Transverse Density Fluctuations around the Ground State Distribution of Counterions near One Charged Plate:...

Area of Science:

• Statistical Mechanics
• Soft Matter Physics
• Physical Chemistry

Background:

• The Dean-Kawasaki (DK) equation models overdamped Brownian particles, forming the foundation of stochastic density functional theory.
• The linearized DK equation has previously validated Onsager theory for symmetric electrolyte conductivity.

Purpose of the Study:

• To investigate density fluctuations and transverse dynamics of strongly coupled counterions near a charged plate using the linear DK equation.
• To identify characteristic length scales governing counterion dynamics in this confined system.

Main Methods:

• Application of the linear Dean-Kawasaki equation to analyze counterion density fluctuations.
• Focus on transverse dynamics along the charged plate surface.
• Comparison of derived crossover length with the Wigner-Seitz radius from 2D plasma theory.

Main Results:

• A crossover scale in transverse counterion dynamics was identified.
• Above this scale, dynamics appear frozen; below it, diffusive behavior is observed.
• The characteristic crossover length is analogous to the Wigner-Seitz radius in 2D equilibrium plasma theory.

Conclusions:

• The linear DK equation successfully characterizes a dynamical crossover for counterions near a charged plate.
• The findings provide a new perspective on equilibrium and non-equilibrium phenomena in confined ionic systems.
• Further investigation into longitudinal dynamics, including advective and electrical reverse-flows, is warranted.