Nonlocal dielectric response of the electrode/solvent interface in the double layer problem

1981 ◽  
Vol 59 (13) ◽  
pp. 2031-2042 ◽  
Author(s):  
A. A. Kornyshev ◽  
M. A. Vorotyntsev
Keyword(s):  
Experimental Data ◽  
Dielectric Function ◽  
Double Layer ◽  
Dielectric Response ◽  
Solvent System ◽  
Differential Capacitance ◽  
General Description ◽  
Compact Layer ◽  
Poisson Boltzmann ◽  
Layer Problem

A theory of the double layer in the electrolyte solution near the electrode surface is formulated in terms of the most general description of the electrode/solvent interface, the ionic plasma being treated in the Poisson–Boltzmann approximation. As a result, the differential capacitance of the electrochemical contact is calculated. In the case of low ionic concentrations [Formula: see text] it takes the form: C−1 = CGC−1 + C*−1, where the CGC is the Gouy–Chapman nonlinear differential capacitance and C* is a "constant" capacitance, not depending on the concentration, but possessing a possible dependence on the charge of the electrode. The "compact layer" capacitance C* is expressed through a unified nonlocal dielectric function of the electrode–solvent system. This may be considered as a formal approval of Grahame's parametrization of experimental data. But the physical meaning of the compact layer capacity is reconsidered subject to the relation obtained with the nonlocal dielectric function. The latter reflects the electronic structure of the metal and the structure of the solvent in contact. Thereby, the possible reasons for the dependence of the "compact layer" capacity on the nature of the electrode, solvent, and the interaction between them are revealed. A generalization of the results on the case of a more general description of ionic plasma is discussed.

A mean spherical approximation study of the capacitance of an electric double layer formed by a high density electrolyte

2010 ◽  
Vol 75 (3) ◽  
pp. 303-312 ◽  
Author(s):  
Douglas Henderson ◽  
Stanisław Lamperski ◽  
Christopher W. Outhwaite ◽  
Lutful Bari Bhuiyan
Keyword(s):  
Double Layer ◽  
Linear Response Theory ◽  
Differential Capacitance ◽  
Double Layers ◽  
Spherical Approximation ◽  
Mean Spherical Approximation ◽  
Simple Extension ◽  
Restricted Primitive Model ◽  
Poisson Boltzmann ◽  
Small Electrode

In a recent grand canonical Monte Carlo simulation and modified Poisson–Boltzmann (MPB) theoretical study of the differential capacitance of a restricted primitive model double layer at high electrolyte densities, Lamperski, Outhwaite and Bhuiyan (J. Phys. Chem. B 2009, 113, 8925) have reported a maximum in the differential capacitance as a function of electrode charge, in contrast to that seen in double layers at lower ionic densities. The venerable Gouy–Chapman–Stern (GCS) theory always yields a minimum and gives values for the capacitance that tend to be too small at these higher densities. In contrast, the mean spherical approximation (MSA) leads to better agreement with the simulation results than does the GCS approximation at higher densities but the agreement is not quite as good as for the MPB approximation. Since the MSA is a linear response theory, it gives predictions only for small electrode charge. Nonetheless, the MSA is of value since it leads to analytic results. A simple extension of the MSA to higher electrode charges would be valuable.

scholarly journals Some Analytic Expressions for the Capacitance and Profiles of the Electric Double Layer Formed by Ions Near an Electrode

2015 ◽  
Vol 43 (2) ◽  
pp. 55-66
Author(s):  
Douglas Henderson
Keyword(s):  
Double Layer ◽  
Electric Double Layer ◽  
Practical Importance ◽  
Differential Capacitance ◽  
Spherical Approximation ◽  
Mean Spherical Approximation ◽  
Low Concentrations ◽  
Analytic Expressions ◽  
Poisson Boltzmann ◽  
High Concentrations

Abstract The electric double layer, which is of practical importance, is described. Two theories that yield analytic results, the venerable Poisson-Boltzmann or Gouy-Chapman-Stern theory and the more recent mean spherical approximation, are discussed. The Gouy-Chapman-Stern theory fails to account for the size of the ions nor for correlations amoung the ions. The mean spherical approximation overcomes, to some extent, these deficiencies but is applicable only for small electrode charge. A hybrid description that overcomes some of these problems is presented. While not perfect, it gives results for the differential capacitance that are typical of those of an ionic liquid. In particular, the differential capacitance can pass from having a double hump at low concentrations to a single hump at high concentrations.

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.

Beyond Poisson–Boltzmann: Images and correlations in the electric double layer. II. Symmetric electrolyte

1988 ◽  
Vol 89 (7) ◽  
pp. 4358-4367 ◽  
Author(s):  
Phil Attard ◽  
D. John Mitchell ◽  
Barry W. Ninham
Keyword(s):  
Double Layer ◽  
Electric Double Layer ◽  
Poisson Boltzmann

Influence of a size asymmetric dimer on the structure and differential capacitance of an electric double layer. A Monte Carlo study

2017 ◽  
Vol 226 ◽  
pp. 98-103 ◽  
Author(s):  
Stanisław Lamperski ◽  
Lutful Bari Bhuiyan ◽  
Douglas Henderson ◽  
Monika Kaja ◽  
Whasington Silvestre-Alcantara
Keyword(s):  
Monte Carlo ◽  
Double Layer ◽  
Electric Double Layer ◽  
Monte Carlo Study ◽  
Differential Capacitance ◽  
Asymmetric Dimer

Electric condensation of divalent counterions by humic acid nanoparticles

2016 ◽  
Vol 13 (1) ◽  
pp. 76 ◽  
Author(s):  
Herman P. van Leeuwen ◽  
Raewyn M. Town
Keyword(s):  
Humic Acid ◽  
Charge Density ◽  
Double Layer ◽  
Ion Pairs ◽  
Ion Pairing ◽  
Counterion Condensation ◽  
Counterion Binding ◽  
Satisfactory Description ◽  
Poisson Boltzmann ◽  
Very High

Environmental context Humic acids are negatively charged soft nanoparticles that play a governing role in the speciation of many ionic and molecular compounds in the environment. The charge density in the humic acid nanoparticle can be very high and the binding of divalent cations such as Ca2+ appears to go far beyond traditional ion pairing or Poisson–Boltzmann electrostatics. A two-state approach, combining counterion condensation in the intraparticulate double layer and classical Donnan partitioning in the bulk of the particle, provides a satisfactory description of the physicochemical speciation. Abstract Experimental data for divalent counterion binding by soil humic acid nanoparticles are set against ion distributions as ensuing from continuous Poisson–Boltzmann electrostatics and a two-state condensation approach. The results demonstrate that Poisson–Boltzmann massively underestimates the extent of binding of Ca2+ by humic acid, and that electric condensation of these counterions within the soft nanoparticulate body must be involved. The measured stability of the Ca2+–humic acid associate is also much greater than that predicted for ion pairing between single Ca2+ ions and monovalent negative humic acid sites, which also points to extensive electrostatic cooperativity within the humic acid particle. At sufficiently high pH, the charge density inside the humic acid entity may indeed become so high that the bulk particle attains a very high and practically flat potential profile throughout. At this limit, all the intraparticulate Ca2+ is at approximately the same electrostatic potential and the status of individual ion pairs has become immaterial. A two-state model, combining counterion condensation in the charged intraparticulate part of the double layer at the particle–medium interface and Donnan partitioning in the uncharged bulk of the humic acid particle, seems to lead the way to adequate modelling of the divalent counterion binding for various particle sizes and different ionic strengths.

High-frequency ventilation

1984 ◽  
Vol 64 (2) ◽  
pp. 505-543 ◽  
Author(s):  
J. M. Drazen ◽  
R. D. Kamm ◽  
A. S. Slutsky
Keyword(s):  
Experimental Data ◽  
Gas Exchange ◽  
Dead Space ◽  
Gas Transport ◽  
Physical Models ◽  
High Frequency Ventilation ◽  
General Description ◽  
Wide Range ◽  
Dead Space Volume ◽  
Space Volume

Complete physiological understanding of HFV requires knowledge of four general classes of information: 1) the distribution of airflow within the lung over a wide range of frequencies and VT (sect. IVA), 2) an understanding of the basic mechanisms whereby the local airflows lead to gas transport (sect. IVB), 3) a computational or theoretical model in which transport mechanisms are cast in such a form that they can be used to predict overall gas transport rates (sect. IVC), and 4) an experimental data base (sect. VI) that can be compared to model predictions. When compared with available experimental data, it becomes clear that none of the proposed models adequately describes all the experimental findings. Although the model of Kamm et al. is the only one capable of simulating the transition from small to large VT (as compared to dead-space volume), it fails to predict the gas transport observed experimentally with VT less than equipment dead space. The Fredberg model is not capable of predicting the observed tendency for VT to be a more important determinant of gas exchange than is frequency. The remaining models predict a greater influence of VT than frequency on gas transport (consistent with experimental observations) but in their current form cannot simulate the additional gas exchange associated with VT in excess of the dead-space volume nor the decreased efficacy of HFV above certain critical frequencies observed in both animals and humans. Thus all of these models are probably inadequate in detail. One important aspect of these various models is that some are based on transport experiments done in appropriately scaled physical models, whereas others are entirely theoretical. The experimental models are probably most useful in the prediction of pulmonary gas transport rates, whereas the physical models are of greater value in identifying the specific transport mechanism(s) responsible for gas exchange. However, both classes require a knowledge of the factors governing the distribution of airflow under the circumstances of study as well as requiring detail about lung anatomy and airway physical properties. Only when such factors are fully understood and incorporated into a general description of gas exchange by HFV will it be possible to predict or explain all experimental or clinical findings.

Erratum: Beyond Poisson–Boltzmann: Images and correlations in the electric double layer. I. Counterions only [J. Chem. Phys. 88, 4987 (1988)]

1990 ◽  
Vol 92 (5) ◽  
pp. 3248-3248 ◽  
Author(s):  
Phil Attard ◽  
D. John Mitchell ◽  
Barry W. Ninham
Keyword(s):  
Double Layer ◽  
Electric Double Layer ◽  
Chem Phys ◽  
Poisson Boltzmann ◽  
Layer I

scholarly journals Jonscher indices for dielectric materials

2019 ◽  
Vol 09 (06) ◽  
pp. 1950046
Author(s):  
C. L. Wang
Keyword(s):  
Experimental Data ◽  
Asymptotic Behavior ◽  
Dielectric Relaxation ◽  
Time Domain ◽  
Dielectric Response ◽  
Relaxation Function ◽  
Dielectric Materials ◽  
Dielectric Response Function ◽  
Barium Stannate ◽  
Two Parameters

Two parameters are proposed as Jonscher indices, named after A. K. Jonscher for his pioneering contribution to the universal dielectric relaxation law. Time domain universal dielectric relaxation law is then obtained from the asymptotic behavior of dielectric response function and relaxation function by replacing parameters in Mittag–Leffler functions with Jonscher indices. Relaxation types can be easily determined from experimental data of discharge current in barium stannate titanate after their Jonscher indices are determined.

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