Nonlinear Rheology of Lightly Sulfonated Polystyrene Ionomers

Mar 5, 2013 - ... of low molecular weight lightly sulfonated polystyrene ionomers (SPS) .... Journal of Polymer Science Part B: Polymer Physics 2017 5...
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Nonlinear Rheology of Lightly Sulfonated Polystyrene Ionomers Xiuying Qiao†,‡ and R. A. Weiss*,† †

Department of Polymer Engineering, The University of Akron, Akron, Ohio 44325-0301, United States State Key Laboratory of Metal Matrix Composites, Shanghai Jiao Tong University, Shanghai 200240, China

‡

ABSTRACT: The effects of nonlinear deformation on the melt rheology of low molecular weight lightly sulfonated polystyrene ionomers (SPS) were investigated with dynamic, steady shear, and transient shear experiments. Changes in the viscosity and elasticity of the ionomers that occurred in large deformation flows were explained in terms of changes in the nanodomain microstructure of the ionomers. Large strains (or strain rates) significantly reduced the elasticity that resulted from a physical network produced by the ionic nanodomain structure. Recovery of the viscoelastic properties was rapid once the strain (strain rate) was removed. A three-region viscosity vs shear rate flow curve was observed, and the different regions were explained in terms of changes in the microstructure of the ionomer. Increasing the sulfonation level or the Coulomb energy of the ion-pair generally shifted the flow curve to higher shear rates. Shear flows produced no stress overshoot behavior upon start-up of the flow and the stress growth was relatively rapid even for low shear rates. In general, while the nanodomain microstructure produced high elasticity of the ionomers, the nonlinear rheological behavior of SPS differed significantly from that produced by chain entanglements.

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INTRODUCTION Ionomers are relatively hydrophobic polymers that contain a small amount of ionic groups chemically bonded to the polymer backbone. They have attracted much attention due to the dramatic effects of the ionic species on their physical, mechanical and rheological properties.1 Applications of ionomers include membranes (e.g., electrolytic cells,2 fuel cells3 and reverse osmosis,4 packaging,5 blend compatibilization,6 thermoplastic elastomers,7 drilling fluids,8 and shapememory polymers.9 Intermolecular dipolar interactions of the ionic species produce microphase separation of nanometersized ionic aggregates, which provide a physical-cross-linked network that affects the properties of ionomers. The cross-links are not permanent and can be reversibly disrupted by applying heat, solvent or stress, which permits melt or solvent processability. It is generally thought that melt fluidity of ionomers at elevated temperatures occurs due to “ion hopping” of ion-pairs from one aggregate to another,10 even though a microphase separated structure persists to extremely high temperatures.11 The association and aggregation of the ionic species increase the melt elasticity and melt viscosity of ionomers. Because of their high viscosities and the long relaxation times of the dipole−dipole or ionic interactions,12,13 most rheological studies of ionomers, especially for sulfonated polymers, have focused on the linear behavior.14−17 Linear behavior, though, is generally observed only for a limited range of low strain or strain rates. Polymer processing operations are usually performed with nonlinear stresses and strains that can affect the ionomer © 2013 American Chemical Society

microstructure. Thus, nonlinear rheological characterization is important for understanding how these complex materials behave in actual manufacturing processes. Nonlinear studies are also beneficial for elucidating changes in the micro- or nanoscale structure of ionomers that determine the macroscopic properties of those materials. There is relatively little known about the nonlinear viscoelastic response of ionomers under large deformation and the structural changes and structure recovery that occur during and upon cessation of melt flow. A small number of studies have reported steady shear behavior of ionomers, including studies with polymer backbones based on polyethylene,14,18,19 polypropylene,20 poly(styrene-co-ran-butyl methacrylate),21 polyester,22,23 and polystyrene.24−29 Nonlinear extensional flows have also been used to characterize the rheological behavior of ionomers, but that literature is very limited.22,30−32 Steady state experiments using drag flows (e.g., parallel plates or cone and plate geometries) are complicated by instabilities that may occur due to high elasticity of ionomer melts that, for example, can produce expulsion of the fluid from the gap at high shear rates. That “gap jumping” effect can be eliminated by using capillary flows,20,24−26 but that introduces other complications, e.g., stick−slip flow, entrance effects, and melt fracture. Received: December 26, 2012 Revised: February 25, 2013 Published: March 5, 2013 2417

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In two previous papers,29,30 we examined the linear dynamic shear, steady state shear and nonlinear extensional flow of the alkali metal salts of a model oligomeric sulfonated polystyrene ionomer (SPS). Intermolecular dipolar associations between the ionic groups produced extremely high melt viscosities, comparable to what would be expected from polystyrenes with molecular weights as much as 1000 times that of the SPS oligomers. The extensional flow behavior differed from that of entangled high molecular weight polymers in that the stress increased with extension until catastrophic failure occurred at a critical strain, which was attributed to cohesive failure of the ionic aggregates.30 For steady shear flow, shear thinning behavior was observed, but for the ionomers with the strongest intermolecular interactions, a weak shear thickening of the melt was also observed.29 Melt extrusion of those low molecular weight ionomers produced melt fracture characterized by a regular helical structure.30 This paper continues our rheological investigation of these oligomeric sulfonated polystyrene ionomer melts with a report of large amplitude oscillatory shear (LAOS), steady shear and transient shear flows, and stress recovery following nonlinear flow. As in the two previous studies,29,30 the ionomers were prepared from a narrow molecular weight distribution polystyrene (PS) with Mw = 4000 g/mol. That molecular weight is far below the entanglement molecular weight of PS (Me ∼ 17 000 g/mol),33 so that any perturbation of the nonlinear dynamics from that of oligomeric polystyrene can be attributed solely to the interchain associations of the ionic groups. The ionomers were fully neutralized alkali metal salts with sulfonation levels up to 6.5 mol %.

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4000, MSPS4.8−4000, and MSPS6.5−4000 ionomers, respectively). A parallel plate fixture with a diameter of 25 mm and a gap ∼0.5 mm was used for the strain sweep experiments, and a cone-and-plate fixture with a diameter of 25 mm and a cone angle of 0.04 rad was used for the steady shear and transient shear experiments. In some experiments, especially if the stresses became too high, a parallel plate fixture with a diameter of 8 mm was used. Prior to each experiment, the vacuumoven-dried samples were kept at 240 °C for 5 min in the fixture to eliminate effects of the prior thermal history. The effects of nonlinear strains on the properties of the MSPS6.5 ionomers were assessed from dynamic strain sweeps at 240 °C using a constant frequency of ω = 1 rad/s and covering a strain amplitude range from γ = 0.03% to 100%. The effect of large amplitude oscillatory shear (LAOS) on the temporal response of the rheological properties of CsSPS6.5 and KSPS6.5 ionomers was determined at 240 °C with dynamic time sweep experiments using strains of 2.5%, 6%, 16% and 40% and an angular frequency of ω = 1 rad/s. Steady and transient shear flow tests were also run for the SPS ionomers at 240 °C. After each nonlinear deformation, the structure recovery characteristics were measured using time-resolved dynamic measurements in the linear response region (ω = 1 rad/s; γ = 0.3%).

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RESULTS AND DISCUSSION Characteristics of the SPS Ionomers. The properties of the ionomers used in this study are summarized in Table 1.

Table 1. Properties of N = 39 Sulfonated Polystyrene Ionomers DS = 2.5 mol %

DS = 4.8 mol %

DS = 6.5 mol %

cation

aa (nm)

cq/ab (nm−1)

Tg (°C)

cq/ab (nm−1)

Tg (°C)

cq/ab (nm−1)

Tg (°C)

Li Na K Rb Cs

0.058 0.102 0.138 0.149 0.170

0.43 0.25 0.18 0.17 0.15

86 86 86 85 86

0.83 0.47 0.35 0.32 0.28

91 90 91 90 91

na 0.64 0.47 0.44 0.38

na 98 99 100 97

EXPERIMENTAL SECTION

Materials. Low molecular weight polystyrene (PS), Mw = 4000 g/ mol; Mw/Mn = 1.06) was purchased from Pressure Chemical Co (Pittsburgh, PA, USA). The sulfonation of PS was carried out with acetyl sulfate in dichloroethane (DCE) solution according to the method of Makowski et al.34 That chemistry randomly substitutes sulfonic acid groups predominantly at the para-position of the phenyl ring.35 Acetyl sulfate was prepared by slowly adding concentrated sulfuric acid to a 60% excess of acetic anhydride in DCE at 0 °C. This was then added to a stirred 10% solution of PS in DCE at about 50 °C and the reaction was continued for 1h, after which it was terminated by the addition of 2-propanol. The sulfonic acid derivative of SPS was isolated by steam-distillation of the solvent, washed three times with boiling water, dried in air at 70 °C for 1 day, and finally dried at 120 °C in a vacuum oven for 1 week. Three different SPS samples, with degree of sulfonation (DS) of 2.5, 4.8, and 6.5 mol %, were prepared. The DS was determined by elemental sulfur analysis (Galbraith Laboratories, Inc., Knoxville, TN) and was defined as the average number of sulfonate groups per 100 styrene repeat units. The DS values of the 2.5, 4.8, and 6.5 mol % SPS samples corresponded to an average of 1, 2, and 2.6 sulfonate groups per chain, respectively. Alkali metal salts (Na, Rb, and Cs) of SPS were prepared by adding dropwise a 50% excess of the appropriate metal hydroxide or acetate dissolved in methanol or methanol containing a small amount of water into an agitated 15% (w/v) solution of SPS in a 90/10 (v/v) mixture of toluene and methanol. After 30 min the neutralized SPS was recovered by steam-distillation and washed and dried as described above for the SPS. The sample nomenclature used hereafter is MSPSn, where M represents the metal cation (Na, Rb, or Cs) and n is the DS. The degree of polymerization for all the ionomers was N = 39. Rheology Measurements. Nonlinear viscoelastic measurements were made with a strain-controlled Advanced Rheometric Expansion System (ARES), model G2 (TA Instruments, New Castle, DE) at 240 °C, which was much higher than the glass transition temperature (Tg) of the MSPS ionomers (Tg ∼ 85, 90, and 100 °C for the MSPS2.5−

a

a = ionic radius of the cation. bq = charge of the cation =1; c = sulfonate concentration (equiv/mol).

Although the sulfonation levels used corresponded to an average of 1.0, 2.0, and 2.6 sulfonate groups per chain, because the sulfonation reaction is random, not each chain contains equal number of sulfonate groups. The sulfonation distribution can be represented by a binomial distribution function35 P(x) =

N! px (1 − p)N − x (N − x) ! x!

(1)

where P(x) is the probability that a chain with a degree of polymerization N contains x sulfonate groups, and p is the probability of a monomer being sulfonated, which is the same as the mole fraction of sulfonated styrene units (i.e., the degree of sulfonation divided by 100). For the three sulfonation levels used in this study, p = 0.025, 0.048, and 0.065. The distributions for the three ionomers, Figure 1, indicate that each contains a significant fraction of chains that are unsulfonated and chains that have more than the average value of sulfonate groups. In that regard, these are not ideal model ionomers, but they are the best that can be achieved with the simple chemistry used here. For over four decades, similar SPS ionomers have been widely studied and characterized with respect to understanding the properties and structure of ionomers, even though it has been known that the sulfonation distribution is heterogeneous. 2418

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Figure 1. Probability distribution P(x) as a function of the number of ionic groups per chain, x, for the SPS ionomers (N = 39 and sulfonation levels of 2.5, 4.8, and 6.5 mol %).

It has been widely reported that many properties of ionomers scale with the total electrostatic energy of the material, E = cEc, where c is the concentration of ion-pairs, Ec is the Coulomb energy of an ion-pair (Ec = keqcqa/a), ke is Coulomb’s constant, a is the separation of the two ions (essentially the ionic radius of the cation), and qc and qa are the charges of the cation and anion, respectively.36 For sulfonate ionomers qa = 1, so E ∼ cqc/ a, or as expressed hereafter, cq/a. The values of cq/a and properties for the SPS ionomers considered in this paper are summarized in Table 1. Tg was independent of the Coulomb energy of the ion-pair (∼q/a), but it increased with increasing sulfonation (c) of the ionomer. A previous study showed that the zero-shear viscosity (ηo), zero-shear first normal stress difference (ψ1,o) and the terminal relaxation time (τ) obtained from dynamic linear viscoelastic measurements scaled linearly with cq/a29 for the alkali metal salts of SPS. Large Amplitude Oscillatory Shear (LAOS) Flow. In general, the ionic nanodomain morphology of ionomers controls their rheological properties and as will be shown in this paper, the rheological properties are sensitive to temperature and deformation history. Previous work with ionomers has demonstrated that even for very low sulfonation levels, the equilibrium state of the microstructure and properties is difficult to achieve.37 Figure 2 shows the effect of strain amplitude on the dynamic viscosity (η′) and the fluid elasticity (G′/ω2) of MSPS6.5 at a frequency of ω = 1 rad/s and the recovery of those viscoelastic functions during a time sweep following the strain sweep. Three consecutive strain sweep − time sweep cycles are shown for NaSPS6.5 and CsSPS6.5. Only one cycle was run for RbSPS6.5. For the NaSPS6.5, η′ and G′/ω2 were independent of strain, which suggests that the nanodomain structure was stable even at the high strains used in the strain amplitude sweep. In contrast, for CsSPS6.5 both the viscosity and elasticity decreased as the strain amplitude increased from 0.03% to 100%, though the nonlinearity in the elasticity was much more pronounced. The viscosity of CsSPS actually increased with increasing strain until about a strain amplitude of ∼5% (noted by arrows in Figure 2) where the viscosity began to decrease rapidly. The nonlinearity in elasticity began at very low strains. The increase in viscosity with strain amplitude is surprising and no explanation of that phenomenon is obvious, except that the torque values measured for the CsSPS6.5 were relatively low, near the resolution of the instrument, and the error in those data may be quite large. However, the increase in viscosity was reproduced over three experimental cycles, so one cannot rule

Figure 2. Effect of three consecutive strain sweep and time recovery cycles on dynamic viscosity (η′) and the elasticity (G′′/ω2) of the MSPS6.5 ionomers. T = 240 °C and ω = 1 rad/s. For the strain sweeps, γ varied from 0.0025% to 100% for RbSPS6.5 and 125% for NaSPS6.5 and CsSPS6.5. The first value shown in each of the three strain sweeps is 0.0025% and the strain increased exponentially with time to the maximum strain at the dividing line between the strain and time sweeps. For the recovery (time) sweeps, γ was fixed at 0.3%, which was within the LVE behavior of the ionomers.

out that a microstructural change in the ionomer improved the ionic network that would account for the viscosity increase. No such increase in the elasticity was observed, and the rapid decrease in elasticity, even at small strain amplitudes, suggests that the large macroscopic deformation tends to weaken the ionic network structure, which contradicts the speculation given in the previous paragraph that increasing strain at low amplitudes may improve the ionic structure. The viscosity of the Rb salt remained relatively constant over the strain amplitude range used, similar to the Na salt, but like the Cs salt, the elasticity decreased rapidly with increasing stain amplitude. The data for the viscosity fluctuated a bit, which adds further credence to the suggestion that the when the stresses were relatively low, i.e., at high temperature, low strain amplitude and low Coulomb energy of the ion-pair (Na > Rb > Cs), the errors in the viscoelastic properties were highest. A rather notable observation from the data shown in Figure 2 is that even when the increasing strain produced half an order of magnitude in the viscosity and about 2 orders of magnitude in elasticity, those viscoelastic properties recovered rapidly to their original values when the nonlinear strain was removed. For example, the viscosity and elasticity of CsSPS6.5 shown in Figure 2 recovered almost immediately when the experiment 2419

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corresponded to the LVE values, even for γ = 40%. These results are consistent with what would be expected from a cross-linked polymer. In this case, it appears that the ionic nanodomain cross-links in NaSPS6.5 were unaffected by the large strains. In contrast to the LAOS behavior of NaSPS6.5, the CsSPS6.5 exhibited a significant strain dependency, especially for the elasticity (G′/ω2). The viscosity (η′) exhibited a small immediate decrease from the LVE value upon start-up of the flow for all the strains used for that sample (2.5, 6.0 and 16%). Following that initial decrease, the viscosity for the lower strain amplitude remained relatively constant. For 16% strain, however, the CsSPS6.5 exhibited some thixotropic behavior, as the viscosity slowly decreased with time, see Figure 3. A larger decrease for G′/ω2 was observed upon start-up, within 10 s of the nonlinear strain being applied, and the magnitude of this immediate reduction in elasticity increased with increasing strain amplitude. After the initial decrease when the strain was applied, the elasticity exhibited a slow, time-dependent decrease for strain higher than 2.5%. For all strains used, the viscosity of the CsSPS6.5 recovered very rapidly to close to the LVE value when the strain was lowered to 0.1−0.3%. The elasticity, however, only recovered to about 30% of the LVE value on the first and subsequent cycles. The results shown in Figure 3 for the CsSPS6.5 can be explained by a strain-dependent change in the microstructure of the ionomer melt. It would appear that when the strain was 2.5% or higher, the integrity of the nanodomain structure was disrupted. One might expect that for the alkali metal salts of MSPS, once viscous flow is achieved the dipole−dipole interactions between ion-pairs control the viscosity behavior and the nanodomain structure (i.e., cross-links) controls the elasticity. Thus, the smaller changes in viscosity suggest that the basic ionic associations persist for the most part at high temperature and high strain. However, the network structure that is formed by “network” chains bridging nanodomains are sufficiently weakened or destroyed at high strain so that the elasticity decreases. Since these polymers were much shorter than their entanglement molecular weight, the elasticity of the ionomer can be attributed solely to the physical cross-links, and the failure for the elasticity to recover after the cessation of the nonlinear deformation indicates some “permanent” change in the ionomer microstructure. Note that previously reported rheo-SAXS results on similar ionomers, but with lower sulfonation level, indicated that the nanodomains persisted during steady shear flow at ∼190 °C and shear rates up to at least 20 s−1. That suggests that complete destruction of the nanodomain structure may not have occurred in the dynamic experiments reported herein, even though the network structure responsible for the elasticity was probably damaged at high strains. However, the recovery periods used were only about 5 min, so it is not known whether the elasticity (and microstructure) may recover completely if sufficient time were allowed. Steady State, Simple Shear Flow. The steady shear properties of various MSPSn, where n = 2.5, 4.8, or 6.5, are shown in Figure 4. The data include measurements made with 25 mm cone and plate (CP) and 8 mm parallel plate (PP) fixtures. The latter was used when the stresses were too high for the larger diameter CP fixture or there was only a limited amount of sample. The data measured with the PP and CP fixtures were in fairly good agreement for the CsSPS4.8 sample

transitioned from a strain sweep, with a maximum strain of 100% at the end of the sweep, to a time sweep where the strain was immediately reduced to 0.3%. That result indicates that any disruption of the ionic network by high deformation can heal very rapidly when the strain was either removed or lowered into the linear response region. The viscosity recovery during the third time cycle for CsSPS6.5, Figure 2, was slower than for the first and second recovery cycle. For that part of the experiment, the material had been in the rheometer for quite a long time at 240 °C, so the differences between the first and second and the third cycles may be due to some degradation of the ionomer. The elasticity of the CsSPS6.5 and RbSPS6.5 also exhibited recovery after the strain sweep, though the recovery was slower than for the viscosity recovery. As with the viscosity data, the recovery time for the elasticity during the third strain−time cycle of CsSPS6.5 took longer (∼5 min) than for the first two cycles, which again, is probably a consequence of polymer degradation. The time-dependence of η′ and G′/ω2 for the NaSPS6.5 and CsSPS6.5 ionomers for the start-up of large amplitude oscillatory shear (LAOS) and the transient following cessation of flow are shown in Figure 3. Four different strain amplitudes were used, 2.5, 6.0, 16 and 40%. The LVE properties measured for γ = 0.1−0.3% are shown by the star symbols at t = 0. The viscoelastic properties of NaSPS6.5 were insensitive to the strain amplitude and the values of η′ and G′/ω 2

Figure 3. Time dependent behavior of η′ and G′/ω2 for start-up of LAOS deformation and the transient after cessation of flow of NaSPS6.5 and CsSPS6.5: (□) γ = 2.5%; (●) γ = 6.0%; (Δ) γ = 16%; (▲) γ = 40%, and the recovery process following lowering the strain to γ =0.1−0.3%. T = 240 °C, and ω = 1 rad/s. The star symbols for t = 0 correspond to the LVE values (γ = 0.3%). 2420

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interpretation of this relaxation time is that it represents a yield phenomenon where substantial or complete breakdown of the physical cross-linked structure occurs, and one might expect that the elasticity of the melt should either disappear or greatly diminish at that point. The relaxation time decreases with increasing sulfonation (and presumably, increasing Coulomb energy of the ion-pair), because the stresses also increase with those variables. One might reasonably expect the yield to occur at a critical value of stress. In the constant viscosity region for the CsSPSn ionomers, even if the nanodomain network were completely destroyed at that point, the dipole−dipole interactions of the Cs−sulfonate groups should still enhance the viscosity with respect to that of the unmodified PS. The meaning of the constant viscosity region for the Na, Rb, and Cs salts of MSPS6.5 in Figure 4 is not clear from the steady state data alone. One would expect the relaxation time for breakup of the cross-link structure to be less than for the Cs salt, which has the lowest Coulomb energy of the alkali metal ion-pairs. Assuming that the critical shear rate for the NaSPS6.5 occurs at a larger value than for CsSPS6.5 (i.e., shorter relaxation time), the constant viscosity region for the NaSPS6.5 seen in Figure 4 should represent a different region of the flow curve than that for CsSPSn. That suggests that the ionomers exhibit a reverse sigmoid shaped flow curve with a constant viscosity region at low shear rate, followed by a shear thinning power-law region and then another constant viscosity region. Figure 5 shows the shear and dynamic viscosity data on the same plot. There is excellent overlap of the dynamic and steady

Figure 4. Steady shear viscosity at 240 °C versus shear rate for MSPSx ionomers: (1) NaSPS6.5 (PP); (2) RbSPS6.5 (PP); (3) CsSPS6.5 (CP); (4) CsSPS6.5 (PP); (5) CsSPS4.8 (CP); (6) CsSPS4.8 (CP) from ref 29; (7) CsSPS2.5 (CP). CP denotes cone and plate fixture and PP denotes parallel plate fixture was used.

(data sets 5 and 6 in Figure 4), but there was considerable difference between the two sets of data for the CsSPS6.5 sample at the lower shear rates (data sets 3 and 4). The shape of the flow curve for data set no. 3 was unusual, so there is some question as to the quantitative reliability of that set of data. However, the two sets of data were qualitatively consistent. The viscosity of the unfunctionalized PS (M = 4000 g/mol) is not shown in Figure 4, because it was too low at 240 °C to make accurate measurements. It was, however, estimated from the measured value of the viscosity at 160 °C (7.3 Pa·s) and the shift factor, see eq 2, calculated from an Arrhenius relationship. log aT =

ηToρo E = R(T − To) ηoTρ

(2)

where E is an activation energy and η, ηo, and ρ, ρo are the viscosities and specific gravities of the polymer at T and a reference temperature, To. For the 4000 g/mol PS, E = 240 kJ/ (mol K).29 Assuming ρoTo /ρTp ∼ 1, eq 1 predicts that η240 ∼ 3 × 10−3 Pa·s, which is insignificant compared to the viscosity values shown in Figure 4 for the MSPS ionomers (note that the viscosity of water at room temperature is ∼1 × 10−3 Pa·s). The viscosities of the ionomers at 240 °C plotted in Figure 4 are 3−7 orders of magnitude greater than that of unmodified PS, which demonstrates the dramatic effect ionic interactions have on the dynamics of polymers. A comparison of the MSPS6.5 ionomers, data sets 1−4 in Figure 4, shows that the viscosity increases with increasing Coulomb energy, i.e., ηNa > ηRb > ηCs, and the data sets 3−7 for the CsSPSn ionomers indicate, as expected, that the viscosity increases as the concentration of ion-pairs increases. With the exception of the Cs-salt, the viscosity of the MSPS6.5 ionomers at 240 °C was independent of shear rate. The CsSPS6.5 and CsSPS4.8 ionomers exhibited a power-law viscosity region at the lower shear rates, and the critical shear rate, γ̇c, at which the shear rate dependence of the viscosity transitioned from power law to constant viscosity behavior increased with increasing sulfonation level, cf., [γ̇c]CsSPS4.8 = 0.0063 s−1 and [γ̇c]CsSPS6.5 = 0.43 s−1. One can assign a relaxation time to the transition, λc = 1/γc, and λc decreased by 2 orders of magnitude when the sulfonation level increased from 4.8 to 6.5 mol %, cf., λc,4.8 ∼ 159 s and λc,6.5 ∼ 2.3 s. One

Figure 5. Steady shear viscosity versus shear rate and complex viscosity versus frequency at 240 °C for MSPSx ionomers: The complex viscosity data are the symbols with the crosshair. The other symbols have the same definition as they did in Figure 4.

state data, in accordance with the Cox−Merz rule.38 The extra feature seen in Figure 5, and not in Figure 4, is the transition from a constant viscosity to a shear thinning region for the NaSPS6.5 at the higher frequencies. That confirms the hypothesis stated above that the constant viscosity regime shown in Figures 4 and 5 for the NaSPS6.5 represents a different region of the flow curve than did the constant viscosity regimes for the CsSPSn and RbSPS6.5 ionomers. The Flow Curve for Ionomers. As was mentioned in the last section, the data in Figure 5 suggests that the flow curve for these ionomers may be described by a reverse sigmoid function, where a constant viscosity region at low shear rates is followed by a pseudoplastic region, which is followed by a second constant viscosity region at high shear rates. The absolute 2421

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position of the reverse sigmoid flow curve on the shear rate axis depends on the concentration of alkali metal sulfonate groups and the strength of the intermolecular dipole−dipole interactions between ion-pairs. These three viscosity versus shear rate regions were identified in Figure 5 for the various ionomers, though for no single material were all three regions of the flow curve observed. On the basis of the flow curve model proposed in Figure 6, the constant viscosity vs shear rate

This picture assumes that an isolated ion-pair within the nonpolar matrix continuous phase, such as shown in the right side of the equilibrium in Figure 7, is thermodynamically unstable. When an ion-pair leaves a cluster, either because of Brownian motion of the chains or when an applied stress pulls the ionic species out of the cluster, that ion-pair pays a large enthalpic penalty to exist in a hydrocarbon phase, though it can recover some of the penalty from the entropy gain. One can represent the equilibrium by a series of reactions of the form k fn

Cn + 1 ⇌ Cn + D k rn

(3)

where Cn represents a cluster with n ion-pairs, D represents a lone ion-pair, kfn and krn are the forward and reverse rate constants for a cluster of size Cn+1. The rate constants are expected to be functions of temperature (T) and stress (τ) (or strain rate). If one assumes that the rate constants are independent of the size of the cluster, then kf

Figure 6. Model for the isothermal flow curve of an ionomer.

Cn + 1 ⇌ Cn + D kr

(4)

and the equilibrium constant for the system is

data observed for the CsSPS2.5 in Figure 5 is in region III of the general flow curve. Similarly, the constant viscosity data for CsSPS4.8 and for RbSPS4.8 are also within region III. However, the constant viscosity region for NaSPS6.5 is region I. In principle, different regions of the flow curve proposed in Figure 6 may be accessed by varying the temperature, sulfonation level, cation used (i.e., cq/a) or the molecular weight of the ionomer. Phenomenological Model for the Three-Region Flow Curve in Figure 6. The flow-model proposed here is based on the commonly accepted morphological model for an ionomer, where the microstructure consists of nm-scale dispersed domains (clusters) that are themselves composed of associations between contact ion-pairs. The clusters contain ionic groups from many different polymer chains, so they act as virtual and multifunctional cross-links. The structure of an unperturbed ionomer is assumed to be that described by Eisenberg’s early theory developed in 1970.39 At equilibrium, the cluster structure is dictated by a balance between the elastic force generated by perturbation of the chain confirmation due to cluster formation and the force that holds the cluster together, which is related to the electrostatic forces or dipolar forces that hold the ion-pair in the cluster. Because of the physical nature of the cross-links, one expects an equilibrium between ion-pairs that are “stuck” in the cluster and those that are freethat is “hopping” from one cluster to another, see Figure 7.

K (T , τ ) =

kf kr

(5)

The stress (or strain) dependence arises from changes in the conformation of the chain which produce an elastic force in the chain segment. When an external stress is applied to the melt, the stress on a clustered ion-pair, (which is also covalently attached to a chain segment) increases, and if the local stress is sufficiently high, an ion-pair is pulled out of the cluster. The elastic force on the chain segments, which arises from entropy changes of the backbone chain, is expected to increase with increasing stress and a reasonable assumption is that the higher the stresses the more likely it is for a chain to pull an ion-pair into the melt. As stated above, a free ion-pair in a hydrophobic medium, i.e., the continuous phase, is thermodynamically unstable, and it is expected that any free ion-pair will hop10 to another cluster. Thus, there is a competition between stress reducing the clusters by pulling out the ion-pairs and healing of the clusters by ion-pair hopping. Then, the reverse rate constant in eq 4 is related to the residence time a free ion-pair, i.e., how long it takes to diffuse from one cluster to another, and the forward rate constant represents the hopping frequency, or the rate at which ion-pairs are pulled out of the cluster. Since there is a rather large thermodynamic driving force for a free ion-pair to return to a cluster, the dynamics of repatriation of an ion-pair to a cluster will be a function primarily of the viscosity of the medium, though viscosity is stress-dependent. The upshot of this model is that the three regions of the flow curve can be explained by a sigmoidal dependence of K on τ, which produces three conditions for the equilibrium constant. For low stress, K ∼ 1 (kf ∼ kr), a dynamic equilibrium is reached and flow of the polymer occurs by an ion-pair hopping mechanism. However, the cluster structure remains relatively unperturbed, because an ion-pair pulled from the cluster rejoins another cluster on a similar time scale as the removal of another ion-pair from another cluster. This behavior accounts for the relatively constant viscosity in region I of Figure 6.

Figure 7. Equilibrium between clustered and free ion-pairs in an ionomer melt. 2422

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transient shear results are consistent with the extensional rheology of the ionomers.30 Although the clusters provided a mechanism for developing elasticity, the strain behavior of the ionomer was distinctly different than for entangled polymers. While entangled polymer develop ductility in tension due to the dynamics of chain disentanglement, the ionomers fail in a brittle manner upon extension due to cohesive failure of the nanodomain network.

As the stress increases, the concentration of free ion-pairs is expected to increase with respect to the concentration of ionpairs in the clusters, i.e., kf increases with stress faster than kr, so that K > 1. That result will produce a more rapid decrease of the viscosity with shear rate, region II. The qualitative picture here is that in regions I and II the ionomer dynamics are controlled by the clusters, which persist within these three regions. Region III represents the condition where kf ≫ kr (K ≪ 1). In that case, the concentration of non-clustered ion-pairs is high and the cluster volume is low, or at least the clusters become inefficient at maintaining a network. In that case, there are limiting returns with regard to pulling ion-pairs from clusters, largely because of the few active network chains remaining. The viscosity is again relatively constant, though it may be expected to decrease somewhat with increasing stress. The viscosity of the ionomer in region IV is very low, though still three or more orders of magnitude greater than the parent PS at 240 °C. Transient Behavior for Steady Shear Flow. Entangled polymer melts and solutions usually exhibit stress growth and stress overshoot due to the orientation and the subsequent chain disentanglement.40 Transient shear data for CsSPS6.5 at 240 °C are shown for a number of shear rates in Figure 8. For a

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CONCLUSIONS Ionomers possess an ionic nanodomain microstructure that produces a physical network due to chains possessing sulfonate groups in different nanodomains. This network structure and the ion−dipole interactions between ionic groups from different chains produces enhancements in the melt viscosity, as well as significant elasticity even when the no chain entanglements are present. The unique aspect of the rheological studies described in this paper was that the molecular weights used were far below the entanglement molecular weight of the parent polymer, so that the rheological behavior was dominated by interactions of the ionic species. High strains or strain rates disrupt the network structure and can produce pseudoplastic behavior, but more distinctive is the significant decrease in the melt elasticity that occurs for large deformation flows. The flow curve of the ionomers exhibited three distinct regimes: (1) a Newtonian-like viscosity region at low shear rates; (2) a power-law shear thinning region above a critical shear rate where yielding of the microstructure occurs; and (3) a second Newtonian region at sufficiently high shear rates. A general phenomenological explanation in terms of an equilibrium between ion-pairs that are “stuck” in an ionic cluster and those that are free to “hop” from one cluster to another was proposed for the dynamics of an ionomer. A stressdependent equilibrium constant, K(τ), was defined as the ratio of a forward rate constant, kf, for removing an ion-pair from a cluster and a reverse rate constant, kr, for repatriating the ionpair into a cluster, i.e., K(τ) = kf(τ)/kr(τ). For low K ∼ 1, which corresponds to a dynamic equilibrium state where the rate of ion-pairs exiting a cluster equals that of ion-pairs rejoining a cluster. That situation produces a shear rate insensitive viscosity. For K > 1 the concentration of ionpairs in the hydrocarbon phase increases at the expense of their concentration in the clusters. The viscosity decreases with shear rate as K(τ) increases. However, the nonaggregated ion-pairs can reduce the enthalpy penalty for being in the hydrocarbon phase by associating through dipole−dipole interactions, which maintains an enhancement of the viscosity significantly above that of the unmodified polystyrene. In this region, the integrity of the nanodomain network disintegrates and elasticity is lost. Finally, for K ≫ 1, the cluster volume is low and the nanodomains remaining have little or no effect on the rheological properties. It is tempting to compare the behavior of ionomers, where enhancements of the viscosity and elasticity are due to intermolecular interactions and the development of a physical network structure to those for highly entangled chains. However, the analogy breaks down for large deformations. Entangled polymers exhibit a spectrum of relaxation times for disentanglement of the chains, and as a result the changes in the rheological properties are gradual. In contrast, the changes in the network structure for an ionomer are rapid, due to cohesive failure of the ionic interactions. As a result, the dynamic

Figure 8. Transient viscosity for start-up of shear for CsSPS6.5 at 240 °C and five different shear rates. The number in parentheses is the shear rate in (s−1).

shear rate of γ̇ = 0.001 s−1, the stress growth region of the startup is seen in Figure 8, but no overshoot of the viscosity (i.e., stress) was observed. Neither stress growth nor stress overshoot was observed for any shear rate between 0.01 and 50 s−1. For the γ̇ = 0.001 s−1, the transient in the stress lasted about 100 s before steady state was achievedor a total strain of 0.1. Using that value as a characteristic strain to reach steady state, the time to reach steady state was estimated to be less than 10 s for γ̇ = 0.01 s−1 and 0.002 s for γ̇ = 50 s−1. Such short times were not resolved in Figure 8. Similar results (not shown) were observed for the RbSPS6.5. It is not surprising that the transient shear behavior of these ionomers was different than for an entangled polymer. Even though these ionomers exhibited significant elasticity, the origin of the elasticity was the ionic network formed from the ionic nanodomains, not chain entanglements. The overshoot in the shear stress for entangled polymers arises from the orientation of the chains between entanglements, which effectively increases the modulus until the chains can begin to disentangle. That mechanism is not present in these ionomers. These 2423

dx.doi.org/10.1021/ma3026496 | Macromolecules 2013, 46, 2417−2424

Macromolecules

Article

(21) Erhardt, P. F.; O’Reilly, J. M.; Richards, W. C.; Williams, M. W. J. Polym. Sci., Polym. Symp. 1974, 45, 139−151. (22) Connelly, R. W.; McConkey, R. C.; Noonan, J. M.; Pearson, G. H. J. Polym. Sci., Polym. Phys. Ed. 1982, 20, 259−268. (23) Greener, J.; Gillmor, J. R.; Daly, R. C. Macromolecules 1993, 26, 6416−6424. (24) Lundberg, R. D.; Phillips, R. R. J. Polym. Sci., Polym. Phys. Ed. 1984, 22, 377−384. (25) Weiss, R. A.; Stamato, H. Polym. Eng. Sci. 1989, 29, 134−139. (26) Weiss, R. A.; Agarwal, P. K.; Lundberg, R. D. J. Appl. Polym. Sci. 1984, 29, 2719−2734. (27) Agarwal, P. K.; Makowski, H. S.; Lundberg, R. D. Macromolecules 1980, 13, 1679−1687. (28) Iwakura, K.; Fujimura, T. J. Appl. Polym. Sci. 1975, 19, 1427− 1437. (29) Weiss, R. A.; Zhao, H. Y. J. Rheol. 2009, 53, 191−213. (30) Ling, G.; Weiss, R. A. Macromolecules 2012, 45, 481−490. (31) Stadler, F. J.; Still, T.; Fytas, G.; Bailly, C. Macromolecules 2010, 43, 7771−7778. (32) Takahashi, T.; Watanabe, J.; Minagawa, K.; Koyamo, K. Polymer 1994, 36, 6722−6728. (33) Graessley, W. W. Polymeric Liquids and Networks: Structure and Properties; Garland Science: New York, 2004; p 454. (34) Makowski, H. S.; Lundberg, R. D.; Singhal, G. H. U.S. Pat. 3,870,841, 1975. (35) Zhang, L.; Katzenmeyer, B. C.; Cavicchi, K. A.; Weiss, R. A.; Wesdemiotis, C. Macro Lett. 2013, 2, 217−220. (36) Eisenberg, A. Macromolecules 1971, 4, 125−128. (37) Weiss, R. A. J. Polym. Sci., Polym. Phys. Ed. 1982, 20, 65−72. (38) Cox, W. P.; Merz, E. H. J. Polym. Sci. 1958, 28, 619. (39) Eisenberg, A. Macromolecules 1970, 3, 147−154. (40) Oakley, J. G.; Giacomin, A. J.; Yosick, J. A. Mikrochim. Acta 1998, 130, 1−28.

changes upon increasing the stress are more dramatic for the ionomers, but similarly, the healing of the physical network structure upon cessation of flow is also much more rapid than for entangled polymers. Clearly, more work is needed to fully understand the flow characteristics of ionomers. One concern with the “model” system used here is that it contains a distribution of ionic groups per chain. A better model system would be one that is more homogeneous with regard to functionality of the chains. A second concern is achieving an equilibrium structure for the ionomer at the beginning of the experiments and characterization of the structure during the experiments. Strong ionic interactions can “pin” the microstructure, so that it is in a nonequilibrium state and may differ from experiment to experiment and from laboratory to laboratory depending on the sample preparation. That has been a problem that has long plagued the field and one for which more attention is probably needed when studying the dynamics of these complex systems.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by a grant from the National Science Foundation (CBET 1066517).

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REFERENCES

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