Repulsion Between Finite Charged Plates with Strongly Overlapped Electric Double Layers

Area of Science:

• Colloid and Surface Science
• Physical Chemistry
• Electrochemistry

Background:

• Screened Coulomb interactions govern forces between charged surfaces in electrolytes.
• At small separations, Debye layers overlap, significantly influencing inter-plate forces.
• Finite object size introduces edge effects not present in infinite systems.

Purpose of the Study:

• To analytically investigate the impact of finite plate length on disjoining pressure.
• To quantify how edge effects modify screened Coulomb interactions.
• To explore the generalizability of these findings to other charged objects near the Debye scale.

Main Methods:

• Analytical calculation of disjoining pressure for uniformly charged flat plates.
• Consideration of systems with finite plate lengths and edge effects.
• Development of a 2D model problem for tractable analytical solutions.

Main Results:

• Disjoining pressure decays as an inverse power of separation for infinite plates.
• For finite plates, screening charges spill out from edges, altering pressure.
• Force reduction (uniform charge density) or increase (constant potential) observed due to edge corrections.

Conclusions:

• Finite size and edge effects are crucial for accurate disjoining pressure calculations.
• The loss of lateral confinement of Debye layers impacts interactions significantly.
• These findings apply broadly to charged objects interacting at the Debye scale.