Nonionic Surfactant Mixtures with an Anionic

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Interactions of Cationic/Nonionic Surfactant Mixtures with an Anionic Hydrogel: Absorption Equilibrium and Thermodynamic Modeling Henry S. Ashbaugh,* Lennart Piculell, and Bjo¨rn Lindman Physical Chemistry 1, Center for Chemistry and Chemical Engineering, Lund University, Box 124, S-221 00 Lund, Sweden Received August 9, 1999. In Final Form: November 16, 1999 Association of mixed dodecyl trimethylammonium bromide (C12TAB) and octaethylene glycol monododecyl ether (C12E8) micelles with a lightly cross-linked sodium polyacrylate gel is examined as a function of surfactant concentration and mixed-surfactant fraction. The interaction of the surfactants with the gel is quantified by absorption isotherms measured using a surfactant-specific electrode, to determine the unabsorbed C12TA+ concentration, and by 1H NMR, to determine the relative fraction of unabsorbed C12E8 to C12TA+. These experiments provide, for the first time, a detailed assessment of the relative affinity of a polyelectrolyte gel for surfactants of varying charge. As might be expected, the gel preferentially absorbs C12TA+ under most conditions owing to electrostatic attraction to the oppositely charged gel. For low initial C12E8 surfactant fractions and moderate C12TA+ concentrations, however, the situation is reversed and the nonionic surfactant is preferentially absorbed. Furthermore, although pure C12TA+ exhibits only one cooperative absorption regime, multiple cooperative absorption regimes are observed with increasing C12E8 surfactant fractions. An absorption model is developed that combines the closed association model, describing ionic surfactant association with an oppositely charged polyelectrolyte, with a mixed micellization model, describing nonionic surfactant association with polyelectrolyte-bound ionic micelles. The model semiquantitatively captures many of the observed absorption trends and provides a basis for interpreting the anomalous absorption behavior with changing surfactant composition. In particular, the model captures the effects of mixed-surfactant micellization in bulk aqueous solution coupled with mixed-surfactant aggregation within the gel network.

* To whom correspondence should be addressed. Present address: Princeton University, Department of Chemical Engineering, The Engineering Quadrangle, Olden St., Princeton, NJ 08544-5263. E-mail: [email protected].

isotherms of the surfactant to the polyelectrolyte. The strength of the attraction between these species is such that the surfactant concentration at which the complex forms, referred to as the critical aggregation concentration (cac), is 1-3 orders of magnitude lower than the critical micelle concentration (cmc) of the surfactant alone.11 The aggregation numbers of surfactants bound to polyelectrolytes are comparable to those of the polymer-free solution,12,13 consistent with the picture that the polyelectrolyte stabilizes the micelles acting as a macrocounterion that does not participate in the aggregate itself.14 In this view, the driving force for association is primarily entropic, resulting from the release of simple counterions to bulk solution upon complexation.15-17 As such, the cac is suppressed with increasing salt concentration, in contrast to the cmc, which decreases with added salt owing to screened headgroup interactions.12,18 The flexibility, linear charge density, and relative hydrophobicity of the polyelectrolyte backbone, however, also moderate the extent by which the cac is lower than the cmc.10,13,15-17 Ionic surfactants display a similar affinity for oppositely charged polyelectrolyte gels.18-29 Moreover, complexation within a gel decreases its volume markedly, which is useful

(1) Interactions of Surfactants with Polymers and Proteins; Goddard, E. D., Ananthapadmanabhan, K. P., Eds.; CRC Press: Boca Raton, 1993. (2) Polymer-Surfactant Systems; Kwak, J. C. T., Ed.; Marcel Dekker: New York, 1998; Vol. 77. (3) Felgner, P. L.; Gadek, T. R.; Holm, M.; Roman, R.; Chan, H. W.; Wenz, M.; Northrop, J. P.; Ringold, G. M.; Danielsen, M. Proc. Natl. Acad. Sci. U.S.A. 1987, 84, 7413. (4) Zhu, N.; Liggitt, D.; Liu, Y.; Debs, R. Science 1993, 261, 209. (5) Kiser, P. K.; Wilson, G.; Needham, D. Nature 1998, 394, 459. (6) Kokufuta, E.; Zhang, Y.-Q.; Tanaka, T.; Mamada, A. Macromolecules 1993, 26, 1053. (7) Goddard, E. D. Colloids Surf. 1986, 19, 301. (8) Lindman, B.; Thalberg, K. In Interactions of Surfactants with Polymers and Proteins; Goddard, E. D., Ananthapadmanbhan, K. P., Eds.; CRC Press: Boca Raton, FL, 1993; p 203.

(9) Hansson, P. Polyelectrolyte induced assembly of ionic surfactants. Doctoral Thesis, Uppsala University, 1995. (10) Hansson, P.; Lindman, B. Curr. Opin. Colloid Interface Sci. 1996, 1, 604. (11) Hayakawa, K.; Kwak, J. C. T. J. Phys. Chem. 1982, 86, 3866. (12) Hansson, P.; Almgren, M. J. Phys. Chem. 1996, 100, 9038. (13) Anthony, O.; Zana, R. Langmuir 1996, 12, 1967. (14) Chu, D.; Thomas, J. K. J. Am. Chem. Soc. 1986, 108, 6270. (15) Wallin, T.; Linse, P. Langmuir 1996, 12, 305. (16) Wallin, T.; Linse, P. J. Phys. Chem. 1996, 100, 17873. (17) Wallin, T.; Linse, P. J. Phys. Chem. B 1997, 101, 5506. (18) Sasaki, S.; Fujimoto, D.; Maeda, H. Polym. Gels Networks 1995, 3, 145. (19) Musabekov, K.; Abilov, Z.; Beisebekov, M. Makromol. Chem. 1984, 185, 1403.

Introduction Association between polymers and polymer gels with surfactants has garnered considerable interest in recent years.1,2 In addition to rheology modification, colloid stabilization, and solubilization applications, polymer/ surfactant mixtures can provide insight into biologically relevant processes, because proteins and DNA are polyelectrolytes and lipids are surfactants. Cationic liposomes, for example, are popular vehicles for gene delivery,3,4 and lipid-coated microgels may be employed for stimulated drug release.5 Focus has also been drawn to polymer gels because their interaction with surfactants can tailor their swelling response to environmental stimuli, so-called “intelligent gels.”6 Along with drug delivery, gels may find application as actuators and in water purification. Oppositely charged surfactants and polyelectrolytes can form micellelike complexes in intimate contact.7-10 Their interactions are typically interpreted by means of binding

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in controlling its properties. Electrical fields, for example, can direct the binding of a surfactant to a gel, thereby contracting the gel anisotropically, much like a muscle.30 Furthermore, in the collapsed state, surfactant aggregates form nanoscale structures within the gel that influence its material properties.31 Polycrystalline cubic order has been observed for sodium polyacrylate (or methacrylate) gel/alkyl trimethylammonium bromide complexes,10,32-34 whereas hexagonal structures have been identified for polydiallyldimethylammonium chloride (PDADMAC) gel/ sodium dodecyl sulfate (SDS) complexes.35-37 More generally, though, the structural order, e.g., cubic/hexagonal/ lamellar, depends on the charge and cross-linking density of the hydrogel network,32 the water content,34,36 and the length of the surfactant hydrocarbon tail.33,37 In contrast to ionic surfactants, nonionic surfactants typically do not interact with polyelectrolytes, barring the presence of hydrophobic groups along the polymer backbone (e.g., polysoaps). Among the most extensively studied nonionic surfactant/polyelectrolyte mixtures are those of the poly(ethylene glycol) monoalkyl ethers, referred to as CiEj, where i and j denote the lengths of the alkyl tail group and poly(ethylene glycol) headgroup, and poly(acrylic acid).38 Under acidic conditions, the protonated acid monomers associate with CiEj surfactants predominantly through hydrophobic interactions or hydrogen bonding with the polymer backbone. Association is evidenced by a reduction in the solution viscosity,39 an increase in the plateau surface tension, and a concomitant reduction in the cmc,40-42 fluorescence,43 and growth of the adsorbed surfactant layer at the air/water interface measured by ellipsometry.40 Under basic conditions, sodium polyacrylate, i.e., the deprotonated form of poly(acrylic acid), no longer interacts with CiEj surfactants, and their association disappears. In turn, the viscosity increases, the surface tension plateau returns to that of (20) Khokhlov, A. R.; Kramarenko, E. Y.; Makhaeva, E. E.; Starodubyzev, S. G. Macromolecules 1992. (21) Filippova, O. E.; Makhaeva, E. E.; Starodubtsev, S. G. Polym. Sci. 1992, 34, 602. (22) Bisenbaev, A. K.; Makhaeva, E. E.; Salerskii, A. M.; Starodubtsev, S. G. Polym. Sci. 1992, 34, 1059. (23) Thanh, L. M.; Makhaeva, E. E.; Starodubtsev, S. G. Polym. Sci. 1993, 35, 476. (24) Philippova, O. E.; Starodoubtzev, S. G. J. Polym. Sci., Part B: Polym. Phys. 1993, 31, 1471. (25) Okuzaki, H.; Osada, Y. Macromolecules 1994, 27, 502. (26) Gong, J. P.; Osada, Y. J. Phys. Chem. 1995, 99, 10971. (27) Okuzaki, H.; Osada, Y. Macromolecules 1995, 28, 4554. (28) Philippova, O. E.; Hourdet, D.; Audebert, R.; Khokhlov, A. R. Macromolecules 1996, 29, 2822. (29) Hansson, P. Langmuir 1998, 14, 2269. (30) Osada, Y.; Okuzaki, H.; Hori, H. Nature 1992, 355. (31) Ober, C. K.; Wegner, G. Adv. Mater. 1997, 9, 17. (32) Zhou, S.; Burger, C.; Yeh, F.; Chu, B. Macromolecules 1998, 31, 8157. (33) Zhou, S.; Yeh, F.; Burger, C.; Chu, B. J. Phys. Chem. B 1999, 103, 2107. (34) Schneider, S. Self-assembly in surfactant/polyelectrolyte systems. Master’s Diploma, Lund University, 1998. (35) Yeh, F.; Sokolov, E. I.; Khokhlov, A. R.; Chu, B. J. Am. Chem. Soc. 1996, 118, 6615. (36) Dembo, A. T.; Yakunin, A. N.; Zaitsev, V. S.; Mironov, A. V.; Starodoubtsev, S. G.; Khokhlov, A. R.; Chu, B. J. Polym. Sci., Part B: Polym. Phys. 1996, 34, 2893. (37) Sokolov, E. L.; Yeh, F.; Khoklov, A. R.; Chu, B. Langmuir 1996, 12, 6229. (38) Saito, S.; Anghel, D. F. In Polymer-Surfactant Systems; Kwak, J. C. T., Ed.; Marcel Dekker: New York, 1998; p 357. (39) Saito, S.; Taniguchi, T. J. Colloid Interface Sci. 1973, 44, 114. (40) Maloney, C.; Huber, K. J. Colloid Interface Sci. 1994, 164, 463. (41) Anghel, D. F.; Saito, S.; Iovescu, A.; Ba˜ran, A. Colloids Surf. A 1994, 90, 89. (42) Anghel, D. F.; Saito, S.; Ba˜ran, A.; Iovescu, A. Langmuir 1998, 14, 5342. (43) Vasilescu, M.; Anghel, D. F.; Almgren, M.; Hansson, P.; Saito, S. Langmuir 1997, 13, 6951.

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the polymer-free solution, and the adsorbed layer is reduced to the thickness of a surfactant monolayer. From a practical standpoint, polyelectrolyte association with ionic/nonionic surfactant mixtures is of interest because such mixtures are ubiquitous in commercial formulations.44,45 Dubin and co-workers have extensively investigated mixed ionic/nonionic surfactant complexation with oppositely charged polyelectrolytes.46-52 By systematically varying the ionic strength and ratio of ionic to nonionic surfactant in a mixture, thereby varying the micelle charge density, they have measured for a number of systems the critical ionic surfactant fraction above which insoluble complexes form, identified by an increase in the solution turbidity.46-52 On the basis of these studies, they established empirical rules governing association.46-51,53 In addition, they have probed the structures formed by SDS/Triton X-100 mixtures and linear PDMDAC at low polymer concentrations using a variety of techniques.46,52 All of these studies, however, were performed well above the cmc’s of the individual ionic and nonionic surfactants and provide little information on the effect of the polyelectrolyte on mixed-surfactant aggregation and binding at low surfactant concentrations where the interaction begins. Creeth et al., on the other hand, have studied the complexation of SDS/C10E6 mixtures with PDMDAC in the vicinity of the cmc using small-angle neutron scattering and neutron reflection.54 Their studies revealed, not surprisingly, that at the surfactant concentration where association begins the bulk micelles and surface-adsorbed surfactant layer are enriched in SDS by the polyelectrolyte, relative to the polymer-free solutions.55 Whereas surfactant mixtures should interact similarly with a polyelectrolyte hydrogel, to our knowledge no experimental studies have been reported. Addition of a nonionic surfactant provides another variable with which surfactant interactions and gel behavior can be tuned. This paper examines the interaction between lightly crosslinked sodium polyacrylate hydrogels and mixed solutions of a cationic, dodecyl trimethylammonium bromide (C12TAB), and a nonionic, octaethylene glycol monododecyl ether (C12E8) surfactant. In particular, we focus on how C12E8 tempers the interaction and complexation of C12TA+ with the gel at surfactant concentrations below and above the cmc. In the first half of this paper, the interaction of C12TA+ with the gel is characterized experimentally by a series of absorption isotherms for which the ratio of C12TAB to C12E8 in the initial aqueous solution in contact with the gel is fixed. In this manner, the net charge of the surfactant solution is varied. After equilibration, the absorption of C12TA+ and C12E8 by the gel is determined (44) Phenomena in Mixed Surfactant Systems; Scamehorn, J. F., Ed.; American Chemical Society: Washington, D. C., 1985; Vol. 311. (45) Mixed Surfactant Systems; Holland, P. M., Rubingh, D. N., Eds.; American Chemical Society: Washington, D. C., 1992; Vol. 501. (46) Dubin, P. L.; Rigsbee, D. R.; McQuigg, D. W. J. Colloid Interface Sci. 1985, 105, 509. (47) Dubin, P. L.; Rigsbee, D. R.; Gan, L.-M.; Fallon, M. A. Macromolecules 1988, 21, 2555. (48) Dubin, P. L.; The´, S. S.; McQuigg, D. W.; Chew, C. H.; Gan, L. M. Langmuir 1989, 5, 89. (49) Dubin, P. L.; Chew, C. H.; Gan, L. M. J. Colloid Interface Sci. 1989, 128, 566. (50) Dubin, P. L.; Curran, M. E.; Hua, J. Langmuir 1990, 6, 707. (51) McQuigg, D. W.; Kaplan, J. I.; Dubin, P. L. J. Phys. Chem. 1992, 96, 1973. (52) Xia, J.; Zhang, H.; Rigsbee, D. R.; Dubin, P. L.; Shaikh, T. Macromolecules 1993, 26, 2759. (53) Odijk, T. Langmuir 1991, 7, 1991. (54) Creeth, A. M.; Cummins, P. G.; Staples, E. J.; Thompson, L.; Tucker, I.; Penfold, J.; Thomas, R. K.; Warren, N. Faraday Discuss. 1996, 104, 245. (55) Penfold, J.; Staples, E.; Thompson, L.; Tucker, I.; Hines, J.; Thomas, R. K.; Lu, J. R. Langmuir 1995, 11, 2496.

Interactions of Surfactant Mixtures with a Hydrogel

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with potentiometry and 1H NMR, respectively. In the following half of the paper, a model for the interaction of mixed ionic/nonionic surfactant solutions with an oppositely charged polyelectrolyte is presented. This model accounts in large part for the observed C12TA+ and C12E8 absorption behavior and provides a basis for interpreting polymer/mixed-surfactant interactions over a range of surfactant compositions. Experimental Section Materials. C12TAB (>99%), C12E8, pyrene (99+%), and sodium hydroxide (98%) were procured from TCI, Nikkol, Jansen, and Eka Nobel, respectively. Acrylic acid (99%) and deuterated-DMSO (99.9 at. % D) were purchased from Aldrich. Sodium chloride (reagent grade), N,N′-methylenebis(acrylamide) (MBAA), N,N,N′,N′-tetramethylenediamine (TEMED, 99%), and ammonium persulfate (98+%) were all obtained from Sigma. All chemicals were used as received. Solutions were prepared using high-quality Millipore water. Preparation of the Gels. Aqueous solutions (10 wt %) of acrylic acid (monomer) and MBAA (cross-linking agent) were polymerized in glass test tubes in the presence of ammonium persulfate (radical initiator) and TEMED (accelerator). The fraction of MBAA in the polymerized network was 0.9 mol %. After polymerization for 12 h at 70 °C, the gels were removed from the test tubes and placed in a large excess of NaOH (0.5 M) to neutralize the acid monomers (pKa ≈ 3.3). The gels were subsequently cut into shorter cylinders and placed in a large bath of 0.01 mM NaOH (pH ≈ 9). The bath was changed every 2 to 3 days for more than a month to maintain the solution pH and to wash unreacted species from the gels. In the bath, the gels swelled to several times their initial volume upon synthesis. To determine the concentration of sodium acrylate monomers in the swollen gels, gel pieces of known mass were placed in an oven (∼120 °C) for several days to evaporate off the water, whereupon the dried gels were weighed. The monomer concentration was found to be 25.2 µmol sodium acrylate (2.40 mg of dry polymer) g-1 of swollen gel. Surfactant/Gel Samples. Gels of known mass (∼2 g) were placed in 0.01 mM NaOH aqueous mixed cationic/nonionic surfactant solutions of known composition. The mass ratio of the initial swollen gel to the surfactant solution was 1 to 8, corresponding to a global gel monomer concentration of 2.8 mM in solution (gel + aqueous phases). All of the samples were equilibrated for at least a month at 25 °C in capped glass vials sealed with Parafilm. After equilibration, the pH of a number of samples was measured. None of these samples were found to have a pH less than 8.5, indicating minimal carbon dioxide poisoning of the solutions. Four series of mixed-surfactant solutions were prepared with varying initial ratios of the cationic to nonionic surfactant: (A) 100 mol % C12TAB/0 mol % C12E8, (B) 75 mol % C12TAB/25 mol % C12E8, (C) 50 mol % C12TAB/50 mol % C12E8, and (D) 25 mol % C12TAB/75 mol % C12E8. In each series, the C12TAB surfactant concentration was varied from ∼0.01 to 10 mM while maintaining a fixed C12TAB/C12E8 ratio. This corresponds to a total surfactant concentration range of 0.01-10 mM and 0.04-40 mM for series A and D, respectively. Concentrations for series B and C lie between these two extremes. While the maximum C12TAB concentration is below its cmc (15 mM), micellization in the solution in contact with the gel occurs at much lower total surfactant concentrations due to the presence of C12E8 (cmc ) 0.1 mM; see below). Gel Volume Determination. The equilibrated gels were removed from the surfactant solutions and weighed after carefully blotting excess water from their surfaces with filter paper. If the density of the gels in the collapsed and swollen states is assumed to be the same (1 g/cm3), the mass ratio of the gels in the final and initial states, m/m0, serves as an approximation to the volume change, V/V0. Free C12TA+ Concentration Determination. The concentration of C12TA+ in the equilibrated samples was evaluated using a surfactant-specific electrode, as described elsewhere.11 In this setup, a reference and a test surfactant solution are brought into contact separated by a plasticized PVC membrane. The potential

Figure 1. Typical response of the surfactant-specific electrode as a function of C12TA+ concentration in the test solution. The C12TA+ concentration of the reference solution is 9.991 mM. The points are the measured response, whereas the line and equation are the least-squares fit to the data (slope 58.5 mV per decade change in C12TA+ concentration). difference between two silver/silver chloride standard electrodes, in contact with the two surfactant solutions via salt bridges, was measured with a Keithely 171 Microvolt Digital Multimeter. The response to standard C12TA+ solutions in 50 mM NaCl support electrolyte was used to calibrate the electrode. Plotted on a log concentration scale, the response was Nernstian with a slope of 58.5 mV per decade change in C12TA+ concentration (Figure 1). Concentrations below 0.001 mM are increasingly unreliable owing to poor electrode sensitivity and were disregarded. Above the cmc, the response of the surfactant-specific electrode is not simply a function of the C12TA+ concentration. This poses a problem in the present systems because mixed micelles form well below the cmc of C12TA+ and within the concentrations of interest. To overcome this difficulty, solutions for analysis were diluted to a concentration below the cmc of the initial mixedsurfactant solution. A small volume of concentrated NaCl support electrolyte solution was added to each test solution so that the concentration of NaCl was 50 mM. Although we are confident that this procedure yields reasonable C12TA+ concentrations over a range of C12E8 fractions, systematic discrepancies may occur for increasing C12E8 fractions with increasing total surfactant concentration owing to the large dilution and longer equilibration times required to obtain accurate potential measurements for smaller surfactant concentrations. As a result, the absorbed C12TA+ could be underestimated at high C12E8 concentrations (see below). The absorbed amount of C12TA+ was determined by taking the difference between the initial and final amounts of C12TA+ in the bulk solution in contact with the gel. Both dilution of the test solutions and the increase in the bulk solution volume due to gel collapse were taken into account for the calculation of the final amount of C12TA+. The absorption fraction of C12TA+, βC12TA+, to the gel was calculated as the ratio of total absorbed C12TA+ to the number of sodium acrylate monomers in the gel. Free C12E8 Concentration Determination. 1H NMR was used to determine the ratio of C12E8 to C12TA+ in the equilibrated solutions. Spectra were recorded on a Bruker ARX500 NMR spectrometer (resonance frequency of 500.13 MHz). Measurements of test surfactant mixtures in d-DMSO indicate that the peaks attributed to the hydrogens bound to the β-carbon adjacent to the surfactant headgroup are distinct and well-suited for determination of their concentration ratio (Figure 2). Because the solutions were initially prepared in water, the equilibrated solutions were placed in an oven for 2 days at 80 °C to evaporate off the water. The dried surfactant mixtures were subsequently resolubilized in d-DMSO. In addition to removing undesirable water, this procedure has the advantages of concentrating the surfactant solutions, thereby improving the sensitivity of the

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Figure 2. 1H NMR spectra of the hydrogens attached to the β-carbon of C12E8 and C12TAB in d-DMSO. The quintuplet at a chemical shift of 1.65 ppm is for C12E8, and the quintuplet at 1.45 ppm is for C12TAB. The long dashed curve is the spectra for pure C12E8, the short dashed curve is the spectra for pure C12TAB, and the solid curve is for a 50.2 mol % C12TAB/49.8 mol % C12E8 mixture prepared following the drying procedure described in the Experimental Section. The composition of the mixture determined by the ratio of the areas of the two quintuplets is 50.0 mol % C12TAB/50.0 mol % C12E8, in agreement with the prepared composition. measurement, and suppressing micelle formation, which can shift the positions of the 1H NMR peaks. To test the reliability of this procedure, aqueous mixed-surfactant solutions of known concentration were prepared for analysis in this manner, and the spectra were measured. The surfactant mixture analyzed in Figure 2 was prepared following this drying procedure. The C12E8 surfactant fraction of the prepared solution was 49.8 mol % compared to the measured surfactant fraction after drying and redissolution of 50.0 mol %, giving us confidence in the drying procedure. Mixed-Surfactant cmc Determination. The cmc’s of the mixed-surfactant solutions in the absence of gel were determined by measuring the steady-state fluorescence of pyrene as a function of surfactant concentration. The ratio of the third to first vibronic peaks of pyrene (III/I) is sensitive to the polarity of its local environment and thereby provides a measure of the onset of micellization because pyrene is hydrophobic.56 Fluorescence spectra were recorded on a SPEX Fluorolog 1680. In water, III/I assumes a value of 0.7. At the onset of micellization, III/I sharply increases and plateaus near a value of 1. The mixed cmc is reported as the concentration at which III/I begins to increase.

Results and Discussion Mixed-Micelle cmc. A typical III/I plot for pyrene as a function of total surfactant concentration is presented in Figure 3. Mixed C12TAB/C12E8 cmc’s determined in this manner are reported in Table 1. The measured cmc’s of pure C12TAB and C12E8 are in agreement with reported values determined by a variety of methods.57 By assuming ideal mixing of surfactants within the micelles, the mixed cmc, C/12, can be shown to be58

R1 (1 - R1) 1 ) + C/12 C/1 C/2

(1)

(56) Kalyanasundaram, K.; Thomas, J. K. J. Am. Chem. Soc. 1977, 99, 2039. (57) Mukerjee, P.; Mysels, K. J. Critical Micelle Concentrations of Aqueous Surfactant Systems; National Bureau of Standards: Washington, D. C., 1970. (58) Clint, J. H. J. Chem. Soc., Faraday Trans. 1 1975, 71, 1327.

Figure 3. Ratio of the third to first vibronic peaks of pyrene as a function of total surfactant concentration for a 25 mol %/75 mol % C12TAB/C12E8 mixture. The cmc (0.12 mM) is taken as the concentration at which III/I begins to increase. The points are the experimental results, and the solid curve is a guide for the eye. Table 1. cmc of C12TAB/C12E8 Mixtures Determined by Pyrene Fluorescence and from Regular Solution Theorya mol % C12TAB/ mol % C12E8 0%/100% 25%/75% 50%/50% 75%/25% 100%/0%

cmc (mM) experimental 0.10 (0.10-0.11) 0.12 0.18 0.36 15 (14-16)

ideal mix 0.10 0.13 0.20 0.39 15

a The numbers in parentheses are reported values of the cmc for the pure surfactants.57

where C/1 and C/2 are the cmc’s of surfactant 1 and 2 alone, respectively, and R1 is the mole fraction of component 1 in the total mixed surfactant. This expression reproduces the mixed cmc’s well over the entire composition range (Table 1). Mixing nonidealities can be accounted for with regular solution theory;59 however, this does not significantly improve the results presented herein. For simplicity, we assume below that micellization is ideal. C12TA+ Absorption. C12TA+ absorption isotherms of sodium polyacrylate gels as a function of the equilibrium aqueous C12TA+ concentration are presented in Figure 4. The shapes of the isotherms are typical of ionic surfactant binding to oppositely charged polyelectrolytes and gels. At low C12TA+ concentrations, the binding is noncooperative and proceeds via ion exchange between sodium counterions and C12TA+, which absorb as monomers. Although this regime is not observed for the series A (100% C12TAB) absorption isotherm, it is observed for C12TA+ concentrations less than ∼0.01 mM for series B (75% C12TAB/25% C12E8), C (50% C12TAB/50% C12E8), and D (25% C12TAB/75% C12E8). Hansson reported that C12TA+ absorbs only as monomers to 0.9 mol % cross-linked sodium polyacrylate gels below a critical absorption fraction of 0.008 ( 0.001, above which the absorbed surfactants aggregate.29 Only one or two points for series A lie below this absorption fraction, so it is not surprising that we are do not observe the initial noncooperative binding regime for this series. The critical absorption fractions for series (59) Holland, P. M. In Mixed Surfactant Systems; Holland, P. M., Rubingh, D. N., Eds.; ACS Symposium Series 501; American Chemical Society: Washington, D. C., 1992; p 31.


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Figure 5. C12TA+ absorption isotherms as a function of the equilibrium aqueous C12TA+ concentration plotted on a loglinear scale. The symbols are defined in Figure 4. Figure 4. C12TA+ absorption isotherms as a function of the equilibrium aqueous C12TA+ concentration plotted on a loglog scale. The closed circles, open circles, closed triangles, and open triangles are the absorption results for series A (100% C12TA+), B (75% C12TA+/25% C12E8), C (50% C12TA+/50% C12E8), and D (25% C12TA+/75% C12E8), respectively. The solid line, long dashed line, short dashed line, and long/short dashed line are the model predictions for series A, B, C, and D, respectively. Series B, C, and D have been shifted down by factors of 10, 100, and 1000, respectively, for clarity.

B through D are less than that reported for pure C12TA+ absorption, although there does not appear to be a trend with increasing C12E8 composition. At intermediate C12TA+ concentrations, the binding becomes cooperative; i.e., the slope of the absorption isotherm increases, signifying micellar aggregation within the network. Although series A and B display only one cooperative regime, series C and D have two distinct cooperative regions. The first cooperative regime for series C and D lies in a narrow C12TA+ concentration range near 0.01 mM and has a greater slope than the second regime between 0.01 and 0.1 mM. Two distinct cooperative absorption regimes have previously been observed for C12TA+ binding to sodium polyacrylate gels for added salt concentrations comparable to the aqueous C12TA+ concentration at the cac.29 We would expect, however, to observe two cooperative absorption regimes for each series if salt effects were the root cause of this behavior. Rather, it is shown below that the second cooperative C12TA+ absorption regime can be attributed to competitive mixed micellization in the gel and bulk aqueous phases. Plotted on a log-linear scale, the maximum C12TA+ absorption for each series decreases with increasing C12E8 fraction (Figure 5). The absorption isotherms of series A and B plateau at βC12TA+ ≈ 1 (charge neutralization) and do not change with increasing surfactant concentration. βC12TA+ passes through a maximum and then decreases with increasing surfactant concentration, however, for greater aqueous C12E8 solution fractions. The maximum C12TA+ absorption fraction for series C is 0.9 and decreases to 0.65 at the highest concentration examined. The binding maximum is reduced to 0.65 for series D and subsequently decreases to 0.2 at the highest concentration examined. These results suggest either that C12TA+ displays a stronger affinity for the aqueous micellar aggregates with increasing C12E8 concentration and desorbs from the

network or that large mixed aggregates within the gel exclude C12TA+ with increasing C12E8 concentration. The C12E8 absorption and gel collapse results presented below, however, do not support C12TA+ exclusion from the gel at these surfactant concentrations. Moreover, it is unlikely that the aqueous surfactant phase undergoes a phase transition at these surfactant concentrations that could increase the affinity of C12TA+ for the aqueous phase. Alternatively, we have observed in subsequent C12TA+ absorption measurements from mixed-surfactant solutions, that the electrode potential of dilute solutions takes longer to equilibrate than those for more concentrated solutions. In addition, the electrode tends to read initially higher surfactant concentrations before equilibration. Considering that large dilutions are required to ensure that the sample is below the cmc (up to a factor of 400 or more for the most concentrated samples of series D) and that the potential readings were typically made within a couple of minutes of immersing the electrode in the sample, we suspect that the observed systematic desorption is an artifact of insufficient equilibration. Indeed, we have found taking multiple measurements of the same sample with longer equilibration times that while C12TA+ desorbs from polyacrylate with increasing C12E8 concentration it is not as significant as that found here.60 C12E8 Absorption. The aqueous surfactant fractions of C12E8 in equilibrium with the gels as determined by 1H NMR are presented in Figure 6. At low C12TA+ concentrations (3 mM), the equilibrium aqueous C12E8 surfactant fraction approaches that of the initial solution, as should be expected, because the total surfactant concentration is in excess to the amount that can be absorbed by the gel. More intriguing, at intermediate C12TA+ concentrations, the aqueous C12E8 fraction can fall below its initial composition, indicating the gels can preferentially absorb the nonionic surfactant over the cationic surfactant. In particular, the aqueous C12E8 fraction falls to a minimum of 0.09 relative to an initial value of 0.25 for series B. (60) Ashbaugh, H. S.; Piculell, L.; Lindman, B., manuscript in preparation.

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Figure 6. Ratio of the C12E8 concentration to the total surfactant concentration in aqueous solution as a function of the equilibrium aqueous C12TA+ concentration. The symbols are the experimental results, the horizontal lines are the initial aqueous C12E8 surfactant fractions, and the curves are the model predictions using the parameters given in Table 2. The symbols and curves are defined in Figure 4.

Figure 7. C12E8 absorption isotherms as a function of the equilibrium aqueous C12TA+ concentration. The symbols and the curves are defined in Figure 4. The error bars denote the error in βC12E8 assuming an error of (0.01 in the aqueous C12E8 surfactant fraction in Figure 6.

Similar, although not as substantial, behavior is observed for series C where the C12E8 fraction dips just below 0.50 in this C12TA+ concentration range. From the equilibrium aqueous C12E8 fraction, C12TA+ concentration, and gel volume (presented below), we can infer the total C12E8 absorbed by the gels. The C12E8 binding fraction, βC12E8, defined as the total absorbed C12E8 divided by the number of gel monomers, is plotted against the aqueous C12TA+ concentration in Figure 7. The C12E8 absorption is not a monotonically increasing function but initially increases and then decreases with increasing surfactant concentration. Absorption of C12E8 becomes more significant at lower C12TA+ concentrations from series B to D. At higher C12TA+ concentrations, βC12E8’s for each series appear to converge. We note that βC12E8 is very sensitive to errors in the measured aqueous surfactant fractions with increasing C12TA+ and C12E8 concentration. Assuming an error of (0.01 in the aqueous C12E8 fraction yields an error of (0.40 in βC12E8 for the highest surfactant

Ashbaugh et al.

Figure 8. Ratio of the final to initial gel volume plotted against the aqueous C12TA+ concentration. The symbols are defined in Figure 4.

concentrations considered for series D. The error in βC12E8, however, quickly decreases with decreasing surfactant concentration for series D and is not as significant for series B and C over the concentration range examined (Figure 7). Nonetheless our results demonstrate that C12E8 desorbs from the gels to a similar extent for each series and should not exclude C12TA+ absorption with increasing surfactant concentration. Gel Collapse. As the concentration of C12TA+ increases, the gels undergo a transition-like collapse, except for series D (Figure 8). Similar behavior has been reported for other surfactant/gel systems. The aqueous C12TA+ concentration at which the collapse occurs (∼0.1 mM) is fairly insensitive to the addition of C12E8. For series D, the gel collapse also begins at 0.1 mM C12TA+ but only gradually approaches a minimum at the highest concentrations considered (>3 mM). The minimum volume of the gels increases with increasing C12E8 concentration from V/V0 ) 0.013 for series A to 0.033 for series D. The increasing minimum volume could be attributed to the decreasing amount of absorbed C12TA+ with increasing C12E8 concentration (Figure 5). Because the gel is not completely neutralized for series C and D, the internal osmotic pressure of the sodium counterions is greater. The magnitude of the collapse is greater than what would be observed if the absorbed C12TA+ acted only as a simple salt, indicating that it is the polyion nature of the absorbed surfactant aggregates that leads to the nearly 2 orders of magnitude reduction in the gel volume.29 When the solution has no bound C12TA+, V/V0 is linear with respect to βC12TA+ (Figure 9). Below βC12TA+ ) 0.65, each series falls on the same line, indicating that to moderately high total surfactant absorption the collapse is dominated by C12TA+ absorption alone. Extrapolating this line to zero volume, we find that the minimum gel volume does not coincide with gel neutralization, but βCmin + ≈ 0.8. Nonetheless, the gel is still able to absorb 12TA C12TA+ beyond the volume minimum. Series A and B, for example, attain a maximum absorption at neutralization. Comparable behavior has been observed for the interaction of cationic surfactants with poly(acrylic acid) gels of varying degrees of ionization with βCmin + ranging from 12TA 0.7329 to 0.8.18 As noted above, the maximum binding fraction of C12TA+ to the gels for series D is 0.65, after which C12TA+ appears to desorb with increasing surfactant concentration. Despite this, the gels continue to collapse


Figure 9. Ratio of the final to initial gel volume plotted against the C12TA+ absorption fraction. The symbols are defined in Figure 4. The inset figure shows the collapse results for series D in detail. The solid line is the fit of eq 10 employing the parameters given in Table 2.

with increasing C12TA+ concentration. As a result, the plot of V/V0 versus βC12TA+ bends back on itself (Figure 9, inset). This result is confounded by the observation that C12E8 desorbs from the gel with increasing surfactant concentration (Figure 7). Thus, the gel appears to collapse while both surfactants desorb, which is curious. One possible explanation for this behavior is that micelles in the aqueous phase exert an external osmotic pressure that deswells the gel. We have tested this possibility by placing a gel sample within a pure 40 mM C12E8 solution. No deswelling of the gel was observed after more than 2 months of equilibration, indicating that this hypothesis is incorrect. As noted above, however, the measured C12TA+ absorption fractions may be underestimated. In this case, it seems likely that for series D C12TA+ absorption regulates the gel collapse and the collapse with net surfactant desorption is an artifact of the measurement. Absorption Model. To interpret the absorption of C12TA+ and C12E8, we have developed a model that combines the closed association model for ionic surfactant binding to an oppositely charged polyelectrolyte12,29,61 with a mixed micellization model for surfactant binding to a hydrophobically modified polymer61-63 to describe the absorption of the nonionic surfactant. A schematic illustration of the modeled equilibrium is given in Figure 10. In the bulk aqueous phase, surfactant monomers coexist with mixed cationic/nonionic micellar aggregates. Similarly in the gel phase, cationic and nonionic surfactant monomers coexist with mixed network bound aggregates. Although the cationic surfactants are thought to bind directly to the network monomers through electrostatic attraction, the nonionic surfactants do not interact directly with the network itself but participate in mixed gel bound aggregates through hydrophobic interactions. The aqueous and gel phases are coupled to each other through equilibrium partitioning of the surfactant monomers. Mixed micelles from the aqueous phase are assumed to be excluded from the gel phase and vice versa. For a given absorption fraction of the cationic surfactant (component 1) to the gel, β1 ) βC12TA+, a portion will be distributed between monomers, β1m, and aggregates, β1a. (61) Linse, P.; Piculell, L.; Hansson, P. In Polymer-Surfactant Systems; Kwak, J. C. T., Ed.; Marcel Dekker: New York, 1998; p 193. (62) Piculell, L.; Thuresson, K.; Ericsson, O. Faraday Discuss. 1995, 101, 307.

Langmuir, Vol. 16, No. 6, 2000 2535

Figure 10. Schematic illustration of the binding equilibria between mixed micellization in the aqueous and gel phases modeled here.

The remaining fraction of gel sites (i.e., gel monomers), β0, are neutralized by simple counterions (component 0, assumed to be sodium) so that

β1 ) β1m + β1a ) 1 - β0

(2)

The maximum cationic surfactant absorption fraction attainable is thereby assumed to be equal to 1 and precludes the possibility of gel charge reversal. Our experimental results support this assumption for the surfactant concentrations of interest (Figure 4). Cationic surfactant monomers partition between the aqueous (w) and gel (g) phases via an ion exchange process replacing the gel sodium ions, + g + g + w S+|w 1m + Na |0 S S |1m + Na |0

(3)

This equilibrium is described by

Kex )

β1mCw 0 β0Cw 1m

(4)

where Kex is the equilibrium exchange constant and Cw 1m and Cw 0 are the concentrations of cationic surfactant monomers and sodium ions in the aqueous phase, respectively. It is important to note that Cw 0 includes not only the sodium ions from surfactant exchange but also those added to the aqueous phase, e.g., from the 0.01 mM NaOH bath.29 The concentration of nonionic surfactant (component 2) monomers in both phases is the same g Cw 2m ) C2m

(5)

based on the assumption that the standard solvation free energy of this component is equivalent in the aqueous and gel phases. This assumption is very good within the water-swollen gels, although deviations are expected as the gel collapses and the absorbed surfactant concentration increases. We retain this simple form, however, which is at least qualitatively correct over the entire range of surfactant absorption considered. In the aqueous phase, the surfactant monomers coexist with mixed micelles. As stated above, we model, for (63) Piculell, L.; Guillemet, F.; Thuresson, K.; Shubin, V.; Ericsson, O. Adv. Colloid Interface Sci. 1996, 63, 1.

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Ashbaugh et al.

simplicity, the equilibrium between the monomers and micelles assuming ideal mixing of the surfactants within the micelles and a pseudo-phase-separation model describing the onset of micellization.58 In this case, the cmc of the mixture is described by eq 1. For total surfactant w w / concentrations, Cw 12 ) C1 + C2 ; below C12, the concentration of each surfactant in monomeric form is simply the total concentration of the individual surfactants / Cw 12 < C12

w Cim ) Cw i

(6a)

Above C/12, the concentration of each surfactant existing as monomers is58 2 w w ) C/i {-(Cw Cim 12 - ∆i) + [(C12 - ∆i) + 1/2 4RiCw 12∆i] }/2∆i

) ln

+ ln x1

(7b)

respectively, where x1 is the mole fraction of the cationic surfactant within the gel-bound mixed aggregates. The cationic surfactant monomers and sodium counterions are assumed to be randomly distributed among the gel sites unoccupied by the bound aggregates ()1 - β1a ) β1m + β0), which are assumed to be immobile and thereby do not contribute to the surfactant mixing entropy within the gel. Equation 7a then is simply the mixing entropy of surfactant monomers among the unaggregated absorption sites. β/1m is the critical absorption fraction of the absorbed cationic surfactant in the absence of the nonionic surfactant, which is moderated by x1. The chemical potentials of the monomeric and aggregated nonionic surfactant in the gel can be expressed as

µg2m/kT ) ln Cg2m

(8a)

µg2a/kT ) ln Cg* 2 + ln(1 - x1)

(8b)

and

respectively, where Cg* 2 is the cmc of the nonionic surfactant within the gel phase, which is assumed to be different than that in aqueous solution. Above the cac, the distribution of surfactants between monomers and aggregates is determined by equating chemical potentials, i.e., µg1m ) µg1a, and µg2m ) µg2a. Below the cac, surfactants exist only as monomers. Above the cac, the monomer concentrations of the cationic and nonionic surfactants satisfy the relationship

β1m β/1m

+

Cg2m Cg* 2m

)1

a C TA+ and C E 12 12 8 are labeled as components 1 and 2, respectively

[1 - (V/V0)min](1 - β1/βmin V 1 ) + (V/V0)min ) V0 (V/V0)min

and

β/1m

value 0.01 mM 0.20 15 mM 0.1 mM 0.008 0.2 mM 0.8 0.025

(7a)

/ where i ) 1 or 2 and ∆i ) (C(3-i) - C/i ). Micellization within the network is treated analogously to mixed micellization in bulk solution. By assuming that mixing is ideal and that the pseudo-phase-separation model describes micellization within the gel, the chemical potentials for the absorbed monomeric and aggregated cationic surfactants are

µg1a/kT

parameter added Na+ concentration Kex C/1 C/2 β/1m Cg* 2 βmin 1 (V/V0)min

the aqueous phase. It cannot be simplified further, however, because the concentration units for the cationic and nonionic surfactants are different. Finally, we must account for changes in the gel volume owing to surfactant absorption, as this will affect the concentrations in the aqueous and gel phases. Rather than resorting to detailed models involving a balance of elastic and osmotic forces, we adopt a phenomenological description of the gel collapse resulting from cationic surfactant absorption alone.18,29 The collapse of the gel is assumed to be linear with the cationic surfactant absorption fraction down to a maximum absorption fraction after which the gel assumes a constant minimum volume This description

/ Cw 12 > C12 (6b)

µg1m/kT ) ln[β1m/(β1m + β0)]

Table 2. Model Parameters for C12TA+/C12E8 Absorption to 0.9% Cross-Linked Sodium Polyacrylate Gela

(9)

This expression is analogous to eq 1 for micellization in

{

β1 e βmin 1 β1 > βmin 1 (10)

is motivated by the experimental results showing that for β1 less than 0.8 the swelling behavior is linear and is dominated by the absorption of the cationic surfactant (Figure 9). Although deviations from eq 10 are observed for series D, we retain this expression with the expectation that comparison with the experimental absorption isotherms is only qualitative at high nonionic surfactant concentrations. The absorption model was solved iteratively. First, the distribution of the cationic surfactant between the aqueous and gel phases was determined by satisfying eqs 4, 6, and 7. Subsequently, the distribution of the nonionic surfactant between phases was determined by satisfying eqs 5, 6, and 8. This sequence was repeated until the surfactant distributions did not vary. By assuming initially that the nonionic surfactant is uniformly distributed between gel and aqueous solution, this procedure converged rapidly. Comparison with Experiment. Model parameters for C12TA+/C12E8 absorption to 0.9% cross-linked sodium polyacrylate gel are given in Table 2. Pure surfactant cmc’s, C/1 and C/2, and the added sodium concentration were set to the experimental values. Parameters associated with C12TA+ absorption, Kex and β/1m, were taken from the work of Hansson29 for 0.9% cross-linked sodium polyacrylate gel. The cmc of the nonionic surfactant within the gel, Cg* 2 , was fitted to the nonionic surfactant binding / data for series B. We note that Cg* 2 is twice C2, indicating a greater free energy penalty for nonionic surfactant aggregation within the polymer network, consistent with the observation that C12E8 does not associate with linear sodium polyacrylate.38,39,41,42 The C12TA+ absorption fraction at which the minimum gel volume is attained, βmin 1 , was taken from experiment, whereas the minimum volume, (V/V0)min, was assumed to be independent of the C12E8 absorption. Although this assumption is different


Figure 11. Predicted C12TA+ binding isotherms demonstrating the onset of two cooperative binding regions with increasing C12E8 composition. The short-long dashed curve is the prediction for series D using the parameters given in Table 2. The solid curve is the binding predictions for a pure C12TAB solution with an effective critical binding fraction of 0.004. The dashed curve is the mole fraction of C12TA+ in the mixed gel bound micelles.

from the experimental observations (Figure 8), model predictions are insensitive to (V/V0)min so long as it is much less than one. Model C12TA+ absorption predictions as a function of C12TA+ concentration are compared with the experimental results in Figure 4. For series A, the model quantitatively describes the absorption of C12TA+ in agreement with previous measurements and model parameters reported by Hansson.29 Adding C12E8, however, tends to shift the predicted absorption isotherms toward lower C12TA+ concentrations. Thus, the model slightly overpredicts the extent of C12TA+ absorption with increasing C12E8 composition. The experiments, on the other hand, indicate that C12TA+ binding within the cooperative absorption portion of the isotherm is similar for each series. Although not apparent from Figure 4, the model provides a qualitative interpretation for the onset of two cooperative C12TA+ absorption regimes with increasing C12E8 composition. Model predictions for series D at C12TA+ concentrations slightly below that examined experimentally are presented in Figure 11. Below 0.001 mM, C12TA+ absorption is noncooperative and proceeds through ion exchange (eq 4). At a C12TA+ concentration of approximately 0.001 mM, the model predicts a sudden increase in C12TA+ absorption due to surfactant aggregation with the network. At slightly greater C12TA+ concentrations, the absorption is less cooperative (Figure 11), similar to what is observed experimentally for series C and D (Figure 4). The predicted mole fraction of C12TA+ participating in bound mixed micelles, x1, falls sharply with increasing surfactant concentration from ∼0.75 at the beginning of micelle formation to 0.5 at the beginning of the second cooperative regime, after which x1 is essentially constant (Figure 11). The beginning of the second cooperative regime coincides with the onset of micellization in the aqueous phase. Thus, addition of C12E8 gives rise to two cooperative binding regimes because the bound aggregate, initially enriched in C12TA+, strongly binds C12E8, thereby reducing x1 and the free energy penalty for micellizing additional C12TA+ (eq 7b). When mixed micelles begin to form in the aqueous phase in competition with micellization in the gel phase, x1 is insensitive to the addition of surfactant because the

Langmuir, Vol. 16, No. 6, 2000 2537

aqueous chemical potentials in a mixed system vary weakly above the cmc. As a result, C12TA+ binds to the gel in the mixed system just as pure C12TA+ would bind with an effective critical binding fraction of x1β/1m ) 0.5 × 0.008 (Figure 11). The model predicts mixed micellization in the aqueous phase for series C only at C12TA+ concentrations close to neutralization of the gel and therefore predicts only one cooperative binding region, in contrast with experiment. The quantitative agreement between the model and experiment could be improved if the model parameters were reoptimized with increasing addition of C12E8 and taking mixing nonidealities into account. Nonetheless, the prediction of multiple absorption regimes without manipulating the model is encouraging and tends to support our competitive micellization hypothesis. Experimental conformation of our competitive micellization hypothesis is complicated by the low experimental sensitivity at low surfactant concentrations. The aqueous cmc evaluated from eq 1 using the measured C12TA+ and C12E8 concentrations indicate that micelles form in the aqueous phase between a C12TA+ concentration just above 0.01 mM for series D. This C12TA+ concentration coincides with the concentration at which the first cooperative binding region ends (Figure 4), supporting the conclusion that aqueous micelles are present in the second cooperative absorption regime. Unfortunately, a similar calculation for series C yields a range over which aqueous micellization could occur in the bulk solution and cannot be compared with the experimental C12TA+ concentration at which the second cooperative binding region begins. To verify our hypothesis, pyrene could be added to the solutions to probe the onset of micellization in the gel and aqueous phases with fluorescence. In addition, surfactants with shorter hydrophobic tail groups could be used, thereby shifting the mixed cac to higher surfactant concentrations that can be measured more accurately. Neither measurements have been performed here. The model predicts the aqueous composition of C12E8 well over the range of surfactant concentrations examined experimentally (Figure 6). In particular, the model reproduces the aqueous phase enrichment of C12TA+ at the intermediate surfactant concentrations observed for series B. Moreover, the model predicts a slight dip in the aqueous C12E8 composition for series C at an equilibrium C12TA+ concentration of 0.1 mM similar to that observed experimentally. The comparison with experiment is the worst for series D, for which the model consistently overpredicts the aqueous C12E8 concentration. This is not surprising, given that the model overpredicts the binding of C12TA+ for this series and breaks down as anticipated. The model captures many of the experimentally observed features of C12E8 absorption (Figure 7). For series B, the model predicts three C12E8 absorption regimes as a function of C12TA+ concentration. At C12TA+ concentrations less than 0.1 mM, C12E8 binding is cooperative and increases with increasing C12TA+ binding to the network. Above an aqueous C12TA+ concentration of 0.1 mM, binding of C12TA+ is saturated (Figure 4). However, C12E8 continues to absorb within the network, although not as strongly. As a result, the bulk aqueous phase is enriched in C12TA+ as shown in Figure 6. Above a C12TA+ concentration of 2.7 mM, C12E8 begins to desorb from the network with increasing C12TA+ concentration. Desorption of C12E8 from the network coincides with the onset of micellization in the aqueous phase for series B. When the mixed cmc is eventually reached in the aqueous phase, eq 6b predicts that the monomer concentration of the surfactant with the lowest cmc, i.e., the nonionic surfactant, is reduced with further surfactant addition. As a

2538


result, the monomer chemical potential within the network, eq 8, is reduced, and the nonionic surfactant desorbs from the network. The C12TA+ concentrations between full absorption of C12TA+ and the onset of micellization in the aqueous phase corresponds to the region in which the aqueous phase is enriched in C12TA+. All three C12E8 binding regimes are observed experimentally for series B, and the agreement with the model is good, although the C12E8 desorption begins at a slightly lower C12TA+ concentration of 2 mM. The experimental desorption, however, does coincide with the calculated onset of aqueous phase micellization evaluated from eq 1. In series C, the onset of micellization within the aqueous phase is slightly below the surfactant concentration at which full C12TA+ binding occurs. Therefore, only a cooperative C12E8 absorption and subsequent desorption are observed both experimentally and for the model. The predicted C12E8 absorption fraction is in reasonable agreement with experiment over the concentration range examined. In particular, the model predicts the magnitude of and concentration at which the maximum C12E8 absorption occurs for series C. Not unexpectedly, the model underpredicts the extent of C12E8 absorption for series D. Despite the shortcomings of the model at high C12E8 compositions, the shape of the absorption isotherm is qualitatively correct and predicts only two absorption regimes because the cmc for this series lies well below the C12TA+ concentration at which maximum C12TA+ absorption occurs. Conclusions The interaction between mixed C12TAB/C12E8 surfactant solutions and sodium polyacrylate hydrogels can be interpreted in terms of coupled mixed micellization in the aqueous and gel phases. Indeed, the most significant

Ashbaugh et al.

experimental parameters influencing the surfactant absorption are the cmc in the aqueous phase and the cac in the gel phase. When the cmc is greater than the concentration for which the network is neutralized by the ionic surfactant, the gel preferentially absorbs the nonionic surfactant over the concentration range from saturation to the cmc. If the cmc lies between the cac and the saturation concentration, however, two ionic surfactant cooperative binding regimes are observed; one between the cac and the cmc and the second between the cmc and the saturation plateau. The absorption model presented herein is in semiquantitative agreement with the experimental results and represents a generalization of previous absorption models that focus either on electrostatic or hydrophobic interactions as the driving force for surfactant/polymer association. The model breaks down with increasing C12E8 concentration, however, indicating our description of mixed-surfactant/polymer interactions is incomplete. More information regarding the interaction between the nonionic surfactant and the gel is necessary for a thorough understanding of mixed-surfactant interactions with increasing nonionic surfactant concentration. To this end, we are presently examining the structure of mixed aggregates within the gel as a function of the nonionic surfactant composition, which will be presented in a forthcoming publication.60 Acknowledgment. The authors are grateful to Dr. Karl-Erik Bergquist who performed the 1H NMR measurements. We also thank Dr. Per Hansson for valuable discussions regarding surfactant interactions with polymers and gels. This work was supported by the Center for Amphiphilic Polymers from Renewable Resources, Lund University. LA9910778

Nonionic Surfactant Mixtures with an Anionic

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