Structural, Electronic and Mechanical properties of all-sp$^2$ graphene allotropes: the specific strength of tilene parent is higher than that of graphene and flakene has the minimal density

TL;DR

This study systematically explores all-$sp^2$ carbon allotropes with low density, revealing novel stable structures, their electronic and mechanical properties, and identifying a density threshold affecting rigidity while maintaining toughness.

Contribution

The paper introduces a method to generate and analyze low-density all-$sp^2$ carbon structures, discovering new stable allotropes with unique properties.

Findings

Some structures have density as low as half of graphene.

A density threshold exists below which mechanical rigidity is lost.

Certain allotropes maintain toughness and strength despite lower density.

Abstract

In this work a systematic approach to the search for all-$sp^2$ bonded carbon allotropes with low density is presented. In particular, we obtain a number of novel energetically stable crystal structures, whose arrangement is closely related to the topology of graphene, by modifying the packing of congruent discs under the condition of local stability. Our procedure starts from an initial parent topology and proceeds to generate daughter architectures derived by lowering the packing factors. Furthermore, we assess both the electronic properties, such as the band structure and the density of states, and the mechanical properties, such as the elastic constants and the stress--strain characteristics, of parent's and daughter's geometries from first-principle simulations. We find, using geometrical packing arguments, that some arrangements lead to a density as low as half that of graphene, obtaining some of the least dense structures of all-$sp^2$ bonded carbon allotropes that could ever be synthesized. Nevertheless, a threshold value of the density exists below which the mechanical rigidity of graphene is irreparably lost, while keeping other mechanical characteristics, such as the specific toughness and strength, almost unchanged with lower weight.