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Supporting Information

Experimental Test for Viscoelastic Relaxation of Polyisoprene undergoing Monofunctional Head-to-Head Association and Dissociation.

Yumi Matsumiya* and Hiroshi Watanabe

Institute for Chemical Research, Kyoto University, Uji, Kyoto 611-0011 Japan

Osamu Urakawa and Tadashi Inoue Graduate School of Science, Osaka University, Toyonaka, Osaka, 560-0043, Japan

S1. Synthesis of PI samples. High-cis linear polyisoprene (PI) was synthesized via living anionic polymerization at 25˚C. Sec-butyllithium and benzene (Bz) were utilized as the initiator and solvent, and all operations were made with a high vacuum line and glass flasks/ampoules having breakable seals and fuse-sealable constrictions. In this study, the anion ends of the PI chains thus obtained were to be modified to carboxylic (COOH) groups through reaction with carbon dioxide (CO2). However, the isoprenyl anion ends of the as-polymerized PI chains having Li+ as the counter cation are known to associate with each other in benzene (and also in other nonpolar solvents) because of Li-Li bridges, and this end-association enhances undesired dimeric-coupling on the reaction with CO2. Thus, in this study, diphenyl ethylene (DPE; ~ 5 eq molar to PI anions) diluted in tetrahydrofuran (THF) was added to the PI anion/Bz solution to modify the isoprenyl anion ends of PI to DPE anions. (DPE itself does not polymerize, so that one DPE anion was attached to the end of each PI chain.) DPE anions are less reactive compared to isoprenyl anions, and THF utilized as the diluent (~ 2 vol% to the PI/benzene solution) is polar to strongly enhance dissociation of the DPE anions, so that this end-conversion allowed us to avoid the dimeric coupling with CO2 and successfully obtain PI having the carboxylic group at the chain end, as explained below. Scheme 1 shows the procedure of the synthesis/purification of the PI samples. At first, the PI-DPE-

Li+/benzene/THF solution thus obtained was split into three flasks. The PI-DPE- anion in one batch was terminated with methanol to recover the linear precursor unimer PI. The unimer PI thus obtained was precipitated from benzene solution into excess methanol to remove impurity (LiOCH3 created by the terminal reaction), and then re-dissolved in benzene containing a small amount of anti-oxidant, butylhydroxytoluene (BHT; ~ 0.05 wt% to PI). This final benzene solution was freeze-dried for ~ 1 day and then further dried in vacuum at 50˚C for two days to recover the unimer PI sample. This sample was sealed in Argon and stored in a deep freezer until use.

Scheme 1. Synthesis and purification of PI-COOH, PI, and (PI)2 samples.

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As a reference, the anion in the second flask was allowed to react with α-α’-dichloro-p-xylene (bifunctional coupler) to obtain the head-to-head coupled PI2 dimer. The coupler content was set to be ~ 90% equimolar to the anion to ensure full reaction of the coupler with the DPE anion ends of the PI chains. The unreacted unimer (~ 10%) was removed through repeated fractionation from benzene/methanol mixed solvents to recover pure PI2 dimer. Finally, the dimer thus obtained was precipitated from a benzene solution into excess methanol (to remove LiOCH3 remaining, if any, after the fractionation), re-dissolved in benzene containing BHT (~ 0.05 wt% to PI), and fully dried/stored in the way explained for the PI unimer. The PI-DPE- anion in the third (main) flask was converted to acid-end PI through reaction with CO2 and then with HCl (cf. Scheme 1). For safe synthesis at a rather small scale avoiding use of a high-pressure CO2 tank, we utilized a reaction apparatus illustrated in Figure S1. F1 and F2 were 300 ml vacuum flasks, and F2 obtained from the synthesis of PI-DPE- anion contained ~ 150 ml of the anion solution (~ 7 g of anion). The apparatus was connected to a reservoir of purified THF through the high vacuum line (not shown here), and ~ 50 ml of pure THF was vacuum-distilled into the flask F1 after full evacuation. Then, the apparatus was sealed at the constriction C. The ampoule A contained ~ 0.2 g of solid CO2 (~ 20 eq molar to living PI anion ends) obtained through vacuum sublimation of commercially available dry ice. The ampoule A was soaked in a liquid nitrogen jar (not shown here) until use. After the apparatus was sealed, the breakable seal S1 was broken, the liquid nitrogen jar was removed, and CO2 was allowed to sublimate and dissolve into THF in the flask F1 chilled at -78˚C with a dry ice/methanol bath. This dissolution reduced the CO2 pressure to avoid high over-pressurization in the apparatus. The apparatus also had a thin, weak breakable seal S3 that served as a safety leak portion in case of high over-pressurization (although the apparatus was not highly over-pressurized in the current synthesis). After dissolution of CO2 in THF, the top part of the flask F2 was chilled with dry ice/methanol and the whole apparatus was turned up side down, and the breakable seal S2 was broken to introduce the CO2/THF solution into the flask F2. Although the solution in the flask F2 was warmer than the CO2/THF solution in F1 (at -78˚C) so that the solvent vapor pressure was higher in F2, the CO2 vapor pressure was high enough to force the CO2/THF solution to rapidly flow into the flask F2. The PI-DPE-

Li+ chains in F2 rapidly reacted with CO2 in this flowing-in solution to convert the PI chain end to COOLi, as noted from immediate disappearance of red color of the anion. Then, the seal S3 was broken to release the pressure, and the apparatus was open to recover the PI-DPE-COOLi sample dissolved in Bz/THF. (Lack of dimeric coupling of the PI-DPE− Li+ anion was confirmed with GPC, as explained in section S2.) The recovered PI-DPE-COOLi solution was dried under reduced pressure, and a small amount of the PI-DPE-COOLi precursor was recovered for later characterization. The remaining majority of the precursor was re-dissolved in THF, and ~ 5 eq molar of HCl aq solution (1N) was added to this THF solution to convert the COOLi group at the PI chain end into the COOH group. (Full conversion was confirmed with NMR, as explained in section S2). Then, the PI-DPE-COOH/THF solution was precipitated in excess MeOH (chilled at 0 ºC) to recover the PI-DPE-COOH sample. This sample was re-dissolved in Bz and dried/stored in a way explained for the PI unimer. No BHT was added to the PI-DPE-COOH sample, because BHT might affect the association/dissociation of the hydrogen bonding between the COOH groups. (Because of this lack of BHT, after each viscoelastic measurement explained in the main text, the samples were subjected to GPC to confirm lack of degradation during the measurement.)

Figure S1. Apparatus for reaction of PI-DPE- anion with CO2.

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S2. Characterization of PI samples. The neat PI unimer sample, the (PI)2 dimer sample after purification (fractionation), and the acid (COOH)-end PI sample were characterized with GPC (CO-8020 and DP-8020; Tosoh) equipped with a refractive index (RI) monitor (RI-8020, Tosoh). Figure S2 shows the GPC-RI signal measured for these samples. The signal of the acid-end PI sample (red curve) is indistinguishable from the signal of the neat PI30 sample (green curve) and shows no detectable amount of a dimeric component (formed if PI-DPE- anion chains were coupled with CO2), confirming the efficiency of monofunctional termination of DPE- anion ends with CO2 dissolved in THF explained in section S1. (If neat PI-

Li+ precursor were to react with CO2 in benzene, the dimeric coupling should have occurred because of aggregation of the precursors through Li-Li bridges in non-polar solvents.) We also note no detectable amount of the unimer component in the signal of the (PI)2 dimer sample, confirming a high efficiency of the purification (fractionation) for the crude product of the reaction with α-α’-dichloro-p-xylene explained in section S1. Utilizing monodisperse PI samples synthesized and characterized in previous studies,1,2 we analyzed the GPC-RI signals (Figure S2) to determine the molecular characteristics of the samples. The results are summarized in Table S2, with the sample code number indicating the molecular weight in unit of 1000. The viscoelastic measurements were conducted for those PI samples diluted with a 1,2-rich oligomeric butadiene (a good solvent for PI), so as to examine the effect of the association/dissociation of the hydrogen bonding between the COOH groups on the relaxation of non-entangled PI chains. The characteristics of this oB3 solvent (after purification explained in the main text) are also shown in Table S1. Figure S3 shows 7Li NMR signal of the PI30-COOH sample and its precursor PI30-COOLi in deuterated chloroform solutions measured with a spectrometer (Bruker Avance III 600US Plus NMR). The 7Li signal clearly noted for the precursor is not detected within the experimental resolution for the PI30-COOH sample. This result confirms the full conversion of the COOLi end group into the COOH group through the reaction with HCl explained in section S1.

Figure S2. GPC-RI signal of neat PI unimer sample, the (PI)2 dimer sample after purification (fractionation), and the acid (COOH)-end PI sample. The signals of the neat unimer (green curve) and acid-end sample (red curve) are indistinguishable from each other.

Table S1. Characteristics of the samples --------------------------------------------- sample code 10-3Mw Mw/Mw ---------------------------------------------

polyisoprene PI30-COOH 30.5 1.02 PI30 30.5 1.02 (PI30)2 61.0 1.02

oligomeric butadiene (solvent) oB3 3.5 1.05 ---------------------------------------------

Figure S3. 7Li NMR signal of PI30-COOH sample and its precursor PI30-COOLi. The signal for PI-COOLi is shifted upward for easy comparison.

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S3. Comparison of viscoelastic data of PI30 unimer and (PI30)2 dimer with Rouse model. The neat PI30 unimer and (PI30)2 dimer chains, having 10-3M = 30.5 and 61. 0 and being dissolved in oB3 at the concentration of 10 wt%, are expected to exhibit the Rouse behavior, as explained for Figures 1 and 2 in the main text. This expectation was quantitatively tested for the

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ΔG ' and

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ΔG" data of those chains. The results are shown in Figure S4. For the Rouse chain composed of N* segments (or subchain), the storage and loss moduli in the continuous limit (for N* >> 1) are simply expressed as3

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ΔG '=cRT

M

ω 2τ p ,G2

1+ω 2τ p ,G2

p =1

N *

∑ ,

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ΔG"=cRT

M

ωτ p ,G

1+ω 2τ p ,G2

p =1

N *

∑ (S1)

where c is the mass concentration of the chain, R is the gas constant, and T is the absolute temperature. (Equation S1, with N* = N and 2N for the unimer and dimer, is equivalent to eq 5 in the main text.) The viscoelastic relaxation time τp,G of pth Rouse mode is expressed in terms of the longest end-to-end fluctuation time τ1 of the unimer chain as

For unimer:

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τ p ,G =τ12p2

(S2a)

For dimer:

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τ p ,G =2τ1p2

(S2b)

N* can be straightforwardly evaluated as N* = M/MR, where MR is the molecular weight of the Rouse segment (MR ≅ 190 for PI).4 N* strongly affects the short time behavior by specifying the high-ω plateau of storage modulus as

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ΔG ' (ω → ∞) = N*cRT/M, but negligibly affects the low-ω relaxation behavior of our interest examined in Figure S4. In Figures S4a and S4b, respectively, the

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ΔG ' and

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ΔG" data of the PI30 unimer and (PI30)2 dimer at several T are compared with the Rouse calculation. With an adequate choice of the τ1 value for the unimer shown in Figure S4c, the

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ΔG ' and

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ΔG" data of both unimer and dimer are excellently described by the Rouse calculation. (All other parameters were determined independently, as explained above.) This result confirms that the PI30 unimer and (PI30)2 dimer chains obey the Rouse dynamics, as considered in the theory for associative PI30-COOH chain. Furthermore, the τ1 value shown in Figure 4Sc is utilized as the fundamental, known parameter in the test of this theory described in the main text. In relation to the above Rouse feature of the unimer and dimer, we note that eq S2a gives a simple relationship between τ1 and the second-moment average terminal relaxation time3 <τ>w,unimer of the unimer:

<τ>w,unimer

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≡ [ΔG ' /ωΔG" ]ω→0

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=τ1

2

Σp ≥1∞ p−4

Σp ≥1∞ p−2 =

π 2τ1

30 for Rouse unimer chain (S3)

(The summation in eq S3 was taken for p = 1- because N* >> 1.) As noted from eq S3, <τ>w,unimer of the Rouse chain is close to the viscoelastic longest relaxation time, τ1/2.

Figure S4. Viscoelastic moduli of (a) PI30 unimer and (b) (PI30)2 dimer, both in oB3 at the concentration of 10 wt%. Black curves show the results of fitting with the Rouse model. Excellent fit was achieved with the longest end-to-end relaxation time of the unimer, τ1, shown in panel c. (τ1 is the only adjustable parameter utilized in the fitting.)

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S4. Some detail of fitting of viscoelastic data of PI30-COOH with theory. As explained in section 4.3 in the main text, we attempted to fit the

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ΔG ' and

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ΔG" data of the PI30-COOH chain with the theoretical modulus (eq 6 combined with eqs 2-4) by utilizing a single fitting parameter, rd. The essence of the theory is the motional coupling of the unimer and dimer through the association/dissociation reaction.5 This coupling splits the intrinsic Rouse modes of the unimer and dimer into several components (g1eo, g2e, and g2o specified by eqs 2b, 3b, and 3e in the main text) and also creates new relaxation modes (g1-2e, g1-2o, g2e-1 and g2e-2o specified by eqs 2c, 2d, 3c, and 3d). As shown in Figure 5 in the main text, a sum of these component g(t) functions, after Fourier-transformation into the frequency (ω) domain, excellently fitted the

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ΔG ' and

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ΔG" data of PI30-COOH. It is informative to examine some detail of this fitting, that is, contributions of respective component functions to the theoretically calculated modulus. For this purpose, Figure S5 shows those contributions

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g' (in the ω-domain) utilized for fitting the storage modulus

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ΔG ' data of PI30-COOH at -20˚C. (Here, we focus on

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ΔG ' because

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ΔG ' is much more sensitive to the slow relaxation modes of our interest as compared to

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ΔG" .) The excellent fit of the data of PI30-COOH at -20˚C was attained with the fitting parameter value of rd = 1.1, and all other parameters were determined from independent experiments or calculated from this rd value: ra/rd = 4.21 from IR data (cf. Figures 3 and 4 in the main text), τ1 = 56 s (cf. Figure S4c in the previous section), and ra = rd {ra/rd} = 4.63. At low ω, the moduli calculated for the unimer and dimer,

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g1' and

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g2 ' (black curves), are largely contributed from the modes newly created by the motional coupling,

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g1− 2e ' and

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g1− 2o ' for the unimer and

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g2e− 1 ' and

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g2e− 2o ' for the dimer, as noted in Figure S5. These contributions are negligibly small at sufficiently high ω, increase on a decrease ω to the terminal relaxation frequency, and then decrease on a further decrease of ω, thereby showing peaks in Figure S5. Correspondingly, the calculated moduli at high ω are dominated by the Rouse modes split by the motional coupling,

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g1eo ' for the unimer, and

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g2e ' and

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g2o ' for the dimer. The ω dependence of the calculated moduli

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g1' and

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g2 ' is determined by a delicate balance of those newly created modes and split Rouse modes.

References

1. Chen, Q.; Matsumiya, Y.; Masubuchi, Y.; Watanabe, H.; Inoue, T. Component Dynamics in Polyisoprene/ Poly(4-tert-butylstyrene) Miscible Blends. Macromolecules 2008, 41, 8694-8711.

2. Watanabe, H.; Chen, Q.; Kawasaki, Y.; Matsumiya, Y.; Inoue, T.; Urakawa, O. Entanglement Dynamics in Miscible Polyisoprene/Poly(p-tert-butyl styrene) Blends. Macromolecules 2011, 44, 1570-1584.

3. Watanabe, H. Viscoelasticity and Dynamics of Entangled Polymers. Prog. Polym. Sci. 1999, 24, 1253-1403. 4. Okamoto, H.; Inoue, T.; Osaki, K. Viscoelasticity and Birefringence of Polyisoprene. J. Polym. Sci. B. Polym. Phys.

1995, 33, 417-424. 5. Watanabe, H.; Matsumiya, Y.; Masubuchi, Y.; Urakawa, O.; Inoue, T. Viscoelastic Relaxation of Rouse Chains

undergoing Head-to-Head Association and Dissociation: Motional Coupling through Chemical Equilibrium. Macromolecules 2015, 48, 3014-3030.

Figure S5. Comparison of normalized theoretical storage moduli of the unimer and dimer,

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g1' and

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g2 ' (black curves) with contributions to those moduli from newly created modes and split Rouse modes (colored curves). These curves were calculated with the parameter, rd = 1.1, that gave excellent fit of the modulus data of PI30-COOH at -20˚C.