On Replacing Poly(ethylene oxide) in Solid Block Copolymer Electrolytes by Poly(glycidyl methyl ether): Morphology and Ionic Conductivity

Abstract

A new family of block copolymer electrolytes, where the “soft” block is synthesized via anionic ring opening copolymerization of ethylene oxide (EO) and glycidyl methyl ether (GME) and the “hard” block is glassy polystyrene (PS), overcomes many of the limitations of poly­(ethylene oxide) (PEO) for battery applications. Two block copolymer systems, PS-b-P­(EO-co-GME) with a GME content of 21% and PS-b-PGME containing a pure PGME block, were prepared, both with narrow dispersity (Đ = 1.03–1.15). All polyether blocks are structural isomers of PEO. Yet, in both structures, the polyether block is fully amorphous at all temperatures. When doped with LiN­(SO₂CF₃) (LiTFSI) at different ratios, the materials provide superior dc-conductivity values in comparison to the established dual ion conductors PS-b-PEO doped with LiTFSI or with LiCF₃SO₃ (LiTf). In addition, PS-b-PGME doped with (LiTFSI) has a higher conductivity (∼1 × 10^–5 S·cm^–1 at the PS glass temperature) than PS-b-P­(EO-co-GME) and a higher conductivity than the structurally similar single ion conductor polystyrene-b-poly­(ethylene oxide-co-(lithium trifluoromethane-sulfonamide)­ethyl glycidyl ether) (PS-b-P­(EO-co-LiTFSAEGE). PGME best combines favorable properties required for the design of the soft block in SPEs based on block copolymers: low liquid-to-glass temperature (T _g) nearly independent of molar mass, favorable molecular structure that can solubilize alkali metal salts, higher dielectric permittivity than PEO, and the absence of crystallization. These results suggest that PGME or PGME-containing polyether copolymers can replace PEO as the “soft” block in future SPEs.

Introduction

Solid-state polymer electrolytes (SPEs) for lithium-ion batteries − have received considerable attention due to their unique characteristics (nontoxicity, thermal stability, flexibility, and processability) as compared to conventional liquid electrolytes. However, current SPEs are not widely applied at present, mainly due to the low ionic conductivity (σ_dc < 10^–3 S·cm^–1) as compared to liquid ones, suggesting that further improvements are necessary in order to meet the demands of future battery technologies. , Current efforts in replacing liquid electrolytes in lithium-ion batteries are centered around poly­(ethylene oxide) (PEO) − in block copolymers (BCP) with a hard phase, usually polystyrene (PS). − In BCPs, the degree of segregation and orientation of the nanodomains relative to the electrodes determine the conductive pathways for lithium cations, while the mechanical properties are governed by the glassy PS block. In this context, lithium salt-doped PS-b-PEO based BCPs represent one of the most intensely studied solid polymer electrolytes (SPE) at present. −

In BCP electrolytes, the electrolyte is directed preferentially to the soft conducting phase. PEO shows favorable interactions with Li salts of alkali metals, possesses a flexible C–O bond, and exhibits relatively high dielectric permittivity (ε’ ∼4.5 at ambient temperature), necessary for the subsequent dissociation of Li salts. This behavior renders PEO a suitable and safer alternative to common liquid electrolytes in lithium-ion batteries. However, the main factors that impede ion transport in copolymers based on PEO are (i) the formation of crystalline complexes with certain Li salts and (ii) its strong tendency for crystallization. With respect to (i), the interaction of PEO with some Li salts is so strong that they give rise to highly crystalline complexes. Fortunately, the tendency for crystalline complex formation can be tuned by the choice of the lithium salt. Common salts for this purpose are lithium bis­(trifluoromethanesulfonyl)­imide (LiTFSI) and lithium triflate (LiTf), with LiTFSI being superior, as it suppresses crystalline complex formation. , With respect to (ii), attempts have been made to suppress the PEO crystallization mainly by modifying the polymer architecture (e.g., grafted architectures, − tapered copolymers , ). In recent work, we introduced the rPEG-concept, aiming at nonimmunogenic PEG-isomers, based on random copolymers of ethylene oxide (EO) and glycidyl methyl ether (GME). This approach can also be exploited to obtain fully amorphous PEO isomers, since a GME content exceeding 21% leads to noncrystallizable PEO copolymers. In addition, the amorphous PGME homopolymer offers a different coordination environment for Li-ions compared to PEO.

Herein, we capitalize on the rPEG strategy toward improving the ionic conductivity of SPEs. The SPEs presented in this work are composed of a hard block (PS) and an amorphous polyether block. The polyether block is synthesized via anionic ring opening copolymerization of ethylene oxide (EO) and glycidyl methyl ether (GME). Two series of block copolymers are synthesized with the hard phase being composed of PS. The soft polyether phase is either composed of a copolymer of EO and GME (rPEG), yielding PS-b-P­(EO-co-GME), or a homopolymer of GME, PS-b-PGME, thus completely replacing PEO. We employ impedance spectroscopy and a combination of thermal, structural, and rheological tools to show that replacing PEO by PGME as the polyether block in diblock copolymers in combination with a PS hard phase is advantageous for SPEs. With a dc-conductivity of ∼1 × 10^–5 S·cm^–1 at the PS glass temperature where the modulus is above 10⁷ Pa, the PS-b-PGME copolymers doped with LiTFSI are superior to the established dual ion conductors PS-b-PEO doped with LiTFSI or with LiTf. Furthermore, based on our results, we provide arguments based on molecular structure, mobility, and dielectric permittivity in favor of the replacement of PEO by PGME as a key component in solid polymer electrolytes for lithium-ion batteries.

Experimental Section

Syntheses

Glycidyl Methyl Ether (GME)

1-Chloro-3-methoxypropan-2-ol (350 g, 2.81 mol) and diethyl ether (350 mL) were added to a three-necked flask with a KPG-stirrer, thermometer, and reflux condenser. The solution was cooled to 0 °C, and NaOH pellets (135 g, 3.37 mol) were added portionwise. Subsequently, the solution was heated to room temperature and stirred for 4 h. The reaction mixture was filtered, and the filtrate was dried over MgSO₄. The solvent was evaporated, and the remaining substance was distilled to yield pure glycidyl methyl ether (185 g, 2.10 mol, 75%).

¹H NMR (300 MHz, CDCl₃) δ (ppm): 3.67–3.61 (dd, 1H, H_c), 3.34 (s, 3H, H_d), 3.30–3.22 (dd, 1H, H_c), 3.13–3.03 (m, 1H, H_b), 2.77–2.70 (dd, 1H, H_a), 2.58–2.51 (dd, 1H, H_a).

ω-Hydroxy-polystyrene (PS–OH)

Styrene (18.20 g, 20.00 mL, 0.17 mol, 85 equiv) was dried over calcium hydride for 1 day and then cryo-transferred into the dried reaction flask. Cyclohexane (40 mL) was transferred in the same way, and subsequently, the flask was kept under vacuum (1 × 10^–3 mbar). The polymerization was initiated via sec-BuLi (1.3 M stock solution, 1.57 mL, 2.00 mmol, 1 equiv) and stirred for 12 h. Ethylene oxide (0.75 mL, 16.4 mmol, 8 equiv) was condensed and dried over sec-BuLi (1.3 M stock solution, 0.62 mL, 2.00 mmol, 0.05 equiv) for 30 min and subsequently transferred into the frozen reaction flask. The reaction was warmed to room temperature and terminated after 4 h. The polymer PS–OH was precipitated in an excess of MeOH-iPrOH (50:50) in quantitative yields and dried in vacuo (Figures S1–S4).

¹H NMR (400 MHz, CDCl₃) δ (ppm): 7.3–6.3 (m, 400H, H_j‑l), 3.29 (br, 2H, H_h), 2.6–1.0 (m, 281H, H_b,c,e,f), 0.8–0.5 (m, 6H, H_a,d).

Polystyrene-block-poly­(ethylene oxide-co-glycidyl methyl ether) and -poly­(glycidyl methyl ether) PS-b-P­(EO-co-GME) and PS-b-PGME

PS–OH (1 g, 0.12 mmol) was dissolved in benzene, lyophilized, and dried at 80 °C under high vacuum (1 × 10^–3 mbar) for 12 h. Tetrahydrofuran (7.5 mL) and cyclohexane (2.5 mL) were cryo-transferred onto the dried macroinitiator, potassium naphthalenide (0.44 M in THF, 0.24 mL, 0.11 mmol, 0.9 eq ) was added, and the mixture was stirred for 30 min.

Glycidyl methyl ether (GME) was dried over CaH₂ overnight and subsequently cryo-transferred. The macroinitiator solution was frozen in liquid nitrogen, and the monomers GME (0.35 mL, 4 mmol) and EO (0.51 mL, 12 mmol) were added sequentially in two steps over 2 days. Both monomers were added in the respective amounts via cryo-transfer and condensed under inert conditions at −78 °C. After each monomer addition, the solution was heated to 50 °C and stirred. Progress and completion of the polymerization were checked via SEC. The polymer was precipitated in water and dried in vacuo to yield a colorless brittle solid (Figures S5–S15).

¹H NMR (400 MHz, CDCl₃) δ (ppm): 7.3–6.3 (m, 385H, H_j‑l), 3.6–3.4 (m, 450H, H_g,h,m‑o,q), 3.4–3.3 (s, 72H, H_p), 2.37–0.80 (m, 267H, H_b,c,d,e,f), 0.8–0.5 (m, 6H, H_a,d).

Poly­(glycidyl methyl ether) (PGME)

2-(Benzyloxy)­ethanol (75 mg, 0.493 mmol) and potassium tert-butoxide (50 mg, 0.44 mmol, 0.9 equiv) were dissolved in benzene, lyophilized, and dried at 60 °C under high vacuum (1 × 10^–3 mbar) for 12 h. The dried initiator salt was dissolved in dry DMSO (25 mL) and stirred for 30 min. Glycidyl methyl ether (GME) was dried over CaH₂ overnight and subsequently cryo-transferred. The initiator solution was frozen in liquid nitrogen, and GME (2.88 g, 2.941 mL, 32.7 mmol) was added. After the addition of the monomer, the solution was allowed to reach room temperature. Progress and completion of the polymerization were monitored via SEC.

The active chain ends were quantitatively deprotonated via an excess of KOtBu (0.116 g, 2.1 equiv) and subsequently end-capped with methyl iodide (0.350 g, 0.153 mL, 2.5 mmol, 5 equiv). To ensure completion, the reaction was stirred for 1 day. The solvent was distilled off, and the polymer was redissolved in DCM and filtered over Celite to remove the salts. Afterward, the solvent was removed and the sample was lyophilized to yield a colorless viscous liquid (Figures S16–S25).

¹H NMR (400 MHz, CDCl₃) δ (ppm): 7.34–7.29 (m, 5H, H_a‑c), 3.67–3.27 (m, 259H, H_e‑k).

NMR Spectroscopy

¹H NMR spectra were recorded on a Bruker Avance III HD 400 spectrometer with 400 MHz and referenced internally to residual proton signals of the deuterated solvent. All spectra were acquired at 23 °C. Spectra were processed and analyzed by utilizing the MestReNova 14.3.3–33362 software.

MALDI-ToF Mass Spectrometry

MALDI-ToF MS measurements were carried out using a Bruker autoflex maX MALDI-ToF/ToF using a smartbeam-II solid state laser with a wavelength of 337 nm. Spectra were recorded using the software Bruker flexControl 3.4 and analyzed using Bruker flexAnalysis 3.4 and Bruker polytools 1.31. The potassium, sodium, and silver salts of trifluoroacetic acid (KTFA, NaTFA, AgTFA) and trans-2-[3-(4-tert-butylphenyl)-2-methyl-2-propenylidene]­malononitrile (DCTB) or 1,8,9-anthracentriol (dithranol) were utilized as ionization salt and matrix, respectively. For sample preparation, the polymers were dissolved in chloroform at 10 mg mL^–1. 20 μL of this solution was combined with 20 μL of a 10 mg mL^–1 solution of the matrix in chloroform. 5 μL of a 0.1 M solution of the salt in methanol was added, and 1 μL of the resulting mixture was spotted onto a MTP 384 ground steel target plate. The solvents were allowed to evaporate completely before the measurement. All measurements were performed in linear mode.

Size Exclusion Chromatography (SEC)

Measurements were conducted using an Agilent 1100 series HPLC system, which included a degasser, isocratic pump (G1310A), autosampler (G1313A), column oven (G1316A), and detectors for refractive index (RI) (G1310A) and variable wavelength (VWD) (G1314A). Separations were carried out employing a four-column setup (MZ-Analysentechnik GmbH) connected sequentially:

• i.HEMA-40 guard column (40 Å pore size, 10 μm particle size, 50 × 8.0 mm)
• ii.HEMA-40 analytical column (40 Å pore size, 10 μm particle size, 300 × 8.0 mm)
• iii.HEMA-100 analytical column (100 Å pore size, 10 μm particle size, 300 × 8.0 mm)
• iv.HEMA-300 analytical column (300 Å pore size, 10 μm particle size, 300 × 8.0 mm)

The eluent consisted of DMF (Fisher Chemical) with 1 mg·mL^–1 of anhydrous LiBr (Acros Organics), delivered at a flow rate of 1 mL·min^–1. Both the column oven and RI detector cell were maintained at 50 °C. Calibration was performed using well-defined polystyrene from PSS (PSS Standards Kit) with molar mass values (M _p) ranging from 682 to 130000 g·mol^–1. Samples were dissolved in DMF (with 1 mg·mL^–1 anhydrous LiBr) at a concentration of 1 mg·mL^–1 with the addition of 1 drop of toluene. The injection of 100 μL of the stock solutions was carried out via the autosampler with a measurement duration of 45 min. Elution times were referenced using toluene as an internal standard. RI traces were analyzed using PSS WinGPC Unichrom V8.31 software.

Differential Scanning Calorimetry (DSC)

The thermal analysis of the PS-b-P­(EO-co-GME) and the PS-b-PGME copolymers doped with LiTFSI, as well as for the undoped ones, was implemented by differential scanning calorimetry through a Q2000 (TA Instruments). The instrument was calibrated for the baseline using a sapphire standard, for the enthalpy and temperature using indium as a standard, and for the heat capacity using sapphire as a standard. In each case, the temperature protocol involved measurements on cooling and subsequent heating with a rate of 20 K/min^–1 in the temperature range of 193–423 K. DSC traces of the bulk and doped PGME homopolymers are presented in Figure S26, Supporting Information.

Small-Angle X-ray Scattering

Small-angle (SAXS) measurements were made with the N8 Horizon vertical setup (Bruker) using a 50 W CuKα radiation (IμS microfocus source with integrated MONTEL optics). The diffraction patterns were recorded on a VÅNTEC-500 2D detector (Bruker) at a sample–detector distance of 660 mm. Intensity distributions as a function of the modulus of the total scattering vector, q = (4π/λ) sin­(2θ/2), where 2θ is the scattering angle and λ = 0.154 nm is the wavelength, were obtained by radial averaging of the 2D data sets. Here, some measurements were made in macroscopically oriented (extruded) filaments with a diameter of 0.7 mm at ambient temperature using a laboratory microextruder. In all patterns, the filament axis had a vertical orientation with the X-ray beam perpendicular to the filament. In this case, the scattered intensity distributions were subsequently integrated along the equatorial and meridional axes. Temperature-dependent measurements of 1 h long were made by slow heating from 303 to 423 K in 10 K steps – with 1 h equilibration time at each temperature, and subsequent cooling. SAXS curves obtained on heating and subsequent cooling for the two copolymer systems are shown in Figures S27–S30, Supporting Information.

Dielectric Spectroscopy (DS)

Dielectric spectroscopy measurements as a function of temperature (i.e., under “isobaric” conditions) were performed with the Novocontrol Alpha high-resolution frequency analyzer, within the frequency range from 10^–2 Hz to 10⁷ Hz, and for temperatures in the range of 193.15 to 423.15 K, with steps of 5 K. Samples were prepared as melts under vacuum by pressing the electrodes to the spacer thickness. The DS measuring cell consisted of two platinum electrodes (20 mm diameter) forming a capacitor. A Teflon spacer was inserted in the sample to keep the distance of the electrodes fixed (about 100 μm). By applying an alternating electric field to the capacitor, the complex impedance, Z*, can be obtained. The complex conductivity function, σ* = σ′ + iσ″, where σ′ and σ″ are the real and imaginary parts, respectively, were calculated from the impedance measurements. To extract the dc-conductivity, the plateau in the real part σ′ was used in the range where σ″ exhibits a minimum. An alternative way to obtain the dc-conductivity is from the random free energy barrier model (RBM). , The limitations of the model are discussed in the Supporting Information (Figure S31). From the same impedance measurements, the complex dielectric function ε*­(ω,T) = ε′(ω,T) – iε″(ω,T), where ε′ is the real part and ε″ is the imaginary part (dielectric losses), was obtained as a function of frequency, f (=ω/2π), and temperature, T. Additional DS data are provided in Figures S32–S37.

Rheology

A TA Instruments AR-G2 with a magnetic bearing that allows for nanotorque control was used for recording the viscoelastic properties of the polymer electrolytes. Measurements were taken with the environmental test chamber (ETC) as a function of temperature. The ETC employs liquid nitrogen vapor (an inert atmosphere) to control the temperature. The samples were prepared on the lower rheometer plate (8 mm) and adjusted to the geometry of the plate, the upper plate was brought into contact, and the thickness was adjusted accordingly. The linear and nonlinear viscoelastic regions were determined via strain amplitude dependence of the complex shear modulus |G*| at a frequency of 10 rad·s^–1. Ιsochronal measurements of the shear moduli at ω = 10 rad·s^–1 were made in the temperature range of 228 and 423 K for the PS-b-P­(EO-co-GME) doped with LiTFSI at ratios r = [Li]:[EO] = 1:32, 1:16, and 1:4. Similarly, the PS-b-PGME copolymer was doped with LiTFSI at r = 1:16 and investigated within the same temperature range.

Results and Discussion

Polymer Synthesis

Synthesis of PGME Homopolymers

To study the effects of molecular weight on ionic conductivity, low dispersity materials as obtained by AROP are advantageous in comparison to higher dispersities due to the prevalence of plasticizing species as is common in MAROP (monomer-activated ring-opening polymerization) or other less controlled methods. The AROP of GME to PGME homopolymers has proven to be a challenge, as a common difficult to remove impurity in GME is its precursor, i.e., epichlorohydrin. Through an alternative route, analytically pure GME can be obtained enabling its anionic polymerization. A series of PGME homopolymers were synthesized utilizing dimethyl sulfoxide (DMSO) as the solvent, 2-(benzyloxy) ethanol as the initiator, and potassium tert-butoxide as the base. The polymers, ranging from 2 to 7 kg mol^–1, exhibit low dispersities (SEC) (Figure ) and a monomodal distribution in MALDI-ToF measurements (Figures S1–S25, Supporting Information).

1.

SEC traces (DMF, PS calibration) of PGME (1.6–5.1 kg mol^–1).

Synthesis of the Precursor Block Copolymer Structure

The macroinitiator ω-hydroxy-polystyrene was obtained via end-capping of living polystyryl lithium with ethylene oxide in cyclohexane (Scheme ). , The SEC traces of this polymer are monomodal and exhibit a low dispersity (Đ). Quantitative end-capping of the living chain ends of PS was verified by MALDI-ToF spectroscopy, as only one significant distribution can be seen. A smaller subdistribution can be assigned to a different counterion (sodium vs silver).

1. Synthesis of the BCP Starting from the Macroinitiator PS–OH.

To obtain the polyether block, anionic ring opening copolymerization (AROP) of EO and glycidyl methyl ether (GME) was employed by using the previously synthesized PS–OH macroinitiator. In contrast to our reported strategy, a mixture of THF and DMSO had to be employed for the synthesis of the rPEG block due to the low polarity of the PS–OH initiator. The PS-b-P­(EO-co-GME) BCPs showed a narrow dispersity of Đ = 1.04 with a monomodal distribution. Integrating the ¹H NMR methyl signal of GME at 3.55 ppm against the initiator signal of PS–OH at 0.54–0.81 provides a GME content of 21%, which is near the theoretical content of 25% and still provides an amorphous polyether domain. Based on the ¹H NMR (Figures and ), the total volume fraction of the polyether domain (f _PEO) was determined to be 37% based on the densities of PS (1.13 g·cm^–3) and rPEG (1.11 g·cm^–3) (Figure ).

2.

¹H NMR spectrum (400 MHz, CDCl₃) of PS-b-P­(EO-co-GME)₁₁₆.

3.

¹H NMR spectrum (400 MHz, CDCl₃) of PS-b-PGME₄₆.

4.

SEC traces (DMF, PS calibration) of PS–OH (blue), PS-b-P­(EO-co-GME)₁₁₆ (red), and PS-b-PGME₄₆ (green).

Doping with LiTFSI

To evenly incorporate the lithium-salt into the BCP structure, a stock solution of LiTFSI in THF was used to realize different [Li]:[EO] ratios by adding the respective amount to the BCP dissolved in THF. The solvent was subsequently evaporated, and the doped BCP was dried under a high vacuum.

Ion Conduction in PGME Homopolymers and PS-b-P­(EO-co-GME) Copolymers

PGME represents a structural polyether isomer of PEO, albeit with different coordination environments for Li-ions based on the methoxy methylene side chains. All PGME homopolymers have a low glass temperature as shown in the DSC traces of Figure S26, Supporting Information. Furthermore, T _g increases only moderately, from 212 to 215 K with increasing molar mass (Table ). This reflects the flexible C–O bonds in the backbone and side group. Upon doping with LiTFSI at a ratio [Li]:[EO] = 1:16, T _g increased within the range from 233 to 238 K, for the respective molar masses, e.g., by ∼22 K. This reflects the association of Li ions to the oxygen atoms. The conductivity measurements for the doped PGME with LiTFSI at a ratio of [Li]:[EO] = 1:16 are shown in Figure . They depict a high dc-conductivity with a small variation with the molar mass. The results for the σ­(T) conform to the Vogel–Fulcher–Tammann (VFT) equation for the conductivity contribution as

$${\sigma }_{dc}(T)={\sigma }_o^{\#}\exp (-\frac{B}{T-T_o})$$ 1

Here, σ _o is the dc conductivity in the limit of very high temperatures, B is the activation parameter, and T _o is the “ideal” glass temperature (parameters are summarized in Table ). PGME exhibits high conductivities, from 1.6 × 10^–4 S·cm^–1 at 323 K to about 10^–3 S·cm^–1 at 368 K. This is associated with the presence of two oxygen atoms that solvate Li ions and the flexible C–O bonds. Overall, PGME presents certain advantages when compared to PEO. The side chains and lack of tacticity completely suppress the tendency for crystallization.

2. Overview of Synthesized PGME Homo- and PS-b-PGME Block Copolymers and [Li]:[EO] Doping Ratios.

sample	M n,SEC [kg mol–1]	M n,MALDI [kg mol–1]	Đ	P n,EO/GME	GME-content [mol %]	[Li]:[EO]	f PGME
PGME#1	1.6	2.2	1.05	22	100	1:16	1
PGME#2	2.2	5.4	1.06	58	100	1:16	1
PGME#3	2.6	4.0	1.05	42	100	1:16	1
PGME#4	3.5	5.0	1.04	54	100	1:16	1
PGME#5	5.1	6.9	1.03	64	100	1:16	1
PS-b-PGME	10.6	12.9	1.07	46	100	0	0.30
PS-b-PGME	10.6	12.9	1.07	46	100	1:32	0.30
PS-b-PGME	10.6	12.9	1.07	46	100	1:16	0.32
PS-b-PGME	10.6	12.9	1.07	46	100	1:8	0.34
PS-b-PGME	10.6	12.9	1.07	46	100	1:4	0.37

5.

(a) Real (open circles) and imaginary (dashed lines) part of the complex conductivity, at the reference temperature of T = 363 K, for the PGME homopolymers doped with LiTFSI at a ratio r = [Li]:[EO] = 1:16. (b) dc-conductivity as a function of the inverse temperature, obtained during cooling. Different colors correspond to different molar masses, as described in Table .

3. VFT Parameters for the Temperature Dependence of the dc-Conductivity, Together with the Glass Temperature of the PGME Homopolymers Doped with LiTFSI with r = 1:16, Obtained by DS (Cooling).

	DS
r = [Li]:[EO]	σο (S·cm–1)	Β (Κ)	T ο (Κ)	T g σ (K)
PGME#1	0.42 ± 0.01	1050 ± 10	195 ± 1	228 ± 1
PGME#2	0.68 ± 0.01	1050 ± 10	195 ± 1	232 ± 1
PGME#3	0.54 ± 0.01	1080 ± 10	196 ± 1	232 ± 1
PGME#4	0.29 ± 0.01	1110 ± 10	195 ± 1	231 ± 1
PGME#5	0.46 ± 0.01	1073 ± 5	197 ± 1	232 ± 1

Another feature of PGME that makes it particularly attractive is its dielectric permittivity. Figure compares three properties of bulk PGME (M _n = 3.5 kg·mol^–1) with bulk PEO (M _n = 5 kg·mol ^–1): the heat flow, the ionic conductivity, and the static dielectric permittivity. Crystallization is absent in PGME in contrast to PEO, and this affects the ionic conductivity. At the PEO crystallization temperature, the ionic conductivity drops by some orders of magnitude, whereas in PGME, it changes smoothly following a VFT dependence. Within the amorphous state, the dielectric permittivity shows the expected temperature dependence, ε′_S ∼ 1/T. At temperatures located above the PEO melting temperature the dielectric permittivity of PEO is higher than that of PGME. However, at temperatures that are more relevant for applications (e.g, T < 333 K), the dielectric permittivity of PEO decreases discontinuously below the crystallization temperature to a value of ε′_S ∼ 4.5 (at ambient temperature). At the same temperature, ε′_S ∼ 9 is because PGME is amorphous. As a result, Coulombic forces in ILs are weakened by a factor of 2 in PGME relative to (crystalline) PEO. In addition, the liquid-to-glass temperature of PGME exhibits a weak dependence on molar mass. These are all favorable features for ion conduction. Yet, PGME, like PEO, suffers from low mechanical stability.

6.

(a) Heat flow, (b) ionic conductivity, and (c) static dielectric permittivity as a function of inverse temperature for the bulk PGME (M _n = 3.5 kg·mol^–1) and bulk PEO (M _n = 5 kg·mol^–1), shown with red and blue colors, respectively. The vertical dashed line represents the crystallization temperature of the PEO.

As a next step, we combine the advantageous GME units into PS-b-P­(EO-co-GME) copolymers with the high T _g polymer PS. First, we discuss diblock copolymers of the type PS-b-P­(EO-co-GME) (). Here, the GME mole content in the P­(EO-co-GME) copolymers varies from 21% to 41%. For a GME content above 20 mol %, PEO is unable to crystallize. We start the discussion with the copolymers with GME content of 21% (Table ). The absence of crystallization is evident in all DSC traces of PS-b-P­(EO-co-GME) copolymers shown in Figure . The traces display high (PS) and low (P­(EO-co-GME)) T _g’s that are dependent on the ratio r = [Li]:[EO] (Figure a,b) and the copolymer composition (Figure c,d). Increasing Li-ion content induces some Li–O coordination, which increases the T _g of the soft P­(EO-co-GME) phase by ∼19 K relative to the neat diblock (Figure a,b). Surprisingly, doping produces a similar effect in the hard (PS) phase. The corresponding increase in T _g is even higher (39 K). This is suggestive of chain stretching at the interface.

1. Overview of Synthesized rPEG Block Copolymers and [Li]:[EO] Doping Ratios.

sample	M n,SEC [kg mol–1]	M n,MALDI [kg mol–1]	Đ	P n,EO/GME	GME-content [mol %]	[Li]:[EO]	f [EO‑co‑GME]
PS–OH	9.5	8.5	1.04	-	-	0	0
PS-b-P(EO-co-GME)	11.1	10.1	1.03	48	31	1:16	0.35
PS-b-P(EO-co-GME)	10.3	11.3	1.12	68	29	1:16	0.40
PS-b-P(EO-co-GME)	10.4	12.0	1.15	67	41	1:16	0.44
PS-b-P(EO-co-GME)	14.5	14.2	1.04	116	21	0	0.36
	14.5	14.2	1.04	116	21	1:3200	0.36
	14.5	14.2	1.04	116	21	1:2400	0.36
	14.5	14.2	1.04	116	21	1:1600	0.36
	14.5	14.2	1.04	116	21	1:1200	0.36
	14.5	14.2	1.04	116	21	1:800	0.36
	14.5	14.2	1.04	116	21	1:400	0.36
	14.5	14.2	1.04	116	21	1:32	0.38
	14.5	14.2	1.04	116	21	1:16	0.40
	14.5	14.2	1.04	116	21	1:8	0.43
	14.5	14.2	1.04	116	21	1:4	0.48

7.

(a) Heat flow traces as a function of temperature for the different r = [Li]:[EO] ratios. Two glass temperatures are evident: one at higher temperatures corresponding to the T _g of the PS block and a lower one related to the T _g of P­(EO-co-GME) block. (b) T _g and T _g as a function of r. (c) Heat flow traces for copolymers with different GME contents and different compositions of the soft phase. (d) Corresponding glass temperatures as a function of f _{(EO‑co‑GME)}.

The investigation of nanophase segregation by SAXS confirms this notion. The SAXS patterns reveal that the neat copolymer is only weakly phase-separated (Figure and Figure S27). Even a minor addition of the electrolyte gives rise to nanophase separation that becomes very evident with increasing ratio r = [Li]:[EO] above 1:32 (Figure a). This is documented by the increasing number of higher order reflections of the lamellar (LAM) nanophase, the narrowing of the first order Bragg peak, and the associated shift of the peak position (Figure b). The complete set of the heating/cooling SAXS data of the copolymers with the different electrolyte content are shown in Figure S28. The lamellar domain spacing increases from 14 nm in the bulk (r = 0) to 24 nm for the diblock doped with r = 0.25. This again signifies a transition from a weakly ordered copolymer with Gaussian chain conformations to a nanophase-separated state with highly stretched chains. The highly ordered LAM morphology provides broad channels for ion transport that are expected to increase the ion conductivity.

8.

(a) SAXS patterns at the reference temperature of T = 303 K, obtained on cooling from higher temperatures, for the block copolymers PS-b-P­(EO-co-GME) doped with LiTFSI. Different colors correspond to different r = [Li]:[EO] ratios. Patterns are vertically shifted for clarity. (b) Domain spacing, obtained from SAXS measurements at 303 K as a function of r. The dashed line is a guide for the eye.

The results of the conductivity measurements for the PS-b-P­(EO-co-GME) samples doped with the LiTFSI are discussed with respect to Figures and and are further summarized in Table . Figure depicts the real (σ′(ω)) and imaginary (σ″(ω)) parts of the complex ionic conductivity σ*­(ω) function plotted as a function of frequency for different r = [Li]:[EO] ratios. The dc-conductivity was extracted from the σ′(ω) plateau at the position of the σ″(ω) minimum. Alternatively, it can be obtained from the Nyquist plots shown in Figure b,c. The latter depicts a distorted semicircle at higher frequencies and a capacitive tail at lower frequencies associated with electrode polarization. In this case, the dc-conductivity is extracted from the resistance R as σ′ = d/RA, where d and A give the capacitor thickness and electrode area, respectively. The distorted semicircle is very evident in the lightly doped copolymers and less so in the highly doped copolymers, reflecting structural changes associated with the unfreezing of the PS dynamics at the interface.

9.

(a) Real (open circles) and imaginary (dashed lines) part of the complex conductivity, at the reference temperature of T = 363 K, for the block copolymers PS-b-P­(EO-co-GME) doped with LiTFSI. Different colors correspond to different r = [Li]:[EO]. The solid lines indicate the dc-conductivity obtained at the plateau of σ′(ω). (b) Nyquist plot for some of the electrolyte concentrations indicated with different colors.

10.

(a) Ionic conductivity as a function of temperature, during cooling, for the block copolymer PS-b-P­(EO-co-GME). Different colors correspond to different r = [Li]:[EO] ratios, as indicated. Colored area indicates the glass transition region for the PS block. (b) Conductivity value as a function of r at a temperature of T = 363 K. Dashed line is a guide for the eye.

4. VFT Parameters for the dc-Conductivity as a Function of the Inverse Temperature, Along with the Glass Temperature of the P­(EO-co-GME) Block, Obtained by DS (Cooling), and the Glass Temperatures of Both P­(EO-co-GME) and PS Blocks, Obtained by DSC (Heating, 20 K/min).

	DS				DSC
r = [Li]:[EO]	σο (S·cm–1)	Β (Κ)	T ο (Κ)	T g σ (K)	T g P(EO‑co‑GME) (Κ)	T g PS (K)
1:4	1.4 ± 0.1	1390 ± 30	209 ± 1	256 ± 1	231 ± 1	363 ± 1
1:8	2.6 ± 0.1	1025 ± 10	206 ± 1	245 ± 1	237 ± 1	364 ± 1
1:16	2.8 ± 0.1	980 ± 10	195 ± 1	233 ± 1	228 ± 1	360 ± 1
1:32	2.6 ± 0.1	990 ± 10	187 ± 1	224 ± 1	218 ± 1	358 ± 1
1:800	4.2 ± 0.1	635 ± 20	219 ± 1	247 ± 1	213 ± 1	336 ± 2
1:1200	4.4 ± 0.1	770 ± 20	211 ± 1	246 ± 1	212 ± 1	332 ± 2
1:1600	4.5 ± 0.1	720 ± 25	212 ± 2	245 ± 1	212 ± 1	324 ± 2
1:2400	4.6 ± 0.1	760 ± 25	210 ± 2	245 ± 1	213 ± 1	320 ± 2
1:3200	4.7 ± 0.1	850 ± 30	204 ± 2	244 ± 1	213 ± 1	322 ± 2
0	6.3 ± 0.1	890 ± 30	201 ± 2	251 ± 1	214 ± 1	323 ± 2

The temperature dependence of the dc-conductivity is shown in Figure . The conductivity values are normalized with respect to the volume fraction of the P­(EO-co-GME) domain. This is based on the assumption that all the Li-ion salt resides in the P­(EO-co-GME) phase, leading to an increase in volume fraction of the conducting domain, which is given by

$$f_{\mathrm{P}(\mathrm{EO}‐\mathrm{co}-\mathrm{GME}{)}_{\mathrm{LiTFSI}}}=\frac{v_{(\mathrm{EO}-\mathrm{co}-\mathrm{GME})}+r·v_{\mathrm{LiTFSI}}}{v_{(\mathrm{EO}-\mathrm{co}-\mathrm{GME})}+r·v_{\mathrm{LiTFSI}}+\left(\frac{M_{\mathrm{PS}}·M_{(\mathrm{EO}-\mathrm{co}-\mathrm{GME})}}{M_{\mathrm{S}}·M_{\mathrm{P}(\mathrm{EO}-\mathrm{co}-\mathrm{GME})}}\right)·v_{\mathrm{s}}}$$ 2

where v _LiTFSI = M _LiTFSI/ρ_LiTFSI N _A, with M _LiTFSI = 287.09 g·mol^–1 and ρ_LiTFSI = 2.392 g·cm^–3, and r is the ratio [Li]/[EO].

Evidently, even a minute amount of electrolyte can increase the dc-conductivity relative to the bulk by orders of magnitude. The σ′(T) dependence follows, in general, the VFT dependence. However, some deviations are observed in the region of the PS T _g (shown with the gray area in Figure a). Although the highest conductivity at 500 K is obtained for the r = 1:4 ratio, at lower temperatures, it is the copolymer with r = 1:32 that exhibits the higher dc-conductivity. This reflects the lower T _g for this electrolyte composition (Figure b). It also shows a strong effect of electrolyte content on the steepness of the σ′(T) dependence. The steepness index (or fragility), defined as m* = ϑ­(log σ)/ϑ­(T _g/T) _T=Tg = BT _g/2.303 (T _g – T ₀), changes from 39 to 70 with increasing r (Figure S33). Values of the dc-conductivity normalized for the [Li]:[EO] content are plotted in Figure b at 363 K. They depict about 4 orders of magnitude increase in conductivity for the copolymer with r = 1:32 relative to the neat copolymer. They further demonstrate the sensitivity toward minor amounts of electrolyte that can increase the conductivity by 2 orders of magnitude. The data for the conductivity are further summarized in Table . The table includes a comparison of the T _g′ as obtained from DSC (Figure ) and from DS (Figure a). For the latter, the estimated conductivity value at T _g was obtained from the Nernst–Einstein equation:

$${\sigma }_{dc}=\frac{n{e}^2}{k_{\mathrm{B}}T}\frac{{\left(\frac{d_2}{2}\right)}^2}{6\tau }$$ 3

Here, n (= ρN _A/M _w, where M _w is the molar mass of the ionic block including the conducting ions and ρ is the mass density), n is the number density of the mobile anions, d (= R ⁺ + R ^–, where R ⁺ = R _Li = 0.076 nm, R ^–= R _[TFSI] = 0.37 nm) is the distance between the [Li⁺] and the [TFSI^–] assuming contact pairs, τ is the characteristic relaxation time at T _g, and k _B is the Boltzmann constant. By employing τ = 100 s, the σ_dc at T _g amounts to ∼10^–14 S·cm^–1. In addition to the dc-conductivity, we extract the characteristic frequency of ion motion from the modulus representation (M* = 1/ε*, Figure S32), and the result is shown in Figure S33. The characteristic frequencies display the same temperature dependence with dc-conductivity.

The results from the thermodynamics and the dc-conductivity can be discussed in terms of the mechanical stability obtained from rheology. Figure depicts combined results for the PS-b-P­(EO-co-GME) copolymer doped with r = 1:32 (further comparison for r = 1:4 is shown in Figure S38). It shows the DSC trace, the normalized dc-conductivity, and the shear modulus |G*|, the latter at a frequency ω = 10 rad/s, all obtained during heating. Despite the different heating rates, some trends are evident. At the PS glass temperature (T ∼ 358 K) the shear modulus is at ∼ 10⁶ Pa and the dc-conductivity is at ∼10^–5 S·cm^–1.

11.

Temperature dependence of the |G*| (black open-circles, ω = 10 rad·s^–1, rate = 5 K·min^–1), the ionic conductivity (blue filled rhombi), and the heat flow (orange solid-line, rate = 20 K·min^–1) for the PS-b-P­(EO-co-GME) copolymer with r = 1:32. Gray area indicates the glass temperature of the PS block.

Next, we explore the effect of GME content on the ion conductivity for the same PS-b-P­(EO-co-GME) copolymers (Table ). The thermal characteristics are shown in Figure c,d, and the respective morphologies and ion conductivities are discussed with respect to Figures and . Note that the copolymers differ in both GME content and the volume fraction of EO-co-GME (Table ). The SAXS curve for the neat PS-b-P­(EO-co-GME) copolymer with 41% GME content and f _{EO‑co‑GME} = 0.42 reveals weak phase separation with a lamellar nanostructure. By incorporation of the electrolyte with r = [Li]:[EO] = 1:16, several Bragg peaks appear with relative positions of 1:2:3:4 with respect to the primary peak, revealing a lamellar (LAM) nanostructure with domain periodicity of 14.95 nm. In the copolymer with 29% GME content and f _{EO‑co‑GME} = 0.40, the nanodomain morphology is again lamellar (domain spacing of 15.7 nm), but the chains are more stretched. For the more asymmetric copolymer (f _{EO‑co‑GME} = 0.35 and with 31% GME content), the diffraction pattern exhibits Bragg peaks with relative positions as 1:3^1/2:2:7^1/2:3:12^1/2 with respect to the first peak, revealing a hexagonally packed cylinder (HPC) structure. Detailed SAXS data obtained for heating/cooling are shown in Figure S29.

12.

SAXS patterns for the PS-b-P­(EO-co-GME) doped with LiTFSI with r = [Li]:[EO] = 1:16. Different colors correspond to different GME volume fractions (f _GME). Specifically, f _{EO‑co‑GME} = 0.35 (green), f _{EO‑co‑GME} = 0.4 (red), f _{EO‑co‑GME} = 0.44 (blue), and gray for the neat copolymer. All patterns refer to 303 K and show Bragg peaks corresponding to hexagonally packed cylinders (HPC), in the case of f _{EO‑co‑GME} = 0.35, while a LAM morphology is evident for the other compositions. Selected 2D images from the oriented fibers are shown as insets.

13.

(a) Real (open circles) and imaginary (dashed lines) part of the complex conductivity, at the reference temperature of T = 363 K, for the block copolymers PS-b-P­(EO-co-GME) with different GME contents doped with LiTFSI for r = [Li]:[EO] = 1:16 as well as for the neat copolymer. Different colors correspond to different volume fractions of the EO-co-GME block. Solid lines indicate the dc-conductivity obtained at the plateau of σ′(ω). (b) Ionic conductivity as a function of temperature during cooling. Again, different colors correspond to volume fractions of the EO-co-GME block. Gray area indicates the glass temperature of the PS block.

The respective conductivities for the different morphologies are listed in Figure . The data suggests a morphology-dependence of the normalized conductivities, from lower ion conductivities in the cylinder-forming f _{EO‑co‑GME} = 0.35 copolymer to the highest in the lamellar copolymer with f _{EO‑co‑GME} = 0.44. In the latter, at the PS glass temperature (T ∼358 K), the shear modulus is at ∼10⁷ Pa and the dc-conductivity is at ∼3 × 10^–6 S·cm^–1 (Figure S39). We note that this value is higher than the dc-conductivity in the single ion conducting P­(EO-co-LiTFSAEGE). Ion conductivity in the present PS-b-P­(EO-co-GME) copolymers is also superior to the established dual-ion conductors PS-b-PEO doped with LiTf or with LiTFSI, all at the same electrolyte ratio r (1:16). Results from the VFT parameters and respective T _g’s are shown in Table .

5. VFT Parameters for the Temperature Dependent dc-Conductivity, Along with the Glass Temperature of the P­(EO-co-GME) Block, Obtained by DS (Cooling), and the Glass Temperatures of Both P­(EO-co-GME) and PS Blocks, Obtained by DSC (Heating).

		DS				DSC
r = [Li]:[EO]	f EO – co – GME	σο (S·cm–1)	Β (Κ)	Το (Κ)	T g σ (K)	Τg P(EO‑co‑GME) (Κ)	T g PS (K)
1:16	0.44	3.2 ± 0.1	1386 ± 70	185 ± 3	241 ± 2	231 ± 3	346 ± 5
1:16	0.40	2.8 ± 0.1	1066 ± 10	197 ± 1	238 ± 1	236 ± 1	358 ± 1
1:16	0.35	2.6 ± 0.1	1078 ± 15	194 ± 1	234 ± 1	234 ± 1	350 ± 1
0	0.42	4.6 ± 0.1	1944 ± 90	156 ± 5	248 ± 2	220 ± 1	350 ± 5

The results of the PS-b-P­(EO-co-GME) copolymers invariably show a strongly increasing degree of nanophase separation with LiTFSI content, together with an increased ionic conductivity and relatively high moduli provided by the PS nanophase. Among the different PS-b-P­(EO-co-GME) copolymers with f _{P(EO‑co‑GME)} = 0.36, the one with the highest conductivity (at T = 363 K) is obtained when doping with r = [Li]:[EO] = 1:32. In comparing copolymers with different compositions and different morphologies, we find that a lamellar nanophase with long-range order maximizes ionic conduction.

Ion Conduction in PEO-Free Copolymers: The PS-b-PGME Case

The results of ionic conductivity in the PS-b-P­(EO-co-GME) copolymers suggested that the incorporation of GME units in the PEO block not only suppressed crystallization of the PEO block but also increased the ionic conductivity as compared to established single- and dual-ion conductors. This motivates full replacement of PEO by PGME, i.e., PS-b-PGME copolymers. For this purpose, a PS-b-PGME copolymer was synthesized with f _PGME ∼0.30 (Table ). The results for the thermal properties, the ion conductivity, and mechanical stability are discussed below. In the DSC trace of the neat copolymer (Figure a), the T _g’s of the PS and PGME segments cannot be clearly discerned. However, with increasing [Li]:[EO] ratio the two T _g’s can be clearly distinguished. Results show an increase of the T _g (PGME) by ∼64 K relative to the respective PGME homopolymer and a smaller increase in the PS T _g.

14.

(a) Heat flow traces as a function of temperature for a PS-b-PGME copolymer for different r = [Li]:[EO]. Two glass temperatures are evident; a high one corresponding to the PS and a lower one related to the T _g of PGME. (b) T _g and T _g plotted as a function of r. The blue triangle corresponds to the PGME homopolymer with a similar molar mass to the respective diblock. Dashed lines are guides for the eye.

These changes in the thermal properties due to LiTFSI addition are accompanied by drastic structural changes. The neat PS-b-PGME copolymer is in the disordered phase (DIS) as evidenced in SAXS (Figure a). This reveals a low interaction parameter that gives rise to correlation hole scattering. Increasing the electrolyte content to r = [Li]:[EO] = 1:32 gives Bragg peaks characteristic of a HPC nanodomain morphology. Further increasing the Li content to r = 1:4 results in a lamellar (LAM) nanodomain morphology with long-range order. Furthermore, the domain spacing increases strongly, as with the PS-b-P­(EO-co-GME) copolymers (Figure b). Detailed heating–cooling SAXS patterns are shown in Figure S30.

15.

(a) SAXS patterns at the reference temperature of T = 303 K, obtained on cooling, for the block copolymers PS-b-PGME doped with LiTFSI along with representative schematics of the nanodomain morphology. The arrows show Bragg reflections that correspond to disorder (DIS), hexagonally packed cylinders (HPC), and lamellar (LAM) morphologies, with increasing r = [Li]:[EO]. (b) Domain spacing as a function of electrolyte content. The dashed line is a guide for the eye.

Ion conductivity shows the expected trends (Figure a and Figure S35). However, in the PS-b-PGME copolymer series, it is the copolymer with r = [Li]:[EO] = 1:16 that exhibits the highest conductivity at 363 K (Figure b). The copolymer with r = 1:32 with the HPC nanophase morphology exhibits again lower conductivity compared with the LAM nanophases. The dc-conductivity in SPEs depends on several factors: the mobility of the ion-conducting phase (thus, the T _g of the soft block), the molar mass and the dielectric permittivity of the soft block, the degree of Li association with the oxygens (degree of complexation), and the type and size of nanochannels (including grain structure and tortuosity). ,, The DS and DSC results are summarized in Table .

16.

(a) Ionic conductivity as a function of temperature, obtained during cooling, for the block copolymers PS-b-P­(GME). Different colors correspond to different r = [Li]:[EO] ratios. The gray area indicates the glass temperature of the PS block. (b) Conductivity value as a function of r at the characteristic temperature of T = 363 K.

6. VFT Parameters for the dc-Conductivity Along with the Glass Temperature for the PGME Block, Obtained by DS (Cooling), and the Glass Temperatures of Both PGME and PS Blocks, Obtained by DSC (Heating).

	DS				DSC
[Li]:[EO]	σο (S·cm–1)	Β (Κ)	T ο (Κ)	T g σ (PGME) (K)	T g PGME (Κ)	T g PS (K)
1:4	1.9 ± 0.1	1230 ± 50	233 ± 2	278 ± 1	278 ± 1	359 ± 1
1:8	2.2 ± 0.1	1110 ± 30	215 ± 1	257 ± 1	259 ± 1	356 ± 1
1:16	1.8 ± 0.1	1080 ± 10	205 ± 1	243 ± 1	247 ± 1	352 ± 1
1:32	1.0 ± 0.1	3510 ± 50	122 ± 3	238 ± 1	236 ± 1	340 ± 1
0	4.5 ± 0.1	3230 ± 70	155 ± 2

A feature of the conductivity data at lower frequencies (Figures , , and ) is the decrease of σ′ due to the electrode polarization (EP). The process signifies the blocking of free ions (charges) at the interface with the electrodes upon applying an ac field. The EP model, proposed earlier by Macdonald and Coelho, , assumes that charges are produced by the dissociation from the same kind of neutral center and enables the determination of the number density, p, and mobility, μ, of conducting ions. The model introduces two characteristic times, τ_σ = ε_s · ε₀/σ_dc and τ_EP = ε_EP·ε₀/σ_dc, which correspond to the onset of ion diffusion and ion polarization at the electrodes, respectively. Here, ε_s is the measured static dielectric permittivity, ε₀ is the permittivity of free space, σ_dc is the measured dc-conductivity, and ε_EP is the dielectric permittivity corresponding to the EP process. The characteristic time scales can be obtained from the analysis of the loss tangent (tan δ = ε″/ε′) using a two-parameter fit for the Debye function as

$$\tan \delta =\frac{\omega {\tau }_{EP}}{1+{\omega }^2{\tau }_{\sigma }{\tau }_{EP}}$$ 4

However, this procedure fails to adequately describe the experimental data, as can be seen in Figure a for PS-b-PGME with r = 1:16. Alternatively, τ_σ and τ_EPcan be obtained, respectively, from the crossing of ε′, ε″, and the minimum of the second derivative of log­(ε′), which also coincides with the maximum of σ″. Following this method, we extracted the number density of conducting ions, p, and their mobility, μ, as

$$p=\frac{1}{\pi l_B{L}^2}{\left(\frac{{\tau }_{EP}}{{\tau }_{\sigma }}\right)}^2,\mu =\frac{e{L}^2{\tau }_{\sigma }}{4{\tau }_{EP}^2{k}_{\mathrm{{\rm B}}}T}$$ 5

where l _B = e ²/(4πε_sε₀ k _Β T) is the Bjerrum length, L is the sample thickness, k _Β is the Boltzmann constant, and T is the absolute temperature. Using these quantities, the dc-conductivity can be calculated as σ_dc = epμ. In Figure b, both p and μ are plotted versus r = [Li]:[EO], in the case of PS-b-PGME copolymer, at 363 K. As expected, p increases with lithium-salt concentration, while μ goes through a maximum for the r = 1:16 where the maximum ionic conductivity is also obtained. In Figure d, p and μ are plotted as a function of the inverse temperature for the same copolymer with r = 1:16. The number density of the conducting ions, p, shows a weak temperature dependence, whereas the respective mobility, μ, increases drastically with temperature largely dictating the dc-conductivity.

17.

(a) Real (open symbols) and imaginary (filled symbols) parts of dielectric permittivity (blue), and complex conductivity (red) along with loss tangent (green pentagons), plotted as a function of frequency, for the PS-b-PGME with r = 1:16 at T = 363 K. The blue, black, and red dashed lines provide the ε_s, ε_EP, and σ_dc values, respectively. The green solid line is a fit to tan δ according to eq . (b) Number density (blue circles) and mobility of conducting ions (red triangles) for the same copolymer as a function of r, at T = 363 K. (c) The real (open symbols) and imaginary (dashed lines) parts of the complex conductivity for the PS-b-PGME with r = 1:16 at different temperatures obtained on cooling. (d) Number density (blue circles) and mobility of conducting ions (red triangles) for the same copolymer shown as a function of the inverse temperature.

The thermodynamic, conductivity, and rheology results for the PS-b-PGME copolymer with r = [Li]:[EO] = 1:16 are compared in Figure . At the PS glass temperature (T ∼350 K), the shear modulus is at ∼10⁷ Pa and the dc-conductivity is at ∼1 × 10^–5 S·cm^–1. These values should be compared with those of the PS-b-P­(EO-co-GME) copolymers.

18.

Temperature dependence of the |G*| (black open-circles, rate = 5 K·min^–1), the ionic conductivity (red filled triangles), and the heat flow (blue line, rate = 20 K·min^–1) in doped PS-b-PGME with the same [Li]:[EO] = 1:16 ratio. The gray area indicates the glass temperature of the PS block.

PS-b-P­(EO-co-GME) vs PS-b-PGME: A Comparison

The moduli and ionic conductivities of the PS-b-P­(EO-co-GME) vs PS-b-PGME copolymers for [Li]:[EO] ratios of 1:32 and 1:16, respectively, corresponding to the electrolyte compositions where conductivity is maximized, are compared in Figure . Between the two copolymer systems, PS-b-PGME is advantageous. First, the modulus of the hard phase is higher below the PS T _g. Second, despite the higher T _g for the soft phase at the specific electrolyte composition, the ionic conductivity in the doped PS-b-PGME exhibits a steeper T-dependence that exceeds that in the PS-b-P­(EO-co-GME) copolymers. As a result, at T = 400 K and r=[Li]:[EO] = 1:16, the dc-conductivity in the PS-b-PGME is at 6 × 10^–5 S·cm^–1 as compared to 2 × 10^–5 S·cm^–1 in the PS-b-P­(EO-co-GME) copolymer. Notably, both values are much higher than in the single ion conducting P­(EO-co-LiTFSAEGE) copolymer (where σ_dc = 3 × 10^–7 S·cm^–1) and higher than in the archetypal dual-ion solid polymer electrolytes PS-b-PEO/LiTFSI (σ_dc = 5.2 × 10^–6 S·cm^–1) and PS-b-PEO/LiTf (σ_dc = 6.3 × 10^–8 S·cm^–1), all reported at 400 K and r = [Li]:[EO] = 1:16.

19.

Comparison of σ_dc and |G*| as a function of temperature for the two cases of PS-b-P­(EO-co-GME) (blue) and PS-b-PGME (red) with [Li]:[EO] ratios of 1:32 and 1:16, respectively. Electrolyte ratios correspond to the respective copolymers with the highest dc-conductivity.

Conductivities in the present PS-b-PGME/LiTFSI and PS-b-P­(EO-co-GME)/LiTFSI copolymers can also be compared with known single ion conductors, namely, polymerized ionic liquids (PILs). − The latter is composed of polymer backbones bearing covalently attached ionic groups. The cationic components in PILs are often based on imidazolium, pyridinium, ammonium, or phosphonium structures, while the anions include bis­(trifluoromethylsulfonyl)­imide ([TFSI]⁻), tetrafluoroborate ([BF₄]⁻), or hexafluorophosphate ([PF₆]⁻). In PILs of particular interest is the possibility to decouple the ion motion from the polymer segmental dynamics, known as ion-polymer decoupling. − According to the latter, ion motion can decouple from the polymer backbone dynamics and persist even below T _g. To make the comparison with the present systems, we choose poly­(1-(4-vinylbenzyl)-3-butylimidazolium)/TFSI (poly­[VBBI]⁺[TFSI]⁻) having a similar T _g to PS-b-PGME/LiTFSI (for the composition r = 1:16). When compared at the same temperature, the two systems bear similar conductivity values, suggesting a common ion-hopping mechanism.

To summarize, the first investigation of PGME as the matrix polyether block in SPEs revealed certain advantages over the currently employed PEO block. Each GME repeat unit has two oxygen atoms that can better solubilize alkali metal salts. In return, PGME is as flexible as the isomeric PEO, but with side chains that inhibit crystallization due to the lack of tacticity. Thus, PGME combines several favorable properties required for the soft block design in SPEs; high segmental mobility that is nearly independent of molar mass, favorable molecular structure that can solubilize alkali metal salts, high dielectric permittivity, and the absence of crystallization. Furthermore, employing shorter rPEG or PGME chains as a polymer plasticizer remains a promising approach toward further increasing ion conductivity.

Although membrane fabrication is beyond the scope of this study, its constraints must be considered when evaluating these polymers for battery applications. The investigated block copolymers exhibit glassy and brittle characteristics at ambient temperatures, which can be attributed to their high PS content. However, PS-b-PGME appears comparatively more malleable than PS-b-rPEG. From a manufacturing perspective, solvent casting and hot pressing are both viable methods for fabricating membranes from these block copolymers. To enable processing via hot pressing or photo-cross-linking, the constituent polyethers would require modification (e.g., through the incorporation of acrylate groups). Work on such cross-linkable systems is currently in progress.

Conclusions

Current SPEs are based on a high molar mass PEO as the conducting polymer matrix. However, PEO-based SPEs suffer from relatively low conductivity as a result of polymer crystallization and strong interactions between EO and Li ions that restrict ion transport. Here, we explore a strategy for improving ion conductivity that is based on a modified polyether block, which represents structural PEO isomers. A series of fully amorphous PGME homopolymers was synthesized via anionic ring opening polymerization of glycidyl methyl ether (GME), showing promising ionic conductivities after LiTFSI doping at room temperature in comparison to PEO. Employing the “rPEG concept” introduced for biomedical purposes in previous work, we substituted PEO by EO-co-GME copolymers in the well-established PS-b-PEO system to obtain a fully amorphous polyether domain isomeric to PEO (a 21% GME content is sufficient to achieve noncrystallizable polyether segments). In another series of block copolymers, we replaced EO completely with GME, resulting in new PS-b-PGME block copolymers. Following doping with LiTFSI, we evaluated the morphology and the ionic conductivity as a function of salt content of these new polymers. The two systems share a common feature: a completely amorphous polyether block. Following doping with LiTFSI, we evaluated the phase state and the ion conductivity as a function of salt content.

With respect to the structure, the PS-b-PGME copolymer with the highest ion conductivity had a lamellar nanophase with broad channels (typically ∼16 nm) and long-range order. With a dc-conductivity of ∼1 × 10^–5 S·cm^–1 at the PS glass temperature where the modulus is above 10⁷ Pa, the PS-b-GME copolymers doped with LiTFSI are superior to the established dual ion conductors PS-b-PEO doped with LiTFSI or with LiTf. In addition, PS-b-PGME doped with LiTFSI has a moderately higher conductivity than PS-b-P­(EO-co-GME) and a considerably higher conductivity than the structurally similar single ion conductor PS-b-P­(EO-co-LiTFSAEGE) as reported in the literature.

PGME best combines favorable properties required for the design of the soft block in SPEs; low T _g that is nearly independent of molar mass, favorable molecular structure that can solubilize alkali metal salts (2 oxygens in GME, 1 in EO), high dielectric permittivity (ε′_S ∼ 9 in PGME as compared to 4.5 in PEO at ambient temperature), and the absence of crystallization (at all temperatures). These results suggest that PGME-containing copolymers can replace PEO in future SPEs.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.macromol.5c02733.

• Additional NMR spectra, MALDI-ToF, SEC, DSC, detailed SAXS, ionic conductivity, and rheological data (PDF)

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I.T. and T.G. contributed equally to this work.

The open access publishing of this article is financially supported by HEAL-Link.

The authors declare no competing financial interest.