Nanopercolation

TL;DR

This study uses molecular mechanics to analyze the geometrical and surface properties of hydrocarbon mantles at the percolation threshold, revealing fractal structures and size-dependent surface behaviors with potential applications in various fields.

Contribution

It introduces a detailed analysis of percolation-disordered hydrocarbon structures, highlighting their fractal nature and surface properties dependent on probe size, confirmed across different topologies.

Findings

Mantles at critical percolation have fractal dimension ~2.5.

Surface area and volume follow power-law scaling with system size.

Properties depend significantly on the probing molecule's radius.

Abstract

We investigate through direct molecular mechanics calculations the geometrical properties of hydrocarbon mantles subjected to percolation disorder. We show that the structures of mantles generated at the critical percolation point have a fractal dimension $d_{f} \approx 2.5$. In addition, the solvent access surface $A_{s}$ and volume $V_{s}$ of these molecules follow power-law behavior, $A_{s} \sim L^{\alpha_A}$ and $V_{s} \sim L^{\alpha_V}$, where $L$ is the system size, and with both critical exponents $\alpha_A$ and $\alpha_V$ being significantly dependent on the radius of the accessing probing molecule, $r_{p}$. Our results from extensive simulations with two distinct microscopic topologies (i.e., square and honeycomb) indicate the consistency of the statistical analysis and confirm the self-similar characteristic of the percolating hydrocarbons. Due to their highly branched topology, some of the potential applications for this new class of disordered molecules include drug delivery, catalysis, and supramolecular structures.