Using Brownian model to study the effect of temperature on diffusion coefficient

Abstract

This study employs molecular simulation techniques, particularly the Brownian motion model, to investigate the influence of temperature on diffusion coefficients. Leveraging Einsteins relationship for calculating diffusion coefficients and a one-dimensional random walk model, we systematically explore the impact of simulation direction, particle quantity, and simulation duration on diffusion behavior. The research extends its scope to three-dimensional Brownian motion simulations, offering insights into the stochastic motion of particles in a fluid. The primary objective is to analyze the relationship between temperature and diffusion coefficients. Through rigorous linear regression analysis, a significant and strong linear association is identified, demonstrating that an increase in temperature correlates with an increase in the diffusion coefficient. The research not only contributes to the fundamental understanding of molecular motion but also provides practical recommendations for simulation parameters, especially in resource-constrained computational environments. The study acknowledges certain limitations in the current Brownian motion algorithm and proposes avenues for future research to enhance computational efficiency and precision. This abstract encapsulates the key methodologies, findings, and implications of the research, laying the foundation for a comprehensive exploration of temperature-dependent diffusion coefficients in molecular systems.