Isolating the Effect of Molecular Weight on Ion Transport of Non-Ionic

Article pubs.acs.org/Macromolecules

Isolating the Effect of Molecular Weight on Ion Transport of NonIonic Diblock Copolymer/Ionic Liquid Mixtures Sharon Sharick,† Jason Koski,‡ Robert A. Riggleman,‡ and Karen I. Winey*,† †

Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States

‡

S Supporting Information *

ABSTRACT: The effects of molecular weight and microdomain orientation on the ionic conductivities of poly(styrene-b-methyl methacrylate) diblock copolymer/1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide (SM/IL) mixtures are assessed through complementary experimental and theoretical techniques. Small-angle Xray scattering revealed that SM/IL mixtures have anisotropic lamellar morphologies, preferentially oriented parallel to the casting substrate. A method for quantifying the morphology factor, or microdomain orientation within the Sax−Ottino model, using 2-D SAXS data is presented and applied to SM/IL mixtures. Ionic conductivity increases by up to an order of magnitude with a 2-fold increase in molecular weight, even when accounting for the morphology type, composition, microdomain orientation, and PMMA/IL glass transition temperature. Self-consistent field theory calculations predict a nonuniform solvent distribution in PMMA/IL microdomains, suggesting that polymer mobility and ion transport are reduced near PS−PMMA microdomain interfaces. Thus, the increase in ionic conductivity with increasing block copolymer molecular weight is associated with having fewer PS−PMMA/IL interfaces per unit volume.

1. INTRODUCTION Ion-containing block copolymers have been the subject of myriad studies in the effort to design superior polymer-based components for energy applications, including solid-state polymer electrolytes for lithium-based batteries1−13 and capacitors,11,14−18 anion exchange membranes for fuel cells,19−30 and efficient active layers in dye-sensitized solar cells.31−34 A subset of these are block copolymers mixed with ionic liquids (ILs), which are low-melting point salts composed of bulky ions. The ILs are liquid at room temperature and offer advantages over other solvents including low vapor pressure; high chemical, thermal, and electrochemical stability; and high neat ionic conductivity. An IL can be chosen that selectively swells one of the polymer blocks, creating a material with a nanostructure of conductive and nonconductive microdomains.35−41 In addition, selecting nonconductive polymer blocks with high glass transition temperatures allows the material to remain a solid film with a high modulus.42−44 Previous investigations of block copolymer/IL mixtures have extensively studied the interrelated effects of composition, glass transition temperature, and morphology on ionic conductivity.13,45−47 In poly(styrene-b-methyl methacrylate) (SM), poly(styrene-b-2-vinylpyridine) (S2VP), and poly(styrene-bethylene oxide) (SEO) diblock copolymers, the addition of ILs depressed the glass transition temperature of the more polar block, increased segmental motion, and increased charge carrier density, leading to increased conductivity.36−38,40,48,49 Increased connectivity of the conductive microdomain upon increasing IL content was also shown to improve ion transport.48 In S2VP/IL © XXXX American Chemical Society

mixtures, increasing IL content corresponded to an increase in segregation strength between PS and P2VP blocks.36 In ILcontaining poly(sulfonated styrene-b-methylbutylene) (SSMB), the anion type dictated the miscibility of the IL with PSS, while sulfonation level was found to affect the amount of IL incorporation.47 Again, ion conductivity increased as PSS microdomains became more connected. Several studies have reported low conductivities in block copolymers at low molecular weight (∼10 kg/mol). In SEO diblock and SEOS triblock copolymers mixed with lithium salt or IL, ionic conductivity was observed to increase with increasing molecular weight of conductive PEO up to 50 kg/ mol.4,49−52 Note that Li+ has strong specific interactions with the ether oxygens in PEO,53 whereas this does not occur for most ILs. These studies employed the Sax−Ottino model54 to further analyze block copolymer conductivity, σSO:

σSO = σcϕc f

(1)

In this expression, σc is the inherent conductivity of the conductive microphase, typically assumed to be the conductivity of a homopolymer with the same salt concentration. The variable ϕc is the volume fraction of the conductive microphase. The model assumes a uniform composition in the microdomain and ignores the impact of interfaces between microphases. Finally, f is the morphology factor, which accounts Received: November 10, 2015 Revised: January 22, 2016

A

DOI: 10.1021/acs.macromol.5b02445 Macromolecules XXXX, XXX, XXX−XXX

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Macromolecules Table 1. Characteristics of Block Copolymer/Ionic Liquid and Homopolymer/Ionic Liquid Mixtures polymer

wILa

ϕcb

⟨σx/σz⟩c

SM-Low

0.24 0.48 0.61 0.69 0.24e 0.49e 0.62e 0.69e 0.24 0.48 0.61 0.69

0.34 0.42 0.48 0.53 0.34 0.42 0.48 0.53 1 1 1 1

2.2 11 12 1.7 2.0 7.4 2.5 11

SM-High

PMMA

± ± ± ± ± ± ± ±

0.7 5 5 0.3 1 8 0.5 4

⟨σn,x⟩d 0.024 0.073 0.028 0.047 0.026 0.34 0.31 0.22

± ± ± ± ± ± ± ±

0.006 0.08 0.003 0.009 0.008 0.4 0.3 0.1

⟨σn,z⟩d 0.018 0.016 0.025 0.17 0.16 0.17 0.53 0.048

± ± ± ± ± ± ± ±

0.002 0.01 0.008 0.04 0.05 0.04 0.3 0.02

Weight fraction of IL in PMMA, eq 3. bϕc = ϕPMMA + ϕIL, eq 4. cTemperature-averaged conductivity anisotropy. dTemperature-averaged normalized ionic conductivity, determined by averaging values calculated by eq 2. ePrepared by slow solvent evaporation. a

segmental mobility. The conductivities of SM/IL mixtures also deviate significantly from values predicted by the Sax−Ottino model. These results suggest that the ion transport mechanism in these block copolymers is distinct from that of homopolymers and the effects of microphase separation, compositional variation in conductive microdomains, interfaces, and grain boundaries, cannot be neglected. This study also clarifies how molecular weight and microdomain orientation impact ion conductivity in diblock copolymer/IL mixtures.

for the shape, orientation, connectivity, and tortuosity of conductive microdomains. When the morphology is isotropic, f is 1/3 for cylinders, 2/3 for lamellae, and 1 for a bicontinuous morphology. Note that the Sax−Ottino model does not consider the effects of molecular weight, grain boundaries, defects, or local variations in σc due to heterogeneous ion distribution within the microdomain. Experimental conductivities from block copolymer systems (σ) can be compared with those predicted by the Sax−Ottino model through the normalized conductivity, σn: σn = σ /(σcϕc f )

2. EXPERIMENTAL METHODS

(2)

2.1. Materials. Two poly(styrene-b-methyl methacrylate) (SM) diblock copolymers were purchased from Polymer Source. Abbreviations SM-Low and SM-High are used throughout the text, corresponding to a lower molecular weight SM (Mn,PS = 21 500 g/ mol; Mn,PMMA = 10 000 g/mol; Đ (SM) = 1.06; ϕPS = 0.71) and a higher molecular weight SM (Mn,PS = 46 100 g/mol; Mn,PMMA = 21 000 g/mol; Đ (SM) = 1.09; ϕPS = 0.71). Poly(methyl methacrylate) (PMMA) was purchased from Polysciences, Inc. (reported molecular weight of 25 000 g/mol). 1-Ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide (EMIm−TFSI) (molecular weight = 391.36 g/mol; > 99% purity) was purchased from Io-li-tec (Tuscaloosa, AL). Toluene (99.9%) was purchased from SigmaAldrich, and acetone (99.9%) was purchased from Fisher Scientific. All materials were used as received. 2.2. Sample Preparation. SM diblock copolymer was dissolved in toluene (10% w/w) and stirred overnight. EMIm−TFSI ionic liquid (IL) was subsequently added to the solutions to achieve the desired compositions and stirred overnight. Clear solutions were obtained. To prepare PMMA/IL mixtures, EMIm−TFSI was added to acetone (2 to 5% w/w) and stirred overnight. PMMA was then added to the solutions to achieve the desired compositions and stirred overnight, producing clear solutions. To prepare SM/IL films, two methods were used, rapid solvent evaporation and slow solvent evaporation. The rapid method involves casting SM/IL/toluene solutions onto Teflon substrates (dimensions: ∼7 mm × 40 mm × 0.8 mm) in a fume hood and allowing the solvent to rapidly evaporate. By visual inspection, most of the solvent evaporated within 15 min. Films were dried in the fume hood, in air at room temperature, for up to 2 days to allow residual solvent to evaporate and then dried at 80 °C under vacuum for 2 days and annealed at 120 °C under vacuum for 2 days. The resulting films were colorless and transparent. The rapid solvent evaporation method resulted in SM-Low/IL films with strong microphase separation (see Results), whereas using the same method produced SM-High/IL films with weak microphase separation. To attain SM-High/IL films with strong microphase separation comparable to SM-Low/IL films, SM-High/IL/toluene solutions were slowly cast by slowly evaporating the solvent (7 days) in an acetone/

Previous reports have attributed low σn values as well as the molecular weight-dependence of conductivity to low-mobility, low-conductivity segments near interfaces between conductive and nonconductive microdomains.51 In S2VP/IL mixtures, however, block copolymer molecular weight was found to have a negligible effect on ion conductivity.37 Further investigation is needed to determine the causes of low σn values and the molecular weight dependence of ionic conductivity in block copolymers. The present work is motivated by several questions: (1) What factors distinguish the ion transport mechanism in block copolymers from that of homopolymer systems? (2) How does block copolymer molecular weight influence ionic conductivity? (3) What is the effect of microdomain orientation on the ionic conductivity? To answer these questions, a series of poly(styrene-b-methyl methacrylate) (SM) diblock copolymer/IL mixtures with two molecular weights and the same volume fractions and IL contents were studied. Anisotropic lamellar morphologies are observed at all investigated compositions and morphology factors are quantified using small-angle X-ray scattering data. The composition profiles of SM/solvent mixtures, determined by self-consistent field theory, reveal a heterogeneous solvent distribution within the PMMA microdomains and a lower solvent content near the PS−PMMA/IL interfaces. The compositional heterogeneity is greater and solvent content at the PS−PMMA/IL interface is lower for lower molecular weight, suggesting that dynamics near the interface are slower for lower molecular weight systems. The bulk ionic conductivity is measured parallel and perpendicular to the preferential lamellar orientation and observed to increase with increasing block copolymer molecular weight; this is attributed to a decreased number density of PS−PMMA/IL interfaces, which are hypothesized to reduce ion and polymer B


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Macromolecules toluene vapor-rich atmosphere (acetone:toluene, 3:1 by volume). This method involved placing a reservoir of acetone/toluene mixture in the vicinity of the samples, covering the samples and reservoir with a large inverted glass Petri dish, and sealing the base of the Petri dish with aluminum foil. Slowly cast films were dried and annealed by the same procedure described in the previous paragraph. Colorless, transparent films were produced. Composition is described in terms of weight fraction of ionic liquid in PMMA/IL, the conductive microphase of the block copolymer. This is given by

wIL =

w w + wPMMA,neat(1 − w)

(3)

where w is the total weight fraction of IL in the SM/IL or PMMA/IL mixture and wPMMA,neat is the weight fraction of PMMA in the neat polymer (wPMMA,neat = 0.318 and 0.313 for SM-Low and SM-High, respectively). The volume fraction of conductive microphase, ϕc, in SM/IL mixtures is determined as follows:

ϕc = ϕPMMA + ϕIL =

wPMMA /ρPMMA + w/ρIL wPMMA /ρPMMA + wPS/ρPS + w/ρIL

(4) Figure 1. Schematic depicting small-angle X-ray scattering experiments conducted in two sample geometries. (a) Intensity as a function of scattering vector qx (=qy) is obtained by azimuthal angle integration from 0 to 360°. (b) Intensity as a function of qz is obtained by azimuthal angle integration from 80 to 100°.

where wPMMA and wPS are the total weight fractions of PMMA and PS in the SM/IL mixture and ρPMMA, ρPS, and ρIL are the bulk densities of PMMA (1.18 g cm−3), PS (1.06 g cm−3), and EMIm−TFSI (1.52 g cm−3).55 Characteristics of SM/IL and PMMA/IL mixtures are listed in Table 1. 2.3. Thermal Characterization. Thermal transitions were characterized using a TA Instruments Q2000 differential scanning calorimeter (DSC). The glass transition temperature (Tg) was assessed from the third heating cycle using the midpoint method. Modulated DSC (mDSC) measurements were also completed by heating samples to 120 °C at 10 °C/min, equilibrating for 10 min, cooling to temperature T1 at 10 °C/min, then cooling to temperature T2 at 2 °C/ min with a modulation of 0.635 °C/min. Values for T1 and T2 are listed in Supporting Information. Peaks in the mDSC derivative reversing heat flow signal were fit with a Lorentzian model (SI, Figures S1, S2), and Tg,PMMA/IL and Tg,PMMA/IL breadth values were determined from the peak center and peak width, respectively. 2.4. Small-Angle X-ray Scattering. Small-angle X-ray scattering (SAXS) was performed on a multiangle X-ray scattering system described previously.48 Scattering data were collected for 1 h using a Bruker Hi-Star two-dimensional detector with a sample-to-detector distance of 150 cm. Two scattering geometries were used, as depicted in Figure 1: (1) with the incident X-ray beam along z (normal to the film) and (2) with the X-ray beam along y (in the plane of the film). Data were analyzed using Datasqueeze software.56 The intensities were first corrected for primary beam intensity, and then background scattering (scattering from an empty cell under vacuum) was subtracted. Isotropic 2-D scattering patterns from Geometry 1 (normal to the film) were integrated azimuthally from 0 to 360° to yield 1-D intensity versus scattering vectors qx and qy. The anisotropic 2-D scattering patterns from Geometry 2 (in the plane of the film) were integrated from 80 to 100° to yield 1-D intensity versus qz. Scattering intensities are reported in arbitrary units (a.u.). Morphologies are classified by comparing higher order peak positions to those of known block copolymer morphologies and scattering form factors.57 2.5. Morphology Factor Analysis. In the Sax−Ottino model, the morphology factor, f, describes the shape and orientation of block copolymer microdomains and corresponds to the fraction of microdomains oriented along the transport direction for a given morphology. Lamellae orientations are described by their normal vectors using Cartesian coordinates x, y, and z. In a simplified scenario, with lamellae oriented exclusively in three orthogonal directions, an isotropic morphology has an equal fraction (1/3) of lamellae oriented normal to x, y, and z, and conduction along the x axis is only permitted through two-thirds of the lamellae, yielding f = 2/3.

Here, morphology factors were determined for the lamellar SM/IL mixtures. 2-D SAXS data from Geometry 2 were integrated over the qrange of the primary peak to produce 1-D profiles of intensity versus azimuthal angle, φ, Figure 2. The area under the intensity curve was integrated: π /4

Ax =

∫0

Az =

∫π /4

π

I dφ +

∫3π /4 I dφ

(5)

3π /4

I dφ

(6)

where Ax and Az are the integrated areas under the intensity versus azimuthal angle curve and correspond to lamellar microdomains with

Figure 2. Example analysis of 2-D SAXS data (Geometry 2). 2-D SAXS data are integrated azimuthally over the q-range of the primary peak (inset, dashed line) to yield intensity versus azimuthal angle (φ) profiles. The area under the intensity curve is integrated to determine the morphology factors, f x and fz, eq 5−8. normal vector components along x and z, respectively. It is assumed that the microdomain orientation is equivalent along the x- and y-axes, so Ax = Ay, which is justified by the isotropic 2-D X-ray patterns from Geometry 1. Lamellae with orientation vector components along y and z will contribute to ion transport in the x direction and lamellae with orientation vector components along x and y will contribute to C


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Figure 3. Small-angle X-ray scattering profiles of SM/IL films with various compositions wIL: (a) 0.24, (b) 0.48, (c) 0.61, and (d) 0.69. Scattering profiles are shown in two directions, qxy from Geometry 1 (filled) and qz from Geometry 2 (open), as well as for SM-Low (circles) and SM-High (diamonds). transport in the z direction. The parameters f x and fz are the morphology factors for transport in the x and z directions, respectively, given by

fx = (A y + A z )/(A x + A y + A z )

(7)

fz = (A x + A y )/(A x + A y + A z )

(8)

For the 4-point (x) setup, L corresponds to the distance between the inner electrodes and A is the cross-sectional area given by A = wt, where w and t are the width and thickness of the sample. For the 2point (z) setup, t corresponds to the sample thickness and A = wl, where w and l are the width and length of the sample. Reported conductivity values are an average of three measurements on the same specimen. 2.7. Self-Consistent Field Theory. Self-consistent field theory calculations (SCFT) were performed to elucidate the effect of molecular weight on the distribution of IL within the microdomain. Using a polymer field theory formalism, polymer chains were modeled as discrete Gaussian chains with degree of polymerization N, where the PMMA and PS blocks of the polymer have degrees of polymerization NPMMA and NPS, such that N = NPMMA + NPS. The statistical segments of the polymer chains are connected with a Gaussian bonding potential

Normalized conductivities in the x and z directions are given by σn, x = σx /(σcϕc fx )

(9)

σn, z = σz /(σcϕc fz )

(10)

where σx and σz are the measured conductivities in-plane and through the film. 2.6. Electrochemical Impedance Spectroscopy. Ionic conductivities were measured by electrochemical impedance spectroscopy using a Princeton Applied Research Parstat 2273 Potentiostat and Powersuite software, operated at ac amplitudes ranging from 20 to 600 mV over a frequency range of 0.1 to 106 Hz. Measurements were performed in an argon-filled glovebox and temperature was controlled using an Instec HCS410 temperature stage (accuracy within 0.1 °C). Impedance values were measured on heating and samples were equilibrated at each temperature (30 to 150 °C, 20 °C steps) for at least 10 min prior to measurement. Impedances were remeasured after cooling to the minimum temperature, and thermal reversibility was confirmed. For SM/IL samples, the in-plane (x) and through-plane (z) conductivities were measured using custom 4-point and 2-point stainless steel electrodes, respectively. PMMA/IL samples were measured using 2-point measurements. Following impedance experiments, sample dimensions were measured using a Marathon electronic digital caliper (0.01 mm precision) and Marathon electronic digital micrometer (0.001 mm precision). For four-electrode measurements, sample thicknesses were typically on the order of 0.15−0.2 mm, and the distance between inner electrodes was between 0.2 and 0.4 cm. The film thicknesses and inner electrode distances were sufficiently large to minimize edge effects in the EIS data. Electrodes were also cleaned with acetone and toluene prior to experiments. The resistance, R, was determined from semicircle fitting of impedance spectra Nyquist plots (-Z″ versus Z′), where R corresponds to the low-frequency, high x-intercept on Nyquist plots. In the case of 2-point measurements on low-resistance materials where no semicircle was observed in the Nyquist plot, the Warburg impedance was fit with a linear regression and R was taken to be the x-intercept. Representative EIS data (Nyquist plots) are shown in Supporting Information, Figure S3. Conductivities were determined according to σx = L/(AR) and σz = t/(AR) for the x- and z-direction, respectively.

nD N − 1

βU0 =

∑∑ i=1 j=1

3(|ri , j − ri , j + 1|)2 2b2

(11)

where nD is the number of diblocks in the system and b is the statistical segment size of the polymer. For simplicity, the ionic liquid is treated as a solvent, S, and Coulombic interactions are neglected. This approximation is based on the assumption that the ionic liquid is not dissociated within the diblock melt. All enthalpic interactions are treated with a purely repulsive Flory-like contact potential,

βU1 =

∑ i 0.9) suggest that ion conductivity in the x-direction for some block copolymer/ IL mixtures should approach values of the equivalent homopolymer/IL mixtures, according to the Sax−Ottino model. Average lamellar lattice parameters, L, were determined from scattering data by fitting the peak positions to L = 2πn/qn, where n is the peak index, Figure 5. Lxy and Lz differ by less than 4% for SM-Low and less than 7% for SM-High. Average thicknesses of PMMA/IL and PS microdomains were also determined, where LPMMA+IL = Lϕc and LPS = L(1 - ϕc). LPMMA+IL increases with wIL more strongly than L for SM-Low and SM-High. LPS increases slightly from wIL = 0 to 0.24 for SM-Low and SM-High, indicating that the addition of IL causes increased stretching of PS chains and sharpening of the PS− PMMA interface. This is due to the strong immiscibility of EMIm−TFSI and PS, which drives the system to reduce unfavorable PS/IL contacts. From wIL = 0.48 to 0.69, LPS decreases due to the increase in chain junction area with increasing IL content, which forces PS chains to expand laterally while simultaneously allowing PS chains to relax perpendicular to the lamellae. Similar results have been reported in block copolymer/homopolymer blends.63 E


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Figure 5. Lamellar domain spacings as a function of composition, wIL, determined by SAXS as a function of orientation, xy (●) and z (red ■), and self-consistent field theory (blue ◆) for SM-High/IL and SMLow/IL mixtures (open and filled symbols, respectively): (a) lamellar period, (b) PMMA/IL microdomain thickness, and (c) PS microdomain thickness.

3.2. Ionic Liquid Distribution in SM-Low/IL and SMHigh/IL Mixtures. Self-consistent field theory (SCFT) calculations were performed to explore the IL distribution within PMMA microdomains as a function of IL content and SM molecular weight. SM/IL mixtures were simulated as A−B diblock copolymer chains with solvent (S) molecules. Values for L, LPMMA+S, and LPS determined from SCFT are shown in Figure 5. The trends are qualitatively similar, with L and LPMMA+S increasing over the composition range and LPS exhibiting a maximum. The experimental values are systematically higher by a factor of 1.1−1.2 and these quantitative discrepancies are attributed to simplifications in the numerical calculations, that omit electrostatic effects and treat the solvent molecules as point particles. The SCFT calculations capture the composition-dependent trends in lamellae morphology as observed by SAXS, indicating that the simulations provide a sufficient description of the diblock copolymer/IL mixtures. Calculated solvent concentration profiles, ϕS, are shown in Figure 6, where z = 0 corresponds to the center of the PMMAsolvent microdomain. For SM-High at wS = 0.24 (Figure 6a), ϕS is nearly uniform across the PMMA/solvent microdomain and as wS increases, ϕS becomes increasingly nonuniform, with a solvent-rich region forming in the center of the microdomain. This is consistent with experimental microscopy data published by Gomez et al. and Noro et al. that revealed concentration gradients in the ion-containing microdomains of lamellar SEO/ LiTFSI and lamellar S2VP/ionic liquid mixtures.35,64 The profiles in Figure 6 also show the increase in microdomain thickness with increasing wS, consistent with the swelling of

Figure 6. SCFT solvent concentration profiles for SM-Low (black) and SM-High (red) as a function of solvent (S) content: wS = (a) 0.24, (b) 0.48, (c) 0.61, and (d) 0.69. Open circles indicate the composition at the PS−PMMA/solvent interface.

PMMA microdomains. There are noticeable differences between the profiles for SM-Low and SM-High at fixed wS. The solvent distribution in SM-High is more uniform, as indicated by the smaller gradient in ϕS across the PMMAsolvent microdomain. In addition, ϕS at the PS−PMMA/ solvent interface, indicated by open circles, is higher for SMHigh compared to SM-Low at wS ≥ 0.48. 3.3. Glass Transition Temperatures of SM/IL Mixtures. Glass transition temperatures (Tg) of PMMA/IL, SM-Low/IL, and SM-High/IL mixtures were found to be strongly coupled with IL content (Figure 7). For the block copolymers, two or three Tgs are observed, consistent with the observed microphase separated morphologies. The composition-dependent Tg in SM diblock copolymer/IL mixtures is attributed to PMMA due to the preferential miscibility of the IL, and the invariant second Tg at ∼100 °C is attributed to PS. The Tg,PMMA/IL decreases with increasing IL content, indicating that PMMA segmental mobility increases with increasing wIL and the IL behaves as a plasticizer. The PS glass transitions are narrow, with breadths ranging from ∼5 to 10 °C. In contrast, the homopolymer/IL mixtures F


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Figure 7. Glass transition temperatures as a function of composition for (a) PMMA/IL (red ◆), (b) SM-Low/IL (●), and (c) SM-High/IL (blue ■) mixtures. Error bars denote Tg breadths. In (a) - (c), lines correspond to predictions by the Gordon−Taylor model, with k = 1. In parts b and c, Tg,PS and Tg,PMMA/IL are represented by open and filled symbols, respectively. (d) Data from parts a−c are plotted together for comparison.

and PMMA/IL microdomains exhibit Tg breadths ranging from 22 to 240 °C. In fact, at wIL = 0.48, an additional Tg is observed at < 0 °C in PMMA/IL, SM-Low/IL, and SM-High/IL mixtures. This nondominant lower Tg,PMMA/IL appears as a broad shoulder in the mDSC derivative reversing heat flow signal (Supporting Information Figure S1). Similarly, Mok et al. observed two broad glass transition features in PMMA/ EMIm−TFSI mixtures (Mn,PMMA = 125 or 335 kg/mol) at wIL ranging from 0.5 to 0.65.65 The authors attributed these results to having regions locally rich in PMMA or EMIm− TFSI, producing two distinct dynamic relaxations. The broad PMMA/IL glass transitions indicate a large distribution of dynamic relaxations in PMMA/IL mixtures and PMMA/IL microdomains. This is consistent with the local compositional heterogeneity in PMMA/solvent microdomains revealed by SCFT calculations of SM diblock copolymer/selective solvent mixtures (Figure 6). Finally, experimental data were compared to model predictions by the Gordon−Taylor equation, which describes the glass transition behavior of a copolymer with ideal volume mixing of two components (no volume change upon mixing).66 This is given by Tg =

ductivities of SM-Low/IL and SM-High/IL mixtures were measured in the x- and z-directions. Representative temperature-dependent ionic conductivity plots are shown in Figure 8 for SM-Low/IL, SM-High/IL, and PMMA/IL mixtures with wIL = 0.48, and analogous plots for the remaining compositions are shown in Supporting Information, Figure S4. Note that the conductivities for homopolymer PMMA/IL mixtures are comparable to those observed at the same composition and temperature by Susan et al. in mixtures of cross-linked PMMA and EMIm−TFSI.67 At all compositions and temperatures, the conductivity of PMMA/IL exceeds that of the diblock copolymer/IL mixtures by half an order to over 2 orders of magnitude. For both SM-Low/IL and SM-High/IL, ionic conductivity is higher in the x-direction than the z-direction at a given molecular weight and composition. This is consistent with the preferential orientation of lamellae as described above by f x > fz. In the x-direction, conductive PMMA/IL lamellae are preferentially oriented along the direction of ion transport. In

w1Tg1 + w2kTg 2 w1 + kw2

(14)

where w1 and w2 correspond to the weight fractions of EMIm− TFSI and PMMA in the PMMA/IL microdomain, and Tg1 and Tg2 correspond to the glass transition temperatures of neat IL (183 K) and neat PMMA (393 K). The empirical fitting parameter, k, is equal to Δβ2/Δβ1 = (β2,R − β2,G)/(β1,R − β1,G), where βR and βG are the coefficients of thermal expansion of the rubbery and glassy states, respectively, and 1 and 2 again correspond to neat EMIm−TFSI and PMMA, respectively. If k = Tg1/Tg2, eq 14 simplifies to the Fox equation, which describes a plasticized polymer with two fully miscible components. For a mixture of PMMA and EMIm−TFSI, this corresponds to k = 0.466. At wIL < 0.5, when the PMMA/IL dynamics are dominated by the segmental relaxations of PMMA chains, the Gordon−Taylor expression with k = 1 describes the Tg,PMMA/IL data; however, the same Gordon−Taylor expression overestimates Tg,PMMA/IL by 56 to 83% at wIL > 0.5. Compositions at wIL > 0.5 correspond to the formation of an IL-rich region in PMMA/IL microdomains according to SCFT calculations (Figure 6). 3.4. Ionic Conductivities of SM/IL and PMMA/IL Mixtures. To probe the effects of microdomain orientation on ionic conductivity in SM/IL mixtures, the ionic con-

Figure 8. Ionic conductivity as a function of inverse temperature and microdomain orientation for (a) SM-Low/IL with f x = 0.85 and fz = 0.30 and (b) SM-High/IL with f x = 0.90 and fz = 0.21. Conductivities of PMMA/IL mixtures are shown for comparison. G


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Figure 9. Ionic conductivity (σx) as a function of inverse temperature for SM-Low/IL (●) and SM-High/IL (blue ■) mixtures at various compositions, wIL = (a) 0.24, (b) 0.48, (c) 0.61, and (d) 0.69. Conductivities of PMMA/IL mixtures (red ◆) are shown for comparison.

Figure 10. (a, b) Normalized x-conductivity and (c, d) normalized z-conductivity as a function of temperature and composition for (a, c) SM-Low/ IL mixtures (filled symbols) and (b, d) SM-High/IL mixtures (open symbols). The σn values were determined using experimental f values. The vertical scales vary to enhance readability of data.

the z-direction, nonconductive PS layers are preferentially oriented normal to the direction of ion transport, creating a highly tortuous pathway for ion conduction. Conductivity anisotropy (σx/σz) values generally decrease with temperature, with the exception of SM-Low-61. Temperature-averaged conductivity anisotropy values (⟨σx/σz⟩) as a function of composition for the eight SM/IL mixtures are listed in Table 1 and vary from ∼2 to 12 with composition. The temperature-dependent x-direction ionic conductivities (σx) are shown in Figure 9. The σx values of all diblock copolymer/IL mixtures increase with temperature due to increased polymer segmental motion, which is coupled with ion transport. Conductivities also increase with IL loading due to the corresponding decrease in glass transition temperature and increase in segmental motion of PMMA chains. The size of conductive microdomains in diblock copolymer/IL mixtures simultaneously increases with increasing IL content. Interestingly, the conductivities of SM-High/IL mixtures are greater than those of SM-Low/IL mixtures in all cases. Conductivities of diblock copolymer/IL mixtures are found to differ by less than a factor of 2 at wIL = 0.24 (barely visible on the log scale of Figure 9), by a factor of 5 at wIL = 0.48, by a factor of 25 at wIL = 0.61, and by a factor of 4 at wIL = 0.69. These differences in conductivity exist despite the two diblock copolymer/IL mixtures having the same morphology type, ϕc, IL content, and similar extents of morphological anisotropy. The conductivity differences are also not commensurate with the difference in lamellar lattice parameters, which differ by a factor of 1.6 between the two molecular weights. Similar trends are seen in the σz values (Supporting Information, Figure S5). Conductivities (σz) of SM-High/IL are greater than SM-Low/ IL by less than a factor of 2 at wIL = 0.24, by a factor of 4 at wIL = 0.48, and by a factor of 66 at wIL = 0.61. At wIL = 0.69, σz values of SM-Low/IL are greater than those of SM-High by less

than a factor of 2 due to the higher anisotropy in SM-High-69 (see Figure 3).

4. DISCUSSION 4.1. Discussion of Diblock Copolymer versus Homopolymer Ion Conduction Mechanism. To gain further insight into the ion transport mechanism of diblock copolymer/ionic liquid and homopolymer/ionic liquid mixtures, the ionic conductivity results were analyzed using the Sax−Ottino model.54 The Sax−Ottino model is based on effective medium theory and treats a block copolymer as a composite of conducting and nonconducting phases, where the length scale of inhomogeneity (in this case, the length scale of microphase separation) is much less than the length scale of the bulk material. This model can be used to directly compare the ionic conductivity of ion-containing microdomains in a block copolymer with that of a homopolymer using the normalized conductivity, eq 2. The Sax−Ottino model does not predict the ionic conductivity of block copolymers to be molecular weightdependent when ϕc is held constant. The SM-Low/IL and SMHigh/IL mixtures studied here have the same ϕc at a given IL content, and σc is assumed to be the experimentally measured conductivity of PMMA/IL at the same IL content and temperature. The σn values as a function of temperature, composition, and molecular weight are shown in Figure 10. Instead of using the assigned morphology factor for isotropic lamellae, f = 2/3, we apply values for f determined from SAXS data (Figure 4). When σn = 1 the experimental conductivity is equal to that predicted by the Sax−Ottino model. It is evident that normalized conductivities for SM/IL mixtures fall below unity, except at 30 °C for SM-High-48 and SM-High-61, which have σn,x = 1.1 and σn,z = 1.1, respectively. For SM-High24 and SM-High-69, and for SM-Low, at all compositions, σn ≤ H


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Figure 11. Ionic conductivity (σx) as a function of inverse temperature normalized by Tg,PMMA/IL for SM-Low/IL (●), SM-High/IL (blue ■), and PMMA/IL (red ◆) mixtures at various compositions, wIL = (a) 0.24, (b) 0.48, (c) 0.61, and (d) 0.69.

4.2. Molecular Weight Dependence of Diblock Copolymer/IL Ionic Conductivity. To uncover the origin of the molecular weight dependence of ionic conductivity in these diblock copolymer/IL mixtures, the Sax−Ottino model is again used as a framework. Each parameter in the model is examined to determine differences between SM-Low/IL mixtures and SM-High/IL mixtures. The morphology factor, f, is first considered. Although f values for SM-High are not always greater than those for SM-Low (Figure 4), σSM‑High is always greater than σSM‑Low. Thus, differences in microdomain orientation are insufficient to account for the observed molecular weight dependence of ionic conductivity. Next, differences in the inherent conductivity of the conductive microdomain, σc, are assessed. Although σc values were not directly measured, ionic conductivity in these systems is correlated with Tg,PMMA/IL. Ionic conductivities (σx) are plotted at a fixed wIL as a function of Tg,PMMA/IL/T in Figure 11 to account for dynamic differences between SM-Low and SMHigh. The conductivity data for SM-Low and SM-High only collapse at wIL = 0.24. At wIL ≥ 0.48, as T approaches Tg,PMMA/IL, differences in conductivity between SM-Low and SM-High become even more pronounced. Similarly, when σz values are plotted at a fixed wIL as a function of Tg,PMMA/IL/T, the data fail to collapse at wIL ≥ 0.48 (Supporting Information, Figure S6). This suggests that at low IL content, the higher conductivity of SM-High is primarily due to its lower Tg,PMMA/IL, whereas at wIL ≥ 0.48, additional factors contribute to the molecular weight dependence of ionic conductivity. Finally, the volume fraction of the conductive microphase, ϕc, is considered. The nominal ϕc values are the same for both molecular weights at the same wIL. However, this does not account for heterogeneity in the IL distribution. Our SCFT calculations suggest that at wIL ≥ 0.48, the IL distribution within PMMA microdomains is nonuniform and the heterogeneity is greater for SM-Low/IL mixtures. This compositional variation is consistent with the large Tg,PMMA/IL breadths observed for SM/IL mixtures and the greater Tg,PMMA/IL breadths seen for SM-Low/IL mixtures. Our SCFT calculations predict that SM-Low/IL mixtures have a higher maximum in the IL concentration profile, which corresponds to a lower Tg,PMMA/IL. On the basis of this, a higher inherent conductivity and higher overall ion conductivity is expected for SM-Low/IL; however, a lower bulk conductivity is observed for SM-Low/IL mixtures compared to SM-High/IL. This suggests that other factors are arresting ion transport in SM-Low/IL mixtures. We propose that because SM-Low has a higher number density of interfaces that reduce segmental mobility and hinder

0.4. This indicates that the Sax−Ottino model overpredicts ionic conductivity values for the majority of investigated SM/IL samples and experimental conditions. Low values of normalized conductivity (less than 0.04) were also observed by Kim et al. in sulfonated styrene−methylbutylene diblock copolymers mixed with imidazolium-based ionic liquids, where low conductivities were attributed to high interfacial roughness between microdomains and increased tortuosity of the conducting pathway.68 In styrene−ethylene oxide diblock copolymers mixed with lithium salt, Panday et al. found the normalized conductivity to be less than 1 when the molecular weight of conductive PEO was below 50 kg/mol, and values even lower than 0.25 were observed when Mn,PEO was less than 20 kg/mol.51 Values of σn = 1 were only observed for Li+-toether oxygen ratios of 0.085. In addition, isotropic values of f were assumed in the work by Panday et al. Overall, the σn values are higher for SM-High than SM-Low. This difference is greater for the intermediate compositions, wIL = 0.48 and 0.61, as seen in the ionic conductivity plots in Figure 9. Both the low values of σn as well as the molecular weightdependence of σn are deviations from the predictions of the Sax−Ottino model. This suggests that additional factors, apart from the volume fraction, morphology type, orientation, and inherent conductivity of the conductive microdomain, must be taken into account to model the ionic conductivity of block copolymers in this molecular weight regime. The orders of magnitude difference in conductivity between the diblock copolymer/IL and homopolymer/IL mixtures suggests that structural attributes in these block copolymer/ IL systems greatly arrest ion transport compared to the homopolymer. Chain stretching is expected to occur in block copolymers due to the microphase separation of PS and PMMA chains. Moreover, our SCFT calculations show pronounced composition variations across the PMMA/IL microdomains. It has been proposed that block copolymers exhibit interfacial suppression of mobility due to the covalent bonding of segments with distinct relaxation behaviors and Tgs. Specifically, segmental relaxation and ion transport in the conductive microdomain may slow down near the interface between conductive and nonconductive segments, the latter of which typically have higher Tgs.52,69,70 In the present study, ions near PS−PMMA interfaces are expected to have reduced mobility due to reduced PMMA segmental mobility, thereby reducing ionic conductivity. Furthermore, our DSC results suggest there may be a broad distribution of dynamic relaxations within the homopolymer PMMA/IL mixture due to the formation of PMMA- and IL-rich regions. I


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tion of lamellae in the plane of the film was quantified by analyzing X-ray scattering data. After accounting for the composition, volume fraction, morphology type, morphology orientation, and Tg, the higher molecular weight diblock copolymer/ionic liquid mixtures exhibit higher ionic conductivities, greater by a factor of less than 2 at wIL = 0.24 to a factor of 66 at wIL = 0.48 (z-conductivity). By self-consistent field theory, it was found that while both molecular weights exhibit nonuniform IL compositions in the PMMA/IL microdomains, the lower molecular weight diblock copolymer displays greater compositional heterogeneity within PMMA microdomains and a lower IL content at PS−PMMA/IL interfaces. Interfaces between PS and PMMA/IL blocks are identified as detrimental to ion transport due to reduced mobility of ions and PMMA segments near the interface. The increase in conductivity with increasing molecular weight is attributed primarily to the correspondingly lower number density of conductivity-suppressing interfaces.

ion transport, SM-Low/IL mixtures have a lower bulk conductivity than SM-High/IL mixtures, despite having the same morphology type, the same volume fraction, and comparable extents of alignment. Since the lamellar lattice parameter of SM-Low is roughly half that of SM-High, SM-Low contains approximately twice the number of interfaces per volume as SM-High. SCFT calculations also suggest that SMLow has a lower IL content at PS−PMMA/IL interfaces compared to SM-High. The interfacial suppression of conductivity is corroborated by the Tg data, where the primary Tg,PMMA/IL values of SM-Low/IL mixtures are higher than the analogous Tgs for SM-High/IL. By increasing the degree of polymerization of the conductive chain, the fraction of lowmobility segments, or PMMA segments affected by PS− PMMA/IL interfaces, and fraction of ions in contact with those segments is reduced. In previous studies of ion-containing SEO systems, an increase in ionic conductivity with molecular weight was attributed to an increase in the dielectric constant of PEO and concentration of dissociated ions in the center of PEO microdomains.49−51 Both phenomena were related to reduced segmental mobility near PS−PEO microdomain interfaces. The SEO/salt mixtures studied by Panday et al.51 and Singh et al.50 exhibited poor long-range order, whereas the SEO/IL solutions characterized by Simone et al.49 were strongly microphase separated with comparable long-range order to the present study. Yuan et al. and Bouchet et al. also showed that the molecular weight dependence of conductivity in SEO/salt52 and SEOS triblock copolymer/salt mixtures,4 respectively, is related to the relative width of the PS−PEO interfacial zone. In the case of the glassy−rubbery interface between semi-infinite polystyrene/poly(n-butyl methacrylate) (PS/PnBMA) homopolymers, Baglay et al. showed that the Tg of rubbery PnBMA was perturbed from its bulk value as much as 150 nm away from the interface.71 For ion-containing diblock copolymers with glassy−rubbery interfaces, it is conceivable that increasing the molecular weight decreases the fraction of segments and mobile ions affected by such Tg perturbation. Sethuraman et al. recently demonstrated that perturbations from bulk dynamics near the glassy−rubbery interfaces of diblock copolymers are primarily dependent on the interfacial width,70 which is not inconsistent with our present rationale. Assuming that the interfacial width is unaffected by molecular weight, interfaces nevertheless influence a smaller fraction of segments in systems with larger microdomains and fewer interfaces. Alternatively, increasing the molecular weight may decrease the fraction of ions that accumulate at the interface due to interfacial polarization effects, thus increasing ion conductivity. These studies, as well as our findings, highlight the need for predictive models for ion transport in block copolymers that account for the influence of interfaces between polymer blocks with distinct segmental dynamics. The role of interfaces is non-negligible in block copolymer systems and signifies an important distinction relative to ion-containing homopolymers that gives rise to significant molecular weight effects.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.5b02445. Modulated differential scanning calorimetry experimental parameters and data and additional reversing heat flow signal plots, Nyquist impedance plots, and ionic conductivity plots for SM/IL and PMMA/IL mixtures (PDF)

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AUTHOR INFORMATION

Corresponding Author

*(K.I.W.) E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors gratefully acknowledge support from the National Science Foundation, Grant Numbers DMR-1506726 (S.S.) and DMR-1410246 (J.K.); the donors of the Petroleum Research Fund, administered by the American Chemical Society, Grant Number ACS PRF 55662-ND7 (R.A.R.); the Nanotechnology Institute; and the Energy Commercialization Institute. The authors are grateful for computational resources made available through XSEDE (TG-DMR150034). We acknowledge the use of facilities at the University of Pennsylvania, funded in part by the MRSEC Program of the National Science Foundation, Grant Number DMR11-20901. The authors also express gratitude to Alexa Kuenstler for assistance with data collection; Dr. Philip Griffin for helpful discussions; and Derrick Smith and Professor Christopher Li of Drexel University for assistance with instrumentation and ionic conductivity experiments, supported by the National Science Foundation, Grant Number CMMI-1334067.

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5. CONCLUSIONS The structure−property relationships of poly(styrene-b-methyl methacrylate) diblock copolymer/ionic liquid mixtures with various compositions and two molecular weights were studied. Processing conditions were controlled so that both molecular weights exhibit strongly microphase separated lamellar morphologies with long-range order. The preferential orienta-

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