A Feynman Path Integral-like Method for Deriving Reaction-Diffusion Equations.

Area of Science:

• Chemical Physics
• Theoretical Chemistry
• Statistical Mechanics

Background:

• Classical reaction-diffusion equations are fundamental in describing chemical kinetics and spatial patterns.
• Microscopic details and intermolecular interactions can significantly alter macroscopic reaction-diffusion dynamics.
• Existing models may not fully capture the interplay between diffusion and reaction, especially in complex systems.

Purpose of the Study:

• To derive a more accurate reaction-diffusion equation for binary systems by considering microscopic trajectories.
• To introduce a novel diagrammatic approach, diffusion-reaction-diffusion (DRD) diagrams, for deriving dynamical equations.
• To investigate the impact of intermolecular interactions on reaction-diffusion dynamics.

Main Methods:

• Summing over microscopic trajectories to derive macroscopic equations.
• Development and application of diffusion-reaction-diffusion (DRD) diagrams, analogous to Feynman diagrams.
• Analysis of the derived equation under conditions with and without intermolecular interactions.

Main Results:

• The newly derived reaction-diffusion equation reduces to the classical form when there are no intermolecular interactions.
• Intermolecular interactions introduce coupling terms between diffusion and reaction, observable at the mesoscopic scale.
• The DRD diagram method is applicable to complex systems like polymerizations.

Conclusions:

• The DRD diagram method provides a more accurate description of reaction-diffusion processes, particularly when intermolecular interactions are present.
• Coupling between diffusion and reaction is a significant factor on the mesoscopic scale due to intermolecular interactions.
• This approach offers a powerful tool for studying chemical reactions in polymeric and other complex systems.