Nonlinear Rheology of Random Sulfonated Polystyrene Ionomers

Article pubs.acs.org/Macromolecules

Nonlinear Rheology of Random Sulfonated Polystyrene Ionomers: The Role of the Sol−Gel Transition Chongwen Huang,† Quan Chen,*,‡ and R. A. Weiss*,† †

Department of Polymer Engineering, University of Akron, Akron, Ohio 44325, United States State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, China

‡

S Supporting Information *

ABSTRACT: The linear and nonlinear rheological behaviors of nonentangled sulfonated polystyrene (SPS) ionomers near the sol−gel transition were studied. When the degree of sulfonation, p, was below the gel point, the ionomer exhibited sol-like linear viscoelastic (LVE) behavior, and shear thinning was observed for steady shear flow. For p close to the gel point, the ionomer showed power-law-like LVE behavior over a wide frequency range. Strain hardening and shear thickening behavior were observed, and their magnitudes depended on the temperature, molecular weight of the PS precursor, and the Coulomb energy of the ion pair. Above the gel point, a distinct rubbery plateau was observed in the dynamic modulus. Melt fracture occurred upon start-up shear, which prevented quantitative examination of the nonlinear rheology. The possible mechanisms for strain hardening and shear thickening near the gel point are discussed with respect to formation of large clusters that nearly percolate in space.

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INTRODUCTION

with a sulfonation level of p = 0.10, but even for that low sulfonation, p > pc (= 0.026). Recently, randomly sulfonated oligomeric polystyrene (SPS) ionomers have been used as a model system for studying the dynamics of ionic associations and the relaxation behavior due to dissociations and ion-pair hopping.5,6,14,16−18 There are two major advantages of using low molecular weight ionomers: one is that the properties are influenced only by the effects of ionic interactions owing to the absence of chain entanglements, and the other advantage is that it allows one to study ionomers below and near the gel point pc. The mean-field theory, developed previously for the dynamics of associative polymer solutions by Rubinstein and Semenov,19,20 was recently modified for bulk ionomers.14 The reversible gelation model14 predicts two transitions in the relaxation behavior when p approaches pc from the sol state. One transition occurs at the Ginzburg point,21 above which the newly formed branched chains, termed clusters (note that the term clusters used herein is different from the term commonly used to describe ionic nanodomains in other ionomer literature), are at their overlap concentration, and the relaxation of branched chain is accordingly governed by critical percolation instead of mean-field percolation. The other transition occurs close to the gel point, where the Rouse relaxation time of the clusters becomes longer than the effective

Ionomers are relatively hydrophobic polymers with small amounts of covalently attached ionic groups (typically, less than 15 mol %), such as sulfonic and carboxylic acids neutralized with metal or ammonium counterions. Ionomers have wide applications as membranes,1 compatibilizers for polymer blends,2 shape memory polymers, and self-healing materials.3 These applications take advantage of the ionic interactions that occur in these materials, which modify their microstructure and the physical, mechanical, and rheological properties. In bulk ionomers, the polar ionic groups usually associate with each other due to the strong electrostatic or dipolar attractions in a relatively nonpolar polymer medium. Interchain associations take the role of physical cross-links that persist for long times and/or to high temperature.4 The nonlinear rheology of SPS and other bulk ionomers has been previously studied,5−13 but in all the prior studies the concentration (mole fraction) of the ionic species, p, was much higher than the gel point pc, where pc ≡ 1/(N − 1) × 100 mol % for a bulk ionomer with a degree of polymerization N.14 At the gel point, each SPS chain contains on average one sulfonate group. For unentangled ionomers, one characteristic of their linear viscoelastic (LVE) properties when p > pc is the appearance of a rubber-like plateau in G′(ω) at frequencies below the rubber-to-glass transition. For high molecular weight, entangled polymers pc is very low, and it is difficult to prepare samples with p < pc. For example, Yu and Weiss15 reported the rheological behavior of SPS ionomers (M = 400 000 g/mol) © XXXX American Chemical Society

Received: September 20, 2016 Revised: November 3, 2016

A

DOI: 10.1021/acs.macromol.6b02057 Macromolecules XXXX, XXX, XXX−XXX

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Figure 1. LVE master curves at Tr = 140 °C for (a) NaSPS4.6 and (b) NaSPS13.5 ionomers with varying sulfonation levels; (c) SPS4.6-2.5 (p ∼ pc) and (d) SPS13.5-0.76 (p ∼ pc) ionomers neutralized with different cations. The colored regions correspond to (I) mean-field percolation behavior, (II) critical percolation behavior, and (III) terminal behavior. The solid curves are the model predictions.

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breakup time, above which the terminal relaxation is controlled by effective breakup, when breakup of the cluster occurs on the chain backbone and produces two daughter clusters of comparable size with relaxation times much shorter than their mother cluster. In contrast, noneffective breakup occurs at the side chain and produces one daughter cluster having similar size as the mother cluster and another smaller satellite cluster.14 The reversible gelation model14 with only two variables, the Rouse time of a Kuhn segment, τ0, and the ionic dissociation time, τs, quantitatively predicts the LVE behavior of neat SPS ionomers and their binary blends as well as the sol−gel transition.14,18 The nonlinear behavior of SPS ionomer melts with p > pc has been reported to exhibit strain hardening, where the transient viscosity before yielding is higher than that predicted from LVE behavior, in extensional flow,17 but not in shear flow.6 Shear thickening is often observed for a variety of associative polymer solutions,22−31 but with the exception of ref 5, it has not been reported for bulk ionomer melts. One hypothesis of the present work was that strain hardening and shear thickening for ionomer melts only occur when p ∼ pc, which would explain why those phenomena have not previously been observed for ionomers with p ≫ pc. That hypothesis was tested by examining the nonlinear shear rheology of the oligomeric SPS samples with p < pc, p ∼ pc, and p > pc. Strain hardening and shear thickening were experimentally observed only when the system was close to the gel point. Although a necessary condition for strain hardening or shear thickening, p ∼ pc was not a sufficient condition. The ionic strength of the ion pair, molecular weight, and temperature also influenced whether those two phenomena were observed.

EXPERIMENTAL DETAILS

Materials. Two oligomeric polystyrenes (PS) with weight-average molecular weights Mw = 4.6K and 13.5K g/mol and narrow polydispersity (PDI < 1.06) were purchased from Pressure Chemical Co. (Pittsburgh, PA). The two PS samples are denoted as PS4.6 and PS13.5, respectively. Concentrated sulfuric acid, 1,2-dichloroethane (DCE), acetic anhydride, toluene, and methanol were purchased from Sigma-Aldrich and used as received. PS was sulfonated using acetyl sulfate as the sulfonating agent.32 Acetyl sulfate was prepared by adding concentrated sulfuric acid to a 60 mol % excess of acetic anhydride in DCE at 0 °C, and the freshly prepared acetyl sulfate was then added over 1 min to a continuously stirred 10 wt % PS/DCE solution (∼200 mL) at ∼50 °C. The reaction was terminated after 1 h by adding ∼2 mL of 2-propanol. The SPS was isolated by precipitation in boiling deionized (DI) water, washed three times with DI water, dried in air at 70 °C for 1 day, and finally dried at 120 °C in a vacuum oven for 1 week. The sulfonation level was determined by sulfur elemental analysis by Robertson Microlit Analysis (Madison, NJ). The sulfonation reaction occurs randomly along the polymer chain, principally at the para-position of the phenyl ring,33 and produces a distribution of chains with varying sulfonation, including some with no sulfonate groups, that can be represented by a binomial distribution.34 Alkali metal salts of SPS were prepared by adding a 1.5 equiv of metal hydroxide or acetate to a 15 wt % solution of the SPS acid derivative in a 90/10 (v/v) mixture of toluene and methanol. After 30 min, the neutralized SPS was isolated following the procedures described above for the sulfonic acid derivative. Six different samples were prepared with degrees of sulfonation p of 1.6, 2.5, and 2.8 mol % for SPS4.6 and 0.20, 0.76, and 1.2 mol % for SPS13.5, which correspond to an average number of ionic groups per chain of 0.7, 1.1, and 1.2 for SPS4.6 and 0.3, 1, and 1.6 for SPS13.5. The sample nomenclature used hereafter is MSPSx-p, where M denotes the cation (Na, K, Rb, Cs), x is the molecular weight of the PS precursor (in kg/ mol), and p is the degree of sulfonation in mol %. Materials Characterization. Linear and nonlinear rheological measurements were carried out with a TA Instruments ARES-G2 B


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failed in the terminal region of G′ since τc depends on τX and τs. This effect was weaker for G″, which is less sensitive to slower relaxation modes than G′. In general, the storage and loss moduli may be represented by summations of multiple Maxwell models:

rheometer. Dynamic frequency sweeps were performed over a temperature range of T = 90−240 °C and a frequency range of ω = 0.16−250 rad/s using either 25 or 8 mm parallel plates. All dynamic measurements were made within the LVE region, which was determined from strain sweep experiments. Time−temperature superposition (TTS) master curves were constructed at the same reference temperature Tr = 140 °C for comparison. For each molecular weight, the glass transition temperatures of the different ionomer samples varied by about 4 °C, so the error in using the same Tr for all samples was small. A cone and plate fixture with a diameter of 25 mm and a cone angle of 0.04 rad was used for steady shear and startup shear experiments. Those experiments were conducted over a temperature range of T = 120−200 °C and shear rates of γ̇ = 0.0001−250 s−1.

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G′(ω) =

∑ Gp p

G″(ω) =

ω 2τp 2 1 + ω 2τp 2

∑ Gp p

(1)

ωτp 1 + ω 2τp 2

(2)

According to eqs 1 and 2, the dynamic moduli in the terminal region (ω ≪ 1/τp) were controlled mainly by the slowest relaxation modes (the largest τp’s). G′(ω) scaled with τp2 (ωτp ≪ 1), and G″(ω) scaled with τp. Therefore, G′(ω) was more sensitive to the changes of the slower relaxation modes than G″(ω). TTS was obeyed better in the terminal region for the SPS4.6-2.5 ionomer, possibly because that sample was already slightly above the gel point where the terminal relaxation is governed by τs. Nevertheless, failure of TTS was observed before the terminal relaxation (indicated by the arrow in Figure 1), where relaxation is dependent on Rouse motions and ionic dissociation. When p > pc (SPS4.6-2.8 and SPS13.5-1.2 ionomers), G′ showed a well-defined plateau and G″ shows a peak before the terminal relaxation. TTS failed for SPS4.6-2.8 and SPS13.5-1.2 ionomers for G″ before the peak due to the overlap of the Rouse and ionic dissociation relaxations as discussed above. The prediction of the reversible gelation model is also shown in Figure 1 for comparison, with fitting parameters, Rouse relaxation time τ0 and ionic dissociation time τs, listed in Table 1. For p < pc, the reversible gelation predicted G″ quite well but

RESULTS AND DISCUSSION

Linear Viscoelastic (LVE) Behavior. Figure 1 shows the LVE master curves at Tr = 140 °C for SPS4.6 and SPS13.5 ionomers with varying sulfonation levels and different cations. The gel points are pc = 2.3 mol % and pc = 0.78 mol % for the SPS4.6 and SPS13.5 ionomers, respectively. The Ginzburg point, the transition between mean-field and critical percolation, was defined as pg = (1 − NK−1/3)pc with NK as the number of Kuhn segments per chain.14 For SPS4.6 and SPS13.5 ionomer, the Ginzburg point corresponds to pg = 1.0 and 0.47, respectively. When the sulfonation degree is below the gel point, p < pc, TTS works well for both NaSPS4.6-1.6 (pg < p < pc) and NaSPS13.5-0.20 (p < pg) ionomers, and no plateau was observed in G′(ω) (see Figures 1a and 1b). The reversible gelation model predicts mean-field behavior, G′(ω) ∼ G″(ω) ∼ ω1, for p < pg, which was not observed in NaSPS13.5-0.20 ionomer. For pg < p < pc, the NaSPS4.6-1.6 ionomer does not exhibit the predicted critical percolation behavior, G′(ω) ∼ G″(ω) ∼ ω2/3, but instead, it shows a power law of G′(ω) ∼ G″(ω) ∼ ω1 before the terminal region. The absence of the predicted power law relation in those ionomers may be attributed to the failure to incorporate the effects of noneffective breakup in the reversible gelation model.18 When p ∼ pc, the SPS4.6-2.5 and SPS13.5-0.76 ionomers showed three distinct power law regions: (1) mean-field behavior, G′ ∼ G″∼ ω1, at high frequencies, (2) critical percolation behavior, G′(ω) ∼ G″(ω) ∼ ω2/3, at intermediate frequencies, and (3) terminal relaxation, G′(ω) ∼ ω2, G″(ω) ∼ ω1, at low frequencies. For the SPS4.6-2.5 ionomers, G′ showed a very weak plateau before the terminal region (see the arrow in Figure 1c), probably due to their slightly higher p than the predicted gel point (p = 2.5 mol % > pc). When p is slightly above pc, a small fraction of percolated network (gel) is formed in the ionomer, and the relaxation of the gel network contributes to the appearance of the weak plateau in G′. For the SPS4.6-2.5 and SPS13.5-0.76 ionomers, decreasing the Coulomb energy of the ion pair, Ec ∼ 1/a where a is the ionic radius of the cation (i.e., varying the cation from Na to Cs decreased Ec by the ratios 1:0.76:0.70:0.64), shifted the terminal relaxation to higher frequency as a consequence of decreasing the ionic dissociation time τs. TTS failed for both SPS4.6-2.5 and SPS13.5-0.76 ionomers due to the different temperature dependences of the Rouse relaxation of the precursor chain at high frequency and ionic dissociation in the terminal region. Specifically, the terminal relaxation of the SPS13.5-0.76 ionomer is governed by effective breakup with an effective breakup time, τc ∼ τX1/4τs3/4 where τX is the Rouse relaxation of the precursor chain.14 Hence, TTS

Table 1. Rouse Relaxation Time (τ0) and Ionic Dissociation Time (τs) Used for SPS4.6 and SPS13.5 Ionomers at 140 °C SPS4.6-1.6 PS4.6 τ0 (μs) τs (s)

τ0 (μs) τs (s)

1.2 n/a

Na

SPS4.6-2.5 Na

3.8 6.6 n/a 2500 SPS13.5-0.20

K

Rb

6.5 6.5 450 250 SPS13.5-0.76

SPS4.6-2.8 Cs 6.7 35

Na 19 5000 SPS13.5-1.2

PS13.5

Na

Na

K

Cs

Na

20 n/a

34 n/a

35 3300

38 320

35 21

96 4340

underpredicted G′. The discrepancy in the experimental and predicted G′ was much more evident in NaSPS4.6-1.6 than NaSPS13.5-0.20 due to its much higher p (p > pg). That result may be a consequence of the failure of the model to account for noneffective breakup of the clusters, which may also explain the higher frequency relaxations and broadening of the overall relaxation of the clusters. When p ∼ pc and p > pc, the model captured G′ and G″ for both the SPS4.6 and SPS13.5 ionomers, except that the plateau modulus, GN, for the former was underpredicted. Since the model assumes all the chain strands (i.e., the chain between sulfonate groups) are stress-bearing, it predicts a higher plateau modulus than the measured for the SPS13.5 ionomers,14,18 as a result of network defects, e.g., dangling chains and loops. The lower predicted plateau modulus for the two SPS4.6 ionomers may be due to the uncertainty in the measurement of the sulfonation level, p, since C


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Although the WLF equation fits the shift factors reasonably well, viscoelastic behavior of the ionomers depends upon two relaxation processes that have different temperature dependences. The first relaxation process was the Rouse-like relaxation of the precursor chain. The shortest Rouse relaxation time, τ0, had a temperature dependence similar to that of PS, though τ0 increased with increasing p (see Table 1) due to increasing Tg with increasing p. The Tg increase is attributed to the phase separation of nanoscale ionic aggregates that restricted motion of the surrounding segments.37 The interactions of the ionic groups also introduced a second, slower relaxation process: the ionic dissociation of the sulfonate−sulfonate interactions. That relaxation time, τs, decreased more rapidly than τ0 with increasing temperature, as indicated by the smaller shift factors for the ionomers at higher temperatures than those for PS. Increasing the ionic content increased the contribution of ionic dissociation to the overall relaxation of the ionomer, which produced a greater temperature dependence of the shift factors at higher temperatures where the relaxation behavior was mainly controlled by the ionic dissociation process. Nonlinear Behavior: Steady Shear Flow. The steady shear flow behavior of SPS4.6 ionomers at 170 °C with different sulfonate concentrations and metal cations is shown in Figure 3a. The NaSPS4.6-1.6 ionomer (p < pc) exhibited Newtonian behavior at low shear rates (γ̇) and shear thinning behavior for γ̇ > 10 s−1. The first normal stress coefficient Ψ1 of the NaSPS4.6-1.6 ionomer was only ∼0.03 Pa·s2 at γ̇ = 40 s−1, indicating weak elasticity. For NaSPS4.6-2.5 (p ∼ pc) η was constant (η0 = zero shear rate viscosity) at low shear rates, followed by shear thickening behavior for γ̇ > 0.025 s−1, and then shear thinning behavior after η reached a maximum at γ̇ = 0.16 s−1 (see orange data in Figure 3a). For NaSPS4.6-2.8 ionomer (p > pc), η = η0 at low shear rate but decreased rapidly at γ̇ > 0.04 s−1 (shown as purple arrow in Figure 3a) as a consequence of melt fracture. With reference to the NaSPS4.61.6 ionomer, increasing p for the NaSPS4.6-p ionomers increased η0 by ∼3 and ∼4 orders of magnitude and the values of Ψ1 by ∼6 and ∼8 orders of magnitude for the NaSPS4.6-2.5 and NaSPS4.6-2.8 ionomers, respectively, as a result of higher concentrations of supramolecular cross-links due to intermolecular dipole−dipole or ion−dipole interactions. All the SPS4.6-2.5 ionomers exhibited similar steady shear viscosity behavior, with constant η at low shear rates and shear thinning at higher shear rates. For the Ψ1(γ̇) data, a zero shear rate first normal stress coefficient, Ψ10 was not observed and Ψ1 decreased monotonically with increasing shear rate. The decrease of Ψ1(γ̇) with increasing shear rate was much greater than that of η(γ̇). In the shear thinning region, η ∼ γ̇−1 and Ψ1 ∼ γ̇−2. Similar behavior, where the shear stress and normal stress difference are essentially independent of the shear rate (σ ∼ γ̇0; N1 ∼ γ̇0), has been reported in other systems where the plastic flow due to a yield stress occurs and which is a consequence of a structural change in the polymer melt, e.g., in hydrophobically associating polymer melts24 and in liquid crystalline polymer melts.38 For the ionomers the yield stress is presumably due to disruption of the ionic aggregates that form the supramolecular network.6 This behavior is distinctly different than the power-law behavior (η ∼ γ̇n−1; Ψ1 ∼ γ̇m−1, where m < n < 1), which arises from disentanglement of long chains. Decreasing Coulomb energy of the ion pair, Ec, decreased η and Ψ1, but it also increased the onset shear rate for the shear thinning (i.e., lower relaxation time), which was due to the lower strength of the intermolecular interactions.

the relaxation close to the gel point is very sensitive to small differences in p. A much better fit was achieved if the value of p was higher by less than 0.1 mol %. The calculated ionic dissociation time τs increased with increasing Coulomb energy Ec of the ion pair and increasing p for both SPS ionomers. However, τ0 was independent of the metal cation, though it increased with increasing p. τ0 for the SPS13.5 ionomers was an order of magnitude larger than for the SPS4.6 ionomers, which was probably due to higher Tg of the former (Tg of PS13.5 is 97 °C, which was ∼17 °C higher than that of PS4.6, 80 °C). Figure 2 shows the shift factors of the SPS4.6 and SPS13.5 ionomers for the master curves in Figure 1, and the constants

Figure 2. Shift factors, aT, for SPS4.6 and SPS13.5 ionomers with Tr = 140 °C. The solid lines are the WLF equation fits. The shift factors for the SPS13.5 ionomers and PS13.5 were shifted for clarity by multiplying by a factor of 100.

Table 2. WLF Constants for PS4.6, PS13.5, SPS4.6, and SPS13.5 Ionomers (Tr = 140 °C) SPS4.6-1.6 PS4.6 C1 C2 (K)

C1 C2 (K)

6.2 111

Na

SPS4.6-2.5 Na

6.6 8.2 114 129 SPS13.5-0.20

K

Rb

SPS4.6-2.8 Cs

Na

8.7 8.9 9.4 11.1 136 138 143 161 SPS13.5-0.76 SPS13.5-1.2

PS13.5

Na

Na

K

Cs

Na

7.5 106

7.3 100

7.8 103

8.0 104

8.2 106

9.5 121

obtained from the WLF equation fit are summarized in Table 2. The WLF constants for the ionomers with p < pc, where TTS works, were similar to those of the parent PS because the relaxation behavior of each was mainly controlled by the Rouse motions. In general, the WLF constants, C1 and C2, increased with increasing p for both ionomers. For the SPS4.6-2.5 and SPS13.5-0.76 ionomers, where p ∼ pc, the WLF constants were relatively insensitive to the choice of the metal cation (Table 2). For the WLF equation, C1 ∝ 1/f r and C2 ∝ f r/αf, where f r is the fractional free volume at Tr and αf is the free volume expansion coefficient.35 Thus, the increase of WLF constants indicates that both fractional free volume and the volume expansion coefficient decrease with increasing p, which can be explained by the densification of polymer due to the strong intermolecular dipolar interactions.36 D


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Figure 3. Steady shear viscosity and the first normal stress coefficient of (a) all the SPS4.6 ionomers at 170 °C and (b) NaSPS4.6-2.5 ionomer at various temperatures.

Figure 4. Effect of temperature on the normalized steady shear viscosity for (a) NaSPS4.6-1.6, (b) NaSPS4.6-2.5, (c) NaSPS4.6-2.8, (d) NaSPS13.50.20, (e) NaSPS13.5-0.76, and (f) NaSPS13.5-1.2 ionomers. The inset pictures show the sample fixture at the end of a steady shear experiment. The open symbols represent samples where melt fracture occurred.

Shear thickening behavior was weak, but clear, for the NaSPS4.6-2.5 ionomer (Figure 3a), and it became weaker as Ec decreased. A very weak shear thickening was observed for the KSPS4.6-2.5 ionomer, but no shear thickening was observed for the ion pair with weaker Ec, i.e., the Rb and Cs salts. A comparison of the steady state viscosity and the complex viscosity revealed that the Cox−Merz rule was not obeyed for these ionomers (data not shown here). This result is due to the thermorheological complexity of ionomers, and it is consistent with reports of the failure of the Cox−Merz rule for other phase-separated melts, such as immiscible blends,39 block copolymers,40 and ionomers.41−43

The temperature dependence of the steady shear behavior of the NaSPS4.6-2.5 ionomer is shown in Figure 3b. η and Ψ1 decreased, and the onset of shear thinning behavior shifted to higher shear rate with increasing temperature due to weakening of the supramolecular bonds. A shear thickening followed by shear thinning behavior was observed at all temperatures studied (150−200 °C), though the intensity of the increase in the viscosity decreased with increasing temperature. Although shear thickening of solutions of associating polymers (such as ionomers) has been reported by various research groups,22−24,26−31 the only report of shear thickening of a polymer melt was that by Weiss and Zhao5 for an ionomer E


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Figure 5. Effect of temperature on the normalized steady shear viscosity for (a) KSPS4.6-2.5, (b) RbSPS4.6-2.5, and (c) CsSPS4.6-2.5 ionomers.

the melt fracture behavior is shown in the inset in Figure 4c, where the sample exuded from between the cone and plate. The open symbols in Figure 4c denote the samples where melt fracture was observed, and except for the small decrease of the viscosity for the experiments where T > 200 °C, melt fracture of the ionomer melts preceded any deviation from constant viscosity of the melt. The melt fracture of SPS ionomer during steady shear is consistent with the catastrophic failure of SPS ionomers during extensional flow. 17 The ionic group associations form an elastic network that is more brittle than an entanglement network in a high molecular weight polymer, since the former lacks the relaxation processes that are provided by diffusional motions of disentanglement of polymer chains.17 The steady shear behavior of the NaSPS13.5 ionomers (Figure 4d−f) showed qualitatively similar behavior as a function of p as did the NaSPS4.6 system. For p < pc (NaSPS13.5-0.20, Figure 4d), the ionomer exhibited shear thinning behavior with no evidence of melt fracture. For p ∼ pc (NaSPS13.5-0.76, Figure 4e), the ionomer melt exhibited shear thinning behavior, and shear thickening occurred at the lowest temperature used, 150 °C. Shear thickening also occurred for KSPS13.5-0.76, but only at 140 °C (Figure S1). No melt fracture was observed for any of the other SPS13.5-0.76 ionomers at any temperature. When the ionic content increased to p > pc (NaSPS13.5-1.2, Figure 4f), however, melt fracture was clearly observed during steady shear flow (see inset picture in Figure 4f). The viscosity of the NaSPS13.5-1.2 ionomers was insensitive to shear rate, except when T > 200 °C, where a relatively small decrease of viscosity occurred above γ̇ > 0.004 s−1. The shape of the flow curves where the viscosity decreased appeared unusual in that the viscosity decreased about 10% but then plateaued until melt fracture occurred at higher γ̇. The high temperature flow curves for the NaSPS4.6-2.8 sample (p > pc) showed a similar trend (Figure 4c). The reason for that behavior is not known, but it is suspected that there may have been either a flow instability that was not visually observed or, perhaps, some degradation of the polymer occurred at these high temperatures. Note, however, that thermogravimetric analysis (not shown) indicated that no desulfonation should have occurred at the temperatures used in these experiments. The effect of the cation on the steady shear behavior of SPS4.6-2.5 ionomers is shown by the data in Figures 4b and 5. These data extend the results reported in ref 5, which reported shear thickening for Li- and Na-salts of a 4000 g/mol SPS ionomer oligomer for T > 160 °C. The data in Figures 3b and 4b confirm the earlier observation of shear thickening behavior

similar to those used in this paper. Four mechanisms have been proposed to explain shear thickening behavior of associating polymer solutions: (1) shear-induced increase of the intermolecular associations,29,44,45 (2) non-Gaussian extension of polymer chains,28,46,47 (3) enhancement of intermolecular associations due to anisotropic deformation of the chains,24−26 and (4) repulsive interactions between flowerlike micelles for telechelic polymer solutions above c*.48 The fourth mechanism can be discounted for the ionomer melts because it is improbable that such micelles form in a dense ionomer melt. However, the other three mechanisms provide possible explanations for the shear thickening behavior of the ionomer melts, though other experiments, e.g., rheo-small-angle neutron scattering, would be required to confirm any specific mechanism. The effects of temperature and sulfonation level on the steady shear behavior of the NaSPS4.6 and NaSPS13.5 ionomers are summarized in Figure 4. The viscosity data, η(γ̇), were normalized by the zero-shear viscosity for each ionomer to facilitate comparisons of the behavior at different temperatures. For each molecular weight, p was varied to compare the behavior of the ionomers below, near, and above the gel point, pc. At all temperatures, the normalized steady shear viscosity of NaSPS4.6-1.6 (p < pc) ionomer exhibited Newtonian behavior at low γ̇, followed by shear thinning behavior. The onset of shear thinning shifted to higher γ̇ (shorter relaxation time) as the temperature increased. No sign of any instability, such as melt fracture, was observed for any temperature or shear rate (see inset in Figure 4a). For NaSPS4.6-2.5 (p ∼ pc) (Figure 4b), as the temperature increased, the onset of shear thickening shifted to higher γ̇ (shorter relaxation time) and the magnitude of the shear thickening became less pronounced, but still observable at temperature as high as 200 °C. No melt fracture was observed during the steady shear experiments (see the inset in Figure 4b). Note that at the higher shear rates in Figure 4b the shear rate dependence of the viscosity approaches η ∼ γ̇−1. In their studies of hydrophobically associating polymer melts, Watanabe and co-workers26 observed a similar result and attributed it to shear banding. Unfortunately no rheo-optical measurements were made in this investigation, so a similar argument cannot yet be made for the ionomer melts, though a future experiment to evaluate that phenomenon would be worthwhile. For NaSPS4.6-2.8 (p > pc), the viscosity remains constant at low γ̇, but it decreased when the γ̇ exceeded a critical value at which melt fracture was clearly observed. A typical example of F


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ionomers. Also, since the temperature dependence of τs is much stronger than that of τ0 (see Table 1), one may conclude that the strength of the ionic associations, i.e., the ionic dissociation time, is the dominant influence on shear thickening. However, the changes of the chain relaxation time due to ionic association cannot be ignored, since the use of that variable in the ratio used for the abscissa of the graph in Figure 6 produced the near superposition of the shear thickening behavior for all the ionomers (cf. Figure 6), while Figure S3 where ηmax/η0 was plotted against only τs cannot yield the same degree of superposition. The effect of the ionic interactions on shear thickening data shown here is similar to what Ma and Cooper28 reported for hydrophobically end-capped poly(ethylene oxide) polymer solutions, where increasing the association strength of the hydrophobic group (i.e., increasing the length of the sticker, alkyl end group), decreasing the molecular weight of the PEO chain or decreasing the temperature produced stronger shear thickening behavior. In Ma and Cooper’s28 system, the hydrophobic end groups formed domains in the aqueous media, which served a similar role as the ionic aggregates in the SPS ionomer melts. In the present work, the effects of temperature, molecular weight, and association strength on shear thickening were similar to those reported by Ma and Cooper,28 but their cumulative effects were effectively captured by a single variable, τs/τ0. That is, large values of τs/τ0 favor shear thickening. Nonlinear Behavior: Startup Shear Flow. Figure 7 shows the viscosity growth function, η+(t) = σ+(t)/γ̇, and the first normal stress coefficient growth function, Ψ1+(t) = N1+(t)/γ̇2, where σ+(t) and N1+(t) are the shear stress and the first normal stress difference, respectively, for the NaSPS4.6 ionomers upon startup of shear flow for various shear rates. Also shown by the solid curves in Figure 7 are the LVE limit predictions calculated from eqs 4 and 5

for the Na-salt, and the data in Figure 5 show that the phenomenon is also exhibited by the K- and Rb-salts of SPS4.62.5, but not the Cs-salt, which has the lowest Coulomb energy. A general trend revealed in Figures 4 and 5 is that shear thickening behavior occurred only when p ∼ pc and weakened with increasing T, increasing molecular weight of the precursor chain and decreasing Coulomb energy of the ion pair. Increasing T produced a larger decrease of τs than of τ0, which was confirmed in Figure 2: the temperature dependence became much stronger than the precursor chain at high T where the moduli were governed by the ionic dissociation. Increasing M of the precursor chain increased the Tg by ∼15 °C, leading to a higher τ0, and a reduction of the Coulomb energy of the ion-pair reduced τs. Those observations suggest that the relative values of the ionic dissociation time, τs, and the Rouse relaxation time, τ0, play a major role in whether shear thickening behavior occurs. The relative strength of shear thickening, defined as ηmax/η0, is plotted as a function of τs/τ0 for the SPS4.6-2.5 and SPS13.50.76 ionomers is shown in Figure 6. A value of ηmax/η0 = 1,

Figure 6. Effect of the τs/τ0 on the magnitude of shear thickening for SPS4.6-2.5 and SPS13.5-0.76 ionomers with different metal cations.

η+(t ) =

indicated by the solid line in Figure 6, corresponds to no shear thickening. The value of τs and τ0 at temperature, T, was calculated by multiplying the value at Tr = 140 °C (see Table 1) by the ratio of the shift factors for each relaxation at the T and Tr τi(T ) = τi(Tr)

a T , i(T ) aT , i(Tr)

∫0

Ψ1+(t ) = 2

t

G(t ′) dt ′

∫0

(4)

t

G(t ′)t ′ dt ′

(5)

where G(t) is relaxation modulus calculated from the dynamic modulus using the iteration method by Watanabe et al.49,50 For p < pc (NaSPS4.6-1.6, Figure 7a), η+(t) at low shear rates, γ̇ = 2.5 s−1, is coincident with the LVE envelope. The viscosity shows a monotonic increase to a steady-state value within ∼0.3 s. For γ̇ > 2.5 s−1 η+(t) exhibits an overshoot before reaching steady state. Similar viscosity (stress) overshoot is typically observed for entangled polymer melts,51,52 where the maximum stress is a yielding phenomenon related to the chain stretching or an overshoot in chain orientation.53,54 Similarly, the stress overshoot in the ionomers is most likely a consequence of the stretching of the network chains, which produces yielding within the nanoscale supramolecular crosslinks due to shear-induced breakup of the ionic associations; i.e., ionic groups are pulled out of the ionic nanodomains to relax the stress in the network chains.6 When γ̇ ≥ 40 s−1, the stress overshoot was followed by a weak stress (viscosity) minimum before the viscosity achieved steady state. The overshoot and undershoot became more apparent as the shear rate increased. Similar behavior was observed for the NaSPS4.61.6 ionomer at other temperatures (140 °C ≤ T ≤ 160 °C) and for NaSPS13.5-0.20 (Figure S4a).

(i = 0, s) (3)

where the subscript i denotes either the Rouse relaxation time (τ0) or the ionic dissociation time (τs). Since TTS failed for these two ionomers (see Figure 1), separate shift factors, aT,i(T), were calculated for τ0 and τs by superposing the G′(ω,T) and G″(ω,T) data at the higher frequencies (regions I and II in Figure 1) to resolve the temperature dependence of the shift factors for τ0 and at lower frequencies (terminal region III in Figure 1) to get the shift factors for τs. These shift factors are shown for temperatures between 140 and 230 °C in Figure S2 and Table S1 and were used in eq 3 to calculate the values of τ0(T) and τs(T). Figure 6 indicates that for both SPS ionomers shear thickening was observed when τs/τ0 exceeded a value of ∼107, and the strength of the shear thickening increased exponentially with increasing τs/τ0. To a first approximation and considering the errors involved in calculating the two relaxation times, the data in Figure 6 seem to correspond to a simple relationship between ηmax/η0 and log(τs/τ0) for all the G


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Macromolecules

Figure 7. Shear viscosity growth function, η+(t), and first normal stress coefficient growth function, Ψ1+(t), measured at 170 °C for various shear rates for (a, d) NaSPS4.6-1.6, (b, e) NaSPS4.6-2.5, and (c) NaSPS4.6-2.8 (the Ψ1+(t) data of NaSPS4.6-2.8 is not shown because reliable normal stress difference data were not obtained). The solid curves correspond to the LVE limit calculated from the dynamic modulus (eqs 4 and 5).

Figure 8. Shear viscosity growth function η+(t) and the first normal stress coefficient growth function Ψ1+(t) of NaSPS4.6-2.5 (p ∼ pc) measured at various temperatures: (a, d) 180 °C, (b, e) 190 °C, (c, f) 200 °C. The solid curves represent the linear viscoelastic limit calculated from dynamic data.

disentanglement that produces yielding of entangled polymers, pull-out of ionic groups from ionic nanodomains at sufficiently high strain should produce a similar effect, i.e., chain retraction, in ionomer melts. The similar stress undershoot in the entangled and supramolecular melts may be expected to have similar origins. One caveat, however, is that although the extensional flow behavior of ionomers and entangled polymers show similar transient behavior, the rate dependencies are very different, so comparisons of the two types of polymers may be an oversimplification and a more comprehensive assessment of

Stress overshoot/undershoot behavior is commonly observed for the nonlinear viscoelastic behavior of polymers, though the molecular origins of the phenomena are not well understood. The stress overshoot is believed to be due to chain retraction produced by stretching and yielding55 or chain alignment,54 and recent work on entangled PS melts by Constanzo et al.56 attributed the stress undershoot behavior to molecular tumbling. Both explanations would appear to also fit the ionomer system. The supramolecular network is stretched during startup shear flow, and in contrast to chain H


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Macromolecules

Figure 9. Shear viscosity growth function η+(t) measured at 170 °C for (a) KSPS4.6-2.5, (b) RbSPS4.6-2.5, and (c) CsSPS4.6-2.5 ionomers. The solid curves correspond to the LVE limit calculated from dynamic date.

Figure 10. Shear viscosity growth function η+(t) of (a) NaSPS13.5-0.76, (b) KSPS13.5-0.76, and (c) CsSPS13.5-0.76 at 170 °C. The solid curves correspond to the linear viscoelastic data calculated from dynamic modulus.

suggested that it may be due to the finite compliance of the instrument.56,57 The η+(t) curves for NaSPS4.6−2.8 (p > pc) are shown in Figure 7c. For γ̇ ≤ 0.025 s−1, the η+(t) curves agreed well with the LVE envelope and the steady-state values for viscosity were the same. For γ̇ = 0.04 s−1, a small stress overshoot was observed, followed by a gradual viscosity decrease until t = 100 s, when melt fracture was observed (shown as black arrow) due to melt fracture. No strain hardening behavior was observed for this sample. Reliable normal stress difference data were not obtained for this sample because this sample was so elastic that the normal force applied to the cone−plate fixture did not relax in the experimental time period. Strain hardening, i.e., η+(t) became larger than the LVE envelope before it achieved the steady value, was observed when the ionomer was close to the gel point (p ∼ pc). In order to further understand this phenomenon startup shear flow behavior of the NaSPS4.6-2.5 ionomer (p ∼ pc) was measured at three different temperatures: 180, 190, and 200 °C (Figure 8). The trends in the η+(t) data for the three temperatures were similar to those discussed above for the data at 170 °C. At lower shear rates γ̇ ≤ γ̇max (γ̇max was defined as the shear rate where the steady shear viscosity η attained its maximum value), the viscosity curves agreed well with the LVE envelope prediction, and the steady-state viscosity values increased with increasing shear rate. At the higher shear rates (γ̇ > γ̇max), stress overshoot and strain hardening were clearly observed. The magnitude of strain hardening decreased with increasing temperature, which is consistent with the decreasing value of the ionic dissociation time τs. The Ψ1+(t) data in Figure 8 for NaSPS4.6-2.5 were similar to the 170 °C data for this ionomer

the origin of the stress overshoot/undershoot behavior in these ionomers is needed. Figure 7d shows the first normal stress coefficient function, Ψ1+(t), for NaSPS4.6-1.6. For γ̇ ≤ 25 s−1, the axial force was too small to measure accurately. For γ̇ ≥ 40 s−1, Ψ1+(t) exhibited an overshoot and the LVE envelope calculated from the dynamic modulus was much higher than Ψ1+(t) at short times. Note that the experimental normal stress difference values were extremely low, so the comparison of the experimental Ψ1+(t) data to the LVE envelope is probably not very accurate. For p ∼ pc (NaSPS4.6-2.5, Figure 7b), η+(t) increased monotonically and coincided with the LVE envelope for very low shear rate, γ̇ ≤ 0.01 s−1. For higher shear rates, the steadystate viscosity increased slightly with shear rate for 0.01 s−1 < γ̇ ≤ 0.16 s−1. The increase of the steady-state viscosity over this shear rate range is consistent with the small viscosity increase over the same shear rate range shown in Figure 3a for NaSPS4.6-2.5. The corresponding Ψ1+(t) data for this ionomer for γ̇ ≤ 0.16 s−1 are not included in Figure 7e because the normal forces were too low to get reliable results. A viscosity (stress) overshoot became apparent for NaSPS4.6-2.5 at γ̇ ≥ 0.4 s−1, where the viscosity before the yielding exhibited a much steeper increase than that of the linear envelope. That result was due to strain hardening similar to what is often observed in shear thickening solutions.24,26,27 For γ̇ ≥ 0.4 s−1, the Ψ1+(t) curves in Figure 7e showed a weak stress overshoot and the time response of the normal stress data was slower than predicted by the LVE envelope calculation. Similar results were also reported for the nonlinear behavior of entangled PS melts.56 The reason for the different time dependencies of the nonlinear and LVE responses is not known, but it has been I


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Macromolecules shown in Figure 7. Ψ1+(t) exhibited similar values for γ̇ ≤ γ̇max and an overshot at γ̇ > γ̇max. The time delay of the Ψ1+(t) response shown in Figure 8 was similar to that shown in Figure 7 for the 170 °C data. Figure 9 compares the viscosity growth functions η+(t) at 170 °C for the K-, Rb-, and Cs-salts of SPS4.6-2.5. Like the NaSPS4.6-2.5 data in Figure 7, the viscosity curves lie on the LVE envelope at low shear rates, γ̇ < γ̇max, and stress overshoot occurred at higher shear rates, γ̇ ≥ γ̇max. The KSPS4.6-2.5 and RbSPS4.6-2.5 ionomers exhibited weak shear thickening behavior at γ̇ ∼ γ̇max. The strength of the shear thickening was greater for the K-salt, which is a consequence of the larger value of τs/τ0. In addition, strain hardening became weaker with decreasing Ec and almost disappeared for the Cs-salt. The weakening of the strain hardening and shear thickening with increasing temperature and decreasing Ec of the ion pair is due to decrease of τs/τ0. This result seems to suggest that the shear thickening is paired with strain hardening at higher shear rates (where shear thinning is observed). The SPS13.5 ionomers showed similar behavior in startup shear flow at 170 °C as that of the SPS4.6 ionomers. Shear thinning behavior was observed when p < pc, and melt fracture occurred when p > pc (cf. Figure S4). However, close to the gel point (p ∼ pc; the SPS13.5-0.76 ionomers), the stress growth behavior differed from that of the SPS4.6 ionomers. For all three salts, almost no strain hardening was observed (Figure 10), and no shear thickening behavior occurred. That result further supports the hypothesis that the shear thickening and the strain hardening behavior in these ionomers are related and that the two phenomena occur only occur at high ratios of τs/ τ0. Note that for the higher molecular weight ionomers the magnitude of τ0 increased by an order of magnitude, but τs was almost the same as for the SPS4.6 ionomers. The observations of weak shear thickening followed by shear thinning behavior, strain hardening accompanying shear thickening, and almost no observable nonlinearity for Ψ1 or Ψ1+(t) at the shear rate range of shear thickening are similar to those reported by Watanabe and co-workers.24−26 for the nonlinear rheology of hydrophobically end-modified ethoxylated urethane (HEUR) solution. Those authors observed shear thickening for weakly percolated, physical networks due to the existence of “superbridges” as network strands, where the superbridge was defined as branched molecules that connected by micellar cores.25,26 They proposed that the origin of shear thickening in their system was the anisotropic distribution of the micellar cores (i.e., anisotropic enhancement of the association of chain strands) in the shear gradient direction rather than the non-Gaussian deformation or shear-induced microstructure changes from intra- to interchain aggregation.25,26 The micelle-like microstructural feature of HEUR solutions is similar to that of the ionic aggregates (or micelles) of SPS ionomer melts. In particular, at p ∼ pc, the ionomer contained an infinitely small amount of percolated network, where the network strands are formed by ionic clusters, defined as branched chains connected by the ionic aggregates. The average size of the network strands decreased with increasing p from infinitely large at p ∼ pc to the size of the precursor chain at p ∼ 2pc. Considering the similar nature of the ionic aggregates with micellar cores and the similar structure of superbridges with ionic clusters, the shear thickening behavior of the SPS ionomers close to the gel point may have the same origin; that is, changes of the spatial distribution of the ionic aggregates

in the shear gradient. Nevertheless, the magnitude of shear thickening in the ionomer melts was much weaker than that observed for associating polymer solutions.26,28 The reason for this difference is probably the higher viscosity of a bulk polymer melt compared with that of a solution where the solvent screens the stress contribution of the small fraction of clusters that play an active role in the shear thickening.

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CONCLUSIONS This study investigated the nonlinear viscoelasticity of sulfonated polystyrene oligomers with degree of sulfonation below, close to, and above the gel point. When the degree of sulfonation is below the gel point, only shear thinning was observed. While above it, melt fracture occurs. Only when the degree of sulfonation is close to the gel point, shear thickening emerges. The magnitude of shear thickening decreases with the increase of temperature, M of PS precursor, and the decrease of the Coulomb energy of the ion pair, all leading to less contrast between Rouse time τ0 and the ionic dissociation time τs. In the startup shear, pronounced stress overshot and strain hardening were observed, and only observed, when ionomer close to the gel point. The shear thickening in viscosity was accompanied by the absence of nonlinearity in the first normal stress difference coefficient. Though the mechanism for the shear thickening is still under debating, those observations would definitely contribute to the understanding of the nonlinear rheology of the random ionomers.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.6b02057. Figures S1−S4; Table S1 (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail [email protected] (R.A.W.). *E-mail [email protected] (Q.C.). ORCID

Chongwen Huang: 0000-0003-0726-3471 R. A. Weiss: 0000-0002-5700-6871 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS C.H. and R.A.W. thank the Polymers Program of the Division of Materials Research at the National Science Foundation (Grant DMR-1309853) for support of this research. Q.C. thanks Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, for financial support. The authors want to thank Prof. Ralph H. Colby and Prof. Dimitris Vlassopoulos for helpful discussions.

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GLOSSARY OF SYMBOLS p, sulfonation degree in mol %; pc, gel point determined from pc ≡ 1/(N − 1) × 100 mol %; pg, Ginzburg point calculated from pg = (1 − NK−1/3)pc; NK, the number of Kuhn segments per chain; τ0, Rouse relaxation time of a Kuhn segment; τs, ionic dissociation time; τX, Rouse relaxation time of the precursor chain with τX = τ0NK2; ηmax, the maximum steady-state viscosity; J


Article

Macromolecules η0, the zero-shear steady state viscosity; γ̇max, the shear rate where the steady shear viscosity η attained its maximum value, η = ηmax.

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