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Analytical approach for collective diffusion: One-dimensional heterogeneous lattice.

Alexander Tarasenko1

  • 1Institute of Physics, Academy of Sciences of the Czech Republic, v.v.i., Na Slovance 2, 18221 Prague 8, Czech Republic.

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This study investigates particle diffusion on heterogeneous chains using theoretical and Monte Carlo methods. Analytical and simulation results show excellent agreement, validating the approach for lattice gas systems.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Computational Chemistry

Background:

  • Particle diffusion on surfaces is crucial in many physical and chemical processes.
  • Heterogeneous surfaces introduce complexities in diffusion dynamics.
  • Understanding diffusion mechanisms is key to controlling surface phenomena.

Purpose of the Study:

  • To investigate particle diffusion on heterogeneous chains.
  • To derive analytical expressions for diffusion coefficients.
  • To validate a theoretical approach against simulation data.

Main Methods:

  • Theoretical approach based on the non-equilibrium statistical operator theory.
  • Kinetic Monte Carlo simulations.
  • Calculation of concentration dependencies for diffusion coefficients.

Main Results:

  • Analytical expressions for diffusion coefficients were derived.
  • Concentration dependencies of center-of-mass and Fickian diffusion coefficients were calculated.
  • Excellent agreement was found between analytical predictions and Monte Carlo simulation results.

Conclusions:

  • The theoretical approach is highly effective for studying particle migration in lattice gas systems.
  • The study validates the applicability of non-equilibrium statistical operator theory for heterogeneous diffusion.
  • This work provides a robust method for analyzing diffusion on complex surfaces.