Linear Viscoelastic and Uniaxial Extensional Rheology of Alkali Metal

Article pubs.acs.org/Macromolecules

Linear Viscoelastic and Uniaxial Extensional Rheology of Alkali Metal Neutralized Sulfonated Oligostyrene Ionomer Melts Gerald H. Ling,† Yangyang Wang,‡ and R. A. Weiss*,† †

Department of Polymer Engineering and ‡Department of Polymer Science, University of Akron, Akron, Ohio 44325, United States ABSTRACT: The linear viscoelastic and nonlinear extensional behavior of melts of alkali metal salts of oligomeric sulfonated polystyrene (SPS) ionomers were characterized by dynamic shear and nonlinear, uniaxial extensional flow experiments. The oligomeric SPS had a weight-average molecular weight of 4000 g/mol, a polydispersity index of 1.06, and a degree of sulfonation of 6.5 mol %. The molecular weight was below the entanglement molecular weight of PS, so all rheological effects were due to association of the ionic dipoles and nanophase separation of the ionic species that provides a transient elastic network. The SPS salts exhibited linear viscoelastic properties similar to well-entangled polystyrene (PS) melts, with a distinct rubbery region that had a shear modulus comparable to that of high molecular weight PS. Time−temperature superposition failed as a consequence of overlapping relaxations for the terminal response of the chain and ion hopping of the ionic dipoles. Unlike entangled PS melts, the modulus of the ionomer increased with increasing extensional strain rate, and a maximum in the stress occurred at a relatively low Hencky strain that was nearly independent of strain rate. The maximum in the stress during stretching was attributed to a catastrophic failure of the physical ionic network. At sufficiently high stress, the chains can pull the ionic groups out of nanophase-separated ionic domains, which significantly disrupts the network microstructure.

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INTRODUCTION Ionomers are a special class of polymers with a relatively small concentration of ionic groups attached to the backbone. The ionic groups are typically salts of sulfonic, phosphonic, or carboxylic acid neutralized usually with metal, ammonium, or phosphonium counterions which assures overall electrical charge neutrality.1 Depending on the ion concentration, degree of neutralization, and choice of counterion, the rheological properties can be significantly different from that of the parent polymer chain. That is due to interchain associations that leads to physical cross-linking2,3 and may also produce microphase separation of nanometer-sized ionic aggregates, often called ionic clusters. Flow at elevated temperatures is still possible, even in the presence of these physical cross-links, due to “ion hopping”,4 whereby ion pairs diffuse from one ionic cluster to another at a characteristic relaxation time. However, the relaxation times are typically long and require many ion pairs to “hop” from ionic cluster to another ionic cluster in order for the center of mass of the chain to diffuse through the matrix.5 Consequently, the melt viscosity and relaxation times of ionomers are significantly higher and longer, respectively, than those of the nonionic parent polymer. The characterization of the rheological behavior of ionomers is complicated for a variety of reasons. Ionomers with wellentangled polymer backbone chains tend to have extremely long relaxation times due to temporary cross-links that can persist well above the degradation temperature,6,7 making them essentially impossible to characterize using conventional instrumentation and techniques. In addition, it is difficult to separate the relaxation mechanisms due to molecular © 2011 American Chemical Society

entanglements, trapped entanglements, and ionic interactions in ionomers. Rubber elasticity models that treat the ionic interactions as simple molecular cross-links tend to underestimate the cross-link density of ionomer melts because of the supramolecular structure of the ionic clusters, and the calculated contribution to the viscoelastic properties of trapped entanglements in ionomers is similar to that of the ionic crosslinks.7 Experimental efforts to understand the dynamics in such systems have involved diffusion and stress relaxation experiments, and models of the rheology have focused mainly on modified reptation models.8−10 The majority of work in the field of ionomers has concerned the linear viscoelastic response attained using dynamic methods because of the long relaxation times and high viscosities of the ionomer melts. Recently, Weiss and Zhao11 reported the steady shear and linear viscoelastic properties of a sulfonated polystyrene ionomer (SPS) and its alkali metal salt derivatives. That study used low molecular weight (4 kg/mol) oligomeric SPS, which facilitated steady shear measurements using conventional parallel and cone and plate geometries. In addition, the effect of ionic interactions on the viscoelastic properties of the ionomers was isolated, since the polymer chain length used was far below the entanglement molecular weight of polystyrene. Thus, the effects of molecular entanglements were eliminated, and the changes in the flow properties of the ionomers were due solely to the effective lengthening of the Received: August 13, 2011 Revised: November 30, 2011 Published: December 19, 2011 481

dx.doi.org/10.1021/ma201854w | Macromolecules 2012, 45, 481−490

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scanning calorimetry (DSC) using a TA Instruments Q200 DSC, a heating rate of 20 °C/min, and a nitrogen atmosphere. The DS of the SPS was determined by elemental sulfur analysis (Galbraith Laboratories, Inc.) and 1H NMR using the procedure described by Baigl et al.19 The DS values calculated from the two methods agreed within 10%. Rheology. Dynamic and steady-shear experiments were performed with a TA Instruments ARES-G2 rheometer equipped with 25 or 8 mm parallel plates. Temperature control was achieved using a convection oven with a dehumidified-air gas source. The SPS samples were prepared by compression molding at 200 °C under vacuum prior to being tested. Frequency sweeps spanning 0.1 to 100 rad/s at temperatures of 120, 140, 160, and 180 °C were performed in the linear viscoelastic (LVE) region to construct a master curve using the time−temperature superposition (TTS) principle. Step shear rates of 0.001−20 s−1 were used to determine the transient stress growth and steady-state properties of the SPS samples. Uniaxial extension measurements were made with a TA Instruments ARES-G2 rheometer equipped with a Sentmanat extensional rheometer (SER) fixture20,21 purchased from Xpansion Instruments. Temperature control was achieved using the same convection oven described above. Attempts to prepare conventional rectangular ionomer samples using a heat press were unsuccessful since the thin samples were too brittle to handle once cooled to room temperature. Furthermore, the samples tend to crack upon cooling as the thermal expansion coefficient of the ionomer and mold linear sheets (polyester, polyimide, or aluminum) were sufficiently different to cause uneven deformation upon cooling. Instead, the ionomers were extruded using a Monsanto capillary viscometer into cylindrical specimens with an average diameter and length of 0.75 mm and 25 mm, respectively. The samples were stored in a desiccator overnight at 50 °C in a vacuum oven prior to being tested to prevent the absorption of water and to establish a constant thermal history for all the samples. Step Hencky strain rates of 0.01− 3 s−1 were used to determine the transient stress growth behavior of the SPS samples at 120, 140, and 160 °C.

polymer chains and the formation of branched and physically cross-linked structures by interchain dipolar associations. The linear and nonlinear viscoelastic properties of those low molecular weight SPS ionomers under shear were comparable to those of a polystyrene with molecular weights as high as 1.5M g/mol. However, little is known about the effect of dipolar associations in ionomers on extensional properties, especially nonlinear behavior, which provided the incentive for the research described in this paper. While there has been considerable interest in the elongational properties of classical polymers,12−15 little work has been done on ionomers. To the best of our knowledge, the only other study of the elongational properties of random ionomers was published almost three decades ago,16 and more recently, Stadler et al.17 described the elongational behavior of telechelic polybutadiene ionomers. Those papers reported extensional viscosities that exceeded the values of the linear viscoelastic envelope predicted from shear experiments. Connelly et al.16 reported that the degree and onset of this deviation, which is often referred to as “strain hardening”, increased as a function of ion concentration, which is unlike the “universal” onset exhibited by typical polymers at a Hencky strain of ∼0.7−1. Stadler et al.17 also reported that the deviation from LVE behavior had an ion concentration dependence but that dependence was not resolved due to the low elongation at break for their ionomers. This paper describes the linear viscoelastic behavior and nonlinear extensional flow behavior of a low molecular weight sulfonated polystyrene ionomer. As with the earlier work on shear behavior,11 a low molecular weight ionomer was used to eliminate the effects of chain entanglements. Although the polystyrene was the same as used in that previous study, the sulfonation level used in the current work was higher.

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RESULTS AND DISCUSSION Linear Viscoelasticity. Figure 1 shows the LVE master curves of the alkali metal salts of SPS as a function of angular frequency, ω. TTS failed for the alkali metal salts, principally in the midrange of reduced frequency, especially for G″. Failure of TTS became more apparent as the Coulomb energy of the ion pair increased (i.e., Na > K > Rb > Cs), as was observed previously for oligomeric SPS with lower DS11 and for telechelic polybutadiene22 ionomers. The failure of TTS for the lowmolecular-weight SPS ionomers contrasts with the observations for high-molecular-weight SPS ionomers7,23,24 and ethylene− methacrylate ionomers5,25 where TTS worked reasonably well. The success of TTS in the latter systems is essentially an artifact due to the large separation between the relaxation times of ion hopping and the terminal behavior of the polymer chain.2 The appearance of a rheologically simple system is a consequence of only one relaxation mechanism being accessed in the time frame of a single experiment. A more complete discussion of this phenomenon is provided by Register and Prud’homme.3 Neutralization of the sulfonate groups produces a substantial change in the rheological properties of the SPS ionomer melts. The most distinct change is the appearance of a rubbery region indicated by a plateau in the storage modulus, G′, and loss modulus, G″, while the transition region (ω ∼ 103) was essentially unchanged. The breadth of the rubbery plateau increased as the Coulomb energy of the ion pair increased from Cs to Na, and the first crossover frequency (ωc), where the values of G′ and G″ cross, was suppressed by almost 3 decades for the Na salt compared with the Cs salt ionomer (Figure 2). The magnitude of the plateau modulus, GN0 , however, was relatively insensitive to

EXPERIMENTAL SECTION

Materials. Low molecular weight polystyrene (PS), Mw = 4 kg/mol, with a polydispersity index, PDI = 1.06, was obtained from Pressure Chemical Co. The PS was converted into a lightly sulfonated polystyrene (SPS) ionomer by reaction with acetyl sulfate in a dichloroethylene solution, according to the procedure of Makowski et al.18 The SPS samples were converted to alkali metal salts by neutralization with an appropriate metal acetate or hydroxide.11 The degree of sulfonation, DS, was 6.5 mol % (defined as the average number of sulfonate groups in 100 styrene repeat units), which corresponds to an average of 2.5 sulfonate groups per chain. However, because the sulfonation reaction occurs randomly, the product actually includes a distribution of PS chains with varying sulfonation levels. This ionomer will heretofore be referred to as SPS6.5, and the notation for the ionomers is MSPS6.5, where M is the alkali metal used for the cation. The samples used in this research and their characteristics are listed in Table 1.

Table 1. MSPS6.5 Ionomer Charge Densities and Glass Transition Temperaturesa a, pm q/a, pm−1 cq/a, nm−1 Tg, °C

PS

Na

K

Rb

Cs

80

102 0.0098 0.64 98

138 0.0072 0.47 99

149 0.0067 0.44 100

170 0.0059 0.38 97

a

c = sulfonate concentration (mol SO3/100 mol styrene), q = cation charge, and a = cation radius. Materials Characterization. The glass transition temperatures (Tg) of the parent PS and the ionomers were measured by differential 482


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(the molecular weight of these ionomers was far below the entanglement molecular weight of PS), as is common in crosslinked or high-molecular-weight neutral polymers. In this case, the plateau in the modulus is a consequence of the temporary crosslinks formed by ionic interactions or the supramolecular cluster microstructure. An apparent molecular weight between the ionic cross-links, Me,app was estimated from GN0 , i.e., the value of G′ at the inflection point in the rubbery plateau region, using the following relationship:26

GN0 =

ρRT Me,app

(1)

where ρ is the mass density of the polymer, R is the ideal gas constant, and T is the absolute temperature. Note that in this context the term entanglement is used herein to represent the physical impediments to translation of the chains, which for the ionomers are the physical, temporary cross-links between ionic groups on different chains. The apparent molecular weight of the SPS ionomer, Mapp, and the number of entanglements per chain, Z, were calculated using eq 227 with the assumption that τ ∝ M3.4.

⎛ Mapp ⎞3.4 τ ⎟⎟ = Z3.4 ≈ ⎜⎜ τe ⎝ Me,app ⎠

Figure 1. Linear viscoelastic master curves of the alkali metal salts of MSPS6.5 shifted to Tref = 140 °C: (a) G′; (b) G″. The vertical shift factor, β, used to construct the master curves was close to unity (±3%) and did not have a significant impact on the master curve construction.

(2)

The parent polystyrene exhibits Rouse dynamics. For entangled chains, the Rouse model is usually valid due to small fluctuations along the contour between entanglements,28 and a crossover time, τR, can be defined from eq 3.29

τR = τ/Z1.4

(3)

For times longer than τR, linear entangled chains relax by reptation. The ionomers described in this paper are not entangled polymers. For a first approximation, the dynamics associated with the physical associations of the ionic groups might be thought of as entanglements in the sense that they are transient. Although it is tempting to assume similar dynamics for the relaxation behavior of these two types of temporary restraints, because of the microphase separation of the associated dipoles into nanodomains, the relaxation behavior restraints in the ionomer are likely to be much different than for molecular entanglements. The terminal response of the system is expected to be a cooperative cascade of motions, whereby an individual ion pair pulls out of a nanodomains and “hops” to another nanodomain, allowing the chain between ionic groups to relax. Thus, translation of chains involves discrete steps wherein the chain moves by sequential ion hopping. This cascade is responsible for the terminal relaxation τ. Little theory exists for the viscoelastic behavior of ionomers and it is not apparent whether large-scale contour fluctuations or a crossover time are applicable to the ionomer melts. For the sake of discussion, τR was calculated for each material using eq 3, and the three regions of viscoelastic behavior that are usually found in entangled systems were determined from the three relaxation times found in eqs 2 and 3. The following discussion analyzes the experimental rheology data for these systems in the context of that of an entangled polymer. No claim is made that this is the proper framework for considering ionomer dynamics, and in fact, it is doubtful that it is. However, it does provide a means to identify the similarities and differences between the melt rheology of an ionomer and that of a molecularly entangled system.

Figure 2. Linear viscoelastic master curves of the alkali metal salts of MSPS6.5 shifted to Tref = 140 °C. Filled symbols represent G′ while the open symbols represents G″ of CsSPS (●), RbSPS (▲), KSPS (■), and NaSPS (▼).

the choice of the cation, which indicates that the network structure formed was only dependent on the concentration of ionic groups, which controls the network microstructure of the ionomer. That observation is also consistent with the previous study of low-molecular-weight SPS ionomers with lower DS.11 The failure of TTS for these SPS ionomers occurred at the intermediate frequencies. The pseudo-master curves shown in Figure 1 were constructed by superimposing the data at low frequencies, i.e., the elastic response, and these pseudo-master curves were used to extract rheological information to help better understand the uniaxial extensional response. The terminal relaxation time, τ, was calculated from the inverse of ωc, and the internal equilibration time, τe, was calculated from the inverse of the second crossover frequency, ωe (see Figure 2). For these materials τ is a consequence of the dynamics of the physical cross-links derived from the nanodomain network, and τe arises from relaxation of the oligomer chain, which, i.e., the network chains. For these materials, the rubbery plateau seen in Figure 1 is not due to covalent cross-links or to molecular entanglements 483


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The high value of Me,app (i.e., a low value of GN0 ) is due to the fact that close to 70% of the PS chains were either unsulfonated or had only one sulfonate group. The unsulfonated and monosulfonated chains are mechanically inactive and do not contribute to the elastic response. On the other hand, a DS of 6.52% corresponds to an average of 2.5 sulfonate groups per chain, which produces a physically cross-linked network in addition to chain extension, thus decreasing Me,app. Uniaxial Extension. Extensional experiments were only performed on the CsSPS and RbSPS ionomers. The acid precursor of SPS did not hold its shape during an extensional test due to its relatively low viscosity and elasticity. The viscosities of the Na and K salts were very high, and those samples could not be extruded at a reasonable rate to fabricate useful specimens. A single 25 mm cylinder of the NaSPS or KSPS required ∼4 h to extrude, and increasing the extrusion pressure to accelerate the extrusion produced melt fracture of the strands (Figure 3). The stress for this sample was ∼0.05 MPa.

The LVE parameters for all the SPS ionomers estimated from the data shifted to different temperatures are listed in Tables 2−5. Table 2. Material Properties of MSPS6.5 at 180 °C sample

τ, s

τe, μs

τR, ms

GN0 , MPa

Z

Me,app, kg/mol

Mapp, kg/mol

CsSPS RbSPS KSPS NaSPS

0.03 0.1 0.6 6.5

2 1.2 1 1.6

0.6 0.9 2.5 120

0.75 0.63 0.68 0.59

17 28 51 88

4.8 5.7 5.3 6.1

81 159 266 532

Table 3. Material Properties of MSPS6.5 at 160 °C sample

τ, s

τe, μs

τR, ms

GN0 , MPa

Z

Me,app, kg/mol

Mapp, kg/mol


0.5 2.5 13 130

34 28 19 31

9.6 23 510 2400

0.67 0.60 0.63 0.60

17 29 52 89

5.3 6.0 5.7 6.0

90 170 295 528


τ, s

τe, ms

τR, s

GN0 , MPa

Z

Me,app, kg/mol

Mapp, kg/mol


20 150 690 5500

1.2 1.3 1 1.3

1 5 13 62

0.68 0.57 0.59 0.56

13 24 40 68

7.1 7.9 8.0 8.4

92 190 320 570


τ, ks

τe, s

τR, ks

GN0 , MPa

Z

Me,app, kg/mol

Mapp, kg/mol


2.2 8.2 85 660

0.2 0.2 0.1 0.1

0.1 0.4 1.5 6.5

0.54 0.54 0.57 0.51

12 17 42 77

6.3 6.5 6.0 6.6

76 110 250 510

Figure 3. Example of melt fracture (top strand) exhibited by KSPS and NaSPS when the extrusion process was accelerated. The bottom strand is an example of the strands used for the extensional tests.

It is remarkable that these low-molecular-weight, unentangled polymers exhibited such behavior. The melt fracture stress for these ionomers was comparable to that reported by Vlachopoulos and Lidorikis 30 for very high-molecular-weight poly styrene (M > 106 g/mol), although the latter polymer is highly entangled and the ionomers had no molecular entanglements. For the ionomers, the dipole−dipole associations of the ionic species play a role similar to that of entanglements with regard to the rheological behavior, but as discussed in the sections that follow, the nonlinear behavior, especially with regard to fracture or failure, is very much different for the two systems. The long extrusion times used to extrude the samples also led to some water absorption by the extruded strand from the ambient atmosphere. The amount of water uptake of SPS varied depending on the DS and the choice of the cation used,31 and for some samples, the amount of absorbed water was significant. Although that water could be removed by drying the specimen after extrusion, this produced a slight deformation of the cylindrical sample, which affects the accuracy of the values reported herein for the extensional experiments. However, while the experimental errors are relatively high, the qualitative aspects of the results reported are believed to be valid. The terminal flow, viscoelastic, and rubbery regions of the rheological response of the ionomers can be calculated for the Hencky strain rates applied during uniaxial extension using the relaxation times calculated from the LVE data. The three regions are distinguished by the Weissenberg number, Wi, which defines the degree of nonlinearity of the flow. For simple uniaxial extension, it is defined as the product of the extension rate and a characteristic relaxation time of the fluid

The average values of GN0 and Me,app for the SPS ionomer salts with three different levels of sulfonation are listed in Table 6 (the data for DS = 2.5 and 4.8 mol % are from Weiss Table 6. Average Plateau Modulus, GN0 , and Molecular Weight between Entanglements, Me,app, for SPS Ionomers with Different Degrees of Sulfonation, DS, at 140 °Ca

a

DS, %

GN0 , MPa

Me,app, kg/mol

2.5 4.8 6.5

0.016 0.21 0.60

220 17 8

Values for DS = 2.5 and 4.8% are from ref 11.

and Zhao11). The average value of Me,app estimated from the LVE data using eq 1 for the SPS ionomer salts with DS = 4.8% is identical to the value reported for PS, Me = 17 kg/mol. However, the corresponding values of Me,app for the SPS ionomer salts with DS = 2.5% and DS = 6.52% were significantly higher and lower, respectively. The two lower sulfonation levels have an average of one and two sulfonate groups per chain, which should only produce chain extension as a consequence of the ionic interactions. The larger than expected Me,app value for DS = 2.5% was attributed to the random sulfonation process and low sulfonation levels.11 484


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Figure 4. Linear viscoelastic master curves of CsSPS and RbSPS shifted to (a, d) 120 °C, (b, e) 140 °C, and (c, f) 160 °C. The dotted lines indicate the terminal flow (I), viscoelastic (II), and rubbery (III) regions probed in the uniaxial extensional experiments.

(see Figure 4). The terminal flow region (I) is defined by Wi = ε̇τ < 1, the rubbery region (II) by Wi = ε̇τR > 1, and the intermediate viscoelastic region (III) by τR−1 > ε̇ > τ−1.32 These regions are shown on the master curves of CsSPS and RbSPS at 120, 140, and 160 °C in Figure 4. The significance of the one region shown on each master curve is that this is the region experimentally accessible at the reference temperature. Figure 5 shows the transient extensional viscosities, ηe+(t), of CsSPS and RbSPS as a function of time for different Hencky strain rates and temperatures. Note that ηe+(t) do not overlap or fall on the LVE envelope. The reason for this anomalous behavior is believed to be related to a rate-dependent network structure that forms due to the dipolar interactions between ionic groups. Even poorer overlap was observed when the isothermal data were shifted using the shift factors obtained from the LVE data, which further emphasizes the breakdown of TTS for these ionomers. The LVE envelope identified by the dotted lines in Figure 5 was not determined from start-up flow measurements, but from the ηe+(t) = 3∫ 0t G(t′) dt′ relationship using the relaxation modulus, G(t), obtained from the dynamic modulus, G*(t). The best agreement was obtained for the Rb salt ionomer at the highest temperature used, 160 °C (see Figure 5f), where the solid line corresponds to the product of Tr and the transient shear viscosity, η+(t), obtained using a shear rate of 0.01 s−1. In general, the extensional viscosity data deviate from these results.

The Cs salt ionomer had the weakest Coulomb force for the ion pair and exhibited the weakest intermolecular interactions of the different salts evaluated, and at elevated temperatures, it is expected to behave rheologically most like the parent polystyrene. Typically, ηe+(t) never exceeds the LVE envelope at low strains or strain rates. However, when the strain or strain rate increases substantially, Tr can deviate from the usual value of three for uniaxial elongation.33 From a comparison of the ηe+(t) data in Figure 5, it is apparent that the choice of counterion affects the deviation of the SPS ionomer data. RbSPS, which has a higher charge density than CsSPS, exhibited Tr > 3 at all Hencky strain rates and temperatures tested, whereas CsSPS primarily only exhibited Tr > 3 at the lowest temperature and highest Hencky strain rate tested. Stadler et al.17 recently reported that a similar deviation of Tr also occurred for polybutadiene telechelic carboxylate ionomers neutralized with Rb, Na, K, and Li. The degree of the deviation that they observed also increased with the Coulomb energy of the ion pair and extension rate, though they also observed an additional anomalous deviation in their Rb salt ionomer at low strain rates. Those authors attributed their observations to two competing mechanisms: one typical of most polymers that occurs at high strain rates and a second one that occurs at low Hencky strain rates whereby ηe+(t) increases as the rate decreases. The latter effect is analogous to the behavior usually 485


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Figure 5. Transient extensional viscosities at different Hencky rates of CsSPS and RbSPS as a function of time at (a, d) 120 °C, (b, e) 140 °C, and (c, f) 160 °C. The dotted curve corresponds to the LVE data measured from shear.

stresses predicted from shear data and was constructed from a quadratic fit to the shear stress data over the range of 0.01− 20 s−1. The maximum stress predictions using the shear data agreed well with experimental values obtained from uniaxial extension. That behavior is expected in conventional entangled polymers, and it suggests that even though the elasticity developed in these low-molecular-weight ionomers is due to physical, dipolar interactions between metal sulfonate groups, the dynamics of these chains has some resemblance to that of entangled chains. The maximum stress should occur when the chains pull out of the ionic clusters, which should correspond to the cohesive strength of the aggregates. The dotted curve shown in Figure 6b corresponds to the stress for GN0 obtained from LVE shear data. Note that σ significantly exceeded that value at high Hencky strain rates, which indicates that the effect of the ionic aggregates on the rheological behavior was actually greater than that of entanglements. When the engineering stress, σeng, is plotted as a function of Hencky strain, ε, a stress maximum that is relatively independent of ε is observed (Figure 7). The maximum occurs at a relatively low value of ε and in most cases, below the theoretical maximum Hencky strain, εmax. These results suggest that there is a limiting value of ε corresponding to extension of the chain between the ionic “entanglements”, i.e., the clusters. During the extensional experiment, the load bearing chains are

found in lightly branched systems with long segmental relaxation times, such as metallocene polyethylenes with longchain branching.34,35 The strain hardening behavior (Tr > 3) observed for the SPS ionomers appears to be more characteristic of the first mechanism described by Stadler et al.,17 though it was poorly developed due to the low extensions at which the sample ruptured. The absence of Stadler et al.’s second mechanism for the SPS ionomers may be due to the much stronger intermolecular interactions of the sulfonate dipoles compared with carboxylate dipoles which produces a higher cohesive strength of the sulfonate ionic clusters, or it may be a result of the absence of chain entanglements, which are present in the polybutadiene ionomers described in ref 17. The higher cohesive strength of the SPS ionic clusters contributes to longer segmental relaxation times, since the chains need to disengage from one cluster and diffuse to another for relaxation of the segment of the chain that includes the ionic group. That effect would also explain the more apparent strain hardening in the SPS ionomer system. The failure to observe the low-rate strain hardening may be due to the inability to extend the SPS filaments sufficiently to achieve steady state. The transient extensional stress data are plotted in Figure 6. The extensional stress, σ, for the SPS ionomer melts only reached steady state for the lowest Hencky strain rates. The solid curve shown in Figure 6b is the locus of the maximum 486


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Figure 6. Transient extensional stresses at different Hencky strain rates of CsSPS and RbSPS as a function of time at (a, d) 120, (b, e) 140, and (c, f) 160 °C.

instability such as necking. The DE model, however, did not fit the data in Figure 7 well. Deviation above the DE limit is not uncommon for polymers and is usually a signature of substantial chain stretching,12,13 which is consistent with the failure mechanism proposed above for the ionomers in extension. For some values of the Hencky strain rates and temperatures, the extensional stress measured for the ionomers was higher than the prediction from RE theory (Figure 7), which is puzzling since one expects the RE prediction to represent an upper limit of the stress. The reason for this behavior is not understood, but several speculative explanations come to mind. One is that the result is a consequence of the difference in the effects of shear and extension on the viscoelastic behavior of ionomers. The elastic network in this case derives from the properties of the nanodomains which act as multifunctional temporary cross-links (or, in the nomenclature used in this paper, entanglements). The RE stress predictions were based on a entanglement density calculated from the shear modulus data, and as shown in Figure 5, the Trouton ratio for these polymers can be greater than three. A Tr > 3 is consistent with a value of σ > σRE when the latter is calculated from the shear modulus. The abnormally high extensional stress of the ionomer melts is more pronounced at higher Hencky strain rates and lower temperatures, which also suggests that it may arise from glassy contributions due to the ionic clusters. Another possible explanation for this behavior could be a rate-dependent ionic network structure whereby the ionic interactions switch from

stretched until the elastic restoring stress equals the cohesive strength of the ionic clusters. Upon further extension, the chain segment containing the ionic group mechanically pulls out of the ionic clusters just prior to full chain extension, which explains the premature maximum relative to εmax and subsequently produces the rapid drop in σeng. This behavior is distinct from that of strain softening of a physically entangled polymer melt, e.g., polystyrene or poly(styrene-co-ranbutadiene).31 Although the isothermal stress maximum values for a 400 kg/mol PS and the SPS ionomers were similar, the Hencky strain for PS was more than twice that of the SPS ionomers. The stress predictions for the CsSPS and RbSPS from calculated from the classical theory of rubber elasticity (RE)

⎛ 1⎞ σeng = GN0 ⎜ν − 2 ⎟ ⎝ ν ⎠

(4) 35

and from the Doi−Edwards model (DE) σeng =

⎡ ⎤ 3 −1 ⎢2ν 3 + 1 − 3ν 3 tan ( ν − 1 ) ⎥ ⎥⎦ 2(ν 3 − 1)ν ⎢⎣ ν3 − 1 5GN0

(5)

ε

where ν = e , are plotted in Figure 7. The RE model does not have any built-in cohesive failure mechanism, and therefore, σeng grows without bound. The DE model does predict a maximum in σeng, but this is due to an elastic mechanical 487


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Figure 7. Engineering stress at different Hencky rates for CsSPS and RbSPS as a function of Hencky strain at 120, 140, and 160 °C. The solid lines denote the calculation from the classical rubber elasticity theory while the dotted curves are based on the Doi−Edwards model.36

intra- to interchain associations. That mechanism has been used to explain the dilatant behavior of ionomer solutions37−39 and, more recently, SPS melts.11 Witten and Cohen40 proposed that the dilatancy is due to the unraveling of polymer chains due to deformation, which results in an increased number of interchain associations at the expense of intrachain associations. Thus, a higher concentration of intermolecular complexes may be formed at higher extension rates leading to higher than expected stresses. At this point, all these explanations are unproven, and more investigation of this phenomenon is needed to identify the origin of the high stress. The maximum σeng normalized by GN0 and temperature for CsSPS and RbSPS is plotted as a function of Wi in Figure 8. All the data collapsed onto a single curve, which indicates that the network structure formed by the ionic clusters and the time constant for the underlying dynamics are independent of the neutralizing cation. The nonlinear scaling of the stress with temperature, however, underscores the competing relaxation times of the ion hopping (τ) and the backbone chain dynamics, where τe is the longest relaxation time. This is consistent with the earlier observation from the LVE data that TTS broke down primarily in G″ due to overlap of the two relaxation processes. The effect is more evident when the Hencky strain at the engineering stress maximum, εmax, is plotted as a function of Wi (Figure 9). The data for each of the three temperatures can be separated into distinct plots with differing slopes, and the slope

Figure 8. Engineering stress maximum for CsSPS and RbSPS as a function of Wi. The engineering stress was normalized with the plateau modulus and temperature. A linear regression suggests that there is slight curvature to the line through the data points.

approaches zero at the lowest temperature (120 °C). This result suggests that the failure mode may be different at each temperature, which is consistent with the three different viscoelastic regimes probed: (1) terminal flow (160 °C), (2) viscoelastic behavior (140 °C), and (3) rubber-like elasticity (120 °C). At higher temperatures, the chains can relax and flow prior to the point of failure leading to a rate-dependent εmax. Higher temperatures also weaken the cohesive strength of the clusters, which allows sufficient chain pull-out to provide the mobility for the chain relaxation. However, as the temperature 488


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of the transient elastic network formed by ionic dipolar interactions can be at least as strong as that produced by molecular entanglements. The strain at the stress maximum, however, for the ionomers was considerably lower than that for entangled PS melts. For high-molecular-weight PS, the stress maximum is a yield point resulting from plastic flow of the melt, while for the ionomers the stress maximum is a catastrophic destruction of the ionic network. Thus, although relatively strong transient networks can be achieved by ionic interactions, they behave in a much more brittle fashion than molecular entanglements. The main difference here is that the ionomer melt network lacks the relaxation process and energy dissipation mechanism that is provided by diffusional motions of disentanglement of polymer chains. That finding could be important in the design of supramolecular polymer systems using ionic or other intermolecular interactions such as hydrogen bonding or transition metal complexes. On the basis of the results described in this paper, one might expect that the development of elastomeric properties is possible with such supramolecular polymers, but the allowable strains may be deficient. As was indicated earlier in this paper, the extensional and nonlinear viscoelastic behavior of ionomers has not been widely studied, and the current understanding is poor. The results described in this paper shows that ionomer melts have some characteristics similar to those of high-molecular-weight, highly entangled polymers. For example, the ionomers described herein had melt viscosities comparable to PS homopolymers with molecular weights in excess of 106 g/mol, and they exhibited transient elastic effects that are commonly observed in entangled polymer melts. The observation of melt fracture of these oligomeric ionomer melts reinforces the similarity to high-molecular-weight polymers. However, the nature of the network structure and how it fails for the ionomers are distinct from those of entangled polymer melts. Many observations reported in this paper need further characterization and definitely would benefit from theoretical advances in the field. It is clear from the nonlinear extensional response that as currently formulated, entanglement or other transient network models cannot describe the behavior of ionomer melts.

Figure 9. Hencky strain corresponding to the maximum in the engineering stress for CsSPS and RbSPS as a function of Wi.

decreases and approaches Tg, segmental chain motion is restricted and the point of failure becomes relatively independent of Wi as seen εmax data for 120 °C for both CsSPS and RbSPS. Hence, the network fails catastrophically as chains pull out of the ionic clusters to accommodate the elevated stresses.

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CONCLUSIONS The incorporation of a small concentration of alkali-metalneutralized sulfonate groups onto unentangled PS chains produced a significant increase in the melt viscosity and the development of significant elasticity. A rubbery plateau was evident in the linear viscoelastic behavior, which indicates the presence of an elastic network, which was due to intermolecular association of ionic dipoles and microphase separation of ionrich nanodomains that provides a physically cross-linked, transient network. Tg of the ionomers was independent of the cation used, which indicates that the network structures of the different salts were identical. Viscous flow of these ionomers is thought to be due to an ion-hopping mechanism, whereby the stress in the network chains relaxes by pulling an ionic segment out of one ionic domain and allowing it to diffuse to another domain. The breadth of the rubbery region and the corresponding terminal relaxation time increased as the size of the cation decreased, which indicates that the strength of the network, or the ion-hopping dynamics, increased with Coulomb energy of the ion pair. Like Tg, however, the magnitude of GN0 was relatively insensitive to the choice of the cation. TTS failed for these materials, which is believed to be a consequence of overlapping relaxation processes, one involving terminal flow of the backbone chain and the other ion hopping of the ionic segments. The uniaxial extension behavior of CsSPS and RbSPS melts differed from that of a molecularly entangled polymer. The isothermal extensional viscosity, ηe+(t), measured at different strain rates did not overlap or fall on the linear viscoelastic envelope. In addition, Tr exceeded the LVE value of 3 at high strain rates and low temperatures for both the Cs and Rb salts, and the amount of that deviation increased with increasing Coulomb energy and decreasing temperature. The origin of that deviation was not determined but may be a consequence of effects such as a rate-dependent ionic network structure or some glassy response of the ionic domains. Further investigation is needed to isolate the source of this anomaly. The maximum stress levels achieved under extension were similar to that of a well-entangled high-molecular-weight PS homopolymer at comparable temperatures and Hencky extension rates. That result indicates that the absolute strength

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AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]. ACKNOWLEDGMENTS This research was supported in part by a grant from the Polymer Division of the National Science Foundation, Grant 0960461.

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