Nonlinear electrostatics: the Poisson–Boltzmann equation

Gray, C.G.; Stiles, Peter J.

doi:10.1088/1361-6404/aaca5a

Cited by 49 publications

(49 citation statements)

References 108 publications

(201 reference statements)

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…5b, respectively. The Debye-Hückel equation was used to describe Debye length: 43 where ε , ε 0 , n bulk , and z were the permittivity of water, the permittivity of a vacuum, the concentration of solution, the valence number, respectively. F , T , and R represented the Faraday’s constant, the absolute temperature, and the universal gas constant, respectively.…”

Section: Resultsmentioning

confidence: 99%

High-performance silk-based hybrid membranes employed for osmotic energy conversion

et al. 2019

View full text Add to dashboard Cite

The salinity gradient between seawater and river water is a clean energy source and an alternative solution for the increasing energy demands. A membrane-based reverse electrodialysis technique is a promising strategy to convert osmotic energy to electricity. To overcome the limits of traditional membranes with low efficiency and high resistance, nanofluidic is an emerging technique to promote osmotic energy harvesting. Here, we engineer a high-performance nanofluidic device with a hybrid membrane composed of a silk nanofibril membrane and an anodic aluminum oxide membrane. The silk nanofibril membrane, as a screening layer with condensed negative surface and nanochannels, dominates the ion transport; the anodic aluminum oxide membrane, as a supporting substrate, offers tunable channels and amphoteric groups. Thus, a nanofluidic membrane with asymmetric geometry and charge polarity is established, showing low resistance, high-performance energy conversion, and long-term stability. The system paves avenues for sustainable power generation, water purification, and desalination.

show abstract

Section: Resultsmentioning

confidence: 99%

High-performance silk-based hybrid membranes employed for osmotic energy conversion

et al. 2019

View full text Add to dashboard Cite

show abstract

“…This implicit treatment of the solvent and electrolyte ions is captured by the Poisson-Boltzmann equation. 45,46 The charge densities due to the two subsystems overlap in an interfacial region and interact not only via mean-field electrostatics but also have cavitation, dispersion and repulsion interactions. The total charge density ρ t (r) can be written as the sum of that due to the quantum subsystem ρ q (r) and the diffuse layer of electrolyte ions ρ d (r).…”

Section: Systemmentioning

confidence: 99%

Electrochemistry from first-principles in the grand canonical ensemble

Bhandari

Peng

Dziedzic

et al. 2021

The Journal of Chemical Physics

View full text Add to dashboard Cite

Progress in electrochemical technologies such as automotive batteries, supercapacitors and fuel cells depends greatly on developing improved charged interfaces between electrodes and electrolytes. The rational development of such interfaces can benefit from the atomistic understanding of the materials involved by first principles quantum mechanical simulations with Density Functional Theory (DFT). However, such simulations are typically performed on the electrode surface in the absence of its electrolyte environment and at constant charge. We have developed a new hybrid computational method combining DFT and the Poisson-Boltzmann equation (P-BE) capable of simulating experimental electrochemistry under potential control, in the presence of solvent and electrolyte. The charged electrode is represented quantum-mechanically via linear-scaling DFT which can model nanoscale systems with thousands of atoms and is neutralized by a counter electrolyte charge via the solution of a modified P-BE.Our approach works with the total free energy of the combined multiscale system in a grand canonical ensemble of electrons subject to a constant electrochemical potential.It is calibrated with respect to the reduction potential of common reference electrodes such as the standard hydrogen electrode and the Li-metal electrode, which is used as a reference electrode in Li-ion batteries. Our new method can be used to predict electrochemical properties under constant potential and we demonstrate this in exemplar simulations of the differential capacitance of few-layer graphene electrodes and the charging of a graphene electrode coupled to a Li metal electrode at different voltages.

show abstract

“…On the other hand, the Boltzmann statistical distribution concerns the probability of finding an ion with a given electrostatic energy (Green, 1956). Therefore, the integration of the two theories in physics leads to the Poisson-Boltzmann Equation (PBE) in its non-linear form (Gray & Stiles, 2018), linearized form (LPB (Hsu & Tseng, 1996) and modified form (MPB) which takes into account the finite size of a molecule /ion (Outhwaite, 1986). Together, they provide a reliable theoretical model for ionic systems and fundamental tools for the industrial applications of such systems.…”

Section: Introductionmentioning

confidence: 99%

Applicability of the Linearized Poisson-Boltzmann Theory to Contact Angle problems and Application to the Carbon Dioxide-Brine-Solid Systems

Amadu

Midanoye

2021

Preprint

View full text Add to dashboard Cite

In colloidal science and bioelectrostatics, the linear Poisson Boltzmann Equation (LPBE) has been used extensively for the calculation of potential and surface charge density. Its fundamental assumption rests on the premises of low surface potential. In the geological sequestration of carbon dioxide in saline aquifers, very low pH conditions coupled with adsorption induced reduction of surface charge density result in low pH conditions that fit into the LPB theory. In this work, the Gouy-Chapman model of the electrical double layer has been employed in addition to the LPBE theory to develop a contact angle model that is a second-degree polynomial in pH. Our model contains the point of zero charge pH of solid surface. To render the model applicable to heterogeneous surfaces, we have further developed a model for the effective value of the point of zero charge pH. The point of zero charge pH model when integrated into our model enabled us to determine the point of zero charge pH of sandstone, quartz and mica using literature based experimental data. In this regard, a literature based thermodynamic model was used to calculate carbon dioxide solubility and pH of aqueous solution. Values of point of zero charge pH determined in this paper agree with reported ones. The novelty of our work stems from the fact that we have used the LPB theory in the context of interfacial science completely different from the classical approach, where the focus is on interparticle electrostatics involving colloidal stabilization.

show abstract

Nonlinear electrostatics: the Poisson–Boltzmann equation

Cited by 49 publications

References 108 publications

High-performance silk-based hybrid membranes employed for osmotic energy conversion

High-performance silk-based hybrid membranes employed for osmotic energy conversion

Electrochemistry from first-principles in the grand canonical ensemble

Applicability of the Linearized Poisson-Boltzmann Theory to Contact Angle problems and Application to the Carbon Dioxide-Brine-Solid Systems

Contact Info

Product

Resources

About