The Role of Solvating 12-Crown-4 Plasticizer on Dielectric Constant

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The Role of Solvating 12-Crown‑4 Plasticizer on Dielectric Constant and Ion Conduction of Poly(ethylene oxide) Single-Ion Conductors U Hyeok Choi† and Ralph H. Colby*,‡ †

Department of Polymer Engineering, Pukyong National University, Busan 48547, Korea Department of Materials Science and Engineering, Pennsylvania State University, University Park, Pennsylvania 16802, United States

‡

S Supporting Information *

ABSTRACT: The role of solvating plasticizer on lithium ion conduction is investigated for a poly(ethylene oxide)-based single-ion conductor, plasticized with 12 wt % 12-crown-4 (12C4). The addition of 12C4 not only increases the static dielectric constant (εs) but also accelerates the ion rearrangement (α2) and segmental motion (α) compared to the host ionomer. A physical model of electrode polarization is used to estimate number density of simultaneously conducting ions and their mobility. The complex of 12C4 with lithium cation lowers the activation energy of simultaneously conducting ions, increasing the simultaneously conducting ion content by >3×. This is consistent with an initial large increase in εs, which is higher than the prediction from the Landau and Lifshitz mixing rule, reflecting that ion aggregates observed in the host ionomer are solvated by 12 wt % 12C4. Furthermore, the dissolution of the aggregates promotes ion mobility owing to an increase in polymer chain flexibility, with a reduction in glass transition temperature. The plasticization directly boosts ionic conductivity of the plasticized ionomer by ∼5× over the whole temperature range studied, revealing that ion motion is assisted by segmental dynamics. transference number less than 0.5,16,17 limiting power density and recharging rates due to anion concentration polarization.18,19 To overcome this challenging issue, of considerable interest are single-ion conductors wherein anions are covalently attached to polymers, thereby achieving Li+ transference numbers close to unity.20−24 Previously, a series of PEObased sulfonated polyester ionomers were synthesized by a twostep melt polycondensation process20 and extensively investigated with the objective of understanding the ion transport mechanism in polymeric single-ion conductors using various experimental25−30 and computational31,32 methods. These sulfonated ionomers with Li+ counterions, however, exhibit room temperature conductivities that are still lower than the minimum practical requirement for single-ion conductors.33 Analysis of electrode polarization in dielectric spectroscopy25 reveals that only a tiny fraction of Li+ counterions are simultaneously participating in conduction, owing to the strong binding energy between Li+ and SO3−, evaluated by ab initio calculations.26,32 This was consistent with strong ionic aggregation in these ionomers, observed by X-ray,26,27 QENS,30 and NMR28 studies. An easy approach to enhancing ionic conductivity in singleion conductors is to introduce solvating plasticizers, which increase polymer chain flexibility by increasing free volume that

1. INTRODUCTION A battery is an electrochemical device consisting of a positive and a negative electrode separated by an electrolyte, which enables ion transfer between the two electrodes. The system makes it possible to store electrical energy as chemical energy during the charging process and release the energy as electrical output during the discharging process.1 Among various battery systems, the most successful rechargeable battery technology is the Li-ion battery (LIB), which was first commercialized by Sony Inc. in 19912 and has been widely used in a variety of portable electronic devices because of long cycle life, high energy and power densities.3−5 More sustainable technologies (for example, the Li−O2 and Li−S systems) have been also the focus of recent research due to their potentially higher energy density.1,6,7 However, the current commercial LIB uses liquid electrolytes (consisting of polar organic liquids with lithium salts), which cause safety issues (such as flammability and explosion), hence limiting the use on a large scale.8,9 Since Wright et al. discovered ionic conductivity in poly(ethylene oxide) (PEO) complexes with alkali metal salt,10 polymer electrolytes are of great interest as promising solutions to substitute for conventional liquid electrolytes owing to their low flammability, good electrochemical stability, and ease of processing.11−13 PEO with lithium salts is one candidate for the solid polymer electrolytes and has been widely investigated.10,14,15 Although PEO/salt electrolytes with large anions [i.e., N(SO2CF3)2−] have low lithium cation dissociation energy, hence exhibiting high conductivities, these mixtures (the anion and cation being both mobile) have Li+ © XXXX American Chemical Society

Received: March 2, 2017 Revised: June 26, 2017

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Macromolecules lowers the glass transition temperature (Tg) as well as promote the dissociation of ions, thereby increasing the number of available charge carriers.34,35 We conducted an extensive investigation of the influence of solvating plasticizers on ion conduction and dielectric response of polysiloxane single-ion conductor blends with poly(ethylene glycol) (PEG)34 and polysiloxane polar copolymers.35 The addition of the plasticizers into the ionomer affected dielectric constant and segmental dynamics, leading to an increase in both the number density of simultaneously conducting ions and their mobility. The X-ray and FTIR studied by O’Reilly et al. on plasticized PEO-based sulfonated polyester ionomers showed that the size of ionic aggregates decreased as PEG plasticizer is added.36 The dissolution of aggregates into ion pairs promoted ion conduction. The focus of the present study is the effects of the addition of the crown ether that Li+ prefers on ion conduction of a plasticized single-ion polymer conductor. The crown ether contains hydrogen, carbon, and oxygen atoms, with each oxygen atom bound between two carbon atoms to form a ring, which usually act as a host for certain metallic cations (i.e., Li, Na, and K).37 The complex of crown ether with a small cation is formed by ion-dipole interaction between the cation and the lone pairs of electrons in the oxygen atoms in the ring structure of the cyclic polyether.38,39 Therefore, much interest has been focused on the effects of crown ethers on the electrochemical properties of solid polymer electrolyte systems. Some of the earliest work using crown ether in polymer−salt complexes was that of Kaplan et al., who observed the effect of the addition of crown ether to poly(vinylene carbonate) containing LiCF3SO3.40,41 Nagasubramanian et al. showed that the addition of 12C4 to PEO electrolytes containing LiCF3SO3, LiBF4, or LiClO4 improved the ionic conductivity of the PEO electrolytes.42,43 The Matsuda group investigated the effects of 12C4 or 15C5 on the conducting behavior of complexes of PEO-grafted poly(methyl methacrylate) and lithium salts: the improvement in the ionic mobility and transference number of Li+ was observed in the plasticized electrolytes.44 12C4 was also investigated as an electrolyte solvent for light-emitting electrochemical cells45 and lithium/air batteries,46 and the additive 12C4 improved their electrochemical performance. Although improvement of ionic conductivity by plasticization has been well established in the polymer/salt systems, the role of the plasticizer in the conduction mechanism is far from being fully understood. In the current investigation, 12C4, whose cavity is large enough to fit one lithium cation, is added to a lithium-neutralized PEO-based single-ion conductor (PEO49Li) with the structure shown in Figure 1. 12C4 is known to have a strong sequential bond dissociation energy when interacting with Li+, of 372 kJ/mol,47 and this allows 12C4 to remain in our ionomer despite the high vapor pressure of 12C4. Herein, the role of 12C4 on the segmental dynamics and ion conduction of single-ion conductors such as dielectric constant, dielectric relaxations, ionic conductivity, concentration of simultaneously charge carriers, and their mobility is reported using dielectric relaxation spectroscopy. Understanding experimental observations in these materials provides useful insights for the design of single-ion conductors for energy applications.

Figure 1. Chemical structures of a poly(ethylene oxide)-based ionomer (PEO-49Li) having ionic isophthalate group (X = 49 mol %) and nonionic isophthalate group (1 − X = 51 mol %) as a random copolymer and the plasticizer, 12-crown-4 (C8H16O4, 12C4). mol % nonionic isophthalate group and the plasticizer, a 12-crown-4 (C8H16O4, referred to as 12C4). The ionomer was synthesized by a two-step melt condensation reaction, as described earlier.20 12C4 was purchased from Tokyo Chemical Industry and used as received. Pure ionomer PEO-49Li, pure plasticizer 12C4, and one mixture with 33 wt % 12C4 were weighed into 10 mL vials. These materials were stored inside desiccators for 50 days before measurement in order to provide enough time for 12C4 to fully diffuse into the ionomer. Dielectric Relaxation Spectroscopy (DRS). Dielectric spectroscopy measurements were conducted on samples that were prepared by allowing them to flow to cover a 3 cm diameter freshly polished brass electrode. To control the sample thickness at 50 μm, silica spacers were placed on top of the sample after it flowed to cover the electrode. Then, a 1 cm diameter freshly polished brass electrode was placed on top, and gravity formed a 50 μm parallel plate capacitor cell as the extra sample was squeezed away (with precise thickness verified after dielectric measurements were complete). The sandwiched samples between two electrodes were placed in the Novocontrol GmbH Concept 40 broadband dielectric spectrometer, after being dried in a vacuum oven at 80 °C for 24 h. The dielectric permittivity was measured using an AC voltage amplitude of 0.1 V for all experiments. Frequency sweeps were performed isothermally from 10 MHz to 0.01 Hz in the temperature range from −20 to 60 °C because the boiling point of 12C4 is between 61 and 70 °C. 1 H NMR. To verify the chemical structure of the blend and to quantitatively determine the amount of 12C4 inside the blend, 1H NMR spectra were recorded on a Bruker DPX-400 spectrometer with XWINNMR software. 20 mg of the PEO-49Li/12C4 mixture after dielectric spectroscopy measurements was dissolved in 0.6 mL of a deuterium oxide solvent (D2O, 99.9%), which was supplied by Cambridge Isotope Laboratories. From the spectra, the actual weight fraction of 12C4 inside the PEO-49Li/12C4 mixture (12 wt %) was estimated (see Supporting Information Figure S1 and Table S1). The final level of 12C4 stops at 12 wt %, where the number densities of Li+ (0.34 nm−3) and 12C4 (0.45 nm−3) are similar, probably indicating that the interaction of 12C4 with Li+ lowers the volatility of 12C4.

3. RESULTS AND DISCUSSION Static Dielectric Constant. Figure 2 shows the angular frequency dependence of the dielectric permittivity spectra ε′(ω) at 298 K, which were horizontally shifted to display the static dielectric constant εs difference among the neat PEO-49Li ionomer, the 12C4 plasticizer, and their PEO-49Li+12C4 blend. The plasticizer 12C4 exhibits the lowest static dielectric constant εs = 13, defined as the low frequency plateau of ε′(ω) before the onset of electrode polarization (EP) (see dashed

2. EXPERIMENTAL SECTION Figure 1 shows the molecular structures of a PEO-based polyester random copolymer ionomer (referred to as PEO-49Li) with 49 mol % ionic sulfonated isophthalate groups with lithium counterions and 51 B

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Figure 2. Dielectric permittivity spectra ε′ at 298 K shifted by horizontal shift factor, a [12C4 (a = 1); PEO-49Li+12C4 (a = 1); PEO-49Li (a = 2.7)], to superimpose in the range 103 < ε′ < 104 and hence compare the static dielectric constants εs, shown as dashed and solid lines, representing the sum of the dielectric constant of all the observed relaxations.48 The inset shows a magnified view of the dielectric permittivity in the range 7 < ε′ < 102.

Figure 3. Temperature dependence of static dielectric constant εs for PEO-49Li, PEO-49Li+12C4, and 12C4 along with the DSC thermogram (solid line) for 12C4.

that the plasticizer 12C4 has a melting phase transition at around Tm = 293 K (see the DSC melting endotherm of 12C4 shown as the solid curve in Figure 3).37 At temperatures below the observed melting transition, the motion of molecules with polar groups is expected to be restricted by the crystallized 12C4, which limits rotation/alignment of dipoles under an applied field, thereby leading to εs increasing on heating near Tm. Upon melting of 12C4, not only the static dielectric constant of the blend follows a similar temperature dependence as those of its host materials but also the enhanced static dielectric constant is observed in the blend. Such a sharp peak in εs near Tm has been observed in polar copolymers blending with semicrystalline plasticizers.35 The composition dependence of εs for the neat ionomer and its blend with 12C4 can be understood through the following Landau and Lifshitz’s dielectric constant mixing rule51

green horizontal line in Figure 2).35 For the neat ionomer and its blend with 12C4, however, ε′(ω) was not clearly observed to plateau before EP but to decrease gradually with increasing frequency, indicating underlying relaxations. Their static dielectric constants (see solid lines in Figure 2) were then obtained from the sum of the dielectric constant of all the observed relaxations (see Figure S2).48 The blend (PEO-49Li +12C4, εs = 31) exhibits higher εs than its host ionomer (PEO49Li, εs = 25) and plasticizer (12C4, εs = 13) at 298 K. The increase in the static dielectric constant arises from the enhanced dipole moment imparted by the ionic groups of sulfonate anions and lithium cations combined with the crown ethers, likely from separated ion pairs, of sulfonate with a 12C4 wrapped Li+ cation. From the previous reports of the neat PEO-based ionomers with lithium counterions,25−27 their ionic species tend to form primarily ion pairs and quadrupoles, the latter having no dipole moment. The stable complexes between crown ethers and lithium cations presumably allow the quadrupoles (SO3−Li+)2 to be separated into the ion pair (SO3−Li+), which contributes to an increase of the static dielectric constant. Furthermore, the dipole moments for a sulfonate−Li ion pair and a 12C4−Li complex, obtained using ab initio calculation,25,49 are mpair = 5.5−7 D and mcomplex ∼ 12 D, respectively. Therefore, the complex of 12C4 with Li+ cation would increase an average distance between Li+ and SO3− of ion pairs. This larger distance eventually contributes to an enhanced dipole moment of the average ion pair compared to the case of just contact ion pairs (SO3−Li+). We next consider the temperature dependence of εs for the PEO-based ionomer, the 12C4 plasticizer, and their blend as shown in Figure 3. PEO-49Li, 12C4, and their mixture at T > Tm = 293 K exhibit a decrease in εs with increasing temperature due to thermal randomization of dipoles.50 For the mixture of PEO-49Li and 12C4, however, εs first increases with increasing temperature until about T = 293 K, and then εs begins to decrease with increasing temperature as observed in the neat ionomer and pure plasticizer. This nonmonotonic temperature dependence is explained by the fact

(εsmix )1/3 = (1 − ΦP)(εsI)1/3 + ΦP(εsP)1/3

εmix s ,

εIs,

(1)

εPs

wherein and are the static dielectric constant of the blend, ionomer, and plasticizer, respectively, and ΦP is the weight fraction of the plasticizer. Here we construct, using Landau and Lifshitz’s mixing rule (eq 1), a universal plot for the dielectric constant of various ionomers and their blends with various plasticizers. The data from these materials and other blend systems,21,35,36 listed in Table 1, are combined into a I 1/3 universal plot in Figure 4 by plotting (εmix against ΦP[1 s /εs) − (εPs /εIs)1/3], which reduces to a universal straight line with intercept of 1 and slope of −1 (see the solid line in Figure 4). In this case, the Landau and Lifshitz’s mixing rule, considering the variations in the local field and local dielectric constant,51 seems to predict well the macroscopic permittivity of the ionomer/plasticizer mixtures at higher plasticizer content (above Φp[1 − (εPs /εIs)1/3] = 0.3), whereas εmix at lower s plasticizer concentrations can be above Landau and Lifshitz’s prediction (see Figure 4). This presumably indicates that the ionomer blends with lower plasticizer contents have additional ion dipoles induced by plasticizers,36 providing an additional source of polarization, which cannot be predicted from the dielectric constant values of the pure components (εIs and εPs ) using the Landau and Lifshitz’s mixing rule. Dielectric Relaxations. To assess the effect of 12C4 plasticizer on polymer chain or ion dynamics of the ionomer C

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Macromolecules Table 1. Physical Values of the Landau and Lifshitz’s Composition Dependence (Eq 1) for Various Polar Polymer, Liquid, or Ionomer/Plasticizer Mixtures T = 303K polar polymer, liquid, or ionomer/plasticizer

εIs

εPs

ΦP (wt %)

siloxane copolymer (SC) siloxane homopolymer (SH)b/ PEG ethylene carbonate (EC)/ propylene carbonate (PC) SBC-10Lic/PEG

50 50

6 11

23, 47, 72, 83 8, 13, 32

35 35

93

64

0.5

21, 35

43d

12d

34

PEO-85Lie/PEG PEO-49Li/12C4

18f 24

11f 13

6, 8, 13, 25, 34, 54, 70 5, 10, 25, 50 12

a

ref

36 current work

a

A series of siloxane-based polar copolymers, where the concentrations of cyclic carbonate and oligomeric PEO units are varied.35 b Siloxane-based homopolymer having cyclic carbonate as the only side chain.35 cSiloxane-based ionomer having 10 mol % lithium tetraphenyl borate and 90 mol % cyclic carbonate as randomly placed side chains.34 dεIs and εPs of SBC-10Li/PEG mixture were reported at 298 K.34 ePEO-based polyester random copolymer ionomer with 85 mol % ionic sulfonated isophthalate groups with lithium counterions and 15 mol % nonionic isophthalate group.36 fεIs and εPs of PEO-85Li/PEG mixture were reported at 313 K.36

Figure 5. Dielectric loss (ε″, filled symbols) and derivative (εder, open symbols) spectra at 258 and 293 K for (a) PEO-49Li and (b) PEO49Li+12C4. The solid curves are fits of the sum of a power law for EP and two derivative forms of the HN function for ion rearrangement α2 and polymer segmental motion α to the 293 K εder data (individual contributions shown as dashed lines).

with 12C4 (Figure 5b) at 258 and 293 K. The blend with 12C4 exhibits two dielectric relaxations designated as α and α2 in order of decreasing frequency, as observed for the neat ionomer. The additional dipolar relaxation α2, which has been observed in single-ion conducting ionomers at lower frequencies,25,34,48,53,54 is primarily related to ion rearrangement34,48 (for example, exchanging states between isolated pairs and aggregates of pairs), in addition to the segmental relaxation α involving the typical characteristics of the glass transition dynamics of portions of the material without ions, at higher frequencies. The peak relaxation frequency maxima ωmax and the relaxation strength Δε of both the α2 and α processes were determined from fitting the relaxation to the Havriliak−Negami function (Supporting Information contains how to determine the peak relaxation frequency ωmax and the relaxation strength Δε). The peak relaxation frequencies ωα2 (filled symbols in Figure 6a) and ωα (open symbols in Figure 6a) follow the Vogel−Fulcher−Tammann (VFT) temperature dependence:

I 1/3 Figure 4. Universal plot of (εmix vs ΦP[1 − (εPs /εIs)1/3] for the s /εs) PEO-49Li blend with 12C4 compared with literature values21,34−36 for polysiloxane-based polar copolymers (SC), polysiloxane-based polar homopolymer (SH) blends with poly(ethylene glycol) (PEG), polar liquid ethylene carbonate (EC) blend with propylene carbonate (PC), polysiloxane-based ionomer (SBC-10Li) blends with PEG, and PEObased ionomer (PEO-85Li) blends with PEG. The solid line indicates Landau and Lifshitz’s mixing rule eq 1 with slope of −1 and intercept of 1. The inset shows the compositional variation in εs for the PEO49Li blend with 12C4 at 298 K and for PEO-85Li blends with PEG at 313 K, where Φ12C4 or PEG is the weight fraction of 12C4 or PEG, and the solid curves are eq 1.

blend, dipolar relaxation processes are evaluated using the dielectric derivative spectra52 εder(ω) = −

π ∂ε′(ω) 2 ∂[ln ω]

⎛ DT0 ⎞ ωmax = ω∞ exp⎜ − ⎟ ⎝ T − T0 ⎠

(2)

(3)

The solid and dashed curves in Figure 6a are fit to eq 3 using the Vogel temperature T0, high temperature limiting frequency ω∞, and strength parameter D, as fitting parameters listed in Table 2, for the α2 and α processes. Adding 12C4 into PEO49Li accelerates the ion rearrangement (α2, filled symbols in Figure 6a) as well as the segmental motion (α, open symbols in

elucidating the relaxation processes by removing the pure-loss conductivity contribution which obscures the loss peaks of interest such as ion rearrangement or segmental relaxation (see Figure 5).25,34,48 Figure 5 displays representative derivative spectra of the PEO-49Li ionomer (Figure 5a) and its blend D

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Figure 3, so that the temperature dependence of Δεα2 is similar to that of εs. Ionic Conductivity. In order to understand the influence of plasticizer on ionic conductivity of PEO-based single-ion conductors, the temperature dependence of DC conductivity σDC shown in Figure 7 is estimated from an approximately 3

Figure 7. Temperature dependence of ionic conductivity σDC for the neat ionomer (PEO-49Li) and its blend with 12C4 (PEO-49Li +12C4). Solid curves are eq 11 with parameters (listed in Table 3) Ea and p∞ (determined by an Arrhenius fit to simultaneously conducting ion content p, Figure 9) and μ∞, D, and T0 (determined by a VFT fit to mobility μ, Figure 10) of those conducting ions. There are two solid curves for the blend because both p and μ change character when a portion of the 12C4 crystallized. The inset shows the normalized conductivity σnor = σblend/σionomer of the ionomer blends with various plasticizers such as PEG,34,36 polysiloxane polar copolymers,35 and polar solvents55 [ethylene glycol (EG), propylene carbonate (PC), and dioctyl phthalate (DOP)].

Figure 6. Temperature dependence of (a) relaxation frequency maxima ωmax and (b) relaxation strengths Δε to the α (open symbols) and α2 (filled symbols) processes. Solid and dashed curves are fits of the VFT equation (eq 3).

Figure 6a). This is consistent with the decrease of DRS Tg (from 237 to 228 K), obtained by extrapolating the VFT fits of the α process (dashed curves in Figure 6a) to 0.01 rad/s, listed in Table 2. The DRS Tgs are also in good agreement with the calorimetric glass transition temperature (denoted DSC Tg) within experimental uncertainty (see Table 2 and Figure S3). This confirms that the α relaxation process observed at higher frequencies (Figure 5) corresponds to the typical dynamic characteristics of the glass transition. In the neat and plasticized ionomers, the relaxation strength for the α2 process (Δεα2, filled symbols in Figure 6b) is larger than that for the α process (Δεα, open symbols in Figure 6b). Increasing 12C4 content from 0 to 12 wt % raises Δεα2 from 15 to 22 at 298 K, suggesting that a small amount of 12C4 allows more ions to rearrange in the α2 process, consistent with 12C4 favoring more separated ion pairs. The stronger α2 process primarily determines the static dielectric constant εs, shown in

decade frequency range where the in-phase part of the conductivity σ′(ω) = ε″(ω)ε0ω is independent of frequency (see Figure 8). The conductivity of the neat ionomer PEO-49Li is relatively low (σDC ∼ 2 × 10−7 S/cm at 25 °C), owing to the formation of ionic aggregates containing multiple ion pairs of Li+SO3− as reported previously.26,27 After mixing PEO-49Li with 12 wt % 12C4, its room temperature conductivity (σDC ∼ 1 × 10−6 S/cm) is almost 5 times higher than the neat ionomer, and plasticization increases the conductivity over the whole temperature range studied (see Figure 7). The inset in Figure 7 displays the composition dependence of the normalized conductivity (σnor = σblend/ σionomer) of ionomer blends with various plasticizers, where each blend conductivity σblend was divided by its corresponding ionomer conductivity σionomer. This reflects that upon addition

Table 2. Fitting Parameters of the VFT Temperature Dependence (Eq 3) of the α2 and α Processes and DRS and DSC Glass Transition Temperatures α2 process

α process

sample

log(ω∞) (rad/s)

D

T0 (K)

log(ω∞) (rad/s)

D

T0 (K)

DRS Tga ± 10 (K)

DSC Tgb ± 3 (K)

PEO-49Li PEO-49Li+12C4

9.7 10.8

6.5 8.2

191 183

10.6 11.7

4.8 7.3

203 185

237 228

240c 230d

a Tg determined from dielectric relaxation spectroscopy (defined at ωα(Tg) = 10−2 rad/s). bTg determined from differential scanning calorimeter (DSC) using 10 K/min heating and cooling rates. cValue from ref 25. dDSC thermograms of PEO-49Li+12C4 are in Supporting Information Figure S3.

E

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wherein εEP is the (considerably larger) effective permittivity after the electrode polarization is complete (see Figure 8). The Macdonald and Coelho model57−60 treats electrode polarization as a simple Debye relaxation with loss tangent ωτEP tan δ = 1 + ω 2τστEP (6) allowing a two-parameter fit (see Figure S4) to determine the electrode polarization time τEP and the conductivity time τσ. The Macdonald and Coelho model then determines the number density of simultaneously conducting ions p and their mobility μ from τEP and τσ 2 1 ⎛ τEP ⎞ p= ⎜ ⎟ πlBL2 ⎝ τσ ⎠

Figure 8. Dielectric response of a blend (PEO-49Li+12C4) to applied AC field at T = 298 K: dielectric constant (ε′, green squares), dielectric loss (ε″, red circles), loss tangent (tan δ, blue triangles), and in-phase part of conductivity (σ′, orange diamonds). The peak of the loss tangent gives the geometric mean of the time scales of conductivity and electrode polarization [(τEPτσ)1/2, dashed lines], then determining the number density of simultaneously conducting ions p and their mobility μ.

μ=

(7)

eL2τσ 4τEP 2kT

(8)

wherein lB ≡ e /(4πεsε0kT) is the Bjerrum length, L is the spacing between electrodes, k is the Boltzmann constant, and T is absolute temperature. The EP analysis has been recently done for various single-ion conductors.20,21,25,34,36,53,54,57,61−65 Figure 9 compares the fraction of cations simultaneously participating in conduction (p is normalized by p0, listed in 2

of a relatively small amount (10 wt %) of plasticizers, the conductivity can be enhanced by 10× (1 < σnor ≤ 10). It has been observed that the addition of crown ethers to organic solutions of Li salts enhances the ionic conductivity.56 The affinity of oxygen in the crown ether toward Li+ encourages ionic dissociation of the salt in the solution. Therefore, the enhanced conductivity from incorporation of 12C4 is not only from solvation, as the ether oxygen dissolves ion aggregates by stabilizing Li+, boosting the concentration of simultaneously conducting lithium ions, but also from lowering Tg by reducing the physical cross-linking, enhancing the lithium ion mobility. To demonstrate these two effects, electrode polarization is next analyzed to determine the number density of simultaneously conducting Li+ cations p and their mobility μ. Conducting Ion Content and Mobility. Simultaneously conducting ion content p and their mobility μ were determined from a physical model of electrode polarization (EP),25,53,57 allowing to separate ionic conductivity σDC into p and μ (since σDC = epμ with e the elementary charge). Electrode polarization occurs at low frequencies, where the transporting ions have sufficient time to polarize at the blocking electrodes during the cycle. That polarization manifests itself in (1) an increase in the effective capacitance of the cell (increasing the apparent dielectric constant) and (2) a decrease in the in-phase part of the conductivity, as the polarizing ions reduce the field experienced by the transporting ions (see Figure 8). The natural time scale for conduction is the time when counterion motion starts to become diffusive εε τσ ≡ s 0 σDC (4)

Figure 9. Temperature dependence of the fraction of cations simultaneously participating in conduction (p divided by the total cation concentration p0). Solid lines are Arrhenius fits to eq 9 with two fitting parameters (Ea and p∞, listed in Table 3).

Table 3, the total cation number density) of the neat ionomer (PEO-49Li) and its blend with 12C4 (PEO-49Li+12C4). The blend exhibits >3 times higher fraction of cations simultaneously participating in conduction (p/p0) compared to the neat ionomer. The temperature dependence of p is well described by an Arrhenius equation ⎛ E ⎞ p = p∞ exp⎜ − a ⎟ ⎝ RT ⎠

wherein εs is the measured static relative permittivity of the sample before EP and ε0 is the permittivity of vacuum. At low frequencies the conducting ions start to polarize at the electrodes and fully polarize at the electrode polarization time scale ε ε τEP ≡ EP 0 σDC (5)

(9)

wherein p∞ and Ea, listed in Table 3, are the conducting ion concentration as T → ∞ and the activation energy for conducting ions, respectively. The fact that p∞ is much smaller than p0 for the blend below the crystallization temperature of 12C4 indicates some of the counterions are too strongly aggregated to participate in ion conduction;34,53,54 6% can F

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Macromolecules Table 3. Fitting Parameters of the Arrhenius Equation for Conducting Ion Content, Eq 9, and the VFT Equation for Conducting Ion Mobility above and below Tt = 293 K where a portion of the 12C4 crystallizes, Eq 10 conducting ion content T > Tt sample PEO-49Li PEO-49Li+12C4 a

p0 (nm−3) 0.39 0.34

a

conducting ion mobility T < Tt

T > Tt

T < Tt

Ea (kJ/mol)

p∞/p0

Ea (kJ/mol)

p∞/p0

μ∞ (cm2 V−1 s−1)

D

T0 (K)

μ∞ (cm2 V−1 s−1)

D

T0 (K)

15.4 13.7

0.89 0.99

b 7.5

b 0.06

0.0016 0.0018

2.6 2.4

212 210

b 0.0031

b 2.8

b 210

Value from ref 25. bThe pure PEO-49Li ionomer does not exhibit a transition in conducting ion content and mobility.

ultimately participate while 94% of the lithium cations are trapped in ion aggregates when a portion of the 12C4 crystallizes. For the neat ionomer PEO-49Li, p∞/p0 is 0.89 (listed in Table 3), reflecting that most of the ions are able to participate in conduction.34,54 Unlike the neat ionomer, its blend with 12C4 shows a transition in conducting ion concentration at Tt = 293 K, 1000/Tt = 3.41 K−1, which is close to the melting temperature of the pure 12C4 (see Figures 3 and 6b). In other words, the blend has two sets p∞S and Ea values, listed in Table 3, one set above and the other below Tt. Above Tt, incorporating a small amount of 12C4 into PEO-49Li results in p∞/p0 ≈ 1 and Ea ∼ 13.7 kJ/mol, indicating that the presence of 12C4 allows ion pairs to be more separated pairs, and then all Li cations are able to take part in conduction with lower activation energy compared to the neat ionomer. Upon the crystallization of 12C4, the activation energy further reduces to Ea ∼ 7.5 kJ/mol, but only 6% (p∞/p0 ∼ 0.06) are not trapped below Tt. This presumably indicates that some fraction of 12C4, that is wrapped around Li+, is not able to crystallize, and although only 6% of the Li cations are in the conducting state with 12C4 wrapping, this state has much lower activation energy (Ea ∼ 7.5 kJ/mol) than either plasticized Li single-ion conductors PEO-85Li/PEG (Ea ∼ 13 kJ/mol)36 or SBC-10Li/ PEG (Ea ∼ 8−14 kJ/mol).34 In any case, both Eas of the blend are lower than that of the neat ionomer (see Table 3), suggesting that ion aggregates observed in the neat ionomer are solvated by 12C4, allowing more lithium cations to participate in conduction. However, the fraction of cations simultaneously participating in conduction is still lower in the temperature range studied, 0.72, the data merge into a single curve, indicating that the effect of 12C4 appears only in the difference in T0. At T0/T < 0.72, however, Li+ ions coordinating with 12C4 have somewhat higher mobility than Li+ ions within the neat ionomer for the same T0/T. The higher ion mobility in the blend may be understood in terms of the lower binding energy of Li cations to the sulfonate anions due to a solvation interaction between Li+ and 12C4 compared to the system without 12C4. This results in a lower energy barrier for cation motion upon addition of 12C4 (above Tt = 293 K). The temperature dependence of σDC(T) shown in Figure 7 has already been evaluated by the Arrhenius fit of p(T) = p∞ exp[−Ea/(RT)] in Figure 9 and the VFT fit of μ(T) = μ∞ exp[−DT0/(T − T0)] in Figure 10: ⎛ ⎛ E ⎞ DT0 ⎞ σDC = eμ∞p∞ exp⎜ − ⎟ exp⎜ − a ⎟ ⎝ RT ⎠ ⎝ T − T0 ⎠

(10)

where μ∞ is the high-temperature limit of the mobility, T0 is the Vogel temperature, and D is the so-called strength parameter (reciprocally related to fragility); those fitting parameters are found in Table 3. The ionic mobility increases upon mixing the ionomer and plasticizer, which goes with the ∼10 K decrease in Tg (see Table 2). Like simultaneously conducting ion content, the blend reveals ionic mobility with a discontinuity at the melting point of pure 12C4. The crystallization of 12C4 results in an increase in D from 2.4 to 2.8 (less fragile) as displayed in

(11)

Equation 11 with parameters listed in Table 3 is shown as the solid curves in Figure 7. The DC conductivity can be further understood using the Barton, Nakajima, and Namikawa (BNN) relation67−70 which is a simple empirical scaling correlation between ionic conductivity σDC and the product of dielectric constant εs and frequency maximum of ion rearrangement ωα2: σDC = Bε0εsωα2 (12) G

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Macromolecules wherein B is the ratio of time scale for ion rearrangement and conduction and ε0 is the vacuum permittivity.48,53,54,71−73 B = 1 indicates that ions move one Debye length in their ion rearrangement time (τα2 = 1/ωα2, reflecting an average time for ion hops). The value of B = 7 for PEO-100Li exhibiting ionic aggregation is higher than that (B = 1.5) for PEO-100Na with fewer ion aggregates (see Figure 11),66 suggesting that more

and segmental dynamics such as ion rearrangement (α2) and segmental motion of regions without ions (α). Upon mixing the ionomer and 12C4, εs increases owing to the 12C4 solvating lithium cations, dissolving ion aggregates, and both α and α2 processes are accelerated due to the 12C4 plasticizing the polymer chain, lowering Tg. Furthermore, the 12C4 enhances the conducting ion contents and their mobility, obtained from electrode polarization: i.e., as 12C4 is added, there are more conducting ions simultaneously contributing not only with lower activation energy but also with higher mobility, suggesting a lower energy barrier for Li+ motion. Therefore, the combination of solvation and plasticization plays a vital role in an improvement in the conductivity of the ionomer bend of 12C4, where ion motion is directly coupled with segmental dynamics.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.7b00467. 1 H NMR spectra of PEO-49Li and PEO-49Li+12C4, dielectric permittivity of PEO-49Li+12C4 at 273 K, fitting procedure of dipolar relaxations, DSC thermograms of PEO-49Li+12C4, and frequency dependence of loss tangent for PEO-49Li and PEO-49Li+12C4 (PDF)

Figure 11. BNN relation of DC conductivity rate σDC/ε0 vs the product of static dielectric constant εs and ion rearrangement frequency ωα2 for the neat ionomer (PEO-49Li) and its blend with 12C4 (PEO-49Li+12C4), including literature data66 for other PEObased single-ion conductors (PEO-100Li and PEO-100Na), where the conductivity rate of the blend PEO-49Li+12C4 was fit to two BNN equations: one set above and the other below the melting phase transition of 12C4, with inset showing σDC/(ε0εsωα2) vs T. The black dashed line indicates the BNN relation eq 12 with B = 1.0, and the colored solid lines are fits of eq 12 with B = 7 for PEO-100Li, B = 4 for PEO-49Li, B = 2.1 and B = 3.8 for PEO-49Li+12C4, and B = 1.5 for PEO-100Na.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (R.H.C.). ORCID

U Hyeok Choi: 0000-0002-0048-9550 Ralph H. Colby: 0000-0002-5492-6189 Notes

The authors declare no competing financial interest.

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aggregates lead to an ion exchange distance at τα2 (the spacing between aggregates) larger than the Debye length, while ionomers with no ion aggregates move ions an average distance equal to the Debye length.73,74 Figure 11 displays that both the ionomer and its mixture with 12C4 follow the BNN relation, suggesting that conductivity is strongly coupled with ion motion (α2 process), but adding 12C4 to the ionomer slightly reduces B from 4.0 to 2.1. In particular, for PEO-49Li+12C4, its conductivity rate was fit to two BNN equations (eq 12): one set (B = 2.1) and the other (B = 3.8) at temperatures above and below the melting phase transition of 12C4, respectively. The higher B value indicates ions aggregating at lower temperatures. This is also reflected in the inset of Figure 11, which shows σDC/(ε0εsωα2) vs T (i.e., the temperature dependence of B). This observation is similar to what was found by Wang et al.73 for sulfonated ionomers, showing that more ionic aggregation in ionomers leads to a higher B value. This demonstrates that plasticization allows the ion rearrangement distance to be closer to the Debye length owing to dissolving ion aggregates.

ACKNOWLEDGMENTS R.H.C. thanks the National Science Foundation (Grant DMR1404586) for financial support. U.H.C. acknowledges support from Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (Grant 2016R1D1A1B03932055).

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REFERENCES

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4. CONCLUSIONS The dielectric response and ion conduction of PEO-based lithium single-ion conductors plasticized with solvating 12C4 are reported from dielectric relaxation spectroscopy. The effect of plasticization is clearly observed in the dielectric constant εs H

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