Showing papers on "Einstein relation published in 1975"
TL;DR: In this paper, a generalized Einstein relation for gaseous ions is shown to be accurate even at high electric field strengths, provided care is taken in the evaluation of the ion temperature, and a comparison with experiment is made for K+ ions in He, Ne, and Ar.
Abstract: A generalized Einstein relation for gaseous ions is shown to be accurate even at high electric field strengths, provided care is taken in the evaluation of the ion temperature. Comparison with experiment is made for K+ ions in He, Ne, and Ar. The validity of this relation means that gaseous ion diffusion coefficients can be calculated from the more easily measured mobilities.
28 citations
TL;DR: Viehland and Viehland as mentioned in this paper measured the longitudinal diffusion coefficients of Li+ and Na+ ions in He, Ne, and Ar at a gas temperature of 300 °K.
Abstract: We have measured, with a drift tube mass spectrometer, the longitudinal diffusion coefficients of Li+ and Na+ ions in He, Ne, and Ar at a gas temperature of 300 °K. The measurements were made as a function of the energy parameter E/N, where E is the electrostatic drift field strength and N is the gas number density in the drift tube. The range of the steady‐state, average ionic energy thereby covered extended from close to the thermal value up to 10.1 eV in the case of Li+ in He and a few eV less in the other ion–atom combinations. The experimental data are compared with the results of computations based on three different equations: the original Wannier equation derived for the polarization attraction model, our modification of this equation, and the generalized Einstein relation discussed in the paper immediately preceding this paper [Larry A. Viehland and E. A. Mason, J. Chem. Phys. 63, 2913 (1975)]. The latter relation is superior to the other two in the present application and gives excellent agreeme...
26 citations
TL;DR: In this article, the diffusion coefficient and the electric mobility of 22Na ions in a sodium silicate glass (25 mol% Na2O) were measured simultaneously at 300°C in an experiment of the type used by Chemla, where the diffusion heat treatment is made in a constant dc electric field.
Abstract: The diffusion coefficient and the electric mobility of sodium (22Na) ions in a sodium silicate glass (25 mol% Na2O) were measured simultaneously at 300°C in an experiment of the type used by Chemla, where the diffusion heat treatment is made in a constant dc electric field. The diffusion coefficient remained unchanged with an applied electric field. The correlation factor in the Nernst-Einstein relation calculated from the simultaneously measured diffusion coefficient and electric mobility was 0.5±0.05.
23 citations
18 citations
13 citations
TL;DR: In this article, a connection between damping and the random driving forces is proposed which preserves quite generally the Einstein relation between the diffusion and mobility coefficients, and an application to the case of a Brownian particle in a critical binary mixture is presented.
Abstract: We solve the familiar Langevin equation with stochastic damping to represent the motion of a Brownian particle in a fluctuating medium. A connection between the damping and the random driving forces is proposed which preserves quite generally the Einstein relation between the diffusion and mobility coefficients. We present an application to the case of a Brownian particle in a critical binary mixture.
11 citations
TL;DR: In this paper, the case and Ornstein-Uhlenbeck treatment of rigid-body Brownian motion was extended to an elastically deformable body in $d$ dimensions, where the motion of Brownian deformations was considered to be locally damped by a retarding friction.
Abstract: Extensions of the Case and Ornstein-Uhlenbeck treatments of rigid-body Brownian motion to an elastically deformable body in $d$ dimensions are given. The motion of Brownian deformations in a fluid is considered to be locally damped by a retarding friction. To describe the expected fluctuations, velocity and displacement space-time correlation functions of a body are obtained from the relaxationfunction theorem. A general equipartition theorem is obtained without postulating certain fluctuating sources. However, it is possible to exhibit those fluctuating sources which would yield our correlation functions, and thus a generalized Einstein relation between fluctuations and retarding dissipations is obtained, which is proved to be necessary and sufficient. Sum rules and both Green's and scattering functions are given for strings, elastically deformable rods, and viscoelastic gels. Curves for the ensemble-average-square displacements and their integrations over the entire length are given.
6 citations
01 Jan 1975
TL;DR: In this paper, it has been shown that correlation factor is not useful in the case of solid electrolytes and the main aim of this paper is to shew that this approach was not useful for the purpose of estimating the mechanism of ion transport.
Abstract: It has been usual to resort to the value of the “correlation factor” when the mechanism of diffusion comes in question. In the area of solid electrolytes, similar efforts have been made in order to estimate the mechanism of ion transport. The main aim of this paper is to shew that this approach is not useful in the case of solid electrolytes. For the sake of simplicity, we limit our discussions here to the vacancy mechanism. However, similar arguments can be applied to any other mechanism as well.
3 citations
TL;DR: In this article, the diffusion coefficient and the electric mobility of 22Na ions in a sodium silicate glass (25 mol% Na2O) were measured simultaneously at 300°C in an experiment of the type used by Chemla, where the diffusion heat treatment is made in a constant dc electric field.
Abstract: The diffusion coefficient and the electric mobility of sodium (22Na) ions in a sodium silicate glass (25 mol% Na2O) were measured simultaneously at 300°C in an experiment of the type used by Chemla, where the diffusion heat treatment is made in a constant dc electric field. The diffusion coefficient remained unchanged with an applied electric field. The correlation factor in the Nernst-Einstein relation calculated from the simultaneously measured diffusion coefficient and electric mobility was 0.5±0.05.
1 citations
01 Jan 1975
TL;DR: In this paper, the authors extended the case and Ornstein-Uhlenbeck treatments of rigid-body Brownian motion to an elastically deformable body in d-dimensional space and provided a generalized Einstein relation between fluctuations and retarding dissipations.
Abstract: Extensions of the Case and Ornstein-Uhlenbeck treatments of rigid-body Brownian motion to an elastically deformable body in d dimensions are given. The motion of Brownian deformations in a fluid is considered to be locally damped by a retarding friction. To describe the expected fluctuations, velocity and displacement space-time correlation functions of a body are obtained from the relaxationfunction theorem. A general equipartition theorem is obtained without postulating certain fluctuating sources. However, it is possible to exhibit those fluctuating sources which would yield our correlation functions, and thus a generalized Einstein relation between fluctuations and retarding dissipations is obtained, which is proved to be necessary and sufficient. Sum rules and both Green's and scattering functions are given for strings, elastically deformable rods, and viscoelastic gels. Curves for the ensemble-average-square displacements and their integrations over the entire length are given. In order to describe the approach toward Brownian equilibrium of a string or an elastic rod, van Lear and Uhlenbeck' used a Langevin equation and postulated (a) the equipartition of energy among vibrational modes, and (b) a, local damping with a constant frictional coefficient. As a result, they verified Zeeman and Houdijk's experiment' and formula' for a Brownian wire suspended in a gas in the long-time limit. The present unified treatment of Brownian deformations of elastic bodies in d dimensions is motivated partly by light-scattering experiments, ' model calculations, ' stochastic solid mechanics, ' and partly by the recent success of Case' in his treatment of the usual rigidbody Brownian motion with the relaxation-function theorem.