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Linear and Nonlinear Viscoelasticity of Semidilute Aqueous Mixtures of a Nonionic Cellulose Derivative and Ionic Surfactants Reidar Lund,† Rolf Andreas Lauten,† Bo Nystro¨m,*,† and Bjo¨rn Lindman‡ Department of Chemistry, University of Oslo, P.O. Box 1033, Blindern, N-0315 Oslo, Norway, and Physical Chemistry 1, Chemical Center, University of Lund, P.O. Box 124, SE-221 00 Lund, Sweden Received July 12, 2001. In Final Form: September 18, 2001 Linear and nonlinear viscoelasticity of aqueous solutions of ethyl(hydroxyethyl)cellulose (EHEC) in the presence of a surfactant (sodium dodecyl sulfate (SDS) or cetyltrimethylammonium bromide (CTAB)) have been examined over an extended polymer concentration regime at different surfactant-to-polymer ratios (r). By tuning the value of r and the polymer concentration, the strength of the polymer-surfactant associations can be modulated. At moderate levels of surfactant addition, the viscosity enhancement is much more pronounced for the EHEC-SDS system than for the EHEC-CTAB system. The frequency dependencies of the dynamic moduli cannot in general be described by a simple Maxwell model, but the rheological behavior is more complex with a distribution of relaxation modes. For EHEC solutions without surfactant, the polymer concentration dependence of the zero-shear viscosity η0 can above the entanglement concentration be described by a power law (η0 ∼ Cx, with x ) 4.1). By addition of CTAB, the main effect is that the power-law regime is extended toward lower polymer concentrations. In the presence of SDS, a more complex picture appears, with three power law regimes for the polymer-surfactant composition giving rise to the strongest association structures. These results can partially be interpreted in the framework of a model by Rubinstein and Semenov (Macromolecules 2001, 34, 1058) for entangled associating polymer solutions. Significant shear-thinning effects and deviations from the Cox-Merz rule are observed for systems exhibiting pronounced polymer-surfactant interactions.
Introduction The synergism of ionic surfactants and nonionic amphiphilic polymers in aqueous solution has attracted a great deal of attention in recent years in fundamental and applied research. This research field is driven by the importance of mixtures of amphiphilic polymers and ionic surfactants in a number of industrial applications including detergents, pharmaceuticals, and paints.1-5 The behavior of this type of systems is governed by a subtle balance between hydrophilic, hydrophobic, and ionic interactions. Aqueous solutions of ethyl(hydroxyethyl)cellulose (EHEC) with the addition of an ionic surfactant constitute a well-studied system6-18 of this class. This † ‡
University of Oslo. University of Lund.
(1) Polymers as Rheology Modifiers; Schulz, D. N., Glass, J. E., Eds.; ACS Symposium Series 462; American Chemical Society: Washington, DC, 1991. (2) Lindman, B.; Tomlin, J.; Carlsson, A. In Cellulosics: Chemical, Biochemical, and Material Aspects; Kennedy, J. F., Philips, G. O., Williams, P. A., Eds.; Ellis Horwood: Chichester, 1993; pp 319-324. (3) Interactions of Surfactants with Polymers and Proteins; Goddard, E. D., Ananthapadmanabhan, K. P., Eds.; CRC Press: Boca Raton, FL, 1993. (4) Macromolecular Complexes in Chemistry and Biology; Dubin, P., Bock, J., Davies, R. M., Schulz, D. N., Thies, C., Eds.; Springer-Verlag: Berlin, 1994. (5) Polymer-Surfactant Systems; Kwak, J. C., Ed.; Marcel Dekker: New York, 1998; Vol. 77. (6) Karlstro¨m, G.; Carlsson, A.; Lindman, B. J. Phys. Chem. 1990, 94, 5005. (7) Lindman, B.; Carlsson, A.; Karlstro¨m, G.; Malmsten, M. Adv. Colloid Interface Sci. 1990, 32, 183. (8) Nystro¨m, B.; Lindman, B. Macromolecules 1995, 28, 967. (9) Walderhaug, H.; Nystro¨m, B.; Hansen, F. K.; Lindman, B. J. Phys. Chem. 1995, 99, 4672, (10) Wang, G.; Olofsson, G. J. Phys. Chem. 1995, 99, 5588. (11) Bloor, D. M,; Wan-Yunus, W. M. Z.; Wan-Badhi, W. A.; Li, Y.; Holzwarth, J. F.; Wyn-Jones, E. Langmuir 1995, 11, 3395.
amphiphilic polymer is characterized by mixed hydrophobic and hydrophilic structural units, and these elements are normally unevenly distributed along the polymer backbone and the substituents may consist of shorter or longer subchains. As a result, a complex structure with an irregular distribution of hydrophobic microdomains is evolved and the interactions between polymer chains and ionic surfactant give rise to the formation of micellar-like clusters involving substituents from one or more EHEC chains. In the presence of ionic surfactants, the surfactant is bound to the polymer and this endows an apparent polyelectrolyte character to the originally nonionic EHEC. The surfactant binding to the polymer usually results in an increase in the cloud point temperature7 of the system (see Figure 1); that is, the solubility of the polymer increases. In semidilute solutions of EHEC in the presence of moderate levels of an ionic surfactant, the surfactant clusters either act as junctions or strengthen already existing connections between segments on different polymer chains. At this stage, the surfactant-promoted interpolymer interaction induces a viscosity enhancement. The viscosity maximum is shifted toward higher surfactant (12) Cabane, B.; Lindell, K.; Engstro¨m, S.; Lindman, B. Macromolecules 1996, 29, 3188. (13) Nystro¨m, B.; Kjøniksen, A.-L.; Lindman, B. Langmuir 1996, 12, 3233. (14) Wang, G.; Lindell, K.; Olofsson, G. Macromolecules 1997, 30, 105. (15) Kjøniksen, A.-L.; Nystro¨m, B.; Lindman, B. Macromolecules 1998, 31, 1852. (16) Lindell, K.; Cabane, B. Langmuir 1998, 14, 6361. (17) Kjøniksen, A.-L.; Nystro¨m, B.; Lindman, B. Colloids Surf., A 1999, 149, 347. (18) Ostrovskii, D.; Torell, L. M.; Nystro¨m, B.; Kjøniksen, A.-L. Macromolecules 1999, 32, 1534.
10.1021/la011072m CCC: $20.00 © 2001 American Chemical Society Published on Web 12/01/2001
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Figure 1. Effect of CTAB and SDS addition on the cloud point of 2 wt % EHEC solutions.
concentration15,19 and assumes higher values as the polymer concentration increases. In a recent rheological study15 on semidilute EHEC solutions in the presence of sodium dodecyl sulfate (SDS), it was shown that the dynamic viscosity passes through a maximum at a certain mass ratio of SDS-to-EHEC (r ) CSDS/CEHEC), which is the same for all the considered polymer concentrations. This ratio was found to be a useful parameter in the analysis of rheological features. It is expected that the magnitude and position of the viscosity maximum are governed by factors such as the type of surfactant, hydrophobicity of the polymer, and the distribution of the hydrophobic microdomains of the polymer. The general picture that emerges is that strengthening of the association network occurs at moderate values of the ratio r, while a gradual disruption of the network takes place at high values of r. Although dynamical8,17,20 and rheological13,15,21 measurements on semidilute aqueous systems of EHEC in the presence of an ionic surfactant have previously been reported, there is a lack of rheological studies, especially in the nonlinear viscoelastic regime, covering an extended polymer concentration range and different polymersurfactant compositions. An issue that has attracted a great deal of rheological interest, both from experimental and theoretical points of view, in recent years is the concentration dependence of the zero-shear viscosity η0. A number of theoretical approaches have been elaborated to describe the concentration dependence of η0 (in form of power laws) in unentangled and entangled solutions of uncharged nonassociating flexible polymers22,23 and polyelectrolytes.24-27 Theoretical models for the description of rheological properties in associating polymer solutions have also been advanced28-32 during the past few years. Moreover, by using Monte Carlo simulation Groot and (19) Piculell, L.; Thuresson, K.; Ericsson, O. Faraday Discuss. 1995, 101, 307. (20) Kjøniksen, A.-L.; Nystro¨m, B.; Lindman, B. Langmuir 1998, 14, 5039. (21) Nystro¨m, B.; Walderhaug, H.; Hansen, F. K.; Lindman, B. Langmuir 1995, 11, 750. (22) De Gennes, P.-G. Scaling Concepts in Polymer Physics; Cornell University Press: Ithaca, NY, 1979. (23) Colby, R. H.; Rubinstein, M. Macromolecules 1990, 23, 2753. (24) Rubinstein, M.; Colby, R. H.; Dobrynin, A. V. Phys. Rev. Lett. 1994, 73, 2776. (25) Dobrynin, A. V.; Colby, R. H.; Rubinstein, M. Macromolecules 1995, 28, 1859. (26) Muthukumar, M. J. Chem. Phys. 1997, 107, 2619. (27) Dobrynin, A. V.; Rubinstein, M. Macromolecules 1999, 32, 915. (28) Leibler, L.; Rubinstein, M.; Colby, R. H. Macromolecules 1991, 24, 4701. (29) Tanaka, F.; Edwards, S. F. Macromolecules 1992, 25, 1516. (30) Semenov, A. N.; Joanny, J.-F.; Khokhlov, A. R. Macromolecules 1995, 28, 1066. (31) Rubinstein, M.; Dobrynin, A. V. Trends Polym. Sci. 1997, 5, 181.
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Agterof33 have studied the equation of state and rheological features of associative polymer networks. Khalatur et al.34 have utilized nonequilibrium molecular dynamics simulations to investigate rheological and other properties of self-associating polymer systems composed of flexible telechelic chains with associating end groups. Quite recently linear viscoelasticity in solutions of associating polymers both near the gelation point and in the reversible network region was considered theoretically for unentangled35 and entangled36 systems. These models address inter alia the dramatic changes of the rheology of associative polymers near the gelation threshold. The models35,36 of Rubinstein and Semenov predict several power law regimes for the concentration dependence of the zero-shear viscosity, and the value of the power law exponent changes depending on the considered concentration regime and whether the solutions of associating polymers are unentangled or entangled. In this paper, we report measurements of linear and nonlinear viscoelasticity for semidilute/concentrated aqueous solutions of EHEC in the presence of the anionic SDS or with the cationic surfactant cetyltrimethylammonium bromide (CTAB). The oscillatory shear and viscosity experiments are carried out over an extended polymer concentration range and at surfactant-polymer compositions (r) representing both weak and strong network associations. To mimic the same polymer-surfactant conditions, each concentration series is conducted at a fixed value of r. The surmise is that the rheological properties of these systems are governed by the coexistence of hydrophobic associations, topological entanglements (at higher polymer concentrations), and possibly also polyelectrolyte effects. The main objective of this study is to elucidate how rheological features, with special reference to the concentration dependence of the zero-shear viscosity, are affected by the intricate interplay of these effects. Experimental Section Materials and Sample Preparation. The EHEC sample employed in this work is designated DVT 89017 and was manufactured by Akzo Nobel Surface Chemistry AB, Stenungsund, Sweden. The degree of substitution of ethyl groups was DSethyl ) 1.9 per anhydroglucose unit, and the molar substitution of ethylene oxide groups was MSEO ) 1.3 per anhydroglucose unit. The number average molecular weight of this sample is approximately 80 000, and the polymer is polydisperse with a polydispersity index (Mw/Mn) of about 2. All these data have been given by the manufacturer. The cationic CTAB and anionic SDS were both purchased from Fluka and were used without further purification. The water was double distilled. Dilute EHEC solutions were dialyzed against pure water for at least 1 week (until the conductivity of the expelled water showed no further decrease) to remove salt (impurity from manufacturing) and other low molecular weight components and were thereafter freeze-dried. As dialyzing membrane, regenerated cellulose with a molecular weight cutoff of 8000 (Spectrum Medical Industries) was used. After freeze-drying, the polymer was redissolved in aqueous media with the desired CTAB or SDS concentrations. The samples were prepared by weighing the components, and the solutions were homogenized by stirring at room temperature for several days. The measurements were (32) Rubinstein, M.; Dobrynin, A. V. Curr. Opin. Colloid Interface Sci. 1999, 4, 83. (33) Groot, R. D.; Agterof, W. G. M. J. Chem. Phys. 1994, 100, 1649 and 1657. Groot, R. D.; Agterof, W. G. M. Macromolecules 1995, 28, 6284. (34) Khalatur, P. G.; Khokhlov, A. R.; Mologin, D. A. J. Chem. Phys. 1998, 109, 9602 and 9614. Khalatur, P. G.; Khokhlov, A. R.; Kovalenko, J. N.; Mologin, D. A. J. Chem. Phys. 1999, 110, 6039. (35) Rubinstein, M.; Semenov, A. N. Macromolecules 1998, 31, 1386. (36) Rubinstein, M.; Semenov, A. N. Macromolecules 2001, 34, 1058.
Viscoelasticity of Polymer-Surfactant Systems performed on EHEC-SDS and EHEC-CTAB systems over an extended EHEC concentration regime at different levels of surfactant addition. In most experiments, the surfactant-topolymer ratio (r) was kept fixed during the variation of the polymer concentration to preserve attuned conditions for the polymer-surfactant mixtures. The polymer concentrations are above the overlap concentration C*, estimated from C* ) 1/[η], where [η] is the intrinsic viscosity. The value of C* varies roughly37 from 0.2 to 0.4 wt % as the SDS concentration increases from 0 to 50 mm. No systematic investigation of the intrinsic viscosity for the EHEC-CTAB system at various conditions exists, but we expect that the change in C* is less pronounced with increasing level of CTAB addition. As discussed below, the relative viscosity will be employed in the estimation of the entanglement concentration. It may be instructive to estimate the typical size of the polymer coils considered in this work and to compare it with the size of a typical micelle formed by the surfactants. This can be accomplished by using the Einstein relation for a sphere: [η] ) 10πNARH3/3M, where NA is Avogadro’s constant, RH is the hydrodynamic radius, and M is the molecular weight. From this relationship, the hydrodynamic radius is found to be approximately 24 nm, which is about six times larger than a typical surfactant micelle. Rheological Experiments. Oscillatory shear and viscosity measurements were conducted in a Bohlin VOR rheometer system using, depending on the viscosity of the sample, a doublegap concentric cylinder, an ordinary concentric cylinder geometry (C14 or C25 cup and bob geometries), or a cone-and-plate geometry, with a cone angle of 5° and a diameter of 30 mm. The double-gap device is applicable for low-viscosity liquids. To prevent dehydration from the solution, a thin layer of low-viscosity silicone oil (the viscoelastic response of the sample is not affected by this layer) was placed onto the top of the measuring unit. The rheometer is equipped with a temperature control unit that was calibrated to give a temperature in the sample chamber within 0.1 °C of the set value. All rheological experiments were conducted at a temperature of 25.0 °C. The values of the strain amplitude were checked to ensure that all oscillatory shear experiments were carried out within the linear viscoelastic regime, where the dynamic storage modulus (G’) and loss modulus (G’’) are independent of the strain amplitude. The oscillating sweep measurements were performed in the approximate frequency (f) domain 0.02-9 Hz. The viscosity experiments were conducted over an extended shear rate range (covering both the linear and nonlinear viscoelastic regimes). The shear rate dependence of the viscosity was usually monitored as a function of increasing shear rate. To investigate possible hysterises effects, the shear-rate dependence of the viscosity of the systems was monitored as a function of increasing shear rate (up-ramp curve), and the subsequent decline in shear rate (down-ramp curve) was also probed. Between measurements, the sample was allowed to equilibrate for some time before the experiments were commenced. No hysterises effects were detected under the considered experimental conditions, and the up-ramp curve and the down-ramp curve coincided.
Results and Discussion Before the results are presented and discussed, it may be helpful for the continuing discussion to give some general aspects on the characteristic behaviors of these EHEC-surfactant systems. The amphiphilic EHEC polymer dissolved in water exhibits a lower consolute solution temperature (LCST) (demixing upon heating). The cloud point of aqueous EHEC without surfactant has been observed15 to decrease with increasing polymer concentration. The surfactants CTAB and SDS are both known8,10,21 to interact strongly with EHEC, and NMR self-diffusion measurements9 have demonstrated that the degree of surfactant binding to EHEC, at a given total surfactant concentration, is higher in the presence of CTAB than with SDS. The adsorption of surfactant to the polymer (37) Hoff, E.; Nystro¨m, B.; Lindman, B. Langmuir 2001, 17, 28.
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gives rise to amended thermodynamic conditions for both the EHEC-CTAB and EHEC-SDS systems; i.e., the cloud points for the systems display higher values as the surfactant concentration increases (see Figure 1). We can see that the cloud point curve, at a given polymer concentration (2 wt %), passes through a shallow minimum at low surfactant concentrations for both systems and then, as the surfactant concentration is increased, is shifted toward considerably higher temperatures for the EHECSDS system than for the EHEC-CTAB system. The same trend (i.e., higher cloud point temperatures for the EHECSDS system) is also observed at the other considered polymer concentrations. These results suggest that at the temperature and polymer-surfactant compositions considered in this work, the thermodynamic conditions are better for the EHEC-SDS mixture than for the EHECCTAB system. In a previous study7 on a more hydrophilic EHEC fraction (DSethyl ) 0.9 and MSEO ) 2.1), the trend was reversed; i.e., higher values of the cloud point for the EHEC-CTAB than for the EHEC-SDS system were reported. This difference in behavior seems to be related to the difference in hydrophobicity of the polymer samples and probably also to how the hydrophobic microdomains are distributed along the polymer backbone. A dynamic light scattering study8 on gelling EHEC-CTAB and EHEC-SDS systems with the same amount of surfactant showed that the characteristic time of the slow relaxation mode (reflecting chain disengagement relaxation) was consistently higher, at temperatures up to the gel point, in the presence of SDS than with CTAB. In addition, the gel strength parameter, determined from oscillatory shear measurements,21 has been found to exhibit higher values for EHEC-SDS than for the EHEC-CTAB system. This finding is consistent with the general view that the interaction between a nonionic polymer and a cationic surfactant is weaker than that with a corresponding anionic surfactant. In a recent rheological investigation38 on EHEC-surfactant interactions, it was argued that cationic surfactants in general have a weaker tendency to assemble in aggregates than their anionic analogues. Furthermore, it has been suggested10 that SDS interacts with both ethyl and ethylene oxide groups, while the cationic surfactant only interacts with the alkyl substituents. To elucidate the effect of polymer-surfactant interactions in semidilute solutions of EHEC in the presence of an ionic surfactant at ambient temperature, let us consider the situations depicted in the drawing in Figure 2. (i) Variation of the Polymer Concentration at Fixed Polymer-Surfactant Ratio. In the absence of surfactant (the mass ratio of surfactant to polymer is zero, r ) 0), the hydrophobic microdomains (associating groups or stickers) of the polymer play an important role for the dynamical and rheological properties of the solutions. The stickers may be “open” (unassociated) or “closed” (associated) with another sticker. The fraction of closed stickers is expected to increase with increasing polymer concentration, and entanglements will gradually become a momentous feature. In the presence of surfactant (r > 0), the number of effective cross-links (each mixed micelle is shared by two or more polymer chains) will increase with increasing EHEC concentration and the entanglement effect is expected to play an important role at high polymer concentrations. (ii) Variation of the Surfactant-Polymer Ratio at Constant Polymer Concentration. At surfactant levels (38) Thuresson, K.; Lindman, B.; Nystro¨m, B. J. Phys. Chem. B 1997, 101, 6450.
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Figure 2. A schematic illustration of the effects of polymer concentration and addition of surfactant on the structural reorganization of the associating network.
above the critical aggregation concentration (the onset of cooperative binding of the surfactant to the polymer), the surfactant will associate cooperatively and the micellartype cross-links will gradually bring polymer chains together (the surfactant works as a cross-linking agent) up to a certain surfactant concentration. At this stage an optimum number of intermolecular cross-links have been formed (viscosity enhancement at a maximum). At higher values of r, a progressive “solubilization” of the hydrophobic microdomains occurs, and this gives rise to a reduction of the number of effective cross-links and the network is gradually disrupted (the viscosity decreases): there is a changeover from polymer-dominated to surfactant-dominated micelles. At high polymer concentrations, the breaking down of the network is inhibited and very high levels of surfactant addition are required for a complete disruption of the network. Polymer-surfactant interaction in solutions of polymers has recently been addressed in theoretical39-41 and simulation42 studies. It has been argued41 that the hydrophobic microdomains of amphiphilic polymers and hydrophobes on the surfactants aggregate into micelles that act as cross-link junctions in various sizes of clusters and also in networks in the semidilute regime. At moderate surfactant concentrations, the network chains are tightly connected to each other by the junctions. However, in the excess of surfactant, many junctions are solubilized, yielding a loosely bound network. Oscillatory Shear Measurements. In Figure 3, effects of the addition of surfactant on the dynamic viscosity η’ at a low frequency of 0.15 Hz are illustrated for the EHEC (2 wt %)-CTAB and EHEC (2 wt %)-SDS systems. A conspicuous feature is that η’ passes through a pronounced maximum (located between 15 and 20 mm SDS) for the EHEC-SDS system, while for the EHEC(39) De Gennes, P.-G. J. Phys. Chem. 1990, 94, 8407. (40) Tanaka, F. Macromolecules 1998, 31, 384. Tanaka, F.; Koga, T. Bull. Chem. Soc. Jpn. 2001, 74, 201. (41) Diamant, H.; Andelman, D. Macromolecules 2000, 33, 8050. (42) Groot, R. D. Langmuir 2000, 16, 7493.
Figure 3. Effect of surfactant addition on the dynamic viscosity (0.15 Hz) of 2 wt % EHEC solutions. The arrows indicate the values of r considered in this work.
CTAB system the maximum is significantly weaker and much broader. These results suggest, in accordance with previous findings,8,10,21 that the polymer-surfactant associations at moderate levels of surfactant addition are significantly stronger in the presence of the anionic SDS surfactant. The results displayed in Figure 3 reveal that both the magnitude and broadness of the viscosity maximum depend on the type of surfactant. The decrease in dynamic viscosity observed at higher amounts of SDS is attributed to a breakdown of the connectivity of the network as the hydrophobic microdomains of the polymer become saturated with surfactant. The lower values of η’ for the EHEC-SDS system as compared with those for the EHEC-CTAB system at high levels of surfactant addition (above 30 mm) indicate that CTAB is inferior to SDS in dissolving the “lumps”12,16 or cross-links between different polymer chains. This may be related to the much lower cloud point temperatures (cf. Figure 1) for the EHEC-CTAB mixtures than for the EHEC-SDS system. In other words, at the temperature of measurement the thermodynamic conditions for EHEC-CTAB are poorer
Viscoelasticity of Polymer-Surfactant Systems
Figure 4. (a) Frequency dependences of the storage modulus G’ and the loss modulus G’’ at the polymer concentrations and values of the surfactant-EHEC ratios indicated. Effects of polymer concentration and value of the surfactant-EHEC ratio (r) on the time of intersection for the EHEC-CTAB (b) and EHEC-SDS (c) systems.
than those of EHEC-SDS, and the former system may be more inclined to form “lumps” of polymer chains. It has previously been observed15 for EHEC-SDS systems that the viscosity maximum is shifted toward higher surfactant concentrations as the polymer concentration increases. However, if a normalized plot is constructed,15 where the dynamic viscosity is plotted as a function of r, the maxima of the dynamic viscosity are located at virtually the same value of r independent of the EHEC concentration, but η’ assumes higher values with increasing EHEC content (the strength of the network increases) and the viscosity maximum becomes broader. In light of this, we have chosen to present the rheological results in terms of the quantity r, which has been kept constant at the considered EHEC concentrations. To vary the strength of the association network, values of r at the maximum of the viscosity (r ) 0.55 for EHEC-CTAB and r ) 0.28 for EHEC-SDS) as well as values below and above the maximum have been probed in this work (see the arrows in Figure 3). Typical illustrations of the frequency dependencies of G’ and G’’ for the indicated polymer-surfactant compositions and polymer concentrations are depicted in Figure 4a for the EHEC-CTAB and EHEC-SDS systems. From G’ and G’’ data the frequency of intersection f* (G’ ) G’’) (this quantity is indicated by arrows in Figure 4a) can be determined for the systems. For some polymer-surfactant systems, f* was located somewhat outside the frequency range accessible to the rheometer, and in these cases f* was determined by linear extrapolation. From the frequency of intersection, the corresponding quantity, the time of intersection τ* ) 1/2πf* can be estimated. This parameter is related to the longest relaxation time and gives information about the lifetime of the associative network. The effects of polymer concentration and composition on the time of intersection for the systems EHEC-CTAB and EHEC-SDS are displayed in parts b and c of Figure 4. In the absence of surfactant, there is only a weak concentration dependence of the characteristic relaxation time despite that all concentrations are in the semidilute
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regime. For the EHEC-CTAB systems, τ* is virtually constant up to 2.5 wt %, while a marked upturn of τ* is a conspicuous feature at higher polymer concentrations for both polymer-surfactant compositions. The latter phenomenon probably reflects an enhanced strength of the network due to polymer-surfactant-mediated crosslinks. However, we should note that at higher polymer concentrations the corresponding values of τ* for the EHEC-SDS mixtures are, except for the solutions with large excess of SDS (r ) 0.72), significantly higher (stronger associations) than those of the EHEC-CTAB mixtures. The general trend for the EHEC-SDS systems is that τ* rises with increasing polymer concentration at all values of r. The strongest concentration dependence of τ* is observed for the surfactant-to-polymer ratio (r ) 0.28) giving rise to the most pronounced viscosity enhancement. The data points at low polymer concentrations for the EHEC-SDS mixture with r ) 0.72 have not been included in the plot because of the large experimental scatter in the values of G’ and G’’ for these low-viscous solutions. These results indicate that the longest relaxation time of the network depends on the type of surfactant, the value of r, and the polymer concentration at a fixed value of r. It is evident that the effective lifetime of the associative network can be tuned by altering these quantities. In the analysis of linear rheology of polymer systems, the simplest model of a viscoelastic fluid, namely, the Maxwell model,43,44 is frequently utilized to describe the frequency dependencies of the dynamic moduli. However, the present EHEC-surfactant mixtures cannot, except at a few conditions, be characterized as Maxwellian fluids (with a single relaxation time that controls the time scale), but a more complex picture, with a broad distribution of relaxation times, emerges. The failure of the Maxwell model to describe rheological data of complex systems has previously been reported38,45,46 for aqueous solutions of a hydrophobically modified EHEC and its unmodified analogue (a different EHEC fraction than used in this study) in the presence of SDS, as well for other amphiphilic polymer-surfactant systems.47,48 Viscosity Measurements. Figure 5 shows a doublelogarithmic plot of the zero-shear viscosity versus polymer concentration for EHEC-CTAB solutions at different values of r. In the absence of CTAB, the concentration dependencies of η0 can be described, both below and above the entanglement concentration, by power laws (η0 ∝ Cx). Since the intrinsic viscosity for the EHEC-CTAB systems has not been determined, we will use the criteria of the relative viscosity suggested previously25 for the overlap concentration (η ) 2ηs for C*, where ηs is the solvent viscosity) and the entanglement concentration Ce (η ≈ 50ηs for Ce). The onsets of the power law regions are indicated in Figures 5 and 6 in terms of Ce. In the absence of surfactant (r ) 0), least-squares regressions (solid lines) yield power law exponents of x ) 1.7 ( 0.2 and x ) 4.1 ( 0.1 (95% confidence intervals) for the unentangled and entangled semidilute regime, respectively (Figure 5a). The former value can be rationalized in the following way. (43) Larson, R. G. The Structure and Rheology of Complex Fluids; Oxford University Press: New York, 1999. (44) Goodwin, J. W.; Hughes, R. W. Rheology for ChemistssAn Introduction; Athenaeum Press, Ltd.: Gateshead, U.K., 2000. (45) Nystro¨m, B.; Thuresson, K.; Lindman, B. Langmuir 1995, 11, 1994. (46) Kjøniksen, A.-L.; Nilsson, S.; Thuresson, K.; Lindman, B.; Nystro¨m, B. Macromolecules 2000, 33, 877. (47) Tsianou, M.; Kjøniksen, A.-L.; Thuresson, K.; Nystro¨m, B. Macromolecules 1999, 32, 2974. (48) Kopperud, H. M.; Hansen, F. K.; Nystro¨m, B. Macromol. Chem. Phys. 1998, 199, 2385.
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Figure 5. log-log plot of the zero-shear viscosity as a function of polymer concentration for the EHEC-CTAB system at the values of surfactant-polymer ratio indicated. Ce denotes the entanglement concentration (see text).
Figure 6. log-log plot of the zero-shear viscosity as a function of polymer concentration for the EHEC-SDS system at the values of surfactant-polymer ratio indicated. Ce denotes the entanglement concentration (see text).
The theoretical prediction for flexible nonassociating neutral polymers in unentangled semidilute solutions is given by23,36 η0 ∝ C1/(3µ-1), where the Flory excluded volume exponent µ ) 0.5 in a θ-solvent (η0 ∝ C2) and µ ) 0.59 in a good solvent (η0 ∝ C1.3). The value of the power law exponent (x ) 1.7) observed for the EHEC-water system may indicate that this system is characterized by marginal thermodynamic conditions. The concentration dependence of the zero-shear viscosity exhibits a much stronger dependence (x ) 4.1) in entangled semidilute EHEC-water solutions. This value is in agreement with that observed from an off-lattice simulation model33 for associative polymer networks. Similar values have been observed for polymer-solvent systems of various natures. For solutions of neutral flexible polymers of high molecular weight in the semidilute entangled regime under good solvent conditions, values of x in the range 4.1-4.6 have been reported49,50 from (49) Adam, M.; Delsanti, M. J. Phys. (Paris) 1982, 43, 549.
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viscosity investigations. Viscosity studies51 of aqueous solutions of hydrophobically modified polyacrylamides revealed values of x in the interval 4.0-4.3 in the semidilute entangled regime. A value of x ) 4.2 was observed52 in a rheological investigation of end-capped polyelectrolytes in the semidilute regime. These values are close to that observed for the present EHEC-water system. On the theoretical side, approaches23,53 for nonassociating neutral flexible polymers in entangled semidilute solutions at good solvent conditions predict η0 ∝ C3/(3µ -1) ∝ C3.9. In addition, theoretical models28,51 for associating polymer solutions have also been developed, and the predicted power law exponents (x ) 4.1-4.2) are consistent with that observed for the EHEC-water system. This value is also compatible with a recent theoretical approach by Rubinstein and Semenov,35,36 where the concentration dependence of the zero-shear viscosity in the sticky Rouse regime is predicted to be described by the power law η0 ∼ C4.2. The above cited theoretical predictions are all compatible with the value of the power law exponent for EHEC-water. In this context, it is interesting to note that in this concentration domain, both experiments and theoretical models give a very similar concentration dependence of η0 for nonassociating “ordinary” polymers and associating polymers. Despite the different nature of the polymers, they exhibit virtually the same viscosity behavior. For the EHEC solutions in the presence of CTAB (see Figure 5b,c), the value of the power law exponent x is almost the same as that observed without surfactant. It seems that the principal impact of CTAB on the viscosity behavior is that the power law range is extended toward lower polymer concentrations in the semidilute regime. The reason for this may be that due to the formation of polymer-surfactant-mediated cross-links at lower EHEC concentrations at these values of r, these junctions act in a similar way as entanglement couplings in surfactantfree solutions. In the spirit of the model of Rubinstein and Semenov for associating polymers36 (cf. the discussion of this model below), we would argue that the intensity of the transformation of intra- into intermolecular associations is extended toward lower polymer concentrations as a result of the surfactant-mediated associations. This finding suggests that not only purely topological entanglements but also specific polymer-surfactant interactions may yield a similar power law behavior. For the EHEC-SDS system, a more complex picture for the concentration dependence of the zero-shear viscosity (see Figure 6) emerges. In this case, the power-law features of η0 are significantly affected by the EHECSDS composition. The difference in viscosity behavior between the EHEC-SDS and EHEC-CTAB systems can probably be traced to the stronger polymer-surfactant interactions operating in the former system. In EHECSDS mixtures, the surfactant works as an efficient crosslinking agent under certain conditions, giving rise to a transient network with strong intermolecular cross-links. By tuning the value of r and the polymer concentration, the lifetime of the network and the frequency of the interchange between intra- and intermolecular associations can be changed dramatically. Under certain conditions, the portion of network chains that are tightly (50) Takahashi, Y.; Isono, Y.; Noda, I.; Nagasawa, M. Macromolecules 1985, 18, 1002. (51) Regalado, E. J.; Selb, J.; Candau, F. Macromolecules 1999, 32, 8580. (52) Tsitsilianis, C.; Iliopoulos, I.; Ducouret, G. Macromolecules 2000, 33, 2936. (53) De Gennes, P.-G. Macromolecules 1976, 9, 594.
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connected to each other by the junctions is high, while in other situations the fraction of junctions that are dissociated is high, resulting in a loosely bound network structure.40 During this process, the lifetime and dynamics of the network are governed36 by the extent of transformation of intramolecular associations into intermolecular ones as the polymer concentration increases. As far as we know, the only model that addresses the concentration dependence of the zero-shear viscosity in entangled solutions of associating polymers and predict several power-law regimes is the approach by Rubinstein and Semenov.36 This model was developed to describe the dynamics and viscosity of entangled solutions of associating polymers with many stickers per chain. In this approach, the transformation of intramolecular into intermolecular associations as well as the prolongation of the effective lifetime of associations at higher concentrations have been taken into account. Although the association mechanism for the polymer-surfactant systems considered in this study is different and probably more complex, we think that this model may be useful in the discussion of the present viscosity results. For EHECsurfactant systems, the intensity of the transformation of intra- into intermolecular associations will be governed by factors such as the total polymer concentration, the value of r, and the strength of the polymer-surfactant interactions. This model of Rubinstein and Semenov identifies five different power-law regimes for the concentration dependence of the zero-shear viscosity
{
C4.2 C6.8 η0 ∝ C8.5 C3.75 C4.7
for for for for for
C < Ce Ce < C < Cren Cren < C < Cs Cs < C < Cle Cle < C < 1
I II III IV V
(1)
where Ce is the entanglement concentration, Cren is a crossover concentration where renormalization of bond lifetime is important, Cs is the overlap concentration of strands between stickers, and Cle denotes the crossover concentration where strands of l monomers between interchain bonds become entangled. Despite that all the predicted crossover regimes have not been detected in this work, and the theoretically devised crossover concentrations are not easily determined from the experimental data, we believe that this approach is instructive in the discussion of the zero-shear viscosity results for the EHEC-SDS mixtures. Region I represents the sticky Rouse regime of unentangled associating polymers at good solvent conditions, and the concentration dependence of η0 reflects the exchange of intra- into intermolecular associations. At higher concentrations (region II, above the entanglement concentration), the viscosity is characterized by the sticky reptation model with unrenormalized bond time (it is assumed that when a bond breaks and the sticker separates from its partner, it can always find an open sticker different from its previous partner), and this model describes the dynamics of entangled solutions at good solvent conditions. In region III we consider sticky reptation in a good solvent with effective or renormalized bond lifetime in entangled solutions of associating polymers with unentangled strands between interchain bonds (C < Cle). The idea behind the concept of renormalized association lifetime is that at these fairly high polymer concentrations, there are few unassociated stickers and it is therefore difficult for a sticker to find a
new partner to associate with after separation with the old one. As a consequence, it is a high probability that, after an unsuccessful search for a new partner, the sticker returns to its old partner and thereby prolonging the effective lifetime of associations. By taking into account the pronounced transformation of intramolecular associations to intermolecular ones with increasing concentration in this region, as well as the renormalization of the lifetime of an association, a strong concentration dependence of η0 is predicted. Region IV is characterized by sticky reptation in a good solvent with renormalized association lifetime and overlapping, but not entangled, strands between stickers (C > CS). At this stage, a much weaker concentration dependence of η0 is predicted because most associations are intermolecular and the possibility for additional intermolecular associations is strongly depleted. In the final regime (region V), we consider a situation with sticky reptation in a good solvent with renormalized bond lifetime and entangled strands between stickers. In this high concentration regime, the model predicts a somewhat stronger concentration dependence of η0 than in region IV. Region V has not been detected under the conditions explored in this work. The reason may be that we have not worked with sufficiently high concentrations (the volume fraction of polymer is much less than 1). In Figure 6a we observe two power-law regimes with different concentration dependence of η0 (x ) 5.8 ( 0.1 and x ) 3.6 ( 0.3) for the EHEC-SDS system with r ) 0.14. The value of Ce indicates that the first domain should correspond to region II (η0 ∝ C6.8) in the above-discussed model. However, the lower experimental value of the exponent may indicate that the solutions in this domain are weakly entangled and the experimental value may reflect crossover effects between regions I (unentangled solutions) and II. Region III is missing and this may indicate that this region is very narrow or that this regime of pronounced transformation of intramolecular associations into intermolecular ones is not promoted at this polymer-surfactant composition. It is possible that the weaker excluded volume interactions of the chains at this value of r set an effective upper limit to the number of chains that can participate in the transformation into intermolecular associations. At higher polymer concentrations, we observe a power-law exponent that is consistent with the theoretically predicted value for region IV. This weaker concentration dependence of the zeroshear viscosity may indicate that at this stage we have a saturation of intermolecular associations. The viscosity results from the EHEC-SDS system with r ) 0.28 (viscosity enhancement at maximum) reveal three power-law regimes (see Figure 6b). The first domain, with x ) 5.5 ( 0.4, probably reflects crossover effects (between regions I and II of the model) of the same type as discussed above. The very strong concentration dependence of η0 (x ) 10.2 ( 0.6) observed in the second domain is in reasonable agreement with the predicted value of 8.5. In the framework of the utilized theoretical approach, this finding suggests that in this concentration regime a very significant transformation of intra- into intermolecular associations occurs. Very strong concentration dependencies of the zero-shear viscosity, with values of the exponent in the range 6-11, have been reported54-58 for (54) L′Alloret, F.; Hourdet, D.; Audebert, R. Colloid Polym. Sci. 1995, 273, 1163. (55) English, R. J.; Gulati, H. S.; Jenkins, R. D.; Khan, S. A. J. Rheol. 1997, 41, 427. (56) Bromberg, L. Macromolecules 1998, 31, 6148. (57) Tsianou, M. Ph.D. Dissertation, Lund University, 1999.
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associating polymer systems of various natures. The decrease of the power law exponent of the viscosity in the third domain (x ) 3.5 ( 0.2) is in good agreement with the theoretical prediction for region IV (see eq 1) and can probably be attributed to the saturation of intermolecular associations at high polymer concentrations. At this stage, most of the transformation of intramolecular into intermolecular associations has already occurred. In the case of EHEC-SDS mixtures with an excess of surfactant (r ) 0.72), two power-law regimes can be distinguished (see Figure 6c), one before and one after the entanglement concentration. The first domain is described by the same power-law exponent as for the EHEC-water system (cf. Figure 5a) in the unentangled semidilute regime. As the entanglement concentration is approached, an abrupt transition to a very strong concentration dependence of η0 (x ) 10.1 ( 0.4) occurs. These findings indicate that the viscosity behavior of the EHEC-SDS mixtures (r ) 0.72) at low polymer concentrations is reminiscent of that of “ordinary” nonassociating polymers in unentangled semidilute solutions at marginal solvent conditions (cf. the first power-law region of Figure 5a). Above the entanglement concentration, we do not observe features that remind of the predictions for regions I and II of the model, but region III of the model seems to portray the concentration dependence of η0 in this domain fairly well. The reason for this pattern of behavior may be that since there is an excess of surfactant, the surfactantmediated network junctions increase extensively at the expense of intramolecular associations as the network evolves. If this behavior is predominant early in the surfactant-mediated network-forming process, features reminiscent of regions I and II of the model may be suppressed. Our conjecture for the absence of region IV (x ) 3.75) of the model at this high value of r is that due to the excess of surfactant, the intense transformation of intramolecular into intermolecular associations is extended up to high polymer concentrations. It is also possible that the transition to region IV is restrained due to electrostatic repulsion at this high level of surfactant addition. It seems that higher polymer concentrations are required to arrest the pronounced transformation of intrainto intermolecular associations and thereby enter region IV. A characteristic feature of many associating polymer systems is the strong shear-rate dependence of the viscosity.46,57-62 Figure 7 shows the effect of shear-rate on the measured viscosity for EHEC-CTAB and EHECSDS mixtures at various values of r at a fixed polymer concentration (2 wt %). The magnitude of the shearthinning effect depends on the value of r and the type of surfactant. In addition (not shown here), this effect becomes more pronounced as the polymer concentration increases. The most marked shear-thinning effects are observed for the system that exhibits the strongest association network and viscosity enhancement. The decrease in viscosity with increasing shear rate can probably be ascribed to the disruption of the network junctions; that is, the rate of junction disruption exceeds the rate at which cross-links are re-formed. In this context we may note that the increase of the cross-link dissociation (58) Chronakis, I. S.; Doublier, J.-L.; Piculell, L. Int. J. Biol. Macromol. 2000, 28, 1. (59) Bromberg, L. Langmuir 1998, 14, 5806. (60) Nystro¨m, B.; Kjøniksen, A.-L.; Iversen, C. Adv. Colloid Interface Sci. 1999, 79, 81. (61) Lauten, R. A.; Nystro¨m, B. Macromol. Chem. Phys. 2000, 201, 677. (62) Chassenieux, C.; Fundin, J.; Ducouret, G.; Iliopoulos, I. J. Mol. Struct. 2000, 554, 100.
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Figure 7. Effect of surfactant-polymer composition on the shear-rate dependence of the viscosity for EHEC-CTAB and EHEC-SDS systems at a fixed polymer concentration of 2 wt %.
Figure 8. Shear viscosity (O) compared to the magnitude of the complex viscosity (0) for the EHEC-SDS system at a polymer concentration of 2 wt % and at the values of r indicated.
rate by shear forces has been studied in Monte Carlo simulation33 of associative polymer networks. This finding suggests that the relaxation time decreases significantly when a network is sheared. For many solutions of flexible nonassociating polymers, the shear viscosity η as a function of shear rate is almost identical to the complex viscosity η* as a function of frequency, an empirical finding known as the Cox-Merz rule.63 This rule is usually not reliable for more complex polymer systems, such as solutions of hydrophobically modified polymers.48,51,54,55,59,64 Shear viscosity and complex viscosity properties of 2 wt. % EHEC solutions at different values of r with SDS are shown in Figure 8 as a function of shear rate or frequency. The most significant deviations from the Cox-Merz rule are observed for the EHECSDS system at values of r giving rise to pronounced viscosity enhancements. In this case, the complex viscosity of the associative polymer is lower than the steady shear viscosity over a broad shear rate/frequency region. This type of behavior has been observed for many associating polymer systems that display shear-thinning effects. Simulation studies of strongly associating polymer sys(63) Cox, W. P.; Merz, E. H. J. Polym. Sci. 1958, 28, 619. (64) Xu, B.; Yekta, A.; Winnik, M. A.; Sadeghy-Dalivand, K.; James, D. F.; Jenkins, R.; Bassett, D. Langmuir 1997, 13, 6903.
Viscoelasticity of Polymer-Surfactant Systems
tems have revealed that the cross-link dissociation rate33 increases with increasing shear rate and shear forces may also induce dramatic structural reorganizations34 of the network. These features indicate that the Cox-Merz rule should not hold for associative networks. Conclusions Polymer-surfactant interaction in aqueous solutions of ethyl(hydroxyethyl)cellulose in the presence of SDS or with the cationic surfactant CTAB has been studied with the aid of rheological methods, in both the linear and nonlinear viscoelastic regime. The experiments were carried out over an extended polymer concentration range at different surfactant-to-polymer ratios (r). The results at moderate levels of surfactant addition revealed strong polymer-surfactant interactions in mixtures of EHECSDS, while weak viscosity enhancements characterized the EHEC-CTAB system. A breakdown of the associating network is observed at high surfactant concentrations, especially in the presence of SDS. With the value of r and the polymer concentration tuned, the strength of the polymer-surfactant associations can be regulated. The main results can be summarized in the following way: (1) The longest relaxation time (time of intersection), associated with the lifetime of the transient network, increases with polymer concentration at a fixed value of r. The highest values of the relaxation time are observed for EHEC-SDS mixtures with r ) 0.28, the value giving rise to the most pronounced viscosity enhancement. (2) In general, the frequency dependences of the dynamic moduli, recorded in the terminal zone of the mechanical spectrum, for these systems cannot be described by a single Maxwell element which suggests that there is not a single relaxation
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time that controls the time scale, but a distribution of relaxation times. (3) For solutions of EHEC without surfactant, the polymer concentration dependence of the zero-shear viscosity η0 above the entanglement concentration can be described by a power law (η0 ∼ Cx, with x ) 4.1). In EHEC-CTAB mixtures, the primary effect of the surfactant is that this power-law domain is extended toward lower polymer concentrations due to the effect of polymer-surfactant-mediated cross-links. In EHEC-SDS solutions a more complex behavior emerges, with three power-law regimes for the EHEC-SDS system (r ) 0.28) with the most prominent polymer-surfactant interactions. At the other values of r, two power-law regimes were observed, but the values of the power-law exponents depend on the surfactant-polymer composition. The concentration dependencies of the zero-shear viscosity were discussed in the framework of the model of Rubinstein and Semenov36 for associating polymer systems. In this model the transformation of intramolecular into intermolecular associations plays an important role. (4) The shear-rate dependence of the viscosity reveals a nonNewtonian shear-thinning effect in strongly associating systems. (5) Significant differences between complex and steady-shear viscosity in the low-shear, low-frequency domains, in contrast to the Cox-Merz rule, are detected in systems with prominent polymer-surfactant-mediated cross-links. The disclosure of different power-law regimes in the concentration dependence of the zero-shear viscosity, and the impact of r and the type of surfactant on this behavior are the most prominent findings of this work. LA011072M
