scholarly journals Electric Double Layer and Orientational Ordering of Water Dipoles in Narrow Channels within a Modified Langevin Poisson-Boltzmann Model

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 1054
Author(s):  
Mitja Drab ◽  
Ekaterina Gongadze ◽  
Veronika Kralj-Iglič ◽  
Aleš Iglič
Keyword(s):  
Charge Density ◽  
Double Layer ◽  
Electric Double Layer ◽  
Energy Functional ◽  
Large Radius ◽  
Charged Surface ◽  
Volume Charge ◽  
Volume Charge Density ◽  
Poisson Boltzmann ◽  
Orientational Ordering

The electric double layer (EDL) is an important phenomenon that arises in systems where a charged surface comes into contact with an electrolyte solution. In this work we describe the generalization of classic Poisson-Boltzmann (PB) theory for point-like ions by taking into account orientational ordering of water molecules. The modified Langevin Poisson-Boltzmann (LPB) model of EDL is derived by minimizing the corresponding Helmholtz free energy functional, which includes also orientational entropy contribution of water dipoles. The formation of EDL is important in many artificial and biological systems bound by a cylindrical geometry. We therefore numerically solve the modified LPB equation in cylindrical coordinates, determining the spatial dependencies of electric potential, relative permittivity and average orientations of water dipoles within charged tubes of different radii. Results show that for tubes of a large radius, macroscopic (net) volume charge density of coions and counterions is zero at the geometrical axis. This is attributed to effective electrolyte charge screening in the vicinity of the inner charged surface of the tube. For tubes of small radii, the screening region extends into the whole inner space of the tube, leading to non-zero net volume charge density and non-zero orientational ordering of water dipoles near the axis.

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.

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.

On the methodology of calculating volume charge density in a MIFGMOS substrate using Poisson’s equation

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Francisco Javier Plascencia Jauregui ◽  
Agustín Santiago Medina Vazquez ◽  
Edwin Christian Becerra Alvarez ◽  
José Manuel Arce Zavala ◽  
Sandra Fabiola Flores Ruiz
Keyword(s):  
Metal Oxide ◽  
Charge Density ◽  
Metal Oxide Semiconductor ◽  
Floating Gate ◽  
Poisson’S Equation ◽  
Oxide Semiconductor ◽  
Volume Charge ◽  
Poisson's Equation ◽  
Content Type ◽  
Volume Charge Density

Purpose This study aims to present a mathematical method based on Poisson’s equation to calculate the voltage and volume charge density formed in the substrate under the floating gate area of a multiple-input floating-gate metal-oxide semiconductor metal-oxide semiconductor (MOS) transistor. Design/methodology/approach Based on this method, the authors calculate electric fields and electric potentials from the charges generated when voltages are applied to the control gates (CG). This technique allows us to consider cases when the floating gate has any trapped charge generated during the manufacturing process. Moreover, the authors introduce a mathematical function to describe the potential behavior through the substrate. From the resultant electric field, the authors compute the volume charge density at different depths. Findings The authors generate some three-dimensional graphics to show the volume charge density behavior, which allows us to predict regions in which the volume charge density tends to increase. This will be determined by the voltages on terminals, which reveal the relationship between CG and volume charge density and will allow us to analyze some superior-order phenomena. Originality/value The procedure presented here and based on coordinates has not been reported before, and it is an aid to generate a model of the device and to build simulation tools in an analog design environment.

Modeling of Electroosmotic Nanoflows With Overlapped Double Layer

2011 ◽  
Author(s):  
Reza Nosrati ◽  
Mehrdad Raisee ◽  
Ahmad Nourbakhsh
Keyword(s):  
Zeta Potential ◽  
Double Layer ◽  
Electric Double Layer ◽  
Potential Distribution ◽  
Present Model ◽  
Ionic Concentration ◽  
Channel Height ◽  
Parabolic Profile ◽  
Poisson Boltzmann ◽  
Volume Method

In the present paper a new model is proposed for electric double layer (EDL) overlapped in nanochannels. The model aimed to obtain a deeper insight of transport phenomena in nanoscale. Two-dimensional Nernst and ionic conservation equations are used to obtain electroosmotic potential distribution in flow field. In the proposed study, transport equations for flow, ionic concentration and electroosmotic potential are solved numerically via finite volume method. Moreover, Debye-Hu¨ckle (DH) approximation and symmetry condition, which limit the application, are avoided. Thus, the present model is suitable for prediction of electroosmotic flows through nanochannels as well as complicated asymmetric geometries with large nonuniform zeta potential distribution. For homogeneous zeta potential distribution, it has been shown that by reduction of channel height to values comparable with EDL thickness, Poisson-Boltzmann model produces inaccurate results and must be avoided. Furthermore, for overlapped electric double layer in nanochannels with heterogeneous zeta potential distribution it has been found that the present model returns modified ionic concentration and electroosmotic potential distribution compare to previous EDL overlapped models due to 2D solution of ionic concentration distribution. Finally, velocity profiles in EDL overlapped nanochannels are investigated and it has been showed that for pure electroosmotic flow the velocity profile deviates from the expected plug-like profile towards a parabolic profile.

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