Capturing Brownian dynamics with an on-lattice model of hard-sphere diffusion

Area of Science:

• Physical Chemistry
• Computational Chemistry
• Statistical Mechanics

Background:

• Conventional master equations model molecular diffusion using lattice-based particle hopping.
• These models often assume constant hopping probabilities, neglecting molecular volume-exclusion effects.
• Existing methods to incorporate volume-exclusion effects are limited.

Purpose of the Study:

• To develop an improved master equation for molecular diffusion that accounts for finite particle size.
• To investigate the impact of nonlinear hopping probabilities on diffusion dynamics.
• To validate the new model against established simulation techniques.

Main Methods:

• Formulation of a new master equation with hopping probabilities based on available space (Scaled Particle Theory).
• Development of a mean-field approximation (MFA) leading to an advection-diffusion partial differential equation.
• Comparison with stochastic simulation algorithm (SSA) results and Brownian dynamics (BD).

Main Results:

• The new master equation and its MFA show good agreement with SSA and lattice-free Brownian dynamics.
• The model accurately captures diffusion dynamics in highly crowded systems.
• Results differ significantly from conventional master equations and those with linear density-dependent hopping.

Conclusions:

• The proposed master equation offers a more accurate description of molecular diffusion, especially in crowded systems.
• Incorporating nonlinear, density-dependent hopping probabilities is crucial for realistic diffusion modeling.
• This approach provides a robust and accurate lattice-based method for simulating diffusion with volume-exclusion effects.