Osmotic pressure between arbitrarily charged planar surfaces: A revisited approach

Area of Science:

• Physical Chemistry
• Colloid and Surface Science
• Electrochemistry

Background:

• The Poisson-Boltzmann framework is commonly used to study ionic solutions between charged surfaces, typically involving solving coupled equations for electrostatic potential and osmotic pressure.
• Existing methods often rely on symmetry arguments and are limited to equally or oppositely charged surfaces.
• Calculating osmotic pressure usually requires determining the electrostatic potential profile, which can be computationally intensive.

Purpose of the Study:

• To develop a more efficient and direct scheme for deriving osmotic pressure between charged surfaces.
• To provide analytical expressions for osmotic pressure that are independent of the electrostatic potential profile.
• To extend the applicability of the method to arbitrary boundary conditions and generalized Poisson-Boltzmann theories.

Main Methods:

• Derivation of analytical expressions for osmotic pressure based on inter-surface separation, salt concentration, and boundary conditions.
• Development of a straightforward calculation scheme that bypasses the need to solve for the electrostatic potential.
• Demonstration of the method's applicability to generalized Poisson-Boltzmann theories, including the sterically modified version.

Main Results:

• Successful derivation of analytical expressions for osmotic pressure.
• The new method eliminates the need for solving coupled differential equations for electrostatic potential.
• The approach is shown to be effective for planar geometries and adaptable to advanced theories like the sterically modified Poisson-Boltzmann theory.

Conclusions:

• The proposed method offers a more efficient alternative for calculating osmotic pressure in ionic solutions between charged surfaces.
• The analytical expressions are versatile, accommodating various surface charge conditions and salt concentrations.
• This technique is valuable for applications in force measurement setups involving differently prepared or potentiostatically controlled surfaces.