting Information. The coexistence curves obtained are different for each initial concentration, with one side of each curve beginning at the cloud point curve and the other side beginning at the shadow curve. The coexistence curve changes shape as the prepared composition decreases from the critical concentration, a result of the polydispersity of the micellar aggregates, as indicated in Figure 1. The coexistence curve that is most complete in Figure 4 (a) or (b) corresponds to the one closest to the critical point. The critical points occur at higher concentrations than do the minima of the cloud point curves. The critical temperature is lower in D2O than in H2O: 44.8 °C in H2O; 43.6 °C in D2O. The critical compositions are the same within error: jc = 0.22 ( 0.01. The prepared compositions of 0.226 and 0.246 by volume 17R4 in H2O and 0.243 in D2O are close to the critical compositions and so allow the coexistence curve in each system to be measured close to the critical point. For these coexistence curves, we can calculate the differences in composition between the two coexisting phases Langmuir 2011, 27(5), 1707–1712

and test eq 4. The differences in volume fraction are shown in Figure 5 for each solvent; parameters from the weighted leastsquares fits are given in Table 4 of the Supporting Information. For these near-critical compositions for both 17R4/H2O and 17R4/D2O, eq 4 adequately describes the data, with β fixed at the Ising value of 0.326, and with Tc as a free parameter. For 17R4/H2O, parameter values are equivalent for the two nearcritical data sets, and the addition of the first correction term (B1 6¼ 0 in eq 4) does not significantly improve the weighted fits. For 17R4/D2O, this first correction term does improve the fit. The slight upward shift for the D2O data in Figure 5 relative to the H2O data reflects the larger value of the leading amplitude B for the D2O system (1.64 ( 0.01 for H2O and 1.78 ( 0.02 for D2O). For other prepared compositions that are not near the critical compositions, the analysis of the shape of the coexistence curve is not straightforward because there are few data near the critical points. We will not present fits of eq 4 to those data here, but just note that using a simple scaling analyses with β as a free parameter can give results like those obtained by Eckert et al. for a polydisperse polymer blend.26 However, we could fit those coexistence curves just as well by adding one correction to scaling term while keeping the exponents at their Ising values. The diameters for all the coexistence curves are quite consistent, as Eckert et al. also observed in their system.26 When extended to the apex of the coexistence curve, the diameter gives a “critical composition” jc that approaches the true critical composition as the prepared composition approaches the critical composition; such is the case here for compositions of 0.226 or 0.246 by volume 17R4 in H2O and 0.243 in D2O. The diameters can be described within error by eq 5 using just the first correction term, fixing β at the Ising value, and fixing Tc at the values obtained from the fits to the coexistence curves. Previous studies have also found the linear and t(1-R) terms in eq 5 to be negligible.15,23,24 The value of the critical composition jc was found to be 0.22 ( 0.01 17R4 by volume for both H2O and D2O, and the diameters have an amplitude D1 = 0.63 ( 0.02.

Discussion and Conclusions We observed three distinct regions as we varied temperature and composition of the amphiphilic triblock copolymer 17R4 in DOI: 10.1021/la104350g

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H2O or in D2O: (I) a visually cloudy region of free copolymers, (II) a visually clear region of micelles, and (III) a two-phase region. By measuring the micellization lines, cloud point curves, and coexistence curves, we determined the locations and shapes of the curves separating these regions. The polydispersity of the micelles causes separate cloud point and shadow curves, with different coexistence curves for each prepared composition. Thus, 17R4 solutions in H2O or in D2O have lower critical consolute points that are not at the minima of the cloud point curves. Our cloud point curve and micellization line for 17R4/H2O are consistent with those published by Zhou and Chu for this system.1 The coexistence curves and their diameters of these triblock copolymer solutions can be described by the critical exponent β of the Ising universality class. We are aware of no prior critical point analysis on triblock copolymer micellar solutions. Deuterating the solvent has a modest effect on the coexistence curve. The location of the critical point is lower in temperature for the D2O (43.6 °C) than for the H2O (44.8 °C) system; the critical compositions are the same within error (jc = 0.22 ( 0.01). On the other hand, the micellization lines differ in concavity: concave up in H2O and concave down in D2O, which indicates different thermodynamics of micellization. For 17R4/H2O, we estimate ΔH°mic = 125 ( 5 kJ/mol, ΔS°mic = 461 ( 17 J/(mol K), and ΔG°mic = -20 ( 11 kJ/mol. For 17R4/D2O, we find similar ° does not seem to values at temperatures above 30 °C, but ΔHmic be constant at lower temperatures and higher concentrations of copolymer. Such a change in ΔH°mic has been noted for the triblock copolmer P94,40 PEO21-PPO47-PEO21, for a tapered statistical copolymer of PEO and PPO,11 and for other similar systems (see references in Kelerakis et al.11 and in Nixon et al.40), where the dilute solutions show behavior consistent with eqs 2 and 3 and with a constant ΔH°mic, but the concentrated solutions show exactly the same kind of change in slope shown above in Figure 3. This change implies a violation of the assumptions used in developing eqs 2 and 3, particularly the assumption of ideal solutions (γn = γs = 1) as the concentration increases. The molecular interpretation suggested by Nixon et al.40 is that the increase in copolymer concentration leads to more hydrogen bonding to the copolymer and a weakening of hydrophobicity ° . Such an effect would then be and thus a reduction in ΔHmic exacerbated in D2O, since the deuterium bonds are stronger than hydrogen bonds. (40) Nixon, S. K.; Hvidt, S.; Booth, C. J. Colloid Interface Sci. 2004, 280, 219–223. (41) Lund, R.; Willner, L.; Richter, D.; Dormidontova, E. E. Macromolecules 2006, 39, 4566–4575.

1712 DOI: 10.1021/la104350g

Huff et al.

Lund et al.41 have noted that diblock copolymer micelles in water can have very long relaxation times. We believe that the consistency of results among laboratories, at different times and places and with different samples, argues for accepting our results as equilibrium phenomena. Of course, studies of the relaxation kinetics of these triblock copolymer systems would be of interest. Micelles may form in both coexisting phases for 17R4 in H2O or D2O, depending on where the micellization line intersects the coexistence curve for the lower critical solution point: An intersection at a volume fraction less than the critical concentration will result in two phases, both containing micelles. If micelles do exist in both coexisting phases, then there can be a difference in the concentrations of micelles in the two phases: a partitioning of micelles between phases. Furthermore, since the micelles have a distribution of sizes (eq 1), there can be fractionation of the micelles between phases: a difference in the average aggreagation number, a difference in the average size of a micelle, and even a difference in the forms of the distributions of the micelles in each phase. In addition, the free copolymers are themselves also systems of fixed polydispersity that can partition and fractionate between phases. Our understanding of partitioning and fractionation between phases is still evolving even for systems of fixed polydispersity, and is still more complex for the nonfixed polydispersity of self-assembling systems.42-44 The partitioning and fractionation for 17R4 in H2O and D2O are interesting issues for further work. The shapes and sizes of structures of 17R4 in D2O in the three regions have been studied by scattering techniques and will be presented in a separate paper.45 Acknowledgment. We thank Simone Wiegand for helpful conversations. The work at The College of Wooster was supported by NSF REU grant no. DMR-0649112, and by the Research Corporation. For the work at the University of Maryland, College Park, we acknowledge the donors of the Petroleum Research Fund, administered by the American Chemical Society, for their support of this research. Supporting Information Available: Tables of the micellization line data, cloud point data, and coexistence curve data. This material is available free of charge via the Internet at http://pubs.acs.org. (42) ten Brinke, G.; Szleifer, I. Macromolecules 1995, 28, 5434–5439. (43) Shresth, R. S.; MacDonald, R. C.; Greer, S. C. J. Chem. Phys. 2002, 117, 9037–9049. (44) Norman, A. I.; Manvilla, B. A.; Frank, E. L.; Niamke, J. N.; Smith, G. D.; Greer, S. C. Macromolecules 2008, 41, 997–1008. (45) Clover, B. C. Ph. D. dissertation; The University of Maryland, College Park, MD, 2010.

Langmuir 2011, 27(5), 1707–1712