Rheological properties of multisticker associative polyelectrolytes in semidilute aqueous solutions


  • Piotr Kujawa,

    1. Institut Charles Sadron, Centre National de la Recherche Scientifique, 6 Rue Boussingault, BP 40016, 67083 Strasbourg Cedex, France
    2. Institute of Applied Radiation Chemistry, Technical University of Lodz, Lodz, Poland
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  • Annie Audibert-Hayet,

    1. Institut Français du Pétrole, 1-4 Avenue de Bois-Préau, 92852 Rueil-Malmaison, France
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  • Joseph Selb,

    Corresponding author
    1. Institut Charles Sadron, Centre National de la Recherche Scientifique, 6 Rue Boussingault, BP 40016, 67083 Strasbourg Cedex, France
    • Institut Charles Sadron, Centre National de la Recherche Scientifique, 6 Rue Boussingault, BP 40016, 67083 Strasbourg Cedex, France
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  • Françoise Candau

    Corresponding author
    1. Institut Charles Sadron, Centre National de la Recherche Scientifique, 6 Rue Boussingault, BP 40016, 67083 Strasbourg Cedex, France
    • Institut Charles Sadron, Centre National de la Recherche Scientifique, 6 Rue Boussingault, BP 40016, 67083 Strasbourg Cedex, France
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Multisticker associative polyelectrolytes of acrylamide (≈86 mol %) and sodium 2-acrylamido-2-methylpropanesulfonate (≈12 mol %), hydrophobically modified with N,N-dihexylacrylamide groups (≈2 mol %), were prepared with a micellar radical polymerization technique. This process led to multiblock polymers in which the length of the hydrophobic blocks could be controlled through variations in the surfactant-to-hydrophobe molar ratio, that is, the number of hydrophobes per micelle (NH). The rheological behavior of aqueous solutions of polymers with the same molecular weight and the same composition but with two different hydrophobic block lengths (NH = 7 or 3 monomer units per block) was investigated as a function of the polymer concentration with steady-flow, creep, and oscillatory experiments. The critical concentration at the onset of the viscosity enhancement decreased as the length of the hydrophobic segments in the polymers increased. Also, an increase in the NH value significantly enhanced the thickening ability of the polymers and affected the structure of the transient network. In the semidilute unentangled regime, the behavior of the polymer with long hydrophobic segments (NH = 7) was studied in detail. The results were well explained by the sticky Rouse theory of associative polymer dynamics. Finally, the viscosity decreased with an increase in the temperature, mainly because of a lowering of the sample relaxation time. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1640–1655, 2004


Over the past 2 decades, water-soluble polymers modified with a small number of hydrophobic groups have become of great interest because of their possible applications in various industrial areas, including oil recovery, paints, pharmaceuticals, cosmetics, and food.1–6 In aqueous solutions, above a certain concentration, these polymers form intermolecular associations because of hydrophobic interactions, and these lead to dramatic viscosity enhancement and gelation. The particular rheological properties of these materials result from the reversible character of the association/dissociation processes of the physical crosslinks under the action of shear.

The subtle interplay between the strong association of the hydrophobic groups and the high water solubility of the hydrophilic parts of the chains, apart from the desired thickening properties, may sometimes lead to phase separation and precipitation.7 Therefore, special problems are linked to the preparation of polymers with both high associative properties and good water compatibility. This goal can be achieved through the addition of charges to the polymeric backbone.8–38 The presence of ionic units along the main chain leads to various improvements in the polymer behavior. First, it ensures better water solubility and a stronger thickening ability because of the coil expansion, which is typical for polyelectrolytes. Moreover, polymers containing ionic sites can be potentially responsible for changes in the ionic strength and pH, and in the case of sulfonated derivatives,8, 9, 12 they have better thermal and hydrolytic stability than their uncharged counterparts. In general, in the case of charged associating polymers, a more complicated rheological behavior is observed in comparison with that of the corresponding neutral polymers because of the competition between attractive (hydrophobic) and repulsive (electrostatic) interactions. Thus, the presence of the charged units may have two opposite effects on the thickening properties: an increase in the viscosity due to coil expansion and a decrease due to a lowering of the hydrophobic association degree arising from the charge repulsion, hindering the interpenetration and overlapping of the macromolecules. By a proper choice of the ionic and hydrophobic group contents, it is possible to produce polymers showing a synergistic enhancement of the thickening efficiency.8, 9, 12, 13, 15

A possible route to obtaining hydrophobically modified polymers is a free-radical micellar polymerization process.10, 39–42 Copolymers based on acrylamide (AM), prepared by this method, have been extensively investigated. In such materials, the presence of only very low amounts of the hydrophobic comonomer (1–2 mol %) is enough to dramatically alter the solution rheological properties. The solubility of the hydrophobic monomer in the reaction mixture is ensured by the addition of a surface-active agent in amounts well above its critical micelle concentration (cmc). Under such conditions, the hydrophobe is preferentially located inside the micelles formed by the surfactant, whereas the hydrophilic monomers are solubilized in the aqueous continuous medium. This strong segregation of monomers between two microphases allows one to synthesize polymers with a multiblock structure, that is, containing small hydrophobic blocks randomly distributed along the backbone. It has been inferred from photophysical and rheological experiments that the length of these hydrophobic segments corresponds roughly to the average number of hydrophobic monomers per micelle (NH).18, 43–51 It has also been clearly established that the thickening efficiency is directly related to the polymer microstructure: the longer the hydrophobic blocks, the greater the thickening efficiency at a constant level of hydrophobe incorporation.48–53

In this report, we describe the micellar synthesis and aqueous solution properties of multiblock polyelectrolytes of AM, sodium 2-acrylamido-2-methylpropanesulfonate (NaAMPS), and N,N-dihexylacrylamide (DiHexAM). A charged monomer bearing a sulfonate group (NaAMPS) was chosen to increase the thermal and chemical stability of the polymers.54–57 Furthermore, this monomer copolymerizes easily with AM in aqueous solutions, and this leads to polymers with a reduced compositional drift.58 It has recently been shown that the situation does not change when the polymerization reaction is carried out in a microemulsion59 or in a micellar medium.60 The choice of a disubstituted AM derivative as the hydrophobic monomer (DiHexAM) is justified by the fact that it minimizes or even suppresses the compositional drift that is observed when monosubstituted AM derivatives are used.50, 61 After describing the synthesis and characterization of the polymers, we focus on their rheological properties in semidilute, salt-free aqueous solutions. The study mainly deals with polymer solutions in the unentangled semidilute regime; the impact of the polymer microstructure on the rheological behavior is described in detail, along with a comparison of the dynamic properties with available theories. Finally, the influence of the temperature on the solution viscosity is briefly discussed.



AM (Aldrich) was recrystallized twice from chloroform and stored in the dark at 4 °C until it was needed. 2-Acrylamido-2-methylpropanesulfonic acid (AMPS; grade 2404) was kindly supplied by Lubrizol and was recrystallized from dry methanol before use. Neutralization at pH = 9 was achieved by the slow addition of AMPS to an aqueous sodium hydroxide solution, and this produced NaAMPS. The hydrophobic comonomer DiHexAM was prepared and purified according to the technique of Valint et al.10, 50 Water was purified with a Millipore Milli-RO/Milli-Q system. Sodium dodecyl sulfate (SDS; Acros) and 4,4′-azobis(4-cyanovaleric acid) (ACVA; Acros) were used as received.

Polymerization Procedure

The polymers were obtained by micellar copolymerization.10, 42 The polymerization procedure was similar to that described elsewhere.49, 50 The monomer concentration in the feed was kept at 2 wt %, and the initiator concentration was set to 0.8 mol % with respect to the monomer feed. Such a high initiator concentration was required53, 62 because of the rather low dissociation constant of ACVA at 50 °C (kd,50°C ≈ 3 × 10−6 s−1).63 The molar ratio for AM, NaAMPS, and DiHexAM in the feed was 85.5/10/4.5. The aqueous solution of hydrophilic monomers, previously deoxygenated by bubbling with N2, was added to the surfactant and the hydrophobic monomer placed in the water-jacketed reactor. The mixture was homogenized under stirring for 30 min, and this was following by heating up to 50 °C and by the addition of the initiator solution (ACVA). The reaction was carried out up to 30–40% conversion (ca. 50 min). For the kinetic experiments, the samples were withdrawn at different reaction times, that is, at different degrees of conversion. The polymers were precipitated in acetone and repeatedly washed in an acetone/methanol mixture (9/1 v/v) to remove the surfactant, residual initiator, and monomers. The samples recovered by filtration were dried under reduced pressure at the ambient temperature for 48 h. Finally, the polymers were dissolved in water/methanol mixtures (1/1 v/v), and precipitation, washing, and drying steps were repeated twice.

The calculation of the initial value of NH was based on the amount of the surfactant used in the synthesis and on the values of the aggregation number (Nagg) and cmc reported in the literature for SDS at the same ionic strength as in the reaction medium (Nagg ≈ 67 and cmc ≈ 2.8 mM):14, 6466

equation image(1)

where [SDS] and [DiHexAM]feed are the molar concentrations of the surfactant and the hydrophobic monomer in the feed, respectively.

The polymer code (N0, N3, or N7) refers to the NH value (0, 3, or 7).

Copolymer Composition

The DiHexAM content was determined by 1H NMR (Bruker AW 60-MHz spectrometer) from the integration of the peaks of the terminal methyl group of the hexyl chains (≈0.8 ppm) and the CH group of the polymer backbone (≈2.2 ppm).50 The measurements were performed in methanol-d4/D2O mixtures (8/2 v/v) at a polymer concentration of 1 wt %.

The weight content in carbon, hydrogen, nitrogen, sulfur, and sodium was obtained by microanalysis. The fraction of the NaAMPS units in the polymer (FAMPS) can be calculated from the following relation:

equation image(2)

where %S and %N are the weight percentages of sulfur and nitrogen in the polymer, respectively.

Molecular Weights

The molecular weights of the samples were determined in methanol/water solutions (7/3 v/v) containing 0.1 M NaCl by static light scattering with a multiangle photometer (Sofica) at 633 nm. The refractive-index increment was measured at the same wavelength on a Brice–Phoenix differential refractometer. The dn/dc value for the hydrophobe-free polymer sample was equal to 0.161 mL/g.

Rheological Measurements

The polymer solutions were prepared by the dissolution of a known amount of the polymer in water. After 48 h of stirring, the solutions were centrifuged for 45 min at 3500 rpm. This procedure allowed us to eliminate the air bubbles trapped in the viscous fluids. No phase separation was observed at this rotation speed.

The viscometry measurements on dilute solutions were performed on a Contraves LS 30 low-shear rheometer equipped with a Couette 2T-2T measuring system (25 °C). The Newtonian viscosity was determined from the measurements at different shear rates ranging from 0.01 to 110 s−1.

Experiments with sufficiently viscous solutions were carried out with a Haake RS100 controlled-stress rheometer equipped with cone–plate geometry (diameter = 20, 35, or 60 mm and angle = 1°). To prevent water evaporation, the measuring system was surrounded with a solvent trap, or for long-time measurements, a low-viscosity silicon oil was added to the edges of the cone. The temperature was controlled with a TC80 Peltier plate system (Haake) and was set to 25 °C unless otherwise stated.

We measured the flow curves with the controlled-stress mode by increasing the shear stress by rectangular steps and waiting at each step until equilibrium was attained (usually <300 s). Linear viscoelasticity experiments were performed on the samples that were viscous enough to provide a meaningful analysis. All measurements were made under strains that led to a linear response and at frequencies of 0.0002–10 Hz. When terminal behavior was observed, the longest relaxation time (TR), the zero-shear viscosity (η0), and the plateau modulus (G0) associated with the slowest relaxation process were determined from the data in the low-frequency range according to a procedure described in detail elsewhere.53 Briefly, TR can be calculated as follows:

equation image(3)

where G′ and G″ are the storage and loss moduli, respectively, and ω is the angular frequency. η0 can be calculated by the extrapolation of the G″/ω dependence on ω to a zero frequency according:

equation image(4)

Finally, G0 can be calculated by the division of η0 by TR.

In some cases, creep-recovery experiments were additionally performed in the regime of the linear response. These measurements are based on the sudden application of a constant stress to the fluid being tested and on the monitoring of the resulting deformation as a function of time. In a typical experiment (e.g., Fig. 10 in ref. 60), a rapid change in the compliance is initially observed, followed by a smooth increase that becomes linear at longer times. The values of η0 and G0 can be obtained from the linear part of the compliance (Je) versus time (t) curve according to the following relationship:

equation image(5)

whereas the relaxation time can be calculated as TR = η0/G0. The creep curves were analyzed with the software supplied by the manufacturer (RheoWin Pro Data Manager 2.93).67

Creep and oscillatory experiments are complementary. For very viscous solutions, the Maxwellian behavior in the terminal regime cannot be observed because of the experimental setup limitations. The creep measurements, however, allow the determination of TR and G0 in this case. However, at low polymer concentrations, creep experiments cannot provide reasonable values for TR and G0 because the elastic part of the response is too small. In that case, the values of interest were determined from oscillatory experiments. It was checked for several solutions of N3 and N0 samples that both methods gave essentially the same results. Furthermore, the rheological behaviors were independent of the waiting time before the measurements were begun (1–5 min).


Polymer Synthesis and Characterization

The synthesis of multisticker hydrophobically associative polyelectrolytes was carried out in a micellar medium in the presence of an anionic surfactant, SDS. In the micellar polymerization process, the hydrophobic monomer is solubilized inside the surfactant micelles, whereas the hydrophilic monomers are localized in the aqueous continuous medium.42 The segregation of the monomers between the micellar interior and the aqueous solution results in a specific hydrophobe distribution in the polymer. In contrast to homogeneous polymerization, which usually leads to a random polymer, micellar polymerization favors the incorporation of the hydrophobic monomers as blocks rather than as isolated units along the backbone.43–45, 68, 69 It has also been shown that the length of the hydrophobic blocks is directly related to the NH number,18, 4351 which additionally governs the thickening properties of the polymers.4853

In our case, one of the hydrophilic monomers, NaAMPS, is anionic, and this significantly influences the hydrophobe incorporation.60 It has recently been shown that, in the presence of this monomer, the incorporation of the hydrophobic monomer at low and intermediate conversions is far from complete, and this has been ascribed to the electrostatic repulsion between the growing macroradicals and the ionic micelles. This effect results in an important heterogeneity of the full-conversion polymers, which significantly reduces their thickening ability.60 Thus, to synthesize polymers with a well-defined structure and a reduced heterogeneity, we carried out the syntheses up to intermediate conversions (30–40%). Our final goal was to obtain polymers that contained about 2 mol % hydrophobic units, and this was achieved, in light of the incomplete incorporation of the hydrophobe, by polymerization with 4.5 mol % DiHexAM in the feed. NH was equal to 7, 3, or 0 (control sample; see Table 1).

Table 1. Characteristics of the Investigated Systems
Sample CodeNHaFeed Composition (mol %)Polymer Composition (mol %)10−6 × Mwdfelf
  • a

    Number of hydrophobes per micelle ≅ hydrophobe block length, (calculated from eq 1).

  • b

    Calculated from elemental analysis data via eq 2.

  • c

    Determined from 1 H NMR spectra.

  • d

    Weight-average molecular weight determined by light scattering in a 0.1 M NaCl MeOH/water (7/3 v/v) solution.

  • e

    Number of hydrophobic blocks per chain (see text).

  • f

    Number of hydrophilic units between two hydrophobic blocks (see text).


Figure 1 shows an example of hydrophobic monomer incorporation into the N3 sample as a function of conversion. The observed trend is analogous to that already reported for AM/NaAMPS/DiHexAM copolymers prepared under different experimental conditions;60 that is, the incorporation of the hydrophobe remains constant at low and intermediate conversions, and this is followed by a rapid increase. Moreover, previous studies have shown that, at low NaAMPS contents in the feed (ca. 10 mol %), the copolymerization of AM and NaAMPS leads to copolymers with a quasirandom microstructure.5860 Thus, stopping the reactions at about 30–40% conversion allows us to obtain polymers with a homogeneous structure, that is, without a significant compositional drift.

Figure 1.

Incorporation of DiHexAM as a function of the monomer conversion for the N3 sample.

The experimental conditions of the polymer synthesis and the polymer characteristics are gathered in Table 1. All the samples are characterized by a similar level of charged monomer incorporation (ca. 12 mol %) and similar weight-average molecular weights (ca. 2 × 106). Also, both hydrophobically modified polyelectrolytes (N7 and N3) have the same concentration of DiHexAM units (2.2 mol %). If we assume that the length of the hydrophobic blocks corresponds to the initial value of NH, this means that the N7 polymer contains hydrophobic blocks of around 7 DiHexAM units, whereas those of the N3 sample are much shorter (hydrophobic block length ≈ NH = 3).

The polymers cannot be characterized by size exclusion chromatography in an aqueous medium because of their high molecular weights and, in the case of associative samples, because of adsorption and aggregation phenomena. However, the unmodified AM/NaAMPS copolymers prepared under identical experimental conditions, but in the presence of mercaptoethanol as a chain-transfer agent, have a polydispersity index (weight-average molecular weight/number-average molecular weight) of approximately 2. Knowing that mercaptoethanol behaves as an ideal chain-transfer agent for AM polymers,53 we can assume a similar polydispersity index for the samples synthesized in the absence of a chain-transfer agent and in the presence of the hydrophobic monomer. On the basis of these considerations, it is possible to calculate the average number of hydrophobic blocks (i.e., stickers) per macromolecule (f) and the length of the hydrophilic strand between two sticker points (l). In the calculations, it is additionally assumed that the length of the hydrophobic block corresponds exactly to the NH number. The results, presented in Table 1, indicate that, because of the high molecular weights of the polymers, they contain many stickers per chain, which are separated by quite long hydrophilic sequences. The length of the hydrophobic blocks is much smaller (ca. 45 times) than that of the hydrophilic strands. Moreover, and as mentioned previously, on the basis of the values of the reactivity ratios of the AM/NaAMPS monomer pair and because of the low ionic monomer content in the polymer ([NaAMPS] ≈ 12 mol %), we can assume that the ionic units are randomly distributed in the hydrophilic strands.58 This means that each hydrophilic segment of the macromolecule contains on average 37 or 17 NaAMPS units for the N7 and N3 samples, respectively.

Onset of Hydrophobically Driven Aggregation

In dilute water solutions, the polymers show typical polyelectrolyte behavior, with an increase in the reduced viscosity as the polymer concentration decreases (results not shown). This is typical for charged macromolecules that reach a more and more extended conformation upon dilution. Upon a further decrease of the polymer concentration, the reduced viscosity exhibits a maximum and starts to decrease. This effect is usually attributed to the presence of ionic impurities, which act as an added salt, thereby increasing the ionic strength and leading to a screening of the electrostatic repulsions at very low polymer contents.70

In the case of hydrophobically modified polymers, the viscosity in water already starts to considerably increase at low polymer concentrations, as shown in Figure 2, where η0, determined from steady-state, creep, and oscillatory experiments, is plotted as a function of the polymer concentration. Note that the values determined by the three methods are in good agreement.

Figure 2.

Effect of the concentration on η0 of the samples. The closed symbols represent steady-state measurements, the open symbols represent creep measurements, and the cross-centered symbols represent oscillatory experiments. The vertical line divides the regions of entangled and unentangled regimes (Ce ≈ 1 wt %). The labels on the lines are the values of the scaling exponents.

It is apparent from these data that at high dilutions (polymer concentration < 0.02 wt %), the viscosity of all the solutions remains about the same, whatever their hydrophobic modification. However, at C ≈ 0.02 wt %, the viscosity of the N7 sample starts to rapidly increase, and this can be identified as the onset of the assembling of the individual macromolecules into multichain clusters. At higher concentrations (ca. 0.05 wt %), the viscosity rises abruptly, about 3 orders of magnitude, which can be identified as the gelation point [or gelation concentration (Cg)]. This concentration corresponds to the formation of a temporary interconnected network of clusters by a percolation process.

The viscosity enhancement of the N3 sample is more modest. It starts to deviate from the curve obtained for the hydrophobe-free sample at a 0.2 wt % concentration, and there is no further sharp increase in the viscosity as for the N7 sample. Thus, in the case of associative polyelectrolytes in water, the onset of aggregation is affected by the polymer microstructure: the longer the hydrophobic blocks, the smaller the concentration above which the intermolecular associates are formed (see Fig. 2). This is in contrast to the behavior of the neutral associative polyacrylamides, for which it has been observed that the critical concentration of the viscosity increase does not depend on NH or on the content of hydrophobic units in the polymer.53 This difference may be due to the fact that, for polyelectrolytes, the concentration range within which the chains overlap but are not yet entangled is much broader than that of neutral polymers.71, 72 In fact, when the polymeric charges are screened, the viscosity enhancement starts at the same polymer concentration for both N7 and N3 samples (e.g., 0.12 wt % in a 0.1 M NaCl aqueous solution). The salt effect on the behavior of these associating polyelectrolytes will be discussed in a forthcoming article.73

In contrast to the behavior of the two associative polymers, the viscosity of the unmodified N0 sample increases smoothly up to 1 wt %, and this indicates that the system is still in the unentangled regime, that is, below the critical entanglement concentration (Ce). In fact, the exponent of the dependence of η0 on the polymer concentration (Cp) for the unmodified polymer (η0Cp0.65) is not far from what is theoretically predicted for polyelectrolytes in the regime between the critical overlap concentration (C*) and Ce0Cp0.50).72, 74 Because the molecular weights of the three polymer samples studied here are very similar, we can assume that the entanglement onset is the same for the associative and nonassociative polymers, and this allows us to distinguish between the regimes of the entangled and unentangled systems (separation indicated by the dotted line in Fig. 2).

These results can be compared to those obtained for nonionic associative polyacrylamides containing 1 mol % DiHexAM units.53 For example, for a polymer with a weight-average molecular weight of approximately 2 × 106 synthesized at NH = 3.2, the critical concentration above which the viscosity rapidly increases is located at about 0.15 wt %. This corresponds almost exactly to the critical concentration of the N3 sample containing a twofold amount of hydrophobic units (ca. 2 mol % DiHexAM). As it is well known that a slight increase in the hydrophobe level strongly affects the association process,42 we can conclude that in the case of associative polyelectrolytes, a higher hydrophobe level is required to exhibit a strong viscosity enhancement, in comparison with neutral polymers. In agreement with previous findings on other hydrophobically modified polyelectrolytes, this can be attributed to a decrease in the degree of associations between the hydrophobes, arising from intermolecular electrostatic repulsions, that hinder the overlapping and interpenetration of the chains.13, 17, 19

Rheological Properties of the N7 Sample Above the Gelation Threshold (C > 0.05 Wt %)

The N7 sample contains quite long hydrophobic blocks (∼7 DiHexAM units), and this leads to an important viscosity enhancement and to unique rheological properties. Examples of the flow curves are shown in Figure 3. These curves are characterized by a Newtonian plateau at low shear stress and a shear-thinning zone with a well-defined onset. Moreover, in the intermediate concentration region (0.05–0.1 wt %), a small shear-thickening zone can be observed. The mechanism of this phenomenon, usually occurring only in a narrow concentration range, in the vicinity of C*, is not fully understood.75 It may be due to the rearrangement of the sample structure and a shear-induced change from intramolecular associations to intermolecular associations27, 76 or in terms of non-Gaussian chain stretching.77, 78

Figure 3.

Flow curves for the N7 sample at various concentrations in water. The arrows indicate the fracturing of the samples.

The discontinuity observed in the flow curves (Fig. 3) at a critical shear stress has already been reported for other associating polymers.20, 29, 30, 79, 80 This phenomenon can be ascribed to a total destruction of the associating network structure. Above the apparent yield stress, the hydrophobic interactions do not influence the dynamics of the solutions, and the behavior is analogous to that of the unmodified polymer. It has been proposed that the inverse of the shear rate just before the discontinuity can be identified with the lifetime of an intermolecular junction.79 In the case studied here, the shear rate measured just before the discontinuity is practically independent of the concentration (in the concentration range of 0.08–1 wt %) and has a value of about 3 × 10−3 s−1, which gives an estimate of the average lifetime of the hydrophobic junctions of about 330 s. It must be noted that the gel-like solutions of N7 fracture easily under a high shearing force, and this is usually accompanied with their ejection from the rheometer-measuring body.

In Figure 4, typical results of the oscillatory experiments are shown. Even at low concentrations, G′ is always higher than G″, both being almost frequency-independent. The crossover frequency and the terminal behavior cannot be observed because of the limited experimentally accessible frequency range. Thus, the N7 sample shows a gel-like response, which is characteristic of weak, physically crosslinked gels.81

Figure 4.

G′ and G″ as functions of the frequency for the N7 sample at two concentrations in water.

The most striking features of the N7 polymer solutions, that is, gel-like properties with an apparent yield stress and frequency-independent relaxation spectra, have been observed for aqueous solutions of amphiphilic block copolymers, such as Pluronics82 or oxyethylene–oxybutylene copolymers.83, 84 For these polymers, the peculiarities in the rheological behavior were attributed to the presence of ordered phases composed of packed cylindrical micelles.85 In our case, as previously pointed out, the supramolecular structure is formed by the interconnection of the multichain clusters.

Scaling Behavior of the N7 Sample In the Semidilute Unentangled Regime

At low polymer concentrations, in the regime in which the chains overlap but are not yet entangled, associating sequences self-assemble to form a transient network, and this results in a significant viscosity enhancement. In this section, we analyze the rheological parameters (i.e., η0, TR, and G0) of the N7 sample in the framework of the available theoretical approaches.

In the unentangled regime, the viscoelasticity of the hydrophobe-free polymer N0 is too low to allow an accurate determination of the values of TR and G0.74 As discussed earlier, the viscosity of the solutions increases with a 0.65th-power law of the concentration, which is not far from the theoretical predictions for this concentration regime (η0C0.50).72 Although the properties in the entangled regime are not the main subject of this report, we may add that at higher concentrations, the unmodified polymer (1 wt % < C < 20 wt %) also behaves in agreement with the predictions. In particular, its relaxation time is concentration-independent in the range of 1 wt % < C < 3 wt % and is equal to about 30 ms (results not shown). This scaling behavior is characteristic of polyelectrolytes in the concentration range within which the chains can form effective entanglements but are still below the critical concentration of the electrostatic blob entanglements.72 Finally, above a threshold concentration of 3 wt %, the systems behave like neutral polymer solutions in the entangled regime (e.g., the viscosity increases at about a fourth power of the polymer concentration; see Fig. 2).

The formation of a transient network for associative polymers in the unentangled regime was recently theoretically discussed in great detail.86, 87 The model assumes that each polymer chain contains a large number f of stickers separated by long hydrophilic fragments composed of l monomer units. This picture can be easily applied to the polymers studied here (see Table 1 for the values of f and l). However, the available theory is based on the assumption that only pairwise association is allowed; it was originally formulated only for neutral polymers, and this could be a serious limitation in the case considered here.

In general, three different concentration regimes are predicted for semidilute solutions of unentangled associative polymers.86, 87 Above the gel point, the viscosity starts to increase, being proportional to a power of distance to the gel point [i.e., to a reduced concentration (CCg)/Cg]. The percolation theory implies that the scaling exponent 3.55 is valid in the vicinity of the gel point. At higher polymer concentrations, the number of intramolecular associations strongly decreases in favor of intermolecular ones, and this is accompanied by an increase in the lifetime of the hydrophobic clusters. Because of these effects, the viscosity is predicted to rise sharply as the distance from the gel point increases {η0 ∝ [(CCg)/Cg]6.00}. Finally, far above the gelation point, at which the strands between two stickers start to overlap, the fraction of the intermolecular associations remains almost constant, and TR increases only weakly with the concentration; this results in a much weaker scaling relation, η0 ∝ [(CCg)/Cg]1.15.

Figure 5(a) shows a log–log representation of the N7 polymer viscosity versus the reduced concentration (CCg)/Cg, where Cg is 0.05 wt %. The data can be fitted by two straight lines with different slopes. A similar behavior was observed experimentally by Knaebel et al.88 for hydrophobically modified alkali-soluble emulsions (HASE)-type copolymers. At the highest concentrations, the dependence of the viscosity on the reduced concentration levels off considerably, in quantitative agreement with the model, which predicts an exponent of 1.15. On the contrary, at lower concentrations, our experimental data do not agree with the theoretical predictions, the dependence of the viscosity upon the concentration being less important than that predicted (≈2 instead of 3.55).

Figure 5.

(a) η0, (b) TR, and (c) G0 versus the reduced concentration for the N7 polymer above the gelation threshold. The closed symbols represent steady-state measurements, and the open symbols represent creep measurements. The solid lines are the theoretical predictions, and the labels are the values of the scaling exponents.

An approximate expression for the critical reduced concentration above which the strands between the stickers start to overlap is given by87

equation image(6)

where ν and z are the critical exponents in good solvent conditions and are equal to 0.59 and 0.225, respectively. This approximation leads to a crossover reduced concentration of about 8.2, whereas the value observed experimentally is around 2. Note that the exponent of the power law below the crossover reduced concentration, as well as the value of the latter, is highly sensitive to the value of Cg, the determination of which is subject to some uncertainty.

We have not found any experimental evidence of the regime that is located between the two previously described and that is characterized by a high scaling exponent (a sixth-power relation between the viscosity and reduced concentration). However, the range of concentrations within which it manifests itself may be very limited (e.g., much narrower than half a decade), and makes it problematic to detect (e.g., see Figs. 10 and 11 in ref. 37 for experimental results and Fig. 6 in ref. 87 for theoretical predictions).

The variations of the terminal relaxation time and G0 with the reduced concentration are shown in Figure 5(b,c). It appears that TR is almost independent of the distance from the gelation threshold, whereas G0 behaves similarly to η0, with a crossover at a reduced concentration of about 2.

With respect to TR, the theoretical predictions describe well its variation above the crossover reduced concentration, but they fail below it [Fig. 5(b)]. In the latter regime, the fraction of the intermolecular sticking points increases with the polymer content, and the theory predicts the following relationship: TR ∝ [(CCg)/Cg]1.00. This is not observed in our case, the relaxation time being almost concentration-independent. However, in the regime within which the strands between the stickers can overlap, the very weak dependence of the relaxation time on the polymer concentration, which is experimentally observed [Fig. 5(b)], agrees with the theoretically predicted power law {TR ∝ [(CCg)/Cg]0.15}. At this stage, when the spacers between the hydrophobic groups strongly overlap, most stickers form the intermolecular bonds. Therefore, TR in this case is essentially influenced by the effective association lifetime and not by the equilibrium between intramolecular and intermolecular aggregates.87

As for the variations of G0 [Fig. 5(c)], they agree well with the predictions over the whole concentration range. The data can be fitted by two straight lines with slopes of 2.55 and 1.00. This agreement, observed for the elastic properties of the system, could be fortuitous because of the rather large deviations of the variations of TR and η0 with respect to the model.

The difference between our results and the theoretical predictions near the gelation threshold could be due to the ionic character of the systems because the model used here was derived for neutral polymers. At low polymer concentrations, the strands between the stickers have a stretched conformation due to the presence of the charges along the polymeric backbone. On the contrary, the model describes well the associative polyelectrolytes at higher concentrations. In this regime, the charges are already screened enough not to influence the dynamic properties, and the scaling relations follow the laws predicted for neutral systems.

An additional feature of the rheological behavior of the N7 sample to be emphasized concerns its flow behavior. The flow curves showing the discontinuity at a certain shear stress are also predicted theoretically from the behavior of the frequency-dependent viscosity.87 It has been postulated that, at low frequencies, the viscosity of the associating polymer solutions, which is governed by the lifetime of the reversible clusters, should be very high and shear-independent. In the high-frequency region, the viscosity should be also nearly constant and independent of the polymer concentration, with a much lower value of the order of that of the unmodified analogue solution. The ratio of the two plateau values should strongly increase with the polymer concentration. In our flow experiments (Fig. 3), although a well-defined viscosity plateau cannot be seen at high shear rates, we do observe a strong drop in the viscosity, which increases with the polymer concentration.

Influence of the Polymer Microstructure On the Rheological Properties

This section deals with a comparison between the rheological properties of N7 and N3 samples. The two polymers contain the same concentrations of ionic and hydrophobic units, but they have different microstructures (see Table 1). In the case of the N7 sample, the hydrophobes are incorporated as quite large blocks (NH = 7), whereas NH of N3 sample is much smaller (NH = 3).

We have already seen that the length of the hydrophobic blocks seriously affects the critical concentration for the intermolecular aggregation and that it influences the thickening properties. The critical concentration of the intermolecular aggregation for the N3 sample is about 10 times larger than that of the N7 polymer (see Fig. 2). The sample with longer hydrophobic blocks is also a much more powerful thickening agent. A comparison of the flow curves obtained for the hydrophobically modified and unmodified samples is shown in Figure 6. The flow curve of the N3 polymer is characterized by a Newtonian plateau at low shear stresses, followed by a smooth viscosity decrease in the shear-thinning zone. This is in contrast to the behavior of the N7 sample, for which an apparent yield stress is observed, above which the viscosity decreases abruptly by several orders of magnitude (see Fig. 3). For a given concentration, the viscosity of the N3 polymer solution is much lower than that of N7, but it is still significantly higher than that of the unmodified polymer. Moreover, the relaxation spectra of the N3 polymer show a clear terminal zone with a crossover frequency in the experimentally accessible range, in contrast to the behavior of the N7 sample (Fig. 7).

Figure 6.

Flow curves of the polymers in water. The arrows indicate the fracturing of the samples.

Figure 7.

G′ and G″ as functions of the frequency for the N3 (0.70 wt %) and N7 (0.80 wt %) samples.

The strong viscosity dependence on the hydrophobic block length has been extensively discussed in the literature: the longer the blocks, the greater the thickening ability. This is an indication that the average size of the stickers is more effective in the viscosity enhancement than their number.18, 47, 4953 The very different character of the flow curves, as well as the relaxation spectra, observed for the N7 and N3 samples stresses the importance of the polymer microstructure on the thickening abilities. From a thermodynamic point of view, the length of the hydrophobic stickers is believed to influence mainly the binding energy, that is, the energy of sticker attraction, which in turn affects the fraction of the associated stickers and the average aggregate lifetime: the longer the hydrophobic block size, the larger the binding energy. This implies a stronger tendency to gelation.87

Finally, we can add that the relatively narrow concentration gap in the unentangled regime in which the N3 polymer is in the aggregated state (0.2 wt % < C < 1 wt %), does not allow us to determine unambiguously the values of the scaling exponents. As already observed for the N7 sample [Fig. 5(c)], the value of G0 for the N3 sample increases strongly with the polymer concentration (results not shown). However, for a given concentration, G0 of the N3 sample is more than one order of magnitude lower than that of N7. We may also note that, as for the N7 sample, the terminal relaxation time in the unentangled N3 solutions is nearly independent of the polymer concentration (Fig. 8), with, however, a much lower value (ca. 40–50 s vs ca. 2000 s). These values are still much higher than those found for the unmodified N0 polymer, about 0.030 s. From these results, it can be concluded that the enormous viscosity enhancement observed for N7 is primarily due to the very long relaxation time of this sample.

Figure 8.

TR as a function of the polymer concentration for the N3 sample (data from creep measurements). The label on the line is the value of the scaling exponent.

Additionally, the measurements above the entanglement concentration for the N3 polymer (1 wt % < C < 10 wt %) show that its behavior is similar to that of neutral associative polyacrylamides.52, 53 That is, the viscosity increase with the polymer concentration is not far from the theoretical prediction of η0C3.75, which is characteristic of the sticky reptation model of associative polymers,89, 90 and TR varies approximately as C2.5 (Fig. 8), which is close to the predictions for polymer concentrations above the strand overlapping.

Temperature Effect On the Viscoelastic Behavior

The influence of the temperature on the rheological behavior of associating polymers is an important parameter to be considered for some applications, such as drilling fluids or tertiary oil recovery, for which the temperature of the oil reservoir depends on its depth and on the nature of the crude oil and can vary from 25 to 150 °C.91 However, only a few studies have dealt with the evolution of the thickening properties with temperature. In most cases, in the semidilute regime, a significant decrease in viscosity has been observed with increasing temperature, suggesting a concomitant decrease in the strength of the hydrophobic associations.13, 26, 29, 32, 51, 76, 92 In contrast, in the dilute regime, temperature-enhanced viscosity has been observed due to the disruption of the intramolecular interactions.13, 9294

In this study, we have investigated the effect of the temperature for the N7 sample well below the entanglement concentration (C = 0.09 wt %; Fig. 9 and Table2) and for the N3 polymer in the entangled regime (C = 5 wt %; Table 2). In both cases, the viscosity at room temperature is about 2 times higher than that measured at 50 °C. The results depicted in Figure 9 clearly indicate that the viscosity loss is mainly due to a reduction of the relaxation time and, therefore, to that of the lifetime of the hydrophobic junctions. At both temperatures, the critical shear stress at which a significant viscosity loss of the samples takes place is the same [Fig. 9(a)]. In light of the higher values of η0 at 25 °C, this implies that the corresponding average lifetimes of the hydrophobic associates are also higher. The comparison of the relaxation spectra reported in Figure 9(b) shows that at high frequencies, G′ and G″ are very similar at both temperatures. However, the crossover frequency point and the terminal zone shift to higher frequencies as the temperature increases. The values of the rheological parameters gathered in Table 2 confirm these qualitative trends. The terminal relaxation time is reduced by a factor of about 2 as the temperature increases from 25 to 50 °C, whereas G0 is only slightly affected (factor = 1.2). These preliminary results for the temperature effect are in agreement with a more detailed study on neutral associating polyacrylamides.95

Figure 9.

Influence of the temperature (25 and 50 °C) on the rheological behavior of the N7 sample (0.09 wt %): (a) flow curves and (b) oscillatory spectra. The arrows indicate the fracturing of the samples.

Table 2. η0, TR, and G0 at 25 and 50 °C for the Hydrophobically Modified Polymers in the Unentangled (N7) and Entangled (N3) Regimes
Polymer SampleTemperatureη0 (Pa s)TR (s)bG0 (Pa)b
  • a

    Determined from steady-state controlled-stress experiments.

  • b

    From creep measurements.

N7 (C = 0.09 wt %)25 °C1,040,a 1,110b29800.37
 50 °C550,a 478b15400.31
N3 (C = 5 wt %)25 °C43,800,a 36,200b181020.0
 50 °C16,700,a 17,800b107016.6

If we assume that the hydrophobic association is an entropically driven process, at higher temperatures, the formation of aggregates is favored, and this would result in a viscosity increase, contrary to what has been observed here. In fact, we must also consider that the strength of the associations will decrease as the temperature is raised. As a result, the lifetime of the aggregates decreases as the temperature increases; this is this parameter that controls the viscosity, as already pointed out for nonionic multisticker polyacrylamides.51


The systems investigated in this article are associative multisticker polyelectrolytes based on AM, NaAMPS, and DiHexAM units. Two samples with the same molecular composition ([DiHexAM] ≈ 2 mol %) and same molecular weight but with hydrophobic blocks of different lengths (NH = 3 or 7) were investigated.

The results stress the importance of the microstructure on the rheological behavior of these polymers. As the length of the hydrophobic sequence increases in the hydrophilic backbone, the onset of the hydrophobically driven association shifts to lower concentrations. Above this critical concentration, a pronounced viscosity enhancement and the formation of a transient network can be observed.

The dynamics of the polymer with the longest hydrophobic segments (NH = 7) have been studied in the semidilute unentangled regime. Two regimes have been identified. Near the gelation threshold, the viscosity increases strongly with the polymer concentration. At higher polymer contents, a much weaker concentration dependence of the viscosity is found, and this is theoretically predicted for the regime in which the strands between the neighboring hydrophobic blocks start to overlap.

The relaxation process of the polymer solutions strongly slows down as NH increases. The solutions of the polymer that bears long hydrophobic blocks (NH = 7) are characterized by extremely long relaxation times, of the order of thousands of seconds in the unentangled regime. In contrast, much shorter relaxation times (40–50 s) have been observed in the same concentration range for the sample with shorter hydrophobic blocks (NH = 3).

The viscosity of both samples decreases as the temperature increases, mainly because of a lowering of the relaxation time. However, even at high temperatures (50 °C) and in the unentangled semidilute regime, the values of the viscosity are still quite high, and the gel-like structure of the solutions is preserved. This proves that these polymers are interesting candidates for some practical applications under a variety of physical conditions.


This research was supported by a Marie Curie Fellowship of the European Community Program “Energy, Environment, and Sustainable Development” (ENK6-CT2001-50025). The authors thank the referees for helpful comments on the discussion of the results.