Abstract
The presented family of one-dimensional (1D) polyanionic borophosphates is discussed in the context of a growing class of intermediate temperature electrolytes. The borophosphates are noteworthy for exhibiting high thermal stability under a highly reducing H2 atmosphere. Here, we report the electrolyte characteristics observed in rubidium borophosphate (Rb3H2[BOB(PO4)3]) and cesium borophosphate (Cs3H2[BOB(PO4)3]) (a new compound) as newly identified members of the proton-conducting 1D borophosphate polyelectrolyte family. Ab initio molecular dynamics simulations of the compounds suggest extremely high H+ mobility correlated with gyrational mobility of the borophosphate chains, which is similar in character to that of previously reported borosulfate proton electrolytes. Particularly noteworthy is the proton conductivity of the Cs3H2[BOB(PO4)3] variant, which has the highest conductivity of any of the borophosphates so far, found to be on the order of 10 –5 S·cm –1 (250 °C and 0.2 atm of water). Cs3H2[BOB(PO4)3] was found to be the best-performing 1D borophosphate electrolyte due to the combination of the highest observed proton conductivity, the greatest thermal stability, and attractive mechanical properties. This represents an important advance for intermediate temperature proton conductors and provides a viable path to improve electrolytes for intermediate temperature hydrogen fuel cells.
Introduction
Solid acid fuel cells (SAFCs) enable improved hydrogen fuel cell performance by harnessing material properties at “intermediate temperatures” – operating temperatures above polymer electrolyte fuel cells (PEMFCs) and below solid oxide fuel cells (SOFCs). − These intermediate temperatures, commonly defined as the range 100–350 °C, allow for improved fuel cell operation while avoiding the need for expensive high-temperature refractory materials, such as those used in SOFCs. − At intermediate temperatures, polymer electrolytes that require liquid water as the proton conductor, e.g., in PEM fuel cells, become unusable, while SOFC ceramics exhibit oxide mobility too low to be practical. − Achieving favorable and improved operational metrics by utilizing intermediate temperatures therefore necessitates the utilization of proton-conducting solid materials with sufficient thermal stability.
Solid acids are protic materials that are solid at room temperature and have been investigated as electrolyte membranes in SAFCs since the mid-1990s. − Many solid acid electrolyte materials contain protic alkali polyanions (e.g., CsHSO4 and CsH2PO4) exhibiting a ‘superprotonic transition’ manifesting as a temperature threshold above which a dramatic improvement in ionic conductivity is observed. Cesium dihydrogen phosphate (CsH2PO4, “CDP”) in particular has emerged ,− as a leading membrane material for SAFC applications due to significant proton conduction above its ∼225 °C superprotonic transition temperature, combined with good stability in a hydrogen fuel cell environment (i.e., reducing/H2 atmosphere at temperatures approaching and exceeding 250 °C). Above the superprotonic transition temperature, rotational disorder of the intrinsic protic species (H2PO4 –) leads to a phase change in the crystal structure and facilitates improved proton exchange between neighboring phosphate anions, which increases conduction by approximately 3 orders of magnitude. ,− However, CDP is thermodynamically unstable toward dehydration above 200 °C, requiring active hydration with a constant flow of highly humidified (p H2O ∼ 0.3 atm) gas to force its chemical equilibrium toward monomeric H2PO4 –. ,, Motivated to circumvent these material shortfalls and push the upper temperature boundary of these solid acid membrane materials, we investigated a class of compounds characterized by one-dimensional boron-containing polyanion chains. Recently, we discovered high proton conductivity in several borosulfate materials, with the chemical formula X[B(SO4)2], which have one-dimensional (1D) polyanionic chains alternating between a pair of SO4 2– anions and a boron decorated by cations in the lattice (X = NH4, K, etc.). , In general, these materials are thermally stable under air up to 250 °C and require no active humidification to prevent thermal decomposition.
Herein, we continue our discussion of another promising group of compounds that substitute sulfates with the more chemically and thermally robust phosphate anion: the borophosphates. These crystalline solid acid polyelectrolytes are shown here to be highly thermally stable within the range of intermediate temperature SAFC operation while exhibiting promising ionic conductivity at elevated temperatures. The syntheses comprise easily scalable, low-temperature (<200 °C) flux reactions using ionic liquid solvent, yielding 10s of grams of material. This represents a notable simplification over previously reported borophosphate synthesis reactions that are typically conducted at elevated temperature in molten salt fluxes , as well as our own previous efforts. Decreased temperatures and consistent methodology across the syntheses of all four borophosphates examined herein allow trivial interchange, and intermixing, of cations in the resulting products for future studies.
The anionic chain structure of each of the investigated borophosphate compounds, [BOB(PO4)3] n 5n–, is charge-balanced either with five (5) smaller metal cations per repeat unit, such as in Na5[BOB(PO4)3], or three (3) cations and two protons occupying crystallographically distinct positions on phosphate (P–O) oxygens, which influence the material properties as discussed further below. The cesium borophosphate variant (CsBOB) in particular is notable for its potential use as a solid polyelectrolyte membrane material due to its relatively high ionic conductivity and suitably high thermal stability. Ab initio molecular dynamics (AIMD) computational simulations demonstrate similarities to the borosulfate class of materials, , in that gyrational mobility of the 1D chains observed at elevated temperatures facilitates proton hopping along and between chains.
Experimental Methods
Reagents were purchased from commercial vendors in ≥98% purity and used as received, except where otherwise noted. Rubidium and cesium dihydrogen phosphates (RbH2PO4 and CsH2PO4, respectively) were synthesized from the respective carbonates as described below. Exposure of 1-butyl-3-methylimidazolium bromide (BMIM-Br) to air was minimized to prevent deliquescence in the presence of atmospheric moisture.
Synthesis of Rubidium and Cesium Dihydrogen Phosphate (RbH2PO4 and CsH2PO4)
The rubidium and cesium dihydrogen phosphate starting materials were synthesized by reacting the carbonate salt of the alkali metal desired (M2CO3, where M = Rb+ or Cs+), dissolved in water, with an equimolar amount of phosphoric acid (85 wt % H3PO4 in H2O) added slowly and dropwise to prevent excess generation of heat and bubbling from CO2 production. Once the addition of phosphoric acid was complete and no further CO2 generation was observed, an excess of methanol was added to precipitate white dihydrogen phosphate salt from the colorless solution. The solid products were then filtered and washed with additional methanol. The purity of these salts was confirmed by powder X-ray diffraction.
General Synthetic Protocol for Loop-Branched Borophosphates
Ammonium-, sodium-, rubidium-, and cesium-containing borophosphates were synthesized in a low-temperature flux reaction using ionic liquids (e.g., 1-butyl-3-methylimidazolium bromide) in a Teflon-lined stainless-steel autoclave by heating the reactants statically between 100 and 250 °C for between 24 h and 1 week. The solid white products were then washed sequentially with glacial acetic acid, isopropanol, and diethyl ether to remove residual ionic liquid and unreacted phosphate salts. Example reactions are presented below.
Ammonium Borophosphate – (NH4)3H2[BOB(PO4)3] a.k.a. “NH4BOB”
5.360 g (40.59 mmol) of diammonium hydrogen phosphate ((NH4)2HPO4) was ground with 2.395 g (38.74 mmol) of boric acid (H3BO3) in a mortar and pestle and added to a 200 mL Teflon-lined steel autoclave. Approximately 20 g of solid 1-butyl-3-methylimidazolium bromide (BMIM-Br) was added on top of the ground reactants. The solids in the reaction vessel were gently mixed before being sealed and heated without stirring in a convection oven for 2 hours at 200 °C. After removal from the oven, the liquid BMIM-Br supernatant was decanted from the solid product and the remaining solid was washed with isopropanol in a fritted funnel. The solid white product was then ground with a small amount of glacial acetic acid to break up large chunks and to dissolve unreacted phosphate salts. The solid was then placed back into a fritted funnel and washed with more glacial acetic acid, followed by isopropanol, and finally with diethyl ether. The product was dried in an oven at 50 °C overnight, yielding 4.565 g (89% isolated yield) of white powder.
Sodium Borophosphate – Na5[BOB(PO4)3] a.k.a. “NaBOB”
19.386 g (161.58 mmol) of sodium dihydrogen phosphate (NaH2PO4) and 22.975 g (161.84 mmol) of disodium hydrogen phosphate (Na2HPO4) were ground with 9.964 g (161.2 mmol) of boric acid (H3BO3) and added to a 200 mL Teflon-lined steel autoclave. Approximately 70 g of BMIM-Br was added on top of the ground reactants. The solids in the reaction vessel were stirred slightly before being sealed and heated without stirring in a convection oven for 3 days at 180 °C. The postsynthesis processing of NaBOB is the same as NH4BOB, described above, and isolated 30.786 g (35.25 g theoretical = 87.3% yield) of white powder.
Rubidium Borophosphate – Rb3H2[BOB(PO4)3] a.k.a. “RbBOB”
15.177 g (83.18 mmol) of rubidium dihydrogen phosphate (RbH2PO4) was ground with 3.377 g (54.62 mmol) of boric acid (H3BO3) and added to a 200 mL Teflon-lined steel autoclave. Approximately 80 g of BMIM-Br was added on top of the ground reactants. The solids in the reaction vessel were stirred slightly before being sealed and heated without stirring in a convection oven for 4 days at 150 °C. The postsynthesis processing of RbBOB is the same as NH4BOB, described above, and isolated 14.072 g (89% yield) of white powder.
Cesium Borophosphate – Cs3H2[BOB(PO4)3] a.k.a. “CsBOB”
19.112 g (83.14 mmol) of cesium dihydrogen phosphate (CsH2PO4) was ground with 3.374 g (54.57 mmol) of boric acid (H3BO3) and added to a 200 mL Teflon-lined steel autoclave. Approximately 80 g of BMIM-Br was added on top of the ground reactants. The solids in the reaction vessel were stirred slightly before being sealed and heated without stirring in a convection oven for 4 days at 150 °C. The postsynthesis processing of CsBOB is the same as NH4BOB, described above. Isolated 18.276 g (93% yield) of white powder.
Formation of Consolidated Disc-Shaped Pellets for Electrochemical Impedance Spectroscopy
Disc-shaped pellets (400–900 μm thick) of each sample were prepared by pressing 400–900 mg of each material in a 19.05 mm (0.75 in.) diameter break-away tungsten-carbide die press to ≈240 MPa in a uniaxial hydraulic press. Maximum pressure was applied at room temperature, and then the samples were heated to 200 °C overnight (or 150 °C overnight for NH4BOB). This procedure was optimized to produce sintered discs with the best final densities while constrained by the relatively low decomposition temperature of ∼275 °C for the material. The bulk density of these pellets (2.85 cm2 area) was determined using a digital micrometer for the thickness and an analytical balance for mass. Bulk densities were compared to single-crystal densities established by crystal structure data to determine the fraction of the theoretical density and a qualitative extent of consolidation.
Physical and Structural Characterization
Powder X-ray diffraction (PXRD) was used to ensure the crystallinity and purity of bulk products. Powder diffraction patterns were collected at room temperature using Cu Kα (λ = 1.54 Å) radiation with a Rigaku SmartLab diffractometer and are available in the Supporting Information Section (Figures S1–S4). Single-crystal X-ray diffraction was used to determine the crystal structure of the two novel borophosphate materials: NH4BOB ((NH4)3H2[BOB(PO4)3]) and CsBOB (Cs3H2[BOB(PO4)3]). Single crystals were isolated from the bulk reaction and mounted on a MiTeGen MicroMount with vacuum grease. Structure determination was done by collecting reflections using 0.5° ω scans on a Bruker D8 Quest diffractometer equipped with a Photon II detector using Mo Kα (λ = 0.71073 Å) radiation at 302(2) K for NH4BOB and 100(2) K for CsBOB. The data were integrated using the SAINT software package within the APEX III software suite, and absorption corrections were applied using SADABS. Both crystal structures were solved via intrinsic phasing using ShelXT and were refined using SHELX2018–1 within the APEX III suite. All non-hydrogen atoms were located via the difference Fourier map and refined anisotropically. In the NH4BOB structure, hydrogen atoms on the phosphate and ammonium moieties were also located in the Fourier map. While the hydrogens on the ammonium cations were located, several DFIX commands were necessary to lightly restrain the N–H bond distances. No hydrogen atoms were found in the equivalent areas for CsBOB, and thus were not modeled. Compounds were visualized with Mercury, and figures were made with CrystalMaker and ORTEP. Table S1 shows the crystallographic data for the compounds, and Tables S2 and S3 detail selected bond and hydrogen bond interaction distances, respectively. ORTEP figures showing thermal ellipsoids at 50% are provided in the Supporting Information section (Figures S5 and S6). Structural data is available at the Cambridge Structural Database (CSD) for the compounds presented, with deposition numbers of 2407840 and 2407841 for NH4BOB and CsBOB.
Thermal stability of the materials under an inert/oxidizing atmosphere was assessed using simultaneous thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC) acquired on a Netzsch Jupiter system. Approximately 25 mg of each material was placed into an alumina crucible and heated to 750 °C under an argon atmosphere at a heating rate of 10 K/min (Ar gas flow rates of 20 mL/min sample and 20 mL/min protective gas flow). Thermograms showing the thermal decomposition of NH4BOB, NaBOB, RbBOB, and CsBOB in an inert environment are provided in Figures S7–S10. Thermal decomposition under an oxidizing atmosphere (40% O2 in Ar balance) was not noticeably different than that under the argon atmosphere and is not shown herein. The thermal decomposition under a reducing (H2) atmosphere at elevated temperature was assessed in a high-pressure thermogravimetric analysis (HP-TGA) instrument: a custom-assembled TA Instruments TGA-HP 150S equipped with a Rubotherm magnetic suspension balance enclosed in a custom-made chamber purged with dinitrogen gas. Approximately 50 mg of material was placed in an alumina crucible and kept under static hydrogen (1 atm, maintained by the automated system venting/repressurizing as necessary) while heating to elevated temperatures in a stepwise fashion.
Infrared (IR) spectroscopy using a Thermo Scientific iS50 ATR instrument was employed to elucidate the presence and habit of hydrogen in each material and to confirm the absence of organic contaminants. IR spectra of each material are provided in the SI (Figure S11). While the fingerprint regions (400–1300 cm–1) of all spectra are very similar, the region from 1300–3500 cm–1 contains broad peaks with shifts indicative of the acidity of phosphate hydrogen.
Ionic conductivities of all four borophosphates (NH4BOB, NaBOB, RbBOB, and CsBOB) were determined from electrochemical impedance spectra (EIS) acquired on a Gamry Reference 3000 potentiostat. To collect EIS, monolithic disc-shaped pellets of all three materials were pressed, overnight (approximately 18 h), in a 19.05 mm (0.75 in.) break-away tungsten-carbide die at 18,000 lbs (equating to 280 MPa pressure) and at various temperatures: 150 °C for NH4BOB; 200 °C for RbBOB and CsBOB; and 250 °C for NaBOB. The elevated temperature used for NaBOB was necessary to achieve good consolidation, while the depressed temperature used for NH4BOB was maintained well below its decomposition temperature. The pellets were then placed between two 0.75-in. diameter stainless-steel mesh discs as electrical contacts, and the three-part membrane-electrode assembly (MEA) was wrapped with Teflon tape around the edges to hold the components together without impeding perpendicular gas flow. The assembly of sample and porous contacts was mounted in a stainless-steel test fixture (Figure S12, Supporting Information), through which humidified nitrogen was passed over both sides of the sample during heating and cooling cycles. The incoming gas was passed through a heated stainless-steel bubbler system set to 60 °C to target 0.2 atm of H2O in the flowing nitrogen gas stream, except for NH4BOB, which was conducted under dry (unhumidified) nitrogen due to its elevated hygroscopicity. The temperature of the steel test cell was controlled by four direct current (DC)-powered internal resistive cartridge heaters with feedback from an internal thermocouple, allowing precise temperature control while minimizing alternating current (AC) electrical interference during electrochemical impedance spectroscopy (EIS). Impedance spectra were collected over time upon cooling at a rate of 0.5 °C min–1 from 250 (200 °C for NH4BOB) to 150 °C. A combined plot of conductivity (σ) vs inverse temperature (1000/T) (Figure ) was prepared by extracting resistance (R) from simple circuit model (Figure S13) fits of the raw impedance spectra (Bode plots, Figures S14–S17 in Supporting Information) and converting to conductivity as , where t is the pellet thickness and A is its area (2.85 cm2). Parameters for the Arrhenius fits shown in Figure are given in Table S5.
4.
Ionic conductivity at various temperatures for all borophosphate materials analyzed (NH4BOB, green squares; NaBOB, gray diamonds; RbBOB, red left triangles; and CsBOB, blue right triangles). Humidified nitrogen gas (0.2 atm H2O, closed symbols) was used for all materials except for NH4BOB, where unhumidified nitrogen gas was used (open symbols). Arrhenius (i.e., exponential vs 1/T) fits are shown as solid, colored lines. A table of fitting parameters for the Arrhenius fits is presented in Table S5 in the SI.
Scanning electron microscopy (SEM) was performed using a Thermo Fisher Scientific Quattro environmental SEM at 20 kV to capture images of the loose powder and the consolidated pellets of each material as a qualitative investigation of crystallite size and shape, condensation of the solid, and overall porosity. These images are provided below in the Supporting Information (Figures S18–S21).
Molecular Dynamics Simulations
Ab initio molecular dynamics (AIMD) simulations were run to calculate the proton/hole (i.e., proton vacancy) diffusivity in loop-branched borophosphates. We used an NRL-developed AIMD formulation with input forces and energies imported from the Vienna Ab Initio Simulation Program VASP using the Perdew–Burke–Ernzerhof (PBE) approximation to the exchange correlation functional. All calculations were begun by creating 2 × 1 × 1 supercells of borophosphate comprising 8 formula units with a total of 184 atoms. Initial atomic positions were populated from the experimentally determined crystal structures of the compounds.
Simulations were classified as either: “charge neutral” – e.g., chemically unmodified from the input structure; “proton excess” – containing an extra H+; or “proton deficient” – containing a proton vacancy. For “proton excess” simulations, an extra H atom was added to the simulation supercell in the vicinity of a phosphate (PO4) unit; this H· radical was converted to a proton by subtracting an electron from the overall count. For “proton deficient” simulations, one of the PO4H hydrogens in the supercell was removed and an electron added to the overall count. Overall charge neutrality of the supercell was maintained by adding a uniform (diffuse) negative/positive background charge.
MD simulations with variable cell shape (NPT) were run for up to 40 ps with time steps of 0.5 fs at 900 K to evaluate proton diffusivity by tracking H atomic positions over time. The time step of 0.5 fs was chosen to be sufficiently small that proton trajectories were stable; i.e., protons would not move to unrealistically high-energy positions from one frame to the next. Mean squared displacements (MSDs) were calculated by averaging the squared displacements of each H atom from its starting position at t = 0 over the course of the simulation. Average hydrogen diffusivity is calculated as the slope of a linear fit to the MSD versus time. For systems with a charge defect, the charge carrier (H+ or vacancy) MSD/diffusivity is calculated by multiplying the hydrogen MSD/diffusivity by the number of hydrogens over which this defect is distributed, i.e., the number of hydrogens in the system.
Results and Discussion
Unlike the borosulfates, which are predominantly one-dimensional polyanionic chain compounds, relatively few examples of 1D borophosphates exist in the literature. − ,, This is generally due to a tendency of borophosphates to form two-dimensional (2D) and three-dimensional (3D) crystalline compounds, or amorphous glassy materials, arising from 3-fold coordination of phosphate tetrahedra to multiple other species. In our search for published borophosphates suitable for intermediate temperature proton conduction, we drew from our prior observations with the borosulfates that for high polyanion gyrational mobility, compounds with low dimensionality are necessary. In addition, desirable compounds must contain anionic chain units with intrinsic acidic protons (because they do not require hydrolysis to form protic charge carriers).
The structures of ammonium borophosphate (NH4BOB, Compound 1) and cesium borophosphate (CsBOB, Compound 2) are presented here as newly discovered members of the overarching family of 1D borophosphate compounds herein referred to as “BOB”s for their characteristic boron–oxygen–boron bridges contained within the polyanionic chain. While the structural formula presented – [BOB(PO4)3] – is evocative of this atypical bridge, a structurally more accurate description of the 1D chain repeat unit may be [BO(PO4)2B(PO4)], as the two boron atoms are bridged by both the oxide and two phosphate moieties, these clusters being subsequently bridged by a third, crystallographically distinct phosphate unit. This family of borophosphates also includes the previously discovered isostructural sodium and rubidium compounds: NaBOB and RbBOB. , All consist of the same pentavalent [BOB(PO4)3]5– repeating unit that propagates as a 1D chain exhibiting one of two habits, wherein the nominally pentavalent fragment is charge-balanced by either five monovalent species in the lattice (such as in NaBOB), or three species in the lattice plus two protons on phosphate moieties on the chain (observed in isomorphous NH4BOB, RbBOB, and CsBOB). Examples of each orientation are listed in Figure . The packing of the parallel 1D chains in the isostructural materials CsBOB and NH4BOB is shown in Figure .
1.
Cesium borophosphate (CsBOB, top) and sodium borophosphate (NaBOB, bottom), showing the two types of borophosphate 1D chains; X3H2[BOB(PO4)3] and X5[BOB(PO4)3]. Orange and gray polyhedra are phosphorus and boron atoms, respectively, while oxygen atoms are red. Hydrogen atoms (only observed in CsBOB) are brown, while cesium and sodium atoms are pink and yellow, respectively. The figure of NaBOB is created from the structural data presented in ICSD-401178 (ICSD release 2024.2).
2.
Packing of the borophosphate chains in ammonium borophosphate (NH4BOB, left) and cesium borophosphate (CsBOB, bottom), compounds 1 and 2, respectively, showing the variation in packing courtesy of the size of the cation.
The size of the lattice cation likely dictates the preference for one habit over the other, with smaller cations (e.g., Na+) fitting within the lattice space between chains, while larger cations (e.g., Cs+) must be paired with smaller protons for charge balance. Notably, our attempts at preparing lithium (LiBOB) and potassium (KBOB) variants using equivalent methodologies resulted only in the recovery of starting materials, likely due to these cations’ sizes not being well-matched to either observed crystalline habit, i.e., too small (LiBOB) or not quite large enough (KBOB).
For NH4BOB, all hydrogen positions are well-determined in the single-crystal diffraction pattern; thus, a table of well-defined hydrogen bonds for Compound 1 is provided in the SI (Table S3). Ambiguity in the position of hydrogen atoms in the Fourier map for Compound 2 means that assignment of specific hydrogen bonding interactions is difficult for CsBOB. Infrared spectra collected on all materials (Figure S11) confirm the presence of hydrogen in the isomorphous materials NH4BOB, RbBOB, and CsBOB, being absent only in NaBOB. The IR spectra of CsBOB and RbBOB show a phosphate νO–H stretching mode shifted to much lower wavenumber/energy than in NH4BOB (∼1700 vs ∼2400 cm–1), which is consistent with enhanced acidity of these protons and increased likelihood that they are disordered in the crystal structure. While the NaBOB and RbBOB borophosphate variants have been previously discussed structurally , and as potential electrolyte materials, the properties of RbBOB and CsBOB – namely, their thermal and chemical stability in reducing environments and ionic conductivity at elevated temperature – have not yet been explored in the context of electrolytes for use as membrane materials in hydrogen fuel cells.
The thermal stability of the BOBs under both argon (Figures S7–S10) and hydrogen (Figure ) increase in the order of NH4BOB < CsBOB ≈ RbBOB ≪ NaBOB. The varying stability of these materials appears to be related to decomposition pathways producing gaseous products, such as NH4 + → H+ + NH3(g) and condensation of phosphates (PO4 3–) with loss of water, e.g., 2 HOPO3 → O3P–O–PO3 + H2O(g). RbBOB and CsBOB both contain hydrogen atoms on phosphate units capable of condensing to pyrophosphate. The mass loss observed in thermal gravimetric analysis (TGA) experiments conducted under argon shows losses of 3.8 and 3.1% between 200 and 450 °C for RbBOB and CsBOB, respectively. These losses are consistent with a loss of one water molecule per formula unit. As NH4BOB contains both hydrogen atoms on phosphate units and ammonium cations in the lattice, it loses 30% of its initial mass between 250 and 600 °C, which is slightly more than the expected 25.4% mass loss consistent with the release of 3 NH3 + 2.5 H2O per formula unit. Meanwhile, NaBOB contains no species easily lost by rearrangement into gaseous products and thus exhibits negligible mass loss up to at least 750 °C; the large exotherm that onsets at 700 °C coincides with a transition from crystalline NaBOB to a glass. Similar transitions into glassy products are observed for RbBOB and CsBOB above 500 °C.
3.
Thermal gravimetric analysis of NH4BOB, NaBOB, RbBOB, and CsBOB under approximately 1 atm of hydrogen gas to determine the thermal stability and decomposition temperature of each material under reducing conditions. HP-TGA data for NaBOB has been published elsewhere (Ridenour).
While TGA analyses performed under oxidizing and inert atmospheres are a commonly reported metric for most materials, these metrics do not paint a complete picture of a material’s suitability for operation in a hydrogen fuel cell. Quantifying thermal stability under reducing conditions (e.g., H2 atmosphere) of any potential hydrogen fuel cell electrolyte or electrode material is essential to determining its suitability for use in actual devices. For the borophosphates discussed herein, thermal decomposition trends observed in H2 were found to follow a trend similar to assessments performed under an inert environment. TGA thermograms obtained under 1 atm of H2 are shown in Figure . These measurements were performed in a custom-built high-pressure thermal gravimetric analysis instrument under isothermal conditions increased in a stepwise manner, unlike the inert atmosphere TGA thermograms, which were obtained at a standard temperature ramp rate of 10 K/min. NaBOB is shown to be stable under H2 up to at least 450 °C, the highest temperature achievable by the instrument. The ∼1% apparent decrease in mass over the course of the 24-h-long experiment is likely to be due to balance drift rather than actual thermally induced mass loss. While NH4BOB and RbBOB appear to begin decomposition at a ∼50 °C lower temperature under H2 than under an inert atmosphere (∼200 and ∼350 °C, respectively), these perceived differences can likely be chalked up to the very slow effective ramp rate (≤0.6 K/min) under H2. Comparing the thermograms, we assert that the family of borophosphates, excepting NH4BOB with its loss of 20–30% mass between 200 and 300 C, exhibits negligible reductive instability under conditions necessary for intermediate temperature fuel cell operation.
Having assessed that three out of four borophosphates studied exhibit acceptable thermal stability under reductive and inert conditions, the ionic conductivities of these materials (in pellet form) were subsequently measured using electrochemical impedance spectroscopy (EIS). Disc-shaped pellets were pressed from loose powder at an elevated temperature (∼200 °C) under uniaxial pressure to achieve dense, well-consolidated monoliths. On average, densities of each pellet (determined by dividing mass by volume) were between 80 and 95% of single-crystal density in all cases without the assistance of a sintering aid. A table of example pellet masses, sizes, and densities is provided in the SI (Table S4).
To be an effective electrolyte, a solid material must not only achieve useful proton conductivity but also must be impermeable to the fuel (e.g., H2) and oxidizer (e.g., O2), necessitating good consolidation. Scanning electron microscopy (Quattro S ESEM, Thermo Fisher Scientific) of the faces of specific pellets (Figures S18 and S21) shows further qualitative evidence of appropriate consolidation. Furthermore, to provide some initial indication of material mechanical properties, indentation measurements were made using a Hysitron Ubi-1(Bruker) micro indenter with a high load head. The indentations were performed with 1N maximum load with a Berkovich indenter tip. The Oliver and Pharr method was used to calculate hardness and reduced modulus from load vs displacement curves. The hardness values were approximately 1 GPa for NH4BOB, RbBOB, and CsBOB, and a value around 2.2 GPa for NaBOB, with reduced modulus values between 22 and 37 GPa. The hardness values were significantly higher than reported CDP hardness (0.2 to 0.3 GPa), suggesting that the borophospahtes potentially have attractive mechanical properties for device fabrication. , Graphs of these data are provided in the SI (Figures S22 and S23).
Monolithic pellets were subsequently sandwiched between two porous stainless-steel disc-shaped electrodes, and the three-piece assembly was affixed together and sealed at the edges by wrapping with PTFE tape, leaving the center of the disc assembly accessible to flowing gases. These assemblies were placed inside a temperature-controlled stainless-steel test cell (shown and illustrated in Figure S12) through which dry N2 gas was initially flowed across both sides of the assembly. For NaBOB, RbBOB, and CsBOB, at temperatures above 150 °C, feed gases were humidified by bubbling through a sealed, magnetically stirred, heated stainless-steel bubbler set to 60 °C to target 0.2 atm partial H2O pressure, while for measurements with NH4BOB, only anhydrous feed gas could be used to prevent deliquescence of the electrolyte. Potentiostatic EIS spectra were collected every 20 min on cooling from 250 (or 200 °C in the case of NH4BOB) to 125 °C at a ramp rate of 0.5 °C/min (approximately 10 °C between spectra).
Conductivities of each electrolyte as a function of temperature (Figure ) were calculated by fitting impedance spectra as described in the Experimental Section. Under the conditions explored, CsBOB shows the highest ionic conductivity – above 10–5 S/cm – at elevated temperatures (>200 °C), while NaBOB exhibited, on average, the lowest conductivities at all temperatures (10–7–10–8 S/cm). Although NH4BOB showed the highest ionic conductivity among all materials below 200 °C, its increased sensitivity to moisture compared to the other BOBs, and limited operational temperature window restrict its applicability as an intermediate temperature hydrogen fuel cell electrolyte. All measured conductivities in the range 150–250 °C followed an Arrhenius (i.e., log σ ∼ T –1) relationship, suggesting a hopping conduction mechanism of the mobile species with a well-defined activation energy for motion.
It should be expected that NaBOB would be the least ionically conductive of these four materials as it contains no intrinsic protons in its structure. The conductivity that was measured arises either from small amounts of hydrolytic defects (analogous to K[B(SO4)2]) or from a low degree of innate Na+ diffusivity equivalent to D Na+ ∼ 10–16 m2/s at 250 °C (assuming a mobile Na+ concentration of 1.8 × 1022 cm–3). While NaBOB had the lowest ionic conductivities, it is the most thermally stable (≥450 °C under an H2 environment and up to 750 °C in argon) and may therefore be well-suited to other, nonproton-based high-temperature electrochemical device applications. What is more surprising is that RbBOB exhibited only slightly elevated conductivity compared to NaBOB despite its high intrinsic proton concentration (6.3 × 1021 H+/cm3) and their relatively high acidity. The isomorphous CsBOB, on the other hand, exhibits a >100-fold improvement in conductivity over RbBOB at 250 °C and elevated conductivity vs RbBOB over the entire temperature range studied. We speculate the elevated conductivity of CsBOB correlates with disorder of the protons in its crystal structure. Although not quite reaching the exceptional proton conductivity of CDP (σCDP ≈ 2.2 × 10–2 S/cm at 240 °C in 0.4 atm H2O), the current benchmark for viable solid acids electrolytes, CsBOB (σCsBOB ≈ 10–5 S/cm at 250 °C in 0.2 atm H2O) warrants further investigation and optimization; particularly in light of it being more stable and requiring less humidification for optimum stability and performance.
To determine whether one should expect protons to be sufficiently mobile in these materials to explain the measured conductivities, we performed ab initio molecular dynamics (AIMD) simulations of 2 × 1 × 1 (i.e., 8 formula unit, 184 atom) supercells over trajectories of ≥10 ps (using 0.5 fs time steps) at a simulation temperature of 900 K to quantify proton motion under various conditions. While hydrogen atom trajectories were monitored for stoichiometric, charge-neutral systems of NH4BOB, RbBOB, and CsBOB, long-range atomic diffusion was negligible (<1 Å2 RMS displacement, Figure S24) over the tens of picoseconds duration of the simulations. (And, necessarily, NaBOB has no protons to simulate under these “ideal” conditions.)
This result should not be particularly surprising; conductivity is the product of mobility and carrier density, and it is exceedingly unlikely that all, or even most, of the protons in a material will be mobile “charge carriers” at any particular time. This is true even in highly acidic, aqueous proton exchange membrane materials, where the “effective” proton/calculated charge carrier concentration is substantially less than the number of acidic moieties (e.g., −SO3H) per unit volume. − Although pure compounds such as water, imidazole, acetic acid, and phosphoric acid all exhibit excellent proton mobility as liquids, their high proton conductivities result from small amounts of autoionization to form low concentrations of highly mobile protic defects. − The process of autoionization is statistically unlikely to be observed in a simulation volume of ∼1000 Å3 on a time scale of ≪ 0.1 ns, which is realistic for AIMD simulations run on computational clusters over the span of weeks. This may be thought of in a complementary way: if all phosphate protons in NH4BOB, RbBOB, or CsBOB were considered to be active charge carriers (a carrier density of ∼6 × 1021 H+/cm3), an observed conductivity of 0.1 S/cm would require an average proton diffusivity of 10–9 m2/s (equivalent to the self-diffusivity of water at 4 °C), , which would result in a measured MSD of only 1 Å2 in 10 ps of simulation time! Conductivities on the order of those experimentally observed in CsBOB at 250 °C (10–5 S/cm) could be explained by vanishingly small hydrogen displacements observed on computationally accessible time scales when averaged over all protons in CsBOB.
However, carrier mobility can be probed separately from ionization equilibria by investigating perturbed systems containing extrinsic protic defects in the form of excess protons or proton vacancies (i.e., “holes”). This formalism is also useful for probing proton mobility in systems where the form of the protic defect is structurally uncertain – e.g., an adsorbed water molecule accepting a proton from the bulk or a hydrolytic point defect in a crystallite providing a source of highly acidic protons; in our case, it is also necessary to computationally characterize H+ mobility in NaBOB. Systems (2 × 1 × 1 supercells) were prepared as described in the Experimental Section containing either an excess proton charge-balanced by a uniform negative background charge or a proton vacancy charge-balanced by a uniform positive background charge. Taken together, these complementary cases can be thought of as describing a system where a defect pair arising from autoionization has diffused apart to a sufficient distance that Coulombic interactions are negligible and where recombination cannot occur on the time scale of the simulation. As carrier concentration can typically be changed in a material by tweaking its chemical composition/environment, carrier mobilities are a better comparison of the intrinsic ability of a material to conduct.
The mean squared displacement of a charge (H+ or vacancy) in each material is plotted in Figure . This value is calculated as the average MSD of protons in each system multiplied by the number of protons in that system. We have enforced that there should be a single charge carrier in these systems (the extrinsic H+ or vacancy), but the simulation is tracking atomic positions, not charges; since the effective charge is divided (nonuniformly in time and space) across all protons, multiplying the atomic MSD by the number of protons tracked recovers the MSD of a unit charge.
5.
Effective mean squared displacements of an excess positive (H+, dark line) or negative (vacancy, light line) charge in NH4BOB (green), RbBOB (red), and CsBOB (blue) as well as an excess proton in NaBOB (yellow). Diffusivity values and errors are presented in Table S6 in the SI.
Unlike the relative lack of hydrogen motion observed in the charge-neutral systems (Figure S24), extrinsic charge carriers diffuse quite readily in all of the BOBs simulated herein. The a and b crystallographic axes of these BOBs are 6.5 and 8 Å in length, meaning that the charge carrier in each of these simulations diffuses far enough over the course of the simulation that its motion is unlikely to be constrained to a local energetic minimum. Qualitatively, both excess H+ and vacancies exhibit similar mobilities, which is desirable to maximize conductivity. Although the data shown in Figure over ≤60 ps display significant noise, linear regressions over the time frame fit modestly well and give defect diffusivities in the range of 1–4 × 10–8 m2/s. Viewed from the angle of defect mobility specifically, this should make the borophosphates excellent candidates for intermediate temperature proton conductors. Given how high both H+ and vacancy mobilities are at 900 K in AIMD simulations, it is very likely that low conductivities observed experimentally at 250 °C (523 K) are the result of either grain boundary transport problems or, more likely, low charge carrier concentrations. Indeed, it is also quite likely that water adsorbed at grain boundaries positively impacts both of these limitations.
Conclusions
In summary, we have identified and demonstrated that a group of 1D borophosphates exhibits the requisite characteristics to be considered as potential electrolytes for proton-conducting hydrogen fuel cells. These materials are thermally and chemically stable to environmental conditions (elevated temperatures and a reducing hydrogen atmosphere) encountered in intermediate temperature solid acid fuel cells (SAFC). Specifically, the CsBOB variant represents a promising new compound with significant ionic conductivity and thermal stability, even under highly reducing conditions, and we submit that it is well-suited for use as the membrane material for hydrogen fuel cells. The borophosphates, at elevated temperatures, appear to behave similarly to the borosulfate series of materials, wherein proton mobility was driven by the gyrational motion of the 1D chains, lowering the energy barrier for proton hopping along and between chains. Computational molecular dynamics calculations determined that proton diffusivities for this compound are on the order of 1–4 × 10–8 m2/s and that the modest ionic conductivities observed experimentally are likely the result of extremely low carrier densities, stemming from a low concentration of defects. Efforts are currently underway to investigate the use of these 1D borophosphates in hydrogen fuel cell systems as well as to modify the formulation of the electrolyte to further improve ionic conductivity.
Supplementary Material
Acknowledgments
This work is funded by the NRL Base Program.
The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.5c04320.
PXRD patterns, tables of crystallographic information, and bond distances; ORTEP images, TGA/DSC data; FTIR, test cell images and diagrams; electrochemical circuit models, bode plots, pellet consolidation statistics; hardness and reduced modulus statistics; Arrhenius fitting and proton diffusivity parameters; and SEM images are all provided in the Supporting Information (SI) Section provided free of charge (PDF)
Borophosphate (CIF)
There is a patent application currently submitted and pending acceptance, entitled Ammonium Borophosphate as a Proton Conducting Solid Electrolyte for Solid Acid Fuel Cells (US2023042717A1).
The authors declare no competing financial interest.
References
- Uda T.. Thermodynamic, thermomechanical, and electrochemical evaluation of CsHSO4. Solid State Ionics. 2005;176(1–2):127–133. doi: 10.1016/j.ssi.2004.04.017. [DOI] [Google Scholar]
- Sasaki K. A., Hao Y., Haile S. M.. Geometrically asymmetric electrodes for probing electrochemical reaction kinetics: a case study of hydrogen at the Pt–CsH2PO4 interface. Phys. Chem. Chem. Phys. 2009;11(37):8349–8357. doi: 10.1039/b909498a. [DOI] [PubMed] [Google Scholar]
- Lorenz O., Kühne A., Rudolph M., Diyatmika W., Prager A., Gerlach J. W., Griebel J., Winkler S., Lotnyk A., Anders A., Abel B.. Role of Reaction Intermediate Diffusion on the Performance of Platinum Electrodes in Solid Acid Fuel Cells. Catalysts. 2021;11(9):1065. doi: 10.3390/catal11091065. [DOI] [Google Scholar]
- Tada S., Tajima S., Fujiwara N., Kikuchi R.. High-performance anode for solid acid fuel cells prepared by mixing carbon substances with anode catalysts. Int. J. Hydrogen Energy. 2019;44(48):26545–26553. doi: 10.1016/j.ijhydene.2019.08.100. [DOI] [Google Scholar]
- Orozco D. C., Dyck O., Papandrew A. B., Zawodzinski T. A.. A parametric study of the solid acid fuel cell cathode. J. Power Sources. 2018;408:7–16. doi: 10.1016/j.jpowsour.2018.03.030. [DOI] [Google Scholar]
- Lim D.-K., Liu J., Pandey S. A., Paik H., Chisholm C. R. I., Hupp J. T., Haile S. H.. Atomic layer deposition of Pt@CsH2PO4 fot the cathodes of solid acid fuel cells. Electrochim. Acta. 2018;288(20):12–19. doi: 10.1016/j.electacta.2018.07.076. [DOI] [Google Scholar]
- Chou Y.-S., Stevenson J. W., Singh P.. Novel Refractory Alkaline Earth Silicate Sealing Glasses for Planar Solid Oxide Fuel Cells. J. Electrochem. Soc. 2007;154:B644. doi: 10.1149/1.2733868. [DOI] [Google Scholar]
- Ormerod R. M.. Solid oxide fuel cells. Chem. Soc. Rev. 2003;32:17–28. doi: 10.1039/b105764m. [DOI] [PubMed] [Google Scholar]
- Chou Y.-S., Stevenson J. W., Meinhardt K. D.. Electrical Stability of a Novel Refractory Sealing Glass in a Dual Environment for Solid Oxide Fuel Cell Applications. J. Am. Ceram. Soc. 2010;93(3):618–623. doi: 10.1111/j.1551-2916.2009.03466.x. [DOI] [Google Scholar]
- Figueiredo F. M. L., Marques F. M. B.. Electrolytes for solid oxide fuel cells. WIREs Energy Environ. 2013;2(1):52–72. doi: 10.1002/wene.23. [DOI] [Google Scholar]
- Hu X., Yang B., Ke S., Liu Y., Fang M., Huang Z., Min X.. Review and Perspectives of Carbon-Supported Platinum-Based Catalysts for Proton Exchange Membrance Fuel Cells. Energy Fuels. 2023;37(16):11532–11566. doi: 10.1021/acs.energyfuels.3c01265. [DOI] [Google Scholar]
- Parekh A.. Recent developements of proton exchange membrances for PEMFC: A review. Front. Energy Res. 2022;10:956132. doi: 10.3389/fenrg.2022.956132. [DOI] [Google Scholar]
- Dane A. B., Haile S. M., Liu H., Secco R. A.. High-Temperature Behavior of CsH2PO4 under Both Ambient and High Pressure Conditions. Chem. Mater. 2003;15(3):727–736. doi: 10.1021/cm020138b. [DOI] [Google Scholar]
- Haile S.. Superprotonic conductivity in Cs3(HSO4)2(H2PO4) Solid State Ionics. 1995;77:128–134. doi: 10.1016/0167-2738(94)00291-Y. [DOI] [Google Scholar]
- Ikeda A., Kitchaev D. A., Haile S. M.. Phase behavior and superprotonic conductivity in the Cs1–xRbxH2PO4and Cs1–xKxH2PO4systems. J. Mater. Chem. A. 2014;2(1):204–214. doi: 10.1039/C3TA13889E. [DOI] [Google Scholar]
- Kim G., Griffin J. M., Blanc F., Halat D. M., Haile S. M., Grey C. P.. Revealing Local Dynamics of the Protonic Conductor CsH(PO3H) by Solid-State NMR Spectroscopy and First-Principles Calculations. J. Phys. Chem. C. 2017;121(50):27830–27838. doi: 10.1021/acs.jpcc.7b09063. [DOI] [Google Scholar]
- Taninouchi Y.-k., Uda T., Awakura Y., Ikeda A., Haile S. M.. Dehydration behavior of the superprotonic conductor CsH2PO4 at moderate temperatures: 230 to 260 °C. J. Mater. Chem. 2007;17(30):3182–3189. doi: 10.1039/b704558c. [DOI] [Google Scholar]
- Chisholm C.. Superprotonic behavior of Cs2(HSO4)(H2PO4) – a new solid acid in the CsHSO4–CsH2PO4 system. Solid State Ionics. 2000;136–137(1–2):229–241. doi: 10.1016/S0167-2738(00)00315-5. [DOI] [Google Scholar]
- Chisholm C. R. I., Merle R. B., Boysen D. A., Haile S. M.. Superprotonic Phase Transition in CsH(PO3H) Chem. Mater. 2002;14(9):3889–3893. doi: 10.1021/cm020297v. [DOI] [Google Scholar]
- Haile S. M., Boysen D. A., Chisholm C. R. I.. et al. Solid acids as fuel cell electrolytes. Nature. 2001;410:910–913. doi: 10.1038/35073536. [DOI] [PubMed] [Google Scholar]
- Haile S. M.. Materials for Fuel Cells. Mater. Today. 2003;6(3):24–29. doi: 10.1016/S1369-7021(03)00331-6. [DOI] [Google Scholar]
- Boysen D. A., Uda T., Chisholm C. R. I., Haile S. M.. High-performance solid acid fuel cells through humidity stabilization. Science. 2004;303:68–70. doi: 10.1126/science.1090920. [DOI] [PubMed] [Google Scholar]
- Otomo J., Tamaki T., Nishida S., Wang S., Ogura M., Kobayashi T., Wen C.-j., Nagamoto H., Takahashi H.. Effect of water vapor on proton conduction of cesium dihydrogen phosphateand application to intermediate temperature fuel cells. J. Appl. Electrochem. 2005;35(9):865–870. doi: 10.1007/s10800-005-4727-4. [DOI] [Google Scholar]
- Chisholm C. R. I., Haile S. M.. Entropy Evaluation of the Superprotonic Phase of CsHSO4: Pauling’s Ice Rules Adjusted for Systems Containing Disordered Hydrogen-Bonded Tetrahedra. Chem. Mater. 2007;19:270–279. doi: 10.1021/cm062070w. [DOI] [Google Scholar]
- Ward M. D., Chaloux B. L., Johannes M. D., Epshteyn A.. Facile Proton Transport in Ammonium Borosulfate - An Unhumidifid Solid Acid Polyelectrolyte for Intermediate Temperatures. Adv. Mater. 2020;32(42):2003667. doi: 10.1002/adma.202003667. [DOI] [PubMed] [Google Scholar]
- Chaloux B. L., Ridenour J. A., Johannes M. D., Epshteyn A.. Comparing Proton Conduction in Potassium and Ammonium BorosulfateIsostructural Inorganic Polyelectrolytes Exhibiting High Proton Mobility. Adv. Energy Sustainability Res. 2022;3(8):2200029. doi: 10.1002/aesr.202270017. [DOI] [Google Scholar]
- Ridenour J. A., Chaloux B. L., Johannes M. D., Finn M. T., Ryou H., Epshteyn A.. High thermal stability 1D borophosphate proton conducting polyelectrolytes. MRS Adv. 2023;8:811–815. doi: 10.1557/s43580-023-00663-6. [DOI] [Google Scholar]
- Ewald B., Prots Y., Menezes P., Natarajan S., Zhang H., Kniep R.. Chain structures in alkali metal borophosphates: synthesis and characterization of K3[BP3O9(OH)3] and Rb3[B2P3O11(OH)2] Inorg. Chem. 2005;44(18):6431–6438. doi: 10.1021/ic050441p. [DOI] [PubMed] [Google Scholar]
- Xiong D.-B., Chen H.-H., Yang X.-X., Z J.-T.. Low-temperature flux synthesis and characterizations of two 1-D anhydrous borophosphates: Na3B6PO13 and Na3BP2O8 . J. Solid State Chem. 2007;180(1):233–239. doi: 10.1016/j.jssc.2006.09.034. [DOI] [Google Scholar]
- Bruker; SAINT, Bruker AXS Inc.: Madison, Wisconsin, USA, 2013. [Google Scholar]
- Bruker; APEX III, Bruker AXS Inc.: Madison, Wisconsin, USA, 2013. [Google Scholar]
- Krause L., Herbst-Irmer R., Sheldrick G. M., Stalke D.. SADABS. J. Appl. Crystallogr. 2015;48:3–10. doi: 10.1107/S1600576714022985. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Sheldrick G. M.. ShelXT. Acta Crystallogr., Sect. A: Found. Crystallogr. 2008;64:112–122. doi: 10.1107/S0108767307043930. [DOI] [PubMed] [Google Scholar]
- Sheldrick G. M.. SHELX2018-1. Acta Crystallogr., Sect. C: Struct. Chem. 2015;71:3–8. doi: 10.1107/S2053229614024218. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Macrae C. F., Sovago I., Cottrell S. J., Galek P. T. A., McCabe P., Pidcock E., Platings M., Shields G. P., Stevens J. S., Towler M., Wood P. A.. Mercury 4.0: from visualization to analysis, design and prediction. J. Appl. Crystallogr. 2020;53:226–235. doi: 10.1107/S1600576719014092. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Palmer, D. C. CrystalMaker. CrystalMaker Software Ltd.: Begbroke, Oxfordshire, England, 2014. [Google Scholar]
- Farrugia L. J.. WinGX and ORTEP for Windows: An Update. J. Appl. Crystallogr. 2012;45:849–854. doi: 10.1107/S0021889812029111. [DOI] [Google Scholar]
- Groom C. R., Allen F. H.. The Cambridge Structural Database in Retrospect and Prospect. Angew. Chem. Int. Ed. 2014;53:662–671. doi: 10.1002/anie.201306438. [DOI] [PubMed] [Google Scholar]
- Groom C. R., Bruno I. J., Lightfoot M. P., Ward S. C.. The Cambridge Structural Database. Acta Crystallogr., Sect. B:Struct. Sci., Cryst. Eng. Mater. 2016;72:171–179. doi: 10.1107/S2052520616003954. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Bernstein N., Johannes M. D., Hoang K.. Origin of the Structural Phase Transition inLi7La3Zr2O12. Phys. Rev. Lett. 2012;109(20):205702. doi: 10.1103/PhysRevLett.109.205702. [DOI] [PubMed] [Google Scholar]
- Kresse G., Hafner J.. Ab initiomolecular dynamics for liquid metals. Phys. Rev. B. 1993;47(1):558. doi: 10.1103/PhysRevB.47.558. [DOI] [PubMed] [Google Scholar]
- Perdew J. P., Burke K., Ernzerhof M.. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996;77(18):3865. doi: 10.1103/PhysRevLett.77.3865. [DOI] [PubMed] [Google Scholar]
- Hauf C., Friedrich T., Kniep R.. Crystal Structure of pentasodium catena-(diborato-triphosphate), Na5[B2P3O13] Z. Kristallogr. - Cryst. Mater. 1995;210:446. doi: 10.1524/zkri.1995.210.6.446. [DOI] [Google Scholar]
- Bruns J., Höppe H. A., Daub M., Hillebrecht H., Huppertz H.. Borosulfates-Synthesis and Structural Chemistry of Silicate Analogue Compounds. Chemistry. Chemistry. 2020;26(36):7966–7980. doi: 10.1002/chem.201905449. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Zagorac D., Müller H., Ruehl S., Zagorac J., Rehme S.. Recent developments in the Inorganic Crystal Structure Database: theoretical crystal structure data and related features. J. Appl. Crystallogr. 2019;52:918–925. doi: 10.1107/S160057671900997X. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Oliver W. C., Pharr G. M.. An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J. Mater. Res. 1992;7(6):1564–1583. doi: 10.1557/JMR.1992.1564. [DOI] [Google Scholar]
- Bagryantseva I. N., Ponomareva V. G., Khusnutdinov V. R.. Intermediate temperature proton electrolytes based on cesium dihydrogen phosphate and poly (vinylidene fluoride-co-hexafluoropropylene) J. Mater. Sci. 2021;56(25):14196–14206. doi: 10.1007/s10853-021-06137-0. [DOI] [Google Scholar]
- Ponomareva V., Bagryantseva I., Shutova E.. Novel nanocomposite systems based on cesium dihydrogen phosphate: Electrotransport structural, morphological and mechanical characteristics. Inorg. Chem. Commun. 2024;162:112256. doi: 10.1016/j.inoche.2024.112256. [DOI] [Google Scholar]
- Haile S. M., Chisholm C. R., Sasaki K., Boysen D. A., Uda T.. Solid acid proton conductors: from laboratory curiosities to fuel cell electrolytes. Faraday Discuss. 2007;134:17–39. doi: 10.1039/B604311A. [DOI] [PubMed] [Google Scholar]
- Kreuer K. D.. Proton Conductivity: Materials and Applications. Chem. Mater. 1996;8:610–641. doi: 10.1021/cm950192a. [DOI] [Google Scholar]
- Mauritz K. A., Moore R. B.. State of Understanding of Nafion. Chem. Rev. 2004;104:4535–4585. doi: 10.1021/cr0207123. [DOI] [PubMed] [Google Scholar]
- Liu R.-l., Wang D.-Y., Shi J.-R., Li G.. Proton conductive metal sulfonate frameworks. Coord. Chem. Rev. 2021;431:213747. doi: 10.1016/j.ccr.2020.213747. [DOI] [Google Scholar]
- Agmon N.. The Grotthuss mechanism. Chem. Phys. Lett. 1995;244(5–6):456–462. doi: 10.1016/0009-2614(95)00905-J. [DOI] [Google Scholar]
- Marx D., Tuckerman M. E., Hutter J., Parrinello M.. The nature of the hydrate excess proton in water. Nature. 1999;397:601–604. doi: 10.1038/17579. [DOI] [Google Scholar]
- Vilčiauskas L., Tuckerman M. E., Bester G., Paddison S. J., Kreuer K.-D.. The mechanism of proton conduction in phosphoric acid. Nat. Chem. 2012;4:461–466. doi: 10.1038/nchem.1329. [DOI] [PubMed] [Google Scholar]
- Knight C., Voth G. A.. The Curious Case of the Hydrated Proton. Acc. Chem. Res. 2012;45(1):101–109. doi: 10.1021/ar200140h. [DOI] [PubMed] [Google Scholar]
Associated Data
This section collects any data citations, data availability statements, or supplementary materials included in this article.







