Analytical approach for collective diffusion: one-dimensional homogeneous lattice

Area of Science:

• Physics
• Physical Chemistry
• Materials Science

Background:

• Understanding particle diffusion on surfaces is crucial for catalysis and materials science.
• Lattice gas models are widely used to study adsorbed particle behavior.

Purpose of the Study:

• To investigate particle diffusion on a homogeneous one-dimensional chain.
• To compare theoretical predictions with simulation results for diffusion coefficients.

Main Methods:

• Theoretical approach using the non-equilibrium statistical operator.
• Kinetic Monte Carlo simulations.
• Calculation of concentration-dependent diffusion coefficients.

Main Results:

• Concentration dependencies of center-of-mass and Fickian diffusion coefficients were calculated.
• Analytical results showed perfect agreement with numerical simulation data.
• Lateral interactions between adsorbed particles were considered.

Conclusions:

• The analytical expressions derived from the non-equilibrium statistical operator approach accurately describe particle migration in lattice gas systems.
• The study validates theoretical models for diffusion on one-dimensional surfaces.