Modified Linearized Poisson-Boltzmann Theory. Dynamic and Thermodynamic Properties of 1 : 1 Electrolytes

2000 ◽  
Vol 53 (12) ◽  
pp. 989
Author(s):  
Tuncer Kaya
Keyword(s):  
Distribution Function ◽  
Short Range ◽  
Pair Potential ◽  
Boltzmann Distribution ◽  
Size Parameter ◽  
Moment Conditions ◽  
Poisson Boltzmann ◽  
Short Range Part ◽  
Ion Size ◽  
Range Part

Theoretical electrolyte conductivity and osmotic and activity coefficient relationships that work well over a large range of concentrations, up to 1 mol l–1, are derived from a hypothetical modified linearized Poisson–Boltzmann distribution function. The distribution function is expressed in terms of modified Debye parameter κ and normalization constant α. Both of these parameters are evaluated in terms of concentration and ion-size parameter, d, by the help of moment conditions. The modified Debye parameter κ is also expressed as a function of the usual Debye parameter κD. Also considered is the short-range part of the pair potential crucial to obtain at least qualitative agreement with experimental results of electrolytic solutions, and it is assumed that the short-range part of the potential is discontinuous at ion-size parameter

scholarly journals Долинно-орбитальное взаимодействие в германии, легированном донорами V группы: количественный анализ

2021 ◽  
Vol 55 (10) ◽  
pp. 901
Author(s):  
А.А. Ревин ◽  
А.М. Михайлова ◽  
А.А. Конаков ◽  
В.В. Цыпленков ◽  
В.Н. Шастин
Keyword(s):  
Short Range ◽  
Ritz Method ◽  
Orbit Interaction ◽  
Envelope Function ◽  
Triplet States ◽  
Short Range Potential ◽  
Singlet And Triplet States ◽  
Short Range Part ◽  
Range Part ◽  
Envelope Functions

In the framework of the envelope function approximation, the wave functions of electrons localized at shallow donors P, As, Sb in Ge are calculated taking into account the valley-orbit coupling caused by the donor short-range potential. It is proposed an approach that makes it possible to include inter-valley mixing in the equation for a multi-component envelope function. The calculation of the effects of the valley-orbit interaction was carried out according to the perturbation theory, while the "bare" single-valley functions were found using the Ritz method. The parameters of the short-range part of the potential and the coefficient of inter-valley mixing were found individually for each donor, making it possible to obtain the best agreement with the results of experimental measurements of the energies of the singlet and triplet states. The envelope functions of the 1s(A1) and 1s(T2) states are calculated. The parameters of the valley-orbit interaction are found for each donor. It is also shown how the functions of the excited 2s, 2p0, 2p±, 3p0 states should be modified in order to remain orthogonal to the singlet and triplet functions within the framework of a more rigorous multivalley model.

On the K-dependence of the electrical field in a crystalline slab of oscillating charges

1981 ◽  
Vol 59 (7) ◽  
pp. 929-933 ◽  
Author(s):  
J. Grindlay
Keyword(s):  
Electric Field ◽  
Trigonometric Series ◽  
Wave Vector ◽  
Short Range ◽  
Electrical Field ◽  
Ewald Sum ◽  
Convergent Trigonometric Series ◽  
Short Range Part ◽  
Range Part

The short range part of the electric field of a crystalline slab array of oscillating charges (a) is related to the Ewald sum and (b) can be represented by a rapidly convergent trigonometric series involving the wave vector K. Values for the coefficients of the first few terms of this series are reported for lattice sites in the sc, fcc, bcc, NaCl, CsCl structures and the symmetry directions (1,0,0), (1,1,0), (1,1,1).

Extended excluded volume: Its origin and consequences

2012 ◽  
Vol 85 (1) ◽  
pp. 201-210 ◽  
Author(s):  
Ivo Nezbeda ◽  
Michael Rouha
Keyword(s):  
Short Range ◽  
Infinite Dilution ◽  
Structural Data ◽  
Excluded Volume ◽  
Mechanical Approach ◽  
Short Range Part ◽  
Statistical Mechanical ◽  
The Common ◽  
Nonpolar Fluids ◽  
Range Part

In contrast to the common intuitive/speculative approach based on an analysis of thermodynamic or structural data of (nonpolar) fluids, the statistical mechanical approach is used to extend the excluded volume concept to all other types of fluids. The (extended) excluded volume incorporates, in addition to common nonelectrostatic interactions defining the shape and size of the molecules, also the short-range part of the repulsive interactions between the embedded Coulombic sites. In this study we show that the extended excluded volume concept correctly predicts the behavior of the partial molar volume (PMV) at infinite dilution in different solvents and, particularly, differences between nonpolar and associating solvents. The concept is then applied to estimate the PMV of methanol in water.

scholarly journals Review and Modification of Entropy Modeling for Steric Effects in the Poisson-Boltzmann Equation

Entropy ◽  
2020 ◽  
Vol 22 (6) ◽  
pp. 632
Author(s):  
Tzyy-Leng Horng
Keyword(s):  
Free Energy ◽  
Lattice Gas ◽  
Steric Effect ◽  
Mean Field ◽  
Boltzmann Distribution ◽  
Experimental Conditions ◽  
Ion Concentrations ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation ◽  
Ion Size

The classical Poisson-Boltzmann model can only work when ion concentrations are very dilute, which often does not match the experimental conditions. Researchers have been working on the modification of the model to include the steric effect of ions, which is non-negligible when the ion concentrations are not dilute. Generally the steric effect was modeled to correct the Helmholtz free energy either through its internal energy or entropy, and an overview is given here. The Bikerman model, based on adding solvent entropy to the free energy through the concept of volume exclusion, is a rather popular steric-effect model nowadays. However, ion sizes are treated as identical in the Bikerman model, making an extension of the Bikerman model to include specific ion sizes desirable. Directly replacing the ions of non-specific size by specific ones in the model seems natural and has been accepted by many researchers in this field. However, this straightforward modification does not have a free energy formula to support it. Here modifications of the Bikerman model to include specific ion sizes have been developed iteratively, and such a model is achieved with a guarantee that: (1) it can approach Boltzmann distribution at diluteness; (2) it can reach saturation limit as the reciprocal of specific ion size under extreme electrostatic conditions; (3) its entropy can be derived by mean-field lattice gas model.

scholarly journals A superformula for neutrinoless double beta decay II: the short range part

2001 ◽  
Vol 498 (1-2) ◽  
pp. 35-39 ◽  
Author(s):  
H. Päs ◽  
M. Hirsch ◽  
H.V. Klapdor-Kleingrothaus ◽  
S.G. Kovalenko
Keyword(s):  
Beta Decay ◽  
Short Range ◽  
Neutrinoless Double Beta Decay ◽  
Double Beta Decay ◽  
Short Range Part ◽  
Range Part
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