From mesoscopic to macroscopic models of reactive Brownian nanoparticles.

We develop a quantitative connection between mesoscopic simulations and macroscopic kinetic descriptions for reactive nanoparticle solutions. In concentrated solutions, effective forces, such as electrostatic or van der Waals interactions, modify local concentration profiles around each reactant, their encounter frequencies, and activation free energies. While microscopic simulations provide atomistic insight and macroscopic kinetic theories describe bulk behavior, the intermediate mesoscopic regime remains poorly characterized. Using reactive Brownian dynamics, we simulate nanometric particles interacting through van der Waals and Coulombic forces and undergoing stochastic charge-transfer reactions. We define macroscopic observables-mean concentrations, rate laws, and equilibrium constants-in terms of mesoscopic statistical averages and extract effective kinetic parameters directly from simulation trajectories. We further assess the extent to which classical theories, such as Smoluchowski diffusion-controlled association and Debye-Hückel electrostatics, reproduce the fitted constants. Two macroscopic models are introduced: a minimal one-reaction description and a physically motivated three-step scheme that separates encounter formation from reactive conversion. Comparison between the two clarifies how mesoscopic interactions shape macroscopic parameters.