Size Effects in Carbon Nanotubes

TL;DR

This study investigates how the inter-shell spacing in multi-walled carbon nanotubes varies with tube diameter, revealing that smaller diameters lead to increased spacing due to high curvature effects.

Contribution

It provides a detailed analysis of inter-shell spacing variation with diameter and introduces a model explaining this behavior based on high curvature effects.

Findings

Inter-shell spacing ranges from 0.34 to 0.39 nm.

Spacing increases as nanotube diameter decreases.

High curvature causes increased repulsive force, expanding inter-shell spacing.

Abstract

The inter-shell spacing of multi-walled carbon nanotubes was determined by analyzing the high resolution transmission electron microscopy images of these nanotubes. For the nanotubes that were studied, the inter-shell spacing ${\hat{d}_{002}}$ is found to range from 0.34 to 0.39 nm, increasing with decreasing tube diameter. A model based on the results from real space image analysis is used to explain the variation in inter-shell spacings obtained from reciprocal space periodicity analysis. The increase in inter-shell spacing with decreased nanotube diameter is attributed to the high curvature, resulting in an increased repulsive force, associated with the decreased diameter of the nanotube shells.