Proton Self-diffusion Coefficients Research Articles

In Silico Demonstration of Fast Anhydrous Proton Conduction on Graphanol.

Development of new materials capable of conducting protons in the absence of water is crucial for improving the performance, reducing the cost, and extending the operating conditions for proton exchange membrane fuel cells. We present detailed atomistic simulations showing that graphanol (hydroxylated graphane) will conduct protons anhydrously with very low diffusion barriers. We developed a deep learning potential (DP) for graphanol that has near-density functional theory accuracy but requires a very small fraction of the computational cost. We used our DP to calculate proton self-diffusion coefficients as a function of temperature, to estimate the overall barrier to proton diffusion, and to characterize the impact of thermal fluctuations as a function of system size. We propose and test a detailed mechanism for proton conduction on the surface of graphanol. We show that protons can rapidly hop along Grotthuss chains containing several hydroxyl groups aligned such that hydrogen bonds allow for conduction of protons forward and backward along the chain without hydroxyl group rotation. Long-range proton transport only takes place as new Grotthuss chains are formed by rotation of one or more hydroxyl groups in the chain. Thus, the overall diffusion barrier consists of a convolution of the intrinsic proton hopping barrier and the intrinsic hydroxyl rotation barrier. Our results provide a set of design rules for developing new anhydrous proton conducting membranes with even lower diffusion barriers.

Extremely High Proton Mobility in Nanoscopic Titania Hydrates

Using protons as the ionic charge carriers in energy conversion and storage devices is an attractive prospect, but designing electrode/electrolyte materials with fast proton mobility at room temperature is still a challenge. Here we report on two novel titania hydrates with high proton mobility: one is one-dimensional H2Ti5O11·H2O material with ~2 µm length and ~150 nm width; the other is zero-dimensional TiO2·0.4H2O material with average dimension ~5 nm. To gain a deeper understanding of the correlation between materials local structure and fast proton transport mechanisms, extended X-ray absorption fine structure, high resolution transmission electron microscopy, and nuclear magnetic resonance pulsed field gradient diffusion measurements were conducted. The H-bonded species are identified with nano-confined water located between the TiO6 octahedra layered structures in H2Ti5O11·H2O and on the surface of TiO6 octahedra in TiO2·0.4H2O. The proton self-diffusion coefficients at room temperature are about 4×10−9 m2 s−1 for both H2Ti5O11·H2O and TiO2·0.4H2O, which exceed that in liquid water at ambient temperature by nearly a factor of two. These values decrease to about 1×10−9 m2 s−1 at −25 oC in both materials. These unusually high diffusion coefficients imply a Grotthuss transport mechanism and suggest attractive possible application in proton batteries or resistive switching. Further, this materials protocol can create new opportunities in designing other proton-based electrodes and electrolytes with nano-confined water as the fast proton carrier in solids.

(PEFCE&E 21 Best Student Poster - Third Place) Molecular Dynamics Study of Proton Conductivity at an Interface between Nafion and Graphene Sheet

In order to improve the power generation efficiency of polymer electrolyte fuel cells (PEFC), it is necessary to increase the flux of proton transport inside a proton exchange membrane (PEM) under high temperature and low humidity conditions. Nowadays, the Nafion membrane is used as a reference for all proton exchange membranes. This membrane developed by DuPont company demonstrates a high proton conductivity value, chemical stability and prolonged using in fuel cell conditions in comparison with other membranes. However proton transport properties are greatly reduced when the membranes are degraded. Researches have been actively conducted to solve the problem of proton transport reduction in PEM under high temperature and low humidity conditions by two approaches. One of the research focuses is to design alternative materials based on those engineering polymers, for example, polybenzimidazole, poly(ether sulfone), and poly(ether ketone). Another research focus is the introduction of additives. Among the many additives, carbon nanotubes (CNTs) which are next-generation materials with a high aspect ratio and excellent thermal durability and mechanical properties, have been attracting attention. Previous studies have reported that the PEEK (poly ether ether ketone ) / CNT composite membranes show higher durability than Nafion membranes. And the proton transport properties in Nafion / sulfonated CNT composite membranes are improved over the that of Nafion membranes. It is said that the proton transport property is improved by forming a proton path which is made by the influence of the structural characteristics of CNT. However, the proton transport mechanism at the interface between the carbon surface of CNT and the polymer has not been fully understood. The purpose of this study is to clarify the proton transport mechanism in the interface between the carbon surface region and the polymer region and to evaluate the effects of functional groups with carbon surface by using molecular dynamics (MD) simulations. The surface of a CNT was modeled with a graphene sheet (GS). The diameter of the CNTs used in the experiment is about 10-20 nm, which is beyond capability of our MD simulations, and thus the CNT surface was assumed to be a flat surface. The simulation system is shown in Fig. 1. GSs were placed at the top and bottom of the simulation box, and polymer, water molecules, and hydronium ions were placed between them. In order to evaluate the influence of distances between GSs on structural characteristics and transport property, we prepared calculation systems at the wall distances of 4, 6, 8 and 10 nm. We calculated the density distribution in the direction vertical to the GS and the self-diffusion coefficient of the protons at the GS surface region and the center region. Furthermore, a hydrophilic sulfonated GS was prepared by putting sulfo groups to the hydrophobic GS to investigate the effects of the hydrophilic and hydrophobic GS interface on proton transport. The results of the density distribution showed that the surface of pristine GS and sulfonated GS had water clusters, and that proton self-diffusion coefficient of pristine GS and sulfonated GS were larger than that of bulk Nafion. From these facts, it is considered that the diffusion by the grotthuss mechanism increased by improving the connectivity of the proton path on the GS surface and reducing the tortuosity. As a result, the proton transportability is considered to be improved. Figure 1

Molecular Dynamics Study of Proton Conductivity at an Interface between Nafion and Graphene Sheet

In order to clarify the proton transport phenomena in Nafion/carbon nanotubes (CNTs) composite membranes, we focused on the interfacial transport between Nafion and graphene sheets (GSs). We investigated the water content dependence of proton transport and structural properties at the interface between Nafion and GSs using molecular dynamics simulations. The density distribution, water cluster analysis at the interface region, and the self-diffusion coefficient of protons at the interface region were obtained at different water contents. The self-diffusion coefficients of protons at the interface were larger than those of the Nafion bulk for all the water contents because of the formation of water layer near the interface. Our findings provide insight into the relationship between the proton transport and the interfacial structure at molecular level, which suggests a possible improvement on proton transport with addition of CNTs with high specific surface area.

NMR Investigation of Transport in Polybenzimidazole/Polyphosphoric Acid Membranes Prepared Via Novel Synthesis Route

Previous work by the some of us has demonstrated enhanced electrochemical performance of polybenzimidazole (PBI) membranes with high phosphoric acid content prepared by the so-called PPA process.1 Methods of PBI synthesis that involve casting from an organic solvent cannot incorporate the more rigid PBIs characteristic of the PPA process due to their limited solubility. Recently, a carefully controlled drying method has been discovered in which a gel PBI membrane, made in the PPA process, is transformed into a dense PBI film. This method provides a synthetic route to PBI films without the use of any organic solvents. The dense PBI films with repeat unit para-PBI (Fig.1), were originally developed for flow battery applications. However they also can be re-doped in phosphoric acid to be used as a membrane in high-temperature fuel cells.The re-doped PBI films have displayed unprecedented ionic conductivity at elevated temperatures, similar to the starting PBI gel membranes prepared by the PPA process1, while also exhibiting enhanced mechanical properties. Temperature-dependent conductivity data for two of these films are displayed below. Sample A is the dried, densified, and re-acidified version of sample B, with a much lower acid content, ~18 mol PA/PBI repeat unit compared to 30 mol PA/PBI RU, respectively, but exhibits comparable conductivity (Fig. 2). Thus, in high-temperature fuel cell operation the electrochemical performance is similar, but performance degradation due to mechanical creep is reduced, leading to greater durability of the Version A PBI.In attempting to understand the enhanced proton conductivity of the modified PBI membrane despite its lower acid content, we performed both 1H and 31P nuclear magnetic resonance (NMR) measurements. Proton self-diffusion coefficients for four membranes two (A,C) prepared by the modified process and two (B,D) by the original PPA process, were measured by pulsed gradient NMR and plotted in Fig. 3.The results show significantly enhanced proton diffusivity, both in magnitude and in lower activation energy for sample A, which is consistent with its high conductivity despite lower acid content compared to the original PPA-processed membranes (B, D). We have also performed solid state 1D 31P and 2D 31P{1H} HETCOR NMR measurements, which yield additional information on structural differences between the membranes and how these differences may affect transport properties. Multinuclear NMR Study of the Effect of Acid Concentration on Ion Transport in Phosphoric Acid Doped Polybenzimidazole Membranes, N. Suarez, N.K.A.C. Kodiweera, P. Stallworth, S.G. Greenbaun, S. Yu, and B. Benicewicz, Journal of Physical Chemistry B, 116, 12545-51(2012). Figure 1

Molecular Dynamics Study of the Thickness Dependence of Structure and Mass Transport in Ionomer Thin Film

Polymer electrolyte fuel cells (PEFCs) are promising for automobiles and various applications because of their high power density and low operating temperature. The cost must be reduced without sacrificing performance of cells by decreasing Pt loading. However, at lower Pt loading, the efficiency decreases because mass transport losses largely increase at higher current density. Proton transport resistance is one of the causes of the losses. It is considered that proton transport property in ionomer thin films is improved with increasing the thickness of the films, whereas oxygen transport resistance increases with increasing the thickness. Ionomer thin films with high proton conductivity are required even though the thickness is thin. For this reason, we obtained the thickness dependence of proton transport property and structure property in ionomer thin films using a molecular dynamics method. As the ionomer thin film, Nafion was employed. We constructed a system of the ionomer thin film on carbon surface. The contact angle of carbon surface was set at 90 degrees. To analyze the thickness dependence of proton transport property and structure property, the films with the thickness of 4-10 nm were made by changing the number of the Nafion chains. The analyses have carried out by changing water content to 3 and 14. To analyze a correlation between the dynamics and structural properties of Nafion thin films, dynamics properties were evaluated by self-diffusion coefficient obtained from mean square displacement of protons, and structural properties were evaluated by mass density distributions and maximum water cluster length. We found that at high water content, self-diffusion coefficient of protons has hardly changed by the change of ionomer thickness, whereas at low water content, diffusion coefficient has a peak when the ionomer thickness is around seven nm. At this surface wettability, water cluster connectivity was highest when the thickness is around seven nm, and liquid molecule was concentrated at near ionomer/carbon interface and near ionomer/gas interface in the case of low water content. However, in the case of high water content, water cluster connectivity has hardly changed by the change of thickness. We find the thickness dependence of water cluster connectivity. Self-diffusion coefficient increases with increasing maximum cluster length. Acknowledgment This research is supported by New Energy and Industrial Technology Development Organization (NEDO). We use Integrated Supercomputation System at Institute of Fluid Science. I appreciate all the support we received from everyone.

Influence of morphology on physical properties of poly(2,5-benzimidazole) membranes

In this work, the structural properties of pristine and phosphoric acid doped poly(2,5-benzimidazole) membranes have been investigated by small angle neutron- and X-ray scattering, X-ray diffraction, polarized light microscopy and transmission electron microscopy. The results of our investigation demonstrate formation of crystalline regions with a fractal-like distribution upon aging on length scales ranging from sub-nm up to some micrometres. Transport properties of phosphoric acid doped poly(2,5-benzimidazole) membrane measured by pulsed-field-gradient nuclear magnetic resonance spectroscopy reveal proton self-diffusion coefficients of the system.

Hydrated proton self-diffusion study in ion-exchange membranes by MRI and impedance spectroscopy

Average self-diffusion coefficients of hydrated protons in sulfonated poly (ether sulfone) (SPES), Interpolymer and Nafion 117 membranes are measured by impedance spectroscopy and pulsed field gradient nuclear magnetic resonance (PFG NMR). Self-diffusion coefficient measured by impedance spectroscopy shows two patterns, one is at the low hydration states, i.e. λ = 2–4 and another at the high hydration states (starting from λ = 4). At lower hydration states the diffusion values increases slowly while steep increment is found at higher hydration level. PFG NMR shows similar trend throughout the measurements. The diffusion coefficients at higher temperatures are higher than at lower temperatures as a function of λ for SPES membrane. At the same value of λ, hydrated proton self-diffusion coefficient is found to be increased by 18% from 295.5 to 303 K. The thermo-mechanical properties of the membranes characterised by the means of DSC, TGA and DMA analysis show SPES, stable up to 450 °C and can be used for the high-temperature applications.

Molecular Dynamics Study on Proton Transport in Supported Nafion Ionomer Thin Films on Lennard-Jones Walls

The catalyst layer, one of the components of membrane electrode assembly in polymer electrolyte fuel cells, was modeled by molecular dynamics methods, and proton transport in ionomer thin films was simulated to elucidate the effect of surface wetting interaction on the ionomer thin film morphology and proton transport property. Ionomer thin film properties are considered to be affected by the surface property of supported carbon due to their nano-scale thickness (4-10 nm thick). One of the surface properties is surface wetting interaction basically attributed to the physical or chemical property of surfaces.In this study, modeled Nafion thin films with 4 nm and 10 nm thick were generated on the two ideal LJ smooth surfaces which have different strength of interactions to focus on the effect of the surface wetting interaction on the ionomer thin film morphology and proton transport. Protons exist as hydronium ions in ionomer thin films for chemical stability and are transported by the two transport mechanisms which are the vehicle mechanism (just move as hydronium ions) and the Grotthuss mechanism called proton hopping. It is common that proton transport model is restricted to only the vehicle mechanism when using classical molecular dynamics method, however, our proton transport model includes the Grotthuss mechanism by using aTS-EVB method (anharmonic two-state empirical valence bond method) in order to make proton transport model more reproducible.From the analysis in the ionomer thin films with 4 nm thick, surface wetting interaction was found to affect the orientation of sulfonic group near the surface. The orientation is well-ordered on the higher hydrophobic surface, and the sulfonic groups point to the gas phase direction, while it is randomly distributed on the lower hydrophobic surface, which make differences in the water cluster connectivity and size in ionomer thin films between the two surfaces. Proton transport property was evaluated by the self-diffusion coefficient. The proton self-diffusion coefficient in ionomer thin films was indicated to be improved on higher hydrophobic surface probably because higher hydrophobic surface makes ideal water cluster structures for proton transport in ionomer thin films.As compared to the ionomers with the different film thickness, the proton self-diffusion coefficient in ionomer thin films on higher hydrophobic surface was indicated to decrease in the increase of the film thickness, while that on lower hydrophobic surface was indicated to increase slightly. This result is expected to come from the confinement and interface effects which can be remarkable when the thickness decrease. The ionomer morphology on higher hydrophobic surface has advantages for proton transport probably thanks to the effects as observed in the ionomer with 4 nm thick, while that on lower hydrophobic surfaces has disadvantage. Since the effects can be weaker with the increase in the film thickness, the proton self-diffusion coefficient in ionomer thin films on higher hydrophobic surface was found to decrease with the increase in the film thickness, while that on lower hydrophobic surface was found to increase slightly.

Molecular dynamics study of the effect of wettability of the carbon support on proton transport in Nafion ionomer thin films

Molecular dynamics simulations were carried out to elucidate the effect of the wettability of the carbon support used for Nafion ionomer thin films on proton transport in the ionomer, which is related to the power density of polymer electrolyte fuel cells. The Lennard-Jones wall model was used as the support model for the ionomer to generate two different hydrophobic walls: the high hydrophobic wall (H-wall) and the low hydrophobic wall (L-wall). The proton transport model, including the Grotthuss mechanism, was used to express real proton transport phenomena (In early work, we confirmed that it well reproduces the experimentally measured proton self-diffusion coefficient in a Nafion membrane.) The obtained proton self-diffusion coefficient (DH+) indicated that the DH+ for the H-wall case is larger than for the L-wall case. This is related to the morphology of the films. For the H-wall case, the sulfonic groups that form part of the hydrophilic Nafion side chains were confirmed to be oriented in the direction to the wall in the upper side of the film and opposite from the wall in the lower side of the film, which can lead to the alignment of Nafion molecules and also create lamellar water structures in the film. It was also confirmed that such water structures have better cluster connectivity and larger cluster size, meaning that they serve as better proton transport pathways.

Modeling Proton Dissociation and Transfer Using Dissipative Particle Dynamics Simulation.

We suggest a coarse-grained model for dissipative particle dynamics (DPD) simulations of solutions with dissociated protons. The model uses standard short-range soft repulsion and smeared charge electrostatic potentials between the beads, representing solution components. The proton is introduced as a separate charged bead that forms dissociable bonds with proton receptor base beads, such as water or deprotonated acid anions. The proton-base bonds are described by Morse potentials. When the proton establishes the Morse bonds with two bases, they form an intermediate complex, and the proton is able to "hop" between the bases artificially mimicking the Grotthuss diffusion mechanism. By adjusting the Morse potential parameters, one can regulate the potential barrier associated with intermediate complex formation and breakup and control the hopping frequency. This makes the proposed model applicable to simulations of proton mobility and reaction equilibria between protonated and deprotonated acid forms in aqueous solutions. The proposed model provides quantitative agreement with experiments for the proton self-diffusion coefficient and hopping frequency, as well as for the degree of dissociation of benzenesulfonic acid.

(Industrial Electrochemistry & Electrochemical Engineering Division Student Achievement Award) Anhydrous High-Proton Conductor Based on Ionic Nanopeapods

Here we describe, significant improvement in electrochemical performance of proton exchange membrane fuel cells (PEMFCs) via incorporation of superacid-filled single wall carbon nanotubes (CNTs), called ionic nanopeapod. It has been shown that capillary filling of carbon nanotubes is an effective method to alter their physical characteristics. Here and for the first time, we describe that there is a lot of room for development through modification of the interior space of CNT by tuning its ionic nature to boost the proton transport inside the CNT with or without the presence of water molecules. High-resolution transmission electron microscopy (HRTEM) images confirm the successful modification of the interior space of CNTs. The molecular dynamic simulations revealed that anisotropic alignment of ions/water molecules inside the carbon nanotubes makes wire-like proton chains that can facilitate ionic conductivitions with very low humidity dependency. The experimental results confirm these simulation observations by showing a very high-proton conductivity (>0.2 S.cm-1) at low humidifies. The proton conductivity behavior of the membranes based on Nafion and these ionic nanopeapods is investigated in broad ranges of temperature (25-140°C) and humidity (20-100 RH%). Water and proton self-diffusion coefficients are measured using a DOTY Z-gradient probe by the NMR pulse gradient spin–echo technique (NMR-PGSE), using the Hahn spin–echo pulse sequence to confirm the proton dynamic inside the CNTs in the presence of superacids. Arrhenius plot of NMR-based diffusion coefficients, as well as ionic conductivities (based on the electrochemical impedance spectroscopy), are used to evaluate the ease of proton transportat inside the CNTs. The fabricated nanohybrid nanocomposite membranes showed outstanding characteristics including fourfold increase in the maximum power density. These newly designed ionic nanosystems have great potentials to impact high-performance PEMFC applications.

NMR Investigations of the Protonic Transport Mechanism in Composed Materials on the Basis of Cesium Acid Sulfates and Phosphates

The composite materials Cs(HSO4)1−x(H2PO4)x were investigated by X-ray phase analysis, differential scanning calorimetry, nuclear magnetic resonance (NMR) relaxation, pulsed field gradient NMR (PFG-NMR) and impedance spectroscopy. Three composite materials types x = 0.1 ÷ 0.3 mixture CsHSO4, α-Cs3(HSO4)2(H2PO4), β-Cs3(HSO4)2.5(H2PO4)0.5—compositions of area I; x = 0.4 ÷ 0.5 mixture α-Cs3(HSO4)2(H2PO4) and Cs2(HSO4)(H2PO4)—compositions of area II; x = 0.6 ÷ 0.9 mixture Cs2(HSO4)(H2PO4) and CsH2PO4—compositions of area III, were synthesized. The phase transition temperature from the low-to-high conductive phase for obtained composite materials is notably below (about 100 °C) than that for the individual components. The proton self-diffusion coefficients measured by PFG-NMR are lower than the diffusion coefficients calculated from proton conductivities data. The correlation times τd controlling the 31P–1H magnetic dipole–dipole interaction were calculated according to data of the spin–lattice relaxation on 31P nuclei. The self-diffusion coefficients estimated from the Einstein equation are in good agreement with the experimental self-diffusion coefficients measured by PFG-NMR. It confirms the fact that the proton mobility is caused by the rotation of PO4 anion tetrahedra.

Application of MRI for tissue characterisation of ‘Braeburn’ apple

Magnetic resonance imaging (MRI) has become a well-established technique for non-destructive analysis of the internal (micro)structure of food, and the related heat, gas, water and solutes transport, which is of interest for food processing (e.g., drying), physical tissue damage assessment (e.g., bruising) for online sorting purposes or detection of internal defects (e.g., internal browning), amongst others. In contrast to previous MRI studies which predominantly analysed entire fruit, small samples (diameter ∼10−2m) of ‘Braeburn’ apple were investigated in this study with high-field MRI, providing very local, high-resolution information, in order to identify the capability of MRI for detecting differences in fruit tissue types. The focus was on MRI for tissue characterisation with respect to inner and outer cortex tissue, fertilisation treatment, storage time and internal browning (IB). For this purpose, the proton density (PD), T2 value and self-diffusion coefficient (DC) were measured. No clear distinction could be made between samples with different fertilisation treatments. Differences in storage times could be observed from an increased PD for longer storage times. Inner tissue clearly showed an increased PD, T2 value and DC, compared to the outer tissue. IB could be successfully detected, where the PD, T2 value and the DC of the affected tissue were clearly higher than those of the healthy tissue, but a dependency of these parameters on the degree of tissue degradation was identified. Especially, the DC seemed to be an appropriate parameter regarding IB detection.

Estimation of Self‐Diffusion Coefficients of Small Penetrants in Semicrystalline Polymers Using Single‐Sided NMR

A simple and fast way to measure proton self-diffusion coefficients of small penetrant molecules in semicrystalline polymers is introduced. The approach takes advantage of the strong static gradient of a mobile single-sided NMR sensor and it is demonstrated on PE samples with varying degrees of crystallinity fully saturated in either toluene or n-hexane. The self-diffusion coefficients were measured using the gradient stimulated echo sequence appended with a CPMG. It is also shown for the first time, with demonstration on PE plates several millimeter thick with different aging histories, that one-dimensional profiles of self-diffusion coefficients as a function of depth can be easily obtained.

Perfluoroalkyl Phosphonic and Phosphinic Acids as Proton Conductors for Anhydrous Proton‐Exchange Membranes

A study of proton-transport rates and mechanisms under anhydrous conditions using a series of acid model compounds, analogous to comb-branch perfluorinated ionomers functionalized with phosphonic, phosphinic, sulfonic, and carboxylic acid protogenic groups, is reported. Model compounds are characterized with respect to proton conductivity, viscosity, proton, and anion (conjugate base) self-diffusion coefficients, and Hammett acidity. The highest conductivities, and also the highest viscosities, are observed for the phosphonic and phosphinic acid model compounds. Arrhenius analysis of conductivity and viscosity for these two acids reveals much lower activation energies for ion transport than for viscous flow. Additionally, the proton self-diffusion coefficients are much higher than the conjugate-base self-diffusion coefficients for these two acids. Taken together, these data suggest that anhydrous proton transport in the phosphonic and phosphinic acid model compounds occurs primarily by a structure-diffusion, hopping-based mechanism rather than a vehicle mechanism. Further analysis of ionic conductivity and ion self-diffusion rates by using the Nernst-Einstein equation reveals that the phosphonic and phosphinic acid model compounds are relatively highly dissociated even under anhydrous conditions. In contrast, sulfonic and carboxylic acid-based systems exhibit relatively low degrees of dissociation under anhydrous conditions. These findings suggest that fluoroalkyl phosphonic and phosphinic acids are good candidates for further development as anhydrous, high-temperature proton conductors.

Proton diffusion in LaSrScO 3 single crystals studied by in-situ infrared absorption spectroscopy

The diffusivity of protons in Sr 2+-doped LaScO 3 single crystals was determined by in-situ infrared absorption spectroscopy. It was found that the high-temperature absorption spectrum shows a broad peak due to O–H stretching bands, which differs from that observed at room temperature. The diffusion coefficient was evaluated by two different methods: (1) suddenly changing the water vapor partial pressure and (2) exchanging H 2O and D 2O-saturated atmospheres. The diffusion and the activation energy are limited mainly by the diffusivity of oxygen ion vacancies based on the first measurement method at high temperatures. The proton self-diffusion coefficients were obtained by using the second measurement method, and the activation energy is 0.51 eV.

Effect of acceptor dopants on the proton mobility inBaZrO3: A density functional investigation

In this work, the stability and mobility of protonic defects in acceptor doped $\mathrm{Ba}\mathrm{Zr}{\mathrm{O}}_{3}$ are investigated using density functional theory in conjunction with kinetic modeling. The interaction between the mobile protons and Zr-site substituted trivalent dopants---Ga, Sc, In, Y, and Gd---is assessed by extensive mapping of migration pathways. In all cases, the interaction is attractive, which results in a stabilization, and hence a reduction of the mobility, of the proton. However, its strength and range vary substantially and are found to be strongly correlated to the ionic radius of the dopant. Further, it is shown that the observed correlation is related to a variation in strength of hydrogen bonds formed between protons and next nearest lattice oxygen ions in different environments. Finally, migration barriers and attempt frequencies obtained from first principles are used as input to a jump-diffusion model. The proton self-diffusion coefficient is evaluated for the different substituted phases, and the experimental trend in activation energies is reproduced.

The effects of thermal annealing on commercial Nafion ® membranes

The effect of thermal annealing as a pretreatment procedure for Nafion ® membranes was investigated. Commercial membranes with different thicknesses and ages (all melt extruded films) were considered. After a short heat treatment at 165 °C, the proton conductivity, water permeability, equilibrium water sorption, and self-diffusion coefficient of water and protons increased in all films, with the greatest improvements occurring in thin films (<50 μm). Wide-angle X-ray measurements showed that the annealing procedure decreases the crystallinity of thick films and increases the crystallinity of thin films, in general. Small-angle X-ray measurements showed that annealing may alter the distribution of water within the films. Thermal annealing appears to ‘normalize’ the transport properties of different thicknesses and batches of Nafion ®, reducing the differences in values of measured transport properties between thin and thick membranes.

Proton dynamics in lithium-ammonia solutions and expanded metals

Quasielastic neutron scattering has been used to study proton dynamics in the system lithium-ammonia at concentrations of 0, 4, 12, and 20 mole percent metal (MPM) in both the liquid and solid (expanded metal) phases. At 230 K, in the homogenous liquid state, we find that the proton self-diffusion coefficient first increases with metal concentration, from 5.6x10(-5) cm2 s(-1) in pure ammonia to 7.8x10(-5) cm2 s(-1) at 12 MPM. At higher concentrations we note a small decrease to a value of 7.0x10(-5) cm2 s(-1) at 20 MPM (saturation). These results are consistent with NMR data, and can be explained in terms of the competing influences of the electron and ion solvation. At saturation, the solution freezes to form a series of expanded metal compounds of composition Li(NH3)4. Above the melting point, at 100 K, we are able to fit our data to a jump-diffusion model, with a mean jump length (l) of 2.1 A and residence time (tau) of 3.1 ps. This model gives a diffusion coefficient of 2.3x10(-5) cm2 s(-1). In solid phase I (cubic, stable from 88.8 to 82.2 K) we find that the protons are still undergoing this jump diffusion, with l=2.0 A and tau=3.9 ps giving a diffusion coefficient of 1.8x10(-5) cm2 s(-1). Such motion gives way to purely localized rotation in solid phases IIa (from 82.2 to 69 K) and IIb (stable from 69 to 25 K). We find rotational correlation times (tau(rot)) of the order of 2.0 and 7.3 ps in phases IIa and IIb, respectively. These values can be compared with a rotational mode in solid ammonia with tau(rot) approximately 2.4 ps at 150 K.