Collective diffusion in two-dimensional systems: exact analysis based on the kinetic lattice gas model

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Surface Science

Background:

• Understanding particle diffusion is crucial for materials science and chemistry.
• Existing models often simplify particle interactions, limiting their applicability.
• The Reed-Ehrlich factorization is a common but potentially inaccurate assumption.

Purpose of the Study:

• Derive an exact analytical expression for diffusivity.
• Investigate density and temperature dependence of particle diffusion.
• Examine the impact of lateral interactions and external fields on diffusion.

Main Methods:

• Gradient expansion of local microscopic particle current.
• Transfer matrix methods for correlation functions on a rectangular lattice.
• Generalization to adsorbates with lateral interactions and external fields.

Main Results:

• An exact analytical expression for diffusivity was derived.
• The density and temperature dependence of diffusivity was determined.
• The limitations of the Reed-Ehrlich factorization were demonstrated for complex interactions.

Conclusions:

• The derived expression provides a more accurate model for diffusivity.
• Generalized hopping kinetics significantly influence particle diffusion.
• Assumptions like Reed-Ehrlich factorization may fail under certain interaction conditions.