Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Electrochemical Systems

Electrochemical Systems

Electrochemical systems provide a fascinating insight into the dynamic interplay of charged species within various phases. One notable example is the interaction between a membrane permeable to K⁺ ions but not to Cl⁻ ions, separating an aqueous KCl solution from pure water. As K⁺ ions diffuse through the membrane, they generate net charges on each phase, leading to a potential difference between them.Similarly, when a piece of Zn is immersed in an aqueous ZnSO₄ solution, the Zn metal, composed...

Ionic Crystal Structures

Ionic Crystal Structures

Ionic crystals consist of two or more different kinds of ions that usually have different sizes. The packing of these ions into a crystal structure is more complex than the packing of metal atoms that are the same size.
Most monatomic ions behave as charged spheres, and their attraction for ions of opposite charge is the same in every direction. Consequently, stable structures for ionic compounds result (1) when ions of one charge are surrounded by as many ions as possible of the opposite...

Electric Field of Two Equal and Opposite Charges

Electric Field of Two Equal and Opposite Charges

Atoms generally contain the same number of positively and negatively charged particles, protons, and electrons. Hence, they are electrically neutral. However, the centers of the positive and negative charges do not always coincide. In such a scenario, the electric field of an atom may not be zero.
A separation of the positive and negative charges can lead to a weak, remnant effect of the positive and negative charges. The expectation is that the more the distance between the positive and...

The Electrical Double Layer

The Electrical Double Layer

In the region where two bulk phases meet, an intricate electric charge distribution arises due to charge transfer, ion adsorption, molecular orientation, and charge distortion. This complex distribution is commonly referred to as the electrical double layer.When a solid electrode interfaces with ions in an electrolyte solution, the speed of electron transfer dictates the rates of oxidation and reduction. The electrode acquires a charge through the escape of atoms into the solution as cations or...

Intermolecular Forces

Intermolecular Forces

Atoms and molecules interact through bonds (or forces): intramolecular and intermolecular. The forces are electrostatic as they arise from interactions (attractive or repulsive) between charged species (permanent, partial, or temporary charges) and exist with varying strengths between ions, polar, nonpolar, and neutral molecules. The different types of intermolecular forces are ion–dipole, dipole–dipole, hydrogen bonds, and dispersion; among these, dipole–dipole, hydrogen bonds, and dispersion...

Crystal Field Theory - Tetrahedral and Square Planar Complexes

Crystal Field Theory - Tetrahedral and Square Planar Complexes

Tetrahedral Complexes
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same author

Interplay between an Absorbing Phase Transition and Synchronization in a Driven Granular System.

Physical review letters·2024

Same author

Optimal work in a harmonic trap with bounded stiffness.

Physical review. E·2019

Same author

Planar screening by charge polydisperse counterions.

Journal of physics. Condensed matter : an Institute of Physics journal·2017

Same author

Blast Dynamics in a Dissipative Gas.

Physical review letters·2015

Same author

Memory effect in uniformly heated granular gases.

Physical review. E, Statistical, nonlinear, and soft matter physics·2014

Same author

Kovacs-like memory effect in driven granular gases.

Physical review letters·2014

Search research articles

Related Experiment Video

Updated: Jun 4, 2026

Experimental Methods for Trapping Ions Using Microfabricated Surface Ion Traps

Experimental Methods for Trapping Ions Using Microfabricated Surface Ion Traps

Published on: August 17, 2017

Counter-ions at charged walls: two-dimensional systems.

L Samaj¹, E Trizac

¹Laboratoire de Physique Théorique et Modèles Statistiques, Université Paris-Sud, UMR CNRS 8626, 91405, Orsay, France. Ladislav.Samaj@savba.sk

The European Physical Journal. E, Soft Matter

|March 2, 2011

Summary

This summary is machine-generated.

This study investigates counter-ion behavior in 2D systems, revealing how like-charge attraction emerges at strong coupling. Results show density profile changes and attraction survival at higher coupling constants.

More Related Videos

Picometer-Precision Atomic Position Tracking through Electron Microscopy

Picometer-Precision Atomic Position Tracking through Electron Microscopy

Published on: July 3, 2021

Merging Ion Concentration Polarization between Juxtaposed Ion Exchange Membranes to Block the Propagation of the Polarization Zone

Merging Ion Concentration Polarization between Juxtaposed Ion Exchange Membranes to Block the Propagation of the Polarization Zone

Published on: February 23, 2017

Related Experiment Videos

Last Updated: Jun 4, 2026

Experimental Methods for Trapping Ions Using Microfabricated Surface Ion Traps

Experimental Methods for Trapping Ions Using Microfabricated Surface Ion Traps

Published on: August 17, 2017

Picometer-Precision Atomic Position Tracking through Electron Microscopy

Picometer-Precision Atomic Position Tracking through Electron Microscopy

Published on: July 3, 2021

Merging Ion Concentration Polarization between Juxtaposed Ion Exchange Membranes to Block the Propagation of the Polarization Zone

Merging Ion Concentration Polarization between Juxtaposed Ion Exchange Membranes to Block the Propagation of the Polarization Zone

Published on: February 23, 2017

Area of Science:

Statistical mechanics
Condensed matter physics
Physical chemistry

Background:

Understanding counter-ion behavior is crucial for colloid science and soft matter physics.
Classical Poisson-Boltzmann theory provides a mean-field approximation for charged systems.
Strong coupling regimes often exhibit phenomena not captured by mean-field theories.

Purpose of the Study:

To investigate the equilibrium statistical mechanics of classical point counter-ions in 2D systems.
To compare theoretical predictions from weak-coupling and strong-coupling limits.
To analyze the behavior of density profiles and like-charge attraction at various coupling strengths.

Main Methods:

Formulation on 2D Euclidean space and cylinder surfaces.
Application of weak-coupling Poisson-Boltzmann theory.
Utilizing an exact expansion around the Wigner crystal for strong coupling.
Comparison with exact results from a 1D lattice representation.

Main Results:

Exact solutions for density profiles and pressure at specific coupling constants (β=2, 4, 6).
Observed a fundamental change in density profile decay at β=6 compared to mean-field.
Like-charge attraction persists at β=4 and 6, but is absent at β=2.

Conclusions:

The study provides exact results for 2D Coulomb systems, particularly in the strong coupling regime.
Mean-field theory fails to capture key phenomena like like-charge attraction at higher coupling.
The findings offer insights into the complex behavior of charged particles in reduced dimensions.