Effect of Chain Rigidity on the Decoupling of Ion Motion from

Emmanuel U. Mapesa, Mingtao Chen, Maximilian F. Heres, Matthew A. Harris, Thomas Kinsey, Yangyang Wang, Timothy E. Long, Bradley S. Lokitz, Joshua R...
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Effect of Chain Rigidity on the Decoupling of Ion Motion from Segmental Relaxation in Polymerized Ionic Liquids: Ambient and Elevated Pressure Studies Zaneta Wojnarowska,*,† Hongbo Feng,∥ Yao Fu,# Shiwang Cheng,† Bobby Carroll,∥ Rajeev Kumar,‡,§ Vladimir N. Novikov,∥ Alexander M. Kisliuk,† Tomonori Saito,† Nam-Goo Kang,∥ Jimmy W. Mays,†,∥ Alexei P. Sokolov,†,∥,⊥ and Vera Bocharova*,† †

Chemical Sciences Division, ‡Center for Nanophase Materials Sciences, and §Computational Sciences & Engineering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States ∥ Department of Chemistry and ⊥Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, United States # Department of Aerospace Engineering & Engineering Mechanics, University of Cincinnati, Cincinnati, Ohio 45220, United States S Supporting Information *

ABSTRACT: Conductivity in polymer electrolytes has been generally discussed with the assumption that the segmental motions control charge transport. However, much less attention has been paid to the mechanism of ion conductivity where the motions of ions are less dependent (decoupled) on segmental dynamics. This phenomenon is observed in ionic materials as they approach their glass transition temperature and becomes essential for design and development of highly conducting solid polymer electrolytes. In this paper, we study the effect of chain rigidity on the decoupling of ion transport from segmental motion in three polymerized ionic liquids (polyILs) containing the same cation−anion pair but differing in flexibility of the polymer backbones and side groups. Analysis of dielectric and rheology data reveals that decoupling is strong in vinyl-based rigid polymers while almost negligible in novel siloxane-based flexible polyILs. To explain this behavior, we investigated ion and chain dynamics at ambient and elevated pressure. Our results suggest that decoupling has a direct relationship to the frustration in chain packing and free volume. These conclusions are also supported by coarse-grained molecular dynamics simulations.

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INTRODUCTION

speed up dynamics of the charge carrying units and to improve conductivity.9,10 This can be achieved by lowering the glass transition temperature (Tg) of polymer electrolytes. The mechanism of conductivity where the segmental dynamics of the polymer determine the diffusion of the ions is reminiscent of conductivity in liquids. Currently, design of materials with low Tg encompasses development of polymer electrolytes with high conductivity at room temperature as the major strategy.11 However, at temperatures close to Tg, many of the studied polymer electrolytes yield charge transport significantly faster than the segmental dynamics,12−14 a phenomenon known in superionic glasses, crystals, and proton conductors.15−17 The effective implementation of such time-scale separations (socalled decoupling) of the ion dynamics from segmental dynamics into the design of polymer electrolytes might result in a glassy polymer electrolyte with much higher conductivity. Although fundamental knowledge of the decoupling phenomenon in

Polymer electrolytes are promising candidates to replace conventional liquid electrolytes in various electrochemical devices1,2 due to their nontoxicity, nonflammability, and outstanding mechanical properties.3−5 Within polymer electrolytes, special attention has been paid to synthesis and characterization of polymerized ionic liquids (polyILs) because of their single ion conductivity. The restricted motions of attached (polymerized) ions and fast motion of counterions6 manifested in these materials are advantageous for battery applications. However, the switching from small monomer-like electrolytes to long-chain polymer electrolytes has an adverse effect on the mobility of ions, resulting in an overall decrease of conductivity.7 Nevertheless, the discovery of a novel transport phenomenon found in polymer electrolytes that is not present in small molecular electrolytes could facilitate the development of new strategies to improve their conductivity.8 Many experimental and theoretical works have identified ways to increase conductivity in polymer electrolytes at ambient temperature. It has been shown that accelerating the segmental motions of polymers is the simplest and most efficient way to © XXXX American Chemical Society

Received: June 9, 2017 Revised: July 31, 2017

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DOI: 10.1021/acs.macromol.7b01217 Macromolecules XXXX, XXX, XXX−XXX

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99%, Acros Organics) and 1-methylimidazole (Imi, 99%, Acros Organics) were distilled over CaH2 before use. Toluene was refluxed over sodium overnight before use. All the reactions were carried out under an inert atmosphere. The synthesis procedures are provided below. Synthesis of Poly(N-vinylethylimidazolium). Synthesis of Poly(N-vinylimidazole). The monomer (1-vinylimidazole, 50 g, 0.531 mol) and initiator (AIBN, 0.1 mol %, 0.0872 g, 5.31 × 10−4 mol) along with ∼150 mL of DMF were charged into a round-bottomed flask equipped with a magnetic stirrer. The solution was purged with argon for 20 min and placed in an oil bath. The reaction proceeded at 65 °C for 17 h. The resulting reaction solution was precipitated into ethyl acetate, redissolved in methanol, and reprecipitated into ethyl acetate. The precipitation process was repeated three times. The resulting poly(Nvinylimidazole) was a white powder and was dried under reduced pressure at 40 °C overnight. The isolated yield was ∼54%. According to the literature,23 this reaction condition will give Mn 42 000 g/mol with PDI 1.84. Unfortunately, direct measurements of the molecular weight of polyILs synthesized from this precursor is very challenging and was not performed here because it requires a combination of certain solvents to neutralize the charge of the polymer.

polyILs is important for their rational design, the nature of the decoupling and factors affecting it are not well understood. In the early experimental studies by Sasabe and Saito,18 correlation between the decoupling and the glass-transition temperature (Tg) of polymers was reported, where polymers with high Tg had higher degree of decoupling. In the most recent studies, it has been hypothesized that the decoupling might have a structural origin. For instance, the decoupling has been correlated to the frustration in chain packing in polymers with salt electrolytes.19 The decoupling was also found to increase in more fragile systems.20 An outstanding example of the structural origin of the decoupling has been demonstrated by Ueno and Angell21 where increase in the decoupling was obtained due to addition of small nanoparticles. The underlying mechanism of enhanced diffusion of ions was connected to the formation of inhomogeneity created by nanoparticles. While significant research efforts have been made to ameliorate our understanding about mechanisms of the decoupling, a further understanding of the structural parameters controlling the ion transport is required. In this paper, we examine the effect of polymer chain rigidity on the ion transport of three polyILs containing the same ion− counterion pair. Three aprotic polyILstwo with different side groups connected to rigid vinyl-based backbone and one with a siloxane-based flexible backbonewere synthesized and characterized. The latter demonstrated an impressive room temperature conductivity equal to σdc ≈ 5 × 10−5 S/cm. Because of the single ion conductivity of polyILs, it was possible to develop a deeper insight into the mechanism of the ion transport and its decoupling from the segmental motion, eliminating uncertainties related to the contribution of different ions to the measured conductivity reported for polymer electrolytes22 and ionic liquids. The dielectric measurements performed over wide temperature and pressure ranges were combined with rheological and calorimetric studies to analyze the separation of charge diffusion time scale from segmental dynamics. This analysis revealed a distinct difference in the charge transport between polyILs composed of flexible siloxane and rigid vinyl polymer backbones, especially pronounced under the conditions of high compression. Specifically, in the polyIL with the flexible backbone the decoupling is minimal; however, decoupling increases significantly in the polymer with rigid backbone and semiflexible side groups, reaching the highest value for the polymer with both rigid backbone and side groups. From the analysis of segmental and secondary relaxations, and the comparison of apparent activation volume, the differences in the decoupling were assigned to the frustration in chain packing and the presence of additional free volume that is more pronounced in the rigid chains. These conclusions are supplemented by coarse-grained molecular dynamics (MD) simulations.

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1 H NMR (400 MHz, CD3OD, δ): 1.8−2.3 (br, −CH2CH−), 2.8−3.7 ppm (br, −CH2CH−), 6.6−7.0 ppm (br, −NCHCHN−), 7.0−7.3 ppm (br, −NCHN−). Synthesis of Poly(N-vinylethylimidazolium). Poly(N-vinylimidazole) (5 g) was dissolved in DMF (75 mL) in a round-bottomed flask equipped with a magnetic stirrer. Bromoethane (1.5 equiv, 8.68 g, 5.95 mL) was charged into the reaction flask, and the reaction proceeded at 38 °C for 90 h. Over the course of the reaction, the solution became milky due to the limited solubility of the product. The resulting reaction solution was precipitated into ethyl acetate, redissolved in methanol, and then reprecipitated into ethyl acetate. The precipitation process was repeated three times. The resulting poly(N-vinylethylimidazolium bromide) was dried under reduced pressure at 40 °C overnight. Based on the chemical shift and integration in 1H NMR, the conversion to imidazolium bromide was nearly quantitative, at least 96−97%.

H NMR (400 MHz, CD3OD, δ): 1.3−1.8 (br, −CH2CH3), 2.3−3.2 (br, −CH2CH−), 4.1−4.4 (br, −CH2CH3), 4.5−4.7 ppm (br, −CH2CH−), 7.3−8.2 ppm (br, −NCHCHN−), 9.1−9.8 ppm (br, −NCHN−). TFSI exchange was conducted in methanol with 1.5 equiv of LiTFSI. The product was precipitated into DI water and redissolved in acetone and precipitated into DI water. Precipitation and water rinsing were repeated several times. Synthesis of Poly(N-vinyldiethylene glycol ethyl methyl ether imidazolium). Poly(N-vinylimidazole) (1.77 g) was dissolved in DMF (40 mL) in a round-bottomed flask equipped with a magnetic stirrer. Diethylene glycol−2-bromoethyl methyl ether (1.17 equiv, 5 g) was charged into the reaction flask, and the reaction proceeded at 80 °C for 48 h. The resulting reaction solution was precipitated into ethyl acetate, redissolved in methanol, and then reprecipitated into ethyl acetate. The precipitation process was repeated three times. The resulting poly(N-vinyldiethylene glycol ethyl methyl ether imidazolium bromide) was dried under reduced pressure at 40 °C overnight. Based on the chemical shift and integration in NMR, the conversion to imidazolium bromide was quantitative, 100%. 1

MATERIALS AND METHODS

Materials. 1-Vinylimidazole (99%) was purchased from Alfa Aesar and thermally distilled under vacuum prior to use. N,N-Dimethylformamide (DMF, anhydrous, amine free, 99.9% Alfa Aesar), ethyl acetate (ACS, BDH), methanol (ACS, BDH), bromoethane (>99%, Sigma-Aldrich), diethylene glycol−2-bromoethyl methyl ether (>94%, TCI), and lithium hexafluorophosphate (LiPF6, 98%, Alfa Aesar) were used as received. Azobis(isobutyronitrile) (AIBN, 98%, Sigma-Aldrich) was recrystallized from methanol prior to use. Polymethylhydrosiloxane (PMHS, MW ∼ 2400 g/mol, Gelest), platinum(0)−1,3-divinyl-1,1,3,3tetramethyldisiloxane complex solution in xylene, Pt ∼ 2% (Pt[dvs], Aldrich), and lithium bis(trifluoromethane)sulfonimide (LiTFSI, 99.95%, Aldrich) were used as received. 5-Bromo-1-pentene (B5B, B

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H NMR (400 MHz, CD3OD, δ): 2.3−3.2 (br, −CH2CH−), 3.4 (br, −OCH 3 ), 3.5 −3.9 (br, −OC H 2 C H 2 O−) , 3 . 9−4.1 ( br, −NCH2CH2O−), 4.2−4.6 (br, −NCH2CH2O−), 4.6−4.8 ppm (br, −CH2CH−), 7.3−8.2 ppm (br, −NCHCHN−), 9.0−9.8 ppm (br, −NCHN−). TFSI exchange was conducted in methanol with 1.5 equiv of LiTFSI. The product was precipitated into DI water and redissolved in acetone and again precipitated into DI water. Precipitation and water rinsing were repeated several times. Similar PolyILs where an oligomer of ethylene glycol was attached to the styrene type imidazolium-based monomer were reported earlier showing promising RT conductivity.24 Synthesis of Polymethylhydrosiloxane-graft-5-Imidazolium1-pentene Bis(trifluoromethane)sulfonamide (Poly-MHSIm TFSI). Synthesis of Polymethylhydrosiloxane-graf t-5-Bromo-1-pentene (Poly-MHSIm B5B). To a predried two-neck round-bottom flask equipped with a condenser, a rubber septum, and a magnetic stirrer was added PMHS (2.0 g, 0.84 mmol) and B5B (5.0 g, 33.6 mmol, 40 equiv) The reactor was purged with Ar for 20 min followed by the addition of Pt[dvs] (30 μL). The reaction mixture was then stirred at 60 °C. The reaction progress was monitored using 1H NMR spectroscopy. Upon the completion of reaction, the solvent was removed and precipitated into excess methanol to obtain brown oil. Yield: 5.9 g, 98%. 1H NMR δ (CDCl3, 500 MHz): 3.41 (−CH2−Br); 1.86 (−CH2CH2−Br); 1.28− 1.53 (−CH2CH2−); 0.53 (Si−CH2); 0.07 (Si−CH3). Synthesis of Polymethylhydrosiloxane-graf t-5-Imidazolium-1pentene Bromide (Poly-MHSIm Br). To a two-neck round-bottom flask equipped with a condenser and a magnetic stirrer was added the solution of PMHS-B5B (2.4 g, 0.36 mmol) in DCM (30 mL) and 1methylimidazole (1.03 g, 12.5 mmol, 35 equiv). The reaction was stirred at 70 °C for 72 h. Upon the completion of the reaction, the solvent was removed under reduced pressure, and the product was recovered by washing with DCM three times and drying in a vacuum oven at 40 °C. Yield: 3.2 g, 98%. 1H NMR δ (D2O, 500 MHz): 8.95 (NCHN); 7.56 (CH3NCHCHN); 4.26 (NCH2−); 3.95 (N−CH3); 2.14−1.27 (4H, −CH2−CH2−); 0.58(Si−CH2); 0.10 (Si−CH3). Mass (ESI) m/z: 78.92 (Br). Synthesis of Polymethylhydrosiloxane-graf t-5-Imidazolium-1pentene Bis(Trifluoromethane)sulfonamide (Poly-MHSIm TFSI). To a one-neck round-bottom flask equipped with a magnetic stirrer was added the solution of PMHSIm-Br (1.0 g, 0.11 mmol) in deionized water (DI H2O) (20 mL) followed by the addition of LiTFSI (1.3 g, 6.9 mmol, 64 equiv). The mixture was stirred at room temperature for 7 days. The precipitation was further washed with DI-H2O three times and dried in a vacuum oven at 40 °C. Yield: 1.5 g, 99%. 1H NMR δ (acetoned6, 500 MHz): 8.87 (NCHN); 7.66 (CH3NCHCHN); 4.30 (NCH2−); 4.02 (N−CH3); 2.03−1.30 (4H, −CH2−CH2−); 0.61 (Si−CH2); 0.13 (Si−CH3). Mass (ESI) m/z: 279.92 (TFSI). 1

Special care was taken to remove any water from the samples. Before any measurements, the samples were extensively dried in the vacuum oven at temperature above 393 K for 3−4 days in the differential scanning calorimetry (DSC) pan or in the dielectric cell. Samples were sealed and transferred to the dielectric spectrometer or DSC system, where they were further heated at ∼393 K for 30−60 min in a nitrogen atmosphere to remove surface water and to further equilibrate the sample before measurements. In DSC measurements, several heating and cooling cycles were performed until the Tg value was unchanged. The Tg obtained from DSC was used as a reference for BDS measurements. Dielectric Measurements at Ambient and Elevated Pressure. Isobaric dielectric measurements at ambient pressure from 10−1 to 107 Hz were carried out using a Novocontrol GMBH Alpha dielectric spectrometer. For the isobaric measurements, the samples were placed between two stainless steel electrodes of the capacitor with a gap of 0.1 mm. The dielectric spectra of polyILs were collected over a wide temperature range. The temperature was controlled by the Novocontrol Quatro system with the use of a nitrogen gas cryostat. Temperature stability of the samples was better than 0.1 K. For the pressuredependent dielectric measurements, we have used the same capacitor, filled with the examined sample, which was then placed in the highpressure chamber and compressed using the silicone oil. Note that during the measurement the sample was in contact with stainless steel and Teflon. Pressure was measured by the Nova Swiss tensometric pressure meter with a resolution of 0.1 MPa. The temperature was controlled within 0.1 K by means of a liquid flow provided by a Julabo thermal bath. Rheological Measurements. Small-amplitude oscillatory shear (SAOS) measurements were carried out on a stress-controlled rheometer AR2000ex (TA Instruments) with a parallel plate of 4 mm in diameter. The gap between the plates is 1000 μm. For poly-MHSIm TFSI, we measured the spectra of angular frequency range from 100 to 0.1 rad/s at different temperatures from 243 to 423 K with an interval of 1 K close to the liquid glass transition and 5 K in the supercooled liquid state. For poly-EGIm TFSI, we measured the spectra at temperatures from 268 to 403 K with a temperature interval of 5 K. For the polyEtVIm TFSI sample, the temperature range was from 348 to 453 K. The amplitude changes with the temperatures and is set to around 0.03% close to Tg that increases to 1% at temperatures above 373 K. Differential Scanning Calorimetry (DSC) Measurements. DSC measurements were performed on TA Q2000. The samples were hermetically sealed in aluminum pans while using an empty pan for reference. These samples were initially equilibrated at 383 K for 30 min, then cooled down to 183 K, and heated up to 453 K. The heating and cooling cycle was performed with a rate of 10 K/min and repeated three times to make certain the results were reproducible. The glass transition C

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Macromolecules Table 1. Physicochemical Properties of Studied PolyILsa

Tg = glass transition temperature; Tg from DSC scan with heating rate 10 K/min; mP = isobaric fragility; Rσ = decoupling index; α = the fractional Walden exponent; ΔV#σ = activation volume for conductivity; ΔV#s = activation volume for segmental motions. a

quantities (represented with an asterisk) to the physical quantities are t* = t/τ = t/(mσ2/ε)1/2, T* = T/(ε/kB), and q* = q/(4πε0σε). Simulations were executed by first distributing the counterions randomly in a cubic box and then introducing the monomers as per a self-avoiding random walk. 500 chains with 40 beads per chain were simulated using molecular dynamics code, LAMMPS.28 Each chain contained 10 equally spaced charges along the backbone and equal number of neutralizing counterions. After the initial configuration was generated, the overlap between the monomers and counterions was removed by a soft potential, with the Coulombic interaction turned off at this stage. The system was subsequently equilibrated for 1 million time steps with a time step size 0.005τ at the temperature of 1.0ε/kB and zero pressure in the isothermal−isobaric (NPT) ensemble. All types of interaction potentials described above were turned on at this stage. The glass transition temperature, T*g , is estimated through a rapid quench simulation at a cooling rate of 2 × 10−5τ−1. The intersection of two linearly fitted lines in the high- and low-temperature regimes of the specific volume Vsp(ρ−1) versus temperature curves, respectively, indicated the location of T*g . The calculation of the Voronoi volume is conducted through Voro++, which is an open source software library for the computation of the Voronoi diagram.29

temperature was estimated as the midpoint of the step in specific heat on heating. Molecular Dynamics Simulations Details. A coarse-grained model of the charged homopolymers with counterions was developed by modifying the Kremer−Grest bead−spring model.25,26 All monomers/counterions interacted through the modified and truncated Lennard-Jones (LJ) 12−6 potential parametrized by ε (the potential depth) and σ (the intermolecular distance at which the potential equals zero) 12 ⎛⎛ ⎛ σ ⎞6 ⎞ σ ⎞ ULJ(r ) = 4ε⎜⎜⎜ ⎟ −⎜ ⎟⎟ ⎝ r − rEV ⎠ ⎟⎠ ⎝⎝ r − rEV ⎠

(1)

where rEV= 0 for the monomer-monomer interactions and rEV = 2R − σ for the counterion−counterion interactions27 so that R is a measure of the counterion radius. In eq 1, r is the distance between interacting species. The LJ potential was truncated by setting the cutoff distance to be 2.5σ for the neutral monomer−neutral monomer and the oppositely charged monomer−counterion pairs. The cutoff distance was set to be 1.22σ for similarly charged monomer−monomer and counterion− counterion pairs so that it stays purely repulsive. Different values of R were chosen to study the effects of the counterion size. In this work, results for R = 0.5σ are presented, and other details will be presented elsewhere. The bonded interaction between adjacent monomers was described by the finitely extensible nonlinear elastic (FENE) potential Ubond(r ) = − (1/2)(kR 0 2) ln(1 − (r /R 0)2 )

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RESULTS The chemical structures of the studied polyILs are presented in Table 1. Poly-EtVIm TFSI is characterized by a rigid (vinyl) polymer backbone (R) and rigid ethylimidazolium side group (R) and for convenience will be referred to as R-R. Poly-EGIm TFSI contains a rigid polymer backbone and a semiflexible side group (semiF) due to three repeating units of flexible ethylene glycol attached to the rigid imidazolium cation. Thus, in the text below poly-EGIm TFSI will be abbreviated as R-semiF. PolyMHSIm TFSI has a flexible (siloxane) backbone (F) and a rigid side group containing imidazolium cation connected to alkyl chain and will be referred to as F-R. Mechanical Measurements. The segmental mobility of the polymer chain for polyILs was measured by rheology. The dynamic shear loss modulus G′′ for poly-MHSIm TFSI is shown in Figure 1A for the frequency range of 1.5 × 10−2−15 Hz measured at temperatures ranging from 235 to 241 K in steps of 2 K. The master curve is constructed using the time−temperature superposition (TTS) and is presented in Figure 1B. Similar results were also obtained for the other two polyILs (data not shown).

(2)

with R0 = 1.5σ and k = ε/σ . Chain rigidity is introduced by the bending interaction described by the squared cosine potential 2

Ubend(r ) = k bend(cos θ − cos θ0)2

(3)

where θ is the angle between consecutive covalent bond vectors, θ0 is chosen as 2π/3, and kbend = 10ε. The charged monomers and the counterions interacted via a long-range Coulomb potential with a cutoff distance of 10σ after a careful optimization and accuracy so that qiqj Ucoul(r ) = 4πε0εsr (4) where qi is the charge of the monomer/counterion, ε0 is the vacuum permittivity, and the dielectric constant εs is chosen as 50 to simulate the effects of moderately polar polymeric melts. The standard reduced LJ units are used throughout the paper; i.e., all physical quantities are expressed in the units of m, σ, ε, and Boltzmann constant kB unless otherwise stated. Some of the formulas relating reduced or unitless D

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Ambient and High Pressure Dielectric Measurements. The conducting and dynamic properties of polyILs were evaluated using ambient and high pressure BDS measurements. The dielectric response of poly-MHSIm TFSI at ambient pressure for selected temperatures is presented in permittivity (Figure 2A) and conductivity (Figure 2B) formalism. Since the

Figure 1. (A) The imaginary part of the shear response for poly-MHSIm TFSI. (B) Shear relaxation loss spectra scaled by the maximum of G″ plotted as a function of frequency. (C) Mechanical relaxation times plotted as a function of temperature for poly-MHSIm TFSI, poly-EtVIm TFSI, and poly-EGIm TFSI. Solid lines correspond to VFT fits of experimental data. (D) Mechanical relaxation times scaled with Tg/T.

Use of TTS provides an estimate of the segmental relaxation time, τs, over a broad temperature range. The shear modulus relaxation times τs of poly-MHSIm TFSI, poly-EGIm TFSI, and poly-EtVIm TFSI, taken directly from the inverse of G′′(ω) maximum, are plotted as a function of 1000/T in Figure 1C and parametrized by means of the Vogel−Fulcher−Tamman (VTF) equation: ⎛ B ⎞ τs = τ0 exp⎜ ⎟ ⎝ T − T0 ⎠

Figure 2. Representative dielectric relaxation spectra of poly-MHSIm TFSI measured at ambient pressure presented as the imaginary part of dielectric permittivity (A) and as the real part of electric conductivity σ′(f) (B). (C) Temperature dependence of dc conductivity data of polyMHSIm TFSI, TFSI, poly-EtVIm TFSI, and poly-EGIm TFSI. The solid lines denote the VFT and Arrhenius parametrization of experimental data.

(5)

where τ0 is the high-temperature limit of the relaxation time with a typical value of ∼10−13 s; T0 and B are fit parameters. To quantify the steepness of the temperature dependence of τα(T) close to Tg, we calculated fragility parameter, mP, using the VFT parameters: ∂ log(τ ) mP = ∂(Tg /T )

P = const, T = Tg

dielectric data of all studied polyILs are similar, the experimental results are presented only for poly-MHSIm TFSI sample. Dc conductivity, σdc, originating from the translational motions of charge carriers in the electric field dominates the dielectric spectra of poly-MHSIm TFSI (Figure 2). The dc conductivity appears as the plateau region in the real part of complex conductivity function σ′(f) as well as in the steep increase in the dielectric loss ε′′( f) at lower frequencies. Since the ions cannot penetrate into the metallic electrodes and are blocked at their interface, the decrease in σ′( f) associated with the electrode polarization effect is observed at the lowest frequencies.30,31 On the other hand, during cooling, when the mobility of ions dramatically slows down and the contribution of dc conductivity to the σ′(f) spectra also decreases, power law behavior of σ′( f) becomes visible at higher frequencies (Figure 2B). In the permittivity representation, the secondary relaxation (labeled as

(6)

To calculate the values of mP, the glass transition was defined as T at which τs = 1000 s. Poly-MHSIm TFSI has the highest fragility of m = 120, while for poly-EGIm TFSI and poly-EtVIm TFSI the fragility is 92 and 88, respectively (Figure 1D). All these materials are considered fragile. The dynamic fragility was used to calculate the apparent activation volume parameter for structural dynamics, ΔV#s , in ion conducting systems following the equation ΔV s# = 2.303R(dTg /dP)mP

(7)

where dTg/dP describes the pressure sensitivity of structural relaxation. The values of ΔV#s calculated for the studied here polyILs are listed in Table 1. E

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Macromolecules γ-process), originating from local motions, also becomes visible (inset to Figure 2A). Figure 2C presents the temperature dependence of the dc conductivity for all studied polyILs. All samples reveal similar behavior of σdc: a decrease in temperature results in changing the conductivity behavior from a VFT-like to an Arrhenius type with a characteristic crossover observed at a temperature related to Tg for the given system.32−35 The value of log σdc(T−1) at Tg is very different for studied materials and is equal to −8.5, −11, and −13.5 [log(S/cm)] for poly-EtVIm TFSI, poly-EGIm TFSI, and poly-MHSIm TFSI, respectively. The behavior of σdc under various T−P conditions for polyMHSIm TFSI, poly-EGIm TFSI, and poly-EtVIm TFSI is presented in Figure 3. The mobility of charge carriers markedly

where σ0 is the value of dc conductivity at atmospheric pressure, R is the gas constant, and ΔV#σ is an apparent activation volume commonly related to the local volume expansion required for ionic transport. A completely different high-pressure conductivity behavior is observed for poly-MHSIm TFSI (Figure 3A). The log σdc(P) of poly-MHSIm TFSI exhibits a nonlinear dependence on pressure and can be parametrized by means of the following equation:36 ⎛ C ⎞ σdc = σ0 exp⎜ − ⎟ ⎝ P0 − P ⎠

(9)

This relation suggests that ΔV#σ is not constant with pressure for poly-MHSIm TFSI. In such case the common practice is to calculate the apparent activation volume in the limit of ambient pressure using the following equation: ⎛ d log σdc ⎞ ΔV σ# = 2.303RT ⎜ ⎟ ⎝ dp ⎠T

(10)

where T is the temperature of isotherm. Additionally, the characteristic crossover of isothermal log σdc(P) data for poly-MHSIm TFSI seems to occur at the same dc conductivity as at ambient pressure conditions (around 10−14 S/ cm). In contrast, the values of σdc determined at Pg of poly-EGIm TFSI and poly-EtVIm TFSI are markedly lower compared to those measured at Tg and ambient pressure conditions.

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DISCUSSION Presented results clearly demonstrate an increase in Tg with the increase in the rigidity of both backbone and side groups. The difference in Tg reaches 111 K (Table 1) between rigid (R-R poly-EtVIm TFSI) and the flexible (F-R poly-MHSIm TFSI) backbones. The Tg of R-semiF poly-EGIm TFSI is lower than that for R-R due to the presence of the flexible ethylene glycol side chains. Chain rigidity also has a significant effect on the dc conductivity. At a given temperature, the conductivity decreases with decrease in flexibility of the polymer chains and the side groups. In our experiments, room temperature (RT) conductivity of the R-R poly-EtVIm TFSI is the lowest while the highest RT conductivity of σdc ≈ 5 × 10−5 S/cm (Figure 2c) is found for F-R poly-MHSIm TFSI with siloxane backbone. Interestingly, RT conductivity of poly-MHSIm TFSI is higher than the values found for phosphonium-based polyILs reported by Colby and co-workers37 but slightly lower than the highest value of σdc reported in the literature for siloxane-based polyILs (σdc = 6.7 × 10−5 S/cm).38 The observed experimental correlation between the rigidity of the polymer chains, their Tg’s, and conductivity is reported in the literature from studies with other ionic materials and constitutes an important tool for the design materials with high ionic conductivity.39−41 The opposite trend of σdc with chain flexibility is obtained when the conductivity data are presented vs Tg/T (Figure 4A). The lowest conductivity at Tg is found for the polyILs with flexible backbone F-R, while R-R poly-EtVIm TFSI is characterized by the highest value of σdc. The origin of such behavior is related to the mechanism of conductivity initially discovered in low molecular weight glass-formers and associated with the decoupling of the ion motion from segmental dynamics.42−45 To understand the microscopic details of the decoupling phenomenon, we compared the values of σdc at Tg for our polyILs (Figure 4A). They are ∼10−8.5, ∼10−11, and ∼10−13.5 S/cm for

Figure 3. Dc conductivity data at elevated pressure of poly-MHSIm TFSI (A), poly-EGIm TFSI (B), and poly-EtVIm TFSI (C) measured under various isothermal conditions.

slows down under pressure, resulting in a dramatic decrease of ionic conductivity. As an example, σdc of poly-MHSIm TFSI decreases by more than 6 decades under the isothermal compression at 260 K (Figure 3A). An important feature shared by all here studied polyILs is the crossover in isothermal pressure dependence of σdc, again reflecting the liquid−glass transition at some pressure Pg. Nevertheless, the studied samples reveal a distinct difference in the pressure dependence. The variations in dc conductivity accompanying isothermal compression of supercooled poly-EtVIm TFSI and poly-EGIm TFSI (Figure 3B,C) follow the equation36 ⎛ P ΔV # ⎞ σ ⎟⎟ σdc = σ0 exp⎜⎜ − ⎝ RT ⎠

(8) F

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Figure 4. (A) The dc conductivity at ambient pressure plotted vs Tg/T. (B) The modified Walden plot constructed for all studied herein polyILs at ambient pressure. (C) The dc conductivity at elevated pressure plotted vs P/Pg. (D) The modified Walden plot constructed for all studied herein polyILs at elevated pressure.

of the Walden plot demonstrates that R-R poly-EtVIm has the highest decoupling characterized by the smallest power law exponent (α) of 0.43; R-semiF poly-EtVIm has α = 0.57, while FR poly-MHSIm TFSI shows the weakest decoupling (α = 0.7). Correlation between the decoupling exponent and chain flexibility found from the Walden plot agrees well with the behavior of the decoupling index (Rσ) at Tg discussed above. This suggests that ion transport is faster than segmental dynamics not only at but also above Tg, which is extremely important for a fundamental understanding of the mechanism of decoupling. The differences in the decoupling are also noticeable in highpressure dielectric studies. In analogy to the plot of log σdc vs Tg/ T, the selected isotherms presented vs P/Pg can be used to analyze the decoupling at Pg (Figure 4C). For low molecular weight ionic glass-formers, the σdc(Pg) is usually of the order ∼10−15 S/cm.51−53 The dc conductivity of R-R poly-EtVIm TFSI at Pg = 250 MPa is 1 order of magnitude lower than at Tg at 0.1 MPa, but the decoupling index is still the largest among studied polyILs (Figure 4C). In contrast, σdc of R-semiF poly-EGIm TFSI compressed isothermally at 303 K reaches the value of 10−15 S/cm already at Pg ≈ 1 GPa, mimicking the behavior of completely coupled F-R poly-MHSIm TFSI. Furthermore, the behavior of σdc(Pg) in poly-MHSIm TFSI remains unchanged under pressure (Figure 3A), resembling the low molecular weight ionic systems. These results indicate that the decoupling of R-R and R-semiF polyILs is pressure-dependent, while polyMHSIm TFSI shows insignificant pressure dependence. To further explore the behavior of decoupling in polyILs with a rigid backbone, we created a Walden plot from the high-pressure data. To construct the Walden plot, we used the time scale of segmental dynamics and conductivity measured at the same temperature and two different pressures: 0.1 MPa and Pg. This approach is based on the assumption that τs at the liquid−glass transition does not depend on the T−P thermodynamic conditions and that it is equal to 103 s.54 The high-pressure Walden plot is presented as solid lines in Figure 4D. The

poly-EtVIm TFSI, poly-EGIm TFSI, and poly-MHSIm TFSI, respectively. According to literature reports,46,47 σdc(Tg) ∼ 10−15 S/cm in ionic systems indicates that the charge transport is fully controlled by the structural relaxation of a given material (e.g., motion of the polymer segments). In all polyILs studied here, the values of σdc at Tg is higher than the typical value for fully coupled systems. As a result, all three TFSI-based polyILs exhibit different degrees of decoupling of ion transport from segmental dynamics. To quantify the magnitude of decoupling, we use a decoupling index defined as Rσ(Tg) = 15 + log σdc(Tg).48,49 This simple approach has been frequently used in the past to estimate the degree of decoupling of the ion conductivity from structural relaxation for various ionic systems without direct measurements of the viscoelastic properties of the materials.50 For our systems, the largest decoupling between the charge transport and segmental relaxation is found for R-R poly-EtVIm TFSI, with Rσ(Tg) = 6.5. The decoupling in R-semiF poly-EGIm TFSI is Rσ(Tg) = 4.0. Furthermore, the exchange of a rigid vinyl backbone to a flexible methylsiloxane chain in the F-R polyMHSIm TFSI resulted in the smallest calculated decoupling, Rσ(Tg) = 1.5. To analyze the decoupling over a broad temperature range, we constructed a modified Walden plot where σdc is plotted vs inverse τs (estimated from rheology) in a double-logarithmic scale (Figure 4B). The “ideal” line in the Walden plot corresponds to the case of complete coupling of ion conductivity to structural relaxation and full dissociation of all ion pairs. It has the slope of 1, corresponding to the case of σdc ∝ τα−1, and is usually normalized to Li or K conductivity in dilute aqueous solutions. The data above this line correspond to the superionic regime with motion of ions faster than structural relaxation, while the data below this line usually indicate bad ion pair dissociation. For the Walden plot analysis, the decoupling between ion conductivity and structural relaxation is characterized by the decoupling exponent ε estimated by fitting experimental data with a power law distribution σdc ∝ τs−α, with ε = 1 − α. Analysis G

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behavior of decoupling in these materials. Furthermore, it appears that in the studied polyILs the values of the decoupling at ambient pressure drastically differ from each other. From Figure 5A, the maximal decoupling is found in the R-R polyIL while in the F-R polymer the decoupling is minimal. Since the R-R and RsemiF polyILs have the same rigid backbone but different decoupling at ambient pressure, to explain this behavior we have to assume that both the polymer backbone and side groups affect the decoupling at ambient pressure. Indeed, from studies of nonionic polymers, it is known that polymers with both rigid backbone and side groups are difficult to pack which is reflected in their high fragility.39 In nonionic polymers by means of MD simulation, it was demonstrated that difficulties in packing of rigid chains resulted in formation of excessive free volume comparing to the flexible chains.41 By computing the temperature dependence of the specific volume of the flexible and rigid ionic polymers (see Figure 1S in the Supporting Information), we came to the same conclusions. The specific volume at Tg is higher in the case of rigid polyILs compared to the flexible ones. Since the van der Waals volume of monomers in the rigid and the flexible polymers are almost the same, the increase in specific volume can be explained only by an increase in free volume. As a consequence, one can hypothesize that the different degree of decoupling in studied polyILs is directly connected to the difference in free volume resulted from the dissimilarity in the packing ability between rigid and flexible chains in polyILs. To explain the experimentally observed changes of decoupling with structure at ambient and high pressure, we need to assume that the amount of free volume is changing in the following manner: R-R > R-semiF > F-R. Furthermore, it is reasonable to assume that amount of free volume should affect the time scale of segmental dynamics and secondary motions of polymers differently due to the sensitivity of these motions to density fluctuations.55,56 The sensitivity of segmental dynamics to pressure, characterized by the pressure coefficient of the glass transition temperature (dTg/dP), is presented in Figure 5B. The smallest value of dTg/dP is observed for R-R poly-EtVIm TFSI (∼75 ± 15 K/GPa), while for F-R poly-MHSIm polyIL this parameter is the largest (∼125 ± 5 K/ GPa). These results indicate that in the polymers with flexible backbones the segmental dynamics under pressure is affected stronger than in the polyILs with rigid backbones. These results can be explained if we assume a minimal free volume for flexible and maximal free volume for rigid polyILs and invoke free volume models.67

decoupling exponent is changing from 0.57 at ambient pressure to 0.92 at elevated pressure for R-semiF poly-EGIm TFSI, while rigid chains show variations in the decoupling exponent from 0.43 to 0.67. It is important to note that to the best of our knowledge, these results are the first time when the change in the decoupling under the pressure is observed for aprotic polyILs. This is in contrast to well-studied low molecular weight aprotic ionic conductors, where the data obtained for isothermal and isobaric pathways superimpose onto each other.51 There might be a number of reasons responsible for suppressed decoupling under pressure. For instance, the pressure-dependent rate of ion dissociation can lead to a reduction of charge carriers. If this would be the leading mechanism, then full coupling between conductivity and segmental motions is expected to happen at the same pressure for polyILs containing the same cation−anion pairs. However, as it is clearly seen from the plot of σdc(Tg) vs pressure (Figure 5A),

Figure 5. (B) Glass transition temperature as a function of pressure for studied polyILs. (A) logσdc at Tg as a function of pressure.

the full coupling (σdc = 10−15 S/cm) in the case of poly-EtVIm TFSI is expected at a pressure much higher than 1 GPa, when poly-EGIm TFSI is already coupled. In contrast, the flexible polyMHSIm TFSI is almost coupled at ambient pressure and its σdc(Tg) shows a very weak pressure dependence. This suggests that another mechanism is responsible for the suppression of the decoupling under pressure. One way to rationalize these results is to connect decoupling to the chemical structure of studied polyILs. From Figure 5A it appears that the slope of logσdc(Tg) plotted as a function of pressure is similar for polyILs with rigid polymer backbone (∼2.97 GPa−1) and drastically larger compared to F-R polymer for which the slope is practically zero. These results suggest that the flexibility of the polymer backbone determines the pressure

Figure 6. (A) Secondary motions found in the systems. (B) Arrhenius behavior of conductivity for polyILs scaled with Tg/T. The activation energy for conductivity (Ea) is determined from linear fit of conductivity. H

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Figure 7. (A) Activation volume for conductivity as a function of temperature. (B) Activation volume for ion and segmental dynamics calculated in the limit of ambient pressure at the liquid−glass transition for flexible and rigid polyILs.

method involves the dynamic modulus coefficient (M) proposed by Ingram:48

Figure 6A presents characteristic relaxation times of secondary motions in the studied polyILs at temperatures much below Tg.57 Two types of secondary relaxations are visible in the BDS spectra of the investigated systems. The β-mode is present only in polyEGIm TFSI and reflects motions of the ethylene glycol chains.58 The γ-relaxation detected in all three studied polyILs correlates with a rotational motion of imidazolium cation.59 Analysis of the γ motions reveals that indeed it is the fastest in the R-R polyIL and is the slowest in the F-R. The activation energy of the γmotions also follows the same trend; i.e., it increases with increase in chain flexibility. The speeding up of secondary motions is expected in the materials with a lower density, which is in line with the idea of excess free volume formed in rigid polymers. Surprisingly, the activation energy (Ea) of dc conductivity obtained from the fitting of the Arrhenius equation to the experimental data at T < Tg is the highest in F-R poly-MHSIm TFSI, while R-R has the lowest Ea (Figure 6B). The change in Ea with chain rigidity means that not only local motions but also ion transport are strongly affected. Taking into account that Coulombic interactions between ion pairs should be comparable in the studied polyILs, the observed increase in the activation energy below Tg found for F-R chains should reflect the difficulty of ions to diffuse. The latter can be a result of the limited available space in the polymer with flexible backbone to initiate the ion diffusion. The opposite is true for R-R polyILs. To explain the suppression of local dynamics and ion transport in F-R, we need to assume a minimal amount of free volume present in this polyIL. The observed correlation between secondary relaxation, decoupling, and chain rigidity is strong, albeit indirect, evidence that supports our hypothesis of free volume controlling charge transport in polyILs. Unfortunately, the direct measurement of free volume is a challenging task. However, some insight into the role of free volume can be obtained from analysis of the activation volume of conductivity and segmental relaxation. Generally, the apparent activation volume ΔV# can be understood as a volume required to start any dynamic processes such as ion jump or structural relaxation. The activation volume for conductivity decreases with increase in temperature in nonlinear fashion (Figure 7A). One of the ways to describe temperature dependence of ΔV# is to use a simple exponential function (Figure 7A). This approach is in line with literature reports for ionic liquids60,61 and nonionic glassformers.36 There are two ways to estimate the conductivity activation volume at Tg. The first approach is based on simple extrapolation of experimentally determined ΔVσ#(T) data while the second

M=

Epact ΔV

#

=

Tg dTg /dP

(11)

Using examples from a few polymer electrolytes, CKN, and some molecular liquids, it was shown that regardless of the relaxation processes studied (dc conductivity or segmental dynamics), the changes in apparent activation energy (Epact = 2.303R(d log σdc/ dT−1)) are proportional to variations of ΔV# with proportionality coefficient M known as dynamic modulus. Therefore, using eq 11, one can quantify the activation volume ΔV#σ at any temperature condition including Tg. The values of the conductivity activation volume at Tg obtained by means of former method are equal to ∼90 cm3/mol for the rigid chain, ΔV#σ ∼ 105 cm3/mol for polyILs characterized by rigid chain and semiflexible side group, and ∼207 cm3/mol for poly-MHSIm TFSI with a flexible backbone (Figure 7B). Importantly, the values of ΔV#σ estimated by means of the latter procedure are notably close to the values obtained from the method of exponential extrapolation. Namely, ΔVσ#(Tg) for poly-MHSIm TFSI is found to be equal 225 ± 15 cm3/mol, while poly-EGIm TFSI and R-R poly-EtVIm TFSI are characterized by much lower ΔVσ# at Tg − 105 ± 12 cm3/mol and 98 ± 20 cm3/mol, respectively. It is notable that the values of ΔVσ# determined for polyILs with a rigid backbone are close to the molar volume of TFSI anion taken from ref 62 (98 cm3/mol). Furthermore, ΔV#σ of flexible poly-MHSIm TFSI is 2 times higher (Figure 7B). At the same time, the activation volume for segmental relaxation determined at the liquid glass transition of two polyILs with rigid polymer chain (ΔV#s ≈ 130−160 cm3/mol) is ∼1.5 times larger than the conductivity activation volume in these materials (Figure 7B). In contrast, for poly-MHSIm TFSI ΔV#sα and ΔV#σ are both above 200 cm3/mol, supporting the idea of the coupling of ion and segmental dynamics in this polymer. To put numbers of activation volume into perspective, it is important to note that in the case of highly decoupled single cation glasses the value of ΔV#σ is similar to the actual sizes of conducting ions. In order to make the “fast hops” the dominating charge transport mechanism in these materials, no additional relaxation of the network is required. So, the behavior of our R-R and R-F polyILs with an activation volume close to the molar volume of TFSI anion at Tg resembles the behavior observed in superionic glasses. We hypothesize that such a situation is possible if ions can easily find a pathway in the material without causing any significant disturbance in the polymer matrix. The latter should correlate with the amount of free volume available I

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Macromolecules in the system. On the other hand, ion hopping in materials with limited free volume will be affected by the polymer segments, which will ultimately result in a larger activation volume required for the hop. This is in agreement with our experimental results for flexible poly-MHSIm TFSI, where the conductivity activation volume is almost 2 times larger than the actual size of the TFSI anion and is comparable to the activation volume of segmental relaxation. The latter suggests that the polymer chain is involved in the ion transport in this polymer. On a side note, in cases of polymer electrolytes with two conducting ions the reported value of ΔV#σ was either smaller than the largest ion or larger than the smallest ions in the system, which caused uncertainties in the data interpretation. On the contrary, in the case of single ion conducting polyILs such uncertainties are excluded. To estimate the free volume at Tg, we use a phenomenological correlation between free volume and activation volume reported in the literature, where the total volume required for ion transport is defined as follows:63

Vtot = Vfree + ΔV #

Figure 8. Free volume of the counterions for R* = R/σ = 0.5 so that Vfree = average Voronoi volume per counterion −4π(R/σ)3/3 and the diffusion constants of the counterions (in units of σ2/ε) as a function of Tg*/T*. It is shown that both the free volume and the diffusion constant of the counterions increase with the introduction of angular potential not only at the glass transition temperature but also at all the temperatures higher than the glass transition temperature.

(12)

where Vfree is free volume while ΔV# is the conductivity activation volume. This equation was used previously where it was experimentally validated for certain temperatures.64 To account for the decrease in the activation volume with temperature65,66 (Figure 7A), Fontanella et al. assumes a constant Vtot for a given material. Then the increase of activation volume with temperature and pressure can be attributed to a decrease in free volume (as per eq 12). If this assumption is correct, then at the Kauzmann temperature (T0) Vfree is diminished, leaving the total volume equal to the activation volume. In such a case, free volume can be calculated as follows: Vfree(Tg) = ΔV #(T0) − ΔV #(Tg) #

agreement with previous studies on neutral homopolymer melts.41 It is clearly seen from Figure 8 that the free volume for the counterions is always larger in rigid polymers compared to the flexible ones when presented as a function of Tg*/T*. Furthermore, higher values of the diffusion constants of the counterions (D) are obtained in the melts of rigid polymer chains in comparison with the flexible ones (Figure 8). Correlating the diffusion constants with the free volume of the counterions suggests that the presence of free volume is the likely reason for the fast ion motion in rigid polymers, in qualitative agreement with the experimental results presented in this paper. From our experimental data and MD simulations, one can clearly conclude that polyILs with well-packed flexible backbones are characterized by a lower free volume, resulting in a substantial slowing down of ion diffusion at the same segmental relaxation time, and a lower degree of the decoupling. On the other hand, rigid chains due to the frustration of packing create some excess intermolecular space (higher free volume) which aids in accelerating ion motion.

(13)

#

where ΔV (T0) and ΔV (Tg) denote the conductivity activation volume at T0 and Tg, respectively. The same exponential functions (Figure 7A) were used to extrapolate ΔVσ# to T0 while the values of T0 were taken directly from fitting of the log σdc(T) data to the VFT equation. The values of Vfree estimated from eq 13 are 2120 ± 70 (at T0 = 235 K), 709 ± 80 (at T0 = 201 K), and 624 ± 50 cm3/mol (at T0 = 194 K) for R-R, R-semiF, and F-R, respectively. This suggest that the structure of polymer plays a preeminent role in the formation of the free volume here; both the polymer chain and side groups contribute to the frustration of chain packing and formation of free volume. However, because of phenomenological nature of eq 12 and failure of the free volume to describe dynamics at high pressures, additional experimental and theoretical efforts have to be applied to further validate conclusions. We have verified the effects of backbone rigidity on the local packing and diffusion of counterions using coarse-grained MD simulations. In particular, the free volume for the counterions was estimated as the difference between the average Voronoi volume and the van der Waals volume of the counterions.67 These results are shown in Figure 8 along with the diffusion constants of the counterions estimated from their mean-square displacements at different temperatures. The temperature is scaled by the glass transition temperature (Tg*), estimated from the change in slope of the specific volume vs temperature curves (shown in the Supporting Information). In particular, for R = 0.5σ, Tg* = 0.40 and 0.53 for the flexible and the semiflexible chains, respectively. An increase in Tg with the introduction of bending penalty in the interaction potential is in qualitative

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CONCLUSIONS We studied the effect of chain rigidity on the ion transport mechanism in three polymerized ionic liquids with different backbone and side group structures, while keeping the ion pair the same. The results of the dielectric measurements combined with mechanical relaxation data have clearly shown that at ambient pressure conditions the charge transport in rigid polyEtVIm TFSI is much faster than the segmental relaxation of the polymer. This result is in contrast with the flexible poly-MHSIm TFSI where these two processes were found to be coupled. In this case, the conductivity of the ions is limited by the rate of the polymer segmental motions. The polymer segmental dynamics can be effectively accelerated by reducing Tg of the materials. The latter is achieved by tuning the structure of the polymer chain. In our study, the highest RT conductivity (5 × 10−5 S/cm) is found in polyMHSIm TFSI with a flexible backbone and is one of the highest values found for dry polyILs. Decoupling of ion motions from the J

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(7) Ogihara, W.; Washiro, S.; Nakajima, H.; Ohno, H. Effect of cation structure on the electrochemical and thermal properties of ion conductive polymers obtained from polymerizable ionic liquids. Electrochim. Acta 2006, 51, 2614−2619. (8) Sangoro, J. R.; Iacob, C.; Agapov, A. L.; Wang, Y.; Berdzinski, S.; Rexhausen, H.; Strehmel, V.; Friedrich, C.; Sokolov, A. P.; Kremer, F. Decoupling of Ionic Conductivity From Structural Dynamics in Polymerized Ionic Liquids. Soft Matter 2014, 10, 3536−3540. (9) Elmahdy, M. M.; Chrissopoulou, K.; Afratis, A.; Floudas, G.; Anastasiadis, F. H. Effect of Confinement on Polymer Segmental Motion and Ion Mobility in PEO/Layered Silicate Nanocomposites. Macromolecules 2006, 39 (16), 5170−5173. (10) Das, S.; Ghosh, A. Effect of plasticizers on ionic conductivity and dielectric relaxation of PEO-LiClO4 polymer electrolyte. Electrochim. Acta 2015, 171, 59−65. (11) Obadia, M. M.; Jourdain, A.; Serghei, A.; Ikeda, T.; Drockenmuller, E. Cationic and dicationic 1,2,3-triazolium-based poly(ethylene glycol ionic liquid)s. Polym. Chem. 2017, 8, 910. (12) Imrie, T.; Ingram, M. D.; McHattie, G. S. Ion Transport in Glassy Polymer Electrolytes. J. Phys. Chem. B 1999, 103 (20), 4132−4138. (13) Wang, Y.; Fan, F.; Agapov, A. L.; Yu, X.; Hong, K.; Mays, J.; Sokolov, A. P. Design of superionic polymersNew insights from Walden plot analysis. Solid State Ionics 2014, 262, 782−784. (14) Wang, Y.; Fan, F.; Agapov, A. L.; Saito, T.; Yang, J.; Yu, X.; Hong, K.; Mays, J.; Sokolov, A. P. Examination of the fundamental relation between ionic transport and segmental relaxation in polymer electrolytes. Polymer 2014, 55, 4067−4076. (15) Angell, C. A. Fast ion motion in glassy and amorphous materials. Solid State Ionics 1983, 9−10, 3−16. (16) Ingram, M. D.; Imrie, C. T. New insights from variabletemperature and variable-pressure studies into coupling and decoupling processes for ion transport in polymer electrolytes and glasses. Solid State Ionics 2011, 196, 9−17. (17) Wojnarowska, Z.; Paluch, Z. Recent progress on dielectric properties of protic ionic liquids. J. Phys.: Condens. Matter 2015, 27 (7), 073202. (18) Sasabe, H.; Saito, S. Relationship between Ionic Mobility and Segmental Mobility in Polymers in the Liquid State. Polym. J. (Tokyo, Jpn.) 1972, 3, 624. (19) Wang, Y.; Agapov, A. L.; Fan, F.; Hong, K.; Yu, X.; Mays, J.; Sokolov, A. P. Decoupling of Ionic Transport from Segmental Relaxation in Polymer Electrolytes. Phys. Rev. Lett. 2012, 108, 088303. (20) Agapov, A. L.; Sokolov, A. P. Decoupling Ionic Conductivity from Structural Relaxation: A Way to Solid Polymer Electrolytes? Macromolecules 2011, 44, 4410−4414. (21) Ueno, K.; Angell, C. A. On the Decoupling of Relaxation Modes in a Molecular Liquid Caused by Isothermal Introduction of 2 nm Structural Inhomogeneities. J. Phys. Chem. B 2011, 115 (48), 13994− 13999. (22) Pas, S. J.; Ingram, M. D.; Funke, K.; Hill, A. J. Free volume and conductivity in polymer electrolytes. Electrochim. Acta 2005, 50, 3955− 3962. (23) Green, M. D.; Salas-de la Cruz, D.; Ye, Y.; Layman, J. M.; Elabd, Y. A.; Winey, K. I.; Long, T. E. Alkyl-Substituted N-Vinylimidazolium Polymerized Ionic Liquids: Thermal Properties and Ionic Conductivities. Macromol. Chem. Phys. 2011, 212, 2522−2528. (24) Jia, Z.; Yuan, W.; Sheng, C.; Zhao, H.; Hu, H.; Baker, G. L. Optimizing the electrochemical performance of imidazolium-based polymeric ionic liquids by varying tethering groups. J. Polym. Sci., Part A: Polym. Chem. 2015, 53, 1339−1350. (25) Kremer, K.; Grest, G. S. Dynamics of entangled linear polymer melts: A molecular-dynamics simulation. J. Chem. Phys. 1990, 92, 5057. (26) Wong, C.; Clarke, J. H. R. Molecular dynamics simulation of microstructure and counterion transport in dry ionic heteropolymers. J. Chem. Phys. 2002, 116, 6795. (27) Liu, J.; Wu, S.; Zhang, L.; Wang, W.; Cao, D. Molecular dynamics simulation for insight into microscopic mechanism of polymer reinforcement. Phys. Chem. Chem. Phys. 2011, 13, 518−529. (28) Plimpton, S. J. Comput. Phys. 1995, 117, 1.

structural relaxation is another mechanism of conductivity found in our systems. We have demonstrated that the degree of decoupling increases with increase in chain rigidity. The ambient and high pressure experimental data analyzed in terms of fractional Walden rule, dTg/dP coefficient, and activation volume provided evidence supporting the idea of the free volume controlling the decoupling of ion transport from segmental dynamics. Specifically, the frustration in chain packing and formation of additional free volume were proposed to be the plausible mechanism for the enhanced decoupling found in rigid polyILs. The idea of free volume as a driver for the decoupling was also independently confirmed in our MD simulations. Our finding of a possible mechanism of decoupling provides importance guidance for the design of polymer electrolytes where motion of the ions will be effectively accelerated by creating an additional free volume using rigid fragments in the structure of the polymer electrolytes.

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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.7b01217. Specific volume as a function of temperature in rigid and flexible charged polymers determined from MD simulations (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*(Z.W.) E-mail [email protected]. *(V.B.) E-mail [email protected]. ORCID

Zaneta Wojnarowska: 0000-0002-7790-2999 Hongbo Feng: 0000-0002-8806-6041 Shiwang Cheng: 0000-0001-7396-4407 Rajeev Kumar: 0000-0001-9494-3488 Tomonori Saito: 0000-0002-4536-7530 Nam-Goo Kang: 0000-0003-3492-9080 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by Laboratory Directed Research and Development program of Oak Ridge National Laboratory, managed by UT-Battelle, LLC, for the U.S. Department of Energy. S.C. and A.P.S. acknowledge partial financial support by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division.

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REFERENCES

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DOI: 10.1021/acs.macromol.7b01217 Macromolecules XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.macromol.7b01217 Macromolecules XXXX, XXX, XXX−XXX