Theoretical interpretation of the limiting electric conductivity in ionic solution

The physical essence of the limiting equivalent ionic conductivity in solution, λ⁰_i, has been a continuing challenge over almost a century. Here I briefly present an ab initio theoretical treatment providing (1) a new insight into the nature of λ⁰_i, and (2) a mathematical formula for computing λ⁰_i. In the new treatment, one assumes that any chosen ion i is surrounded by a spherical body of oriented solvent dipoles carrying the charge of the counterion, and the bulk solvent is a continuum with no molecular detail. λ⁰_i is thus the result of the tandem operation, at hydrodynamic equilibrium, of the dipole body's electrophoretic and relaxation forces exerted on the drifting ion. λ⁰_i is found to be proportional to the radius of ion i, and independent of the ionic charge. From experimental λ⁰_i's, the ion radius can be computed as ‘electric radius.’ An electric ion-radius scale so derived compares well with other ion-size scales. The current theory expresses λ⁰_i using only universal constants and unitary factors of the ionic solution, and it sheds new light on the fundamental nature of ion and charge transport in a polar liquid medium.     

Simplified electrostatic model for the thermodynamic excess potentials of binary strong electrolyte solutions with size-dissimilar ions

Modern theories of electrolyte solutions are physically accurate but difficult to apply for real-life systems; a need therefore exists to theoretically derive simplified and practically useful mathematical expressions for thermodynamic excess functions. This can be done by incorporating ion-size dissimilarity into the classical Debye-Hückel model [Physik Z. 24, 185 (1923)], under conditions at which non-electrostatic contributions are negligible. If the contact distance between the central (β) ion and a cloud (α) ion is a for counter-ions and b for co-ions, two basic cases exist, b < a and b > a. In both, a ‘smaller-ion shell’ (SiS) at the edge of the ionic cloud, bordered by the spherical surfaces of radius b and a, admits only the smaller α ions [Thomlinson and Outhwaite, Mol. Phys. 47, 1113 (1982)]. In the b < a case, the SiS contributes an ionic repulsion effect and the overall extra-electrostatic potential energy, Ψ _{b < a} (κ) ? κ, reciprocal screening length–exhibits a minimum. For b > a, the SiS contributes an ‘extra ionic attraction’ and the overall extra-electrostatic energy, Ψ _{b > a} (κ) declines monotonically with increasing κ. The entire Ψ contribution, Ψ_±, is a linear combination of the Ψs of the two counter β ions. The effectiveness of Ψ_± is demonstrated for real-life electrolyte systems, based on experimental mean ionic activity coefficients and their concentration dependencies. Fitting theory with experiment generates ion-size parameters that represent realistic interionic collision distances in solution, unlike parallel parameters based on other simplified theories.     

Ionic conduction and effect of immobile cation substitution in binary system (AgI)4/5–(PbI2)1/5

Samples of stoichiometry (AgI)₄(PbI₂)_1?x (CdI₂) _x , (0 ≤ x ≤ 0.4), have been prepared and studied by electrical conductivity, X-ray powder diffraction and DSC techniques. The ionic conductivity of samples was found to increase with temperature, and an abrupt increase at phase transition temperature was observed. The Cd⁺²-doped samples exhibited lower phase transition temperature compared to that of the pure samples. The ionic conductivity decreases with an increase in Cd⁺² content in pre-transition, while enhances in conductivity result in Cd⁺² content samples of x ≤ 0.2 in the post-transition region. Different resources of investigation confirmed the solubility limit of Cd⁺² in the high-temperature phase to be x = 0.2. The change in the ionic conductivity of Cd⁺²-doped samples is explained by the increase in the defect concentration and the free volume available in the lattice. The drop in phase transition temperature of Cd²⁺-doped systems is attributed to the lattice distortion and the increase in the defect–defect interaction.     

Study of assorted interactions of an ionic liquid in significant solvent systems using compensated equation of Fuoss conductance and vibrational mode

Qualitative and quantitative analyses of molecular interaction prevailing in ionic liquid tetrabutylphosphonium methanesulfonate [Bu₄PMS] in dimethyl sulfoxide (DMSO), N,N-dimethyl formamide (DMF) and N,N-dimethyl acetamide (DMA) probed by electrical conductances and Fourier transform infrared (FT-IR) measurements have been reported at 298.15 K. Corresponding conductance data have been analysed using the Fuoss conductance-concentration equation (1978) for ion pair formation. The limiting ionic conductances (λ _o ^± ) have been estimated from the appropriate division of the limiting molar conductivity value of tetrabutylammonium tetraphenylborate [Bu₄NBPh₄] as the ‘reference electrolyte’. The diffusion coefficient (D) has been obtained from Stokes-Einstein relation and the ionic mobility (i) for [Bu₄P]⁺ and MS^? using appropriate equation. The results have been discussed in terms of dipole-dipole interactions, hydrogen bond formation and structural aspect of the solvents and configurational theory. The FT-IR spectra have also been studied to predict the interactions occurring in the system.

Ionic mobility and ionic association of singly charged ions in glycerol

Experimental molar conductivity data for KCl, NaCl and LiCl in glycerol at 298.15?K were analysed by least-square fitting in the concentration range 0.5–100?mol?m^?3in order to compute the values of the molar conductivity at infinite dilution Λ⁰and the Onsager constant S. Using previously measured transference numbers and assuming the Kohlrausch infinite dilution law, the limiting ionic mobilities were deduced. The results obtained show that the transport mechanisms in this solvent and other similar hydrogen-bonded solvents such as water and ethylene glycol are the same. The data were also interpreted in terms of ion–ion and ion–solvent interactions using the Fuoss paired ion model in the concentration range 0.5–100?mol?m^?3. The fitting of Fuoss’ equation of 1978 to these data led us to an estimate of the ionic association by computing the conductimetric pairing constants. The latter were further analysed by Gilkerson's equation to yield the difference between the solvation energy of the free ions and the ion pairs. The computed values allow an estimation of whether the electrolyte is a structure maker or a structure breaker.     

Determination of the ionic conductivity of Sr-doped lanthanum manganite by modified Hebb–Wagner technique

The Hebb–Wagner polarization method with the electron blocking electrode has been discussed in this paper in aim to determine a partial ionic conductivity of Sr-doped lanthanum manganite. The “limiting current” in the proposed system was measured using the two-point DC technique with additional Pt electrode between LSM and blocking electrode. The electrochemical model based on bulk diffusion processes and Boltzmann statistics has been also described. The ionic conductivity calculated with the use of proposed model for La_0.7Sr_0.3MnO_3+δ was 5.3×10⁻⁴ S cm⁻¹ at 800 °C and the activation energy of ionic conductivity was found to be (0.60±0.02) eV. This result is in agreement with previous literature reports and indicates the workability of the modified Hebb–Wagner system.     

Oxide ion conductivity and relaxation in CaREZrNbO7 (RE = La, Nd, Sm, Gd, and Y) system

CaREZrNbO₇ (RE = La, Nd, Sm, Gd and Y) system changed from fluorite (F)-type to pyrochlore (P)-type structure when the ionic radius ratios, r(Ca²⁺–RE³⁺)_av/r(Zr⁴⁺–Nb⁵⁺)_av were larger than 1.34. Thus, the La, Nd, and Sm compounds have a cubic P-type structure and the Gd and Y ones have a defect F-type structure. The electrical conductivity was measured using complex-plane impedance analysis over a wide temperature (300–750 °C) and frequency (1 Hz–1 MHz) ranges. The conductivity relaxation phenomenon was observed in these compounds and the relaxation frequencies were found to show Arrhenius-type behavior and activation energies were in good agreement with those obtained from high temperature conductivity plots. These results support the idea that the relaxation process and the conductivity have the same origin. The ionic conductivity of CaREZrNbO₇ (RE = La, Nd, Sm, Gd and Y) system showed the maximum at the phase boundary between the F-type and P-type phases. On the other hand, the activation energy for the conduction decreased in the F-type phase and increased in the P-type phase with increasing ionic radius ratio. Among the prepared compounds, CaGdZrNbO₇ showed the highest ionic conductivity of 9.47 × 10^− 3 S/cm at 750 °C which was about twice as high as that observed in Gd₂Zr₂O₇ (4.2 × 10^− 3 S/cm at 800 °C). The grain morphology observation by scanning electron microscope (SEM) showed well-sintered grains. AC impedance measurements in various atmospheres further indicated that they are predominantly oxide ion conductors at elevated temperatures (> 700 °C).     

Thermal conductivity of fluids with steeply repulsive potentials

We consider the thermal conductivity of steeply repulsive inverse power fluids (SRP) in which the particles interact with a pair potential, φ(r) = ε(σ/r)ⁿ. The time correlation function for the heat flux, C_λ(t), and the time average, C_λ(0) are calculated numerically by molecular dynamics simulations, and accurate expressions for these are also derived for the SRP fluid. We show, by molecular dynamics simulations, that close to the hard-sphere limit this time correlation function has the same analytic form as for the shear and pressure correlation functions for the shear and bulk viscosity, i.e. C_λ(t)/C_λ(0) = 1 ?T* (nt*)² + 0((nt*)⁴), where T* = k _B T/ε, is the reduced temperature, k _B is Boltzmann's constant and t* = (ε/σ²)^1/2 t is the reduced time. The thermal conductivity for the limiting case of hard spheres is numerically very close to that given by the traditional Enskog relation. At low densities the normalized relaxation times are typically largest for the thermal conductivity, followed by shear and then bulk viscosity. Close to the maximum fluid density, the latter two increase rapidly with density (especially for the shear) but continue a monotonic decline for the thermal conductivity. This reflects the relative insensitivity of the thermal conductivity to the approach to the fluid-solid phase boundary.     

Influence of calcium substitution on the phase transition and ionic conductivity in BICAVOX oxide ion conductor

Samples of Bi₄Ca _x V_{2? x} O_{11?(3 x /2)?δ} in the composition range 0.07 ≤ x ≤ 0.30 were prepared by conventional solid state reactions. The stability of different phases as a function of composition was analysed by X-ray powder diffraction, FT-IR spectra, differential thermal analysis and AC impedance spectroscopy. For the compositions x ≤ 0.10, monoclinic α-phase structure is retained at room temperature. For x = 0.13, orthorhombic β-phase is observed, whereas for x ≥ 0.17, high O^2?conducting tetragonal γ-phase is stabilised. However, the highest ionic conductivity σ_300°C = 3.27 × 10^?4 S cm^?1 was observed for x = 0.17. This higher value of conductivity of the substituted compound as compared to the parent compound can be attributed to the increased oxygen ion vacancies generated as a result of cation doping. AC impedance spectroscopy reveals the fact that this ionic conductivity is mainly due to the grain contribution.     

准一维多链无序体系跳跃电导特性

在单电子紧束缚近似下,建立了准一维多链无序体系直流、交流电子跳跃输运模型,通过计算探讨了无序模式、维度效应、温度及外场对其直流、交流电导率的影响.计算结果表明:准一维多链无序体系的直流、交流电导率随着格点能量无序度的增大而减小,非对角无序具有增强体系电子输运能力的作用.随着链数的增加,体系的直流、交流电导率增大,但格点能量无序度较小时,维度效应的影响不明显.在对角无序情况下准一维多链无序体系的交流电导率随温度的升高而增大,而在非对角无序模式下却随温度的升高而减小,但对于直流情况,体系的直流电导率随温度的升     

Lithium ion transport and ion-polymer interaction in PEO based polymer electrolyte plasticized with ionic liquid

The polyethylene oxide (PEO) based lithium ion conducting polymer electrolytes complexed with lithium trifluoromethanesulfonate (LiCF₃SO₃ or LiTf) plasticized with an ionic liquid 1-ethyl 3-methyl imidazolium trifluoromethanesulfonate (EMITf) have been reported. Morphological, spectroscopic, thermal and electrochemical investigations demonstrate promising characteristics of the polymer films, suitable as electrolyte in various energy storage/conversion devices. Significant structural changes have been observed in the polymer electrolyte due to the ionic liquid addition, investigated by X-ray diffraction (XRD) and optical microscopy. The ion-polymer interaction, particularly the interaction of imidazolium cation with PEO chains, has been evidenced by IR and Raman spectroscopic studies. The optimized composition of the polymer electrolyte i.e. PEO_25.LiTf + 40 wt.% EMITf offer room temperature ionic conductivity of ~ 3 × 10^− 4 S cm^− 1 with wide electrochemical stability window and excellent thermal stability. The ‘σ versus 1/T’ curves show apparent Arrhenius behavior below and above melting temperature. The ionic conductivity has been observed due to Li⁺ ions, as confirmed from ⁷Li-NMR studies, though the component ions of ionic liquid and anions also contribute significantly to the overall conductivity.     

Preparation and properties of a gel polymer electrolyte system based on poly-ε-caprolactone containing 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide

Gel polymer electrolytes (GPE) obtained by immobilizing a solution of zinc triflate (ZnTr) in an ionic liquid, namely 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide [emim][Tf₂N] within a biodegradable polymeric matrix of poly-ε-caprolactone (PCL) were prepared by a simple solvent cast technique for different concentrations of the ionic liquid. The electrolyte with the composition 75 wt% PCL: 25 wt% ZnTr+100 wt% [emim][Tf₂N] showed the highest ionic conductivity of 1.1×10⁻⁴ S cm⁻¹ at 25 °C and favored by the rich amorphous phase of the GPE as confirmed from room temperature X-ray diffraction analysis (XRD). The morphology of the GPE was examined using scanning electron microscopy (SEM) which revealed the homogeneity of the prepared GPE system. The temperature dependence of electrical conductivity of the GPE followed the Arrhenius behavior. The Zn²⁺ ionic transport number has been determined to be ~0.62 which denotes the predominant contribution of zinc ion towards total ionic conductivity. The electrochemical stability window of GPE is found to be 2.5 V with a thermal stability upto 200 °C. This eco-friendly and safe electrolyte may be used to fabricate compostable batteries, in future, with a suitable selection of other components of the battery system.     

Experimental and theoretical spectroscopic studies of ortho derivatives of methyl p-dimethylaminobenzoate

Steady-state spectroscopic studies of two ortho (-OCH₃ and -OH) derivatives of methyl p-dimethylaminobenzoate have been performed. The absorption spectra of molecules under study are analyzed taking into consideration results of quantum chemical semiempirical calculations. The fluorescence spectra of these molecules possess in polar solvents two bands, i.e., the locally excited and intramolecular charge transfer (ICT) fluorescence band. Their intensity ratio as well as the fluorescence/phosphorescence intensity ratio determined at 77 K depends on the solvent polarity. Theoretical studies of the TICT phenomenon have been made in order to explain the dual emission of molecules under study. Calculated electric dipole moments of these molecules in the ground, S₀, and excited, S₁(LE) and S₁(ICT) states, have been compared with experimentally determined data. Theoretically determined transition energies, ΔE_i, oscillator strengths, f_i, and electric dipole moments μ_S0, μ_S1(LE) and μ_S1(ICT) of the planar donor-acceptor (D/A) conformer agree with experimental data. According to Marcus theory inner- and outer-solvatation sphere reorganization energies (λ_out, λ_in) are calculated using the determined spectroscopic properties of molecules under study.     

Effect of ionization of impurity centres by electric field on the conductivity of superlattice

The electric fieldE₀effect on ionization on impurity centres and on the conductivity of superlattices (SLs) has been studied theoretically. It is observed that as the fieldE₀increases the current rises, reaches a maximum, then falls off, i.e. show a negative differential conductivity (NDC). Further increase inE₀leads to an exponential rise of the current. This occurs aroundE₀=3×10⁴ V cm⁻¹. Hence the current density field shows a ‘N’ shape characteristics as against the ‘n’ shape characteristics in the absence of impurity.     

Field enhanced Li ion conduction in nanoferroelectric modified polymer electrolyte systems

Nanocomposite polymer electrolyte (NCPE) films based on polyethylene oxide (PEO) complexed with lithium perchlorate (LiClO₄) and nanosized ferroelectric ceramic fillers such as BaTiO₃, SrTiO3 have been prepared using solution cast technique. The films showed very good mechanical stability when exposed to ambient atmospheres for prolonged periods. Lithium ion transport studies revealed that the conductivity is predominantly ionic. The effect of electric field on ionic conductivity of NCPE films was investigated. One order enhancement in conductivity due to the field was observed at 323 K. NCPE films exhibited conductivity of 3.46?×?10^?5 Scm^?1 at 323 K. NCPE films were characterized using differential scanning calorimetry (DSC) and X-ray diffraction (XRD) technique. The DSC and XRD studies revealed reduced crystallinity which confirmed the higher amorphous phase and hence the improved ionic conductivity.     

The effect of point defects on the ionic conductivity of RbAg4I5 solid electrolytes

Abstract

The effect has been studied of additive coloring on the magnitude of ion conductivity of RbAg₄I₅ crystals. It has been found that slight changes of silver stoichiometry of 10^?3 at.% can lead to considerable variations of the ionic conductivity Δ[sgrave]_i/[sgrave]_i ? 0.1. The dependence has been observed of the magnitude of ion conductivity on the ratio between the integral intensities of the main bands in the photoluminescence spectrum of the γ-phase of RbAg₄I₅ which associated with the luminescence centres containing vacancies and interstitials of silver cations.     

Effect of iron doping at Mn-site on complex impedance spectroscopy properties of Nd0.67Ba0.33MnO3 perovskite

The effect of Fe-doping at Mn-site on the structural and electrical properties of Nd_0.67Ba_0.33Mn_1?xFe_xO₃ (0 ≤ x ≤ 0.05) perovskites has been investigated. X-ray diffraction patterns show that the structural parameters change slightly due to the fact that the Fe³⁺ ions replacing the Mn³⁺ have similar ionic radius. The electrical properties of these samples have been investigated using complex impedance spectroscopy technique. a function of the frequency at different temperatures. When increasing the Fe-content, a decrease of dc conductivity was observed throughout the whole explored temperature range and the deduced activation energy values are found to increase from 128 meV for x = 0 to 166 meV for x = 0.05. The curves of the imaginary part of impedance (Z″) show the presence of relaxation phenomenon in our samples. The complex impedance spectra show semicircle arcs at different temperatures and an equivalent circuit of the type of R_g + (R_gb//C_gb) has been proposed to explain the impedance results.     

Effects of plasticizer and nanofiller on the dielectric dispersion and relaxation behaviour of polymer blend based solid polymer electrolytes

Solid polymer electrolytes consisted of poly(ethylene oxide) (PEO) and poly(methyl methacrylate) (PMMA) blend (50:50 wt/wt%) with lithium triflate (LiCF₃SO₃) as a dopant ionic salt at stoichiometric ratio [EO + (CO)]:Li⁺ = 9:1, poly(ethylene glycol) (PEG) as plasticizer (10 wt%) and montmorillonite (MMT) clay as nanofiller (3 wt%) have been prepared by solution cast followed by melt–pressing method. The X–ray diffraction study infers that the (PEO–PMMA)–LiCF₃SO₃ electrolyte is predominantly amorphous, but (PEO–PMMA)–LiCF₃SO₃–10 wt% PEG electrolyte has some PEO crystalline cluster, whereas (PEO–PMMA)–LiCF₃SO₃–10 wt% PEG–3 wt% MMT electrolyte is an amorphous with intercalated and exfoliated MMT structures. The complex dielectric function, ac electrical conductivity, electric modulus and impedance spectra of these electrolytes have been investigated over the frequency range 20 Hz to 1 MHz. These spectra have been analysed in terms of the contribution of electrode polarization phenomenon in the low frequency region and the dynamics of cations coordinated polymer chain segments in the high frequency region, and also their variation on the addition of PEG and MMT in the electrolytes. The temperature dependent dc ionic conductivity, dielectric relaxation time and dielectric strength of the plasticized nanocomposite electrolyte obey the Arrhenius behaviour. The mechanism of ions transportation and the dependence of ionic conductivity on the segmental motion of polymer chain, dielectric strength, and amorphicity of these electrolytes have been explored. The room temperature ionic conductivity values of the electrolytes are found ∼10⁻⁵ S cm⁻¹, confirming their use in preparation of all-solid-state ion conducting devices.     

Dielectric and anelastic relaxation of crystals containing point defects

A theory is developed which describes the linear, reversible, time-dependent response of a crystal containing point defects to stress or electric fields, respectively known as anelastic and dielectric relaxation. Such relaxation occurs because of the redistribution of the defects among sites which are initially equivalent, but which becomes inequivalent in the presence of the external field. The macroscopic behaviour of such a crystal is found to be describable in terms of the symmetry which can be assigned to the defect. This defect symmetry determines whether or not the crystal will undergo dielectric or anelastic relaxation and, if relaxation can occur, which specific coefficients of elastic compliance or electric susceptibility show the relaxation effect. The latter information, called the ‘selection rules’ tells, in effect, which combination of stress or electric field components is capable of redistributing the defects. Tables are given for these selection rules for all possible defect symmetries in each of the 32 crystal classes. It is also shown that a hitherto unobserved phenomenon of piezoelectric relaxation may occur; the selection rules for this effect are also given.

Aside from its symmetry, the defect can be described as an electric dipole in terms of a suitable dipole moment vector μ, and as an ‘elastic dipole’ in terms of a tensor λ. It is shown that the defect symmetry determines the number of independent components of μ and λ. Finally, a thermodynamic theory is developed which permits calculation of the relaxation strengths for those compliance, susceptibility, and piezoelectric coefficients which undergo relaxation, in terms of the independent components of μ and λ. Applications of the theory to specific cases are then reviewed.     

The effect of sulfide substitution in the mixed conductor Cu7PSe6

Cu₇PSe₆ is a mixed conductor exhibiting structural phase transitions above and below room temperature that are accompanied by step-like changes in electrical conductivity. The substitution of S²⁻ for Se²⁻ in Cu₇PSe₆ significantly enhances electrical conductivity at room temperature compared to that observed for the pure compound. In the case of Cu₇P(Se_0.80S_0.20)₆, a nearly temperature-independent electrical conductivity exceeds 1 S/cm with no evidence of any phase transitions throughout the temperature interval 200-400 K. However, the ionic contribution accounts for just 2% of the total electrical conductivity in this solid solution at room temperature.