Contact Kinetics in Fractal Macromolecules

TL;DR

This paper develops an analytical framework to compute the mean first contact time between monomers in fractal macromolecules, revealing a universal scaling law that matches simulation results.

Contribution

It introduces a non-Markovian analytical method for first contact kinetics in fractal polymers, accounting for non-equilibrium conformations at contact.

Findings

Derived a simple scaling relation for MFCT involving equilibrium distance and spectral dimension.

Predictions agree well with numerical stochastic simulations.

Established a universal relation independent of microscopic details.

Abstract

We consider the kinetics of first contact between two monomers of the same macromolecule. Relying on a fractal description of the macromolecule, we develop an analytical method to compute the Mean First Contact Time (MFCT) for various molecular sizes. In our theoretical description, the non-Markovian feature of monomer motion, arising from the interactions with the other monomers, is captured by accounting for the non-equilibrium conformations of the macromolecule at the very instant of first contact. This analysis reveals a simple scaling relation for the MFCT between two monomers, which involves only their equilibrium distance and the spectral dimension of the macromolecule, independently of its microscopic details. Our theoretical predictions are in excellent agreement with numerical stochastic simulations.