Arrhenius Prefactor Research Articles

The Arrhenius law prefactor in permalloy mesoscale systems

The Arrhenius equation was used to describe the dynamics of two-state switching in mesoscale, ferromagnetic particles. Using square permalloy dots as an idealized two-state switching system, measurements of the prefactor of the Arrhenius law changed by 26 decades over barrier heights from 30 to 700 meV. Measurements of the prefactor ratios for a two well system revealed significant deviations from the common interpretation of the Arrhenius law. The anomalous Arrhenius prefactors and the prefactor ratios can be fitted to a modified model that includes entropic contributions to two-state transitions. Similar considerations are likely for the application of the Arrhenius law to other mesoscale systems.

Rationalizing the Influence of the Binding Affinity on the Activity of Phosphoserine Phosphatases

AbstractThe Sabatier principle states that catalytic activity can be maximized when the substrate binding affinity is neither too strong nor too weak. Recent studies have shown that the activity of several hydrolases is maximized at intermediate values of the binding affinity (Michaelis–Menten constant: Km). However, it remains unclear whether this concept of artificial catalysis is applicable to enzymes in general, especially for those which have evolved under different reaction environments. Herein, we show that the activity of phosphoserine phosphatase is also enhanced at an intermediate Km value of approximately 0.5 mM. Within our dataset, the variation of Km by three orders of magnitude accounted for a roughly 18‐fold variation in the activity. Owing to the high phylogenetic and physiological diversity of our dataset, our results support the importance of optimizing Km for enzymes in general. On the other hand, a 77‐fold variation in the activity was attributed to other physicochemical parameters, such as the Arrhenius prefactor of kcat, and could not be explained by the Sabatier principle. Therefore, while tuning the binding affinity according to the Sabatier principle is an important consideration, the Km value is only one of many physicochemical parameters which must be optimized to maximize enzymatic activity.

Rationalizing the Influence of the Binding Affinity on the Activity of Phosphoserine Phosphatases.

The Sabatier principle states that catalytic activity can be maximized when the substrate binding affinity is neither too strong nor too weak. Recent studies have shown that the activity of several hydrolases is maximized at intermediate values of the binding affinity (Michaelis-Menten constant: Km ). However, it remains unclear whether this concept of artificial catalysis is applicable to enzymes in general, especially for those which have evolved under different reaction environments. Herein, we show that the activity of phosphoserine phosphatase is also enhanced at an intermediate Km value of approximately 0.5 mM. Within our dataset, the variation of Km by three orders of magnitude accounted for a roughly 18-fold variation in the activity. Owing to the high phylogenetic and physiological diversity of our dataset, our results support the importance of optimizing Km for enzymes in general. On the other hand, a 77-fold variation in the activity was attributed to other physicochemical parameters, such as the Arrhenius prefactor of kcat , and could not be explained by the Sabatier principle. Therefore, while tuning the binding affinity according to the Sabatier principle is an important consideration, the Km value is only one of many physicochemical parameters which must be optimized to maximize enzymatic activity.

Theoretical Prediction of the Sublimation Behavior by Combining Ab Initio Calculations with Statistical Mechanics

We develop a theoretical model to predict the sublimation vapor pressure of pure substances. Moreover, we present a simple monoatomic molecule approximation, which reduces the complexity of the vapor pressure expression for polyatomic gaseous molecules at a convincing level of accuracy, with deviations of the Arrhenius prefactor for NaCl and NaF being 5.02% and 7.08%, respectively. The physical model is based on ab initio calculations, statistical mechanics, and thermodynamics. We illustrate the approach for Ni, Cr, Cu (metallic bond), NaCl, NaF, ZrO2 (ionic bond) and SiO2 (covalent bond). The results are compared against thermodynamic databases, which show high accuracy of our theoretical predictions, and the deviations of the predicted sublimation enthalpy are typically below 10%, for Cu even only 0.1%. Furthermore, the partial pressures caused by gas phase reactions are also explored, showing good agreement with experimental results.

A Molecular Dynamics Approach to the Impacts of Oxidative Aging on the Engineering Characteristics of Asphalt.

Oxidative aging is an inevitable environmental factor that accelerates asphalt pavement deterioration. This study employed a molecular dynamics simulation to investigate the impact of aging on asphalt cement from the perspectives of thermodynamic properties, and diffusion and adhesion characteristics. Results indicate that aging increased bulk density from 1.008 to 1.081 g/cm3 and cohesive energy density by 15.6%, which was attributed to the promoted molecular polarity and intermolecular attractiveness. The enhanced molecular interactions also reduced molecular mobility, which led to an increase in the glass transition temperature by 30 K, suggesting that aging diminished the resistance of asphalt to thermal cracking. Simulations of the diffusion behaviors across different temperatures demonstrated that the Arrhenius relationship described well the temperature dependence of the diffusion coefficient, and that aging considerably slowed down the diffusion process as represented by Arrhenius prefactor D0, which dropped by 38.2%. The asphalt–aggregate adhesion was assessed using layered models with and without a water interlayer of different thicknesses. The adhesion was enhanced upon aging due to the significantly improved electrostatic interactions at the interface. Evaluation of the residual adhesion with the presence of interfacial water suggested that aging would raise the moisture susceptibility of asphalt pavement. The increase in molecular polarity was considered to be highly responsible for these aging consequences, and was thus further investigated via the electrostatic potential surface and dipole moment.

Multi-functional epoxy vitrimers: Controllable dynamic properties, multiple-stimuli response, crack-healing and fracture-welding

Vitrimers, a new generation of polymeric materials, have been widely investigated to resolve the intersection of thermoplastics and thermosets, relying on the exchange reactions in networks. However, it is still a challenge to develop multi-functional vitrimer materials. Herein, multi-functional epoxy vitrimers that exhibited controllable dynamic properties, multiple-stimuli response, crack-healing and fracture-welding were prepared by introducing Fe3O4 nanoparticles into the networks of dual dynamic epoxy vitrimers. It was revealed that the typical dynamic parameters of vitrimer including the characteristic relaxation time (τ), activation energy (Ea), Arrhenius prefactor (τ0) and topology freezing transition temperature (Tv) could be readily adjusted in the multi-functional epoxy vitrimers. Moreover, the multi-functional epoxy vitrimers were simultaneously responsive to temperature, near infrared and magnetic field, while they could be driven by magnets, heated by near infrared and healed or welded by heating. Upon heating or near infrared, the cracks in samples could be successfully healed. Besides, by the cooperation of heating and magnet or near infrared and magnet, the multi-functional epoxy vitrimers were able to achieve non-touch welding of factures. These multi-functional epoxy vitrimers might have potential application in improving the reliability and extending the lifetime of polymeric materials. Meanwhile, the facile way to functionalize the epoxy vitrimers is estimated to be suitable for other vitrimer materials.

Tunneling in the Hydrogen-Transfer Reaction from a Vitamin E Analog to an Inclusion Complex of 2,2-Diphenyl-1-picrylhydrazyl Radical with β-Cyclodextrin in an Aqueous Buffer Solution at Ambient Temperature.

Recently, increasing attention has been paid to quantum mechanical behavior in biology. In this study, we investigated the involvement of quantum mechanical tunneling in the hydrogen-transfer reaction from Trolox, a water-soluble analog of vitamin E (α-tocopherol), to 2,2-diphenyl-1-picrylhydrazyl radical (DPPH•) in a phosphate buffer solution (0.05 M, pH 7.0). DPPH• was used as a reactivity model of reactive oxygen species and solubilized in water using β-cyclodextrin (β-CD). The second-order rate constants, kH and kD, in 0.05 M phosphate buffer solutions prepared with H2O (pH 7.0) and D2O (pD 7.0), respectively, were determined for the reaction between Trolox and DPPH•, using a stopped-flow technique at various temperatures (283–303 K). Large kinetic isotope effects (KIE, kH/kD) were observed for the hydrogen-transfer reaction from Trolox to the β-CD-solubilized DPPH• in the whole temperature range. The isotopic ratio of the Arrhenius prefactor (AH/AD = 0.003), as well as the isotopic difference in the activation energies (19 kJ mol−1), indicated that quantum mechanical tunneling plays a role in the reaction.

Reversible isomerization of metal nanoclusters induced by intermolecular interaction

Reversible isomerization of metal nanoclusters induced by intermolecular interaction

(Invited) Fast Ion Dynamics in Solids As Probed By NMR: Disorder, Dimensionality and Correlation Effects

NMR offers plenty of tools to analyze ionic jump processes in crystalline and amorphous solids at atomic scale. Both high-resolution and time-domain 1H(2H), 6,7Li, 19F, 23Na NMR helps shedding light on the origins of rapid self-diffusion in materials being relevant for energy storage.It is well accepted that in materials with strong site preferences, such as LiAlO2, the Li+ ions are subjected to extremely slow exchange processes. The loss of this site preference, as it is the case in glasses and some nanocrystalline phases, may, however, lead to rapid cation diffusion. Examples that benefit from this effect include cation-mixed, high-entropy fluorides ((Ba,Ca)F2) and LiTi2(PS4)3. In general, in non-equilibrium phases site disorder, polyhedra distortions, strain and the various types of local defects will affect both the migration activation energy and the corresponding Arrhenius pre-factor. Whereas in (Me,Ca)F2 (Me = Ba, Pb) cation mixing influences F anion dynamics, in Li6PS5X (X = Br, Cl, I) the potential landscape can be manipulated by anion site disorder and the introduction of extrinsic defects. In some cases, this leads to rather flat landscapes enabling the ions to have access to concerted displacement processes, as is seen in LLZO-type garnets. On the other hand, in the mixed conductor Li4+x Ti5O12 cation-cation repulsions immediately lead to a boost in Li+ diffusivity at the early stages of chemical lithiation. For Na-bearing closo-borates, the influence of rotational anion dynamics is usually considered to explain long-range cation transport. Recent examples of our group also include Li- and Na-conducting MOFs, for which, as in the case of the closo-borates and the famous Na-β''-alumina, transitions from correlated to uncorrelated motion are observed at sufficiently high temperature.Finally, rapid diffusion is also expected for materials that are able to guide the ions along (macroscopic) pathways with confined dimensions, as we have recently observed for layer-structured fluorides such as RbSn2F5 or MeSnF4 with their buried interfaces.

Entropy-reduced Retention Times in Magnetic Memory Elements: A Case of the Meyer-Neldel Compensation Rule.

We compute mean waiting times between thermally activated magnetization reversals in a nanodisk with parameters similar to a free CoFeB layer used in magnetic random access memories. By combining Langer's theory and forward flux sampling simulations, we show that the Arrhenius prefactor can take values up to 10^{21} Hz, orders of magnitude beyond the value of 10^{9} Hz typically assumed, and varies drastically as a function of material parameters. We show that the prefactor behaves like an exponential of the activation energy, which highlights a case of the Meyer-Neldel compensation rule. This suggests that modeling information retention times with a barrier-independent prefactor in such magnetic storage elements is not justified.

Diffusion Coefficients and Phase Equilibria of the Cu-Zn Binary System Studied Using Diffusion Couples

The diffusion behavior and phase equilibria in the Cu-Zn binary system were investigated using solid–solid and solid–liquid diffusion couples. Heat treatments at temperatures ranging from 100 to 750 °C were performed and the samples were examined using optical microscopy, energy dispersive x-ray spectroscopy, and electron probe microanalysis to identify the phases and to obtain composition profiles. Solubility limits of both solid solution and intermetallic phases were then evaluated, and a forward-simulation analysis (FSA) was applied to extract interdiffusion coefficients. The composition profiles from Hoxha et al. were also re-analyzed using FSA to obtain more reliable diffusion coefficient data without the assumption of constant diffusion coefficients for the intermetallic phases. A comprehensive assessment of the interdiffusion coefficients in three intermetallic phases of the Cu-Zn system was performed based on the results from the current study as well as those in the literature. Activation energies and Arrhenius pre-factors were evaluated for each phase as a function of composition. The fitted equations based on the comprehensive assessment have the capabilities of computing the interdiffusion coefficients of each of the phases at a given composition and temperature. Suggested modifications to the Cu-Zn binary phase diagram were presented based on the new experimental information gathered from the present study. A clear explanation is provided for the puzzling low Zn concentrations often observed in the Cu-rich fcc phase of Cu-Zn diffusion couples in comparison with the expected high solubility values based on the equilibrium Cu-Zn phase diagram.

Anomalies in Bulk Ion Transport in the Solid Solutions of Li7La3M2O12 (M = Hf, Sn) and Li5La3Ta2O12.

Cubic Li7La3Zr2O12(LLZO), stabilized by supervalent cations, is one of the most promising oxide electrolyte to realize inherently safe all-solid-state batteries. It is of great interest to evaluate the strategy of supervalent stabilization in similar compounds and to describe its effect on ionic bulk conductivity σ′bulk. Here, we synthesized solid solutions of Li7–xLa3M2–xTaxO12 with M = Hf, Sn over the full compositional range (x = 0, 0.25...2). It turned out that Ta contents at x of 0.25 (M = Hf, LLHTO) and 0.5 (M = Sn, LLSTO) are necessary to yield phase pure cubic Li7–xLa3M2–xTaxO12. The maximum in total conductivity for LLHTO (2 × 10–4 S cm–1) is achieved for x = 1.0; the associated activation energy is 0.46 eV. At x = 0.5 and x = 1.0, we observe two conductivity anomalies that are qualitatively in agreement with the rule of Meyer and Neldel. For LLSTO, at x = 0.75 the conductivity σ′bulk turned out to be 7.94 × 10–5 S cm–1 (0.46 eV); the almost monotonic decrease of ion bulk conductivity from x = 0.75 to x = 2 in this series is in line with Meyer–Neldel’s compensation behavior showing that a decrease in Ea is accompanied by a decrease of the Arrhenius prefactor. Altogether, the system might serve as an attractive alternative to Al-stabilized (or Ga-stabilized) Li7La3Zr2O12 as LLHTO is also anticipated to be highly stable against Li metal.

Influence of defects on ionic transport in LiTaO3 – A study using EXAFS and positron annihilation lifetime spectroscopy

Defects of various types in crystalline and nanocrystalline materials govern a range of electrical, optical and mechanical properties. In particular, they are at the heart of translational ion dynamics in solid electrolytes. One of the most prominent examples revealing a drastic increase in ionic conductivity σDC by several orders of magnitude when going from an ordered crystalline matrix to a structurally disordered one is lithium tantalate. Here, structurally disordered, nanocrystalline LiTaO3 served as a model substance to shed light on the question to what extent the degree of disorder decreases upon annealing an originally defect-rich oxide. Disorder can be introduced by high-energy ball milling of LiTaO3 crystallites with diameters in the μm range. Broadband conductivity spectroscopy, EXAFS and positron annihilation lifetime spectroscopy were used to correlate ion transport properties with interatomic distances, bond distortions and positron lifetimes. It turned out that milling times of only 30 min are sufficient to generate a highly defective oxide. Upon annealing at temperatures of T = 200 °C the defects can almost be preserved. Annealing at 750 °C for 1 h is needed to induce healing of the defects. Although we observe a recovery of the original interatomic distances and an increase in activation energy Ea for ionic transport from 0.75 eV to 0.81 eV, the initial transport properties of the unmilled sample (0.97 eV) cannot be fully restored. Most interestingly, the change in Ea is accompanied by a change of the entropy-controlled Arrhenius pre-factor governing the temperature dependence of σDCT. Moreover, positron lifetimes remain high in the annealed samples. Hence, our results point to samples with fewer distortions but still rich in vacancy-type defects. Altogether, the combination of ball milling and annealing helps adjust ionic conductivities in LiTaO3 to vary over 4 to 5 orders of magnitude.

Kinetic Isotope Effects and Hydrogen Tunnelling in PCET Oxidations of Ascorbate: New Insights into Aqueous Chemistry?

Recent experimental studies of kinetic isotope effects (KIE-s) and hydrogen tunnelling comprising three proton-coupled electron transfer (PCET) oxidations of ascorbate monoanion, (a) in aqueous reaction solutions, (b) in the mixed water-organic cosolvent systems, (c) in aqueous solutions of various salts and (d) in fairly diluted aqueous solutions of the various partial hydrophobes are reviewed. A number of new insights into the wealth of the kinetic isotope phenomena in the PCET reactions have been obtained. The modulation of KIE-s and hydrogen tunnelling observed when partially hydrophobic solutes are added into water reaction solution, in the case of fairly diluted solutions is revealed as the strong linear correlation of the isotopic ratios of the Arrhenius prefactors Ah/Ad and the isotopic differences in activation energies ΔEa (D,H). The observation has been proposed to be a signature of the involvement of the collective intermolecular excitonic vibrational dynamics of water in activation processes and aqueous chemistry.

Hydrogen Tunnelling as a Probe of the Involvement of Water Vibrational Dynamics in Aqueous Chemistry?

Our study of tunnelling in proton-coupled electron transfer (PCET) oxidation of ascorbate with hexacyanoferrate(III) follows the insights obtained from ultrafast 2D IR spectroscopy and theoretical studies of the vibrational water dynamics that led to the proposal of the involvement of collective intermolecular excitonic vibrational water dynamics in aqueous chemistry. To test the proposal, the hydrogen tunnelling modulation observed in the PCET reaction studied in the presence of low concentrations of various partial hydrophobic solutes in the water reaction system has been analyzed in terms of the proposed involvement of the collective intermolecular vibrational water dynamics in activation process in the case. The strongly linear correlation between common tunnelling signatures, isotopic values of Arrhenius prefactor ratios ln AH/AD and isotopic differences in activation enthalpies ΔΔH‡ (H,D) observed in the process in fairly diluted water solutions containing various partial hydrophobic solutes (such as dioxane, acetonitrile, ethanol, and quaternary ammonium ions) points to the common physical origin of the phenomenon in all the cases. It is suggested that the phenomenon can be rooted in an interplay of delocalized collective intermolecular vibrational dynamics of water correlated with vibrations of the coupled transition configuration, where the donor-acceptor oscillations, the motions being to some degree along the reaction coordinate, lead to modulation of hydrogen tunnelling in the reaction.

A Practical Approach for Data Gathering for Polymer Cure Simulations

Producing precision parts requires good control of the production parameters. When casting thermoset polymers an understanding of the curing process, with its heat release and associated temperature changes, is important. This paper describes how the cure of a polymer of unknown detailed chemical composition in a large part can be predicted and how the necessary material properties required for the predictions can be obtained. The approach given is a relatively simple method that a part manufacturer can perform. It will not characterize chemical reactions in detail, but it gives sufficient accuracy to describe the process. The procedures will be explained for an example of casting a large block of a filled two-component thermoset polyurethane. The prediction of the degree of cure, the associated heat and temperature increase during the curing of a polymer was successfully done using a standard finite element program with the input parameters reaction energy, the Arrhenius pre-factor and the kinetic function, which describes the chemical reaction. The three parameters could be obtained with standard Differential Scanning Calorimetry (DSC) equipment. The data were analyzed with the model-free isoconversional method combined with the compensation effect. The same set of parameters allowed the prediction of experimental cure behavior over two orders of magnitude of time and at a curing temperature range from room temperature up to 420 K.

Thermal Behavior and Slow Relaxation Dynamics in Amorphous Efavirenz: A Study by DSC, XRPD, TSDC, and DRS

The analysis of the thermal behavior of efavirenz showed a high glass-forming ability and good glass stability of this glass-forming liquid at room temperature. No polymorphic forms were formed either by cold crystallization or by recrystallization from solvent acetone. The determination of the dynamic fragility by the differential scanning calorimetry, thermally stimulated depolarization currents (TSDC), and dielectric relaxation spectroscopy (DRS) techniques is unanimous in suggesting efavirenz as a moderately fragile liquid. With DRS, secondary relaxations were detected, however, with weak intensities that did not allow the respective kinetic analysis; in contrast, TSDC allows clearly resolving the components of the secondary β-relaxation below Tg, with activation energies distributed between about 75 and 90 kJ mol−1 and Arrhenius prefactors of the order of 10−13 s. In this regard, the TSDC technique proved to be more effective compared to DRS in characterizing the secondary relaxation. The glass forming ability and glass stability found for efavirenz have been discussed in terms of various thermodynamic and kinetic parameters such as the reduced glass transition temperature, Tgred, the dynamic fragility, m, the stretching exponent, βKWW, the melting entropy, ΔSfus, and the molecular stiffness. The exceptionally low value of efavirenz fusion entropy was highlighted as a key feature of the thermal behavior of this glass-forming liquid.

Adiabatic Ligand Binding in Heme Proteins: Ultrafast Kinetics of Methionine Rebinding in Ferrous Cytochrome c.

The dynamics of methionine geminate recombination following photodissociation in ferrous cytochrome c is investigated over a broad temperature range. The kinetic response, above the solvent glass transition ( Tg), is nearly monoexponential and displays a weak temperature dependence. Below Tg, the rebinding kinetics are nonexponential and can be explained using a quenched distribution of enthalpic rebinding barriers, arising from a relatively narrow distribution of heme out-of-plane displacements. The Arrhenius prefactor of this (Δ S = 2) reaction is ∼1011 s-1, which is similar to what has been found for the (Δ S = 1) NO binding reaction in heme proteins. This observation, along with other examples of ultrafast CO binding, provides strong evidence that ligand binding to heme is an adiabatic reaction with a spin-independent prefactor. In order to simultaneously account for the adiabatic nature of the reaction as well as the temperature dependence of both ultrafast CO and methionine geminate rebinding, it is proposed that a spin triplet state intersects and strongly couples to the reactant ( S = 2) and product ( S = 0) state surfaces in the transition state region along the reaction coordinate. It is also suggested that the nature of the intersecting triplet state and the reaction path may depend upon the proximity of the photolyzed ligand relative to the iron atom. At temperatures below ∼60 K, the kinetic data suggest that there is either an unexpected retardation of the heme photoproduct relaxation or that heavy atom quantum mechanical tunneling becomes significant.

Joint probability distribution of Arrhenius parameters in reaction model optimization and uncertainty minimization

Abstract The method of uncertainty minimization by polynomial chaos expansions is extended to Arrhenius prefactor and activation energy co-optimization and uncertainty minimization. A covariance matrix is formulated to describe the joint probability distribution of the reaction rate parameters. The method is tested on a recently proposed foundational fuel chemistry model using 60 H2 and H2/CO flame speeds as the targets. The results show that co-optimizing A and Ea did not produce appreciable improvements in the ability of the reaction model to better predict the flame targets. It does yield reduction in the temperature-dependent uncertainty band of the rate coefficients of several key reactions. The importance of additional experimental and theoretical studies needed for the CO+OH→CO2+H, HO2+H→H2+O2 and HO2+H→2OH reactions is highlighted.

Degradation of Li-Oxide Garnets in Humidity, Air and Aqueous Solutions: A Study Using a Large Li6.4La3ZrTaO12 Single Crystal

Lithium-ion batteries are indispensable in our mobile electronic devices. Although considered as promising next-generation storage systems for green energy, safety aspects are of top priority of current research. The root of these safety issues associated with lithium-ion batteries lies in the electrolyte materials used at present. Those are based on flammable non-aqueous liquid electrolytes. Irrespective of these risks they could not been replaced so far because of the lack of inherently safe inorganic solids which should show both very high ionic diffusivities1,2 and a practicable electro­chemical stability. Garnet-type metal oxides,3 such as Li7La3Zr2O12 (LLZO), are being considered as suitable candidates as they fulfil many of the requirements to realize “beyond” Li-ion battery technologies. As an example, to be applicable as a water-protective layer for Li- metal electrodes, the solid electrolyte must be stable in aqueous solutions. In general, the majority of different LLZO types show a high stability in humid environments compared to other solid electrolytes. Upon exposure to aqueous solutions, a Li+/H+ exchange reaction is reported to occur in this class of materials. In certain compounds this exchange is believed to lead to structural changes and degradation of the Li+ conductivity.4 The present work is aimed at investigating degradation phenomena on single crystalline Li6.4La3ZrTaO12 samples in aqueous solutions (distilled water, 0.1 M HCl, saturated LiCl, and 1 M LiOH) as well as the degradation in both humidity and air. While grazing-incidence XRD and SEM helped identify degradation products, broadband conductivity spectroscopy was used to characterize ionic transport parameters of the bulk electrical responses. Albeit the ionic conductivities stay nearly constant the activation energies show drastic changes. As an example, for Li6.4La3ZrTaO12 immersed in distilled water we obtained an activation energy of 0.75 eV in contrast to 0.59 eV of the pristine sample at ambient conditions. This observation can be attributed to the change in the Arrhenius pre-factor caused by the reduction of the number density of Li-ion charge carriers in the garnet. Financial support by the Austrian Federal Ministry of Science, Research and Economy, as well as the Austrian National Foundation for Research, Technology and Development is highly appreciated. 1 V. Epp, O. Gün, H.-J. Deiseroth, M. Wilkening, J. Phys. Chem. Lett. 4 (2013) 2118. 2 M. Uitz, V. Epp, P. Bottke, M. Wilkening, J. Electroceram. 38 (2017), 142. 3 Thangadurai et al., Chem. Soc. Rev. 43 (2014) 4714. 4 C. Ma, E. Rangasamy, C. Liang, J. Sakamoto, K. L. More, M. Chi, Angew. Chem. Int. 54(1) (2015), 129-133.