Buckling and competition of energy and entropy lead conformation of single-walled carbon nanocones

TL;DR

This paper develops a continuum model to analyze the conformation of single-walled carbon nanocones, explaining their preferred geometry through energy and entropy considerations, and predicting optimal structural parameters consistent with experiments.

Contribution

It introduces an analytical continuum model that combines elastic, defect, and entropy energies to predict the optimal conformation of carbon nanocones, including their cone angle and size.

Findings

Predicted cone angle of 19.2 degrees matches experimental data.

Model estimates nanocone radius at 0.35 nm.

Critical length of nanocones is 24 nm, aligning with observations.

Abstract

Using a continuum model, expressions for the elastic energy, defect energy, structure entropy, and mixing entropy of carbon nanocones are proposed analytically. The optimal conformation of carbon nanocones is studied by imposing minimization of free energy and analyzing the effects that the buckling of a nanocone's walls have during formation. The model explains the experimentally observed preference of 19.2 degrees for the cone angle of carbon nanocone. Furthermore, it predicts the optimal conformation of carbon nanocones to result in a cone angle of 19.2 degrees, radius of 0.35 nm, and critical length of 24 nm, all of which agree very well with experimental observations.