Dynamics of Telechelic Ionomers with Distribution of Number of Ionic

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Dynamics of Telechelic Ionomers with Distribution of Number of Ionic Stickers at Chain Ends Shilong Wu,†,‡ Shuang Liu,† Zhijie Zhang,† and Quan Chen*,†,‡ †

State Key Lab Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Renmin St. 5625, Changchun 130022, Jilin, P. R. China ‡ University of Chinese Academy of Sciences, 19A Yuquan Rd., Beijing 100049, P. R. China

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S Supporting Information *

ABSTRACT: A new type of ionic telechelic polymer, characterized by a distribution of the number x of ionic groups (sulfonated styrene neutralized by sodium) at the chain ends, was synthesized by a two-step reversible addition−fragmentation chain transfer (RAFT) polymerization with a bifunctional agent. The chain backbone was polystyrene (PS) having a molecular weight of ∼3000 g/mol, and the average number of ionic groups per chain end, m = ⟨x⟩, varied from 0.22 to 1.3. These ionic groups associated with each other to form flower-like micelles, as revealed from small-angle X-ray scattering, and those micelles were organized into a network for m > 0.53. Correspondingly, the linear viscoelastic modulus of the ionomer showed the sol-to-gel transition with increasing m > 0.53, and slow viscoelastic relaxation activated by the ionic dissociation was noted for samples well above the gel point (for m ≥ 0.70). This relaxation had a broad mode distribution (power-law type distribution accompanied by undetectably slow terminal relaxation), which made a strong contrast to a narrow, almost single Maxwellian mode distribution observed for a model telechelic ionomer having exactly one ionic group per chain end. Thus, the broad relaxation mode distribution seen for the new type of ionomer was attributed to the distribution of the ionic group number x at the chain end: This distribution resulted in a multibranched sol structure on a time scale longer than the dissociation time for the chain end with x = 1 but shorter than the time for the chain ends with x ≥ 2, and the power-law type mode distribution reflected motion of the sol chains activated by dissociation of the chain ends with x = 1.

1. INTRODUCTION Telechelic polymers are defined as the linear polymers retaining physicochemical (or chemical) activity only at both ends of the chain backbone. In this study, we focus on telechelic polymers having associative groups (hereafter termed stickers) at the chain ends. This type of telechelic associative polymers usually exhibits morphology and dynamics different from those of random associative polymers having the stickers randomly distributed along the chain backbone. For example, telechelic associative polymers can form isolated flower-like micelles at low concentrations in solutions, wherein the chain ends and backbone form the micellar core and corona, respectively. At concentrations moderately above a critical threshold, the micellar cores are scarcely dispersed, and the distance between cores is usually much larger than the size of the precursor chains, whereas the system shows dynamic features of elastic network, e.g., plateau modulus whose relaxation relies on dissociation of the chain ends, meaning that these micellar cores are connected. Therefore, it was proposed that a fraction of the chains formed a long, linearly associated sequence termed the superbridge that connects those cores, leading to formation of a scarce, transient gel network.1,2 A distance between the micellar cores decreases with increasing concentration of the telechelic chains and becomes © XXXX American Chemical Society

comparable to the chain size to form a dense, transient gel network in concentrated solutions.1,2 The network strands therein are termed bridge. In both semidilute and concentrated solutions, some fraction of the chains take either loop or dangling chain conformations, thereby not contributing directly to the network connectivity.1−16 In analogue to the superbridges, it was proposed that a fraction of the loops in the semidilute solutions were composed of the long sequence of linearly associated backbones and thus termed superloop.1,2 In contrast, the loops in the concentrated solutions are mostly composed of a single chain backbone. The structural evolution explained above leads to rich rheological behavior.1,3,7−9,13−15,17−23 In particular, when the gel network is formed, the telechelic systems become elastic in a time scale shorter than the dissociation time of either bridge or superbridge. The corresponding plateau modulus is expressed as GN = v bridgekT

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Received: August 17, 2018 Revised: February 20, 2019

A

DOI: 10.1021/acs.macromol.8b01776 Macromolecules XXXX, XXX, XXX−XXX

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Figure 1. Synthesis route of triblock telechelic ionomers TPS-m.

where vbridge is the number density of elastically active bridges and/or superbridges, k is the Boltzmann constant, and T is the absolute temperature. The stress relaxation of the gel network relies on the sticker dissociation activated by segmental motion. Therefore, the ratio of the characteristic time of sticker dissociation, τs, to an attempt time of segmental motion, τ0, can be related to the association energy, Ea, as24−28 τs/τ0 = exp(Ea /kT )

attributed this behavior to the cooperative, simultaneous dissociation of five anions or cations located in one Kuhn segment.29 Of course, the fully cooperative, simultaneous dissociation explained above is not the only possible mechanism governing the viscoelastic relaxation. For example, in the relaxation of a given ABA copolymer cross-linked by C, all hydrogen bonds on the block A do not need to dissociate simultaneously if another ABA copolymer approaches the given copolymer and exchange their hydrogen bonds. (This situation is similar to cooperative replacement of adsorbed polymer chains by free chains.30) Thus, detailed features of the viscoelastic relaxation of our telechelic ionomers should be dependent on the interaction among the ionic stickers in each micellar core explained earlier. A key factor for this interaction could be the number of stickers per aggregate. For random ionomers, experiments and simulation suggest various shapes of ionic aggregates, for example, string-like, sheet-like, and sphere-like aggregates, depending on the ionic species as well as on the dielectric constant of the surrounding medium,14,31−36 but 5−10 ion pairs are usually contained in each of those aggregates. This number of the ionic stickers per aggregate is determined by a compromise between a decrease of the electrostatic energy on association and a loss of the conformational entropy of a backbone span between ionic stickers. The number would be larger for our telechelic ionomers because their ionic stickers are located only at the chain ends so that the entropic penalty for the whole backbone of the ionomer due to the end association would be smaller than that for the random ionomers. Consequently, we may safely assume that the cooperativity in the dissociation of the stickers is stronger for our telechelic ionomers than for ordinary random ionomers. Then, the distribution of the number x of the ionic groups (stickers) at the chain end is expected to result in a distribution of the association energy Ea(x) (cf. eq 3), thereby broadening the viscoelastic relaxation as compared to that in the random ionomers or in the telechelic ionomers without x-distribution. This expectation is tested in this study. It turned out that the xdistribution indeed leads to very rich rheological behavior that includes the sol-to-gel transition seen on an increase of the average ⟨x⟩ from 0.22 to 1.3 and the very broad relaxation due to the x-distribution. Details of these results are presented in this article.

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Now, we focus on the ionomers having ionic groups as the stickers. Ordinary ionomers have a narrow (or no) distribution in the association energy (electrostatic energy) Ea and dissociation time τs of the stickers, thereby serving as good model materials for testing molecular theories. In fact, for such ionomers with Ea being significantly larger than the thermal energy (Ea > 10kT), experiments revealed narrow (almost single-Maxwellian in an extreme case) terminal viscoelastic relaxation in the time scale of τs being much longer than the time scale of chain relaxation between stickers.8,13 This observation lends support for sticky chain theories.13,23 Nevertheless, a distribution of Ea and τs offers an opportunity of more deeply understanding the dynamics of associative polymers. In addition, this distribution could be more preferred in real application. Thus, in this study, we focus on the telechelic ionomers having the ionic stickers at the chain ends, attempt to introduce a distribution in the number of ionic groups x per chain end, and examine the effect(s) of this distribution on the structure and viscoelastic relaxation of the telechelic ionomers. Specifically, for this case, the association energy Ea and dissociation time τs should be a function of x, so that eq 2 is rewritten as τs(x)/τ0 ∼ exp(Ea(x)/kT )

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The detailed expression of the function Ea(x) relies on the cooperativity in dissociation of the x stickers at the chain end. If those stickers exhibit f ully cooperative dissociation, we expect Ea(x) = xEa(1). An example of this expression of Ea(x) can be found in the study by Lodge and co-workers,16 who examined relaxation of ABA type block copolymers transiently crosslinked by a homopolymer C via hydrogen bonding between A and C (A = poly(2-vinylpyridine), B = poly(ethyl acrylate), and C = poly(4-hydroxystyrene)). The terminal relaxation time was found to increase exponentially with the number of hydrogen bonds per copolymer (possibly because of the cooperative, simultaneous dissociation of those bonds required for relaxation),16 which is in harmony with the above expectation. Another example is found for coacervate of polyanion and polycation (poly(isobutylene-alt-maleate sodium) and poly(diallyldimethylammonium chloride)) examined by Colby and co-workers.29 They found that Ea is roughly 5 times the Ea of a single pair of the anion and cation29 and

2. EXPERIMENTAL SECTION 2.1. Sample Synthesis and Characterization. 2.1.1. Telechelic Ionomers with Distribution of a Number of Ions per Chain End. Figure 1 explains the synthesis procedure. The RAFT bifunctional agent 1,4-bis(n-butylsulfanylthiocarbonylsulfanylmethyl) (CTA) was synthesized first, as described in Scheme S1 and Figure S1 of the Supporting Information. Macro-CTA polystyrenes (PSs) were B

DOI: 10.1021/acs.macromol.8b01776 Macromolecules XXXX, XXX, XXX−XXX

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Macromolecules synthesized via RAFT polymerization of purified styrene (St; 4 g, 0.04 mol, 99.5%) with RAFT agent (CTA) and an initiator, 2,2′azobis(isobutyronitrile) (AIBN) in toluene, with a targeted degree of polymerization (DP) of 30 as set by the molar ratio of St:CTA:AIBN = 30:1:0.2. Details are explained in Scheme S2 and Figure S2. Macro-CTA PSs thus obtained were quenched and separated into five portions, one terminated to obtain the precursor. The other four were mixed with AIBN and ionic monomers (sodium 4-vinylbenzenesulfonate) (SSNA) in DMF at a ratio of SSNA:MacroCTA:AIBN = 3.2:1:0.2, 2.6:1:0.2, 1.6:1:0.2, and 1.2:1:0.2, respectively, to synthesize four telechelic polystyrene (TPS) samples with the targeted average number of ions per end m = 1.6, 1.3, 0.8, and 0.6. One additional sample with the targeted m = 0.25 was synthesized afterward with the same procedure. We tried to match the PS precursor molecular weight of this sample with that of TPS samples explained above. The molecular weights of two PS precursors were determined with gel permeation chromatography (Agilent PL-GPC 200) at high temperature (150 °C) equipped with the refractive index (RI) and low-angle light scattering (LALS) monitors. Trichlorobenzene was used as the eluent, and commercially available monodisperse polystyrenes (TSKgel, Tosoh Biosciences) were utilized as the elution standards. The number-average molecular weight Mn of the precursor was 2900 g/mol for the samples with the targeted m ≥ 0.6, and Mn = 2400 g/mol for the sample with the targeted m = 0.25; see Figure S4 for the GPC data. Mn of those precursors were well below the entanglement molecular weight Me = 18000 g/mol of PS.37 The mass fraction of sodium ion in the sample, wion, was determined through inductively coupled plasma optical emission spectroscopy (ICP-OES) analysis conducted with a Thermo iCAP 6300 spectrometer. The spectrometer was calibrated with a standard NaCl aqueous solution (with name code GSB 04-1738-2004) purchased from Guobiao (Beijing) Testing & Certification Co., Ltd. A considerably large amount of the sample (∼0.1 g) was consumed in each measurement to determine wion accurately. The actual number m of sodium ion per chain end (averaged for all chains) was unequivocally obtained from wion and Mn of the precursor through a relationship wion = 2mMion/(Mn + 2mMSS), with Mion (= 23 g/mol) and MSS (= 206 g/mol) being the molecular weights of sodium ion and sodium styrenesulfonate, respectively. The actual and targeted values of m are listed in Table 1. For all samples, the actual value is slightly smaller (by a factor of 10−20%)

than the targeted value. Hereinafter, we use the sample code TPS-m, thereby explicitly showing the actual m value determined as above. For example, TPS-0.53 refers to the telechelic polystyrene sample having 0.53 ions per chain end on average. The actual m value is in turn related to the distribution of the number of sodium ion x at respective chain ends as m = ∑xP(x), with P(x) being the number fraction of the end carrying x ions. P(x) appearing in this relationship is utilized later in our discussion of the viscoelastic modulus. 2.1.2. Conventional Telechelic Ionomer Having Exactly One Ion per Chain End. Figure 2 explains the synthesis procedure of a conventional telechelic ionomer utilized as a reference of TPS-m. Macro-CTA was synthesized and characterized through the same procedure as that for TPS-m, and its molecular weight distribution is summarized in Figure S4 (together with those of the precursors of TPS-m samples). The Macro-CTA was subjected to reaction with excessive m-chloroperoxybenzoic acid to oxidize the trithiocarbonate group into sulfonic acid.38 The crude product was precipitated in excessive methanol, and the precipitant, mainly HO3S−PS−SO3H, was further purified with silica gel column chromatography utilizing chloroform and then THF as the eluent. The purified HO3S−PS− SO3H sample was first subjected to the acid−base titration, which indicated ∼90% of the chain ends contain sulfonic acid groups. The sample was further neutralized with 1.5 equiv of sodium hydroxide to obtain NaO3S−PS−SO3Na. The NaO3S−PS−SO3Na sample was isolated by precipitation, filtration, and dried at 150 °C in a vacuum oven for 1 week. Hereinafter, this reference sample is termed rTPS. 2.2. X-ray Scattering. Before X-ray scattering experiments, the samples were annealed in a vacuum oven first at 120 °C for 1 week and then at higher T ≥ Tg + 60 °C for at least 1 day (with the highest annealing temperature within 200 °C). We did not attempt to use higher temperatures since the PS sample would degrade slowly at T > 200 °C. The scattering measurements were conducted by utilizing the Anton Paar GmbH (Austria) SAXSess system with an image plate detector. The exposure time was ∼20 min per sample. The setup was equipped with a sealed tube X-ray generator that used a copper anode operating at 40 kV and 50 mA. The X-ray wavelength was 0.154 nm. Because the X-ray source is of linear shape, only one-dimensional scattering profiles were obtained by converting the intensity distribution on the image plate through an analysis software provided by the manufacturer. We noted that micelles were formed in TPS-m samples with high m (≥0.7). Those TPS-m samples and the rTPS sample were also subjected to 2-dimensional X-ray scattering measurements using a NANOSTAR SAXS system (Bruker AXS) to confirm that our annealing procedure efficiently erased possible orientation of the micelles during the sample preparation. 2.3. DSC Measurement. Differential scanning calorimetry (DSC) measurements were conducted with a TA Q20 differential scanning calorimeter. The samples were heated to 200 °C and kept there for 10 min to remove the thermal history, cooled to 0 °C at a rate of −10 °C/min, and then heated again up to 200 °C at the rate of 10 °C/ min. DSC traces were recorded during the second heating process. 2.4. Rheological Measurement. Before the frequency sweep measurements, the precursor PS, TPS-m samples with m ≤ 0.70, and rTPS samples were annealed in a lab vacuum oven, first at 120 °C for 1 week and then at higher T ≥ Tg + 60 °C for at least 2 days. The TPS-1.0 and TPS-1.3 samples did not flow easily even at 200 °C, so that these samples were annealed in vacuum at 120 °C for 1 week and then molded into pills at ∼200 °C with a homemade mold. These pills were further annealed in a lab vacuum oven at high T = 180−190 °C for 1 day before the frequency sweep measurements. After annealing, all samples were loaded on a laboratory rheometer (either MCR302 from Anton Paar or ARES-G2 from TA Instru-

Table 1. Important Parameters for PS Precursor and Six Ionomer Samples samples

Mn

Mw/Mna

mb

m

Tg (°C)

Tiso (°C)

PS TPS-0.22 TPS-0.53 TPS-0.70 TPS-1.0 TPS-1.3 rTPS

2900 2500 3100 3200 3300 3400 3100

1.4

0 0.25 0.6 0.8 1.3 1.6 1

0c 0.22c 0.53c 0.70c 1.0c 1.3c 0.90d

74 75 79 82 85 87 91

118 119 123 125 128 130 134

1.35

a

Mw/Mn of the TPS samples should be similar to that of the PS precursor considering the small number of ionized monomers per chain. bTargeted m value calculated from a ratio of the number of monomers between styrene and sulfonated styrene during the synthesis. cActual m value determined from ICP-OES analysis of Na. dActual m value determined from acid−base titration.

Figure 2. Synthesis route of rTPS. C

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Macromolecules ments) to obtain the storage and loss moduli, G′ and G″. Parallel plate geometries of the diameter of 8 and 3 mm were utilized to measure the rubbery (≤107 Pa) and glassy moduli (≥107 Pa), respectively. (The 3 mm parallel plate geometry was chosen to avoid errors due to a compliance problem of the rheometer for hard, glassy material.) During the sample loading, we compressed the sample slowly to minimize flow-induced orientation of the micelles. The TPS samples were equilibrated at a loading temperature (∼200 °C) for half an hour before the frequency sweep measurements. Small-angle oscillation shear measurements were conducted at temperatures ranging from 90 to 220 °C, with the strain amplitude in the linear regime (γ ≤ 10%, as confirmed by the strain amplitude sweeps). All rheological measurements were conducted in dry nitrogen environment to prohibit humidity and degradation of the samples.

The correlation peak explained above is not clearly resolved for the TPS-m samples with m ≥ 0.7, probably because that peak is masked by stronger scattering from the micelles giving a peak at qpeak = 0.5−0.6 nm−1. This qpeak corresponds to an intermicellar spacing of ∼11−13 nm being much larger than the chain size R. This feature, interionic spacing much larger than chain size, had been observed in extensive studies by Jérôme and co-workers40−42 and attributed to the supramolecular organization of the ionic clusters. In our TPS-m samples, the supramolecular structure should correspond the micellar aggregates of the ions at the chain ends. Because the intermicellar distance is much larger than the chain size, it is likely that the micelles are connected by the superbridges instead of the bridges, as schematically illustrated in Figure 4.

3. RESULTS 3.1. Structure. Figure 3 plots the X-ray scattering intensity I(q) against the magnitude of wave vector q for the TPS-m

Figure 4. Schematic illustration of the superbridge formed between micelles.

It is noteworthy that shoulders appear at the high q side of the peaks of TPS-1.0 and TPS-1.3. Thurn-Albrecht and coworkers attributed this feature to the intensification of repulsive interaction between the micelles that results in liquid-like order of the micelle position.43,44 They also suggested two other types of interaction between micelles: a repulsive interaction of corona chains and an attractive interaction resulting from tension of intermicellar bridges/ superbridges. An enhancement of the repulsive interaction with increasing m would result in a narrower distribution of the intermolecular distance (even though the distribution is still liquid-like), which possibly has led to the appearance of the shoulder at higher q.43−45 For further characterization of the structure in our TPS samples, the inset of Figure 3 compares the ionic Bragg spacing D = 2π/qpeak of those samples (circles with the same color as that of the scattering profiles) with that of random SPS reported in the literature (black squares).46−53 The solid line is a power law fitting for random SPS, D ∼ p−0.23±0.05 with p being the fraction of ion-containing monomers in all monomers. This fitting suggests that the number of ions per cluster in random SPS, ∼D3p = p0.31±0.15, increases with increasing p, whereas the distance between aggregates (D ∼ p−0.23±0.05) decreases with p. The ionic spacing observed for TPS-0.22 (brass color) and 0.53 (purple) is much smaller, while that of TPS-0.70 (red), −1.0 (green), and −1.3 (blue) is much larger than D of the random SPS samples. This result supports our assignments of the high q peaks (for m ≤ 0.53) to the correlation of the chain ends, and the low q peaks (for m ≥ 0.7) to the average distance between micellar cores. Following this assignment, we may attribute a slight decrease of D on an increase of m (≥0.70) to the densification of micelles. The structure evolution explained above can be related to change of a distribution of number of ions per chain end, x (= 0, 1, 2, 3, ...). Here, we try to make a very rough estimation of this distribution based on the Poisson distribution function:

Figure 3. Scattering intensity I(q) (in logarithm scale with horizontal gridlines showing decades in the scale) plotted against magnitude of scattering vector q for PS and TPS-0.22, -0.53, -0.70, -1.0, and -1.3. Inset compares ionic spacing D between random sulfonated PS (squares) in the literature46−53 and telechelic PS (circles) in this study, where p is a number fraction of ionized monomers in all monomers.

samples. A weak scattering peak emerges at qpeak = 2−3 nm−1 for the TPS-0.22 and TPS-0.53 samples. In contrast, a low q peak emerges at qpeak = 0.5−0.6 nm−1 for the TPS-0.70, TPS1.0, and TPS-1.3 samples, and this peak becomes more prominent with increasing m. This result suggests a certain transition at m = 0.53, as discussed below. The peaks at qpeak = 2−3 nm−1 noted for TPS-0.22 and TPS0.53 correspond to a spacing of D = 2.1−3.1 nm. This spacing is close to an average end-to-end distance R = ⟨R2⟩1/2 = 3.3 and 3.6 nm estimated for TPS-0.22 and TPS-0.53, respectively, with the aid of ⟨R2⟩/M = 4.37 × 10−3 nm2 of PS found in the literature.39 This correlation peak is not seen for the PS precursor (black curve). Thus, the peak seems to detect a correlation of the ionic ends of respective telechelic chains carrying the ionic groups (that have a strong scattering contrast compared to the PS backbone).

P(x) = e−mm x /x! D

(4) DOI: 10.1021/acs.macromol.8b01776 Macromolecules XXXX, XXX, XXX−XXX

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Macromolecules This distribution is the simplest approximation on the basis of an assumption that the chain ends reacted with equal probabilities during the second stage of polymerization (i.e., polymerization of the ion-containing monomers). Figure 5a shows the Poisson distribution function P(x) for several average values of m = ⟨x⟩ = ∑xP(x) as indicated. This

Figure 6. DSC traces corresponding to the glass transition process of the PS and TPS samples. Tg is chosen as the middle point of the glass transition region, as indicated in arrow. The inset compares the literature Tg of random SPS ionomers synthesized from PS precursor with Mn = 3800 g/mol (squares) and Tg of our TPS ionomers.

with p is moderately weaker for the TPS-m ionomers compared with the SPS ionomers. Eisenberg and co-workers pointed out that segmental motion of ionomers is restricted in a region near the ionic aggregates, thereby leading to increase of Tg.36,54 Taking this molecular view, we can consider a difference of ion arrangement in the telechelic TPS-m and random SPS ionomers. For the TPS-m samples, the ionic groups are always separated along the chain backbone by a length scale comparable to the chain length. In comparison, the average distance between the ionic groups is smaller for the random SPS samples (of the same ion content) and decreases with increasing ion content. This difference should account for the weaker increase of Tg with ion content for the TPS-m ionomers than the random SPS ionomer. Another mechanism that may also contribute to the different p dependence of Tg is that the TPS-m samples of high m form larger ion aggregates, leading to smaller interface area where the restriction of segments is expected. 3.4. Linear Viscoelasticity. For the TPS-m samples and their precursor PS (for m ≥ 0.53), Figure 7 compares (pseudo)master curves of storage and loss moduli, G′ and G″, and tan δ reduced at a reference temperature, Tr = 130 °C. This Tr was selected so as to observe both Rouse and ionic dissociation processes of the TPS-m samples in the frequency sweep measurement (at Tr). The corresponding horizontal shift factor aT is later shown in Figure 8. To construct the master curves, we first normalized the rubbery moduli by an intensity factor of Tr/T. In principle, an intensity factor of ρrTr/ρT should be chosen for the moduli having an entropic origin. However, a change of ρ with T is much weaker than a change of T itself; therefore, the former change is innocuously ignored here. We shifted the normalized G′ and G″ horizontally to construct the (pseudo-)master curves. During the horizontal shifting, we noted that the time temperature superposition (tTs) works reasonably well for the PS and TPS-0.22 samples; only a slight failure is noted in the glassy-to-rubbery transition zone (at ω = 104−106 rad/s). This slight failure was attributed to a difference in temperature dependencies of glassy and rubbery moduli of PS, as reported in the literature.56−58

Figure 5. (a) Poisson distribution of a number of ions at chain end calculated for TPS-m samples as indicated. (b) Dependence of fractions of nonsticker, P(0), single-ion sticker, P(1), and multi-ion sticker, 1− P(0) − P(1), on average number of ionic groups per chain end. P(0) and P(1) are calculated from the Poisson distribution.

P(x) allows us to classify the chain ends into three types, namely, the nonsticky ends having a fraction P(0), the singleion ends having a fraction P(1), and the remaining multi-ion ends of fraction 1 − P(0) − P(1). Figure 5b shows plots these fractions against m. The fraction of sticky ends (red and green regions) increases with increasing m whereas the fraction of nonsticky ends (blue region) decreases, which would result in the formation of flower-like micelle for large m. This trend is somehow similar to that in aqueous solutions of the telechelic chains with hydrophobic ends, wherein the flower-like micelles connected by superbridges are formed at high concentrations of the chains.1,2 3.3. Thermal Analysis. DSC traces of the PS and TPS samples are compared in Figure 6. The glass transition temperature Tg is evaluated as the midpoint in the transition region, as indicated by the arrows. Tg clearly increases with m, suggesting that the ionic aggregation restricts segmental motion to enhance T g, as noted in various random ionomers.36,54 The inset of Figure 6 compares Tg of PS and TPS-m ionomers examined in this study and that for random SPS ionomers (black squares) reported in the literature;46,55 The precursor of SPS has Mn = 3800 g/mol not significantly different from Mn of our PS and TPS-m samples (cf. Table 1).46,55 In a range of ionic content p < 10%, an increase of Tg E

DOI: 10.1021/acs.macromol.8b01776 Macromolecules XXXX, XXX, XXX−XXX

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Figure 8. Shift factor aT utilized in Figure 7. In (a), aT is plotted against T − Tr, with Tr = 130 °C for the TPS-m and PS (precursor) samples as indicated. In (b), the reduced shift factor aT,iso, defined in terms of the isofrictional temperature Tiso, is plotted against T − Tiso. For all samples, Tiso is chosen to be 43 ± 1 °C higher than Tg.

Kohlrausch−Williams−Watts (KWW) form (eq 5b) and Rouse form (eq 5c),56,59−61 with the latter considering the molecular weight distribution as well.

Figure 7. (Pseudo-)master curves of storage and loss moduli, G′ and G″, and tan δ of the TPS-m samples as indicated and their precursor PS. All these curves are reduced at Tr = 130 °C. In (a) and (b), the thin solid curves are moduli of the PS precursor fitted by eq 5, and thick solid lines at ωaT < 0.1 s−1 represent a power law regime of TPS0.53. The horizontal dashed line in (a) is a plateau of G′ expected for TPS-1.3 if we regard all chains having two sticky ends as being elastically active.

G(t ) = Gg (t ) + Gr(t )

(5a)

Gg (t ) = Gg (0) exp( −[t /τKWW ]β )

(5b)

Nj

Gr(t ) =

∑ wjρRT /Mj∑ exp(−t /τR,j(q)) j

In contrast, for the TSP-m samples with higher m ≥ 0.53, a strong failure of tTs is clearly seen for G″ and tan δ (panels b and c) at low ω < 1 rad/s where the relaxation due to ionic dissociation starts to manifest. This failure occurs because of the difference in the activation energies for the ionic association and segmental motion explained for eq 1. For these high-m samples, we shifted the data according to a protocol developed in our previous studies.27,28 Namely, we first shifted the high frequency moduli corresponding to Rouse-type relaxation until the best superposition was achieved for G″ (being more sensitive to fast relaxation than G′). In contrast, we shifted the low frequency moduli corresponding to the ionic dissociation until the best superposition was achieved for G′ (being more sensitive to the slower relaxation than G″). The pseudo-master curve constructed in this way would reasonably represent the relaxation mode distribution at Tr.28 For the PS precursor, we attempted to fit the G′ and G″ data as a sum of the glassy and rubbery contributions to the relaxation, as shown by eq 5a (in the time domain). Specifically, we assumed that the glassy and rubbery relaxation moduli in the time domain, Gg(t) and Gr(t), have the

q=1

(5c)

In eq 5b, Gg(0) is the glassy modulus at t → 0, τKWW is a characteristic glassy relaxation time, and β is a stretching exponent specifying the broadness of relaxation mode distribution (lower β means broader mode distribution). In eq 5c, ρ (= 1.05 g/cm3) is the density, R is the gas constant, and τR,j(q) = τ0 sin−2[qπ/2(Nj + 1)] is the characteristic time of the qth Rouse mode of the jth component having the molecular weight Mj and weight fraction wj. Here, τ0 is the characteristic time of a Kuhn segment having MKuhn = 720 g/ mol, and Nj = Mj/MKuhn is the number of Kuhn segments per jth chain. Among the parameters explained above, Gg(0) was directly evaluated as the G′ value at the highest frequency (where the rubbery contribution is overwhelmed by the glassy contribution), and wj and corresponding Mj were determined from the GPC trace (cf. Figure S4). Thus, we regarded the remaining parameters (β, τKWW, and τ0) as adjustable parameters of our model (eqs 5a−5c) to fit the G′ and G″ data of the precursor PS. In this fitting process, the KWW-type Gg(t) was transferred to the frequency domain via an efficient finite element approximation algorithm.62,63 (The exponential Rouse form F

DOI: 10.1021/acs.macromol.8b01776 Macromolecules XXXX, XXX, XXX−XXX

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Macromolecules

Tiso, irrespective of the ionic content in the sample. Thus, we chose Tiso having almost the same distance to Tg (i.e., Tiso − Tg = 43 ± 1 °C as listed in Table 1) and re-evaluated aT,iso with respect to this Tiso. In Figure 8b, this aT,iso is plotted against T − Tiso. Clearly, the agreement is noted for the plots at low T where the shift factor is obtained from superposition of the high frequency modulus and thus reflects the segmental motion (i.e., T dependence of τ0). In fact, the aT,iso data of all samples at low T are well described by the WLF relationship (eq 6) shown with the solid curve in Figure 8b.

of Gr(t) is straightforwardly converted to the frequency domain.) The best-fit results, obtained with β = 0.47, τKWW = 0.063 μs, and τ0 = 4.2 μs, are shown in Figures 7a and 7b as thin solid curves at ω > 0.1 rad/s. Good agreement between those curves and data suggests validity of these parameter values (in particular, the β and τ0 values) that will be utilized in our discussion of the relaxation of TPS-m ionomers presented later. For the TPS-m ionomers, the glassy G″ peak broadens and shifts to a lower frequency with increasing m, which is in accordance with an increase of Tg and broadening of the glass transition seen earlier for the DSC traces in Figure 6. The change of the rubbery modulus with m is even more remarkable. The TPS-0.22 sample shows power-law-like behavior at low ω, indicating formation of branched sol chains with a wide variety of sizes.64−66 A sol-to-gel transition appears to occur at m = 0.53,26,67−71 where the plateau is hardly detectable and the power law-like behavior G′ = G″/tan(απ/2) = Kωα can be detected at low ω. This power-law-like behavior, shown with the thick solid lines at ω < 0.1 rad/s in Figures 7a and 7b, is characterized with K = 3.2 × 104 Pa sα and α = 0.55. All these features suggest that TPS-0.53 is very close to the critical gel point where a percolated network structure just forms. The corresponding number of ions per chain, 2m = 1.06 (on average), is very close to that expected from the gel point pc = 1/(N − 1) of random ionomers; namely, Npc = N/(N − 1) = 28/27 = 1.04 with N = 28 being the number of monomers in our precursor PS chain. In contrast, the TPS-m samples with higher m ≥ 0.70 show a clear plateau of G′ that increases its magnitude with increasing m, indicating an increase of the network strand density with m (cf. eq 1). This behavior also suggests that the critical gel point is located in a vicinity of m = 0.53. The sol−gel transition behavior can be also related to the distribution of the number of ions per chain end, x. As seen in Figure 5a, the x value (integer) having the largest fraction (largest probability), hereafter denoted x*, is x* = 0 for m ≤ 0.70 and x* = 1 for m = 1.0 and 1.3. Because the conventional (nonionic) telechelic polymers have x* = 1 without the xdistribution and usually exhibit gel-like behavior, the crossover of the x* value from 0 to 1 seen for our TPS-m ionomers on an increase of m from 0.70 to 1.0 (Figure 5a) seems to naturally result in the sol-to-gel transition, as observed. This result in turn suggests that the use of Poisson distribution for x (eq 4) is a reasonable approximation for our TPS ionomers. The sol−gel transition also affects the time−temperature shift factor (horizontal shift factor) aT. Figure 8 compares T dependence of aT of the TPS-m and PS (precursor) samples. As shown in Figure 8a, aT of those samples exhibit mutual deviation when plotted against T − Tr with Tr = 130 °C. This deviation emerges because (1) the glass transition temperature increases with m, thereby strengthening the temperature dependence of segmental time τ0, and (2) the relaxation at high T is governed by the ionic dissociation for the TPS-m samples with m ≥ 0.53 so that aT is controlled by τs having stronger T dependence than τ0 (cf. eq 2). Furthermore, the xdistribution should lead to a distribution of the activation energy Ea(x) (cf. eq 3), which further complicates the T dependence of aT of high-m TPS-m samples at high T. A change of τ0 reflects an increase of Tg, and thus we expect that an adequate choice of the reference temperature (isofrictional temperature Tiso) can compensate the increase of Tg, thereby allowing τ0 to have the same dependence on T −

log aT =

−8.37(T − Tiso) 108 + T − Tiso

(6)

Nevertheless, at high T where the shift factor was obtained from the low frequency modulus reflecting the ionic dissociation, the aT,iso data of TPS-m samples exhibit stronger temperature dependence compared to the WLF relationship. This deviation from the WLF behavior should result from the extra energy Ea required for the ionic dissociation, as expected from eqs 2 and 3.

4. DISCUSSION 4.1. Glass-to-Rubber Transition. In Figure 9, we compare G′ and G″ of all samples reduced at Tiso. For the samples with various m at isofrictional Tiso, the position of the glassy G″ peak is almost the same (cf. Figure 9b), meaning that mobility of a majority of the segments in those samples has been properly normalized. Nevertheless, their moduli in the

Figure 9. Pseudo-master curves of storage and loss moduli, G′ and G″, of the PS and TPS-0.22, -0.53, -0.70, -1.0, and -1.3 samples reduced at respective isofrictional temperatures: Tiso = 118, 119, 123, 125, 128, and 130 °C. The moduli of a randomly sulfonated polystyrene reduced at Tiso = Tg + 43 °C = 133 °C are also shown for comparison.26 The arrow in (b) indicates the dissociation frequency of single-ion sticker in SPS, and the red curves are a fit of the glassy relaxation with the KWW equation. G

DOI: 10.1021/acs.macromol.8b01776 Macromolecules XXXX, XXX, XXX−XXX

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Macromolecules glass-to-rubber transition regime at ω = 102−105 rad/s exhibit different ω dependence and not normalized at Tiso; the modulus increases with m and its ω dependence becomes weaker on the increase of m up to 0.7. This behavior should be partly related to broadening of glassy relaxation with increasing ion content.36,54 To check this idea, we fit the glassy part of modulus for the samples with m ≥ 0.7 with the KWW equation (eq 5b, see solid red curves), and the best fit was achieved with Gg(0) = 108.9 Pa, β = 0.30, and τKWW = 0.020 μs. The stretched exponent β = 0.30 is much smaller than β = 0.47 obtained for bulk PS (cf. solid curves in Figure 7a,b), lending support for the point that the increase of modulus at ω = 102−105 rad/s with m is attributable to broadening of the glassy relaxation. We suspect that there are at least two additional mechanisms affecting the glassy relaxation because of the micelle formation. First, a filler effect may arise from an enhancement of local strain in the matrix due to the hard micellar cores.72−74 We may estimate a ratio of modulus with and without the filler effect through the Guth equation as 1 + 2.5ϕ + 14.1ϕ 2 ≤ 130%, with ϕ ≤ 8.5% being the fraction of ion-containing monomers in this study. Thus, this effect is not the major effect.75 The second mechanism is related to a certain topological constraint to the motion of the Rouse segments of the tethered corona chains, including the dangling chains, loops/superloops, and bridges/superbridges, because the micellar core is impenetrable. The delay of the viscoelastic relaxation by this type of constraint has been observed in block copolymers76−78 and nanoparticle-tethered polymers.79,80 In particular, Archer and co-workers noted that the delay for the relaxation of nanoparticle-tethered polymers is more significant than expected from the Tg increase.79,80 This mechanism could increase the modulus in a glass-to-rubber transition regime, thereby broadening the mode distribution therein. 4.2. Rubbery Modulus. We here focus on the number of ions at the chain end, x, to discuss the elastic features of the TPS samples. As explained earlier in Figure 5b, the chain ends can be classified into three types. Namely, a chain with x = 0 for one end would be either a solvent (if x = 0 also for the other end) or a dangling chain (if x ≥ 1 for the other end). These chains would not contribute to the plateau of G′ noted in Figure 7a. In contrast, chains having x ≥ 1 at both ends could form bridges/superbridges and are elastically active. The fraction of these chains can be estimated as (1 − P(0))2 = 0.039, 0.17, 0.22, 0.40, and 0.53 for m = 0.22, 0.53, 0.70, 1.0, and 1.3, respectively, where P(0) is the fraction of the chains having x = 0 at one end (cf. Figure 5a). Thus, the m value at the gelation point of our TPS samples, m ≅ 0.53 (cf. Figures 7 and 9), suggests that a percolated network is formed when the fraction of the chains having two sticky ends exceeds 0.17. The x distribution, affecting the P(0) value discussed above, can help us to better understand the relaxation behavior seen in Figure 9. For TPS-1.3, the plateau modulus is expected to be GN = vkT(1 − P(0))2 = 105.7 Pa if all chains having two sticky ends are elastically active. This GN value, shown in the horizontal dashed line in Figure 7a, obviously overestimates the real plateau modulus. Thus, the number density of elastically active strands is much smaller than the fraction of the chains having two sticky ends, which agrees with our previous argument that the strands connecting the micellar cores are mostly in the superbridge form. Another mechanism lowering the plateau could be related to the network defects

because of elastically inactive loops or superloops (note that the chains having two sticky ends in the superloops have been counted in the factor of (1 − P(0))2 discussed above).81,82 For further investigation of the effect of x-distribution on the relaxation of our TPS-m ionomers, Figure 9 includes G′ and G″ data of random sulfonated polystyrene (SPS) reported in the literature.26 The data in ref 26, reduced at Tg + 45 °C, have been shifted to our isofrictional temperature, Tg + 43 °C, via a horizontal shift by a factor of 10−0.1 (to account for the −2 °C change of reference T).26 This SPS sample was synthesized from partially sulfonated PS precursor having Mn = 3800 g/ mol and a fraction of ionized monomers p = 4.8%. Thus, the average number of ions per this SPS sample, pMn/M0 = 1.8 (with M0 = 104 g/mol being the molecular weight of styrene monomer), is similar to the number (= 2) in our TPS-1.0 sample. Nevertheless, the relaxation behavior following the plateau is quite different for the SPS and TPS-1.0 samples, as discussed below. The SPS sample exhibits terminal relaxation immediately after the ionic dissociation, as noted from the sharp G″ peak followed by the terminal tail of G″ ∝ ω. This almost Maxwellian terminal relaxation of the SPS sample is related to its average number of ions per chain, 1.8, that allows dissociation of one ion to activate the full relaxation. Consequently, the peak frequency of G″ (∼10−4.1 rad/s; cf. arrow in Figure 9b) should represent reasonably the dissociation frequency of single-ion sticker, 1/τs(1) where “1” represents the single-ion sticker. In contrast, our TPS-1.0 sample exhibits gradual power-law like relaxation at low ω without attaining the terminal relaxation. This lack of terminal relaxation suggests that a certain structure remains due to the x-distribution (that automatically yields multi-ion stickers), as discussed in detail in the next section. In addition, the frequency ∼10−3.8 rad/s at the onset of the power-law like relaxation, possibly representing a characteristic frequency for the ionic dissociation in TPS-1.0, is slightly higher than the dissociation frequency of the SPS sample. This delicate difference could be related to the superbridge structure in TPS-1.0. When the superbridge strand illustrated in Figure 4 starts to break up, it is unlikely that the two sites (red circles) at the center of the two micellar cores break up simultaneously. It is more likely that one site of the superbridge having the lowest association energy will break up first, and the resulting fragments of the superbridge will relax like the tethered chain.83 In comparison, the superbridge would not be the major component in the SPS sample. Thus, the dominance of this superbridge dissociation may increase the effective breakup frequency in the TPS-1.0 sample.26,84 4.3. Comparison with Conventional Telechelic Ionomers. On the basis of the comparison between the random sulfonated polystyrene (SPS) sample and our TPS-m samples presented in the previous section, one may ask what the key effect of x-distribution is in the dynamics of our telechelic ionomers (TPS-m samples). Figure 10 answers this question by comparing the modulus of the TPS-1.0 and rTPS samples, the latter having nearly one ion at the chain end, namely, having almost no x-distribution. The data of these samples are compared at the isofrictional temperature, Tiso = Tg + 43 °C, with Tg of rTPS, 91 °C, was a little higher than Tg of TPS-1.0, 85 °C, possibly because rTPS has a higher fraction of sticky ends than TPS-1.0; 1 − P(0) = 0.9 (determined form the acid−base titration) for rTPS and 0.63 for TPS-1.0 (determined from the Poisson equation). In addition, rTPS H

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tion).83 In contrast, TPS-1.0 shows much broader relaxation mode distribution, characterized by a power-law-like behavior at frequencies lower than a characteristic frequency of the dissociation of single-ion stickers, which should reflect the effect of x distribution as explained below. Figure 10 detects the relaxation in a time scale not significantly longer than a characteristic time for dissociation of the single-ion stickers. In that time scale, it is unlikely for the multiple-ion stickers to dissociate, as noted from a simple estimate below. The characteristic time of Kuhn segment, τ0, is estimated to be τ0 ∼ O(10−4) s (of the order of 10−4 s). The characteristic time of dissociation of single-ion sticker, τs(1), is estimated to be τs(1) ∼ O(104) s for x = 1. Then, we find exp(Ea(1)/kT) = τs(1)/τ0 = O(108) (cf. eq 1), and accordingly the characteristic time of dissociation of bi-ion sticker is estimated as τs(2) = τ0 exp(Ea(2)/kT) = O(1012) s with an assumption of Ea(2) = 2Ea(1) for a case of fully coupled motion of the two ions attached to the chain end. This τs(2) value suggests that the dissociation of multiple-ion ends is quite unlikely in the range of frequency examined in Figure 10. Then, among all types of stickers, only the single-ion sticker plays a central role in the relaxation. For TPS-1.0, the fraction of the single-ion sticker is estimated from the Poisson distribution as P(1)/(1 − P(0)) = 0.58. Therefore, in the range of frequency examined in Figure 10, only a fraction of superbridges can break up, leading to a certain sol-like structure (self-similarly branched chains) remaining even after dissociation of all single ion sites. This type of relaxation of sol-like structure (formed via associations of the multi-ion stickers) activated by the dissociation of the single-ion stickers may be responsible for the power-law-like relaxation at low ω for TPS-1.0.

Figure 10. Comparison of modulus data of TPS-1.0 and rTPS with and without distribution of a number of ions at the chain end. The data are compared at the isofrictional temperature, Tiso = Tg + 43 °C (= 128 °C for TPS-1.0 and 134 °C for rTPS). The inset compares scattering profiles of those sample.

and TPS-1.0 have difference in the chemical environment for their ionic groups. The sulfonic group in TPS-1.0 is covalently bound to the phenyl ring, whereas the same group in the rTPS sample is bound to alkyl backbone of the chain. This difference in the chemical environment may affect the association energy of the sulfonic group and accordingly the dissociation time. Despite this difference, rTPS serves as an ideal reference sample for the TPS-m samples, as discussed below. In Figure 10, we note at least three noteworthy differences for these two samples. The first difference is on the ionic dissociation frequency: This frequency for rTPS, ∼10−2.5 rad/s, is considerably higher than the frequency for TPS-1.0, ∼10−3.8 rad/s. This difference is presumably attributed to the different association energy because of the different chemical environment for the sulfonic groups explained above; the sulfonic groups bound to phenyl ring shows higher association energy than those bound to alkyl backbone. We also note that the TPS-1.0 and rTPS samples exhibit different scattering profiles (see the inset of Figure 10). In particular, there should be certain assembling of the ionic aggregates of rTPS that leads to prominent scattering at low q, but those aggregates appear to be different from the aggregates in TPS-1.0. This structural difference suggests that the difference in the chemical environment would lead to a difference in the localized packing and assembling behavior of the ionic groups in the two samples. The second rheological difference between TPS-1.0 and rTPS is found for the plateau modulus being significantly smaller for the former (see Figure 10). This difference suggests that the x-distribution in TSP-1.0 leads to less amount of sticky chain ends because the chains having at least one nonsticky end (with x = 0) are elastically ineffective. A fraction of elastically active chains having x ≥ 1 at both ends can be evaluated as a ratio of the factor of (1 − P(0))2 for TPS-1.0 and rTPS. This ratio, larger for rTPS by a factor of ∼2, reasonably accounts for the difference of the plateau modulus seen in Figure 10. The third rheological difference is noted for the relaxation mode distribution at low ω. The rTPS sample shows narrowly distributed relaxation characterized by sharp G″ peak followed by terminal tails of G″ (∝ ω) and G′ (∝ ω2). Uneyama and coworkers attributed this narrowly distributed relaxation to multiple dissociation sites in the superbridges that has the same probability of dissociation (thanks to no x-distribu-

5. CONCLUDING REMARK Ionomers are classified in several groups according to the location of ionic groups in the polymeric backbone. Telechelic ionomers refer to ionomers with well-defined ionic groups attached to the chain ends. This study introduced a certain distribution of the number of ionic groups, x, and, accordingly, a distribution of the dissociation energy Ea of the chain ends. This distribution of Ea leads to rich rheological behavior seen neither in random ionomers nor in conventional telechelic ionomers having no x-distribution. In particular, the telechelic ionomers with x-distribution exhibit power-law like relaxation with no detectable terminal relaxation. This slow and broad relaxation is attributable to motion a multibranched sol structure emerging on dissociation of only the single-ion stickers (without dissociation of the multiple-ion stickers). If we further increase the ion content to a level that gel network can be formed by the multi-ion stickers, we may expect an additional plateau after dissociation of the single-ion stickers, enabling the system to exhibit double-network behavior. To test this idea is considered as an interesting future work. The broad relaxation could be useful in applications requiring dissipation of energy over a wide time scale. This distribution has been realized previously though different approaches; for example, the skin of golf balls is usually made of ionomers containing more than one type of counterions, such as Na, K, or Zn, to realize high toughness and impact resistance in various weather conditions.14 Another example is the double-network gels that have a sacrificial network in addition to a structure-sustaining network thereby efficiently dissipate the energy through rupture of the former network.85 I

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(8) Stadler, F. J.; Pyckhout-Hintzen, W.; Schumers, J. M.; Fustin, C. A.; Gohy, J. F.; Bailly, C. Linear Viscoelastic Rheology of Moderately Entangled Telechelic Polybutadiene Temporary Networks. Macromolecules 2009, 42 (16), 6181−6192. (9) Stadler, F. J.; Still, T.; Fytas, G.; Bailly, C. Elongational Rheology and Brillouin Light Scattering of Entangled Telechelic Polybutadiene Based Temporary Networks. Macromolecules 2010, 43 (18), 7771− 7778. (10) Koga, T.; Tanaka, F. Theoretical Predictions on Normal Stresses under Shear Flow in Transient Networks of Telechelic Associating Polymers. Macromolecules 2010, 43 (6), 3052−3060. (11) Vlassopoulos, D.; Pakula, T.; Fytas, G.; Pitsikalis, M.; Hadjichristidis, N. Controlling the self-assembly and dynamic response of star polymers by selective telechelic functionalization. J. Chem. Phys. 1999, 111 (4), 1760−1764. (12) Vlassopoulos, D.; Pitsikalis, M.; Hadjichristidis, N. Linear dynamics of end-functionalized polymer melts: Linear chains, stars, and blends. Macromolecules 2000, 33 (26), 9740−9746. (13) van Ruymbeke, E.; Vlassopoulos, D.; Mierzwa, M.; Pakula, T.; Charalabidis, D.; Pitsikalis, M.; Hadjichristidis, N. Rheology and Structure of Entangled Telechelic Linear and Star Polyisoprene Melts. Macromolecules 2010, 43 (9), 4401−4411. (14) Zhang, L. H.; Brostowitz, N. R.; Cavicchi, K. A.; Weiss, R. A. Perspective: Ionomer Research and Applications. Macromol. React. Eng. 2014, 8 (2), 81−99. (15) Kwon, Y.; Matsumiya, Y.; Watanabe, H. Viscoelastic and Orientational Relaxation of Linear and Ring Rouse Chains Undergoing Reversible End-Association and Dissociation. Macromolecules 2016, 49 (9), 3593−3607. (16) Noro, A.; Matsushita, Y.; Lodge, T. P. Thermoreversible supramacromolecular ion gels via hydrogen bonding. Macromolecules 2008, 41 (15), 5839−5844. (17) Zhuge, F.; Hawke, L. G. D.; Fustin, C. A.; Gohy, J. F.; van Ruymbeke, E. Decoding the linear viscoelastic properties of model telechelic metallo-supramolecular polymers. J. Rheol. 2017, 61 (6), 1245−1262. (18) Zhuge, F.; Brassinne, J.; Fustin, C. A.; van Ruymbeke, E.; Gohy, J. F. Synthesis and Rheology of Bulk Metallo-Supramolecular Polymers from Telechelic Entangled Precursors. Macromolecules 2017, 50 (13), 5165−5175. (19) Park, G. W.; Ianniruberto, G. A new stochastic simulation for the rheology of telechelic associating polymers. J. Rheol. 2017, 61 (6), 1293−1305. (20) Ahmadi, M.; Hawke, L. G. D.; Goldansaz, H.; van Ruymbeke, E. Dynamics of Entangled Linear Supramolecular Chains with Sticky Side Groups: Influence of Hindered Fluctuations. Macromolecules 2015, 48 (19), 7300−7310. (21) Fetters, L. J.; Graessley, W. W.; Hadjichristidis, N.; Kiss, A. D.; Pearson, D. S.; Younghouse, L. B. Association Behavior of EndFunctionalized Polymers 0.2. Melt Rheology of Polyisoprenes with Carboxylate, Amine, and Zwitterion End Groups. Macromolecules 1988, 21 (6), 1644−1653. (22) Davidson, N. S.; Fetters, L. J.; Funk, W. G.; Graessley, W. W.; Hadjichristidis, N. Association Behavior in End-Functionalized Polymers 0.1. Dilute-Solution Properties of Polyisoprenes with Amine and Zwitterion End Groups. Macromolecules 1988, 21 (1), 112−121. (23) Amin, D.; Likhtman, A. E.; Wang, Z. W. Dynamics in Supramolecular Polymer Networks Formed by Associating Telechelic Chains. Macromolecules 2016, 49 (19), 7510−7524. (24) Rubinstein, M.; Colby, R. H. Polymer Physics; Oxford University Press: New York, 2003. (25) Semenov, A. N.; Rubinstein, M. Thermoreversible Gelation in Solutions of Associative Polymers. 1. Statics. Macromolecules 1998, 31 (4), 1373−1385. (26) Chen, Q.; Huang, C. W.; Weiss, R. A.; Colby, R. H. Viscoelasticity of Reversible Gelation for lonomers. Macromolecules 2015, 48 (4), 1221−1230.

Such multiple scale energy dissipation is essential for natural materials and living organisms to achieve hardness and toughness simultaneously.86 The distribution of energy may also lead to unique nonlinear rheology under shear87 or elongational flow,88 and the mechanism of such nonlinearity is an interesting subject for future study.

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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.8b01776. Scheme S1 and Figure S1: synthesis route and 1H NMR spectra of 1,4-bis(n-butylsulfanylthiocarbonylsulfanylmethyl) benzene (CTA); Scheme S2 and Figure S2: synthesis route and 1H NMR spectra of MacroCTA; Scheme S3: synthesis route of the TPS-m samples; Schemes S4, S5 and Figure S3: synthesis route and 1H NMR spectra of rTPS; Figure S4: dw/d log M versus MW determined in GPC for the TPS-m and rPS precursors (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected]. ORCID

Quan Chen: 0000-0002-7771-5050 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Q.C. acknowledges the National Natural Science Foundation of China (21722407 and 21674117). Z.Z. acknowledges the National Natural Science Foundation of China (21873095). We thank Prof. Shengxiang Ji of the CIAC for the help and discussion in the synthesis.

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REFERENCES

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DOI: 10.1021/acs.macromol.8b01776 Macromolecules XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.macromol.8b01776 Macromolecules XXXX, XXX, XXX−XXX