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Rheology of Mixed Solutions of an Associating Polymer with a Surfactant. Why Are Different Surfactants Different? Lennart Piculell,* Monica Egermayer, and Jesper Sjo¨stro¨m Physical Chemistry 1, Center for Chemistry and Chemical Engineering, Lund University, P.O. Box 124, S-221 00 Lund, Sweden Received November 15, 2002. In Final Form: February 18, 2003 The effects of nine different anionic and cationic micelle-forming surfactants on the viscosity and viscoelasticity of semidilute solutions of hydrophobically modified hydroxyethyl cellulose (HMHEC) were studied. All added surfactants gave rise to the well-established viscosity maximum with increasing surfactant concentration, but the total surfactant concentration at the maximum, as well as the magnitude of the viscosity enhancement, varied widely between the different surfactants. A detailed analysis of the oscillatory shear data for the most viscous samples showed that added surfactant affects both the lifetime and the structure of the transient HMHEC-surfactant network, due to mixed micellization between surfactant molecules and the hydrophobic side chains of HMHEC. The viscosity maximum is the result of two opposing effects of increasing surfactant concentration: an increase in the lifetime of mixed micellar cross-links and a decrease in the number of cross-links. All data indicate that the structure of the HMHEC-surfactant network and the compositions of the mixed micellar cross-links are quite similar for the various surfactants, when the mixtures are compared at their respective viscosity maxima. The shifts of the viscosity versus surfactant concentration curves between the various surfactants may thus be rationalized in terms of differences in lifetimes of the mixed micellar junctions and in the proportions of free (monomeric) surfactant. The free surfactant concentration at a given degree of surfactant binding is proportional to the critical micelle concentration of the surfactant. The lifetime of a mixed micellar cross-link increases with surfactant chain length and with the nature of the hydrophilic headgroup according to the series trimethylammonium < ammonium ≈ diethoxysulfate < sulfate.
Introduction A hydrophobically modified polymer (HMP) consists of a hydrophilic backbone to which small amounts of hydrophobic substituents, so-called hydrophobes, are attached. Semidilute aqueous solutions of HMPs exhibit enhanced viscosity, compared to solutions of nonmodified polymer, that arises from reversible intermolecular associations between the hydrophobes. The interactions between HMPs and surfactants have been a subject of extensive research in recent years.1 One reason for this interest is that added surfactant strongly affects the rheological properties of an aqueous HMP solution. This is important in applications, where HMP and surfactants generally occur together. For single-chain surfactants forming small spherical micelles, the typical result of increasing the surfactant concentration is that a maximum in the viscosity is observed at a surfactant concentration close to the critical micelle concentration (cmc) of the pure surfactant.2-10 The fact that such a * To whom correspondence should be addressed. (1) Piculell, L.; Thuresson, K.; Lindman, B. Polym. Adv. Technol. 2001, 11, 1. (2) Gelman, R. TAPPI Proceedings of the International Dissolving Pulps Conference, Geneva, 1987; TAPPI Press: Atlanta, 1987; p 159. (3) Dualeh, A. J.; Steiner, C. A. Macromolecules 1990, 23, 251. (4) Tanaka, R.; Meadows, J.; Williams, P. A.; Phillips, G. O. Macromolecules 1992, 25, 1304. (5) Nystro¨m, B.; Thuresson, K.; Lindman, B. Langmuir 1995, 11, 1994. (6) Thuresson, K.; Lindman, B.; Nystro¨m, B. J. Phys. Chem. B 1997, 101, 6450. (7) Nilsson, S.; Thuresson, K.; Hansson, P.; Lindman, B. J. Phys. Chem. B 1998, 102, 7099. (8) Panmai, S.; Prudhomme, R. K.; Peiffer, D. G. Colloids Surf., A 1999, 147, 3. (9) Piculell, L.; Nilsson, S.; Sjo¨stro¨m, J.; Thuresson, K. ACS Symp. Ser. 2000, 765, 317.
maximum has been observed for many chemically different combinations of HMP and surfactant implies a universality in the underlying molecular mechanisms. Indeed, recent work from our laboratory has shown that the relation between the surfactant concentration at the viscosity maximum, cs,max, and the cmc can be rationalized in terms of the surfactant binding isotherm. The latter gives the relation between the concentration of “free” monomeric surfactant and the composition of the mixed micellar aggregates that act as cross-links between HMP molecules.9,11 This is schematically illustrated in Figure 1. The main conclusions from the analysis were that the stoichiometry of the mixed micelles is similar for different micelle-forming surfactants at the viscosity maximum and that the differences in cs,max for different surfactants may be attributed to the difference in the concentration of free surfactant at the maximum. At a fixed composition of the mixed micelles, the equilibrium free surfactant concentration is, naturally, greater for a surfactant with a high cmc. If the nature of the binding of surfactants to the HMP hydrophobes seems to be at least qualitatively understood, there are still issues that need to be clarified and predictions to be tested. One issue concerns to what extent the initial increase in viscosity by added surfactant is caused by an increase in the number of mixed micellar cross-links, or an increase in their lifetimes, or both.7,9,10,12 Another issue concerns the large quantitative differences in the viscosity enhancement obtained for different added (10) Jime´nez-Regalado, E.; Selb, J.; Candau, F. Langmuir 2000, 16, 8611. (11) Piculell, L.; Thuresson, K.; Ericsson, O. Faraday Discuss. 1995, 101, 307. (12) Thuresson, K.; So¨derman, O.; Hansson, P.; Wang, G. J. Phys. Chem. 1996, 100, 4909.
10.1021/la020912+ CCC: $25.00 © 2003 American Chemical Society Published on Web 03/19/2003
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immersed in surfactant solutions, as a simple method to detect surfactant binding to HEC.16,17 Experimental Section
Figure 1. Schematic illustration of the effects of an added micelle-forming surfactant on the viscosity of a semidilute solution of a hydrophobically modified polymer.
surfactants. If the assumption of a similar amount of bound surfactant at the viscosity maximum is correct, then this would imply that the structure of the network is also similar and that the difference in viscosity between different surfactants is essentially due to differences in the lifetimes of the mixed micellar junctions. This hypothesis has not been systematically tested, although previous work has suggested large differences in junction lifetimes for different surfactants.6,10 For the most widely studied HMP, namely, hydrophobically modified hydroxyethyl cellulose (HMHEC), another problem exists in the interpretation of the differences between different surfactants. It has repeatedly been shown that certain surfactants bind also to nonsubstituted HEC.9,13-17 This binding is, in fact, a micellization at the polymer, which occurs at a critical association concentration, cac, that is lower than the bulk cmc. The binding to the HEC “backbone” could complicate the analysis of surfactant binding to HMHEC. In particular, it raises the question as to whether the assumption made in our previous analysis, that the surfactant binds essentially only to the HMHEC hydrophobes at the viscosity maximum, was warranted.11 Recent studies have shown that the total binding of sodium dodecyl sulfate, NaC12S, to HEC and HMHEC is quite similar at high surfactant concentrations.9 This implies that at high surfactant concentrations the binding to the HEC backbone actually dominates. The aim of the present investigation is to gain more insight into the reasons behind the quantitative differences in the effects of different surfactants on the rheology of HMP solutions in general and HMHEC in particular. To that end, we here report measurements of the rheological behavior of semidilute solutions of HMHEC mixed with nine different micelle-forming surfactants. The selected surfactants include both those that do and those that do not bind to the HEC backbone. The choice of surfactants was based on very recent studies, where we used the equilibrium swelling of chemically cross-linked HEC gels, (13) Goddard, E. D.; Hannan, R. B. In Micellization, Solubilization and Microemulsions; Mittal, K. L., Ed.; Plenum Press: New York, 1977; Vol. 2, p 835. (14) Sivadasan, K.; Somasundaran, P. Colloids Surf. 1990, 49, 229. (15) Tanaka, R.; Meadows, J.; Phillips, G. O.; Williams, P. A. Carbohydr. Polym. 1990, 12, 443. (16) Sjo¨stro¨m, J.; Piculell, L. Langmuir 2001, 17, 3836. (17) Lynch, I.; Sjo¨stro¨m, J.; Piculell, L. Manuscript in preparation.
Materials. HMHEC with the commercial name Natrosol Plus grade 331 was obtained from Aqualon. According to the manufacturer, the molecular mass of the polymer is ca. 250 000 g/mol. HMHEC contains grafted C16 alkyl chains to an extent that corresponds to approximately 0.54 mM alkyl chains in a 1 wt % aqueous solution of the polymer. The degree of hydroxyethyl group substitution is 3.3.7 Prior to use, HMHEC was dissolved in water to a concentration of 1 wt %. Low molecular impurities, such as salt, were removed by dialysis against Millipore filtered water in a Filtron Ultrasette device. The dialysis was performed until the expelled water showed a conductivity of less than 2 µS/cm. After freeze-drying, the HMHEC was stored in a plastic jar. Table 1 lists the surfactants used in this study together with their abbreviations and cmc values. For the surfactants that bind to HEC, the cac values are also given. NaC14S and C12ACl were from Lancaster, NaC12S from BDH, NaC12(EO)2S from Kao Chemicals GmbH, C16TABr from Merck, C12TABr from TCI-GR, and C12TACl from Acros. All surfactants were used without further purification. A pure sample of NaC8BS was prepared by Professor P. Botherel, Domain Universitaire, Talence, France. C16TAAc was prepared from C16TABr by ion exchange to the hydroxide salt, followed by titration with acetic acid. The ionexchange resin was Dowex 1 from Sigma. Millipore filtered water was used in all experiments. Sample Preparation. Stock solutions (2 wt %) of HMHEC were diluted with an appropriate amount of surfactant solution and water to achieve 3 mL samples with the desired surfactant concentrations and a final polymer concentration of 1.000 ( 0.002 wt %. The samples were mixed well and equilibrated for at least 3 days at 25 °C. Rheological Experiments. Oscillatory shear and steady shear measurements were conducted on a Physica UDS 200 rheometer equipped with a 1° cone and plate geometry of 50 or 70 mm in diameter, depending on the sample viscosity. Oscillatory experiments were performed for high-viscosity samples (above 1 Pa s). The storage modulus (G′), the loss modulus (G′′), and the complex viscosity (η*) were measured over the frequency range 0.05-6 Hz. The values of the stress amplitude were checked in order to ensure that all measurements were performed within the linear viscoelastic region, where the dynamic storage moduli are independent of the applied stress. The complex viscosity was obtained from G′ and G′′ through eq 1.
η* ) (G′2 + G′′2)1/2/ω
(1)
Here ω is the angular frequency of oscillation. For the highviscosity samples, the reported viscosity values are the complex viscosities extrapolated to zero frequency. For low-viscosity samples (below 1 Pa s), steady shear experiments were performed in the range of 0.5-3000 s-1, and the reported viscosity values, η, correspond to the plateau values observed at low shear rates. All rheological measurements were performed at 25 °C.
Results Experimental Design. The purpose of the present study was to establish similarities and differences between different micelle-forming surfactants in their effect on the rheology of semidilute HMHEC solutions. To that end, we used a fixed concentration of 1 wt % HMHEC (the overlap concentration is ca. 0.2 wt %)15 and studied the effect of increasing concentration for the surfactants listed in Table 1. The surfactants are chosen on the following grounds. Both cationic and anionic surfactants are included, and all (except C12TACl) have been tested in gelswelling experiments for their ability to bind to nonmodified HEC.16,17 The two alkyl sulfates, NaC8BS, and C16TAAc bind, whereas the others do not. The list includes mainly C12 surfactants, to enable a direct comparison of
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Table 1. Data on Surfactants Used systematic name
abbreviation
cmc/mMa
cac/mMb
cs,max/mMc
ηmax/Pa sc
sodium tetradecyl sulfate sodium dodecyl sulfate sodium dodecyl-di(ethylene oxide)-sulfate sodium octylbenzenesulfonate hexadecyltrimethylammonium acetate hexadecyltrimethylammonium bromide dodecyltrimethylammonium bromide dodecyltrimethylammonium chloride dodecylammonium chloride
NaC14S NaC12S NaC12(EO)2S NaC8BS C16TAAc C16TABr C12TABr C12TACl C12ACl
2.05 8.1 2.2d 11 1.8d 0.9 16 20 15
1.3 6.0 10 1.6d NDe -
3.0 7.0 5.0 11 3.2 3.2 15 19 17
35 16.3 6.5 8.0 2.4 3.2 0.67 0.32 4.8
a Values are from ref 18 except where indicated. b For binding to HEC; values were taken from ref 16 except where indicated. Dashes indicate the absence of binding. c Obtained from the data in Figure 2 (by interpolation, when necessary). d Values are from ref 17. e Not determined, but not expected.
Figure 2. Variation of zero-shear viscosities for 1 wt % aqueous HMHEC with various added ionic surfactants: NaC14S (open triangles, point up), NaC12S (open circles), NaC12(EO)2S (open squares), NaC8BS (open triangles, point down), C16TAAc (filled diamonds), C16TABr (filled triangles, point down), C12TABr (filled circles), C12TACl (filled triangles, point up), and C12ACl (filled squares).
the effects of varying the headgroup, but two longer chain surfactants have also been included, to assess the effect of alkyl chain length. Finally, for two of the cationic surfactants the counterion has been varied, since significant counterion specific effects are well established for cationic surfactants.19-21 Viscosities. Figure 2 gives an overview of the zeroshear viscosities obtained for all investigated samples and highlights the questions that we wish to address in this study. The results for each surfactant show the qualitative features illustrated in Figure 1: The viscosity has a pronounced maximum ηmax, at a certain surfactant concentration cs,max. On the other hand, the values of both ηmax and cs,max display large quantitative variations among the surfactants tested; cf. Table 1 where all values are listed. The value of cs,max clearly correlates with the surfactant cmc (a higher cmc leads to a higher cs,max), as will be discussed in more detail below. By contrast, there seems to be no single surfactant characteristic that correlates with the value of ηmax. The five surfactants that give the largest viscosity enhancement are NaC14S, (18) Mukerjee, P.; Mysels, K. J. Critical Micelle Concentrations of Aqueous Surfactant Systems; National Bureau of Standards, U.S. Government Printing Office: Washington, DC, 1971. (19) Anacker, E. W.; Ghose, H. M. J. Phys. Chem. 1963, 67, 1713. (20) Pashley, R. M.; McGuiggan, P. M.; Ninham, B. W.; Brady, J.; Evans, D. F. J. Phys. Chem. 1986, 90, 1637. (21) Bales, B. L.; Zana, R. J. Phys. Chem. B 2002, 106, 1926.
Figure 3. Frequency dependencies of G′ (solid line), G′′ (dashed line), and η* (dotted line) for 1 wt % HMHEC in 7.0 mM aqueous sodium dodecyl sulfate. Thin lines indicate limiting slopes of 1 and 2. Arrows indicate the crossover coordinates.
NaC12S, NaC8BS, NaC12(EO)2S, and C12ACl. This group includes both anionic and cationic surfactants, with low or high cmc values and with bulky or small headgroups. Moreover, this group of surfactants includes two (C12ACl and NaC12(EO)2S) that do not bind to the HEC backbone. Mechanical Spectra. The most viscous samples of the five most viscosifying surfactants were clearly viscoelastic. Oscillatory measurements on these samples gave “mechanical spectra” of the type shown in Figure 3, featuring a crossover of G′ and G′′ as the frequency of oscillation was increased. In agreement with earlier results on hydrophobically modified cellulose ethers,4,6 the spectra could not be fitted to a single Maxwell element. In fact, within the accessible frequency window the spectra that showed a crossover did not reach the low-frequency plateau of the complex viscosity, or the limiting slopes of 2 and 1, respectively, for log G′ and log G′′ when plotted against log ω. Consequently, neither the terminal relaxation times nor the plateau moduli could be extracted from the oscillatory measurements on these systems. We have therefore used the crossover coordinates to characterize the mechanical spectra. These coordinates will be referred to as the crossover modulus, Gc, and angular frequency, ωc, respectively. From ωc, we may define an apparent relaxation time as
τc ) 1/ωc
(2)
Since the HMHEC/surfactant mixtures display a wide distribution of relaxation times, the absolute values of Gc and τc have no clear physical meaning in these systems. We will use these parameters for relative comparisons
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Figure 5. Normalized mechanical spectra (see text) for 1 wt % HMHEC in 4.1, 7.0, or 10.6 mM aqueous NaC12S. Solid and dashed lines refer to G′ and G′′, respectively.
Figure 4. Variation of the crossover modulus (a) and the apparent relaxation time (b) of 1 wt % aqueous HMHEC with the total concentration of added NaC14S (open triangles, point up), NaC12(EO)2S (open squares), NaC12S (open circles), NaC8BS (open triangles, point down), or C12ACl (filled squares). Crosses indicate locations of the viscosity maxima for the various surfactants.
only, as a convenient means to describe how the mechanical spectra change with concentration and type of added surfactant. When interpreting such trends, we will make the reasonable assumptions that changes in Gc and τc indicate changes in the number and the lifetime of the mixed micellar cross-links, respectively. Figure 4 shows how the crossover modulus and the apparent relaxation time vary with surfactant concentration for the five surfactants that give the highest viscosity. For experimental reasons, the data sets are limited to the most viscous samples; therefore, wider ranges of surfactant concentration are covered for the most viscosifying surfactants. Clear trends are seen. For a given surfactant, the crossover modulus decreases with increasing surfactant concentration (Figure 4a), and the decrease begins already at a surfactant concentration below cs,max. The highest value of Gc observed is similar for all surfactants. By contrast, the range of values of the apparent relaxation time varies considerably for different surfactants (Figure 4b). For most surfactants, an increase in the relaxation time with increasing surfactant concentration is clearly seen. The increase begins far below cs,max, but it continues beyond cs,max. It thus appears that both the degree of cross-
linking (as monitored by Gc) and the dynamics (as monitored by τc) vary across the viscosity maximum in 1 wt % HMHEC solutions with different surfactants. Indeed, the maximum in viscosity may be seen as a result of two opposing trends: A decrease in the modulus and a slowing down of the dynamics. Superposition plots give further support to the conclusion that both the degree of cross-linking and the dynamics of the HMHEC/surfactant mixtures vary with increasing surfactant concentration. Figure 5 shows three mechanical spectra for mixtures with NaC12S. The selected surfactant concentrations correspond to the viscosity maximum and to the lowest and highest surfactant concentrations where mechanical spectra could be obtained. All spectra are normalized relative to the crossover point; that is, the frequency axis shows ω/ωc, and the modulus axis, the moduli divided by Gc. Clear trends are seen for the lowfrequency parts of the spectra (below ωc): The slopes of both G′ and G′′ increase with increasing surfactant concentration. In fact, at the highest surfactant concentration investigated, the limiting slopes of 2 and 1 are approached. The same trends were seen for the other surfactants (not shown). The fact that the normalized spectra do not overlap indicates that not only the overall time scale of the relaxation (as monitored by τc) but also the distribution of relaxation times changes with surfactant concentration. Most likely, the latter feature can be attributed to a change in the degree of cross-linking. Discussion Surfactant Concentration at the Viscosity Maximum. We have previously argued that the similarity of the nonmonotonic viscosity versus concentration curves for different surfactants implies a certain universality of HMP/surfactant mixures.11 More specifically, we expect that at the viscosity maximum, the mixed micellar aggregates that cross-link the HMP molecules should be similar for such surfactants that normally form small, spherical micelles. The argument goes as follows. At the viscosity maximum, there are no pure surfactant micelles, devoid of HMP hydrophobes. Pure surfactant micelles only appear when the HMP molecules have been saturated with surfactant molecules, which occurs at much higher surfactant concentrations, where the viscosity has leveled off at a low value. Hence, the total surfactant concentration at the viscosity maximum can be described
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Rewriting eq 7 in terms of β and γ, we obtain the desired relation showing that γ is completely determined by β.
γ ) β /(1 + β)
Figure 6. Correlation between cmc and the total surfactant concentration at the viscosity maximum in 1 wt % HMHEC for all investigated surfactants. The solid line is a linear fit to all data points (taken from Table 1). The dotted line represents cs,max ) cmc. The dashed line indicates the concentration of bound surfactant which, according to the analysis in the text, is roughly the same for all surfactants.
as a sum of the concentrations of bound (in mixed micelles) and free surfactant,
cs,max ) cb,max + cf,max
(3)
with the subscripts f and b for free and bound, respectively. Now we introduce the stoichiometry of the mixed micelles as the binding ratio,
β ) cb/ch
(4)
where ch is the concentration of HMP hydrophobes in the mixed micelles. The binding ratio is the simplest parameter that characterizes the mixed micelle. We also define the reduced free surfactant concentration,
γ ) cf/cmc
(5)
which relates the concentration of monomeric surfactant to its maximum concentration, that is, the cmc. Using definitions 4 and 5, we can rewrite eq 3 as
cs,max ) βmaxch + γmaxcmc
(6)
If the stoichiometry of the mixed micelles at the viscosity maximum is the same for a series of different surfactants, then βmaxch should be a constant at a fixed HMP concentration. If, furthermore, the reduced free surfactant concentration is the same for all the surfactants at the viscosity maximum, then eq 6 predicts that a plot of cs,max against cmc should give a straight line. Figure 6 shows that the data for all surfactants of our investigation indeed are well represented by such a plot. Why, then, should γmax be constant for all surfactants? This should be the case if the surfactant binding isotherm, which describes the relation between the reduced free surfactant concentration and the stoichiometry of the mixed micelles, is the same for the different surfactants. For the simple and instructive case of ideal mixing in the micelles, this is strictly true. In the latter case, the following relation holds between the composition of the mixed micelles and the free surfactant concentration.22
cf ) [cb/(cb + ch)]cmc
(7)
(8)
The ideal mixing model, just like the analogous Raoult’s law for the partial pressures above liquid mixtures, becomes increasingly accurate for the dominating component as its fraction in the mixture approaches unity. In other words, we expect that eq 8 should be a reasonable approximation under conditions when the mixed micelles are dominated by surfactant molecules. From the intercept and the slope of the fit in Figure 6, and using the value ch ) 0.54, we obtain γmax ) 0.87 and βmax ) 3.4. This means that at the viscosity maximum the mixed micelles are dominated by surfactant molecules and that the free surfactant concentration in equilibrium with these aggregates is close to the cmc. A similar analysis was made previously,11 using data from a study by Tanaka et al.4 on HMHEC with a different set of surfactants (including nonionics and carboxylates, but no cationics). The latter analysis gave the values γmax ) 0.7 and βmax ) 3. Viscosity and surfactant binding data from our previous study9 yield γmax ) 0.6 and βmax ) 4 for mixtures of NaC12S and HMHEC. Although there is some spread in the numbers obtained, these independent estimates nevertheless yield reasonably similar values of γmax and βmax. In their study of hydrophobically modified ethyl hydroxyethyl cellulose (HMEHEC) with different surfactants, Thuresson et al. also made an analysis of their results in terms of eq 6.6 They found a satisfactory agreement, with reasonable values for γmax and βmax. In this context, we note that other authors, observing that for some surfactants cs,max < cmc while cs,max > cmc for others, have speculated that this might reflect differences in the mode of interaction between the surfactant and the HMP.8 Figure 6 shows, however, that the observed behavior is entirely expected; the dotted line cs,max ) cmc crosses the line fitted to the experimental data. For surfactants with a low cmc, the bound surfactant fraction dominates at the viscosity maximum, and cs,max > cmc. For surfactants with a high cmc, on the other hand, the free surfactant fraction dominates and cs,max < cmc, since cf < cmc. The exact location of the crossover (where cs,max ) cmc) will, of course, depend on ch. Tanaka et al.,4 Panmai et al.,8 and Jime´nez-Regalado et al.10 found that cs,max increased only weakly in mixtures with NaC12S when ch was increased, by increasing either the HMP concentration or the degree of modification of the chains. Again, this behavior is predicted by eq 6. In an experiment where ch is increased, cf,max ) γmaxcmc should be constant while cb,max ) βmaxch increases. However, since the former term typically dominates for mixtures with NaC12S (cf. Figure 6), the relative increase in cs,max is weak. What determines the maximum viscosity? The findings in Figure 6 are consistent with the notion that the mixed micellar aggregates are quite similar for different surfactants at the viscosity maximum. This, in turn, would imply that the overall structures of the polymer-surfactant networks are quite similar for the different surfactants at the viscosity maxima. For the solutions that give the highest viscosities, we have an indirect means of testing this assumption, by examining their mechanical spectra more closely. We have seen in Figures 4 and 5 above that for a given surfactant, the apparent relaxation time, the crossover modulus, and the (22) Ogino, K.; Abe, M. Mixed Surfactant Systems; Marcel Dekker: New York, 1993.
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Figure 7. Superposition of normalized mechanical spectra for 1 wt % HMHEC in aqueous NaC14S, NaC12(EO)2S, NaC12S, NaC8BS, and C12ACl. Solid and dashed lines refer to G′ and G′′, respectively. All data refer to mixtures at the respective viscosity maxima for the different surfactants.
Figure 8. Correlation between the crossover parameters Gc,max (filled circles), τc,max (filled squares), and the maximum viscosity for 1 wt % HMHEC in aqueous NaC14S, NaC12(EO)2S, NaC12S, NaC8BS, and C12ACl. All data (taken from Table 1) refer to mixtures at the respective viscosity maxima for the different surfactants. The dashed line is a linear fit to the τc,max data.
low-frequency slopes of the moduli vary with surfactant concentration. On the other hand, the analysis above implies that at the viscosity maximum the systems should be structurally quite similar. Consequently, the variation between different systems should be essentially only dynamic. Further analyses of our data indicate that this is indeed the case. Figure 7 compares the normalized mechanical spectra obtained for different surfactants at their respective viscosity maxima. These spectra almost superimpose. This is not a trivial result, given that the normalized spectra for each surfactant vary strongly with the surfactant concentration (cf. Figure 5) and that the variation in surfactant concentration is much larger in Figure 7 than in Figure 5. Moreover, the various systems essentially vary only in their dynamics, not in the crossover modulus. This is shown in Figure 8, where the crossover parameters Gc,max and τc,max have been plotted against the maximum viscosity ηmax for the five surfactants that give the largest viscosity enhancement. The variation in Gc,max is relatively small and shows no clear trend. This agrees with the notion
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that the degree of cross-linking is similar for all surfactants at the viscosity maximum. By contrast, τc,max is strongly correlated with ηmax; in fact, the two quantities are essentially proportional. This variation in dynamics should reflect variations in the lifetime of the hydrophobes in the mixed micellar junctions. An increased lifetime should (all other things being equal) lead to an increase in τc, although the two quantities are not simply related.23,24 Absence of Effects of Binding to the HEC Backbone. The rheology of the various HMHEC-surfactant mixtures seems rather insensitive to whether the surfactant binds to the HEC backbone. This might seem surprising. However, we believe that the explanation is that no significant binding to the backbone occurs at or below the viscosity maximum, since the free surfactant concentration at this point is still low compared to the cac for surfactant binding to the backbone.9 This conclusion might not apply to all systems where binding to the backbone occurs, but it seems to hold at least for HMHEC, since the cac for HEC is only marginally lower than the cmc. Our previous investigation of the binding of NaC12S to HMHEC indicates that the free surfactant concentration at or below the viscosity maximum is cs,max. Comparing the Surfactants. Our results (cf. Figure 2 and Table 1) confirm trends observed previously for mixtures of ionic surfactants and nonionic HMPs, that is, that anionic surfactants generally give larger viscosity enhancements than cationics6,8,10 and that the effect decreases with decreasing chain length in a homologous series of surfactants.4,6 In our results, these trends are illustrated by the decrease of ηmax in the series NaC14S > NaC12S > C16TABr > C12TABr. It is also interesting to compare the effects of changing the headgroup structure for surfactants bearing the same charge. Previously, Tanaka et al. found quite similar values of ηmax for alkanoate and alkyl sulfate surfactants when comparing alkyl chains of the same length.4 Our results indicate that the viscosifying effect decreases when the headgroup is made bulkier, both for anionic and cationic surfactants. Thus, NaC12(EO)2S gives smaller effects than NaC12S, and C12TACl gives much smaller effects than C12ACl. NaC8BS is not directly comparable to the other anionic surfactants, since the benzene group may be considered as part of the hydrophobic “tail” rather than the hydrophilic “head”. Finally, there are some small, but significant, counterion effects for the cationic surfactants. The bromide counterion gives a larger viscosity enhancement than the chloride or acetate ion. Moreover, the decrease in viscosity at surfactant concentrations above cs,max is more gradual for C16TABr than for C12TAAc. This difference is an expected consequence of the fact that the bromide counterion, as opposed to the acetate counterion, gives rise to significant micellar growth of the cetyltrimethylammonium surfactant as the concentration is increased above the cmc.25,26 Earlier studies have shown that a larger aggregation number of the surfactant gives rise to a more extended viscosity maximum with increasing surfactant concentration.6,8,27,28 This is because the decrease in (23) Leibler, L.; Rubinstein, M.; Colby, R. H. Macromolecules 1991, 24, 4701. (24) Jime´nez-Regalado, E.; Selb, J.; Candau, F. Macromolecules 1999, 32, 8580. (25) Ilekti, P.; Martin, T.; Cabane, B.; Piculell, L. J. Phys. Chem. B 1999, 103, 9831. (26) Hansson, P.; Jo¨nsson, B.; Stro¨m, C.; So¨derman, O. J. Phys. Chem. B 2000, 104, 3496.
Rheology of Mixed Polymer-Surfactant Solutions
viscosity beyond cs,max is mainly caused by an increase in the number of mixed micelles and hence a decrease in the number of HMP hydrophobes per micelle. By contrast, for the dodecylammonium surfactant, which has a shorter alkyl chain, the micelles remain small and spherical in the concentration range investigated here, irrespectively of the counterion (chloride or bromide).21,26 This is consistent with our finding that there is no difference in width of the viscosity maxima produced by C12TABr and C12TACl. Mechanical Spectra: Comparisons with Previous Findings. The most detailed rheological studies to date on HMP/surfactant mixtures are those on HMEHEC by Thuresson et al.6,29 and on hydrophobically modified polyacrylamide (HMPAm) by Jime´nez-Regalado et al.10 These systems show both similarities and differences with the HMHEC/surfactant mixtures. Both HMEHEC and HMPAm show a nonmonotonic variation of τc with surfactant concentration, with a maximum that occurs either close to6 or beyond10 cs,max. The existence of a similar maximum at some concentration significantly above cs,max is suggested by our data for NaC12S and NaC8BS. However, because of the rapid decrease in viscosity at surfactant concentrations above cs,max, we were unable to extend our measurements of mechanical spectra to higher surfactant concentrations to test this point further. As regards the modulus, Jime´nezRegalado et al. found no variation in Gc with surfactant content for mixtures of HMPAm with NaC12S.10 By contrast, Thuresson29 found that the fitted plateau modulus varied strongly with surfactant concentration, displaying a broad maximum, for all tested surfactants. Notably, at least for anionic surfactants, the plateau modulus was found to be significantly influenced by surfactant binding to the EHEC main chain. Possibly this is why for HMEHEC, in contrast to our findings for HMHEC, the maximum in the modulus occurred either at or above cs,max. In another study on the same type of mixtures, Thuresson et al. found that the number of hydrophobes per mixed micelle started to decrease already before the viscosity maximum.12 This is consistent with the notion of a decrease in network connectivity prior to cs,max. The relaxation time distributions, as evidenced by the mechanical spectra, also vary between different systems. Jime´nez-Regalado et al. found that the low-frequency parts of the mechanical spectra for HMPAm, almost up to ωc, were superimposable and could be fitted to a single Maxwell element (one relaxation time), both with and without added surfactant. These results are clearly different from ours (cf. Figure 5). The difference does not seem to be attributable to HMP concentration, since the findings of Jime´nez-Regalado et al. were found to hold at all polymer concentrations above the overlap concentration. Evidently, the HMPAm/surfactant systems are in some respects simpler than those based on hydrophobically modified cellulose ethers. For the latter systems, on the other hand, Thuresson et al. reported extended mechanical spectra, corresponding to a distribution of relaxation times, for various HMEHEC/surfactant mixtures.6 Moreover, they found that the width of the distribution passed (27) Sarrazin-Cartalas, A.; Iliopoulos, I.; Audebert, R.; Olsson, U. Langmuir 1994, 10, 1421. (28) Piculell, L.; Guillemet, F.; Thuresson, K.; Shubin, V.; Ericsson, O. Adv. Colloid Interface Sci. 1996, 63, 1. (29) Thuresson, K. Solution properties of a hydrophobically modified polymer. Doctoral Thesis, Lund University, Lund, Sweden, 1996.
Langmuir, Vol. 19, No. 9, 2003 3649
through a maximum close to cs,max, to approach the limiting case of a single relaxation time at high surfactant concentrations. Conclusions The main findings of the present study and the conclusions that could be drawn from them may be summarized as follows. All tested surfactants gave rise to similar nonmonotonic effects on the viscosity of 1 wt % HMHEC solutions, with an initial increase followed by a viscosity maximum and then a decrease in viscosity. There were large quantitative variations among the surfactants. The viscosity-enhancing efficiency increased with increasing surfactant chain length and with the nature of the hydrophilic headgroup according to the series trimethylammonium < ammonium ≈ diethoxysulfate < sulfate. When different surfactants were compared, the concentration of surfactant required for the maximum viscosity was found to vary linearly with the cmc. This indicates that the observed differences in the total surfactant concentration at the maximum mainly reflect differences in the free surfactant concentration. For a given added surfactant, significant changes in both the degree and the dynamics of the cross-linking occurred with increasing surfactant concentration across the viscosity maximum. The mechanical spectra from oscillatory measurements, obtained at different surfactant concentrations, could not be superimposed by simple shifts along the frequency and modulus axes. The apparent relaxation time was found to increase monotonically, whereas the crossover modulus decreased. This indicates that the lifetimes of the mixed micellar junctions increase across the maximum, whereas the degree of cross-linking by mixed micellar junctions decreases. The maximum in viscosity results from the opposing effects of these two trends. Results obtained at the viscosity maximum showed many similarities for different surfactants. The mechanical spectra were nearly superimposable by shifts along the frequency and modulus axes. While the crossover modulus was nearly constant, the apparent relaxation time was found to increase with increasing viscosity in a nearly proportional fashion. These results imply that the structures of HMHEC-surfactant mixed solutions are quite similar at the viscosity maximum and that the differences in viscosifying efficiency between the different surfactants are due to differences in the lifetimes of the mixed micellar junctions. The rheology of the HMHEC-surfactant mixtures was insensitive to whether the surfactant could bind to the HEC backbone. This implies that the binding to the HEC backbone is insignificant around the viscosity maximum and that a massive binding to the HEC backbone occurs only at surfactant concentrations high above the maximum, where the viscosity has already decreased substantially. Acknowledgment. This work was financed by the Centre for Amphiphilic Polymers from Renewable Resources (CAP) at Lund University (M.E. and J.S.) and by the Swedish Research Council (L.P.). Anna Svensson and Iseult Lynch are acknowledged for the preparation and cmc determination of C16TAAc. We thank Krister Thuresson for valuable discussions. LA020912+
