Boundary homogenization for patchy surfaces trapping patchy particles.

Area of Science:

• Chemical Physics
• Biological Physics
• Statistical Mechanics

Background:

• Particle-surface interactions are crucial in chemical and biological systems.
• Previous theories addressed uniform reactivity or patchy surfaces/particles, but not both.
• Accurate trapping rate estimation is vital for understanding complex physical processes.

Purpose of the Study:

• To develop a theoretical framework for estimating trapping rates when both particles and surfaces possess reactive patches.
• To investigate the influence of translational and rotational diffusion on trapping dynamics.
• To validate theoretical predictions with computational simulations.

Main Methods:

• Formulation of a stochastic model and derivation of a five-dimensional partial differential equation.
• Application of matched asymptotic analysis to determine the effective trapping rate.
• Computation of electrostatic capacitance using a kinetic Monte Carlo algorithm.
• Utilizing Brownian local time theory for heuristic trapping rate estimation.

Main Results:

• The effective trapping rate depends on the electrostatic capacitance of a four-dimensional duocylinder.
• A simple heuristic estimate closely matches the asymptotic result.
• Kinetic Monte Carlo simulations confirm the accuracy of the derived trapping rate and homogenization theory.

Conclusions:

• The developed theory provides an accurate method for estimating trapping rates in systems with dual patchy reactivity.
• The findings advance the understanding of diffusive particle interactions at surfaces.
• This work offers a robust framework for future studies in related physical and biological phenomena.