Communication: relative diffusion in two dimensions: breakdown of the standard diffusive model for simple liquids

Area of Science:

• Soft matter physics
• Computational physics

Background:

• Diffusion is a fundamental process in physical and chemical systems.
• Understanding diffusion in different dimensions is crucial for modeling various phenomena.

Purpose of the Study:

• To analyze the relative diffusion constant (DΣn(r)) and self-diffusion constant (Dn) in two (n=2) and three (n=3) dimensions using molecular dynamics simulations.
• To investigate the system size dependence of diffusion constants under periodic boundary conditions.
• To evaluate the applicability of the standard Smoluchowski model assumption (DΣn(r) ≈ 2Dn) in different dimensions.

Main Methods:

• Molecular dynamics simulations of identical soft spheres.
• Analysis of relative diffusion constant DΣn(r) and self-diffusion constant Dn.
• Varying interparticle distance (r) and system size (L).

Main Results:

• Self-diffusion constant (Dn) is a function of system size (L) in both 2D and 3D.
• The relation DΣn(r = L/2) ≅ 2Dn(L) holds for both n=2 and n=3.
• In 2D, diffusion constants increase logarithmically with their argument, but are highly sensitive to perturbations, limiting their growth in large systems.
• The standard Smoluchowski assumption (DΣn(r) ≈ 2Dn) leads to significant errors for n=2.

Conclusions:

• The system size dependence of diffusion constants must be considered, especially in 2D.
• The commonly used Smoluchowski model assumption is not universally applicable and can lead to substantial inaccuracies in two-dimensional systems.
• Further research is needed to develop more accurate models for diffusion in low-dimensional systems.