Diffusion limited reactions in confined environments

We study the effect of confinement on diffusion limited bimolecular reactions within a lattice model where a small number of reactants diffuse amongst a much larger number of inert particles. When the number of inert particles is held constant the rate of the reaction is slow for small reaction volumes due to limited mobility from crowding, and for large reaction volumes due to the reduced concentration of the reactants. The reaction rate proceeds fastest at an intermediate confinement corresponding to volume fraction near 1/2 and 1/3 in two and three dimensions, respectively. We generalize the model to off-lattice systems with hydrodynamic coupling and predict that the optimal reaction rate for monodisperse colloidal systems occurs when the volume fraction is ~0.18. Finally, we discuss the application of our model to bimolecular reactions inside cells as well as the dynamics of confined polymers.