Association of Hydrophobically End-Capped Poly (ethylene oxide). 2

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Articles Association of Hydrophobically End-Capped Poly(ethylene oxide). 2. Phase Diagrams J. Franç ois,* E. Beaudoin, and O. Borisov* Laboratoire de Physico-Chimie des Polyme` res, Universite´ de Pau et des Pays de l’Adour/ CNRS; 2 Avenue du President Angot, Helioparc, 64053 Pau, France Received October 31, 2002. In Final Form: April 29, 2003 The solubility of hydrophobically end-capped poly(ethylene oxide) (PEO) was studied in pure water and in the presence of salts as a function of temperature. Behaviors of R and R,ω-modified PEO of various molecular weights and different numbers of carbons in the aliphatic end groups were compared. Experimental results show that phase separation in aqueous solutions of PEO with one end group occurs at a higher temperature than that for unmodified PEO of the same molecular weight. On the contrary, the solubility of difunctionalized PEO (with two aliphatic end groups) is strongly depressed in comparison to that for the unmodified samples. This loss of solubility increases upon increasing temperature and salinity. All the presented results are consistent with a theoretical model assuming an equilibrium structure of “starlike” or “flowerlike” micelles for mono- and difunctionalized PEO, respectively. To explain the observed behavior, one must take into account both the short-range interactions between the EO monomers, which vary with temperature and the salinity, and bridging attraction between flowerlike micelles for difunctionalized PEO.

1. Introduction This paper is the third of a series concerning the selfassembly in aqueous solutions of hydrophobically modified poly(ethylene oxide) (PEOM). Up to now, a great interest has been devoted to difunctionalized PEO because it exhibits very interesting thickening properties in aqueous solutions.1-4 Many viscosimetric and rheological measurements have been performed on samples prepared by polycondensation of R,ω-dihydroxylated PEO with a diisocyanate and an alcohol (HEUR).5-16 The disadvantages of such samples * Authors to whom correspondence should be addressed. (1) Glass, J. E. Polymer in Aqueous Media, Performances through Association. Adv. Chem. Ser. 1989, 223. (2) Schultz, D. N.; Glass, J. E. Polymer as Rheology Modifiers. Adv. Chem. Ser. 1991, 462. (3) Back, J.; Valint, P. L., Jr.; Pace, S. I.; Siano, D. B.; Schutz, D. N.; Turner, S. R. Water Soluble Polymers for Petroleum Recovery; Plenum Press: New York, 1986, Vol. 147. (4) Glass, J. E. Hydrophilic polymers. Performances and Environmental Acceptability. Adv. Chem. Ser. 1995, 248. (5) Jenkins, R. D. Ph.D. Dissertation, Lehigh University, Bethlehem, PA, 1990. (6) Santore, M. M. Ph.D. Dissertation, Princeton University, Princeton, NJ, 1990. (7) Hulden, M.; Sjoblom, E. 64th Colloid and Interface and Nucleation Symposium; Bethlehem, PA, 1990; Reprints 206. (8) Maechling-Strasser, C.; Franç ois, J.; Clouet, F.; Tripette, C. Polymer 1992, 33, 627. (9) Maechling-Strasser, C.; Clouet, F.; Franç ois, J. Polymer 1992, 33, 1021. (10) Yekta, A.; Duhamel, H.; Brochard, P.; Adiwidjaja, H.; Brochard, P.; Winnik, M. A. Macromolecules 1993, 26, 1829. (11) Yekta, A.; Duhamel, H.; Adiwidjaja, H.; Brochard, P.; Winnik, M. A. Langmuir 1993, 9, 881. (12) Nystro¨m, B.; Walderhaug, H.; Hansen, F. K. J. Phys. Chem. 1993, 97, 7743. (13) Persson, K.; Abrahmsen-Alami, S.; Stilbs, P.; Walderhaug, H.; Hansen, F. K. Colloid Polym. Sci. 1992, 270, 465. (14) Walderhaug, H.; Hansen, F. K.; Abrahmsen-Alami, S.; Persson, K.; Stilbs, P. J. Phys. Chem. 1993, 97, 8336. (15) Franç ois, J. Progress Org. Coat. 1994, 24, 67.

are the multimodal distribution of the PEO chains with respect to the molecular weight5-8 and a not-wellcontrolled number of hydrophobe groups per chain. Nevertheless, many different investigation methods were applied for these imperfect samples, such as NMR,13,14 fluorescence,10,11 and light scattering,8,9,12 to follow the first steps of association at a low concentration and to determine the critical association concentration, CAC. It was yet well-established that the hydrophobe groups can associate in water to form nanodomains that can act as temporary cross-links and result in an enhancing of the viscoelastic properties of the solutions. More recently, chemists have made efforts to better control the polydispersity in the molecular weight and composition of PEOM.17-19 Model polymers fully modified and of very narrow polydispersity have provided justification to extend the investigation methods and to explore a wider range of concentrations.20-31 For example, X-ray and neutron (16) Annable, T.; Buscall, R.; Ettelaie, R.; Whittlestone, D. J. Rheol. 1993, 695, 3714. (17) Lundberg, D. J.; Glass, E.; Eley, R. R. J. Rheol. 1991, 35, 1255. (18) Fonnum, G. Ph. D. Dissertation, Institute of Organic Chemistry, Norway Technical University, Trondheim, Norway, 1989. (19) Kaczmarski, J. P.; Glass, J. E. Macromolecules 1993, 26, 5146. (20) Abrahmsen-Alami, S.; Alami, E. S.; Franç ois, J. J. Colloid Interface Sci. 1996, 179, 20. (21) Alami, E.; Rawiso, M.; Isel, F.; Beinert, G.; Binana-Limbele, W.; Franç ois, J. Hydrophilic polymers. Performances and Environmental Acceptability; Adv. Chem. Ser. 1995, 248. (22) Franç ois, J.; Maıˆtre, S.; Rawiso, M.; Sarazin, D.; Beinert, G.; Isel, G. Colloids Surf. 1996, 112, 251. (23) Beaudoin, E.; Borisov, O.; Lapp, A.; Billon, L.; Hiorns, R.; Franç ois, J. Macromolecules 2002, 35, 7436. (24) Chassenieux, C.; Nicolai, T.; Durand, D. Macromolecules 1997, 30, 4952. (25) Ulyanova, N.; Trabukina, E.; Sabaneeva, N. V.; Bykova, E. N.; Kallistov, O. V.; Klenin, S.; Franç ois, J. Polym. Sci., Ser. A 1998, 40, 622. (26) Gourier, C.; Beaudoin, E.; Duval, M.; Sarazin, D.; Maı¨tre, S.; Franç ois, J. J. Colloid Interface Sci. 2000, 230, 41. (27) Beaudoin, E.; Gourier, C.; Lapp, A.; Franç ois, J. Macromol. Symp. 1999, 146, 171.

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Figure 1. Schematic representation of the formation of starlike and flowerlike micelles for mono- (a) and difunctionalized (b) PEO.

scattering studies20-23 performed on semidilute solutions have completed the light scattering,24-28 NMR,29 or fluorescence30,31 measurements made on dilute solutions. It has been demonstrated that the association corresponds to the formation of a network of interconnected “flowers” that can exhibit a liquid crystalline order for low enough molecular weight, Mw20 (for example, Mw < 6000 for aliphatic end groups of 12 carbons). It has also been observed that, according to the polymer composition, phase separation occurs as soon as micelles are formed, as a result of intermicellar bridges.31 Such a phenomenon is expected when polymer associates at a CAC that is very low and then the formation of a homogeneous network of close-packed micelles occurs at a much higher concentration. The solubility diagrams of all the polyethers in aqueous solutions exhibit two different types of demixing: (i) At a high concentration, the polymer chains crystallize upon cooling and phase separation occurs between a pure crystalline phase and a solution.32,33 We do not consider this concentration range in this paper. (ii) At a low concentration, it is well-known that the PEO-water system presents a “closed-loop solubility diagram” with a lower critical solution temperature (28) Beaudoin, E.; Gourier, C.; Hiorns, R.; Franç ois, J. J. Colloid Interface Sci. 2002, 251, 398. (29) Chassenieux, C.; Nicolai, T.; Durand, D.; Franç ois, J. Macromolecules 1998, 31, 4035. (30) Beaudoin, E.; Borisov, O.; Hiorns, R.; Franç ois, J. Langmuir, in press. (31) Maıˆtre, S. Ph.D. Universite´ Louis Pasteur, Strasbourg, France, 1997. (32) Hager, S. L.; Macrury, T. D. J. Appl. Polym. Sci. 1980, 25, 1669. (33) Bogdanov, B.; Mihailov, M. J. Polym. Sci., Polym. Phys. Ed. 1985, 23, 2149.

(LCST) around 100 °C, extrapolated at infinite molecular weight.34-35 Many theoretical attempts were made to explain this type of diagram and predict the binodal demixing curve.36-41 Some models are based upon highly directional bonds between water and polymer molecules (Ising model or other models based on statistical mechanics).36-38 A more recent approach of Matuyama and Tanaka39 introduces into the Flory-Huggins theory a solvatation equilibrium giving the fraction of “free” and “solvated” sites on the chains as a function of temperature. Karlstro¨m40 considers that the affinity for water of the PEO conformers is different, the trans conformers being assumed to be less polar than the gauche ones. The phase separation should be due to the decrease of the gauche population when the temperature increases. For end-capped chains, which have a hydrophobic group at one or two chain extremities, micellization occurs in an aqueous solution and leads to the formation of hydrophobe nanodomains equivalent to the cores of micelles formed by a low-molecular-weight surfactant. Monofunctionalized chains form micelles with starlike PEO coronae, whereas difunctionalized chains form flowerlike micelles (in the latter case, both chain extremities are localized in the hydrophobic core; Figure 1). Under good solvent conditions, the micellar coronae are repulsive, whereas when the (34) Bailey, F. E.; Callard, R. W. J. Appl. Polym. Sci. 1959, 1, 56. (35) Saeki, S.; Kuhawara, N.; Nakata, N.; Kanako, M. Polymer 1976, 17, 685. (36) Barker, J. A.; Fock, W. Discuss. Faraday Soc. 1953, 15, 188. (37) Scatchard, G.; Wilson, G. M. J. Am. Chem. Soc. 1954, 86, 133. (38) Kjellander, R.; Florin, E. J. Chem. Soc., Faraday Trans. 1981, 77, 2053. (39) Matuyama, A.; Tanaka, F. Phys. Rev. Lett. 1990, 65, 341. (40) Karlstro¨m, G. J. Phys. Chem. 1985, 89, 4962. (41) Goldstein, R. E. J. Chem. Phys. 1984, 80, 10.

Hydrophobically End-Capped Poly(ethylene oxide)

temperature increases above the LCST and the solvent gets poor for PEO coronal chains and (macro) phase separation occurs as a result of the attraction between monomers of coronal chains. On the contrary, for solutions of difunctionalized chains two mechanisms of the phase separation are visible, (1) similar to that for monofunctionalized chains upon a decrease of the solvent conditions for PEO and (2) via intermicellar bridging even in good solvent. The interplay between these two mechanisms of intermicelle aggregation and phase separation is rather delicate. For this reason, comparison of the results obtained for the solubility of mono- and difunctionalized samples at variable temperature can be very instructive. Besides, as many industrial samples are not fully modified, it is also interesting to consider phase separation in the solutions of partially functionalized polymers, as this will be presented in a forthcoming paper. In the first papers of this series, we have discussed the first step of aggregation, that is, micellization of PEOM in a solution. The variation of the CAC with the polymer composition (i.e., degree of functionalization and length of the PEO chain) has been studied by using light scattering26 and fluorescence.30 We have shown that the micellization of monofunctionalized PEO corresponds to the “closed association” model and that the CAC values are consistent with those measured for low-molecularweight surfactants if one takes into account a much stronger repulsion of the long PEO chains in the micellar coronae. Although a much lower value of the CAC for difunctionalized samples than that for the monofunctionalized ones can be expected from theoretical considerations, the experimentally found CACs are not as different. This observation may be explained by the intramolecular association of hydrophobe groups within difunctionalized PEOM chains. The present paper aims at the comparative study of the phenomenon of phase separation in solutions of monoand difunctionalized PEOM. This enables us to separate the effects of a poor solvent on the PEO chains from that of bridging. Polymer composition, temperature, and salinity are varied. It is, indeed, well-known that increases in both the temperature and the salinity tend to decrease the solvent quality of water for PEO (decrease in the LCST, when some salts are added in the solution). The change of the PEO chain conformation with these parameters (temperature and salt concentration) must probably modify the phase separation limits when it exists already at room temperature and in pure water or provoke the phenomenon. The rest of the paper is organized as follows: We describe our experimental system and obtained results in sections 2 and 3, respectively. Theoretical considerations are presented in section 4. The paper is ended by discussion and conclusions in section 5. 2. Experimental Section Samples and Nomenclature. The preparation of the associating PEO has been already described in the first paper of this series.30 We used three types of samples, which were characterized by NMR spectroscopy, size-exclusion chromatography, and UV-visible spectroscopy: mono- and difunctionalized samples prepared by the reaction of commercial ω- or R,ωhydroxylated PEO on alkyl tosylates, denoted respectively Mt and Dt; a difunctionalized sample obtained by the reaction of commercial R,ω-hydroxylated PEO with alkyl isocyanate, denoted Di14; and a monofunctionalized sample prepared by direct anionic polymerization of ethylene oxide using the initiator potassium hexadecyloxide, denoted Ma. Table 1 gives the characteristics of the polymer samples.

Langmuir, Vol. 19, No. 24, 2003 10013 Table 1. Characteristics of the Polymer Samplesa samples

Mw (g mol-1)

i

f

CAC

Samples Prepared by Functionalization with Alkyl Tosylates Dt0 2000 12 0.96b Dt1 6000 12 0.92b 9 × 10-4d 0.94c 3 × 10-4e Dt2 10 000 12 0.90b 2 × 10-3d 0.88c 4 × 10-4e Dt3 20 000 12 0.95b 7 × 10-3d 0.97c 7 × 10-4e Dt4 35 000 12 0.97b 1.9 × 10-2d 0.95c 1.1 × 10-3e Mt1 20 000 12 0.92b 4 × 10-2d 2 × 10-3e Mt2 20 000 18 0.95b 3 × 10-4d 1.5 × 10-5e Samples Prepared by Functionalization with Alkyl Isocyanate Di6 20 000 18 0.96b Di14 32 000 16 1.00c 1 × 10-3d 35 × 10-5e Ma

Sample Prepared by Direct Polymerization 16 000 16 1.00** 3 × 10-4d 2 × 10-5e

a M w is the weight-average molecular weight of the PEO precursor, as was determined by size exclusion chromatography in THF; i is the number of carbon atoms in the aliphatic end groups; and f is the degree of functionalization determined by NMR and UV spectroscopy. b Determined by NMR spectroscopy. c Determined by UV spectroscopy. d Units of g g-1. e Units of mol L-1.

NaCl (Aldrich, 99+% purity) and KBr (Prolabo, 98.5% purity) were dried for several hours at 90 °C and used directly without further purification. All solutions were prepared with water distilled three times over quartz. Depending on their concentrations, the solutions were stirred between 24 h and several days before use. Turbidimetry. In some cases, the cloud points of the polymer solutions were measured with a Mettler FP 81 apparatus, with a continuous change of the temperature. Tc is the temperature at which an abrupt change in the turbidity is registered (cloud point). This is an indication of the phase separation. In most cases, aqueous solutions were prepared in Pyrex tubes, after weighing the two constituents. The diameters of the tubes were 12 mm with a flat bottom, and the height of the solution was close to 10 mm. The mixtures were homogenized at 40 °C for several days, and then the phase separation was visually observed as a function of the temperature (0 < T < 100 °C) by putting the tubes in a thermostated oven. Some measurements of the height of the two phases were made at room temperature.

3. Results ω-Functionalized PEO. We did not observe any lowering of the LCST with respect to that of homologous unmodified PEO for samples Mt1 and Mt2, neither by simple visual observation nor by measurements with the automatic turbidimeter. Observations were made only for temperatures < 100 °C. The LCST values of the unmodified homologous polymer (Mw ) 20 000) is about 103 °C, as was deduced from the experimental studies of Saeki et al.,35 and the LCST for Mw ) 16 000 can be evaluated as 108 °C. The behavior of sample Ma has been checked at temperatures higher than 100 °C in carefully closed vessels with thick sides. The variation of the cloud point Tc versus the concentration is reported in Figure 2 and compared with those obtained with the sample Di14 and its unmodified PEO homologue (Mw ) 32 000). (The LCST is the minimum value of the Tc ) f(C) curves.) The curve corresponding to Ma lies much further above that of the unmodified PEO, which shows that the solubility of Ma is improved by the presence of aliphatic chains. This result suggests that the formation of micelles with repulsive PEO coronae prevents (macro) phase separation in a polymer

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Figure 2. Cloud point versus polymer concentration: sample Ma ([); unmodified PEO, Mw ) 32 000 (0); and Di14 (2).

Figure 4. Cloud point versus polymer concentration: PEO 10 000 (full line), PEO 2000 (dotted line), Dt0 (b), Dt1 (9), Dt2 (0), Dt3 (2), and Dt4 (O).

Figure 3. Variation of the LCST as a function of 1/Mw (Mw is the molecular weight of the PEO segment) for sample Mt1 (0), for the series of Dt samples (6000 < Mw < 35 000; 2), and for low-molecular-weight surfactants [carbon number in the aliphatic chain i ) 12 (0) and i ) 16 ([)].

solution. This effect is reminiscent of those obtained with polystyrene (PS) stars or comblike PS.42 It was, indeed, shown that the upper critical solution temperature (UCST) of PS in cyclohexane (theta point ) 34.5 °C for linear PS) was significantly lowered for grafted or starlike samples with respect to linear ones. It is reasonable to think that micelles of PEOM behave as polymer stars. It is interesting to compare our results with those already obtained for low-molecular-weight surfactants of the same chemical nature: the CiEj surfactants of formula (CiH2i+1)-(CH2CH2O)jH, which are also characterized by a LCST value.43,44 In Figure 3, we have gathered several results and plotted the LCST for CiEj and Mt1 as a function of 1/Mw (where Mw is the molecular weight of the PEO block), which may reflect the hydrophobicity of the polymer. Unfortunately, data for 6 × 10-5 < 1/Mw < 3 × 10-3 are missing, but the results obtained for i ) 16 suggest that the LCST roughly varies as the reciprocal molecular weight, at least for Mw < 20 000; the best linear fit of the data leads to the following empirical law:

LCST ) 132.4 - 2.4 × 103(1/Mw) °C

(1)

r,ω-Functionalized PEO. Figure 4 allows a comparison of the solubility behaviors of R,ω-functionalized PEO (42) Decker, D.; Rempp, P.; Benoit, H. Makromol. Chem. 1969, 125, 136. (43) Herrington, T. M.; Sahi, S. S. J. Colloid Interface Sci. 1988, 121, 107. (44) Becher, P. J. J. Colloid Sci. 1961, 16, 49.

of the series Dt0-Dt4. On the same plot, the behaviors obtained by Saeki et al.35 for polymers of molecular weights Mw ) 1 × 106 and 104 are also reported. The range of solubility of difunctionalized PEO strongly decreases upon decreasing Mw, a result completely different from that obtained with monofunctionalized ones. Whereas the presence of one end group enhances the solubility in the latter case with respect to pure PEO, the presence of two groups at each extremity strongly depresses this water solubility. Besides, the shape of the demixing lines differs from those generally observed with pure PEO. If one considers the sample Dt0, the demixing line exhibits two branches: a decreasing branch at low concentration and an increasing and branch at higher concentrations. It is not possible to determine the cross point of these two branches, which is probably much lower than 0 °C. When the molecular weight increases, the absolute values of the slopes of these two branches progressively decreases and it becomes possible to determine the minimum (the critical point in the phase diagram), which can be called the “LCST” even if it probably does not have a physical origin the same as that for pure PEO. In Figure 3, we compare the variation of the LCST versus 1/Mw for lowmolecular-weight surfactants with that obtained with difunctionalized PEO of the same length of the hydrophobe segments (i ) 12). If we exclude samples Dt0, which phaseseparates down to 0 °C, the LCST varies almost linearly versus 1/Mw for these R,ω-functionalized PEOs (Figure 3). For i ) 12, the following equation is obtained:

Tc ) 98 - 5.3 × 105(1/Mw) °C

(2)

For comparison, we present in Figure 5 data for difunctionalized PEO of Mw ) 20 000 end-capped with aliphatic chains of 12 and 18 carbons, which exhibit demixing in an aqueous solution at room temperature. In Figure 5, the demixing lines for Dt3 and Di6 are reported. This illustrates the expected influence of the length of the hydrophobic group (an extension of the two-phase region) because solutions of the Dt3 phase-separate only above 71 °C (Figure 4). Just above LCST, the difference in the concentrations of the poor and rich phases is much lower than classically observed above a LCST or below a UCST of homopolymers. It is interesting to compare two systems that phase-


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demixing at room temperature occurring at a low polymer concentration (C < 1.5 × 10-2 and 2 × 10-2 g mL-1 for NaCl and KBr, respectively). It should be noted that the shape of the demixing lines in the presence of salts is quite different for pure PEO and PEOM and look like those observed in Figures 4 and 5 for the less-soluble samples. These results illustrate once again that the change in the solvent quality modifies the repulsion inside the “flower” coronae and induces phase separation. 4. Theoretical Considerations

Figure 5. Cloud point versus polymer concentration: Di6 (9) and Dt3 ([).

Figure 6. Cloud point versus polymer concentration for unmodified PEO (Mw ) 32 000; open symbols) and for Di14 (closed symbols) in pure water (O, b), 3 M KBr (4, 2), and 3 M NaCl (0, 9).

separate at room temperature: Dt0 (Figure 4) and Di6 (Figure 5). It is quite clear that the difference between the concentrations of the pure and rich polymer phases is much higher in the latter case, which can be attributed to a larger aggregation number in the case of longer aliphatic end groups. All these observations show that the origin of the demixing in the case of the difunctionalized samples is different from that in the mono- and unfunctionalized PEO cases. As we will discuss below, their behavior is a signature of the intermicellar bridging that provokes phase separation. To illustrate the effects of salinity on the solubility of the end-functionalized PEO, the phase diagrams are reported in Figure 6 for pure water and in the presence of 3 M NaCl and KBr. As is described in the literature, the LCST of unmodified PEO is lower in the presence of salts than that in pure water (65 and 80 °C for NaCl and KBr, respectively). This behavior indicates that the addition of salts leads to a decrease in the solvent quality of water for PEO chains. The difference in solubility between the two salts agrees with the literature data, which show that the effect of NaCl is greater than that of KCl.35,45 The difunctionalized samples also showed a strong drop in solubility in the presence of salts, the (45) Boucher, E. A.; Hines, P. M. J. Polym. Sci. 1976, 14, 2341.

Let us start from the description of the equilibrium structure of “starlike” micelles of aggregation number Nag, following the scaling approach of Halperin and Alexander.46,47 We have i hydrophobic monomers in end aliphatic groups and j hydrophilic monomers in a PEO chain and make the following assumptions: (i) The size of a hydrophobic monomer is of the same order of magnitude as the size of a hydrophilic monomer and is taken as a unit of length. (ii) The volume fraction of the hydrophobe in the core is τi e 1. (iii) The surface tension at the core/water interface is γ(τi) ≈ τi2. (iv) vj(T) = (Θ - T)/Θ ≡ τ is the excluded volume (binary interaction) parameter for the EO monomers. The temperature ranges τ > 0 and τ < 0 correspond to good or poor solvent conditions for the EO monomers, respectively, and T ) Θ corresponds in our case to the LCST for the infinitely long linear PEO chain (100 °C). At T ≈ Θ, the excluded volume repulsion between the EO monomers are compensated by binary attraction, and as a result, ternary repulsive interactions between EO monomers in the micellar corona become most important. Core and Corona. The radius of the hydrophobic core of the micelle is

Rcore ) (3Nagi/4πτi)1/3

(3)

as follows from the packing condition. The radius of the corona is given48-50 by

Rcorona = j3/5Nag1/5τ1/5

(4)

under good solvent conditions, when the corona is swollen by repulsive binary interactions between the monomers of crowded PEO chains (here and in the following we use the symbol “=” in the case when the numerical prefactor of order 1 is omitted). Upon an increase in the temperature (decreasing solvent strength for PEO), the corona of the micelle collapses, as is discussed in ref 50. However, as a result of the significant contribution of ternary repulsion between the EO monomers, the coronal chains remain extended, Rcorona = j1/2Nag1/4, even under the theta regime, T ≈ Θ. The theta conditions, when ternary repulsion dominates over binary interactions, range from τ ≈ τ* to τ ≈ -τ*, where τ* = j-1/2 Nag1/4, that is, even above the LCST. A further increase in the temperature should lead to a strengthening of the monomer-monomer binary attraction and to the collapse of the corona. The onset of (46) Halperin, A. Europhys. Lett. 1989, 8, 351. (47) Halperin, A.; Alexander, S. Macromolecules 1989, 22, 2403. (48) Daoud, M.; Cotton, J. P. J. Phys. (Paris) 1982, 43, 531. (49) Zhulina, E. B Vysokomol. Soedin., Ser. B 1983, 25, 834; Vysokomol. Soedin., Ser. A 1984, 26, 794. Birshtein, T. M.; Zhulina, E. B. Polymer 1984, 25, 1453. (50) Borisov, O. V.; Zhulina, E. B.; Birshtein, T. M. Vysokomol. Soedin., Ser. A 1988, 30, 772. Zhulina, E. B.; Borisov, O. V.; Birshtein, T. M. Vysokomol. Soedin., Ser. A 1988, 30, 780.

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the collapse transition, T ) Θ*, is shifted to higher temperature with respect to that for an infinite linear chain as (Θ* - Θ)/Θ ≡ τ* = j-1/2Nag1/4. We remark that the aggregation number, Nag, also depends on the solvent strength for the PEO, that is, on the temperature (see the following). Therefore, for the above definition of τ* the value of Nag should be also taken at τ ) τ*. Aggregation Number. The equilibrium aggregation number Nag (number of chains associated into a micelle) also depends on the temperature, that is, on the strength of the interaction between coronal chains. Within the scaling approximation, it is given by

Nag = γ6/5(i/τi)4/5 [(3/5) ln j + (1/5) ln τ - (11/25) ln(i/τi) - (4/25) ln γ + ln ln ... + const]-6/5, τ g τ* (5)

Nag = γ6/5(i/τi)4/5[(1/2) ln j - (2/5) ln(i/τi) (1/10) ln γ + ln ln ... + const]-6/5, -τ* e τ < τ* (6) Nag = γ6/5(i/τi)4/5{(1/2) ln j - (2/5) ln(i/τi) (1/10) ln γ - [ln(-τ/τ*) + (τ/τ*)2 - 1] ln ln ... + const}-6/5, τ e -τ* (7) As follows from eqs 5-7, the aggregation number is an increasing function of the length of a hydrophobic chain, Nag ∼ i4/5, and decreases logarithmically with increasing length of the coronal chain, j. An increase in the temperature leads to an increase in the aggregation number as a result of a weakening of the repulsive interactions in the micellar corona (decrease in τ) and also an increase in γ(T). We remark that γ(T) should be also affected by an increase in the concentration of the EO monomers in the solution surrounding the micellar core. For the structural parameters of the flowerlike micelles comprising Nag difunctionalized chains, we can use (within the accuracy of the scaling approximation) eqs 5-7 with substituting Nag by 2Nag (number of hydrophobic chains) and j by j/2. CAC. The CAC (measured in molar fraction of PEOM) is given for τ e τ* by (see Appendix)

CAC ) exp{-i + γ3/5(i/τi)2/5[(3/5) ln j + (1/5) ln τ (11/25) ln(i/τi) - (4/25) ln γ + ln ln ... + const]2/5} (8) In the poor solvent range, τ e - τ*, the equation for the CAC has to be modified as

CAC ) exp{-i + γ3/5(i/τi)2/5[(1/2) ln j - (2/5) ln(i/τi) (1/10) ln γ - ln(-τ/τ*) - (τ/τ*)2 + 1 - j + ln ln ... + const]2/5} (9) where j = (τ2j)2/3 is the excess interfacial free energy of an individual PEO chain collapsed under poor solvent conditions. As follows from eqs 8 and 9, the CAC is increases as a function of the length of the PEO chain and decreases upon an increase in the temperature (decrease in τ). Equations 8 and 9 are written for the monofunctionalized chains. In the case of the difunctionalized chains, the obvious modification is to substitute i by 2i, which should reflect doubled gain for the association of hydrophobes per chain (also, the numerical constant has to be modified, as is discussed in ref 51). This should lead to a (51) Borisov, O. V.; Halperin, A. Macromolecules 1996, 29, 2612.

significantly smaller value of the CAC for difunctionalized PEOM as compared to monofunctionalized ones because i is on the order of 10 for our case (12 carbons in the hydrophobe segment). However, as we have discussed in ref 51, experimentally measured values of the CAC for difunctionalized chains are not much lower with respect to those for the monofunctionalized ones. This reflects most probably an intramolecular association of hydrophobic ends in individual (nonassociated into micelles) PEOM. Phase Separation in a Solution of Monofunctionalized PEO. At τ < -j-1/2, water is a poor solvent for individual PEO chains that collapse into compact globules. Then, the phase separation of the solution into the dense phase (precipitated globules) and the dilute phase occurs. On the contrary, hydrophobically modified PEO chains associate into micelles rather than phase-separate provided -τ* e τ < -j-1/2. The interaction between micellar coronae remains repulsive even in a certain temperature range above the LCST. At τ e -τ*, the excess free energy, Fs = Nag|τ*/τ|4/3, of the interface between collapsed coronae and water leads to an attraction between micelles. The inversion of the sign of the second virial coefficient of interaction between starlike micelles also occurs at τ ≈ -τ*. As a result, phase separation of the solution into a coexisting concentrated phase (close-packed micelles) and dilute phase occurs at τ < -τ*. Hence, (macro) phase separation in a solution of micelles with PEO coronae should occur at a temperature above the LCST for unmodified linear PEO unless another attractive interaction (like bridging between micelles in the case of difunctionalized chains) is involved. Phase Separation in a Solution of Difunctionalized PEO. Two types of interactions between micelles are important, and two physical mechanisms of phase separation in the micellar solution are visible: (1) The first is short-range (steric) interactions between monomers of the interacting micelles. This interaction becomes important when the coronae of the micelles overlap; under good or theta solvent conditions (τ g -τ*) this interaction is purely repulsive, whereas at τ e -τ* it switches to the attraction that leads to the aggregation of micelles and phase separation. This steric interaction acts similarly for both starlike and flowerlike micelles formed by mono- and difunctionalized PEOM, respectively. (2) The second is that a bridging attraction between flowerlike micelles formed by difunctionalized PEOM appears as a result of the possibility to exchange hydrophobic end segments between the micelles; this attraction is of entropic origin (gain in entropy on the order of kB upon the formation of a bridge) and acts at distances of close contact between the coronae. This bridging attraction appears irrespectively of the solvent strength and leads to the phase separation of the micellar solution even under good or theta solvent conditions for the coronal chains. Hence, it is the bridging attraction that is responsible for the phase separation in the solution of flowerlike micelles formed by difunctionalized PEOM chains at temperatures below the LCST. The solution separates into the dense phase, which consists of close-packed micelles interconnected by multiple bridges, and the dilute phase comprising individual micelles. The concentration (number density) of micelles in the dense phase can be considered equal to the overlap concentration of micelles:

φdense = 1/Rcorona3

(10)


Langmuir, Vol. 19, No. 24, 2003 10017

and the concentration of micelles in the dilute phase is

φdilute ) φdense exp(-bNag1/2) = (1/Rcorona3) exp(-bNag1/2) (11) where bNag1/2 is the free energy gain proportional to the number of bridges formed per micelle in the dense phase and b is a numerical constant. This estimate51 is based on the assumption of mutual interpenetration on the length proportional to the size of the outermost blob in the micellar coronae.48,49 A slightly different exponent (3/10 instead of 1/2) for the dependence of the sticking energy on the aggregation number has been suggested in ref 52. When the critical overlap concentration of linear PEO chains of j monomers (measured in the monomer number density) is introduced

C* = j/Rj3 = j-4/5τ-3/5

(12)

equations 16 and 17 can be transformed into

Cdense = C*Nag2/5

(13)

Cdilute = C*Nag2/5 exp(-bNag1/2)

(14)

As follows from eq 13, the concentration of the dense phase, Cdense, increases with increasing temperature (due to deswelling of the coronae of micelles and increasing Nag) and, at a given temperature, decreases with increasing length of the PEO chain, j. The concentration of the dilute phase, Cdilute, on the contrary, decreases with increasing temperature, as the latter leads to increasing aggregation number, Nag, and enhancing bridging attraction between flowerlike micelles. The dependence of Cdilute on the length of the PEO chain, j, at a given temperature is more complex, but for sufficiently large j it is an increasing function of j due to the exponential term in eq 14. The ratio Cdense/Cdilute, that is, the width of the twophase region, increases with increasing temperature as a result of increasing Nag (eqs 13 and 14). The critical point of the phase diagram corresponds to Nag ∼ 1 and C ∼ C*. We remark, however, that our theory does not allow us to analyze the shape of the phase diagrams in the vicinity of the critical point. Therefore, the latter one can be localized only approximately from the crossover of the dilute and concentrated branches of the phase diagram (i.e., boundaries of the two-phase region). The critical temperature, τ*, can be obtained as a function of the length of the PEO chain, j, by setting Nag = 1 in eq 5. With decreasing molecular weight of the PEO block, the critical point gets shifted toward a lower temperature (this trend reflects weaker coronal repulsion for shorter chains) and a higher concentration. As a result, for sufficiently short PEO chains the critical point in the phase diagram disappears (is formally shifted below 0 °C). It is instructive to estimate the ratio between Cdilute and the CAC:

Cdilute/CAC ∼ exp[-∆F + (2/5) ln Nag - bNag1/2] (15) where ∆F ∼ i + Nag1/2, the free energy of micellization per chain, and we have omitted the numerical factors. If Cdilute > CAC, then there is a range of concentrations corresponding to a very dilute solution where the individual (52) Smenov, A. N.; Joanny, J. F.; Khokhlov, A. R. Macromolecules 1995, 28, 1066.

flowerlike micelles are stable thermodynamically. If, on the contrary, Cdilute < CAC, then the association of individual micelles via bridging occurs just at the CAC. In the latter case, the low-concentration boundary of the two-phase region corresponds to the CAC. Equation 15 is a rather complicated function of the aggregation number of the micelles, and it is only valid if Nag . 1. Nevertheless, two important qualitative conclusions appear: (i) As long as the micelles are stable, ∆F ∼ -i < 0 and i . Nag1/2 and, consequently, Cdilute > CAC. (ii) When Nag . 1, the ratio Cdilute/CAC decreases with increasing Nag because of the term ∼Nag1/2 in the exponent, which reflects an enhancing bridging attraction. 5. Discussion and Conclusion The experimental results presented in the paper can be qualitatively understood from the following considerations: Whatever the systems, the end hydrophobically modified PEO chains form micelles characterized by a small hydrophobic core and a more or less expanded PEO coronae. The three important points to consider are as follows: (i) The solvent quality of water for PEO. This quality can be changed either by changing the temperature or by the addition of additives. In this work, we have considered the effect of temperature and the effect of salts. (ii) The interaction (repulsive or attractive) between PEO coronae, which plays a role in both the case of the mono- and the case of the difunctionalized polymers. (iii) The formation of the intermicellar bridges, which plays a role only in the case of difunctionalized polymers. The solubility in water of the monofunctionalized samples was found to be apparently higher than that of pure PEO; that is, the two-phase region in the phase diagram of the solution is shifted to a higher temperature in the case of monofunctionalized PEO in comparison to that for unmodified PEO. This is explained by the formation of micelles with the PEO coronae, which repel each other and do not aggregate, even in a certain temperature range above the LCST for homologous unmodified linear PEO. Hence, the microphase separation (micellization) allows the system to extend the range of stability with respect to the macrophase separation (demixing). The solubility of difunctionalized samples is, on the contrary, much lower than that of unmodified PEO. This behavior is due without ambiguity to the formation of bridges between the hydrophobic domains. This means that the individual “flowers” attract each other and that they tend to gather in large aggregates or form a dense phase (of a concentration allowing intermicellar bridging) in equilibrium with a dilute phase. The concentration in the dense phase, when the demixing occurs, is equal to the overlap concentration of the “flowers”, Cf*. It increases upon an increase in the temperature (due to decreasing steric repulsion in the micellar corona and increasing aggregation number) and decreases with increasing molecular weight of the PEO chain. The dilute phase comprises either individual flowerlike micelles or dissociated (individual) PEO chains. In the latter case, the low-concentration boundary of the two-phase region corresponds to the CAC for the difunctionalized chains. The concentration in the dilute phase decreases with increasing temperature due to an increase in the aggregation number. Hence, the width of the two-phase region increases with an increase in the temperature (decreasing solvent strength for the PEO chains). In the case of too short end aliphatic groups, the formation of flowerlike micelles is suppressed and the

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phase behavior of the solution is equivalent to that for unmodified PEO. An increase in the number of carbons in the hydrophobic end groups provokes the formation of flowers and demixing and further leads to an increase in the aggregation numbers and, consequently, in a widening of the two-phase region. Our experimental observations indicate that the effect of added salt on the phase behavior of the solution can be well-interpreted in terms of variation of the solvent strength of water for PEO.

The coronal contribution to the free energy can be presented48,49 as

Fcorona = Nag1/2 ln

∆F ) Fcorona + Fcore - i - j

(A1)

where the excess free energy of the core/water interface is given by

Fcore ) (36π)1/3γNag-1/3(i/τi)2/3

(A2)

and i > 0 is the free energy gain upon the transfer of a hydrophobic chain from an aqueous environment into the core. j > 0 is the conformational free energy of a PEO chain in the solution. All the energetic values are expressed in kBT units.

(A3)

At τ e -τ*, the free energy of the corona reads50

(

Fcorona = Nag1/2 ln

Appendix: Free Energy of the Micelles The equilibrium aggregation number is determined by the balance between the repulsive interaction of the coronal chains and the excess free energy of the core/water interface. Nag can be obtained by minimizing the differential free energy per chain in a micelle and in the dissociated state:

Rcorona , τ e -τ* Rcore

)

Rcorona Rcore

- Nag1/2[ln(-τ/τ*) +

τ)τ*

(τ/τ*)2 - 1] (A4)

where the negative sign of the second term (which decreases with decreasing τ) reflects the attractive binary interactions between EO monomers under poor solvent conditions. Then, taking into account explicit expressions for Rcorona under good and theta solvent conditions we obtain eqs 5-7. In the asymptotic limit τ , -τ*, the attractive interactions in the corona dominate and Fcorona = -Nag1/2(τ/τ*)2; that is, the interactions between coronal chains do not counterbalance the interfacial free energy of the core anymore. The growth of micelles with increasing temperature in the range τ , -τ* is limited by conformational elasticity (and finite extensibility) of the hydrophobic chains. The CAC (measured in molar fraction of PEOM) is related to the difference in the free energy per chain involved in an optimal micelle and that in the dissociated state (in the solution) as ln(CAC) ≈ ∆F. LA0208833

Association of Hydrophobically End-Capped Poly (ethylene oxide). 2

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