Langmuir 1999, 15, 4335-4343
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Physical Gelation of Hydrophobically Modified Polyelectrolytes. 1. Homogeneous Gelation of Alkylated Poly[acrylamide-co-sodium acrylate] Y. Yang,†,‡ D. Schulz,§ and C. A. Steiner*,| Graduate Program in Polymer Chemistry, The City University of New York, New York, New York 10031, Exxon Research and Engineering Company, Annandale, New Jersey, 08801, and Department of Chemical Engineering, The City College of New York, and Graduate Faculties of Chemistry and Engineering, The City University of New York, New York, New York 10031 Received March 10, 1998. In Final Form: March 8, 1999 Stiff, viscoelastic hydrogels have been fabricated from hydrophobically modified poly(acrylamide-cosodium acrylate) (HRAM). These materials are macroscopically homogeneous but microscopically heterogeneous, containing hydrophobic aggregates that bridge polymer chains in a three-dimensional network. The charge level at which the dynamic storage modulus is maximized for a given polymer concentration corresponds closely with the charge level giving a maximum in hydrophobicity of the aggregates, suggesting a link between the mechanical stability of these aggregates and their ability to exclude water effectively. The gel point, where the system first exhibits viscoelastic behavior, may also be identified from discontinuities in the hydrophobicity (as measured by the fluorescence spectra of solubilized pyrene) and equivalent conductivity with polymer concentration. The effects of various aspects of polymer architecture on hydrogel properties have been investigated. The dynamic storage modulus of the network exhibits a maximum with backbone charge at constant polymer concentration, with a charge level in the range 3.58-4.81 mol % Na acrylate producing the stiffest gels in C8-substituted HRAMs. An increase of two methylene units in the length of the side chains results in up to 1 order of magnitude increase in the dynamic storage modulus of the gels at constant polymer molecular weight. The anionic surfactant sodium dodecyl sulfate (SDS) exhibits a synergistic effect on gel formation by promoting the formation of intermolecular hydrophobic aggregates despite the presence of negatively charged groups on the backbone. In contrast, the effect of sodium chloride on gel properties is not as pronounced. A literature review on the effects of polymer architecture on the macroscopic phase behavior of hydrogel-forming hydrophobically modified water-soluble polymers is presented.
Introduction It is well-known that hydrophobically modified watersoluble polymers (HMWSPs) self-assemble in aqueous solution, with the hydrophobic side chains forming micellelike aggregates that exclude water. When these aggregates bridge multiple polymer backbones, a high bulk viscosity results. This property has been exploited industrially in applications such as viscosification of solutions and stabilization of dispersions. There is a substantial body of literature detailing the effects of structural aspects of the polymer on the solution properties of aqueous systems containing HMWSPs, with particular attention paid to the viscosity. In addition to forming highly viscous solutions, aqueous systems containing HMWSPs may organize into viscoelastic hydrogels. The hallmark of a viscoelastic material is the presence of a so-called rubbery plateau in its dynamic rheological spectra. This means that under an oscillatory applied shear, there exists some range of applied frequency, ω (s-1), over which the material behaves more like an elastic solid than a viscous fluid, and its response * To whom correspondence should be addressed. † Present address: National Starch & Chemical Co., Bridgewater, NJ 08807. ‡ Graduate Program in Polymer Chemistry, The City University of New York. § Exxon. | Department of Chemical Engineering, The City College of New York, and Graduate Faculties of Chemistry and Engineering, The City University of New York.
is independent of applied frequency. Thus the dynamic storage (or “elastic”) modulus, G′, exceeds the dynamic loss (or “viscous”) modulus, G′′, and G′ is invariant with ω. In constrast, in polymer solutions G′′ is everywhere greater than G′. Thus the physical distinction between a hydrogel and a polymer solution is that the intermolecular linkage points in a gelled network are mechanically stable over some range of applied shear stress, while those in a solution are not. Mechanical stability implies thermodynamic stability as well, and in this report we will show that the hydrophobic aggregates in nongelled aqueous solutions of HMWSPs contain relatively more water than in the gelled systems, indicating that microphase separation in nongelled systems is incomplete. Potential applications of hydrogels made from HMWSPs include controlled release of pharmaceutical1 or agricultural agents, where the microdomains serve as reservoirs for an organic solute to be released over long times, or separation processes, where the hydrophobic domains serve as sinks for organic solutes permeating the aqueous network. While the existence of hydrogels has been reported for many HMWSP systems, relatively little attention has been paid to the effects of polymer architecture on the physical properties of the materials. For hydrogels to form at all, the polymer chains must first be solubilized to a measurable extent in the solvent, a requirement that poses difficulties due to the differences in polarity of the (1) Varelas, C. G.; Dixon, D. G.; Steiner, C. A. J. Controlled Release 1995, 34, 185.
10.1021/la980285h CCC: $18.00 © 1999 American Chemical Society Published on Web 05/14/1999
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backbones and the side chains. Once a gel has formed, its mechanical strength will depend on the balance between forces driving the side chains into aggregates and those opposing the aggregation process. The driving force for aggregation is directly related to the concentration of available (aqueous phase) side chains in the solution, the energy of interaction binding the side chains in stable aggregates, and the conformational entropy of the backbone. It is inversely related to the magnitude of the intermolecular electrostatic repulsion arising due to the charge (if any) on the backbones. This gives rise to a very complex relationship between gel properties and various aspects of polymer architecture. For example, long side chains will be relatively insoluble in aqueous solutions, and these groups will also have an adverse effect on the conformational entropy of the backbones due to steric hindrance. On the other hand, long side chains will have a high driving force for aggregation due to their incompatibility with water, and a high negative free energy of binding within hydrophobic aggregates should such aggregates form.2,3 A high level of charge on the polymer backbone will render its radius of gyration in aqueous solution relatively high, driving a high proportion of side chains into solution. However, the backbone charge will also make the polymer relatively inflexible, as well as resistant to intermolecular hydrophobic aggregation due to electrostatic repulsion. Hydrogel networks may form in water, brine, or mixed aqueous/organic solvents. Simple surfactants below the critical micelle concentration (cmc) have been found in many cases to induce gel formation by forming aggregates resembling mixed micelles with side chains from multiple polymer molecules, as referenced in detail below. In addition to their characteristic two-phase structure at the microscopic level, some amphiphilic hydrogels phase separate from the bulk precursor solution, either at ambient temperature or upon heating. This macroscopic phase behavior has important practical ramifications. For example, swelling and deswelling of hydrogels, as discussed in a review article by Gehrke,4 may be exploited to generate a mechanical force, to dewater coal slurries, e.g., or to release drugs embedded in the gel matrix at a controlled rate. Macromolecules such as proteins and enzymes will be excluded from a shrunken hydrogel phase and form a concentrated supernatant.5 Also, gels are being used commercially as an intermediary state for the production of fibers and synthetic membranes,6 where the ultimate properties of the dehydrated material derive from the gel structure in the swollen state. We present below a literature review aimed at identifying the influence of structural aspects of HMWSPs on their macroscopic phase behavior in the gelled state, followed by results of our investigations on the effects of polymer architecture on the structure and properties of a hydrophobically modified poly(acrylamide)-based polymer that forms macroscopically homogeneous hydrogels. In a subsequent report we will present our results on macroscopically heterogeneous hydrogels formed from other poly(acrylamide)-based copolymers. (2) Molyneux, P. In Water-Soluble Polymers: Synthesis, Solution Properties and Applications; Shalaby, S. W., McCormick, C. L., Butler, G. B., Eds; Symposium Series Vol. 467; American Chemical Society: Washington, DC, 1991; ACS p 232. (3) Annable, T.; Buscall, R.; Ettelaie, R.; Whittlestone, D. J. Rheol. 1993, 37, 695. (4) Gehrke, S. H. In Advances in Polymers Science; Springer-Verlag: Heidelberg, 1993; Vol. 110, p 81. (5) Freitas, R. F. S.; Cussler, E. L. Chem. Eng. Sci. 1987, 42, 97. (6) Keller, A. Faraday Discuss. 1995, 101, 1.
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Background and Literature Review In an effort to elucidate the influence of various structural features on the tendency for gels to form and the macroscopic phase behavior of aqueous systems containing HMWSPs, we have conducted an extensive review of the literature on gelation of HMWSPs. Note that in this discussion, we include as “gels” systems with reportedly very high (∼104 cP) apparent viscosities and shear-thinning behavior, even when dynamic rheological evidence was not available to confirm their viscoelastic character. Table 1 gives details of the structure of all of the polymers discussed below, along with the appropriate references. Our review has led to some interesting insights. For example, ethyl hydroxyethyl cellulose (EHEC) solutions in water exhibit a drop in viscosity with increasing temperature. On the other hand, when ionic surfactants are present, the same polymer forms homogeneous viscoelastic hydrogels at temperatures ∼40-50 °C and phase separates above a cloud point (CP) that increases with surfactant concentration.7-11 Thus the surfactant enables the polymer molecules to form a stable, three-dimensional network, while at the same time rendering the polymer more hydrophilic (hence more soluble) by adsorbing, headgroup out, onto the ethyl groups of the EHEC. On the other hand, hydrophobically modified (HM) EHEC containing 1.7 mol % branched nonylphenyl groups exhibits relatively high viscosity at 25 °C in the presence of long-chain alcohols, inorganic salts, or anionic surfactants and a lower cloud point than similar solutions of the parent polymer.12 Thus the reduced water solubility of the hydrophobically modified polymer and its tendency to interact with amphiphilic cosolutes drive both its phase behavior and its rheological properties. Reports from different laboratories on hydrophobically modified ethoxylated urethane (HEUR), which is a polymer consisting of a linear poly(ethylene oxide) chain end-capped with a water-insoluble hydrocarbon, indicate that this polymer tends to form a homogeneous viscoelastic network in ionic surfactants and water when the polymer contains on average 1.7 hydrophobic groups per chain (i.e., 70% of the macromolecules are disubstituted and 30% are monosubstituted),13,14 but if the hydrophobe substitution level is 100% the HEUR will phase separate out of solution with a sulfonated surfactant.15 Water-soluble hydrophobically modified hydroxyethyl cellulose (HMHEC) has been shown to exhibit both homogeneous16 and heterogeneous17,18 gelation in surfactant solutions below the critical micelle concentration (cmc), and also heterogeneous gelation above a critical concentration of polymer in water (7) Carlsson, A.; Kralstrom, G.; Lindman, B. Colloids Surf. 1990, 47, 147. (8) Nystrom, B.; Kjoniksen, A.-L.; Lindman, B. Langmuir 1996, 12, 3233. (9) Nystrom, B.; Walderhaug, H.; Hansen, F. K.; Lindman, B. Langmuir 1995, 11, 750. (10) Cabane, B.; Lindell, K.; Engstrom, S.; Lindman, B. Macromolecules 1996, 29, 3188. (11) Zhang, K.; Karlstrom, G.; Lindman, B. Prog. Colloid Polym. Sci. 1992, 88, 1. (12) Thuresson, K.; Nilsson, S.; Lindman, B. Langmuir 1996, 12, 2412. (13) Zhang, K.; Xu, B.; Winnik, M. A.; Macdonald, P. M. J. Phys. Chem. 1996, 100, 9834. (14) Xu, B.; Yekta, A.; Li, L.; Masoumi, Z.; Winnik, M. A. Colloids Surf. A: Physicochem. Eng. Aspects 1996, 112, 239. (15) Mast, A. P.; Prud′homme, R. K.; Glass, J. E. Langmuir 1993, 9, 708. (16) Tanaka, R.; Meadows, J.; Williams, P. A.; Phillips, G. O. Macromolecules 1992, 25, 1304. (17) Sivadasan, K.; Somadundaran, P. Colloids Surf. 1990, 49, 229. (18) Goddard, E. D. J. Colloid Interface Sci. 1992, 152I, 578.
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Table 1. Structural Features of Gel-Forming HMWSPs classification
hydrophobea
EHEC
CH3CH2
HM-EHEC
branched nonylphenyl C16H33-
HEUR HMHEC
RAM
HRAM HM-(poly-Naacrylate) HRAM-AA HPMC HM-PGA HM-poly(maleic anhydride-co-ethyl vinyl ether) a
C8 C12 C12 C12-C24 C12-C18 C12-C24 C12 C16 branched nonylphenyl N-C6N-methyl-N-C5N,N-diC6N-4-ethylbenzyl N-methyl-N-4ethylbenzyl N-4-ethylphenyl C8, C10 C12-C18 C18 N-(4-C10-phenyl) C12 HO(CH2)3C12 or C14 C8 or C12
hydrophobe level
molecular weight
water soluble (yes/no)
refs
1.9 per anhydroglucose " " 1.3-1.5 per anhydroglucose 0.6-0.7 per anhydroglucose 1.7 mol %
660 000 (Mv) 150 000 (Mv) 80 000 (Mn) 80 000 (Mn) 100 000 100 000
yes yes yes yes yes yes
[7] [7] [8-10] [8-11] [12] [12]
1.7 per chain 1.2-2 per chain 2.1 wt % 1.3 wt % 4.2-8.0 wt % 1.2% 1 wt % 2 g/dL) blends of hydrophobically modified (end-capped) poly(ethylene glycol) with the parent watersoluble PEG, where neither polymer alone tended to phase separate,44 and polymer JR 30M (Union Carbide), a high MW cationic cellulose derivative, in SDS.38 As a special case of collapsed or collapsible gels we will also consider some chemically cross-linked systems. Both unmodified and hydrophobically modified cross-linked poly(acrylic acid) gels collapse to the same extent on absorption of cationic surfactant, indicating that Coulombic attraction plays the major role in the network structure of these systems. Still, anionic surfactant can bind to these networks and promote shrinkage, provided the hydrophobe level is high enough that the tendency to form hydrophobe/hydrophobe interactions can prevail over electrostatic repulsion.45 On the other hand, in cross-linked gels of polyacrylamide modified with poly(ethylene oxide) pendant groups, swelling is higher in SDS than in water and increases with [SDS] up to the cmc before dropping back down.46 This was attributed to the inherent incompatibility between the water-soluble backbones and the more hydrophobic side chains in these polymers, and the increased osmotic pressure inside the gel arising due to absorption of the SDS. Cross-linked gels of poly(Nisopropylacrylamide) (NIPA) gels,5,47-51 which collapse at 34 °C, cellulose ethers with some incorporated hydrophobe,52 which collapse in the range 35-60 °C, and poly(2-hydroxyethyl methacrylate) (poly-HEMA)53 have been found to collapse at temperatures at or near the lower (37) Thalberg, K.; Lindman, B. Langmuir 1991, 7, 277. (38) Leung, P. S.; Goddard, E. D. Langmuir 1991, 7, 608. (39) Branham, K. D.; Davis, D. L.; Middleton, J. C.; McCormick, C. L. Polymer 1994, 35, 4429. (40) Alli, D.; Bolton, S.; Gaylord, N. J. Appl. Polym. Sci. 1991, 42, 947. (41) Sinquin, A.; Hubert, P.; Marchal, P.; Choplin, L.; Dellacherie, E. Colloids Surf. A: Physicochem. Eng. Aspects 1996, 112, 193. (42) McCormick, C. L.; Chang, Y. Macromolecules 1994, 27, 2151. (43) Thuresson, K.; Nilsson, S.; Lindman, B. Langmuir 1996, 12, 530. (44) Annable, T.; Ettelaie, R. J. Chem. Phys. 1996, 93, 899. (45) Philippova, O. E.; Hourdet, D.; Audebert, R.; Khokhlov, A. R. Macromolecules 1996, 29, 2822. (46) Piculell, L.; Hourdet, D.; Iliopoulos, I. Langmuir 1993, 9, 3324. (47) Hoffman, A. S. J. Controlled Release 1987, 6, 297. (48) Hirotsu, S. J. Chem. Phys. 1988, 88, 427. (49) Beltran, S.; Hooper, H. H.; Blanch, H. W.; Prausnitz, J. M. J. Chem. Phys. 1990, 92, 2061. (50) Bai, T. H.; Okano, T.; Kim, S. W. J. Polym. Sci. B: Polym. Phys. Ed. 1990, 28, 923. (51) Abe, T.; Egawa, H.; Ito, H.; Nitta, A. J. Appl. Polym. Sci. 1990, 40, 1223. (52) Harsh, D. C.; Gehrke, S. H. J. Controlled Release 1991, 17, 175. (53) Gehrke, S. H.; Biren, D.; Hopkins, J. J. J. Biomater. Sci., Polym. Ed. 1994, 6, 375.
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critical solution temperature (LCST) of the component macromolecules. Swelling of cross-linked partially hydrolyzed polyacrylamide gels has been found to depend on the solvent composition in acetone/water solutions54,55 and the pH in water,56 again reflecting the importance of chain solubility, hence dimensions, on the macroscopic phase behavior of hydrogel systems. Taken together, the results of these studies show that for a given HMWSP backbone, macroscopic phase separation is observed under conditions where the polymer itself is only marginally soluble (i.e., near its critical point). Further, the process of precipitated gel formation is promoted by conditions such as the presence of surfactant below the cmc or shielding of backbone charges by salt, which drive aggregation of the hydrophobic side chains. A critical level of long-chain hydrophobic substituents is a requirement of the formation of physical (i.e., not chemically cross-linked) gel precipitates, and the side chains must be solubilized first in the bulk to allow them to assemble. In this and a subsequent article57 we discuss the phase behavior and hydrogel properties of new hydrophobically modified polyacrylamide-based polymers. This paper deals with water-soluble terpolymers of acrylamide (AM), alkylacrylamide (R), and sodium acrylate (formed by hydrolysis (H) of the amide), abbreviated HRAM. HRAM forms homogeneous viscoelastic gels in water, 10 mM NaCl, and sodium dodecyl sulfate (SDS) solutions. The second paper57 will describe our results on macroscopic phase separation and gel formation in poly(AM-cododecylamine-co-Na acrylate-co-acrylic acid), or HRAMAA, with a higher hydrophobicity than HRAMs that did not phase separate under similar conditions. Materials and Methods The polymers used in this study were prepared by micellar copolymerization of acrylamide (AM) and alkylacrylamide (R) followed by hydrolysis (H) with NaOH to introduce sodium acrylate (NaA) groups on the backbone. Details of their synthesis and aqueous solution properties are reported elsewhere.58 All HM polymers used in this study had linear alkyl side chains 8 or 10 carbons in length, hydrophobe levels of 1.5 wt %, and weight average molecular weights (Mw) (3.5 ( 0.4) × 106 for the C8substituted polymers and (3.7 ( 0.4) × 106 for the C10 material. Hydrolysis levels ranged from 1.53 to 24.1 mol % (based on total monomer units). Polyacrylamide (PAM) and hydrolyzed polyacrylamide (HPAM) with a hydrolysis level of 23.8 mol %, synthesized by micellar polymerization of AM, were used as the control polymers. Mw of the PAM and HPAM was (1.5 ( 0.3) × 106. Polymers are designated HRAMn-x or HPAM-x, where n is the number of carbons in the side chains and x is the mol % NaA. Sodium dodecyl sulfate (SDS) was obtained from J. T. Baker Chemical Co. Sodium chloride and pyrene were from Aldrich. All samples were prepared by mixing dry polymer with water or aqueous SDS solutions containing 0.5-10 mM surfactant (critical micelle concentration (cmc) for SDS in pure water ) 8 mM at 25 °C59) for 24 h under very mild stirring. For samples to be used for fluorescence measurements, the water was first saturated with pyrene (solubility ) 6 × 10-7 M60). Samples were (54) Ilavsky, M. Macromolecules 1982, 15, 782. (55) Tanaka, T. Phys. Rev. Lett. 1978, 40, 820. (56) Gehrke, S. H., Andrews, G. P., Cussler, E. L. Chem. Eng. Sci. 1986, 41, 2153. (57) Wu., S.-Y.; Yang, Y.; Varadaraj, R.; Couzis, A.; Steiner, C. A. Manuscript in preparation. (58) Yang, Y. Synthesis and Characterization of Hydrophobically Modified Polyacrylamide-Based Polymers and Their Hydrogels. Ph.D. Thesis, The City University of New York, 1996. (59) Mukerjee, P.; Mysels, K. In Critical Micelle Concentrations of Aqueous Surfactant Systems; National Bureau of Standards: Washington, DC, 1971. (60) Binana-Limbele, W.; Zana, R. Macromolecules 1987, 20, 1331.
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Langmuir, Vol. 15, No. 13, 1999 4339 Table 2. Solubilility and Gel Points of HRAMs in Water58 polymer
solubility (g/dL)
gel point (g/dL)
HRAM8-1.53 HRAM8-3.58 HRAM8-4.81 HRAM8-24.1 HRAM10-0.26 HRAM10-0.48 HRAM10-2.28 HRAM10-23.7
>0.8 >0.8 >0.8 >1.5 0.8 >1.5
0.2-0.3 0.2-0.3 0.5 1.5-3 no gel forms no gel forms 0.05 0.6-0.7
Figure 1. Identification of the gel point of HRAM10-23.7: (open symbols) G′′, (closed symbols) G′; (O) 0.6 g/dL; (0) 0.7 g/dL (gel point); (4) 1.5 g/dL. allowed to stand at least 72 h before any measurements were made to allow the systems to stabilize. Dynamic mechanical measurements were performed using a Haake (Fisons Instruments, Edison, NJ) rotovisco RV-20 rheometer fitted with a parallel-plate sample cell operating in an oscillatory mode. The frequency range of the measurements was from 0.136 to 60.4 s-1. The rheometer is interfaced to a personal computer and driven by a software package called OSC20 supplied by the manufacturer. The torque and phase angle were measured and the storage and loss moduli of the samples were obtained. All measurements were conducted at 25 °C. Steady-state fluorescence measurements of polymer solutions and gels were performed on a Spex Fluorolog-2 Model 112A fluorescence spectrophotometer (Spex Industries, Inc., Edison, NJ). The pyrene spectra were obtained by exciting the solutions at 310 nm and recording the emission over the range 350-450 nm at room temperature. The electrolytic conductivity of polymer solutions at room temperature was measured using a WPA CM 35 conductivity meter (WPA Scientific Instrument, Linton Cambridge, England).
Figure 2. Effects of polymer concentration and hydrolysis level on G′0 of HRAM8 hydrogels. Hydrolysis level (mol % NaA) ) (O) 1.53, (0) 3.58, (]) 4.81.
Results and Discussion The hydrogels we investigated in this study are stiff, macroscopically homogeneous, clear materials. Unlike polymer solutions, the gels may be lifted from their containers with a spatula and will retain their shape even when not supported by the vessel walls. They are compressible and will spring back to their original shape on release of pressure, and they may be cut with a razor or other sharp cutting edge, Viscoelastic Properties in Water. We define the gel point of a particular polymer as the lowest concentration of that polymer in water at which the frequency spectra of the storage and loss modulus (G′ and G′′, respectively) coincide over the frequency range ω ) 6.28-60.4 s-1. This range was selected because it encompassed the plateau region in the rheological spectra of all of our gels. Typical rheological spectra at concentrations below, at, and above the gel point are shown in Figure 1 for HRAM10-23.7. The transition from solution to viscoelastic gel as the polymer concentration is increased may be seen clearly. Gel points in water for all the HRAMs in this study were reported elsewhere58 and are given in Table 2. Neither of the control polymers formed gels up to a concentration of at least 1.5 g/dL, demonstrating the unmistakable role of the side chains in gelation. No networks formed with the unhydrolyzed RAMs or low (0.26 or 0.48 mol %) NaA level HRAMs, whose solubility in water is very low (∼0.1-0.2 g/dL). However, all of the HRAMs with NaA levels g1.53 mol % form clear, macroscopically homogeneous, viscoelastic hydrogels in water. The gel point of HRAM
Figure 3. Effects of polymer concentration and hydrolysis level on G′0 of HRAM10 hydrogels. Hydrolysis level (mol % NaA) ) (b) 2.28, (2) 23.7, (0) HRAM8-3.58 (included for comparison).
increases with NaA level at constant side chain length. Thus gel formation requires a certain minimum level of backbone charge to permit solubilization of the polymer in water, but is inhibited by intermolecular electrostatic repulsion when the backbone charge is very high. Similar results have been reported elsewhere with HRAM.29 In addition, the gel point decreases with hydrophobe length at constant NaA level and Mw. This is perhaps the most significant result we presentsit demonstrates (as will be reinforced with additional data, below) the importance of small differences in the water-solubility of the side chains on both the solubility and the gel properties of HMWSPs in water. The structure of the polymer has a profound effect on the plateau storage modulus, G′0 of HRAM gels in water. This is illustrated in Figures 2 and 3, showing G′0 vs polymer concentration for HRAM8 and HRAM10 hydrogels, respectively. (Note: G′0 is defined as the average G′
4340 Langmuir, Vol. 15, No. 13, 1999
at ω > 6.28 s-1 (seven frequencies total).) G′0 of all the gels goes up with polymer concentration. This is due both to an increase in the total hydrophobe content of the system and a decrease in the degree of dissociation of the polyelectrolytes,61 permitting more extensive intermolecular association. All of the gels exhibit a break in the function G′0 vs [polymer] followed by a steep increase in the slope. The position of this break will be seen to coincide with discontinuities in functions of other properties as well. In addition, G′0 at constant polymer concentration exhibits a maximum with NaA level on the backbone. This maximum occurs somewhere between 1.53 and 4.81% NaA for HRAM8 (Figure 2); we postulate the existence of an analagous peak for HRAM10. The maximum reflects the balance between the dual effects of backbone charge, i.e., permitting solubilization of the hydrophobes in the aqueous phase, on one hand, while at the same time inhibiting the close approach required for intermolecular aggregation of the hydrophobes. The dynamic storage modulus of the C10 gels (Figure 3) is an order of magnitude higher than that of the C8 gels (Figure 2) for constant polymer concentration and hydrolysis level. Thus the C10 aggregates are more resistant to shear and to intermolecular electrostatic repulsion than the C8 aggregates, as expected given that the activation energy for disengagement of hydrophobic clusters increases with hydrophobe length.3 In common with simple surfactant micelles, the aggregates of C10 side chains probably have a higher aggregation number than those of C8 chains, a factor that would contribute to a higher G′ as well. In addition, on the basis of earlier studies,24 we expect that a only a fraction (∼30% for HMHEC) of the side chains are incorporated into these assemblies. Thus it is possible that there is a higher total number of aggregates in the C10 system as well, given that the longer hydrophobes are more driven to aggregate in solution. This will only be the case if the process of aggregation is not opposed by limits on the conformational entropy of the backbone posed by the longer side chains, which apparently is not a significant effect in our systems. Conductivity of HRAM Systems in Water. The equivalent conductivity, Λ, of our polymer solutions and gels reveals interesting correlations between the degree of dissociation (hence the radius of gyration) of the macromolecules and the rheological properties of the systems. Λ, in units of Ω-1 m2 equiv-1, is defined as the electrolytic conductivity κ (Ω-1 m-1) per unit concentration (equiv/L). It provides a measure of the degree of dissociation, R, of the charged species weighted by the quantity m (m2 s-1 V-1), defined as the sum of the mobilities of all the ions under an applied voltage (V). In our polyelectrolyte solutions and gels, the mobility of the polymer backbones is small compared with that of the Na+ counterions and may be neglected. The effects of polymer structure on Λ are shown in Figure 4. Here Λ was obtained by dividing the measured electrolytic conductivity, κ, by both the NaA level and polymer concentration, giving the conductivity per unit sodium acrylate in each system. The degree of dissociation of a polyelectrolyte goes down with total charge present in the solution. Moreover, the mobility of the free Na+ ions will be inversely related to the viscosity of the solution, which goes up with NaA level at constant HRAM concentration.58 Thus the decrease in Λ with NaA level seen at low (
