Exact diffusion coefficient for a chain of beads in one dimension using the Einstein relation

2005 ◽  
Vol 72 (6) ◽  
Author(s):  
G. Terranova ◽  
H. O. Mártin ◽  
C. M. Aldao
Keyword(s):  
Diffusion Coefficient ◽  
One Dimension ◽  
Einstein Relation ◽  
A Chain

The probability distribution of the extent of a random chain

1941 ◽  
Vol 37 (3) ◽  
pp. 244-251 ◽  
Author(s):  
H. E. Daniels ◽  
F. Smithies
Keyword(s):  
Probability Distribution ◽  
Three Dimensions ◽  
One Dimension ◽  
Shortest Distance ◽  
A Chain ◽  
Random Configuration

1. Introduction and summary. A chain of N links is allowed to assume a random configuration in space. The extent of the chain in any direction is defined as the shortest distance between a pair of planes perpendicular to that direction, such that the chain is contained entirely between them. In the present paper the probability distribution of the extent is discussed, starting with a chain in one dimension for which formulae are derived for the probability and mean extent for all values of N. The limiting forms for large N are then considered. The results are extended to the case of a chain in three dimensions, and it is shown that the extents in two directions at right angles tend to be independently distributed when N is large. It is assumed that the links are infinitely thin, so that a point in space may be occupied by the chain any number of times.

scholarly journals On a Conjecture about Diffusion of Gaseous Ions

1973 ◽  
Vol 26 (6) ◽  
pp. 897 ◽  
Author(s):  
Gregory H Wannier
Keyword(s):  
Diffusion Coefficient ◽  
Einstein Relation

A previous conjecture by the author about the diffusion coefficient of gaseous ions is restated more precisely, thereby eliminating, in particular, an error of a factor of two which seemed to be contained in it in certain cases. The conjecture, which is essentially an extension of the Nernst-Einstein relation to situations not close to equilibrium, is made plausible by a Langevin-type derivation.

Electrical conductivity and Einstein relation modeling in phosphorene

2019 ◽  
Vol 33 (06) ◽  
pp. 1950033
Author(s):  
E. Mansouri ◽  
J. Karamdel ◽  
M. T. Ahmadi ◽  
M. Berahman
Keyword(s):  
Diffusion Coefficient ◽  
Fermi Energy ◽  
Carrier Mobility ◽  
2D Materials ◽  
Einstein Relation ◽  
Fundamental Parameters ◽  
Electron Diffusion Coefficient ◽  
Energy Formula ◽  
Higher Carrier Mobility ◽  
And Diffusion

Investigation on (2-dimensional) (2D) materials is growing significantly due to the fundamental electronic properties in the direct inherent bandgap, higher carrier mobility, and easier exfoliation. Phosphorene as a new 2D configuration has presented excellent potential in electronic and optoelectronic applications. In this study, the conductivity of monolayer phosphorene and Einstein’s relations as fundamental parameters in semiconductor manufacturing are analytically modeled. In addition, dependency of conductivity on normalized Fermi energy ([Formula: see text]) is demonstrated. According to the simulation results, conductivity and Einstein’s relation are completely dependent on temperature, therefore, rising up the temperature leads to conductivity and diffusion coefficient (Dn) growth. Indeed, conductivity is saturated when the normalized Fermi energy exceeds than 6. Also, the conductivity and Einstein’s relation dependency to voltage are studied. Results show that carrier conductivity and the electron diffusion coefficient (Dn) increase by amplifying the voltage.

Darstellung und Kristallstruktur von K2Pd02 / Synthesis and Crystal Structure of K2Pd02

1974 ◽  
Vol 29 (1-2) ◽  
pp. 10-12 ◽  
Author(s):  
Horst Sabrowsky ◽  
Welf Bronger ◽  
Dieter Schmitz
Keyword(s):  
Crystal Structure ◽  
Structure Type ◽  
Chain Structure ◽  
Unit Cell ◽  
One Dimension ◽  
Ternary Oxide ◽  
Orthorhombic Unit Cell ◽  
Synthesis And Crystal Structure ◽  
X Ray ◽  
A Chain

The ternary oxide K2PdO2 has been prepared by a reaction between K2O and PdO. X-ray investigations suggest a chain-structure-type which corresponds to that of K2PtS2. The planar oxygen coordinations of the palladium atoms are connected laterally in one dimension. The orthorhombic unit cell (a = 8.523, b = 6.089, c = 3.119 Å) contains two formula units.

Fractional Exponent of the Modified Stokes-Einstein Relation in the Metallic Glass-Forming Melt Pd43Cu27Ni10P20

2010 ◽  
Vol 146-147 ◽  
pp. 1463-1468
Author(s):  
Masahiro Ikeda ◽  
Masaru Aniya
Keyword(s):  
Diffusion Coefficient ◽  
Glass Transition ◽  
Transition Temperature ◽  
Glass Transition Temperature ◽  
Metallic Glass ◽  
Bond Strength ◽  
Coordination Number ◽  
Einstein Relation ◽  
Glass Forming ◽  
Highly Correlated

The diffusion coefficient in the metallic glass-forming systems such as Pd-Cu-Ni-P exhibits a marked deviation from the Stokes-Einstein (SE) relation in the proximity of the glass transition temperature. Such a deviation is characterized by the fractional exponent p of the modified SE expression. For the material Pd43Cu27Ni10P20, it has been reported that it takes the value p = 0.75. In this work, it is shown that the value of p is highly correlated with the ratio ED / ENB, where ED and ENB are the activation energies for diffusion coefficient D and cooperativity NB defined by the Bond Strength-Coordination Number Fluctuation (BSCNF) model. The present paper reports that for the metallic glass-forming melt Pd43Cu27Ni10P20, the fractional exponent p can be calculated accurately within the framework of the BSCNF model.

The influence of diffusion on the current-voltage curve in a flame ionization detector. II

1992 ◽  
Vol 438 (1903) ◽  
pp. 361-370 ◽  
Keyword(s):  
Diffusion Coefficient ◽  
Applied Voltage ◽  
Flame Ionization Detector ◽  
Three Dimensions ◽  
Einstein Relation ◽  
Ionization Detector ◽  
Flame Ionization ◽  
Voltage Curve ◽  
Current Voltage ◽  
Current Voltage Curve

This article is a continuation of an earlier article with the same title which extended the analysis of the current-voltage curve of the flame ionization detector near the origin of the curve, in terms of both mobility and diffusion of the flame ions oxonium hydrates. It is shown here that diffusion dominates the current only when the value of the applied voltage is much less than 1 V. The theory of the instrument using only diffusion is given in one, two and three dimensions. Experiments have been performed on a flame ionization detector using applied voltages up to 5 V and the current extrapolated to zero applied voltage. From this value of the current the ionic diffusion coefficient was obtained which agrees with that deduced from the Einstein relation and the measured value of the mobility. The theory also yields a method of obtaining the diffusion coefficient from the slope of the current-voltage curve at the origin but the coefficient so obtained is incorrect because the voltage interval of 1 V is too large and to use the theory successfully would need the region of the current-voltage curve much closer to the origin.

scholarly journals DIFFUSIVE TRANSPORT IN PERIODIC POTENTIALS: UNDERDAMPED DYNAMICS

2008 ◽  
Vol 08 (02) ◽  
pp. L155-L173 ◽  
Author(s):  
G. A. Pavliotis ◽  
A. Vogiannou
Keyword(s):  
Diffusion Coefficient ◽  
Periodic Potential ◽  
Diffusion Tensor ◽  
Brownian Particle ◽  
One Dimension ◽  
Diffusive Transport ◽  
Periodic Potentials ◽  
Arbitrary Dimensions ◽  
Higher Order Corrections ◽  
Rigorous Method

In this paper we present a systematic and rigorous method for calculating the diffusion tensor for a Brownian particle moving in a periodic potential which is valid in arbitrary dimensions and for all values of the dissipation. We use this method to obtain an explicit formula for the diffusion coefficient in one dimension which is valid in the underdamped limit, and we also obtain higher order corrections to the Lifson-Jackson formula for the diffusion coefficient in the overdamped limit. A numerical method for calculating the diffusion coefficient is also developed and is shown to perform extremely well for all values of the dissipation.

Drift velocity for a chain of beads in one dimension

2006 ◽  
Vol 74 (2) ◽  
Author(s):  
G. Terranova ◽  
H. O. Mártin ◽  
C. M. Aldao
Keyword(s):  
Drift Velocity ◽  
One Dimension ◽  
A Chain
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