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Updated: Jun 22, 2026

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
Published on: September 26, 2016
Lattice model of diffusion-limited bimolecular chemical reactions in confined environments
Jeremy D Schmit1, Ercan Kamber, Jané Kondev
1Department of Physics, Brandeis University, Waltham, Massachusetts 02454, USA. schmit@maxwell.ucsf.edu
Abstract:
We study the effect of confinement on diffusion-limited bimolecular reactions within a lattice model where a small number of reactants diffuse among 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 a volume fraction near 50%. 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 approximately 19%. Finally, we discuss the implications of our model for bimolecular reactions inside cells and the dynamics of confined polymers.
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