Self-Assembly in Aqueous Solutions of Polyether-Modified Poly

Below the gelation temperature both relative and zero-shear viscosities grow as the square root of total polymer concentration, defining polymer solut...
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Langmuir 1998, 14, 5806-5812

Self-Assembly in Aqueous Solutions of Polyether-Modified Poly(acrylic acid) Lev Bromberg† Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 Received June 23, 1998. In Final Form: August 7, 1998

Self-assembly in aqueous solutions of poly(ethylene oxide)-b-poly(propylene oxide)-b-poly(ethylene oxide)g-poly(acrylic acid) has been studied. The onsets of aggregation and the relative viscosity increase coincide. Below the gelation temperature both relative and zero-shear viscosities grow as the square root of total polymer concentration, defining polymer solutions as semidilute and unentangled. Significant differences between complex and steady-shear viscosities in the low-shear, low-frequency regions are observed, in contrast to the Cox-Merz rule. Gelation is characterized by the appearance of well-defined, slow relaxation modes above frequencies corresponding to the liquidlike flow. The gel elasticity can be related to the functionality of aggregates that increases with the polymer concentration.

Introduction Polyelectrolytes that contain some amount of hydrophobic groups often exhibit peculiar viscosity enhancement in aqueous solutions, which stems from a strong tendency of hydrophobic groups to form interchain aggregates above a certain threshold concentration.1,2 Hydrophobically modified poly(acrylic acid) (HMPAA) is among the most studied charged rheology modifiers as it is readily available in a variety of molecular weights.2-9 Typically, HMPAA is synthesized by modification of PAA in its acidic form by alkylamines in an aprotic solvent in the presence of a coupling agent such as N,N′-dicyclohexylcarbodiimide.3,9,10 The PAA-alkylamine coupling results in the attachment of alkyl chains with m carbon atoms (m ) 8, 12, 14, 18, etc.) onto a PAA backbone. The hydrocarbon group used for modification is extremely hydrophobic and water insoluble at any temperature. Recently, we have introduced a concept of poly(propylene oxide) (PPO) group as a temperature-sensitive hydrophobe.11,12 Attachment of the PPO group onto a polyelectrolyte adds temperature sensitivity to an already pH-sensitive polymer, thus creating a dually responsive material.13 A novel class of † All inquiries should be directed to: 15 Sherwood Rd., Swampscott, MA 01907. E-mail: [email protected].

(1) Water-Soluble Polymers; Shalaby, S. W., McCormick, C. L., Butler, G. B., Eds. ACS Symposium Series 467; American Chemical Society: Washington, DC, 1991; Chapters 1, 11, 14, and 22. (2) Bokias, G.; Hourdet, D.; Iliopoulos, I.; Staikos, G.; Audebert, R. Macromolecules 1997, 30, 8293. (3) Wang, T. K.; Iliopoulos, I.; Audebert, R. Polym. Bull. 1988, 20, 577. (4) Petit, F.; Audebert, R.; Iliopoulos, I. Colloid Polym. Sci. 1995, 273, 777. (5) Audebert, R.; Iliopoulos, I.; Hourdet, D. Polimery 1997, 42, 237. (6) Tribet, C.; Porcar, I.; Bonnefont, P. A.; Audebert, R. J. Phys. Chem. B 1988, 102, 1327. (7) Philippova, O. E.; Hourdet, D.; Audebert, R.; Khokhlov, A. R. Macromolecules 1997, 30, 8278. (8) Philippova, O. E.; Hourdet, D.; Audebert, R.; Khokhlov, A. R. Macromolecules 1996, 29, 2822. (9) Magny, B.; Iliopoulos, I.; Audebert, R. In Macromolecular Complexes in Chemistry and Biology; Dubin, P., Bock, J., Davies, R. M., Schulz, D. N., Thies, C., Eds. Springer-Verlag: Berlin, 1994; pp 51-62. (10) Hourdet, D.; L’allouret, F.; Audebert, R. Polym. Prepr. 1993, 34 (1), 972. (11) Bromberg, L. Polymer 1998, 39, 5663. (12) Bromberg, L. Macromolecules 1998, in press. (13) Bromberg, L. J. Phys. Chem. B, in press.

thermogelling materials has emerged where PAA segments are grafted onto Pluronic poly(ethylene oxide)-bpoly(propylene oxide)-b-poly(ethylene oxide) (PEO-PPOPEO) block copolymers via C-C bonding.12-22 High molecular weights and extreme temperature sensitivity characterize these PEO-PPO-PEO-PAA copolymers, so that above certain temperatures their semidilute aqueous solutions can form reversible gels with significant elastic (14) Bromberg, L.; Lupton, E. C.; Schiller, M. E.; Timm, M. J.; McKinney, G. W.; Orkisz, M.; Hand, B. Int. Pat. Appl. WO 97/00275, 1997. (15) Bromberg, L. E.; Ron, E. S. Adv. Drug Delivery Rev. 1998, 31, 197. (16) Huibers, P. D. T., Lupton, E. C., Bromberg, L. E., Hatton, T. A. Supplement Chemical Engineering Progress; Annual Meeting of the American Institute of Chemical Engineers; Los Angeles, 1997; paper 93c. (17) Bromberg, L.; Orkisz, M.; Roos, E.; Ron, E. S.; Schiller, M. J. Controlled Release 1997, 48, 305. (18) Huibers, P. D. T.; Bromberg, L. E.; Lupton, E. C.; Hatton, T. A. Manuscript in preparation. (19) Bromberg, L. Ind. Eng. Chem. Res. 1998, in press. (20) Bromberg, L. J. Phys. Chem. B 1998, 102, 1956. (21) Bromberg, L. E.; Mendum, T. H. E.; Orkisz, M. J.; Ron, E. S.; Lupton, E. S. Proc. Polym. Mater. Sci. Eng. 1997, 76, 273. (22) We wish to acknowledge a large number of publications dedicated to thermoassociative systems comprising poly(acrylic acid) modified with oligoalkylamine or polyether groups. These systems were introduced by Audebert and co-workers (see refs 2-10 herein, as well as: Hourdet, D.; L’allouret, F.; Audebert, R. Polymer 1994, 35, 2624. L’allouret, F.; Hourdet, D.; Audebert, R. Colloid Polym. Sci. 1995, 273, 1163. L’allouret, F.; Maroy, P.; Hourdet, D.; Audebert, R. Rev. Inst. Fr. Pet. 1997, 52, 117. Hourdet, D.; L’allouret, F.; Durand, A.; Lafuma, F.; Audebert, R.; Cotton, J.-P. Macromolecules 1998, in press) and Hoffman et al. (Hoffman, A. S.; Chen, G. Int. Pat. Appl. WO 95/24430, 1995. Hoffman, A. S.; Chen, G. H.; Kaang, S. Y.; Ding, Z. L.; Randeri, K.; Kabra, B. In Advanced Biomaterials in Biomedical Engineering and Drug Delivery Systems; Ogata, N., Kim, S. W., Feijen, J., Okano, T., Eds., Springer: Tokyo, 1996; pp 62-66. Hoffman, A. S.; Chen, G.; Kaang, S.; Priebe, D. T. Proc. Inte. Symp. Controlled Release Bioact. Mater. 1995, 22, 159. Chen, G.; Hoffman, A. S.; Ron, E. S. Proc. Int. Symp. Controlled Release Bioact. Mater. 1995, 22, 167. Hoffman, A. S.; Chen, G.; Wu, X.; Ding, Z.; Kabra, B.; Randeri, K.; Schiller, M.; Ron, E.; Peppas, N. A.; Brazel, C. Polym. Prepr. 1997, 38, 524). These graft copolymers are related to the copolymers described in the present study. However, the C-C bonding between polyether and polyelectrolyte resulting from the unique synthetic route is a feature that brands the copolymer at hand a distinct chemical entity (refs 14, 15, and 20). Aqueous solutions of this copolymer exhibit unparalleled symmetry between temperatureand concentration-dependent scaling of rheological properties (ref 12). Useful “smart hydrogels” depicted in the popular literature (Chem. Eng. News 1997, 75, 26) are actually the system originating from the recent invention (ref 14). The author is grateful to an anonymous reviewer for drawing his attention to a number of relevant references.

S0743-7463(98)00737-9 CCC: $15.00 © 1998 American Chemical Society Published on Web 09/12/1998

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Figure 1. Surface tension (A) and viscosity (B) of Pluronic-PAA aqueous solutions (pH 7.0) as functions of total polymer concentration (Cp). In part A, arrows indicate intercepts of the aggregated and nonaggregated regions; in part B, ηr (open points) and ηo (filled points) stand for relative viscosity and zero-shear rate viscosity measured at 15 °C, respectively. Solid lines represent relations ηr ∼ Cp0.5 and ηo ∼ Cp0.5 and are drawn to guide the eye only. In B, arrows indicate the critical aggregation concentration (CAC) determined from surface tension data at 19.5 and 25.5 °C. A Pluronic-PAA fraction was used throughout that had number-average and weight-average molecular masses of 3.1 × 106 and 3.6 × 106, respectively.

moduli.12 Scaling relations among transient rheological properties in such gels appear to be in agreement with the Rouse model and are consistent with the percolation theory.12 In the present work, we aimed at establishing concentration boundaries of semidilute regime in the PEO-PPO-PEO-PAA solutions, as well as elucidating effects of temperature on the range of Rouse-like behavior of the copolymer chains, which implies an unentangled regime.23,24 Dynamic moduli of the copolymer gels could be related to functionality of the polymer aggregates that serve as cross-links. Experimental Section Materials. Pluronic F127 NF was kindly donated by BASF Corp. and used without further treatment. It has a formula EO100PO65EO100, nominal molecular weight 12600, molecular weight of PPO segment 3780, 70 wt % of EO, and cloud point above 100 °C. Poly(ethylene oxide)-b-poly(propylene oxide)-b(poly(ethylene oxide))-g-poly(acrylic acid) (CAS No. 186810-811) was synthesized by dispersion/emulsion polymerization of acrylic acid along with simultaneous grafting of poly(acrylic acid) onto a Pluronic backbone as described in detail elsewhere.13,19 In this work, we refer to the ensuing copolymer as PluronicPAA. The polymer was fractionated at 15 °C by size-exclusion chromatography (SEC) as previously described.13 The polymer consisted of 43% Pluronic F127 and 57% poly(acrylic acid) as measured by FTIR and NMR.19,20 All other chemicals, gases, and organic solvents of the highest purity available were obtained from commercial sources. Procedures. To prepare solutions of Pluronic-PAA the polymer samples were dispersed in distilled water and gently stirred at 4 °C for 48 h. The pH was adjusted to 7.0 ( 0.1 with 5 M NaOH as needed. The solutions were filtered through Acrodisc nylon filters (Gelman Sciences) with pore diameters of 0.8 µm, deoxygenated by nitrogen flow, and stored at 4 °C. Polymer concentration in the solutions was controlled within (0.005%. Viscometric titration was performed using a Cannon AutoVisc II automatic viscosity measuring system (Cannon Instrument Co.) equipped with a near-infrared optical sensor for meniscus detection and thermostatic air chamber for temperature control to within 0.01 °C. Relative viscosity (ηr) was expressed as a ratio of the polymer solution and solvent viscosities, respectively. (23) Semenov, A. N.; Rubinstein, M. Macromolecules 1998, 31, 1373. (24) Rubinstein, M.; Semenov, A. N. Macromolecules 1998, 31, 1386.

Rheological measurements within angular frequency (ω) range of 0.628 mrad s-1 to 628 rad s-1 (minimum strain 6 × 10-5) were performed using a controlled stress Rheolyst Series AR1000 rheometer (TA Instruments) with a cone and plate geometry system (cone: diameter, 4 cm; angle, 2°; truncation, 57 µm) equipped with a solvent trap. Temperature control (internal resolution 0.016 °C) was provided by two Peltier plates. Equilibrium flow experiments were conducted in a stepped ramp mode with the shear stress as a controlled variable. Oscillatory shear experiments were performed in both frequency and temperature ramp modes. Minimum strain and stress were 0.0143% and 6 mPa, respectively. The Wilhelmy plate method (Sigma 701 automatic tensiometer, KSV Instruments, Ltd.) was employed for measuring the surface tension of the copolymer solutions. Temperature control within 0.05 °C was achieved using a refrigerated bath/circulator. The platinum Wilhelmy plate was washed with acetone, rinsed in Milli-Q water, and flamed until red-hot before each measurement.25

Results and Discussion Semidilute Regime. As our recent study of PluronicPAA solutions demonstrated,12 the viscosity above gelation threshold, even at polymer concentrations yielding strong elastic gels, scaled in accordance with the Rouse modelbased dynamics, which implies a nonentangled regime.23,24 Intrigued by this counterintuitive result, in the present work we addressed the question of how wide, concentration-wise, a nonentangled, semidilute region can be. Surface tension and viscosity data in the absence of added salt for the Pluronic-PAA at several temperatures are presented in Figure 1, plotted vs copolymer bulk concentration. A change in slope was observed in the surface tension curve at a characteristic copolymer concentration, after which the surface tension values decreased more gradually. This change, indicating the onset of aggregation of Pluronic-PAA molecules, shifted from 0.038% at 19.5 °C to 0.015% at 25.5 °C, in accord with the observed critical micellization temperatures (CMT) in Pluronic 26 and Pluronic-PAA20 solutions. (25) Nikas, Y. J.; Puvvada, S.; Blankschtein, D. Langmuir 1992, 8, 2680. (26) Alexandridis, P.; Athanassiou, V.; Fukuda, S.; Hatton, T. A. Langmuir 1994, 10, 2604.

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Figure 2. Phase diagrams for aqueous solutions of Pluronic-PAA with no added salt. C*, CAC, and M stand for overlap concentration, critical aggregation concentration, and weight-average molecular weight, respectively. C* is arbitrarily determined at ηr ) 2, as in ref 29. Solid lines represent relation C* ∼ M-2 and are drawn to guide the eye only. Polydispersities of the polymer fractions used were about 2.0 (ref 13).

Conformations of these copolymers at the air-water interface may be substantially different (see Appendix). The beginning of aggregation in Pluronic-PAA solution at either 19.5 or 25.5 °C manifested by the change of the surface tension behavior (Figure 1A) coincided with the onset of the relative viscosity increase (Figure 1B). It is interesting to observe that at 15 °C, which is well below the gelation threshold,12 both relative and zero-shear viscosities grew as the square root of total polymer concentration (Cp), in accordance with the empirical Fuoss law27 (η ∼ Cp1/2). The relative viscosity exceeded 2 within a wide concentration range (0.01% < Cp e 1%), indicating low overlap concentration (C*). At 15 °C, no transition to the scaling exponents higher than 0.5 (which would imply the beginning of the entangled regime, Ce) was observed. Hence, below gelation temperatures the salt-free28 Pluronic-PAA solutions can be described as unentangled and semidilute. Rubinstein and co-workers29,30 predicted that in this regime the dynamics of the polyelectrolyte chain is Rouse-like. The concentration range C* < Cp < Ce for the long-chain polyelectrolytes under salt-free conditions can be as wide as 3 orders of magnitude, i.e., be substantially wider than in the case of uncharged polymers or polyelectrolytes under Θ-conditions (high-salt limit30). Phase diagrams for Pluronic-PAA developed for different temperatures (Figure 2) show that the unentangled regime (defined as C* < Cp < CAC) became narrower as the temperature rose from 18 to 25.5 °C. No aggregation was observed below 18 °C, and no clearly defined semidilute regime was detected above 26 °C. It must be emphasized that even above CAC the system may still remain within the unentangled regime, as indicated by the validity of the Rouse-like dynamics.14 Thus the region C* < Cp < CAC should be defined as semidilute, unentangled, and nonaggregated. At present, it is hard to define the C > CAC range as unentangled without a lot of guessing. The results in Figure 2 actually illustrate the mechanism of gelation via temperature-induced aggregation of PPO segments.20 Importantly, within the experimental error31 relation C* ∼ M-2 held at all temperatures studied. Since (27) Fuoss, R. M. Discuss. Faraday Soc. 1951, No. 11, 125. (28) Aqueous solutions exposed to air absorb carbon dioxide, which dissociates and yields about 4 µM effective ion concentration (Cohen, J.; Priel, Z.; Rabin, Y. J. Chem. Phys. 1992, 88, 7111). (29) Rubinstein, M.; Colby, R. H.; Dobrynin, A. V. Phys. Rev. Lett. 1994, 73, 2776. (30) Dobrynin, A. V.; Colby, R. H.; Rubinstein, M. Macromolecules 1995, 28, 1859.

all polymer fractions had the same PAA and Pluronic content and polydispersity, it is reasonably to assume that M was proportional to the degree of PAA polymerization (DP). Hence, we observe the relation C* ∼ DP-2 predicted for the rodlike polyelectrolytes in the low salt limit.30 Further evidence for the rodlike conformation of the Pluronic-PAA is the Mark-Houwink parameter a > 132 observed in our SEC experiments at low added salt concentrations.13 Gelled State. The SEC13 and viscometric titration techniques present one drawback of high shear rates developed in capillaries. Although no detectable degradation (depletion of molecular weight) was observed when the same polymer fraction was repeatedly run through our SEC system, potential shear thinning effects cannot be ruled out in a high molecular weight polyelectrolyte solution (reference in ref 28). Steady shear and oscillatory shear experiments in a wide range of shear rates and frequencies provide mechanistic insights into dynamics of physical networks formed in solutions of associative polymers.23,24,33-36 Figure 3 depicts rheological master curves obtained for a 1% Pluronic-PAA solution within a temperature range of 15-45 °C. Complex (η*) and steadyshear (η) viscosities measured at different temperatures were combined to form master curves for a well-defined Pluronic-PAA fraction according to the time-temperature superposition principle.37,38 Curves were shifted horizontally with T ) 15 °C as a reference state. Analysis of the master curves by the Cross model fit39 reveals that there were about 3.9-fold, 1.6-fold, and 3.7-fold differences in the fitted zero-rate and infinite-rate viscosities and consistency, respectively. It should be noted that the values (31) Repetition of the C* measurement at 18 °C with the same polymer fraction in triplicate gave a 14% deviation, which provides an estimate for an accuracy of the C* determination. (32) Parameters a and K are incorporated into the Mark-Houwink equation relating intrinsic viscosity of a polymer solution [η] to the polymer molecular weight ([η] ) KMa) (Cooper, A. R. In Polymers: Polymer Characterization and Analysis; Kroschwitz, J. I., Ed., Wiley: New York, 1990; p 481. Yamakawa, H. Modern Theory of Polymer Solutions; Harper and Row: New York, 1971). (33) Xu, B.; Yekta, A.; Winnik, M. A.; Sadeghy-Dalivand, K.; James, D. F.; Jenkins, R.; Bassett, D. Langmuir 1997, 13, 6903. (34) Prud’homme, R. K.; Wu, G.; Schneider, D. K. Langmuir 1996, 12, 4651. (35) Yu, J. M.; Blacher, S.; Brouers, F.; L’Homme, G.; Je´roˆme, R. Macromolecules 1997, 30, 4619. (36) Chassenieux, C.; Nicolai, T.; Durand, D. Macromolecules 1997, 30, 4952. (37) Ferry, J. D. Viscoelastic Properties of Polymers; Wiley: New York, 1980. (38) Winter, H. H., Mours, M. Adv. Polym. Sci. 1997, 134, 165.

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Figure 3. Master viscosity data obtained for a 1% w/v Pluronic-PAA aqueous solution (pH 7.0) in the temperature range 15-45 °C. In part A, complex viscosity (η*) was measured at oscillatory stress of 60 mPa; in part B, steady-shear viscosity (η) was measured in equilibrium flow experiments. Solid lines show the Cross model fit.39 The data are shifted using a shift factor aT along the abscissa axis with the reference state at 15 °C.

were most sensitive to temperature.40 However, the limiting power-law function was identical (i ) 0.92 in both cases). The inflection on the η* vs aTω function at high frequencies may be related to the contribution of the Rouse modes.41 Overall, we find that there were significant differences (depending on temperature) between η* and η values in the low shear, low-frequency regions. Hence, the Cox-Merz rule42 is not satisfied. This seems to be a common occurrence for associating polymers.33 To test correlation between high-shear SEC data and complex viscosity obtained in a wide range of frequencies at low oscillatory stress, the molecular weight distribution (MWD) was calculated43 based on an η* vs ω master curve (Figure 3B). The MWD was compared to that obtained by SEC with the same polymer sample (Figure 4). It can be seen that the viscosity data that span the frequency range from the Newtonian to the power-law region yielded MWD, which correlated well with the SEC measurement. This finding conforms to the validity of the SEC results13 and hints at the robustness of the MWD computation method. Linear viscoelastic properties of the gelled PluronicPAA solutions were assessed at minimal stresses allowed (39) The Cross model (Cross, M. M.J. Colloid Sci. 1965, 20, 417) suggests the following relation between viscosity η and shear rate (γ˘ )

η)

η o - η∞ 1 + (cγ˘ )i

+ η∞

where ηo is the zero-rate viscosity, η∞ is the infinite-rate viscosity, c is the consistency, and i is the rate index. (40) The zero-rate viscosity (ηo) is a function of the distance to the gelation threshold:  ) T/Tg - 1, where Tg is the gelation temperature determined at a given concentration by the Winter-Chambon method.12 (41) Ferry, J. D. Viscoelastic Properties of Polyisobutylene Melts; Wiley: New York, 1980. (42) The Cox-Merz rule establishes relation between the steady shear rheology of a polymer and its linear viscoelastic behavior (Cox, W. P.; Merz, E. H. J. Polym. Sci. 1958, 28, 619. Milner, S. T. J. Rheol. 1996, 40, 303):

η′′ η′

2 0.5

[ ( )]

η(γ˘ ) = η* ) η′(ω) 1 +

at ω ) γ˘

where η′ and η′′ are real and imaginary components of the viscosity, ω is the angular frequency, and γ˘ is the shear rate. (43) The viscosity function (master curve) was related to the MWD by using a differential computation method (Malkin, A. Y.; Teishev, A. E. Polym. Eng. Sci. 1991, 31, 1590. Shaw, M. T.; Tuminello, W. H. Polym. Eng. Sci. 1994, 34, 159. Gordon, G. V.; Shaw, M. T. Computer Programs for Rheologists; Hanser: Munich, 1994. Liu, Y.; Shaw, M. T. J. Rheol. 1998, 42, 453).

Figure 4. Molecular weight distribution results obtained by SEC at 15 °C13 (dotted line) and by differential method (open points). The final slope magnitude was chosen as 0.92 for the differential method.43

by the rheometer and at T ) 37 °C exceeding the onset of gelation 12 (Figure 5). At this temperature, elastic gels were observed throughout the concentration range studied (0.5 e Cp < 3.0%). The G′ and G′′ data were fitted to the single-mode Maxwell model.44 The increase of the gel strength with the polymer concentration is reflected in the raise of plateau modulus (Go). The data in Figure 5 show that the Maxwell model provided adequate fit in the area of low (10-4-10-2) frequencies at Cp e 1%. That is, at low frequencies, relatively dilute gels exhibited Maxwell liquid behavior (44) A single-mode Maxwell model can be described by the following relations between the frequency-dependent storage (G′) and loss (G′′) moduli:

G′(ω) )

Go$2τ2

; 1 + $2τ2

G′′(ω) )

Go$τ ; 1 + $2τ2 G′′($) ) [G′($)Go - G′($)2]0.5

where Go and τ are the plateau modulus and the terminal relaxation time, respectively (Bird, R. B.; Armstrong, R. C.; Hassager, O. Dynamics of Polymeric Liquids; Wiley: New York, 1987, Vol. I.

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Figure 5. Dynamic moduli of Pluronic-PAA gels as functions of angular frequency at 37 °C. Oscillatory stress is 6 mPa. G′ (circles) and G′′ (triangles) were fitted with the one-mode Maxwell model (solid lines) as described in ref 43. Numbers stand for concentration in w/v %.

G′ ∼ ω2; G′′ ∼ ω1 at ω < ωo where ωo may be defined as a cutoff frequency corresponding to relaxation times longer than the ones of the network.24,45 It should be pointed out that at sufficiently low frequencies most liquids can be described by the above dependencies of G′, G′′ on ω. No clearly defined ωo values were observed as the “glass transition” region spans about 2 orders of magnitude of frequency. As the gels became more concentrated, the ωo values shifted to still lower frequencies, so that at Cp > 3% no liquidlike behavior was observed at 37 °C within the frequency range allowed by the rheometer. Since the single-mode Maxwell model did not fit well the G′ data throughout the entire ω range, it is clear that our system possessed more than one relaxation time. Nevertheless, the plateau moduli could be estimated from the high-frequency region.12 The elasticity of the network at ω > ωo caused a deviation of the loss modulus values predicted by the Maxwell model from the observed ones. This can be rationalized in terms of much higher relaxation times of the networks than the Maxwell fluids. As can be seen in Figure 6, where data is presented in the form of the Cole-Cole plots, regions of calculated G′ (dashed line) matching the experimental data (solid points) became shorter as concentration increased. The G′ data that fit the Maxwell model yield perfect semicircles (solid lines) with G′ ) Go at the intersection with the horizontal axes. The Go values increase with the concentration. To summarize the oscillatory stress results, we conclude that the gelation in the Pluronic-PAA solutions is characterized by the appearance of well-defined, slow relaxation modes (τmax) above frequencies corresponding (45) Adam, A.; Lairez, D. In Physical Properties of Polymeric Gels; Cohen Addad, J. P., Ed.; Wiley: New York, 1996; Chapter 4.

to the Maxwell flow (1/τmax > ωo). At times longer than τmax, the system is adequately described by the single relaxation time τ ) τmax. The departure from the semicircular shape with the increasing storage modulus observed in the high-frequency regime (Figure 6) can be attributed to the Rouse-like modes.46,47 Overall, our system is dissimilar to the solutions of telechelic associative polymers (described by the single-mode Maxwell model) from the multiple relaxation times standpoint. We have recently shown that the relaxation times increase as a function of the Cp values above gelation threshold.12 The dynamics of the gels appears to be consistent with the Rouse model.12 As the polymer concentration increases, the number of multiple junctions48,49 in the gel raises, as discussed below. Network Functionality. The formation of micellelike aggregates in Pluronic-PAA solutions at elevated temperatures has been demonstrated by light scattering,17 SANS,16,18 dye solubilization,21 and DSC13,50 techniques. The micellization occurs due to entropy-driven aggregation of the PPO segments.12,19,50 The micelles work as cross-link junctions at high enough concentrations.51,52 It is reasonably to assume that the long-chain PluronicPAA molecules are shared between several aggregates (junctions), thereby creating bridging chains. These bridging chains are the components of the network responsible for its elasticity.52 The high-frequency equi(46) Khatory, A.; Lequeux, F.; Kern, R.; Candau, S. J. Langmuir 1993, 9, 1456. (47) Fischer, P.; Rehage, H. Langmuir 1997, 13, 7012. (48) Tanaka, F.; Edwards, S. F. Macromolecules 1992, 25, 1516. (49) Tanaka, F.; Edwards, S. F. J. Non-Newtonian Fluid Mech. 1992, 43, 247, 272, 289. (50) Bromberg, L. E.; Goldfeld, M. G. Polym. Prepr. 1998, 39, 681. (51) Tanaka, F.; Ishida, M. Macromolecules 1996, 29, 7571. (52) Tanaka, F. Macromolecules 1998, 31, 384.

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Figure 6. Cole-Cole plots of dynamic moduli of Pluronic-PAA gels at 37 °C. Filled points show the experimental data. A solid line is computed using plateau modulus obtained from the best fit to the G′ vs. ω plots such as those in Figure 5. Dashed line illustrates the best fits from the G′ vs. ω and G′′ vs. ω plots. Numbers stand for polymer concentration in w/v%.

librium storage modulus (Ge) of the network is thus proportional to the molar density of the elastically effective chains (νeff), as has been forwarded in the early theory by Green and Tobolsky (GT)54

Ge ) νeffRT

(1)

where R is the gas constant and T is the absolute temperature. Tanaka and Edwards48,49 and Tanaka and co-workers51,52,55 later modified the GT theory. It should be noted that, despite possible effects of the temperature- and concentration-dependent rates of recombination and disengagement of the chains in the junctions,23,51 in the case when Ge can be measured, νeff could still be obtained from eq 1. In the present study, it was of interest to estimate the functionality of the networks formed above gelation threshold (C > Cgel; T > Tgel) where lifetimes of aggregates are high enough. We have seen that the entanglements of PAA segments are unlikely in the Pluronic-PAA networks, and therefore their contribution to the elasticity can be neglected. Defining functionality (F) as an average number of bridging chains per aggregate

F )2νeff/[aggregate]

(2)

d applying eq 1, we obtain

F ) 2GeN/RTCPPOCp

(3)

where N is the number of hydrophobic (PPO) segments per aggregate, CPPO (mol/g) is the content of PPO segments per Pluronic-PAA, and Cp (g/m3) is the polymer concentration. An estimate of N from 10 to 40 can be retrieved from the concurrent SANS study for an average aggregation number of PPO segments in a core of the aggregate formed in 1% Pluronic-PAA solution in D2O.16,18 We may adopt the higher estimate (N ) 40) that is consistent with the aggregation number (N ∼ 50) obtained in the Pluronic F127 solutions.34 The concentration dependence of F is shown in Figure 7. At T ) 37 °C the viscoelastic gels possess 2-10 bridging chains per junction. The F values represent an average (53) Graessley, W. W. Adv. Polym. Sci. 1982, 47, 68. (54) Green, M. S.; Tobolsky, A. V. J. Chem. Phys. 1946, 14, 80. (55) Tanaka, F.; Ishida, M. Macromolecules 1997, 30, 3900.

Figure 7. Functionality of the cross-links (multiple junctions) in Pluronic-PAA gels at 37 °C as a function of polymer concentration (Cp). The F value is obtained using the estimate N ) 40 and an assumption that Pluronic-PAA on average contains 11 wt % PPO.20

over the entire system and appear to increase linearly with concentration. It should be noted that each PPO segment in a bridging chain has 65 PO units,20 each of which can be considered to be a hydrophobic “functional” group 52 capable of forming a junction with another PO group. As a Pluronic-PAA molecule is likely to contain more than one PPO segment per chain, it is feasible that the PO units belonging to the same molecule would be connected to junctions with at least three paths to the gel. The chains connected at both ends to the aggregates will be elastically active. Effective F values above 2 (Figure 7) support the gel model that is explicated by the ScanlanCase criterion.56,57 Conclusions Rheological properties of semidilute solutions and gels of a hydrophobically modified polyelectrolyte were studied in the absence of added salt. Self-assembling poly(ethylene oxide)-b-poly(propylene oxide)-b-poly(ethylene oxide)-gpoly(acrylic acid) was chosen as a model copolymer. The (56) Scanlan, J. J. Polym. Sci. 1960, 43, 501. (57) Case, L. C. J. Polym. Sci. 1960, 43, 397.

5812 Langmuir, Vol. 14, No. 20, 1998

onset of aggregation of Pluronic-PAA molecules measured by surface tension shifted concomitantly with the onset of the relative viscosity increase. Both relative and zeroshear viscosities grew as the square root of total polymer concentration below the gelation threshold, in accordance with the Fuoss law. This is an evidence of the semidilute and unentangled regime in the Pluronic-PAA solutions of up to 1% concentration. The semidilute regime (polymer concentrations between overlap concentration C* and the onset of aggregation) becomes narrower with the temperature. This result is in accord with the mechanism of gelation via temperature-induced aggregation of PPO segments.20 The relation C* ∼ M-2 predicted for the rodlike polyelectrolytes in the low-salt limit30 is observed. In the steady-shear and oscillatory shear experiments, we find that there are significant differences between complex and steady-shear viscosities in the low-shear, lowfrequency regions, in contrast to the Cox-Merz rule. Gelation in the Pluronic-PAA solutions is characterized by the appearance of well-defined, slow relaxation modes (τmax) above frequencies corresponding to the Maxwell flow. At times longer than τmax the system is adequately described by the single relaxation time τ ) τmax. The highfrequency modes around plateau modulus appear to be Rouse-like. The gel elasticity can be described by network functionality whereby the propylene oxide groups serve as hydrophobic “functional” group capable of forming pairwise junctions with another set of PO groups. Acknowledgment. The author is grateful to Prof. Michael Rubinstein for helpful insights into state-of-theart theories.

Bromberg

Appendix To estimate average area per molecule (A), the simplest form of the Gibbs adsorption isotherm was applied to the area of 10-4% < Cp < 10-2%58,59

A ) -[(NA/RT)(dγ/d(ln Cp))]-1 where NA is Avogadro’s number, γ is the surface tension, R is the molar gas constant, and T is the absolute temperature. Estimates of A ) 5.4 and 5.0 nm2 were obtained at 19.5 and 25.5 °C, respectively. This is 5-10-fold higher area per molecule as compared to Pluronics of 200-300-fold lower molecular weights.26 The micelle cross-section area of ∼1.2 nm2 was obtained for Pluronic F127 solutions.34 As the higher value of the ratio (APluronic-PAA/APluronic) estimate is below (MPluronic-PAA/MPluronic)1/2,60 the structures of Pluronic-PAA and the parent Pluronic F127 61 on the air-water interface can be quite different. A protrusion of PAA and PEO segments in the water subphase can be suggested.61-63 LA980737Q (58) Chattoraj, D. K.; Birdi, K. S. Adsorption and the Gibbs Surface Excess; Plenum Press: New York, 1984. (59) Rosen, M. J. Surfactants and Interfacial Phenomena; Wiley: New York, 1989. (60) de Gennes, P. G. Scaling Concepts in Polymer Physics; Cornell University Press: Ithaca, NY, 1979. (61) Phipps, J. S.; Richardson, R. M.; Cosgrove T.; Eaglesham, T. Langmuir 1993, 9, 3530. (62) Hurter, P. N.; Scheutjens, J. M. H. M.; Hatton, T. A. Macromolecules 1993, 26, 5030. (63) Hurter, P. N.; Scheutjens, J. M. H. M.; Hatton, T. A. Macromolecules 1993, 26, 5592.