Dynamic Mechanical Properties of Networks of Wormlike Micelles

Sep 8, 2016 - The rheological properties of viscoelastic aqueous solutions of wormlike micelles formed by the self-assembly of comblike copolyelectrol...
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Dynamic Mechanical Properties of Networks of Wormlike Micelles Formed by Self-Assembled Comblike Amphiphilic Copolyelectrolytes Fabien Dutertre, Lazhar Benyahia, Christophe Chassenieux,* and Taco Nicolai LUNAM Université, UMR CNRS 6283 IMMM-PCI, Université du Maine, Avenue Olivier Messiaen, 72085 Le Mans, Cedex 9, France S Supporting Information *

ABSTRACT: The rheological properties of viscoelastic aqueous solutions of wormlike micelles formed by the self-assembly of comblike copolyelectrolytes have been investigated by flow and dynamic measurements. The comblike polymers consisted of a polystyrene backbone grafted with a fixed amount of pendant N,N-dimethyl quaternary ammonium alkyl groups of various lengths ranging from C12 up to C18. Upon increasing concentration, the increase in size of the wormlike micelles and their branching results in the formation of a system spanning network through a percolation process at a critical concentration that decreases when salt is added or when the temperature is decreased. In this manner transient gels are formed with a viscoelastic relaxation time that does not depend on the polymer concentration or on the ionic strength, but their elastic modulus increases with increasing polymer or salt concentration. When the size of the alkyl groups is increased from C12 to C16, the relaxation time increases very strongly, but the temperature dependence remains characterized by the same activation energy. For C18, the systems are frozen at least up to 80 °C.

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INTRODUCTION Recently, we introduced a novel class of amphiphilic copolyelectrolytes formed by polystyrene functionalized with pendant quaternized alkylamine moieties1 (see Figure 1). In

central core was formed by the alkyl chains. A detailed investigation by scattering techniques and cryo-transmission electron microscopy of the structure of these wormlike micelles (WLM) was reported elsewhere.2 It was shown that at low concentrations the polymers are dispersed as individual chains that are collapsed into dense spherical particles with a radius of 2 nm, as is generally observed for polysoap.3 Above a critical concentration that decreases with increasing ionic strength they form cylindrical aggregates that grow in length with increasing concentration. Through a quantitative analysis of the scattering data,1 we have found that the mass per unit length of the rods ranged from 6.7 up to 9.1 kg mol −1 nm−1 when the length of the alkyl groups increased from C12 to C18, which implies that a maximum of six chains are associated in parallel (this number being smaller if the chains are not fully stretched). Longer WLM branched leading to the formation of a space spanning network above a percolation concentration (Cp) that decreased with increasing ionic strength. It was observed that networks of the WLM had interesting viscoelastic properties, but no detailed investigation of these properties has been reported so far, which was the objective of the study presented here. We note that hydrogels were also formed at high concentrations by association of platelets formed by polymers having a functionalization degree ranging from 30 up to 55 mol %, but the properties of these gels are not discussed here. In first approximation, these amphiphilic copolyelectrolytes can be

Figure 1. Chemical structure of copolymers 80Cn.

water these polymers self-assemble with a morphology that depends on the distance between the pendant groups along the chain, but not on the length of their alkyl groups at least between C12 and C18. When the degree of functionalization is between 30 and 55 mol %, the polymers assemble into platelets with a thickness of about 2.5 nm. However, when the polymers are more densely functionalized (65−80 mol %), they assemble into cylinders with a radius of about 2 nm. Varying the length of the alkyl chains between C12 and C18 did not influence the morphology of the assemblies, but it led to small changes in the thickness of the platelets or the cylinders. The latter was close to the twice the contour length of the alkyl chains, which suggests that the platelets consisted of a double layer of associated chains oriented along the plane and that the rods consisted of associated parallel chains. For both structures the charged groups were exposed to the water phase, and the © XXXX American Chemical Society

Received: June 27, 2016 Revised: August 24, 2016

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except that we copolymerized QVBC with small fraction of styrene, which rendered the polymers soluble in water. Finally, we mention the formation of WLM in aqueous solution by amphiphilic diblock copolymers.31−34 Although from the structural point of view diblocks resemble molecular surfactant, their behavior is very different. Often assemblies of diblock copolymers are kinetically frozen35 so that no significant exchange of unimers between different WLM occurs. The viscoelastic properties of these systems are therefore akin to that of suspensions of permanently cross-linked fibrils.36,37 An exception is WLM obtained with block copolymers based on poly(ethylene oxide) combined with poly(propylene oxide) (so-called pluronics)38−41 or polybutadiene.42,43 They form in a narrow range of compositions and/or temperature dynamic WLM that are in thermodynamic equilibrium. Their viscoelastic properties are similar to WLM formed by molecular surfactants.44,45 Here we report for the first time on the rheological properties of aqueous solutions of WLM formed by a polysoap in thermodynamic equilibrium. The polysoap was a copolymer of QVBC and 20% styrene units. The length of the pendent alkyl chains was varied between 12 and 18 carbon atoms. In the following we will first describe in detail the dynamic mechanical behavior of copolymers with dodecyl groups over a wide range of concentrations, temperatures, and ionic strengths. Then we will show the effect of increasing the length of the pendant alkyl groups. We will show that the WLM form transient networks above a critical percolation concentration with a terminal relaxation time that increases sharply with increasing length of the alkyl chains. We will discuss the behavior of WLM formed by this polysoap in comparison with that of WLM formed by molecular surfactants.

viewed as polymerized surfactants, i.e., polysoaps of head type. Therefore, it is useful to briefly consider the rheology of cylindrical micelles formed by charged surfactants. Cationic surfactants are well-known to spontaneously assemble into WLM in water.4,5 In pure water monomeric surfactants (i.e., with a single cationic polar head bound to a single fatty alkyl side chain) form long WLM only at relatively high concentrations, but the transition concentration can be lowered by adding salt or by using hydrotropic counterions.6−9 In the semidilute regime, WLM solutions are viscoelastic characterized by a single relaxation time that is the geometric average between the reptation time of the entangled WLM and their breakage/recombination time.4,5 Under flow, the behavior of WLM is much more complex and less universal; WLM solutions may display either shear thinning or thickening and are also known to give rise to shear banding.10,11 Formation of WLM by oligomeric surfactants has also been investigated.12,13 They consist of several monomeric surfactants with polar heads covalently linked together by spacers. Increasing the oligomerization degree results in a decrease of the concentration at which WLM are formed and thus the concentration at which the viscosity starts to increase rapidly. Furthermore, the viscosity of the WLM solutions formed by oligomeric surfactants passes through a maximum as a function of concentration, which becomes more pronounced with increasing oligomerization degree.14 The maximum viscosity is reached when the WLM become fully entangled. The decrease of the viscosity at higher concentrations is caused by a decrease of the relaxation time and has been related to branching of the WLM.15 It is suggested that sliding of branch points offer a faster route to relax the stress. Branching has been seen in cryo-TEM images,16,17 and the branching point density has been estimated from rheological measurements.15 For a given concentration, increasing the oligomerization degree leads to an increase of the high-frequency elastic modulus.15 Synthesizing surfactants with a higher degree of oligomerization turns out to be difficult.18 However, large polymeric surfactants can be synthesized in various ways. One method is to form complexes of surfactants and oppositely charged polyelectrolytes either by mixing the surfactant molecules with a suitable polyelectrolyte19−21 or by polymerizing the counterions of surfactant.22,23 In the first case, WLM could be formed in a narrow range of compositions, though the rules which control the behavior remain unclear. The relaxation time of these WLM solutions was very long compared to equivalent WLM solutions of monomeric surfactants. In the second case, the viscosity of the WLM often reduced after polymerization of the counterions due to a shortening of the micelles. Alternatively, the surfactant itself may be polymerizable, in which case it is called a surfmer.24 Polymerization of surfmers in order to form polysoaps has attracted a lot of attention and has been recently reviewed.25 In the context of the present study, we need only to consider cationic surfmers of the head type (i.e., when the polar head is very close to the polymerizable group). Polymerization of such surfmers generally leads to insoluble polymers which can however be dispersed in water in the form of colloidal particles.26,27 An exception has been reported by Cochin et al., who have studied the polymerization of n-alkyldimethyl(vinylbenzyl)ammonium chloride (QVBC) (with n = 8, 12, and 16).28−30 The resulting polymers remained in solution during polymerization but were no longer soluble when the powder of purified polymers was redispersed in water. The resulting polysoaps resemble the polymers studied here,

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MATERIALS AND METHODS

Materials. Synthesis of the polymer 80Cn was described before and proceeded in two steps.1 Briefly, the first step consisted in a free radical copolymerization of styrene and vinylbenzyl chloride (VBC) to obtain a precursor polymer which was quaternized in the second step with N,N-dimethylalkylamine where the size of the alkyl group (n) is comprised between 12 and 18 (see Figure 1). The distribution of each comonomer within the chain is statistical. In the following, we will focus on polymers containing 80 mol % VBC. The number-average polymerization degree (DPn = 130) of the precursor polymer and the dispersity (Đ = 1.5) were determined by size exclusion chromatography in THF with online light scattering and refractive index detection. Sample Preparation. The polymers were dispersed in demineralized water (Millipore) and heated at 80 °C until they were completely dissolved and stored at room temperature. In some cases NaCl was added in the form of a concentrated NaCl solution. Addition of salt before or after addition of the polymers did not affect the behavior of the samples. Rheology. Depending on the viscosity of the samples, measurements have been made with stress-controlled rheometers AR-G2 (TA Instruments) and MCR 301 (Anton Paar) equipped with different truncated cone and plate geometries (angles 4°−2°−2°−1° and diameters 20−40−25−60 mm). Samples were covered with paraffin oil and a solvent trap for preventing their drying. Solutions of low viscosity have been measured with a Low Shear 40 from Contraves using a Couette geometry (DIN 412). Oscillatory shear measurements were done within the linear response regime to measure the storage (G′) and loss (G″) moduli. The viscosity (η) of the samples was determined using shear flow measurements at low shear rates or was determined from oscillatory measurements at low frequencies. The values obtained by these methods were in fair agreement (see Figure SI1 of the Supporting Information). The viscosity of the samples has B

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Macromolecules been normalized by that of the solvent to obtain the relative viscosity (ηr). All measurements were done at 20.0 ± 0.5 °C unless specified.

which implies that the relaxation time distribution did not depend on the temperature. This in turn indicates that the relaxation mechanism was independent of the temperature. Frequency−temperature superposition allows one to observe the relaxation process over a broad frequency range. Figure 3b shows master curves that were obtained in this way at different polymer concentrations. The transient networks may be characterized in terms of their terminal relaxation time (τ) taken here as the inverse of the angular frequency where G′ and G″ cross and their elastic shear modulus (Gel) taken as G′ at ωτ = 100. The horizontal shift factors that were used to obtain the master curves describe the temperature dependence of τ, whereas the vertical shift factors describe the temperature dependence of Gel. The values of τ and Gel at 20 °C are plotted as a function of the polymer concentration in Figure 4. Just above the percolation threshold

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RESULTS Figure 2 shows the concentration dependence of the relative viscosity for salt free solutions of 80C12 at different

Figure 2. Concentration dependence of the relative viscosity of 80C12 at various temperatures.

temperatures. ηr increased sharply by several orders of magnitude at a critical concentration (Cp) that increased with increasing temperature from 43 g/L at 20 °C to 70 g/L at 60 °C. After the initial sharp increase, the viscosity continued to increase more weakly at higher concentrations. The initially rise of the viscosity was stronger at lower temperatures. The dynamic mechanical properties were investigated in more detail by measuring the frequency dependence of the oscillatory shear moduli. Figure 3a shows the results obtained for C = 98.3 g/L at different temperatures. The frequency dependence is typical for viscoelastic systems that are characterized by solidlike behavior at high frequencies and liquidlike behavior at low frequencies. As was mentioned in the Introduction, structural analysis of the solutions has shown that the polymers form branched WLM at higher concentrations. Therefore, we interpret the rheological behavior in terms of the formation of a transient network above a critical percolation concentration. Results obtained at different temperatures could be superimposed using horizontal and vertical shift factors,

Figure 4. Concentration dependence of the elastic modulus (circles) and the viscoelastic relaxation time (triangles) for aqueous solutions of 80C12 at 20 °C.

(Cp = 43 g/L) the network still contained many defects (dangling ends, loops), but these defects disappeared rapidly with increasing concentration, which explains the rapid initial increases of both τ and Gel. The relaxation time of fully formed networks at C ≫ Cp was independent of the polymer concentration and is determined by the lifetime of the transient cross-links. However, the elastic modulus continued to increase

Figure 3. (a) Frequency dependence of the shear moduli for 80C12 at 98.3 g/L at different temperatures (G′ and G″ are respectively shown as closed and open symbols). (b) Master curves obtained by frequency−temperature superposition for 80C12 at different concentrations in water (Tref = 20 °C). C

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salt strongly reduced Cp from 43 g/L in salt-free water to 2.8 g/ L at 35 mM NaCl. The effect of the ionic strength on the frequency dependence of the shear moduli was studied for networks formed at different ionic strengths at a fixed polymer concentration of C = 50 g/L. Figure 7a shows examples of master curves obtained by frequency−temperature superposition. The relaxation time was little influenced by the addition of salt apart from a small increase of τ between 0 and 5 mM NaCl (see Figure 7b). The latter was probably caused by the fact that 50 g/L is close to Cp at low ionic strength. The activation energy of the relaxation process was found to be independent of the ionic strength within the experimental error (results not shown). Contrary to the terminal relaxation time, the elastic modulus of the transient networks increased significantly with increasing ionic strength (Figure 7b). Gel has the same power law dependence on the concentration as the viscosity for C > 5 g/L (Gel ∝ C3) because η ∝ Gτ and τ is independent of the concentration. It was shown elsewhere1,2 that the local structure of the WLM does not change in the presence of salt but that screening of electrostatic interaction favors branching, which explains the increase of Gel. The effect of the temperature on the elastic modulus is shown in Figure 8 for gels at different polymer concentrations in pure water and with 35 mM NaCl. For C ≫ Cp, Gel decreased weakly with increasing temperature. However, when the concentration is closer to Cp, we observed a sharp decrease of Gel, and above a critical temperature the systems no longer formed an elastic network. These observations show that the branching density decreases with increasing temperature. These results confirm the observation reported in ref 2, where we showed for low polymer concentrations that the size of the WLM decreases with increasing temperature. The process of depercolation with increasing temperature will be discussed in detail below. Effect of the Length of the Pendant Alkyl Groups. Relaxation of the networks slowed down hugely with increasing length of the pendant alkyl groups. This is illustrated in Figure 9 that shows the frequency dependence of networks at C = 100 g/L. The relaxation time increased approximately exponentially with the alkyl length by a factor of 20 per alkyl group (see inset). The results are given here for Tref = 80 °C because the relaxation of the 80C16 was too slow to determine accurately at lower temperatures. Therefore, for 80C16 only results obtained at 80 °C are shown. No results are shown for 80C18 because this system relaxed too slowly even at 80 °C. Interestingly, the elastic modulus was not much influenced by the alkyl length. The small decrease of Gel with increasing alkyl length can be explained by the small decrease of the molar concentration at the same mass concentration. The strong increase of the bond lifetime caused the viscosity of networks formed by 80C14, 80C16, and 80C18 to be much higher than that of 80C12. As a consequence, the sol−gel transition could be easily identified by tilting the tubes. Figure 10 shows that at 20 °C the percolation threshold at different salt concentrations shifted to lower polymer concentrations when the alkyl length was increased from C12 to C14, but the effect of further increasing the alkyl length on Cp was small. We showed above for 80C12 that Cp increased with increasing temperature (see Figure 2). An increase of Cp was observed also for 80C14 and 80C16, but only for T > 20 °C and T > 40 °C, respectively (see Figure SI2 of Supporting Information). For 80C18 we observed no effect of the temperature on Cp

significantly with increasing concentration, because the crosslink density increased. The terminal relaxation time decreased strongly with increasing temperature. Figure 5 shows that the temperature

Figure 5. Temperature dependence of the viscoelastic relaxation time for 80C12 at different concentrations in water. The dashed line represents a linear least-square fit of the results at higher polymer concentrations.

dependence of τ is independent of the concentration and has a linear dependence in an Arrhenius representation with apparent activation energy Ea = 130 kJ/mol. For fully formed networks Gel decreased weakly with increasing temperature. Only at concentrations close to Cp did Gel have a strong dependence on the temperature as we will discuss below. It follows that for fully formed networks the observed decrease of η with increasing temperature was caused principally by the decrease of τ, whereas the increase of η with increasing polymer concentration was caused by the increase of Gel. Influence of the Ionic Strength. The effect of the ionic strength was investigated by adding NaCl up to 35 mM. At higher NaCl concentrations the systems visually phase separated. In Figure 6 the concentration dependence of the relative viscosity for solutions containing 35 mM NaCl is compared with that of salt-free solutions. In both cases a steep increase is observed at the percolation threshold followed by a weaker increase at higher concentrations. However, addition of

Figure 6. Concentration dependence of the relative viscosity for solutions of 80C12 in water (circles) and with 35 mM NaCl (triangles). D

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Figure 7. (a) Master curves obtained by frequency−temperature superposition with Tref = 20 °C for 80C12 at 50 g/L in water (squares), 10 mM (triangles), and 35 mM (circles) NaCl. (b) Influence of the concentration of NaCl on the elastic modulus (circles) and the viscoelastic relaxation time (triangles) for solutions of 80C12 at 50 g/L.

Figure 8. Temperature dependence of Gel for gels at different polymer concentrations in pure water (a) and in 35 mM NaCl (b).

Figure 9. Master curves obtained by frequency−temperature superposition with Tref = 80 °C for solutions in water at 100 g/L of 80C12 (circles), 80C14 (triangles), and 80C16 (squares). Inset shows the variation of the corresponding viscoelastic relaxation time as a function of the length of the alkyl side chain.

Figure 10. Dependence of the percolation concentration at 20 °C with the ionic strength for 80Cn copolymers.

establish if they depend strongly on the alkyl length. The results of this investigation are shown in the Supporting Information. The principal conclusion is that qualitatively the dependence of Gel and τ on the concentration, temperature, and ionic strength is the same for 80C14 and 80C12. Interestingly, the activation energy of the viscoelastic relaxation of 80C14 is the same as that of 80C12 even though the relaxation time was almost 3 orders of magnitude larger.

even at 80 °C.46 A possible reason for this behavior will be discussed below. The extremely slow relaxation of 80C16 and 80C18 rendered a systematic investigation of the effects of concentration, temperature, and ionic strength on the relaxation time impossible for these systems. Even for 80C14 such an investigation is hampered by slow restructuring after cooling a heated solution to room temperature. Nevertheless, we have investigated the effects of concentration and temperature on the dynamic mechanical properties for this system in order to

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DISCUSSION Self-assembly of the polysoap 80Cn in aqueous solution led to the formation of WLM in thermodynamic equilibrium if the E

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Figure 11. Frequency dependence of G′ (closed symbols) and G″ (open symbols) for 80C14 at 32 g/L (a) and 40 g/L (b) for different temperatures.

to topological constraints, which will lead to a strong, but progressive, increase of the viscosity. In the absence of the formation of cross-links between the rods, there is no critical gel concentration as was observed here. Furthermore, the relaxation time increased strongly with increasing polymer concentration for both flexible and rigid polymers, which was not observed for the systems studied here, whereas we found that τ was independent of the concentration. If we nevertheless assume that the origin of the elasticity of the network is entropy, we may calculate the molar mass of the elastically active chains (Me) as Gel = CRT/Me where R is the gas constant. In this way we find for Me values down to 22 kg/ mol. This corresponds to lengths between entanglements or cross-links down to 3 nm, using the molar mass per unit length of the rods obtained from scattering measurements,1 which is close to the diameter of the rods. It is clear that the origin elasticity of the self-assembled comblike polyelectrolytes cannot be understood in terms of rubber elasticity and is therefore different from that of amphiphilic block copolymers or flexible WLM formed by surfactants. Cryo-TEM showed that a network is formed by branched rods. For the fully formed network at concentration significantly larger than Cp, the distance between the branching points is smaller than the persistence lengths of the rods. A schematic drawing of the network formation is given in Figure 12. When such a network is stressed in the linear regime, deformation is possible only by deformation of the branching points or by bending of the rods between the branch points. In

length of the pendant alkyl chains was less than C18. For 80C18 the assemblies were kinetically frozen even at 80 °C. Elsewhere, we showed that the length of the WLM increases with increasing concentration and that longer WLM branch.2 Contrary to WLM formed by molecular surfactants, the WLM formed by 80Cn were rigid with a persistence length of at least a few hundred nanometers. Therefore, entanglements do not play a significant role in the mechanical properties of semidilute solutions of 80Cn, which constitutes a major difference with surfactant WLM for which the strong increase of the viscosity with increasing concentration is attributed to entanglement. Percolation of Branched Polymeric WLM. The strong increase of the viscosity above a critical concentration is caused by percolation of WLM that are cross-linked via the branch points. The effect of percolation on the mechanical properties is best seen for copolymers with larger alkyl groups that relax very slowly. Solutions of 80C16 or 80C18 flowed freely at C = 25 g/ L, whereas at C = 30 g/L they did not flow when titled. The percolation transition can also be observed by cooling solutions close to Cp because Cp decreased with decreasing temperature. Figure 11a shows the frequency dependence of the shear moduli for 80C14 at C = 32 g/L and for different temperatures. At T = 40 °C the frequency dependence is typical for a lowviscosity liquid. With decreasing temperature one observes increasing slow relaxation due to the formation of large interpenetrating WLM clusters. At a critical temperature (30 °C), G′ and G″ showed the same power law frequency dependence, which is characteristic for gels at the percolation threshold. At lower temperatures G′ became independent of the frequency and larger than G″ over a range of frequencies, which is characteristic for gels. However, the plateau modulus and the power law dependence did not extent to the lowest frequencies because the cross-links were not permanent. If the lifetime of the cross-links is shorter than the inverse of the oscillation frequency, the imposed stress can relax by spontaneous breakage of the cross-links. This phenomenon is more clearly observed for solutions at C = 40 g/L shown Figure 11b. If the bond lifetime is not very long, percolation leads to a sharp increase of the viscosity rather than to gelation. In this case, the viscosity decreases gradually with increasing temperature because the bond lifetime decreases until the system depercolates, causing to a sharp decrease of the viscosity. Origin of the Elastic Modulus. It was already mentioned that the elasticity of the transient networks cannot be attributed to entanglement of the WLM because they are extremely rigid. Of course, semidilute solutions of rigid rods are also subjected

Figure 12. Schematic representation of the self-assembly mechanism responsible for the formation of a percolated network of branched cylindrical aggregates upon increasing polymer concentration or ionic strength. F

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Macromolecules the first case Gel is proportional to the concentration of branch points (Cbr), which means that the concentration of branch points is proportional to C3 since we found that Gel ∝ C3. In the second case, we need to consider that the force (F) needed to bend rigid rods with length L is proportional to L−3. Gel is given by Gel ∝ FCbr. Since L is related to the ratio C/Cbr, the concentration dependence of Gel on C can be therefore be explained by bending of the rods if Cbr is proportional to C3/2. Unfortunately, we were not able to quantify the concentration dependence of the branch point density in order to determine whether bending or branch point deformation caused the elastic response. In either case the results reported here show that the elasticity does not depend on the length of the alkyl chains, which implies that resistance to bending or deformation of branch points is not significantly influenced by the thickness of the alkyl cores of the rods. Gel decreases weakly with increasing temperature for fully formed gels and very strongly close to the percolation concentration. As was pointed out above, this is most likely related to the decreases of the branching density and not to a decrease of either the binding rigidity or the deformability of the branch points. Origin of the Viscoelastic Relaxation. The shear stress can relax either by scission of the rods or breakage at the branch points. As was mentioned in the Introduction, formation of a transient network of cross-linked WLM has also been observed for oligomeric surfactants. It was suggested that for these systems the branch points could slide along the WLM, which would allow relaxation of the imposed stress. In the case of WLM formed by polysoaps studied here such a mechanism is highly unlikely. Therefore, the observed relaxation of the stress must be caused by breakage and recombination of the WLM. It seems more likely that breakage occurs at the branch points, which are defects of the micellar structure, than between branch points, but we have no experimental proof that this is indeed the case. In either case breakage involves the cooperative release of alkyl chains from the hydrophobic core of the WLM. The relaxation is characterized by a broad distribution of relaxation times (see Figures 3 and 7). If the relaxation rate is determined by dissociation of branching points, it is not surprising that it is characterized by a broad distribution of relaxation times as their structure on the molecular level will not be the same and therefore involves cooperative release of the same number of alkyl chains. Even if relaxation is caused by scission of the rods, a broad distribution is expected because scission would occur at weak point in the self-assembled rods. These weak points will also vary in structure. We find that the relaxation time distribution broadens at higher concentrations, which could indicate an increase the structural variability of the branch points. It is illustrative to compare in this context the systems investigated here with hydrophilic polymers capped on both ends with alkyl chains that form transient networks by selfassembly of the alkyl chains into spherical micelles. These networks can relax the imposed stress by release of a single alkyl chain from the hydrophobic core, and as might be expected, the relaxation time was found to increase with increasing alkyl length.47 However, for a given alkyl length the relaxation time was found to be orders of magnitude faster than for the WLM networks studied here, and the dependence on the alkyl length was much weaker. This comparison shows that breakage within the WLM network involves the cooperative release of several alkyl groups. Quantitative comparison of the

variation of the relaxation time with the alkyl length suggests that the cooperative release involves three alkyl groups. It is perhaps not surprising that growth of the WLM and formation of branch points is favored by screening of the electrostatic repulsion by adding salt. However, the relaxation time did not depend significantly on the ionic strength, which corroborates the suggestion that release of alkyl chains is the limiting factor for breakage. For 80C12, growth and branching of the WLM micelles with increasing concentration were slightly weaker at higher temperatures leading to an increase of Cp (see Figure 2). We suggest that this effect is caused by the loss of entropy due to self-assembly and counterion condensation, which overcompensates the stronger hydrophobic interaction. However, this effect of the temperature on Cp was not observed at lower temperatures if the alkyl chains were longer. The reason is that equilibration of the systems slows down with decreasing temperature and becomes imperceptibly slow at low temperatures. All solutions were equilibrated at 80 °C and subsequently cooled. Solutions at concentrations just below Cp at 80 °C rapidly formed a network at 20 °C for 80C12 but for 80C14 equilibration was very slow. For 80C16 slow changes could be observed over a period of weeks, while 80C18 was kinetically frozen.

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CONCLUSION

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ASSOCIATED CONTENT

Comblike amphiphilic copolyelectrolytes are polysoaps that in aqueous solution can form wormlike micelles in thermodynamic equilibrium. Branching of the WLM leads to the formation of a system spanning network above a critical percolation concentration. Relaxation of the stress by spontaneous restructuring of the WLM network is an activated process that involves cooperative release of about three alkyl chains from the hydrophobic core. Breakage and recombination render the network transient causing solutions at C > Cp to behave as viscoelastic liquids. The terminal relaxation time increases very strongly with increasing length of the pendant alkyl chains, causing polysoaps with longer alkyl chains to behave as covalent hydrogels. The elastic modulus of the networks is determined by the cross-link density which increases with increasing polymer concentration but does not depend on the alkyl length. Screening of the electrostatic interaction by addition of monovalent salt favors growth and branching of the micelles leading to a reduction of the percolation concentration and an increase of the elastic modulus. However, the relaxation time is not influenced by addition of salt because it is determined by the release of alkyl chains.

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.6b01369. Comparison of flow and complex viscosities on the same sample (80C12, 10 g/L, and 35 mM NaCl); variation of the percolation concentration with the temperature for 80Cn copolymers; viscoelastic properties of 80C14 as a function of concentration and temperature (PDF) G

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected], Ph +33 (0) 2.43.83.39.12 (C.C.). Notes

The authors declare no competing financial interest.

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DOI: 10.1021/acs.macromol.6b01369 Macromolecules XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.macromol.6b01369 Macromolecules XXXX, XXX, XXX−XXX