Plane-wave approach to the exact van der Waals interaction between colloid particles

Area of Science:

• Physical Chemistry
• Colloid Science
• Computational Physics

Background:

• Calculating van der Waals (Casimir) interactions is computationally demanding.
• Existing multipole basis methods have limitations in accuracy and efficiency.

Purpose of the Study:

• Introduce a novel plane-wave basis approach for numerically exact van der Waals interaction evaluation.
• Investigate the influence of salt concentration and geometry on Casimir interactions.

Main Methods:

• Utilized a plane-wave basis set for interaction calculations.
• Employed discrete Fourier transforms to exploit rotational symmetry in plane-sphere and sphere-sphere geometries.
• Applied the method to polystyrene and mercury colloid systems in aqueous solutions.

Main Results:

• Demonstrated advantages of the plane-wave basis over the multipole basis.
• Quantified significant errors in the proximity force approximation at low salt concentrations.
• Observed repulsive interactions for mercury droplets at larger distances under negligible screening.
• Highlighted the strong dependence of the effective Hamaker parameter on scattering geometry.

Conclusions:

• The plane-wave method offers a more accurate and efficient way to compute Casimir interactions.
• Proximity force approximation inaccuracies are more pronounced than previously thought, particularly in low ionic strength media.
• Scattering geometry is a critical factor influencing the effective Hamaker parameter.