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Roles of Chemical Functionality and Pore Curvature in the Design of Nanoporous Proton Conductors Grayson L. Jackson,† Dominic V. Perroni,†,§ and Mahesh K. Mahanthappa*,†,‡ †

Department of Chemistry, University of Wisconsin−Madison, 1101 University Avenue, Madison, Wisconsin 53706, United States Department of Chemical Engineering & Materials Science, University of Minnesota, 421 Washington Avenue, S.E., Minneapolis, Minnesota 55455, United States

‡

S Supporting Information *

ABSTRACT: Nanoporous proton-transporting media are critical components in fuel cells and other electrochemical devices, yet general molecular design criteria for new materials with enhanced performance remain obscure. Aqueous lyotropic liquid crystals (LLCs) comprise a platform for detailed studies of the molecular-level features governing proton transport in monodisperse, water-filled nanopores lined with well-defined chemical functionalities. We report new alkylsulfonic acid LLCs that exhibit H+ conductivities as high as σ = 380 mS/cm at 80 °C, which rival those of more acidic, perfluorinated polymers, thus demonstrating that the acidity of the pore functionality is not the sole determinant of proton transport. Direct experimental comparisons of LLCs with convex and concave nanopores of similar dimensions indicate that H+ conductivities therein sensitively depend on the hydration state of the acid functionalities and the pore curvature. These experiments suggest that judicious manipulation of pore curvature provides a new means for optimizing the activities of proton-exchange membranes and nanoporous solid acid catalysts.

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INTRODUCTION Future renewable energy generation, storage, and utilization strategies rely on the development of electrochemical devices with polymer electrolyte membranes that selectively and efficiently transport ions between the constituent electrodes.1,2 Proton exchange membranes (PEMs) are key components in membrane-based artificial photosynthesis of renewable H2(g) and other solar fuels3,4 and in fuel cells5−7 that convert energy stored in chemical bonds into electrochemical work. Useful and well-studied PEMs such as Nafion, Aquivion,8 and 3M perfluorosulfonate ionomers9 may be summarily described as perfluorinated polyethylenes decorated with perfluoroalkylsulfonic acid side chains. Hydration with water induces these superacidic polymers to form percolating networks of waterfilled nanochannels within a fluoropolymer matrix.10 Watermediated H+ transport occurs through these concave nanopores, which exhibit widely variable dimensions and tortuosities.11,12 In spite of their well-defined chemical compositions, the supramolecular morphologies of these hydrated ionomers remain hotly debated, and methods for improving their performance remain obscure.5,8 Specifically, the dependences of the observed H+ conductivities on nanopore diameter and curvature, pore functionality and its pKa, and hydration state remain poorly understood even at 100% relative humidity. We seek to understand how ion transport in the water-filled nanopores of aqueous lyotropic liquid crystals (LLCs) depends on their specific pore structures. Recent studies reveal that confinement of aqueous electrolytes in sub-5 nm pores leads to © XXXX American Chemical Society

anomalously high conductances, which may stem from differences in water structure, dynamics, and ion hydration.13 However, few studies have experimentally interrogated how nanopore dimensions and curvature affect ion conduction therein. A molecular-level understanding of the features governing H+ transport in water-filled nanochannels requires detailed investigations in chemically and supramolecularly welldefined model systems. The water concentration-dependent self-assembly of ionic surfactants provides convenient access to LLCs, with structurally periodic and monodisperse water-filled nanopores with diameters ∼0.7−4 nm.14,15 In these LLCs, the chemical incompatibility between the hydrated ionic headgroup functionalities and the alkyl tails drives all of the surfactant headgroups to the interface between the hydrophobic and hydrophilic domains. Thus, the pore functionalities are specified by the surfactant headgroups, while the water content and alkyl tail structure determine the pore dimensions and curvatures. LLC self-assembly potentially enables access to a wide variety of morphologies with different pore interfacial curvatures decorated with acidic functionalities (Figure 1), offering a platform for theoretically16 and experimentally studying water-mediated H+ transport in functional nanochannels. Received: June 28, 2017 Revised: September 14, 2017

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DOI: 10.1021/acs.jpcb.7b06366 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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anhydrous and anaerobic THF prior to use. Type I ultrapure water was obtained from a ThermoScientific Barnstead NANOpure system (18 MΩ resistance). 1 H and 13C NMR spectra were recorded on a Bruker Avance400 with Smartprobe or Avance-500 with DCH cryoprobe spectrometer. 1H NMR spectra were referenced relative to the residual protiated solvent peak in CD3OD or to TMS in CDCl3. Mass spectrometry was performed using a Waters (Micromass) LCT electrospray ionization TOF spectrometer operating in positive ion detection mode with a sample cone voltage of 20 V. Combustion analyses (C, H, and S) were performed by Atlantic Microlab, Inc. (Norcross, GA). Surfactant Synthesis. Complete experimental details associated with the multistep surfactant syntheses are provided in the Supporting Information. We briefly describe these syntheses here. Deprotonation of isopropyl nonanesulfonate (1) with nBuLi/HMPA at −78 °C in tetrahydrofuran (THF),17 followed by alkylation with 1,4-dibromobutane and subsequent column chromatography yielded docosane-9,14-bis(isopropyl sulfonate) (2; Scheme 1a). Saponification of the isopropyl

Figure 1. Hydration of sulfonic acid-based amphiphiles affords access to lyotropic liquid crystals comprising water-filled nanopores lined with ionic functionalities specified by the surfactant headgroups (blue circles) and mobile counterions (green circles). Judicious variation of the surfactant tail structure (red lines) and the water content leads to double gyroid (G) phases with structurally uniform and percolating nanochannels with either (A) convex or (B) concave interfacial curvatures.

Scheme 1. Syntheses of (a) Gemini Bis(sulfonic acid) (SO3H-74) and (b) Branched Sulfonic Acid (C16-SO3H) Amphiphiles

Herein, we describe the syntheses and aqueous LLC selfassembly behaviors of new alkylsulfonic acid amphiphiles, and we characterize their H+ conductivities. By rationally manipulating the surfactant molecular structures, we access water-filled nanopores lined with sulfonic acids having both concave and convex curvatures. In both confining environs, we find that the proton conductivity depends most sensitively on the acid hydration state, and it peaks at intermediate hydrations. In comparably hydrated LLCs with similar pore diameters and surface densities of functional groups, our measurements further demonstrate that pores with convex interfacial curvatures exhibit H+ conductivities that are much higher than those of concave pores. Consequently LLCs with convex pores at intermediate hydrations exhibit H+ conductivities as high as 173 mS/cm at 22 °C and 380 mS/cm at 80 °C with proton transfer activation energies as low as Ea = 0.08 eV (1.84 kcal/mol). Thus, nanopore curvature emerges as an important design consideration in the development of next-generation proton-transporting membranes, with potentially broader applications for the development of highly active, nanoporous solid acid catalysts.

esters furnished SO3H-74. We also synthesized the branched sulfonic acid amphiphile C 16 -SO 3 H (Scheme 1b) by nucleophilic displacement of 7-(bromomethyl)pentadecane with Na2SO3 in a refluxing aqueous ethanol solution, followed by acidification with gaseous HCl (see the Supporting Information for synthetic details). After purification, each surfactant was azeotropically freeze-dried from benzene and analyzed for elemental purity and water content. Elemental Analysis: Anal. Calcd for SO3H-74 C22H46S2O6· 2.05H2O: C, 52.05; H, 9.95; S, 12.63; Found: C, 52.07; H, 9.78; S, 12.27. Anal. Calcd for C16-SO3H C16H34SO3·0.85H2O: C, 59.72; H, 11.18; S, 9.96; Found: C, 59.79; H, 11.10; S, 10.01. LLC Sample Preparation. Specific quantities of SO3H-74 and C16-SO3H were massed into 4 dram vials in an argon− filled glovebox. Accounting for the residual water present in the freeze-dried amphiphile discerned from elemental analyses, Type I ultrapure water was added to SO3H-74 and C16-SO3H outside of the glovebox to achieve the specified hydration number w0 = (total moles H2O)/(moles −SO3H headgroup). These mixtures were homogenized by consecutive high-speed centrifugation (4 950g) followed by hand-mixing with a spatula. LLCs thus obtained were structured solids (with no excess water present), which were allowed to rest for at least 24 h prior to X-ray analysis and were subsequently used in proton

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EXPERIMENTAL SECTION Materials and Methods. Sodium 1-nonanesulfonate and 7-(bromomethyl)pentadecane were purchased from TCI America (Philadelphia, PA). Sodium 1-nonanesulfonate was dried at 50 °C under vacuum for 8 h prior to use. All other materials and reagent grade solvents were purchased from Sigma-Aldrich (Milwaukee, WI) and used as received unless otherwise noted. 1,4-Dibromobutane was distilled, degassed, and stored under nitrogen and away from light. Hexamethylphosphoramide (HMPA) and pyridine were distilled from CaH2 and stored under nitrogen. 2-Propanol (iPrOH) was stirred over MgSO4(s) prior to use. Anhydrous and anaerobic THF was obtained by sparging analytical grade solvent with nitrogen for 30 min followed by cycling through a column of activated alumina for 12 h in a Vacuum Atmospheres, Co. solvent purification system. n-Butyllithium (2.6 M in hexanes) was titrated using recrystallized diphenylacetic acid in B

DOI: 10.1021/acs.jpcb.7b06366 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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RESULTS AND DISCUSSION Recent work by the groups of Gin18 and Mahanthappa19 demonstrates that gemini (“twin head-twin tail”20) surfactants form thermally stable lamellar (Lα), double gyroid (G) and hexagonal (H193) networks, and cylindrical (H) phases over wider amphiphile concentration windows than their single-tail surfactant analogs. These particular network and cylindrical phases comprise convex, water-filled nanopores (Figure 1A). Consequently, we synthesized the gemini bis(sulfonic acid) surfactant SO3H-74 from commercially available sodium nonanesulfonate as depicted in Scheme 1a. To target LLC morphologies featuring concave nanopores (Figure 1B), we synthesized a branched amphiphile (C16-SO3H) (Scheme 1b). The water concentration-dependent LLC morphologies of SO3H-74 were investigated by temperature-dependent, synchrotron small-angle X-ray scattering (sSAXS; see Figures S1 and S2). For SO 3H-74, we recorded sSAXS patterns corresponding to three distinct LLC phases (Figure 2A) in

conductivity measurements. This resting period allows for the relaxation of any residual stresses in the sample induced by the sample preparation protocol. When not in use, LLC samples were stored in Teflon-capped vials sealed with Parafilm whenever possible to avoid dehydration (a change in w0). Small-Angle X-ray Scattering (SAXS). Synchrotron SAXS analyses were conducted at the 12-ID-B beamline of the Advanced Photon Source (APS) at Argonne National Laboratory (Argonne, IL) utilizing a beam energy of 14 keV (λ = 0.8856 Å) and a 2.027 m sample-to-detector distance. A silver behenate standard sample was used to calibrate all recorded scattering patterns (d100 = 58.38 Å). 2D-SAXS patterns were recorded on a Pilatus 2M detector (25.4 cm × 28.9 cm rectangular area) with 1475 × 1679 pixel resolution. Samples were sealed in hermetic alodined aluminum DSC pans (TA Instruments, New Castle, DE), which were equilibrated for 5 min at the desired temperature using a Linkam DSC hotstage prior to X-ray exposure (typical exposure times of 0.1 s). Detector-corrected 2D-SAXS patterns were azimuthally integrated using the DataSqueeze software package (http://www. datasqueezesoftware.com) to generate one-dimensional I(q) versus q intensity profiles. See the Supporting Information for further experimental details. Electrochemical Impedance Spectroscopy (EIS). EIS measurements were conducted using a custom-made, hermetically sealed sample holder in a two-probe geometry using Pt blocking electrodes. The Pt electrodes were cleaned prior to use by manual polishing and electrochemical cyclic voltammetry sweeps in 0.5 M H2SO4(aq). LLC samples were loaded into a Teflon O-ring (6 mm inner diameter, 1.8 mm thick) snugly surrounded by a Viton O-ring of slightly larger diameter, which was sandwiched between the two Pt electrodes (∼0.1 mm thick). This sample sandwich was then placed between stainless steel electrodes in a sample cell machined from polyether ether ketone. The top and bottom electrodes were connected by temperature-shielded copper wires to a Metrohm Autolab PGSTAT302N electrochemical impedance analyzer (with FRA32M modules), which was controlled using the Nova 1.10 software. Electrochemical impedance measurements were performed at 100 logarithmically spaced frequencies over the range 5 mHz ≤ ω ≤ 100 kHz with an applied AC amplitude of 5 mV. Temperature-dependent conductivity measurements were made by placing the sample cell into a Thermo Scientific Lindberg Blue M vacuum oven fitted with an OMEGA (CN7800) temperature controller with an accuracy of ±0.2 °C. For all measurements, samples were allowed to thermally equilibrate for at least 1 h. EIS data for each LLC sample was analyzed using the equivalent circuit model R ion + [QDL(RCTW)] depicted in Figure S4. Rion, which represents the solution resistance of the LLC nanochannels, corresponds to the high-frequency intercept (near the origin) of the Nyquist plot (Figure S4). Each sample was measured in triplicate, and the average value and standard deviation were used to determine Rion. The proton conductivity was then calculated as σ = L/ARion, where L is the LLC sample thickness and A is the cross-sectional area of the Teflon O-ring measured with VWR-brand digital calipers before and after the measurement (accuracy ±0.03 mm). See Tables S2 and S3 for a complete summary of the conductivity data.

Figure 2. Representative azimuthally-integrated one-dimensional sSAXS intensity profiles recorded at 25 °C reveals the compositiondependent LLC phase behavior of sulfonic acid amphiphiles. (A) SO3H-74 forms lamellae (Lα) at a headgroup hydration w0 = 4.75, a normal double-gyroid network (GI) with a small amount of 3Dhexagonal (HI193) network (small peaks identified by “*” are the (110) and (220) reflections of HI193) at w0 = 7.40, and normal hexagonally packed cylinders (HI) at w0 = 18.2. (B) C16-SO3H forms inverse hexagonally packed cylinders (HII) at w0 = 5.0, inverse double gyroid (GII) at w0 = 10, and Lα at w0 = 20.

the headgroup hydration number range w0 = (total moles H2O)/(moles −SO3H) = 4.75−20. Because both amphiphiles were isolated as hydrates (see Experimental Section for elemental analyses), the calculated w0 values include both the residual water in each amphiphile along with the water added to produce each LLC. LLCs formed at the low hydration w0 = 4.75 were soft, optically birefringent solids that exhibited sSAXS patterns consistent with lamellar (Lα) morphologies with bilayer spacings a ≈ 2.6 nm (q* = 2.40 nm−1).21 When 7.40 C

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The Journal of Physical Chemistry B ≤ w0 ≤ 9.38, we observe complex phase coexistence of two network (N) phases. Specifically, we observed 18 sSAXS peaks associated with an exceptionally well-ordered double gyroid morphology (Ia3d̅ symmetry) with unit cell parameter a ≈ 7.29 nm (q* = 0.861 nm−1), coexisting with a small amount of a tetracontinuous 3D-hexagonal (H193) network phase (P63/mcm symmetry).22 When w0 = 10−20, SO3H-74 LLCs are stringy, birefringent solids with sSAXS signatures that match hexagonally packed cylindrical micelles (H). Within the H phase, the cylinder center-to-center distances vary slightly from 3.7 nm (q* = 1.96 nm−1) at w0 = 10 to 3.9 nm (q* = 1.86 nm−1) at w0 = 19.7, implying only small changes in the water pore diameters with increasing water content. Further headgroup hydration (w0 ≥ 22) yields freely flowing, disordered micellar solutions. The w0 versus temperature aqueous LLC morphology map for SO3H-74 is shown in Figure 3A. The phase sequence Lα→ N

which the lipid tail comprises the matrix and water is confined within concave sulfonic acid-lined nanopores. Electrochemical impedance spectroscopy measurements of the bulk proton conductivities of these sulfonic acid LLC solids strongly suggest that water content is the most significant factor governing their proton conductivities. From the ambient temperature proton conductivity (σ) versus headgroup hydration number (w0) plot in Figure 4A (based on data in

Figure 3. Aqueous LLC phase portraits: (A) SO3H-74, in which Lα = lamellae, a = Lα/GI/HI193 coexistence, NI = normal double gyroid (GI) coexisting with small amounts of the HI193 network, HI = normal hexagonally packed cylinders, S = sponge, and Iso = micellar solution; (B) C16-SO3H at 25 °C, in which HII = inverse hexagonally packed cylinders, GII = inverse double gyroid, and Lα = lamellae. A two-phase coexistence window is observed between the pure GII and Lα phases for C16-SO3H. The gray areas represent unexplored regions of the phase diagram.

Figure 4. (A) Ambient temperature proton conductivity (σ) versus hydration number (w0) for SO3H-74 (squares) and C16-SO3H (circles) LLCs exhibits a peak in the hydration-dependent conductivity. (B) Molar conductivity (Λm) versus w0 for both LLCs, which normalizes for sulfonic acid number density, demonstrates that normal LLCs with convex nanopores exhibit significantly higher proton conductivities.

Table S2), we observe that the SO3H-74 Lα phase (w0 = 4.73) exhibits a modest conductivity of 14.0 mS/cm. Addition of water triggers a phase transition to the NI network phase with percolating nanopores, which is accompanied by an increase in conductivity by more than a factor of 3. Within the narrow NI window, the proton conductivity is extremely sensitive to headgroup hydration with a maximum value of 128 mS/cm at w0 = 8.68. Ichikawa et al. observed similar nonlinear increases in proton conductivity in zwitterionic sulfobetaine surfactant GII LLCs doped with triflimide (HNTf2) upon incremental addition of water, albeit with significantly lower overall conductivities ≤ 30 mS/cm.23 In studies of (NH4)2(adp)[Zn2(ox)3]·nH2O metal−organic frameworks (MOFs), Sadakiyo et al.24 also noted that proton conductivity increased from 10−12 S/cm at 0% RH to 8 × 10−3 S/cm at 100% RH, which is one of the highest-reported ambient temperature proton conductivities for MOFs.25 However, our current study of LLCs differs fundamentally from these studies of MOFs. In MOFs, the crystal structure dictates a pore size while the %RH determines the fraction of the pore filled by water. In our LLCs and in hydrated polymer membranes, the pore remains

→ H → micelles with increasing w0 implies that these LLCs are “normal” phases (Type I), in which water comprises the matrix as depicted in Figure 1A. Accounting for the dimensions of the hydrophobic surfactant tail, water is thus nanoconfined between convex sulfonic acid-lined interfaces situated ∼1.7−2.5 nm apart (see Figure S3). For C16-SO3H, we also recorded three different types of sSAXS patterns over the hydration range w0 = 5−30 (Figure 2B). At low hydrations, C16-SO3H forms hexagonally packed cylinders with center-to-center distances ∼2.9 nm (q* = 2.50 nm−1). Increasing hydration to w0 = 10 resulted in the formation of a stiff, optically nonbirefringent sample with 8 sSAXS peaks corresponding to a double gyroid morphology (q* = 0.819 nm−1). In the range w0 = 15−30, we observed soft, birefringent samples with sSAXS traces that match lamellar morphologies with layer spacings ∼3.4−4.8 nm. The aqueous phase behavior for C16-SO3H at 25 °C is summarized in Figure 3B. The phase progression H → G → Lα on increasing hydration implies these LLCs are “inverse” (Type II) phases in D

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The Journal of Physical Chemistry B completely filled at all hydrations while the diameter increases as water is added. At higher hydrations, SO3H-74 forms a HI phase with a peak conductivity of 173 mS/cm at w0 = 13. However, the H+ conductivities of these LLCs decrease upon further hydration in the ordered HI phase; we return to this point below. We observed similar trends in the hydration-dependent conductivities of C16-SO3H LLC solids (Figure 4A and Table S3). At low hydration (w0 = 5), the HII phase exhibits a H+ conductivity of 1.1 mS/cm. Conductivity peaks at 49 mS/cm at w0 = 10 in the GII phase, probably due to the formation of percolating conductive channels.23,26,27 Further increases in hydration result in a phase transition to the Lα phase, wherein H+ conductivity exhibits a peak value of 32 mS/cm at w0 = 10. Further increases in LLC hydration state lead to diminished conductivities. The H+ conductivities of SO3H-74 LLCs are significantly higher than those of C16-SO3H, even upon normalizing for the volume density of −SO3H groups (Figure 4B). Note that this analysis assumes that all sulfonate groups are situated at the hydrophobic/hydrophilic domain interface due to their mutual chemical incompatibility. This notion is supported by studies of related alkylsulfate surfactants at oil−water interfaces, which demonstrated that the sulfate headgroups remained highly hydrated.28 Some of this conductivity difference may be attributed to differences in macroscopic water channel connectivity, especially between the HI phase of SO3H-74 and the Lα phase of C16-SO3H. Within the network phases, we expect the differences in molar conductivity to be independent of LLC grain size and macroscopic tortuousity. The higherorder SAXS peaks indicate high degrees of long-range order. Because we observe the (721) reflection for SO3H-74 (w0 = 8.56, a = 75 Å), we estimate that its grain size is ≥500 Å. Similar analysis of C16-SO3H at w0 = 10 indicates the grain size is ≥400 Å. Using the Nernst−Einstein equation to estimate the proton diffusion coefficients in our materials, we estimate that our EIS measurements only probe proton motions at the ∼30 Å length scale at the highest investigated frequency (100 kHz). Thus, grain boundaries should not significantly impact the measured proton conductivities in these network phases. The molar conductivity (Λm) in the SO3H-74 NI phase at w0 = 8.68 is a factor of 2 greater than that in the C16-SO3H GII phase at w0 = 10, even though both phases comprise networks of percolating water channels of similar dimensions as determined from X-ray analyses (d ∼ 22 Å, see the Supporting Information for details of this calculation and Figure S3). Using the molecular dimensions of the surfactants and an established geometric model for the gyroid morphology,29 we estimate that the interfacial area per surfactant headgroup is almost identical for both phases: 51 Å2 for SO3H-74 and 53 Å2 for C16-SO3H (see Table S1 in the Supporting Information and associated description of this calculation). Thus, this difference in molar conductivity does not apparently stem from a difference in the interfacial density of sulfonic acid functional groups. The numerical difference in Λm is most likely a lower bound, as the conductivity of SO3H-74 LLCs increases with hydration until w0 = 13. The H+ conductivities of SO3-74 LLCs are strongly temperature-dependent, achieving values as high as 380 mS/ cm at 80 °C in the HI phase at w0 = 12. From analyses of these conductivity data using the Arrhenius relationship ln σ(T) = ln σ0 − (Ea/RT), we determined the apparent activation energy (Ea) and prefactor (σ0) for each LLC composition (Figure 5

Figure 5. (A) Apparent H+ transfer activation energy (Ea) and (B) prefactor (σ0) versus SO3H-74 surfactant headgroup hydration number (w0) plots derived from triplicate, temperature-dependent EIS measurements, which indicate that Ea and σ0 for proton transfer generally decreases with increasing w0 within a given LLC morphology window.

and Table S2). The apparent activation barriers for H+ transport range from 1.84 to 3.65 kcal/mol (0.08−0.16 eV), suggesting extremely facile proton transfer in the normal LLC phases.30,31 In hydrated zwitterionic inverse GII LLCs doped with triflimide, Ohno and co-workers previously reported higher energy barriers for proton transport (0.15−0.43 eV).23 Kitagawa and co-workers also noted higher activation energy barriers (0.21−0.47 eV) for fully hydrated (95% RH) MIL-53 MOFs, which decrease as the pore functionality becomes more acidic.32 We note that within each of the NI and HI LLC phase windows, the values of Ea and σ0 generally decrease with increasing w0. The observed conductivities of alkylsulfonic acid SO3H-74 LLCs are also higher than those of benchmark PEMs containing difluorosulfonic acids. The peak H+ conductivity of SO3H-74 with w0 = 13 at 25 °C is σ = 173 mS/cm, whereas the best reported conductivity for the fully hydrated perfluorosulfonic acid ionomer Nafion 117 (w0 = 19) is only 75 mS/cm under comparable conditions.27 Although the macroscopic LLC conductivity is apparently 2.3 times higher, the number density of −SO3H groups therein is ∼3 times higher than in Nafion 117. Thus, these two materials have comparable molar conductivities (Λm), albeit with different acidic functionalities at different w0’s. The conductivity of Nafion 117 is 60 mS/cm at w0 = 13 and 25 °C, which translates into Λm that is 8% lower than that of SO3H-74.5,33 On the other hand, Λm for Nafion 117 is only ∼35% greater than that of SO3H-74 at w0 = 19, in spite of the more acidic difluorosulfonic acid moieties in Nafion 117. Because the difference in the dilute aqueous solution pKa’s for CF3SO3H and CH3SO3H is ΔpKa ≥ 10,34 our data demonstrate that high proton conductivities are achievable with significantly less acidic alkylsulfonic acid materials. The observed peaks in H+ conductivity in both the SO3H-74 and C16-SO3H LLCs mirror experimental observations of the water concentration-dependent conductivities of homogeneous monoprotic acid solutions. For CH3SO3H(aq), we measured a peak in the overall conductivity at w0 = 12 (see Figure S5) in agreement with a previous report.35 Monoprotic acids such as HCl, CH3COOH, HNO3, CF3SO3H, triflimide, and ptoluenesulfonic acid universally exhibit similar peaks in their water concentration-dependent conductivities.36−40 Heterogeneous gels of sulfonic acid-based polymers41 and membranes of sulfonic acid-grafted copolymers42,43 also exhibit similar behaviors. These conductivity trends in both homogeneous E

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curvature and mitigates electrostatic repulsions, thereby facilitating proton dissociation and solvation.50 The increased population of mobile, bulk-like water molecules within the water channels probably increases the frequency of fluctuations in the nanoconfined water networks required for productive proton transfer by the Grotthuss mechanism.51,52 These factors generally lead to lower values of Ea as w0 increases within a given morphology, albeit with some exceptions. The concurrent decrease in the value of σ0 likely reflects the lower diffusivity of the larger protonated water clusters. The molar H+ conductivity of the convex SO3H-74 LLC nanopores is at least twice as large as that of concave C16-SO3H nanochannels at similar hydrations (w0 = 8.68 and 10, respectively) (Figure 4), in spite of having similar percolating double gyroid water channel diameters of ∼22 Å and similar areal surface densities of acidic headgroups. Miller et al.53 and Wang et al.54 previously observed that interfacial confinement of carboxylic acids significantly shifts their pKa’s. Thus, the degree of acid dissociation (α) within a nanopore and the resulting aH3O+ depend sensitively on its diameter and curvature. At concave interfaces, we surmise that closely bound ion pairs form to mitigate Coulombic repulsions between adjacent −SO3− headgroups arising from proton dissociation (Figure 1B). However, convex interfaces possibly lead to higher α values and high conductivities because of the larger separation between the resulting hydrated ion pairs in the aqueous channel (Figure 1A). This line of reasoning is further supported by our observation of even higher conductivities in the more convex pores of the SO3H-74 HI-phase LLCs, as compared to the less highly curved NI phases. On the basis of recent experiments and molecular dynamics simulations,55 we anticipate that convex interfaces will lead to faster water rotational dynamics that should enhance water-mediated proton transport. These results highlight how pore curvature and hydration dictate H+ activity in the rational design of acidic nanoporous media. For a given acidic functionality, these results suggest that its activity and ultimate performance may be specifically tailored by controlling pore hydration and interfacial curvature.

and heterogeneous electrolytes stem from the same underlying principles described below. The conductivity of a strongly acidic, aqueous electrolyte depends on σ ≈ ka H2Oa H3O+ ⎛ 1 = k ⎜⎜ − α (1 )( a H 2O − αaHA ) ⎝

⎞ ⎟αaHA a H O3/2 ⎟ 2 ⎠

where k is a bimolecular rate constant for proton transfer; aH2O, aH3O+, and aHA are the activities of H2O, H3O+, and the acid (HA), respectively; and α is the degree of acid dissociation (see the Supporting Information for derivation and application of this expression). Note that the established theoretical framework developed by Peckham et al.44 to describe this phenomenon neglects contributions from aH2O. However, the above expression highlights the strong dependence of proton conductivity on water content (aH2O). The value of aH2O·aH3O+ is small when the acid solution is either very concentrated (low w0) or very dilute (high w0), as either aH2O → 0 or aH3O+ → 0. At a molecular level, there is insufficient water in a highly concentrated acid solution to facilitate ion pair dissociation, which leads to a low aH2O·aH3O+ value. In a dilute electrolyte, aH2O·aH3O+ is small due to a low concentration of fully dissociated ions. Therefore, one expects aH2O·aH3O+ to peak at some intermediate w0, which manifests in a maximum value in the concentration-dependent conductivity. While the exact w0 for peak conductivity in homogeneous electrolytes depends solely on the molecular structure of the acid HA, the location and magnitude of the peak for heterogeneous electrolytes also depends on nanopore curvature as directly demonstrated by the data for SO3H-74 and C16-SO3H. Aqueous proton conduction in the LLCs primarily occurs by a combination of protonated water cluster diffusion and fast Grotthuss hopping of protons through networks of hydrogenbonded water molecules. We speculate that when the amount of water (w0) is sufficient to hydrolyze the acid yet insufficient to fully solvate and stabilize the H+, proton mobility by both water-mediated mechanisms is very high and leads to a peak in conductivity at intermediate hydrations for both LLC systems. Increasing the w0 beyond a critical amount leads to solvated H+ stabilization in larger water clusters,45−47 within which the protons may be delocalized. As the cluster size increases with w0, the delocalization of protons over larger clusters renders Grotthuss-type hopping the dominant H+ transport mechanism,48,49 while cluster diffusion slows. In spite of this crossover in the predominant H+ transfer mechanism, the dilute nature of the solution at high w0 leads to a decrease in the overall aH3O+ and the observed H+ conductivity. In other words, the H+ conductivity decreases across the HI phase window of SO3H-74 and the lamellar window of C16-SO3H as the electrolyte becomes more dilute. The observed decreases in both the Arrhenius activation energy (Ea) and the prefactor (σ0) for proton conduction in the NI and HI LLC phases of SO3H-74 are also consonant with the above molecular picture. At the lowest hydration in a given phase, nanoconfinement of the acidic functionalities in smaller pores disfavors ion dissociation and lowers α. Increasing the LLC hydration increases the water nanochannel diameter and

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CONCLUSION Our results demonstrate that the proton conductivities of acidic nanoporous materials sensitively depend on multiple factors. Contrary to conventional wisdom,32,56−59 the acidity of the interfacial functionalities is not the most important determinant of proton conductivity. While highly acidic functionalities increase proton activity, especially at low hydrations, proton conductivity also sensitively depends on water activity. The hydration state and interfacial curvature of the nanopores further dictate the proton dissociation equilibrium of the pore wall acids, while also altering the dynamics of nanoconfined water within the structure.60 These studies suggest a new means for designing efficient, next-generation water-filled acidic membranes with high proton conductivities. For a given pore wall chemical functionality, the pore diameter should spatially constrain the acid hydration state to simultaneously maximize the dissociated proton and water activities. Proton conductivity may be further enhanced by designing convex pores lined with densely packed acidic groups. Thus, judicious manipulation of the interfacial curvatures and pore diameters of nanoporous acidic materials may enable their enhanced performances as electrolytes in myriad energy applications. We anticipate that these molecular F

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design principles will also inform the synthesis of high activity mesoporous solid acid catalysts, wherein proton activity crucially determines catalytic activity.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.7b06366. Amphiphile synthesis and characterization details, sSAXS, electron density reconstructions and geometric interfacial area per surfactant calculations, conductivity measurements, and derivation of the functional dependence of proton conductivity on activity (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Grayson L. Jackson: 0000-0003-0663-3274 Mahesh K. Mahanthappa: 0000-0002-9871-804X Present Address §

D.V.P.: Schlumberger Technology Center, 110 Schlumberger Dr., Sugarland, TX 77478. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Marc A. Hillmyer for helpful discussions regarding bulk electrolyte solution conductivities. We gratefully acknowledge financial support for this work from the U.S. Department of Energy (DOE)-Basic Energy Sciences (BES) DESC0010328. Synchrotron SAXS analyses were conducted at Sector 12 of the Advanced Photon Source at Argonne National Laboratory, which is supported through the U.S. DOE Contract DE-AC02-06CH11357 under GUP-37637 and GUP-50116, with respective help from Dr. James Jennings and Carlos BaezCotto. This work also utilized University of Wisconsin Madison instrumentation facilities funded in part by NSF CHE9974839 and CHE-1048642 and materials characterization facilities funded by DMR-0832760 and DMR-1121288. G.L.J. acknowledges a National Defense Science and Engineering Graduate (NDSEG) Fellowship from the U.S. Department of Defense.

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REFERENCES

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