Finite thickness and charge relaxation in double-layer interactions

Area of Science:

• Colloid and Interface Science
• Physical Chemistry
• Computational Physics

Background:

• The classical Gouy-Chapman model approximates colloidal particle interactions using semi-infinite double layers.
• This model provides a foundational understanding but neglects the finite size of colloidal particles.

Purpose of the Study:

• To extend the Gouy-Chapman model by incorporating finite colloid thickness.
• To investigate the impact of finite size on colloidal interaction forces and related properties.
• To analyze charge redistribution on finite colloids and its effect on interactions.

Main Methods:

• Utilized a mean-field approach based on the Poisson-Boltzmann (PB) equation.
• Derived a closed-form solution for the interaction force in finite-size colloids.
• Employed a density functional theory derived from the PB equation to study charge relaxation.

Main Results:

• Developed a modified interaction force model accounting for finite colloid thickness and additional double layers.
• Demonstrated recovery of Debye-Hückel theory and semi-infinite colloid results in appropriate limits.
• Showed that fixed total colloidal charge redistributes to minimize system energy, influencing interactions.

Conclusions:

• Finite colloid geometry significantly modifies interaction forces beyond the classical Gouy-Chapman approximation.
• The derived PB model offers a more accurate description for finite-sized colloidal systems.
• Charge relaxation is a critical factor affecting colloidal interactions in finite-sized systems.