Interfacial Effects in Conductivity Measurements of Block Copolymer Electrolytes

Abstract

The ionic conductivity in lamellar block copolymer electrolytes is often anisotropic, where the in-plane conductivity exceeds the through-plane conductivity by up to an order of magnitude. In a prior work, we showed significant anisotropy in the ionic conductivity of a lamellar block copolymer based on polystyrene (PS) and a polymer ionic liquid (PIL), and we proposed that the through-film ionic conductivity was depressed by layering of lamellar domains near the electrode surface. In the present work, we first tested that conclusion by measuring the through-plane ionic conductivity of two model PIL-based systems having controlled interfacial profiles using impedance spectroscopy. The measurements were not sensitive to changes in interfacial composition or structure, so anisotropy in the ionic conductivity of PS-block-PIL materials must arise from an in-plane enhancement rather than a through-plane depression. We then examined the origin of this in-plane enhancement with a series of PS-block-PIL materials, a P(S-r-IL) copolymer, and a PIL homopolymer, where impedance spectra were acquired with a top-contact electrode configuration. These studies show that enhanced in-plane ionic conductivities are correlated with the formation of an IL-rich wetting layer at the free surface, which presumably provides a low-resistance path for ion transport between the electrodes. Importantly, the enhanced in-plane ionic conductivities in these PS-block-PIL materials are consistent with simple geometric arguments based on properties of the PIL, while the through-plane values are an order of magnitude lower. Consequently, it is critical to understand how surface and bulk effects contribute to impedance spectroscopy measurements when developing structure–conductivity relations in this class of materials.

Introduction

Block copolymer electrolytes are a class of materials of interest for a number of electrochemical applications, ranging from lithium ion batteries to fuel cells to carbon capture.¹⁻⁸ Typically, these materials consist of a polymer electrolyte block linked to an insulating block that provides mechanical stability. Provided that χN is sufficiently high, where χ is the Flory–Huggins interaction parameter between the two blocks and N is the overall degree of polymerization, the material self-assembles into classical block copolymer mesophases.⁹ The impact of self-assembled morphology on ionic conductivity is often captured by the morphology factor f, developed by Sax and Ottino based on an effective medium approach to link bulk structure and transport in randomly oriented block copolymer morphologies.¹⁰ Here f is defined as

1

where σ₀ is the ionic conductivity of the block copolymer material, σ_c is the ionic conductivity of the electrolyte block as measured from a homopolymer, and ϕ_c is the volume fraction of the electrolyte block in the block copolymer.¹¹ Expected values of f for cylinder, lamellar, and gyroid morphologies are f ≃ 1/3, 2/3, and 1, respectively, based on an idealized geometry of each morphology.^10,12 The interpenetrating network that produces the high theoretical morphology factor of the gyroid phase makes it attractive for three-dimensional ion transport. However, the gyroid is usually only stable under a narrow range of composition and temperature,¹³ and the effects of tortuosity could depress the morphology factor to as low as f = 0.47.^14,15 By contrast, randomly oriented lamellae are stable over a wide composition window and can potentially deliver long-range ion transport, provided there is sufficient connectivity of the PIL domain across grain boundaries.⁵

Several studies of lamellar block copolymer electrolytes have found morphology factors that are roughly consistent with the predicted value of 2/3 when ionic conductivity is measured in the in-plane direction, i.e., conductivity along the plane of the film.^12,16−18 In contrast, through-plane ionic conductivity (i.e., conductivity across the film thickness) has been shown to be significantly lower in several block copolymer electrolyte systems, producing morphology factors which are below f = 2/3 by factors ranging from roughly 2 to more than an order of magnitude.¹⁹⁻²² This anisotropy in the ionic conductivity has been correlated with structural anisotropy, some of which can be caused by certain processing conditions (melt pressing, electric or magnetic field alignment, shear alignment).^{19,20,23−27} A persistent source of structural anisotropy, however, is thermodynamic in origin, whereby preferential interactions between one block and a surface lead to wetting layers that drive layering of domains.²⁸

In a recent paper, we showed that lamellar block copolymers of polystyrene (PS) and poly(1-(2-acryloyloxyethyl)-3-butylimidazolium bis(trifluoromethanesulfonyl)imide) form highly aligned layers at an air or electrode surface.²⁰ Layering of lamellae at the interface produces alternating continuous regions of PS and polymer electrolyte, in which the PS regions act as a barrier to through-plane ion transport and the polymer electrolyte regions provide low-tortuosity pathways that are favorable to in-plane ion transport. We measured significant anisotropy in the ionic conductivity: the in-plane morphology factors were similar to the expected f = 2/3, as noted by others for the same block copolymer chemistry,^16,17 while the through-plane morphology factors were an order of magnitude lower. We concluded that the surface-induced ordering of lamellar domains was depressing the through-plane conductivity. A similar conclusion was reached by another study that examined a gyroid-forming poly(isoprene-b-styrene-b-ethylene oxide) doped with lithium salt, where the PEO block was the conducting phase, and through-plane ionic conductivity improved by a factor of 7 when the electrodes were coated with a PEO brush.²⁹ The authors hypothesized that this brush layer suppressed the formation of a nonconductive wetting layer at the interface with the electrode.

In this study, we revisit our prior conclusion and consider whether surface effects merely enhance the in-plane conductivity rather than depressing the through-plane conductivity. If so, then the in-plane morphology factors that match the expected value of f = 2/3 could be coincidental, and the true bulk ionic conductivity of PIL-based block copolymers could actually be much lower. This possibility was interrogated using a series of PS and poly(4-vinylbenzyl-butylimidazolium bis(trifluoromethanesulfonyl)imide) block copolymers (PS-b-PIL), a statistical copolymer of styrene and 4-vinylbenzyl-butylimidazolium bis(trifluoromethanesulfonyl)imide (P(S-r-IL)), and a PIL homopolymer. First, we measured the through-plane ionic conductivity of two model PIL-based systems having controlled interfacial profiles: (1) A PS/PIL/PS trilayer, where the thicknesses of the PS layers were ∼0.1% of the overall thickness; and (2) a lamellar PS-block-PIL material cast on both smooth and rough electrodes, which promotes and disrupts the formation of well-defined lamellar layers on the electrode surface, respectively. We then measured both the in-plane and through-plane ionic conductivity for the PS-b-PIL materials, P(S-r-IL), and PIL. Collectively, these studies indicate that an IL-rich wetting layer at the free surface enhances the in-plane ionic conductivity.

Experimental Section

The procedures used for the synthesis and characterization of PS, PIL, and copolymers thereof are detailed in this section, with all synthesis schemes, ¹H NMR spectra, and GPC traces provided in Figures S1–S14. The synthetic protocols of block copolymers, statistical copolymer, and PIL homopolymer were adapted from those reported elsewhere.^17,30 Block copolymers are named PSX–PILY such that X is the M_n of the PS block in kg/mol and Y and is the PIL composition in vol % PIL. The amounts of reactants and solvents given in the procedures for block copolymer synthesis are all taken from the synthesis of PS5-PIL51.

Materials

4-Cyano-4-[(dodecylsulfanyl-thiocarbonyl)sulfanyl]pentanoic acid (chain transfer agent (CTA), >97%), benzene (anhydrous), 1-butylimidazole (98%), and lithium bis(trifluoromethanesulfonyl)imide (LiTFSI, 97%) were used as received from Sigma-Aldrich. Dichloromethane (DCM, 99.9%, HPLC), 4-vinylbenzyl chloride (VBC, 90%), diethyl ether anhydrous (BHT Stabilized/Certified ACS), aluminum oxide (anhydrous), methanol (≥99.8%, ACS Certified), N,N-dimethylformamide (DMF, 99%), acetonitrile (anhydrous, 99.9%), deuterated chloroform (CDCl₃, 99.8 atom % D), dimethyl-d6 sulfoxide (DMSO-d6, 99.9 atom % D), and tetrahydrofuran (THF, ≥ 99.9%, Optima for HPLC) were used as received from Fisher Scientific. Azobis(isobutyronitrile) (AIBN, 98%, Sigma-Aldrich) was purified by recrystallization from methanol. Styrene (S, 99%, Fisher Scientific) was purified of inhibitor by passing through a column packed with aluminum oxide.

Synthesis of PS MacroCTA

Styrene monomer purified of inhibitor (7.84 g, 75.3 mmol), CTA (0.14 g, 0.35 mmol), and AIBN (0.0053 g, 0.032 mmol) were dissolved in benzene (6.4 mL) in a round-bottom flask containing a magnetic stir bar. The flask was then sealed with a rubber septum and the reaction mixture was sparged with argon for 10 min, after which the flask was placed in an oil bath at 70 °C for 18 h. The polymerization was quenched by removing the flask from the oil bath and immersing it in liquid nitrogen until the contents were frozen solid and then removing the septum. Once the contents had thawed, the polymer was precipitated in cold methanol. The polymer was isolated by gravity filtration and then redissolved in a small amount of DCM. The PS macroCTA was again precipitated in cold methanol, collected by gravity filtration and finally dried overnight under vacuum at room temperature (>18 h). Molecular weight and dispersity were determined by gel permeation chromatography (GPC) using THF as the eluent. Purity of the product was confirmed through ¹H NMR using CDCl₃ as the solvent.

Synthesis of PS-b-PVBC Copolymer

Polystyrene macroCTA (1.40 g, 0.275 mmol), AIBN (0.0047 g, 0.029 mmol), and vinylbenzyl chloride (VBC) (4.92 g, 32.2 mmol) were dissolved in benzene (8.25 mL) in a round-bottom flask with a magnetic stir bar. The flask was then sealed with a rubber septum and sparged with argon for 10 min, after which time the flask was placed in an oil bath at 70 °C for 24 h. The reaction was quenched by removing the flask from the oil bath and placing it in liquid nitrogen until the contents were frozen solid, and then removing the septum. Once the contents had thawed, the copolymer was precipitated in cold methanol and then recovered by gravity filtration. The block copolymer, PS-b-PVBC, was isolated by redissolving in a small amount of DCM, precipitating into cold methanol, and finally collected by gravity filtration. It was then dried under vacuum at room temperature overnight (>18 h). Block copolymer composition was determined by ¹H NMR with CDCl₃ as the solvent, using the ratio of the integrated areas of the peaks associated with the 2 ortho protons of the PS and PVBC phenyl rings and the 2 protons associated with the methylene group of the PVBC pendant chain. Chain extension and dispersity were confirmed by GPC using THF as the eluent. The molecular weight of the PVBC block was calculated based on composition from NMR and molecular weight of the PS macroCTA.

Synthesis of PS-b-PVBBuIm-Cl Copolymer

PS-b-PVBC (1.55 g, 0.204 mmol copolymer, 3.25 mmol VBC repeat units) and 1-butylimidazole (1.31 g, 10.5 mmol) were dissolved in DMF (5.0 mL) in a 20 mL glass vial with a stir bar. The vial was placed on a hot plate and stirred at 80 °C for 24 h. After this time, DMF was removed by rotary evaporation and 15 mL of DI water added to the vial and contents stirred until copolymer precipitated. Vial contents added to 150 mL of DI water and stirred to wash. PS-b-PVBBuIm-Cl was collected by gravity filtration, dried at room temperature under vacuum overnight and characterized by ¹H NMR analysis using DMSO-d6 as the solvent.

Synthesis of PS-b-PVBBuIm-TFSI Copolymer

PS-b-PVBBuIm-Cl (1.59 g, 0.118 mmol copolymer, 3.56 mmol chloride anion) and LiTFSI (1.90 g, 6.62 mmol) were dissolved in DMF (5.0 mL) in a 20 mL glass vial with a stir bar. The vial was placed on a hot plate and stirred at 50 °C for 24 h, then removed from heat and allowed to cool to room temperature. The copolymer was precipitated into 50 vol % DI water and methanol, collecting by gravity filtration, washed with an additional 100 mL of DI water, and dried in under vacuum at 40 °C for 24 h. The copolymer was then characterized by ¹H NMR analysis using DMSO-d6 as the solvent. Ion exchange was considered complete when the peak in ¹H NMR at 10.6 ppm, corresponding to hydrogen “e” in PS-b-PVBBuIm-Cl could no longer be detected and was replaced by a peak of roughly equivalent integration at 9.2 ppm, corresponding to hydrogen “e” in PS-b-PVBBuIm-TFSI (Figures S11c and d, S12c and d, S13c and d).

Synthesis of P(S-r-VBC) Copolymer

Styrene (2.7507 g, 26.4 mmol), VBC (4.0201 g, 26.3 mmol), and AIBN (0.0324 g, 0.197 mmol) were mixed in a round-bottom flask with a magnetic stir bar. The flask was then sealed with a rubber septum and sparged with argon for 10 min, after which the flask was placed in an oil bath at 70 °C for 45 min. The reaction was quenched by removing the flask from the oil bath and placing it in liquid nitrogen until the contents were frozen solid and then removing the septum. Once the contents had thawed, the copolymer was precipitated in cold methanol. The copolymer was isolated by gravity filtration and then redissolved in a small amount of DCM. The PVBC was again precipitated in cold methanol, collected by gravity filtration and finally dried overnight under vacuum at room temperature (>18 h). Molecular weight and dispersity were determined by gel permeation chromatography (GPC) using THF as the eluent. The copolymer composition was determined by ¹H NMR with CDCl₃ as the solvent, using the ratio of the integrated areas associated with the of peaks assigned to the 2 ortho protons of the PS and PVBC phenyl rings and the 2 protons associated with the methylene group of the PVBC pendant chain.

Synthesis of P(S-r-VBBuIm-Cl) Copolymer

P(S-r-VBC) (0.4871 g, 0.0138 mmol copolymer, 2.08 mmol VBC repeat units) and 1-butylimidazole (0.7812 g, 6.29 mmol) were dissolved in DMF (4.0 mL) in a 20 mL glass vial with a stir bar. The vial was placed on a hot plate to stir at 80 °C for 24 h, then removed from heat and allowed to cool to room temperature. The copolymer was precipitated by adding 15 mL diethyl ether to the vial and stirring rapid. The copolymer was isolated by gravity filtration and then redissolved in a small amount of DMF. The copolymer was precipitated again in diethyl ether, collected by gravity filtration, dried overnight under vacuum at room temperature (>18 h), and characterized by ¹H NMR using DMSO-d₆ as the solvent.

Synthesis of P(S-r-VBBuIm-TFSI) Copolymer (P(S-r-IL)

P(S-r-VBBuIm-Cl) (0.3103 g, 0.00576 mmol copolymer, 0.864 mmol chloride anion) and LiTFSI (1.2726 g, 4.43 mmol) were dissolved in DMF (4.8 mL) in a 20 mL glass vial with a stir bar. The vial was placed on a hot plate and stirred at 50 °C for 24 h, then removed from heat and allowed to cool to room temperature. The copolymer was precipitated into DI water three times, decanting the DI water and dissolving the copolymer left behind in a small amount of DMF between precipitations. The copolymer was collected by decanting the DI water after the last precipitation, transferring the copolymer to a 20 mL glass vial, and drying overnight under vacuum at room temperature (>18 h). The copolymer was characterized by ¹H NMR using DMSO-d6 as the solvent. Ion exchange was considered complete when the peak in ¹H NMR at 10.2 ppm, corresponding to hydrogen “e” in P(S-r-VBBuIm-Cl) could no longer be detected and was replaced by a peak of roughly equivalent integration at 9.2 ppm, corresponding to hydrogen “e” in P(S-r-VBBuIm-TFSI) (Figure S14b and c).

Synthesis of PVBC Homopolymer

CTA (0.039 g, 0.097 mmol), AIBN (0.0017 g, 0.10 mmol), and VBC (5.73 g, 37.5 mmol) were mixed in a round-bottom flask with a magnetic stir bar. The flask was then sealed with a rubber septum and sparged with argon for 10 min, after which the flask was placed in an oil bath at 70 °C for 24 h. The reaction was quenched by removing the flask from the oil bath and placing it in liquid nitrogen until the contents were frozen solid and then removing the septum. Once the contents had thawed, the polymer was precipitated in cold methanol. The polymer was isolated by gravity filtration and then redissolved in a small amount of DCM. The PVBC was again precipitated in cold methanol, collected by gravity filtration and finally dried overnight under vacuum at room temperature (>18 h). Molecular weight and dispersity were determined by gel permeation chromatography (GPC) using THF as the eluent. Purity of product was confirmed through ¹H NMR using CDCl₃ as the solvent.

Synthesis of PVBBuIm-Cl Homopolymer

PVBC (1.11 g, 0.0822 mmol polymer, 7.28 mmol VBC repeat units) and 1-butylimidazole (2.64 g, 21.3 mmol) were dissolved in DMF (5.5 mL) in a 20 mL glass vial with a stir bar. The vial was placed on a hot plate to stir at 80 °C for 24 h, then removed from heat and allowed to cool to room temperature. The polymer had precipitated overnight. Supernatant solution was decanted and PVBBuIm-Cl dissolved in methanol, the precipitated in diethyl ether 5 times, redissolving in methanol between precipitations. Polymer was then transferred to a 20 mL vial, dried under vacuum at room temperature overnight (>18 h), and characterized by ¹H NMR using DMSO-d₆ as the solvent.

Synthesis of PVBBuIm-TFSI Homopolymer (PIL)

PVBBuIm-Cl (0.71 g, 0.029 mmol polymer, 2.56 mmol chloride anion) and LiTFSI (3.48 g, 12.1 mmol) were dissolved in DMF (7.1 mL) in a 20 mL glass vial with a stir bar. The vial was placed on a hot plate and stirred at 50 °C for 24 h, then removed from heat and allowed to cool to room temperature. The polymer was precipitated into DI water three times, decanting the DI water and dissolving the polymer left behind in a small amount of methanol between precipitations. PVBBuIm-Cl was collected by decanting the DI water after the last precipitation and redissolving the polymer left behind in a small amount of methanol, transferring the solution to a 20 mL glass vial, and concentrating via rotary evaporation. The polymer was then dried under vacuum at 40 °C for 24 h and characterized by ¹H NMR using DMSO-d6 as the solvent. Ion exchange was considered complete when the peak in ¹H NMR at 10.4 ppm, corresponding to hydrogen “e” in PVBBuIm-Cl could no longer be detected and was replaced by a peak of roughly equivalent integration at 9.2 ppm, corresponding to hydrogen “e” in PVBBuIm-TFSI (Figure S10b and c).

Differential Scanning Calorimetry (DSC)

The calorimetric glass transition temperature of each sample was measured using a TA DSC Q2000. Sample were sealed in Tzero low-mass aluminum pans with hermetic lids. Measurements were made using an empty pan as a reference, beginning by annealing at 120 °C for 5 min, then cycling twice times at a rate of 10 °C/min between 120 and −20 °C. Within each cycle and before commencing a temperature ramp, isothermal conditions were maintained for 5 min. The resulting thermograms are given in Figure S23.

Grazing Incidence Small Angle X-ray Scattering (GISAXS)

GISAXS was performed using a Xenocs Xeuss 3.0 instrument equipped with a Cu Kα Xenocs GeniX3D HFVL microfocus source (λ = 0.154 nm) and a single photon counting Dectris Pilatus3 R 300k detector with a 172 μm pixel size. Thin films (100–200 nm) were prepared by spin coating from 5.0 wt % acetonitrile solution at 4000 rpm for 60 s. Thick films (20–50 μm) were prepared by the method described for in-plane impedance spectroscopy measurements. Samples were illuminated at an incidence angle of α_i ≈ 0.20° for thin films, and at 0.10° and 0.2° for thick films, where the critical angle of this material is approximately 0.16°.

Impedance Spectroscopy

Impedance spectroscopy measurements were performed using two distinct electrode configurations in order to probe ionic conductivity in both the through-plane and in-plane directions. Through-plane measurements were performed with a parallel-plate electrode configuration using a Novocontrol High Resolution Alpha Dielectric Analyzer equipped with a Quatro Cryosystem for temperature control. Samples were prepared by casting films approximately 100 μm thick from a solution of 10 wt % polymer in THF onto either a circular electrode of stainless steel (SS) with a diameter of 10 mm or square electrode of highly doped silicon (Si) with an edge length of 10 mm. Sample thickness was measured using a digital micrometer. In a typical preparation, the solution was dripped onto the electrode with a pipet, and the solvent was allowed to evaporate over the course of 1 h in the fume hood. To control the thickness of the film, two 100 μm silica spacers were pressed into the film before the solvent had fully evaporated. A second electrode of the same shape and material with diameter or edge length of 20 mm was then pressed on top in a parallel plate arrangement. The sample, consisting of the top and bottom electrodes, film, and spacers was annealed (small electrode up) under vacuum at 120 °C for 24 h. The sample was then placed in the spectrometer and annealed again at 120 °C under dry nitrogen for approximately 1 h while taking measurements to ensure that the spectra obtained did not change over time. Measurements were then conducted across a range of temperatures, beginning with the annealing temperature of 120 °C. Samples were equilibrated for 10 min at each temperature before beginning a measurement, which was found to be sufficiently long for proper thermal equilibration, as judged by reproducibility of data at a given temperature during thermal cycling. Liquid nitrogen was used by the temperature control system along with a heating element, which enabled control of the sample temperature to within 0.1 K of the set point while preventing the introduction of additional moisture into the system. DC ionic conductivity was taken to be the value of the real conductivity function σ′(ω) at the frequency at which a maximum occurs in the imaginary component of the electrical modulus function M″(ω), where the complex electrical modulus is defined as M*(ω) = 1/ε*(ω).

In-plane measurements were performed with a GAMRY Reference 600 Potentiostat/Galvanostat/ZRA in a two-point probe configuration using electrodes of platinum wire and a Fumatech MK3Measuring Cell. Samples were prepared by casting a film between 18 and 41 μm thick, 20 mm wide, and greater than 1 cm long from a solution of 10 wt % polymer in THF onto a glass slide. In a typical preparation, the solution was drop cast onto the slide and allowed to evaporate over the course of 1 h in the fume hood. Once most of the solvent had evaporated, the film was annealed under vacuum at 120 °C for 24 h. The sample was then placed in the spectrometer. Contact was maintained by a constant force applied via a spring to the glass slide and an isothermal anneal at 100 °C for 1 h. Measurements were made at a range of temperatures, beginning with the annealing temperature of 100 °C. Samples were equilibrated for 1 h at each temperature before beginning a measurement, which was found to be sufficiently long for proper thermal equilibration, as judged by reproducibility of data at a given temperature during thermal cycling. The longer equilibration time compared to the Novocontrol system was attributed to use of a static heating element in the Fumatech cell compared to the use of a controlled flow of heated nitrogen gas in the Novocontrol system. The resistance R was determined from the plateau value of the absolute value of impedance data represented in the form of a Bode plot. Conductivity σ was calculated using the resistance and sample geometry by the equation σ = L/(whR), where w is the width of the film, h is the thickness measured as described above, and L is the distance between electrodes (1 cm). As shown elsewhere, these measurements yield consistent ionic conductivities as thickness is varied in the range of 20–50 μm,³¹ as well as when electrode spacing is varied between 10 and 20 mm (Figure S15).

The methods for determining DC ionic conductivity from through-plane and in-plane measurements were chosen because they convey the frequency dependence of the data, allowing for consideration of both ionic conductivity and the associated dynamics. The σ* and M* formalisms are well established in the scientific community interested in the relationship between molecular dynamics and material properties. Since σ* and M* cannot be accurately calculated for in-plane measurements due to the introduction of fringe effects by the uneven electric field lines inherent to a parallel wire electrode configuration, a Bode plot is used, which allows for a frequency dependent expression of the complex impedance data.

Results and Discussion

Table 1 summarizes the characteristics of all polymers used in this study. Three PS-b-PIL block copolymers and a PIL homopolymer were synthesized using reversible addition–fragmentation chain transfer (RAFT) polymerization, while P(S-r-IL) was synthesized via free radical polymerization for ease of synthesis. The difference in molecular weight and dispersity of P(S-r-IL) compared to PIL and block copolymers was not expected to have a significant impact on results, as ionic conductivity in polymer ionic liquids has been shown to be largely decoupled from the segmental dynamics, resulting in relatively constant conductivity with changing molecular weight for chains larger than oligomers.^32,33 The PIL homopolymer and P(S-r-IL) were used as controls to see whether anisotropic conductivity was unique to the block copolymers. A high molecular weight and low dispersity PS was purchased from Scientific Polymer Products, Inc. and used as received. A bulk lamellar structure was determined for all block copolymers through transmission SAXS measurements of 50 μm films that had been annealed for 24 h at 130 °C (Figure S16). The volume fraction of PIL in each of the block copolymers was calculated from the molecular weight of each block using a density of 1.04 g/mL for PS and 1.50 g/mL for PIL. The density of the PIL was calculated at room temperature from the mass and volume of a pendant PIL droplet, where the latter was measured using a DataPhysics OCA 15EC.

Table 1. Characteristics of polymers.

sample name	Mna (g/mol)	mol % PILb	vol % PILc	Đd	morphologye	d0 (nm)e
PS5-PIL51	13 400	24.5	51.2	1.08	lamellar	11.1
PS8-PIL41	15 900	17.5	40.7	1.10	lamellar	13.8
PS12-PIL35	22 700	14.5	35.4	1.09	lamellar	19.9
P(S-r-IL)	90 600	56.0		1.7	amorphous
PIL	46 000	100.0	100.0	1.11	amorphous
PS	177 800	0.0	0.0	1.03	amorphous

^aDetermined by GPC and NMR.

^bdetermined by NMR.

^cCalculated from M_n,PS, M_n,PIL, and densities of PS (1.04 g/mL) and PIL (1.50 g/mol);

^dDetermined by GPC of the homopolymer or block copolymer prior to quaternization;

^eDetermined by transmission SAXS.

To understand the impact of insulating interfacial layers on the bulk ionic conductivity, as measured by through-plane impedance spectroscopy methods, it is useful to start by considering the origins of interfacial polarization in dielectric media. The phenomenon of interfacial polarization, frequently referred to broadly as Maxwell–Wagner-Sillars (MWS) polarization, arises from the build-up of charge at an interface between two media with different conductivities. The simplest case, proposed by Whitehead and elaborated by van Beek, consists of a bilayer of two materials with different frequency-independent dielectric constants and conductivities.^34,35 Since our aim is to understand interfacial polarization caused by insulating layers at electrode interfaces, we can extend this bilayer to a trilayer system, in which a conducting layer of thickness on the order of 100 μm is sandwiched between two thinner insulating layers, as depicted in Figure 1. When these layers are treated as capacitors in series, a frequency-dependent polarization arises which can be described by the Debye equations,

2

3

where ω is the angular frequency of the electric field, ε′ and ε″ are the real and imaginary components of the complex permittivity, respectively, and ε₀ is the permittivity of free space; τ is the characteristic time of the MWS polarization, σ is the conductivity of the bilayer system as a whole, and ε_S and ε_∞ are the high and low frequency values of the relative permittivity associated with the MWS polarization, respectively. These parameters can be expressed in terms of the thickness, dielectric constant, and conductivity of each layer such that

4

5

6

7

where σ₁ and σ₂ are the conductivities of components 1 (insulator) and 2 (conductor), respectively; ε₁ and ε₂ are the dielectric constants of components 1 (insulator) and 2 (conductor), respectively; h is the thickness of the trilayer system as a whole, h₂ is the thickness of the conducting layer, and h₁ is the thickness of a single insulating layer (for a combined insulator thickness of 2h₁).

Figure 1.

(a) Real and (b) imaginary contributions to the complex conductivity of a system composed of two phases of different conductivities and permittivities, calculated using eqs 2–7. For all cases, h = 100 μm, σ₁ = 6.7 × 10^–16 S/cm, σ₂ = 6.0 × 10^–7 S/cm, ε₁ = 4, and ε₂ = 11.

Figure 1 depicts the real and imaginary parts of the complex conductivity σ*, which is related to the complex permittivity as σ* = iωε₀ε*, calculated from eqs 2 and 3. It is evident that as the fraction of component 1 increases, the value of the σ′ plateau, corresponding to σ₂, remains constant. At the same time, the characteristic frequency of MWS polarization ω_MWS, easily identified as a low frequency peak in σ″, increases as the fraction of component 1 increases. The conductivity the of the total trilayer system σ, which is identical to a simple calculation of conductivity achieved by considering the layers as resistors in series, appears as a second, low frequency plateau in the σ′ spectrum, and is highly dependent on the thickness of the insulating layers. This simple model, however, neglects the frequency dependence of the dielectric function ε* of each layer.

A more complex model is there therefore necessary to fully capture the polarization response of a real polymer system. A model developed by Serghei et al. to describe the process of electrode polarization³⁶ can be adapted to describe interfacial polarizations that arise in a model trilayer system. When these layers are again treated as capacitors in series, the complex dielectric function of the trilayer system can be expressed as

8

where and are the complex dielectric function of the insulating and conducting layers, respectively, h₁ and h₂ are the thicknesses of those layers, respectively, and ε* and h are the complex dielectric function and thickness of the bilayer system as a whole. Separating eq 8 into real and imaginary components yields

9

10

where x = 2h₁/h and y = 1 – x. The complex dielectric function of each layer can be described using an approximation of the random barrier model proposed by Dyre, which considers the hopping of ions in a randomly distributed energy barrier landscape. Solved within the continuous-time random-walk approximation, the complex conductivity function is expressed analytically as

11

12

where σ₀ is the plateau value of σ′ (DC ionic conductivity) and τ_e is the time associated with the attempt rate to surmount the energy barriers that determine long-range conduction.^37,38 Recently, τ_e has been interpreted as the characteristic ion hopping time.²²

In order to employ this model to study the polarization response of a real polymer electrolyte sandwiched between two insulating films, PIL films with a thickness of 100 μm were prepared between stainless steel (SS) electrodes that had been coated with a thin film of PS homopolymer. The procedures for preparing and characterizing these samples are provided in the Supporting Information. The thickness of the PS coating was varied from 18 to 89 nm. Through-plane impedance spectroscopy measurements were performed on these trilayer samples at temperatures ranging from 353 to 243 K. The temperature range was selected in order to remain below the glass transition temperature (T_g) of PS (373 K) but include temperatures above and below the T_g of PIL (273 K).

Figure 2 shows the real and imaginary components of the complex conductivity, σ′ and σ″, respectively, for each of these films. These data were fit using eqs 8–12, and the optimized curves are shown as solid lines in Figure 2. The values of x and τ_e,2 were optimized for each sample and at each temperature as a means of validating the model. Optimized values were compared to known values acquired by other means (thickness of the PS layer was measured by ellipsometry and used to calculate x, while the frequency of the peak in M″ was used to estimate τ_e,2). Variation of the optimized value of τ_e,2 at a given temperature across all three samples was found to be less than 5%, and the temperature dependence was consistent with that of the values estimated from M″. No appreciable temperature dependence was observed for optimized values of x. The value of σ_0,1 was optimized at each temperature for one sample only (electrodes with 89 nm PS coating), then fixed at those optimized values for other samples. Optimized values of σ_0,1 fell within the range reported in the literature.^39,40 The values of σ_0,2, τ_e,1, and ε_∞ were fixed for all samples at all temperatures: σ_0,2 was taken to be the σ′ plateau value of PIL films measured on unmodified SS electrodes; τ_e,1 was estimated using the fit value of σ_0,1 and the Barton-Nakajima-Namikawa relation,^41,42 which states that σ₀ is proportional to ω_c, where ω_c is the critical ion hopping frequency and τ_e = 1/ω_c; ε_∞ was taken to be the high frequency value of ε′. Optimized parameter values are provided as a function of temperature in the Supporting Information (Figures S18 and S19, Tables S1–S3). The model is able to quantitatively describe the data across a wide range of frequencies and temperatures. The deviation between measurement and fitted curve at frequencies below that of electrode polarization can be attributed to additional processes, such as exchange of ions between the bulk and the interfacial layer of charge build-up, which are not captured by this model.⁴³ The thickness of the PS layers calculated from the fit values of x on the basis of a 100 μm trilayer sample agree with those measured using ellipsometry to within 2 nm for the samples with 89 and 16 nm PS layers, and to within 10 nm for the sample with 32 nm PS layers. It is important to note that the second, low-frequency plateau corresponding to the overall “device” conductivity, which exhibited a high dependence on insulating layer thickness in the simple Debye case, is not observable in this system due to the complexity of ion build-up and charge processes that occur at the polarized interface.

Figure 2.

Measured and calculated (a) real and (b) imaginary contributions to the complex conductivity of a 100 μm PIL film sandwiched between PS-coated SS electrodes, where the thickness of the PS coating was 18, 32, or 89 nm. Symbols are measured data points and lines are fit using the model described by eqs 8–12.

Importantly, while the experiment and model both demonstrate that the onset of interfacial polarization shifts to higher frequency as h₁ increases, the plateau value of σ′ (corresponding to σ_DC) remains constant. (The plateau region of σ′ is shown on a linear y-scale in Figure S17.) This outcome shows that the bulk ionic conductivity measured by impedance spectroscopy is not depressed by ultrathin insulating layers at the electrode. Neither these experiments nor the model, however, fully represent the case of lamellar block copolymers with interfacial regions of parallel aligned lamellae. In the PS/PIL/PS trilayer, the boundaries between PS interfacial layers and PIL bulk are clearly delineated and the thicknesses of each layer are known. In a block copolymer, there are several additional factors that cannot be accurately captured by the simple model and trilayer experiment described here, such as the ill-defined boundary between interfacial and bulk regions, differences in domain connectivity within these regions, and additional interfacial polarizations that can arise at domain interfaces and grain boundaries. Therefore, to examine how alignment of lamellar domains at an electrode might contribute to the measured ionic conductivity, films of PS8-PIL41 block copolymers were annealed between either smooth silicon (Si) electrodes or rough SS electrodes. When polymers have very different surface energies, such as PS (42 mN/m at 20 °C)⁴⁴ and PIL (29 mN/m, measured at room temperature from a pendant PIL droplet using a DataPhysics OCA 15EC), wetting layers will form at both the free surface and the substrate. These wetting layers tend to drive layering of lamellar domains parallel to the surfaces, and that layering can propagate all the way through a thin film.²⁸ However, if the substrate is very rough, then the formation of wetting layers can be disrupted.⁴⁵ The Si electrodes are smooth (100-oriented wafer) so lamellar layering is anticipated. However, the SS electrodes are extremely rough at both the nanoscale and microscale, as shown in Figure S20, so it is doubtful that PS-b-PIL lamellae could adopt the parallel orientation across the entire surface. The differences in interfacial structure are illustrated in Figure 3.

Figure 3.

Interfacial and bulk structures that contribute to through-plane and in-plane impedance spectroscopy measurements. PIL and PS lamellae are illustrated in blue and red, respectively. Schematics are not to scale.

To demonstrate that electrode topography will impact lamellar alignment, thin films of PS8-PIL41 (115 nm thick) were cast on both Si and SS followed by annealing under vacuum at 120 °C for 18 h. Films were then inspected for islands and holes using optical microscopy and atomic force microscopy (AFM), the procedures for which are provided in the Supporting Information. In a lamellar block copolymer, islands and holes are observed when domains are aligned parallel to the surfaces and the thickness of the as-cast film is incommensurate with the domain periodicity.⁴⁶ The heights of islands and depths of holes are equal to the domain periodicity d₀ when the air and substrate interfaces are both preferential to one of the blocks. The optical microscopy image in Figure 4a shows the presence of holes after annealing the PS8-PIL41 film on Si, and AFM data in Figure 4b and c demonstrate that the depth of the holes is approximately 14 nm, consistent with the domain periodicity d₀ obtained from bulk transmission SAXS (13.8 nm). In contrast to the results for Si, no islands or holes were observed in the PS8-PIL41 film on SS (Figure 5).

Figure 4.

Island and hole formation observed in a thin film of PS8-PIL41 on silicon by (a) optical microscopy and (b,c) AFM. The film was annealed at 120 °C for 18 h. The AFM height image spans an area of 20 × 20 μm². Horizontal line cut of the AFM height image (b) shows the depth of holes is approximately equal to d₀ = 14 nm.

Figure 5.

Images of PS8-PIL41 thin film on stainless steel obtained by (a) optical microscopy and (b,c) AFM. The film was annealed at 120 °C for 18 h. The AFM height image spans an area of 20 × 20 μm². No evidence of island and hole formation is observed, but it is clear from the horizontal line cut in (b) that the surface is rough.

To confirm the outcomes of island/hole studies, GISAXS data were acquired from PS8-PIL41 thin films on Si and SS substrates (183 and 113 nm, respectively), as shown in Figure 6 as a function of in-plane (2θ) and out-of-plane (α_f) scattering angles. The scattering from thin PS-b-PIL films is weak due to low electron density contrast and the small sample volume, and these challenges are compounded by the low intensity of the laboratory X-ray source. However, if the material assembles into highly ordered lamellae having a preferred through-plane orientation, then the weak scattering would be concentrated into sharp Bragg peaks along the out-of-plane (α_f) axis. In the case of the film on Si (Figure 6a), well-defined Bragg peaks are observed along the out-of-plane axis, and the positions of those peaks (q*, 2q*, 3q*, etc.) are consistent with predictions for a layered lamellar structure (13.8 nm periodicity, 0.2° incident angle).⁴⁷ In the case of the film on SS (Figure 6b), there are no observable signatures of order in either the in-plane (2θ) or out-of-plane (α_f) directions. The weak scattering from randomly oriented lamellae would be spread out in Debye–Scherrer rings,⁴⁸ making it difficult to detect with a laboratory instrument.

Figure 6.

GISAXS data of (a) a 183 nm film of PS8-PIL41 on silicon and (b) a 113 nm film of the same block copolymer on stainless steel. The films were annealed at 120 °C for 18 h. Both samples were measured at an incident angle of 0.2°. The “×” and “○” symbols in part (a) are the predicted Bragg peak positions for a layered lamellar structure with 13.8 nm periodicity.

For thin films on Si, the island/hole formation in microscopy and the signatures of out-of-plane order from GISAXS both indicate the formation of well-defined lamellar layers. For thin films on SS, the absence of islands/holes and the lack of signal in GISAXS suggest that surface-induced layering of lamellar domains is largely absent. Consequently, with evidence that PS-b-PIL lamellae adopt different orientations on Si and SS electrodes, the next step was to check if the conductivity spectra were appreciably different in each case. The through-plane DC ionic conductivity of PS8-PIL41 was measured using both Si and SS electrodes in a parallel plate configuration. In Figure 7a, the real component of the complex conductivity σ′ is shown at three temperatures for both Si and SS electrodes. No clear plateau in σ′ is observed, which is not uncommon in heterogeneous ion-conducting materials such as block copolymer electrolytes due to the presence of additional interfacial polarization that arise at domain interfaces and grain boundaries. In the absence of a plateau, the DC ionic conductivity, σ_DC, is taken to be the value of σ′ at the frequency of the onset of long-range ion hopping, which is the primary process that governs DC ionic conductivity. The onset frequency of ion hopping can be estimated as the frequency at which a maximum occurs in the imaginary modulus function M″ (Figure 7b). Neither the σ′ spectra nor bulk σ_DC (Table S4) were appreciably changed by the choice of electrode material. These data confirm the key outcome of the trilayer experiment, that interfacial structures do not impact the value of σ_DC measured by through-plane methods, contrary to suggestions in prior studies.^20,29 These results also imply that if anisotropic ionic conductivity in PIL-based block copolymer electrolytes is a consequence of domain alignment near surfaces, then it is due to enhancement in the in-plane direction rather than depression in the through-plane direction.

Figure 7.

(a) Real component of the complex conductivity as a function of frequency and (b) DC ionic conductivity as a function of inverse temperature for 100 μm thick PS8-PIL41 films between silicon (open symbols) or stainless steel (solid symbols) electrodes.

Having shown that through-plane ionic conductivity is not impacted by differences in the interfacial structure, the final objective was to test whether the in-plane ionic conductivity is enhanced relative to the through-plane value for these PS-b-PIL materials. The PIL homopolymer and a P(S-r-IL) statistical copolymer were used as controls. The in-plane ionic conductivity of all block copolymers, the PIL homopolymer, and the P(S-r-IL) statistical copolymer was measured in a two-point probe top-contact configuration, as shown schematically in Figure 3. The results were compared to those of the through-plane measurements (SS electrodes), as shown in Figure 8a, and the anisotropy factor for each material is shown in Figure 8b. Ionic conductivity of the PIL homopolymer was close to isotropic, where the ratio of in-plane to through-plane ionic conductivity increased from approximately 0.9 at 100 °C to 1.3 at 30 °C. However, for all block copolymers, the in-plane ionic conductivity was larger than the through-plane ionic conductivity across all temperatures, ranging from roughly 8 times greater in PS8-PIL41 to as much as 19 times greater in PS12-PIL35 at 30 °C (the lowest temperature measured). Interestingly, P(S-r-IL) also exhibited anisotropy in the ionic conductivity, where the ratio of in-plane to through-plane ionic conductivity increased from approximately 1.3 at 100 °C to 3 at 30 °C.

Figure 8.

(a) DC ionic conductivity determined by either through-plane (open symbols) or in-plane (closed symbols) impedance spectroscopy techniques as a function of temperature; and (b) the ratio of in-plane to through-plane DC ionic conductivity as a function of temperature. The dotted line corresponds to the value σ_in/σ_thru = 1 (isotropic).

The question that remains is why the in-plane ionic conductivity is higher than that along the through-plane direction. The logical first consideration is whether or not a difference in the method used to estimate σ_DC between the in-plane and through-plane measurements could account for the discrepancy. However, for an in-plane measurement, the same value of σ_DC is obtained whether the conductivity is calculated from the resistance in the Bode plot (typical for in-plane measurements) or by first calculating σ′(ω) from the impedance and taking the plateau value as σ_DC (typical for through-plane measurements which exhibit a clear plateau in σ′). It is also worth noting that estimating σ_DC as the value of σ′ at the onset frequency of long-range ion hopping, which was done for through-plane measurements in which a clear plateau in σ′ was absent, typically results in a slightly higher value of σ_DC than that from the plateau (Figure S24 in the Supporting Information); if anything, this means the anisotropy factor might be slightly higher than reported in Figure 8b. It is therefore unlikely that differences in the method of analysis for in-plane versus through-plane impedance spectra are playing a role in the observed conductive anisotropy.

As shown in Figure 6, these PS-b-PIL materials assemble into well-defined layers on a flat substrate. A similar phenomena could be expected at the free surface of the film, i.e., the surface that is in contact with the electrode for in-plane impedance spectroscopy measurements, as the PIL block has a lower surface energy than the PS block. Therefore, contact angle measurements were used to detect the presence of a PIL wetting layer. The contact angles of water and diiodomethane were recorded from each block copolymer, the PIL homopolymer, and the PS homopolymer, following the procedures described in the Supporting Information. The thick films used for in-plane impedance spectroscopy measurements were too rough to record a reliable contact angle, so thin spin-cast films (150–300 nm) were used instead. The recorded contact angles are reported in Table 2. The water contact angle for all block copolymers and for the PIL homopolymer was between 78 and 81°, while the water contact angle for the PS homopolymer was 90°. Similarly, the diiodomethane contact angle for all block copolymers and for the PIL homopolymer was between 60 and 66°, while the diiodomethane contact angle on PS was 36°. These data demonstrate that the PIL block is preferred over the PS block at the air interface. This suggests that a PIL wetting layer is present at the surface of all block copolymer films during in-plane impedance spectroscopy measurements.

Table 2. Static Contact Angles of Water and Diiodomethane on Thin Films^a.

sample name	θwater (deg)	θdiiodomethane (deg)
PS	90.4 ± 0.7	36.0 ± 0.4
PIL	80.4 ± 1.5	60.5 ± 0.6
PS5-PIL51	78.6 ± 0.2	65.7 ± 1.4
PS8-PIL41	78.3 ± 0.4	64.0 ± 0.6
PS12-PIL35	78.4 ± 0.3	62.8 ± 0.3

^aAverage contact angle is calculated from three measurements per sample.

GISAXS experiments were performed on the thick block copolymer films used for in-plane impedance spectroscopy measurements to probe the lamellar domain orientations at the free surface. A low incident angle of 0.1° was used to limit the X-ray penetration depth to the top 10–100 nm of the film,⁴⁷ thereby probing the surface structure, although it is important to note that the films are rough so the incident angle (and consequently, the penetration depth) is not well controlled. The results are summarized in Figure 9. A clear difference in degree of ordering at the air interface is observed between the three block copolymers. PS5-PIL51 (Figure 9a) exhibits scattering that is concentrated in Bragg peaks along the out-of-plane direction, consistent with parallel alignment of lamellar domains at the surface, along with a weaker Debye–Scherrer ring that arises from randomly oriented grains. The same features are observed in PS8-PIL41, but the out-of-plane Bragg peaks are weaker and the Debye–Scherrer ring is stronger. PS12-PIL35 has no detectable out-of-plane Bragg peaks but a strong Debye–Scherrer ring.

Figure 9.

GISAXS data of films of (a) PS5-PIL51, (b) PS8-PIL41, and (c) PS12-PIL35 ranging in thickness from 25 to 41 μm, measured at an incident angle of 0.1°.

There is no apparent correlation between the extent of surface ordering and enhanced in-plane conductivity. For an example, PS12-PIL35 exhibits the greatest enhancement of the in-plane ionic conductivity, despite appearing to have nearly isotropic lamellar domain orientations at the air interface. This observation suggests that wetting layers of PIL at the surface could be sufficient to enhance the in-plane ionic conductivity, possibly because this thin conductive layer connects the electrodes in an in-plane (parallel wire) configuration and creates a more direct route for ion transport than is present in the bulk of the material. In addition, it has been suggested that the T_g of a polymer near an air surface is depressed relative to the bulk,^49,50 which could elevate the ionic conductivity of this surface layer. Although a depression in the overall ionic conductivity in thin films of polymer ionic liquids has been attributed to strong interactions between the ionic groups and the substrate,^51,52 no direct measurements of the conductivity at the polymer/air interface have been reported to date. It is notable that P(S-r-IL) also shows an enhancement in the in-plane ionic conductivity by up to a factor of 3 at 30 °C. This raises the question of whether the statistical copolymer, which is amorphous in bulk (determined by transmission SAXS, Figure S21), can restructure at the surface. Certain amphiphilic random copolymers with relatively long pendant chain have been shown to self-assemble in solution and in bulk by rotation of pendant groups along the backbone,.⁵³ and there is evidence of layering at interfaces due to preferential interactions between a surface and one of the repeat unit pendant groups.⁵⁴ We therefore speculate that the IL pendant groups preferentially wet the air interface in P(S-r-IL), resulting in a very thin surface layer with higher ionic content than that of the bulk of the film.

Interestingly, the bulk ionic conductivities of the PS-b-PIL samples (through-plane) were much lower than anticipated. Through-plane morphology factors for PS-b-PIL samples (provided in Figure S22 in the Supporting Information) ranged from f = 0.08 to f = 0.01, which are significantly lower than either the in-plane morphology factors, which ranged from f = 0.38 to f = 0.13, or the idealized lamellar morphology factor of f = 2/3. The value of the idealized morphology factor, however, is in part predicated on the assumption that the properties of the electrolyte block are the same as those of the electrolyte as a homopolymer. The glass transition temperatures of the PS-b-PIL materials, P(S-r-IL) copolymer, and PIL homopolymer, which were measured by DSC and are summarized in Table 3, demonstrate that this assumption is not appropriate for these materials. The T_g associated with the PIL domain in each PS-b-PIL sample is higher than that of the PIL homopolymer at −0.5 °C, and closer in value to that of P(S-r-IL) at 26.0 °C. Similar elevation of the T_g of the PIL domain has been reported by others in weakly segregated copolymers of 1-[(2-methacryloyloxy)ethyl]-3-butylimidazolium bis(trifluoromethanesulfonyl)imide and methyl methacrylate.⁵⁵ While no such elevation was observed for a series of block copolymers of similar chemistry to those studied here,¹⁷ the copolymers considered here have lower molecular weights and likely exhibit a broader interfacial region between domains due to reduced segregation strength, resulting in higher PIL domain T_g’s and lower ionic conductivities.

Table 3. Glass Transition Temperatures of All Polymers, Reported in °C.

sample name	Tg,1	Tg,2
PIL	–0.5
P(S-r-IL)	26.0
PS5-PIL51	25.5	80.1
PS8-PIL41	25.8	89.3
PS12-PIL35	19.1	98.1

Although the precise mechanism that enhances the in-plane ionic conductivity remains unclear, these studies suggest that even very small interfacial rearrangements can lead to anisotropy in the DC ionic conductivity. In light of this finding, and given that interfacial rearrangement in block copolymers is a near-ubiquitous phenomenon, it is important to consider whether in-plane measurements are truly representative of the bulk behavior. Indeed, other studies that probed ionic conductivity of similar lamellar block copolymer chemistries using in-plane impedance spectroscopy have reported ionic conductivities and morphology factors consistent with those in Figures 8a and S22, respectively. Notably, the in-plane morphology factors are close to the expected f = 2/3 value.^16,17,20 However, whether the in-plane values are substantially inflated in other types of block copolymer electrolytes may depend on which block (ionic or nonionic) is attracted to the surface, contrast in the ionic conductivities of each block, as well as continuity of the ionic domains in bulk and near the surface.

Conclusions

This work examined the effects of interfacial structure on anisotropy in the measured ionic conductivity of lamellar PS-b-PIL electrolytes. We first showed that measurements of through-plane DC ionic conductivity in thick (∼100 μm) PIL-based electrolytes are insensitive to changes in the structure/composition at the electrode surface, at least when the interfacial region is a small fraction of the total sample volume. In the context of a thick block copolymer electrolyte, this means that through-plane measurements of the bulk ionic conductivity are not influenced by wetting layers or surface-induced layering of domains. We then showed that the in-plane ionic conductivity in PS-b-PIL electrolytes is roughly an order-of-magnitude larger than the through-plane value, while this anisotropy is absent for a PIL homopolymer control. The extent of in-plane enhancement was not correlated with the degree of interfacial order, as the largest enhancement was observed for a sample with randomly oriented grains near the surface, but appears to be associated with the formation of a thin wetting layer of the lower-energy PIL block. Interestingly, an enhanced in-plane ionic conductivity was also observed for a P(S-r-IL) statistical copolymer at temperatures near the T_g, which suggests that even modest rearrangements of pendant groups near the surface can influence these measurements. With all of these factors in mind, we conclude that through-plane measurements of the bulk ionic conductivity are more reliable than in-plane measurements when informing structure-conductivity relations, as the through-film measurements are insensitive to the types of structures that form at an interface.

Even through-plane impedance techniques, however, have limitations: while they allow for accurate measurement of bulk ionic conductivity, through-plane impedance approaches are sensitive to electrode polarization, which makes it challenging to capture interfacial ion dynamics across the entire film in the low frequency regime.³⁵ For most applications, through-plane transport from one interface of the film to the other is critical. As has been discussed in a previous work,²⁰ a simple effective medium approximation can be used to demonstrate that even a small region of parallel-oriented lamellae at the interface of a film can lead to a decrease in the device conductivity by several orders of magnitude. As such, while bulk ionic conductivity can be measured using through-plane impedance methods, despite the presence of interfacial order, an oriented interfacial region could be detrimental to device performance in applications such as lithium ion batteries.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acspolymersau.2c00068.

• Schemes for synthesis of all types of polymers (homopolymer, statistical copolymer, block copolymer); GPC and NMR data; reactivity ratios for styrene and vinylbenzyl chloride; experimental procedures for ellipsometry, AFM, optical microscopy, contact angle measurements, SAXS, trilayers; temperature dependence of PS layer thickness in trilayers; AFM image of bare SS electrode; SAXS data for statistical copolymer; in-plane and through-plane morphology factors; DSC data; comparison of analysis methods for impedance spectroscopy (PDF)

The authors declare no competing financial interest.