A Simple Statistical Mechanical Approach to the free Energy of the Electric Double Layer Including the Excluded Volume Effect

1996 ◽  
Vol 6 (4) ◽  
pp. 477-491 ◽  
Author(s):  
Veronika Kralj-Igli? ◽  
Ale? Igli?
Keyword(s):  
Free Energy ◽  
Double Layer ◽  
Electric Double Layer ◽  
Volume Effect ◽  
Excluded Volume ◽  
Excluded Volume Effect ◽  
Mechanical Approach ◽  
Statistical Mechanical

scholarly journals Debye-Hückel Free Energy of an Electric Double Layer with Discrete Charges Located at a Dielectric Interface

Membranes ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 129
Author(s):  
Guilherme Volpe Bossa ◽  
Sylvio May
Keyword(s):  
Free Energy ◽  
Double Layer ◽  
Electric Double Layer ◽  
Low Dielectric Constant ◽  
Surface Charges ◽  
Dielectric Interface ◽  
Charge Densities ◽  
Low Dielectric ◽  
Poisson Boltzmann ◽  
The Continuum

Poisson–Boltzmann theory provides an established framework to calculate properties and free energies of an electric double layer, especially for simple geometries and interfaces that carry continuous charge densities. At sufficiently small length scales, however, the discreteness of the surface charges cannot be neglected. We consider a planar dielectric interface that separates a salt-containing aqueous phase from a medium of low dielectric constant and carries discrete surface charges of fixed density. Within the linear Debye-Hückel limit of Poisson–Boltzmann theory, we calculate the surface potential inside a Wigner–Seitz cell that is produced by all surface charges outside the cell using a Fourier-Bessel series and a Hankel transformation. From the surface potential, we obtain the Debye-Hückel free energy of the electric double layer, which we compare with the corresponding expression in the continuum limit. Differences arise for sufficiently small charge densities, where we show that the dominating interaction is dipolar, arising from the dipoles formed by the surface charges and associated counterions. This interaction propagates through the medium of a low dielectric constant and alters the continuum power of two dependence of the free energy on the surface charge density to a power of 2.5 law.

scholarly journals Excluded volume effect enhances the homology pairing of model chromosomes

2016 ◽  
Vol 7 (2) ◽  
pp. 66-75 ◽  
Author(s):  
Kazunori Takamiya ◽  
Keisuke Yamamoto ◽  
Shuhei Isami ◽  
Hiraku Nishimori ◽  
Akinori Awazu
Keyword(s):  
Volume Effect ◽  
Excluded Volume ◽  
Excluded Volume Effect

Excluded volume effect for the nuclear matter equation of state

1991 ◽  
Vol 51 (3) ◽  
pp. 485-489 ◽  
Author(s):  
D. H. Rischke ◽  
M. I. Gorenstein ◽  
H. St�cker ◽  
W. Greiner
Keyword(s):  
Equation Of State ◽  
Nuclear Matter ◽  
Volume Effect ◽  
Excluded Volume ◽  
Excluded Volume Effect

The effect of excluded volume on polymer dispersant action

1975 ◽  
Vol 343 (1635) ◽  
pp. 427-442 ◽  
Keyword(s):  
Free Energy ◽  
High Surface ◽  
Volume Effect ◽  
Polymer Chains ◽  
Excluded Volume ◽  
Density Distributions ◽  
Excluded Volume Effects ◽  
Adsorbed Polymer ◽  
Polymer Distribution ◽  
Dimensional Equation

Polymer-stabilized colloid particles are modelled theoretically by plane surfaces on to which polymer chains are adsorbed by one end only. Interactions between segments of the polymer are treated as an excluded volume effect. It is shown that for high surface densities the polymer distribution function exactly satisfies a one dimensional equation which is solved numerically for two values of excluded volume to give the polymer segment density distributions and the free energy of interaction for various separations of the plane surfaces. It is found that a positive value of excluded volume greatly increases the repulsive free energy compared with that for chains with zero excluded volume, particularly at large separation distances of the surfaces. Excluded volume effects must therefore play an important part in the stabilization of colloids by adsorbed polymer.

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