scholarly journals Extended Poisson–Boltzmann Descriptions of the Electrostatic Double Layer: Implications for Charged Particles at Interfaces

2014 ◽  
pp. 45-56
Keyword(s):  
Double Layer ◽  
Charged Particles ◽  
Electrostatic Double Layer ◽  
Poisson Boltzmann

scholarly journals Lateral capillary interactions between colloids beneath an oil–water interface that are driven by out-of-plane electrostatic double-layer interactions

Soft Matter ◽  
2015 ◽  
Vol 11 (44) ◽  
pp. 8701-8706 ◽  
Author(s):  
Bum Jun Park ◽  
Mina Lee ◽  
Bomsock Lee ◽  
Eric M. Furst
Keyword(s):  
Double Layer ◽  
Charged Particles ◽  
Colloidal Crystals ◽  
Disjoining Pressure ◽  
Water Interface ◽  
Two Dimensional ◽  
Electrostatic Double Layer ◽  
Out Of Plane ◽  
Capillary Interactions ◽  
Oil Water

The electrostatic disjoining pressure between charged particles and a charged oil–water interface generates lateral capillary attractions between adjacent particles beneath the interface, which consequently lead to closely packed, two-dimensional colloidal crystals.

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.

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