Diffusion electrical conductivity relaxation

I. Yasuda and T.J. Hikita, Precise determination of the chemical diffusion coefficient of calcium-doped lanthanum chromites by means of electrical conductivity relaxation, Electrochem. Soc., 141(5) (1995) 1268-1273. 

The Boltzmann integro-differential kinetic equation written in terms of statistical physics became the foundation for construction of the structure of physical kinetics that included derivation of equations for transfer of matter, energy and charges, and determination of kinetic coefficients that entered into them, i.e. the coefficients of viscosity, heat conductivity, diffusion, electric conductivity, etc. Though the interpretations of physical kinetics as description of non-equilibrium processes of relaxation towards the state of equilibrium are widespread, the Boltzmann interpretations of the probability and entropy notions as functions of state allow us to consider physical kinetics as a theory of equilibrium trajectories. These trajectories as well as the trajectories of Euler-Lagrange have the properties of extremality (any infinitesimal part of a trajectory has this property) and representability in the form of a continuous sequence of states of rest. These trajectories can be used to describe the behavior of (a) isolated systems that spontaneously proceed to final equilibrium (b) the systems for which the differences of potentials with the environment are fixed (c) and non-homogeneous systems in which different parts have different values of the same intensive parameters. 

Nomenclature ECR, electrical conductivity relaxation EIS, electrochemical impedance spectroscop) GFA, gas-phase analysis lEDP, isotopic exchange dense profile Perm, membrane permeation Perm + Pot membrane permeation coupled to electrical potential measurement d) D tK, for O2 diffusion and >h for H2 and H2O diffusion. 

Electrical conductivity relaxation (ECR) method. ECR method is rather simple, it does not require expensive equipment and provides high precision in determination of the oxygen chemical diffusion and surface exchange coefficients in mixed ionic-electronic conductors [64-66],... 

Conductivity relaxation studies. In agreement with weight relaxation studies, electrical conductivity relaxation method revealed that oxygen chemical diffusion coefficients in composites are approximately an order of magnitude higher than those in pure perovskite... 

Overbeek and Booth [284] have extended the Henry model to include the effects of double-layer distortion by the relaxation effect. Since the double-layer charge is opposite to the particle charge, the fluid in the layer tends to move in the direction opposite to the particle. This distorts the symmetry of the flow and concentration profiles around the particle. Diffusion and electrical conductance tend to restore this symmetry however, it takes time for this to occur. This is known as the relaxation effect. The relaxation effect is not significant for zeta-potentials of less than 25 mV i.e., the Overbeek and Booth equations reduce to the Henry equation for zeta-potentials less than 25 mV [284]. For an electrophoretic mobility of approximately 10 X 10 " cm A -sec, the corresponding zeta potential is 20 mV at 25°C. Mobilities of up to 20 X 10 " cmW-s, i.e., zeta-potentials of 40 mV, are not uncommon for proteins at temperatures of 20-30°C, and thus relaxation may be important for some proteins. 

Mechanistic Ideas. The ordinary-extraordinary transition has also been observed in solutions of dinucleosomal DNA fragments (350 bp) by Schmitz and Lu (12.). Fast and slow relaxation times have been observed as functions of polymer concentration in solutions of single-stranded poly(adenylic acid) (13 14), but these experiments were conducted at relatively high salt and are interpreted as a transition between dilute and semidilute regimes. The ordinary-extraordinary transition has also been observed in low-salt solutions of poly(L-lysine) (15). and poly(styrene sulfonate) (16,17). In poly(L-lysine), which is the best-studied case, the transition is detected only by QLS, which measures the mutual diffusion coefficient. The tracer diffusion coefficient (12), electrical conductivity (12.) / electrophoretic mobility (18.20.21) and intrinsic viscosity (22) do not show the same profound change. It appears that the transition is a manifestation of collective particle dynamics mediated by long-range forces but the mechanistic details of the phenomenon are quite obscure. 

A variety of techniques has been employed to investigate aliovalent impurity-cation vacancy pairs and other point defects in ionic solids. Dielectric relaxation, optical absorption and emission spectroscopy, and ionic thermocurrent measurements have been most valuable ESR studies of Mn " in NaCl have shown the presence of impurity-vacancy pairs of at least five different symmetries. The techniques that have provided a wealth of information on the energies of migration, formation and other defect energies in ionic solids are diffusion and electrical conductivity measurements. Electrical conductivity in ionic solids occurs by the motion of ions through vacancies or of interstitial ions. In the case of motion through vacancies, the conductivity, a, is given by... 

Following the introduction of basic kinetic concepts, some common kinetic situations will be discussed. These will be referred to repeatedly in later chapters and include 1) diffusion, particularly chemical diffusion in different solids (metals, semiconductors, mixed conductors, ionic crystals), 2) electrical conduction in solids (giving special attention to inhomogeneous systems), 3) matter transport across phase boundaries, in particular in electrochemical systems (solid electrode/solicl electrolyte), and 4) relaxation of structure elements. 

The proper choice of a solvent for a particular application depends on several factors, among which its physical properties are of prime importance. The solvent should first of all be liquid under the temperature and pressure conditions at which it is employed. Its thermodynamic properties, such as the density and vapour pressure, and their temperature and pressure coefficients, as well as the heat capacity and surface tension, and transport properties, such as viscosity, diffusion coefficient, and thermal conductivity also need to be considered. Electrical, optical and magnetic properties, such as the dipole moment, dielectric constant, refractive index, magnetic susceptibility, and electrical conductance are relevant too. Furthermore, molecular characteristics, such as the size, surface area and volume, as well as orientational relaxation times have appreciable bearing on the applicability of a solvent or on the interpretation of solvent effects. These properties are discussed and presented in this Chapter. 

As for the permeability measurements, most techniques based on the analysis of transient behavior of a mixed conducting material [iii, iv, vii, viii] make it possible to determine the ambipolar diffusion coefficients (- ambipolar conductivity). The transient methods analyze the kinetics of weight relaxation (gravimetry), composition (e.g. coulometric -> titration), or electrical response (e.g. conductivity -> relaxation or potential step techniques) after a definite change in the - chemical potential of a component or/and an -> electrical potential difference between electrodes. In selected cases, the use of blocking electrodes is possible, with the limitations similar to steady-state methods. See also - relaxation techniques. 

Diffusion time (diffusion time constant) — This parameter appears in numerous problems of - diffusion, diffusion-migration, or convective diffusion (- diffusion, subentry -> convective diffusion) of an electroactive species inside solution or a solid phase and means a characteristic time interval for the process to approach an equilibrium or a steady state after a perturbation, e.g., a stepwise change of the electrode potential. For onedimensional transport across a uniform layer of thickness L the diffusion time constant, iq, is of the order of L2/D (D, -> diffusion coefficient of the rate-determining species). For spherical diffusion (inside a spherical volume or in the solution to the surface of a spherical electrode) r spherical diffusion). The same expression is valid for hemispherical diffusion in a half-space (occupied by a solution or another conducting medium) to the surface of a disk electrode, R being the disk radius (-> diffusion, subentry -> hemispherical diffusion). For the relaxation of the concentration profile after an electrical perturbation (e.g., a potential step) Tj = L /D LD being - diffusion layer thickness in steady-state conditions. All these expressions can be derived from the qualitative estimate of the thickness of the nonstationary layer... 

We have studied a variety of transport properties of several series of 0/W microemulsions containing the nonionic surfactant Tween 60 (ATLAS tradename) and n-pentanol as cosurfactant. Measurements include dielectric relaxation (from 1 MHz to 15.4 GHz), electrical conductivity in the presence of added electrolyte, thermal conductivity, and water self-diffusion coefficient (using pulsed NMR techniques). In addition, similar transport measurements have been performed on concentrated aqueous solutions of poly(ethylene oxide)... 

Here, 8(f), 8(0), and 8(cx3) are the mean (at time f), initial (at f = 0) and final (as f —> CX3) value of oxygen nonstoichiometry, respectively. By monitoring the temporal variation of the nonstoichiometry 8(f) by either thermogravimetry or a 8-sensitive property (e.g., electrical conductivity), it is possible to determine the two kinetic parameters. With regards to binary systems, it is believed that the relaxation kinetics may be well understood. Chemical diffusion, in particular, has long been understood in the light of chemical diffusion theory [28], or in the light ofthe ambipolar diffusion theory [29]. 

H. Namikawa [1975] Characterization of the Diffusion Process in Oxide Glasses Based on the Correlation between Electric Conduction and Dielectric Relaxation, J. Non-Cryst. Solids 18, 173-195. 

Several extensions and modifications of the electrolyte theory in the first half of the twentieth century should be mentioned Bjeiium [14] introduced the concept of limited electrostatic dissociation (ion pair formation), Onsager and Fuoss extended the DH approach and the ideas of Debye about the electrophoretic and the relaxation effect on transport properties such as electrical conductivity and diffusion coefficients [15]. As already mentioned, the DH description is also the basis of one of the two constituting parts of the DLVO theory in colloidal chemistry. 

An electrolyte solution which is not in equilibrium is exposed to generalized forces that are responsible for irreversible processes, such as transport or relaxation processes. A gradient of the chemical potential of the considered ions is the source of such a force, producing a particle flow that leads to diffusion and to electric conductance. Neglecting activity coefficients (dilute solutions) the flow of ion i is given by the relation (with the convection term omitted)... 

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