Association of Hydrophobically End-Capped Poly (ethylene oxide). 1

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Association of Hydrophobically End-Capped Poly(ethylene oxide). 1. Preparation of Polymers and Characterization of Critical Association Concentrations Emmanuel Beaudoin, Roger C. Hiorns, Oleg Borisov, and Jeanne Franç ois* Laboratoire de Physico-Chimie des Polyme` res, Universite´ de Pau et des Pays de l’Adour/ CNRS, 2 Avenue du Pre´ sident Angot, Helioparc, 64053 Pau France Received August 19, 2002. In Final Form: October 23, 2002 A series of poly(ethylene oxide)s (PEO)s, end-capped with hydrophobic groups, were prepared via various methods and characterized by 1H NMR, UV spectroscopy and size exclusion chromatography. Fully and partially modified difunctional and monofunctional samples were studied. Critical association concentrations (CAC)s were measured, by fluorometry in the presence of pyrene, as a function of PEO chain length and aliphatic chain ends for fully modified samples. It was found that variations in CACs of monofunctionalized PEOs could be well understood through theoretical approaches that took into account the repulsion between PEO chains that hindered micelle formation. Even though theory predicted considerably lower values for difunctionalized samples (with the same ratio of hydrophilic to hydrophobic units) their CAC values were found, however, to be very close to those of monofunctionalized PEOs of equivalent molecular weights. CACs were also measured for partially modified samples, and variations in CAC with degree of functionalization were found to be surprisingly small. The values of CACs obtained were compared to another critical concentration, Cη, at which point viscosity diverges from that of parent PEOs.

1. Introduction There is increasing interest in associative polymers (AP) that exhibit interesting rheological behaviors when dispersed in aqueous solutions.1-4 Among different types of APs, hydrophobically end-capped poly(ethylene oxide)s are perhaps the most attractive due their relatively simple structure. Some years ago, rheological investigations were performed on samples in pure water and in the presence of various additives; however, the samples were prepared by polycondensation reactions and thus exhibited broad molecular weight distributions.5-15 And though these studies allowed an initial understanding of the structure * To whom correspondence should be addressed. E-mail: jeanne. [email protected]. (1) Glass, J. E. Polymer in Aqueous Media, Performances through Association; Advances in Chemistry Series; American Chemical Society: Washington, DC, 1989; No. 223. (2) Schultz, D. N.; Glass, J. E. Polymer as Rheology Modifiers; Advances in Chemistry Series; American Chemical Society: Washington, DC, 1991; No. 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; Advances in Chemistry Series; American Chemical Society: Washington, DC, 1995; No. 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, reprints 206, Bethlehem, 1990. (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. Prog. Org. Coatings 1994, 24, 67.

of the solutions and the association mechanisms involved, certain questions remained unanswered. Importantly, a significant correlation between the structural and rheological properties of a system can only be obtained with model polymers that exhibit narrow molecular weight distributions and well determined and controlled hydrophobic group contents.15 Efforts have been made by several groups to develop methods of preparation and characterization of model samples15-18 and many different investigative methods have been used.15,19-28 The main problems found in modeling the association of poly(ethylene oxide) (PEO) in aqueous solution are defined by (i) the existence of a critical association concentration (CAC); (ii) solubility limits; (iii) association mechanisms; (iv) the structure of the solution and the nature of the aggregates; and finally, (v) the relationship between structural and rheological properties. Preliminary work has been undertaken, using numerous techniques such as fluorescence,10,11,20,28 NMR,28 static and (16) Lundberg, D. J.; Glass, E.; Eley, R. R. J. Rheol. 1991, 35, 6, 1255. (17) Fonnum, G. Ph.D. Dissertation, Institute of Organic Chemistry, Norway Technical University, Trondheim, Norway, 1989. (18) Kaczmarski, J. P.; Glass, J. E. Macromolecules 1993, 26, 5146. (19) Abrahmsen-Alami, S.; Alami, E.; François, J. J. Colloid Interface Sci. 1996, 179, 20. (20) Alami, E.; Rawiso, M.; Isel, F.; Beinert, G.; Binana-Limbele, W.; Franç ois, J. In Hydrophilic Polymers. Performances and Environmental Acceptability; Glass, J. E., Ed.; Advances in Chemistry Series; American Chemical Society: Washington, DC, 1995; No. 248, Chapter 18. (21) Franç ois, J.; Maıˆtre, S.; Rawiso, M.; Sarazin, D.; Beinert, G.; Isel, F. Colloids Surf. 1996, 112, 251. (22) Beaudoin, E.; Borisov, O.; Lapp, A.; Billon, L.; Hiorns, R. C.; Franç ois, J. Macromolecules 2002, 35, 7436. (23) Ulyanova, N.; Trabukina, E.; Sabaneeva, N. V.; Bykova, E. N.; Kallistov, O. V.; Klenin, S.; Franç ois, J. Polym. Sci. Ser. 1998, A, 40, 622. (24) Chassenieux, C.; Nicolai, T.; Durand D. Macromolecules 1997, 30, 4952. (25) Gourier, C.; Beaudoin, E.; Duval, M.; Sarazin, D.; Maı¨tre S.; Franç ois, J. J. Colloid Interface Sci. 2000, 230, 41. (26) Beaudoin, E.; Gourier, C.; Lapp, A.; Franç ois, J. Macromol. Symp. 1999, 146, 171. (27) Beaudoin, E.; Gourier, C.; Hiorns, R. C.; Franç ois, J. J. Colloid Interface Sci. 2002, 251, 398. (28) Chassenieux, C.; Nicolai, T.; Durand, D.; Franç ois, J. Macromolecules 1998, 31, 4035.

10.1021/la020730f CCC: $25.00 © 2003 American Chemical Society Published on Web 02/05/2003

Association of Hydrophobically End-Capped PEO

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Table 1. Characteristics of Samples Prepared from Alkyl Isocyanates with Number Average Molecular Weights (a, Calculated Using UV; b, Given by the Manufacturer; and c, Indicated by SEC) (1 - f) from UV

f from NMR sample name

time (days)

[NCO]/[OH]

a

b

c

a

b

c

0.62 0.72 0.82 0.97 0.94 0.94

0.63 0.74 0.84 1 0.96 0.96 0.31 0.50 0.62 0.83 0.91 0.94

0.43 0.320 0.15 0.06 0.04 0.01

0.40 0.30 0.14 0.06 0.04 0.01

0.41 0.31 0.14 0.06 0.04 0.01

Mn ) 32 000; i ) 18 Dc1 Dc2 Dc3 Dc4 Dc5 Dc6 Dc7 Dc8 Dc9 Dc10 Dc11 Dc12 Dc13

5 2 3 4 5 5 8 1 2 3 4 7 9

1 1.25 1.53 1.78 2.03 0.25 1 1 0.2 1.4 1.6 1.7

0.67 0.78 0.88 1.04 1.01 1.01

Mn ) 32 000; i ) 16 Dc14

dynamic light scattering,23-27 small angle neutron and X-ray scattering,15,19-22 viscosimetry28 and rheological characterization.29-31 Several parameters were investigated including PEO chain length, nature of hydrophobic groups, concentration, salinity26,27,32 and temperature.33 The solution behavior of difunctionalized molecules, which carry hydrophobic groups at both chain ends, has been the focus of most studies. In these systems, there are two association steps to consider: the first corresponding to “micellization” with the formation of flowerlike micelles,34-36 in which each chain incorporates both its chain ends in the same micelle, and the second corresponding to intermicelle bridging and the formation of a loose network.29-34 Two studies using light scattering concluded that the first step is cooperative (closed association) and the second is progressive (open association).24,25 It is difficult to characterize these two processes separately and therefore comparisons with monofunctionalized samples, which carry one hydrophobic group per chain, were considered informative, as the latter associate solely through the first process. However, many commercial samples prepared by polycondensation are polydisperse in composition; i.e., they contain a mixture of di-, mono- and unfunctionalized chains. An important problem is thus related to the influence of the average degree of modification on associative properties. In a series of papers, we shall discuss such influences on the structure and mechanisms of association, starting first with the comparison between monofunctionalized PEO (R-functionalized PEO) against R,ω-functionalized PEOs. In a second step, we shall study partially modified polymers, consisting of a mixture of di-, mono- and unfunctionalized PEOs. The present work deals with the preparation of model polymers, the determination of CACs and the comparison of the results with theoretical predictions. In a previous paper, the association mechanisms of di- and monofunctionalized samples were studied by static (29) Annable, T.; Buscall, R.; Ettelaie, R.; Whittlestone, D. J. Rheol. 1993, 3714, 695. (30) Maıˆtre, S. Ph.D. Dissertation, Universite´ Louis Pasteur, Strasbourg, France, 1997. (31) Beaudoin, E. Ph.D. Dissertation, Universite´ de Pau et des Pays de l’Adour, Pau, France, 2000. (32) Gourier, C.; Beaudoin, E.; Franç ois, J. J. Appl. Rheol., submitted for publication. (33) Beaudoin, E.; Borisov O.; Franç ois, J. J. Colloid Interface Sci., submitted for publication. (34) Semenov, A. N.; Joanny, J. F.; Khokhlov, A. R. Macromolecules 1995, 288, 1066. (35) Halperin, A. Europhys. Lett. 1989, 8, 351. (36) Halperin, A.; Alexander, S. Macromolecules 1989, 22, 2403.

1.00

and dynamic light scattering.25 The determination of the solubility diagram, association mechanisms and structure of concentrated solutions as a function of the degree of functionalization will be described in two forthcoming papers. 2. Experimental Section 2.1. Materials. Methanol, THF and toluene were distilled over their respective drying agents under predried nitrogen prior to use. Hydrochloric acid (37% solution in water), 18-crown-6 (99.5%), 1-dodecanol (98%), 1-hexadecanol (99%), 1-octadecanol (99%), dibutyl didodecyl tin (99%), 1,4-diazabicyclo[2.2.2]octane (98%) and alkyl isocyanates (98%) were used as received and supplied by Aldrich, France. Ethylene oxide (EO) (99.5+%), obtained from Aldrich, France, was distilled through a sealed glass system which had been evacuated to ca. 10-3-10-4 Pa. p-Toluenesulfonyl chloride (99%), supplied by Roth, was used as received. Precursors to modified PEOs were commercially obtained and purified, prior to use, by precipitation from toluene solution in ether. R,ω-Dihydroxy-PEOs (R,ω-HPEOs) with low polydispersity indexes (Ip ) 1.01) and weight average molecular weights of 6000, 10 000, 20 000 and 32 000, as indicated by size exclusion chromatography (SEC), were obtained from Hoechst and used as precursors to difunctionalized polymers. R-Methoxy,ω-hydroxy-PEO (R-MePEO), obtained from Shearwater Polymers Inc., was indicated to have Mw ) 21 400 and Ip ) 1.09 by SEC. 2.2. Preparation of Modified PEOs. 2.2A. Chemical Modification of PEO Using Alkyl Isocyanates. The method used was a variation on that proposed by Kaczmarsky et al.,18 in which PEO was modified by an alkyl isocyanate in the presence of dibutyl didodecyl tin. We used toluene as solvent and 1,4diazabicyclo[2.2.2]octane (DABCO) as catalyst, making the system more convenient to handle. Reactions were carried out in a well dried and argon flushed flask (250 mL). Each PEO was dissolved in toluene (to 30 wt %) at 60 °C, and then DABCO (1 wt %) and the corresponding alkyl isocyanates (100-300% with respect to PEO chain ends) were added. Reaction mixtures were stirred for between 6 and 72 h at 60 °C. Each modified PEO, with varying degrees of functionalization, thus obtained, was then diluted in excess toluene (at least 3 times by volume) and stirred for at least 1 h at 30 °C, during which time the mixture became increasingly turbid, indicating the decomposition of excess isocyanate. The solution was filtered and precipitated in excess ether. The recovered polymer was then rinsed with ether, dried under vacuum, and then dissolved in benzene (to 10 wt %) and again precipitated in excess ether. Table 1 reports the conditions used for the preparation of each sample. The general chemical formula of polymers obtained by the above detailed method was

CH3-(CH2)i-1-NHCOO-(CH2CH2O)j -CONH-(CH2)i-1-CH3

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Table 2. Characteristics of Samples Prepared Using Tosylates as Intermediates (Mt, Monofunctionalized Samples; Dt, Difunctionalized Samples) sample name Dt1 Dt2 Dt3 Dt4 Dt5 Dt6 Mt1 Mt2

no. of C in each hydrophobic group (i)

Mn

12 12 12 12 18 18 12 18

6 000 10 000 20 000 35 000 35 000 35 000 20 000 20 000

f from NMR

(1 - f) from UV

0.92 0.90 0.95 0.97 0.97 1.00 0.92 0.95

0.06 0.12 0.03 0.05

1H

Polymers prepared by this method were denoted Dc and their characteristics are detailed in Table 1. Throughout this paper, the letters i and j are used to denote the number of carbon atoms in the hydrophobic group and the number of ethylene oxide units in the polymer main chain, respectively. 2.2B. Chemical Modification of PEO Using Alkyl Tosylates. To prepare difunctionalized PEOs using alkyl tosylate intermediates, two synthetic steps were required: (i) modification of PEO hydroxyl end groups with (diphenylmethyl)potassium (DPMK) to yield R,ω-potassium dialkylatePEOs, as in

HO-(CH2CH2O)j-1-CH2CH2OH + 2HCPh2-K+ f K+ -O-(CH2CH2O)j-1-CH2CH2O-K+ + 2CPh2H2 and (ii) the subsequent reaction of “living” R,ω-potassium dialkylate-PEO with alkyl tosylates, in which alkyl groups are equivalent to those required in the eventual products, as in

K+ -O-(CH2CH2O)j-1-CH2CH2O-K+ + 2CH3Ph-SO3R f RO-(CH2CH2O)j-1-CH2CH2OR + 2CH3Ph-SO3-K+ DPMK was prepared by adding naphthalene (0.05 mol) and potassium (0.1 mol) to THF (250 mL) in a well dried 500 mL flask flushed with argon. On formation of a black-green color, 0.1 mol of diphenyl methane in THF was added. The mixture was stirred for 48 h at room temperature. Alkyl p-toluenesulfonates (CH3-Ph-SO3-(CH2)i-CH3) were obtained by reactions of p-toluenesulfonyl chloride with the alcohol of the required alkyl group in pyridine. The reactions were performed between -5 and +10 °C or between +35 and +45 °C for C12H25OH and C18H37OH, respectively. For each PEO sample, the same methodology was used. PEO was dissolved in THF (10 wt %) at 40 °C in a dried flask well flushed with dry nitrogen and then DPMK in THF was slowly added, by gastight syringe, until a light purple color was stable. Due to strong interactions between ion pairs at chain ends, the solution became highly viscous. Dodecyl tosylate or octadecyl tosylate was introduced, as a stoichiometric equivalent to PEO chain ends. An immediate drop in viscosity was observed. The temperature was raised to 50 °C, and the mixture stirred for 24 h. Polymers were recovered, purified, and dried as detailed in section 2.2A. Polymers prepared by this method were denoted Mt and Dt for mono- and difunctionalized polymers, respectively, the former having been prepared by the same route, but from the starting polymer R-MePEO; their characteristics are detailed in Table 2. 2.2C. Synthesis of r-Functionalized PEO via Anionic Polymerization. Monofunctionalized PEOs were prepared by the anionic polymerization of EO using the appropriate potassium alkylate initiator and acidified methanol as terminating agent. For example, R-hexadecyl,ω-hydroxy-PEO was prepared using potassium hexadecyloxide as initiator. Although the high vacuum techniques37 required for anionic polymerizations were complex and time-consuming, the previously described methods, which (37) Morton, M.; Milkovich, R. J. Polym. Sci., Part A 1963, 1, 443.

permitted preparation of R,ω-dialkyl polymers, would not have yielded monoalkyl-PEOs. Synthesis of Potassium Hexadecyloxide. Into a flame dried and nitrogen flushed Schlenk tube was placed excess potassium (1 g, 0.026 mol) and THF (100 mL). 1-Hexadecanol (0.25 g, 1.03 × 10-3 mol) was added and dissolved by stirring at room temperature. Potassium hexadecyloxide slowly precipitated. After 18 h of stirring, the precipitate was left to settle, and the excess THF was removed by syringe. The remaining solid lumps of potassium were carefully removed with tweezers. Vacuum drying for 18 h at room temperature gave a fine white powder with yield near 100%. Synthesis of Poly(ethylene oxide) Hexadecyl Ether. The following is a standard method. A 250 mL reactor glass blown with break-seals containing EO (13.6 mL, 12 g, 0.272 mol), potassium hexadecyloxide (0.160 g, 5.70 × 10-4 mol), excess 18-crown-6 (0.3 g, 1.14 × 10-3 mol), and acidified methanol (2 mL), and fitted with a magnetic stirring bar and magnetic breakers, was evacuated and flame dried. Once THF (200 mL) was distilled into the vessel, it was sealed under high vacuum. Potassium hexadecyloxide, as prepared above, was introduced and dissolved into the THF by stirring at 70 °C for 36 h. The solution was then cooled to 30 °C and EO was introduced. The solution was stirred at 50 °C for 24 h, and then at 70 °C for 178 h. Acidified methanol was introduced at room temperature to terminate the reaction. The polymer was precipitated twice from THF (200 mL) into ether (800 mL). The resulting fine white powder was collected by centrifuge and dried under vacuum at room temperature for 72 h to yield 10.9 g (91%). Polymer prepared via this route was denoted as Ma. 2.3. Polymer Characterization. The structures of PEOs and modified PEOs were characterized using 1H NMR, SEC, and UV-visible spectroscopy, whereas the aqueous solution behavior of modified PEOs was characterized using static fluorescence and viscosimetry. 1H NMR. Samples were dissolved in CCl (1%) with hexam4 ethylcyclotrisiloxane as the internal reference. Spectra were recorded over 350 accumulations at probe temperature using a Brucker Avance 400 MHz spectrometer. SEC. In a previous study, it was shown that commercial samples of the HEUR type could be characterized by SEC in THF, a solvent in which interpolymer associations do not occur.8 The study was limited to molecular weights 10 000, let alone modified PEOs, when THF and PL gel columns were used. In addition, water could not be used as an SEC eluent due to association phenomena. Therefore, a water-acetonitrile (70/30 v/v) mixture was used in conjunction with an apparatus equipped with three TSK columns (G 6000 PWXL, G 4000 PWXL, G 3000 PWXL), a Wyatt Technologies Dawn-DSP multiangle laser light scattering detector equipped with a F2 flow cell, and a Waters 410 refractometer. Characterization of Residual Hydroxyl Groups on Modified PEO by UV-Visible Spectroscopy. A convenient route to quantifying the percentage of unreacted hydroxyl groups at the chain ends of otherwise modified PEOs was to convert them first to naphthyl groups so that they could then be characterized by UV spectroscopy. Naphthyl isocyanates are, in general, considerably more reactive than alkyl isocyanates toward hydroxyl groups. Thus, both precursor and alkylated PEOs were treated with naphthyl isocyanate, under the same conditions as those detailed above, except that the solvent was THF. A quasi-complete conversion of residual hydroxyl groups to naphthyl chain ends was obtained after 5 min at 50 °C. UV-visible spectroscopy was performed using a UV 210 PC Shimadzu with ethanol as the solvent. A calibration curve was established using 1-naphthyl carbamate. The maximum absorption observed, λmax, was at 290.8 nm with extinction coefficient, , at 7060 mol-1 cm-1. For PEO precursors, this method allows a theoretical determination of the number average molecular weights, Mn:

Mn )

C2 × 103 AbsmeaPEO

(1)


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in which C is the polymer concentration expressed in g mL-1. AbsmeaPEO is the absorption measured for PEO carrying 100% naphthyl chain ends. Thus, PEO indicated by the manufacturers to have Mn ) 20 000 was found to have Mn ) 21 460 , a value comparable to that obtained by SEC (20 600). For partially functionalized PEO, once treated with naphthyl isocyanate as above detailed, the indicated percentage of residual OH was calculated using either Mn of the precursor (determined by SEC or given by the manufacturer) in

%OH )

MnAbsmea C2 × 103

(2)

or directly from the ratio

%OH )

Absmea AbsmeaPEO

(3)

Static Fluorescence. By using static fluorescence, it is possible to determine critical micelle concentrations (CMC); this method is known to work for low molecular weight surfactants.38 CMCs of samples were evaluated by determining the fluorescence of pyrene dissolved in the solutions. The ratio of the intensities (I1/I3, respectively) of the first to the third peaks of the vibronic fluorescence spectrum of the pyrene “probe” depends on the polarity of its immediate environment. Equal to 1.8-1.9 in water, I1/I3 descends to values lower than 1 in nonpolar solvents. Fluorescence spectra were followed using a Hitachi F-4010 spectrofluorometer between 350 and 500 nm with excitation wavelength set at 335 nm; the pyrene concentration was 5 × 10-7 M. Viscosimetry. Characterization of dispersion viscosities were performed on an automatic capillary viscometer (Viscologic, Sematech) for Newtonian solutions of low concentration. For higher concentrations, we used a low shear viscometer from Contraves LS30 and the viscosities were measured at shear rate, ≈0.1 s-1.

3. Results 3.1. Sample Preparation. Initially, we observed reaction kinetics between octadecyl isocyanate and R,ωdihydroxy-PEOs at stoichiometric ratios of octadecyl isocyanate to hydroxyl groups ([NCO]/[OH]) equal to 3:1 or 1:1. Sampling after different reaction times, however, yielded polymers with various degrees of functionalization. It should be noted that in some cases, the reaction rate of an isocyanate with an alcohol is described as having an apparent order higher than 1 with respect to the alcohol due to its basic character:39,40

dx ) k[NCO][OH]n>1 dt

(4)

Under the conditions used, the reaction rate was found to be first order with respect to both reagents, with a kinetic constant of 0.019 ( 0.02 l mol-1 min-1. To optimize the reactions, we again considered the reaction of a stoichiometric equivalent of reagents, and then various other ratios with different reaction times. Table 1 reports the ratios of reagents used, reaction times, and the near equivalent degrees of functionalization indicated by 1H NMR and UV, within the limits of experimental error. Table 2 details the characteristics of samples prepared using alkyl tosylates. The reaction time required for a quasi-100% yield, under the conditions used, was approximately 1 day. (38) Zana, R. In Surfactants Solutions: New Methods of Investigation; Zana, R., Ed.; Plenum Press: New York, 1987; Chapter 5. (39) Kothandaraman, H.; Venkatarao, K.; Thanoo B. C. Polym. J. 1989, 21, 829. (40) Baker, J. W.; Graunt, J. J. Chem. Soc. 1949, 19, 27.

Figure 1. Fluorometry: variations of I1/I3 versus polymer concentration for a low molecular weight surfactant C12E6 ([) and for associative polymers: Ma (b); Mt2 (+); Mt1 (2), Dc14 ([), and Dt3 (O).

Molecular weight distributions of hydrophobically modified polymers are generally difficult to determine and there is a lack of information on the possible degradation of PEO chains, due to secondary reactions, during chemical modification. We found that SEC characterizations using a water-acetonitrile mixture as the eluent were the most repeatable. The molecular weight distributions were found to be identical, within the limits of experimental error, for precursors and modified polymers; we concluded that no degradation of PEOs modified by alkyl tosylates occurred. Light scattering measurements performed on different samples used in this work at concentrations lower than CAC also gave weight average molecular weights close to those of the precursors.23,25 In this work, we will consider the degree of functionalization as that calculated from Mn values determined by SEC. 3.2. CACs Obtained by Static Fluorescence. Several authors have studied the association of R,ω-hydrophobically end-capped PEO by using pyrene as a “probe” and measuring the ratio of resulting fluorescence intensities I1/I3.38 For low molecular weight surfactants, it is wellknown that I1/I3 decreases upon micellization over a narrow range of concentrations, but that the concentration at which I1/I3 starts to alter generally indicates a lower value of CMC than that determined by other methods. The same behavior is observed with APs, clearly indicating the formation of hydrophobic nanodomains above a particular concentration. Nevertheless, the range of concentrations in which I1/I3 decreases is broad and it is not clear at what concentration the CMC is located.10,11,41 This difference may be qualitatively understood by taking into account the free energy of micelle coronas, which limit the micelle growth. This may indeed explain why the aggregation number of micelles increases in a less cooperative way for polymers than for low molecular weight surfactants.41 For this reason, the term CAC is often preferred to CMC for APs. It is usual to consider that the CMC or CAC is at the intersection between the decreasing curve I1/I3 and its lower plateau, i.e., at the point CACf. One could consider as well the surfactant or polymer concentration value in which the same ratio starts to decrease, at CACs, or the inflection point of the curve CACi. 3.2A. Fully Modified PEO. R-functionalized PEO. Variations in I1/I3 versus polymer concentration C (g g-1) obtained for monofunctionalized samples (Mt1 and Mt2) are compared to that of a low molecular weight surfactant, n-C12H25(C2H4O)6OH (C12E6) in Figure 1. Despite their (41) Alami, E.; Almgren, M.; Brown, W.; Franç ois, J. Macromolecules 1996, 29, 2229.

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Table 3. Comparison of Different Critical Concentrations: C*, Overlap Concentration of Equivalent Unmodified PEO; CAC+, the Critical Association Concentration of Modified PEO; Cη, Concentration at Departure of Viscosity Curves of PEO and Modified PEO sample name

C* (g g-1)

Mt1

2.5 × 10-2

Mt2

2.5 × 10-2

Ma Dc8 Dc10 Dc3 Dc11 Dc13

2.6 × 10-2 2.6 × 10-2 2.6 × 10-2 2.6 × 10-2 6 × 10-2

Dt2

4.2 × 10-2

Dt3

2.6 × 10-2

Dt4

1.8 × 10-2

Dc14

1.9 × 10-2

CAC+ (g g-1) CAC+ (mol L-1) 4 × 10-2 2 × 10-3 3 × 10-4 1.5 × 10-5 3 × 10-4 2 × 10-5 2 × 10-4 4 × 10-4 3 × 10-4 9 × 10-4 3 × 10-4 2 × 10-3 4 × 10-4 7 × 10-3 7 × 10-4 1.9 × 10-2 1.1 × 10-3 1 × 10-3 3 × 10-5

Cη (g g-1)

6 × 10-3 2 × 10-2 1.4 × 10-2 1 × 10-3 1 × 10-3 1× 10-3 1 × 10-2 1 × 10-2 1.5 × 10-2 2 × 10-2 2 × 10-3

high molecular weights, these modified PEOs self-associate well. As expected, the CAC values increased when the number of carbons in the chain ends decreased, or when the PEO molecular weight increased. Table 3 shows that an increase in six carbons in the hydrophobic chain resulted in a decrease in CAC by a factor of approximately 100. The relatively high value of I1/I3, in the polymer high concentration plateau, indicated that a less polar environment surrounded the “probe” probably due to less compact hydrophobic nanodomains being present. This probably corresponded to a low aggregation number for the polymers, with respect to low molecular weight surfactants, as has already been identified in previous studies on R,ω-functionalized PEOs.23-27,41 R,ω-functionalized PEO. In Figure 1, the variations of I1/I3 are also compared for mono- and difunctionalized samples, for two different environments. Mono- and difunctionalized samples, Ma and Dc14, respectively, both had the same end groups; the molecular weight of the latter PEO was twice that of the first. We observed that the CACs of both samples were of the same order of magnitude, with CACDc14 slightly higher than that of CACMa. When R- and R,ω-functionalized PEOs, with the same PEO molecular weight, were compared, the CAC was found to be lower for the difunctionalized polymer (see Table 3). Figure 1 shows that variations in I1/I3 were almost superimposed if the parameter of molar concentration of chain ends was used instead of weight/weight concentrations; however, the curve for Mt1 is shifted to higher concentrations with respect to that of Dt3. The logarithms of CACs, CACi, and CACf (expressed in concentration of hydrophobic groups) versus the number of PEO monomers (j) per hydrophobic group (i′) are plotted in Figure 2 to compare low molecular weight surfactants against modified PEOs with i ) 12. In the case of a low molecular weight surfactant, it is usual to relate CMC to the free standard micellization energy ∆Fm by the general expression42,43 (42) Carless, J. E.; Challis, R. A.; Mulley, B. A. J. Colloid Sci. 1964, 19, 201. (43) Meguro, K.; Takasawa, Y.; Kawahashi, N.; Tabata, Y.; Ueno, M. J. Interface Sci. 1981, 83, 50.

Figure 2. Variations in log(CAC) (CACs) ([), CACi (2), and CACf (9) versus the number of EO units per hydrophobic group.

2.3RT(log CMC - log w) ) ∆Fm

(5)

in which w is the molar concentration of water. It is assumed that ∆Fm can be considered as the sum of two terms, the first related to the attraction of hydrophobic groups, ∆Fmi′, which favors micellization, and the second corresponding to the repulsion between PEO chains, ∆FmPEO:

∆Fm ) ∆Fmi′ + ∆FmPEO

(6)

Meguro et al.43 have shown from CMC measurements of a series of low molecular weight surfactants CiE8, that ∆Fmi′ can be expressed as a contribution from methyl and methylene groups:

∆Fmi′ ) ∆Fmi′(CH3) + ∆FmH(CH2)

(7)

∆Fmi′ ) -2.18-0.85 i (kcal mol-1)

(8)

It should be noted that these values should be considered with some caution, as the data for CMCs of CiEj available in the literature are well dispersed and vary considerably with experimental methods. To a first approximation, it can be assumed that there is an average free energy per carbon ∆Fmi′(C) and that ∆Fmi′ ) i∆Fmi′(C). For difunctionalized surfactants or polymers, ∆Fmi′ ) 2i∆Fmi′(C) if each end group contains i carbons. Plotted in Figure 3 are the variations in 2.3RT(log CMC - log w) versus i for low molecular surfactants42-45 with j ) 6 and for our three monofunctionalized polymers, each with values of j equal to approximately 454 (20000/44). The curves are roughly parallel, which indicates that ∆Fmi′(C) are of the same order of magnitude. More precisely, the fits of these curves leads to

2.3RT(log CAC - log w) ) ∆Fm ) -2.1i + 0.39 (kcal mol-1) (9) 2.3RT(log CAC - log w) ) ∆Fm ) -2.9i + 10 (kcal mol-1) (10) The results obtained with the monofunctionalized polymers through eq 10 are consistent with those previously obtained with low molecular surfactants by eq 9, as the slopes of the curves are close but differ from those given (44) Degiorgio, V.; Corti, M. Physics of Amphiphiles: Micelles, Vesicles and Microemulsions; Italian Physical Society: 1985; p 303. (45) Becker, P. Non Ionic Surfactants; New York, 1967; p 478.


Langmuir, Vol. 19, No. 6, 2003 2063

Figure 3. Variations in ∆Fm versus i for CiE6 (9) and monofunctionalized polymers ([).

Figure 5. Variations in I1/I3 versus hydrophobic group molar concentrations for mono- and difunctionalized samples: Mt2 (0); Dc10 (b); Dc3 (9); Di11 ([).

Figure 4. Variations in ∆Fm versus j for difunctionalized polymers with dodecyl chain ends (i ) 12).

by Meguro et al.43 Unfortunately, we have no data for monofunctionalized polymers with the same value of i and various PEO chain lengths. In Figure 4, we present the plot of 2.3RT(log CAC - log w) versus j for difunctionalized samples with i ) 12. The curve is not linear but can be represented by a logarithmic law:

2.3RT(log CAC - log w) ) -39.2 + 1.84 ln j (kcal mol-1) (11) Let us note that eqs 8-11 are empirical fits that are only given to be comparable with low molecular weight surfactants. We will discuss the physical significance of the two terms of these expressions below. 3.2B. Partially Modified PEO. Samples of variable average degrees of functionalization (f) are constituted of three types of chains: difunctionalized chains of molar fraction f 2; monofunctionalized chains of molar fraction 2f(1 - f); and unfunctionalized chains (1 - f)2. Table 3 shows that the CAC is slightly dependent on the degree of functionalization, which is consistent with the fact that no great difference was previously found between mono- and difunctionalized samples. In Figure 5, the results obtained with samples Di9, Di3, and Di11 are plotted as a function of the molar concentrations of hydrophobic groups (chydro) and can be compared against those obtained for R-functionalized PEOs of the same i ) 18. Interesting enough, all the curves are almost superimposed, confirming that the CAC of difunctionalized polymers is not very different from that of monofunctionalized ones. 3.3. CACs Obtained by Viscosity. 3.3A. r-Functionalized PEO. The viscosity of aqueous solutions of associative samples, (ηPEOM) and of the unmodified analogous samples (ηPEO) were measured versus concentration at room temperature. Figure 6 shows the variations in the ratio R ) ηPEOM/ηPEO for Mt2, Ma, and Dc14. The polymer concentration is consistently higher than the CAC in the range covered in the graph, and it may be observed

Figure 6. Variations in the ratio R (see text) versus polymer concentration: Ma (0); Mt2 ([); Dc14 (2).

that the viscosity of aqueous solutions of modified PEO is always higher than that of PEO solutions. For monofunctionalized samples, R increases slightly with concentration up to a value of about 1.2 at Cη ≈ 8 × 10-3 g g-1 and then increases more significantly. In fact, an initial difference with respect to the unmodified polymer occurs at very low concentrations, probably at CAC ) 3 × 10-4 g mL-1 and cannot be determined. The intrinsic viscosity [η] (obtained by extrapolation of these data to zero concentration) is higher for Mt2 and Ma than that of the PEO analogues and corresponds to the presence of micelles. It has been demonstrated in other studies,31 in which micelles were considered as polymer stars, that the values of [η] are compatible with aggregation numbers Nag 40 and 34, corresponding to hydrodynamic radii of 175 and 165 Å, respectively. The concentration Cη at which the viscosity of Mt2 and Ma diverges more significantly from that of pure PEO can be compared with the critical overlap concentration (C*) of the unmodified PEO:46

C* )

3Mw 4πNRg3

(12)

in which Rg is the radius of gyration. For Mw ) 16 000 and 20 000, values of about 2.5 × 10-2 and 1.6 × 10-2 g mL-1 can be deduced for the molecular dependence of Rg from experimental power laws.47 Cη can be also compared to the overlap concentration of micelles (Cf*), which could be considered as 1/[η]. As an example, for Ma, [η] ) 96 mL (46) De Gennes, P. G. Scaling Concepts in Polymer Physics; Cornell University Press: Ithaca and London, 1979. (47) Denavand, K.; Selser, J. C. Nature 1990, 343, 739.

2064


g-1 leads to Cf* ≈ 10-2 g mL-1, which is very close to the experimental value of Cη obtained. 3.3B. r,ω-Dialkyl-PEOs in Which f > 0.82. It is wellknown that aqueous solutions of R,ω-alkyl-PEOs are characterized by a high viscosity with respect to those of unmodified polymers. Figure 6 gives a typical variation in reduced viscosity ηred obtained with Dc14. The comparison with the behavior of the monofunctionalized PEO shows a more abrupt divergence of ηred from that of pure PEO and at lower concentration Cη. In this case, such a behavior is attributed to the presence of intermicelle bridges. Nevertheless, the details of viscosity variations over a broad range of concentrations, starting from values lower than CAC up to the concentrated regime have not previously been clearly described. Two successive phenomena may influence viscosity: the formation of isolated flowers as in the case of monofunctionalized polymers just above CAC, and at higher concentrations, the formation of bridges. In fact, the increments in viscosity exhibit four distinct domains, three of which are identifiable in Figure 6 on the curve of Dc14: domain 1, C < Cη ) 2 x 10-3 g g-1, in which the ratio R remained close to 1; domain 2, 2 x 10-3 g g-1 < C < 8 x 10-3 g g-1 (Cη2), in which viscosity increased moderately; domain 3, 8 × 10-3 g g-1 < C < 2 × 10-2 g g-1, in which viscosity jumped abruptly (by a factor more than 100). In the fourth domain, the average slope dη/dC decreased again. It has been shown, using static and dynamic light scattering, that the hydrodynamic dimensions of the flowerlike structures of Dc14 (175 Å) approximate in size to those of Ma (155 Å) with an aggregation number (number of chains) twice lower.25 Thus, the flowerlike micelle overlap of Dc14 was expected at a concentration close to that for Ma, but in fact, it was actually 4 times lower. This result indicated that the formation of the first bridges occurred at C ) Cη, prior to flowerlike overlapping. However, the second sharp domain was probably directly related to flowerlike overlapping. Let us note that these experimental findings correspond exactly to the theoretical description of Semenov et al.34 This conclusion was confirmed with the values of Cη obtained from the series of difunctionalized samples with dodecyl chain ends and variable PEO lengths. It is interesting to observe that for the higher molecular weight sample, Dt4, the three concentrations, C*, of pure PEO, CAC, and Cη were similar. When the PEO length decreased, CAC drastically decreased, as described above, and Cη diverged more and more from C* and CAC. In the case of Dt4, the two phenomena of micellization and bridging occurred simultaneously, because isolated chains already overlapped prior to micellization. On decreasing PEO chain length, the strong attraction between hydrophobic groups provoked bridging prior to flowerlike structures overlapping. In other systems, this phenomenon is responsible for phase separation at concentrations close to CAC, as discussed in another work.33 3.3C. r,ω-Functionalized PEO with f < 0.82. Table 3 shows the values of Cη obtained for a series of partially modified PEOs. For the least functionalized PEO, Cη was close to C* and when f increased, Cη decreased and approached CAC. Surprisingly, the divergence appeared for the monofunctionalized PEO, Mt2, at lower concentrations than for R,ω-functionalized PEO, with f ) 0.30 and 0.62, respectively. 4. Discussion The most important result of this study is that though the observed variations in CAC with PEO chain and hydrophobic group lengths is what was qualitatively

Beaudoin et al.

expected, there was no significant difference in CACs between monofunctionalized and difunctionalized samples. r-Functionalized PEO. The CAC values observed for Mt1 and Mt2, as determined by fluorescence, were respectively 4 × 10-2 and 3 × 10-4 g g-1. We obtained the empirical law (5) for variations in CAC, expressed in concentration of hydrophobic groups, for both R- and R,ωfunctionalized PEO with i ) 12. The usual relation between mol fraction of free unimers, x1, and mol fraction of aggregates of Nag unimers, xNag is given by

xNag ) x1Nag exp(-Nag∆G°/RT)

(13)

in which ∆G° is the free energy of transfer of a monomer from water to hydrophobic aggregates or micelles. Following refs 35 and 36, we can divide ∆G° into three terms. The first corresponds to the free energy of transfer of a hydrophobic group from the aqueous environment into the micelle core, the second describes excess free energy at the core-water interface, and the third accounts for repulsion between PEO chains in micelle corona:

∆G°/RT) -B0 + B1Nag-1/3 + B2Nag1/2 log j (14) The latter term is written in the Daoud-Cotton scaling approximation48-50 and assumes that the micelle is like a polymeric star comprising Nag branches each of j monomers. B2 is a numerical factor. However, B1 depends on the surface tension at the core-water interface and the length of the hydrophobic block. From expressions (13) and (14), one can calculate variations in the weight average aggregation number as a function of concentration by using the procedure previously described43 and the set of values (B0 ) 20.3, B1 ) 18.9, and B2 ) 0.144) obtained from comparisons between C12E8 and Mt1. This set of values is the same as that previously determined in ref 43, which is not surprising because the CACs of monoand difunctionnalized samples do not differ. Minimization of the free energy in eq 14, with respect to Nag, gives the number of polymer chains associated in an optimal micelle, Nag,opt ) (2B1/3B2 ln j)6/5, and the estimate for CAC as

(log CAC1 - log w)) ∆G°(Nag,opt)/RT) -B0 + (2/3)3/5(5/2)(B13B22 log2 j)1/5 (15) r-ω-Functionalized PEO. The CAC of solutions of R,ωfunctionalized PEO chains can be estimated in the same way as for R-functionalized chains, if we assume that flowerlike micelles are formed, i.e., that both hydrophobic extremities of each chain are incorporated into the hydrophobic core of the flowerlike micelle. The difference in the free energy of a difunctionalized chain in associated and dissociated states can be written as

∆G°/RT ) -2B0 + 22/3B1Nag-1/3 + 23/2B2Nag1/2 log(j/22/3) (16) in which B0, B1, and B2 are the same as in eq 14 and we have taken into account that each chain contributes two hydrophobic blocks to the core of the micelle and two PEO blocks, of length j/2, into the micelle corona. (48) Daoud, M.; Cotton, J.-P. J. Phys. (Fr.) 1982, 43, 531. (49) Zhulina, E. B. Polym. Sci. USSR 1984, 26, 794. (50) Birshtein, T. M.; Zhulina, E. B. Polymer 1984, 25, 1453. (51) Hunter, R. J. Foundations of Colloid Science; Clarendon Press: Oxford, U.K., 1987.


Figure 7. Values of CAC versus j calculated from eq 15 with B0 ) 20.3, B1 ) 18.9, and B2 ) 0.144 for monofunctionalized samples ([), and from eq 17 for difunctionalized samples of the same molecular weight (9) and of molecular weight two times higher (2).

Minimization of the free energy, eq 16, with respect to Nag gives us the number of difunctionalized chains in one flowerlike micelle Nag,opt ) (2B1/3B2 ln(j/22/3))6/5/2 and the CAC, which is, as expected, much lower for difunctionalized than for monofunctionalized chains.

(log CAC2 - log w)) ∆G°(Nag,opt)/RT ) -2B0 + 5(2/3)3/5(B13B22 log2(j/22/3))1/5 (17) From eqs 15 and 17, theoretical variations in CAC as a function of j can be calculated for both mono- and difunctionalized PEOs (with the same PEO chain length or for difunctionalized PEOs with a length twice that of monofunctionalized equivalents) using the values of B0, B1, and B2 previously determined for i ) 12. The results are reported in Figure 7, which shows that the CAC of difunctionalized samples is predicted, in both cases, to be close to the square of those of monofunctionalized PEOs. However, such differences in the CAC values of monoand difunctionalized samples were not observed for any samples, which indicates that difunctionalized polymers have an aberrant behavior. We should point out, however, that the monofunctionalized samples Mt2 and Mt1 both had two hydrophobic extremities: a long aliphatic chain at one end and a single methyl group at the other. The presence of CH3- may favor micellization and might explain the negligible difference in CAC with respect to difunctionalized samples. However, Ma, which has one hydroxyl end group that cannot play a role in micellization, behaved similarly to the former two samples and exhibited a CAC close to that of an equivalent difunctionalized PEO. We could also question the method of fluorescence used to determine values of CAC. It is known that for associating comblike polymers or polysoap solutions, a drop in I1/I3 occurs at very low polymer concentrations. It is not clear if this phenomenon is due to formation of hydrophobic nanodomains at these concentrations, which should correspond to a true CAC, or an increase in the number of intra- or internanodomains already present at zero concentration. In the case of the latter hypotheses, the partition coefficient of pyrene between water and hydrophobic micelle cores should be taken into account. Such an explanation could not apply to our case, as decreases in I1/I3 also occurred at relatively high concentrations (2% for Dt4 and Mt1). Besides, it has been shown that CAC values determined using other methods (NMR and light scattering) were in good agreement with those obtained by fluorescence, for the same samples as those used in this work.25,28

Langmuir, Vol. 19, No. 6, 2003 2065

Figure 8. Variations in the apparent molecular weight (proportional to the scattered intensity) as a function of polymer concentration for Ma (9) and Dc14 ([).

Therefore, we can ascertain that classical theory fails to explain the experimental results obtained with difunctionalized samples. It may be thought that the theory describes quite correctly the micellization of monofunctionalized polymers but the hypotheses used to predict CAC of difunctionalized polymers should be revised. The model used above, which assumes the formation of isolated flowerlike structures from single chains with unassociated end groups is inappropriate. Two hypotheses may be proposed. First, that the probability of difunctional chains forming loops by intraassociation of end groups at very low concentrations, as indicated by intrinsic viscosity measurements,41 should be considered nonnegligible. If the effect of end-group association is taken into account, the above detailed theoretical approach leads to a considerable increase in CAC. Second, viscosity measurements presented here show that bridges were formed well before the theoretical flower overlap concentration, Cf* was reached. As macroscopic phase separation was not observed in the systems considered here, this would indicate that micellization and bridging were simultaneous. Let us note that in cases when CAC is much lower than Cf*, macroscopic phase separation occurs; this will be discussed in a future paper. Other experimental evidence also supports this assessment. Neutron scattering measurements performed with mono- and difunctionalized samples at concentrations near Cf* were characterized, in both cases, by the presence of a correlation peak.21,22 At low scattering vector values, however, an excess scattered intensity indicated the presence of bridged aggregates of “flowers” only for difunctionalized PEO samples. Figure 8 allows a comparison between the scattered light intensity of solutions of Ma and Dc14 (of CACs, respectively, 3 × 10-4 and 1 × 10-3 g g-1) as a function of concentration. It is clear that just above CAC, the apparent molecular weight of Dc14 diverges from that of Ma due to bridging and the formation of micelle aggregates. It seems that the predictions for micellization of difunctionalized samples should be revised in light of this experimental evidence. If f < 1 is the average degree of functionalization, fractions of difunctionalized, monofunctionalized, and nonfunctionalized chains in solution are equal to f 2, 2f(1 - f), and (1 - f)2, respectively. Nonfunctionalized chains cannot associate into micelles; moreover, as CAC corresponds to very low concentrations (far below the overlap concentration, C*), we can neglect effects of nonfunctionalized chains (for example, screening of excluded volume interactions in micellar coronae) on the micellization of functionalized chains. At 0 < f

Association of Hydrophobically End-Capped Poly (ethylene oxide). 1

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