On the forbidden graphene\u2019s ZO (out-of-plane optic) phononic band-analog vibrational modes in fullerenes

Jesús N Pedroza-Montero,Ignacio L Garzón,Huziel E Sauceda

doi:10.1038/s42004-021-00540-z

Abstract

The study of nanostructures’ vibrational properties is at the core of nanoscience research. They are known to represent a fingerprint of the system as well as to hint the underlying nature of chemical bonds. In this work, we focus on addressing how the vibrational density of states (VDOS) of the carbon fullerene family (Cn: n = 20 → 720 atoms) evolves from the molecular to the bulk material (graphene) behavior using density functional theory. We find that the fullerene’s VDOS smoothly converges to the graphene characteristic line-shape, with the only noticeable discrepancy in the frequency range of the out-of-plane optic (ZO) phonon band. From a comparison of both systems we obtain as main results that: (1) The pentagonal faces in the fullerenes impede the existence of the analog of the high frequency graphene’s ZO phonons, (2) which in the context of phonons could be interpreted as a compression (by 43%) of the ZO phonon band by decreasing its maximum allowed radial-optic vibration frequency. And 3) as a result, the deviation of fullerene’s VDOS relative to graphene may hold important thermodynamical implications, such as larger heat capacities compared to graphene at room-temperature. These results provide insights that can be extrapolated to other nanostructures containing pentagonal rings or pentagonal defects.

Highlights

The study of nanostructures’ vibrational properties is at the core of nanoscience research
Analysis that leads to an interesting and counterintuitive difference between the vibrational modes in fullerenes and the phonon bands in graphene: a severe restriction on the out-of-plane optical band (ZO-modes) in fullerenes in the neighborhood of the Γ symmetric point. These results show that the presence of the pentagonal faces in the fullerene family hinders the smooth convergence of their vibrational density of states (VDOS) to the bulk graphene one
(2) at ≈170 K the rapid growth of the ZO peak in the fullerene equals the cumulative value in graphene, and from that temperature onward the fullerene heat capacity will be larger than the graphene value, reaching its maximum at (3) ≈362 K. These results demonstrate that the excess of vibrational modes created in the ZO band by the pentagonal faces in fullerenes have an impact on the system’s thermodynamics and even overcome the disadvantage imposed by the acoustic gap

Summary

Introduction

The study of nanostructures’ vibrational properties is at the core of nanoscience research. A fundamental question in nanoscience is how the transition from molecular (physical and chemical) properties evolve to bulk behavior as a function of the system size In this regard, several results have been published such as the birth of the localized surface plasmon resonance in Au nanoclusters[30], the evolution of thermodynamical properties on metallic nanoparticles[25,31,32,33], the formation of surface plasmons in sodium nanoclusters[34], as well as the convergence of molecular vibrational spectra to a bulk-like phonon density of states in metal NPs35. Analysis that leads to an interesting and counterintuitive difference between the vibrational modes in fullerenes and the phonon bands in graphene: a severe restriction on the out-of-plane (radial) optical band (ZO-modes) in fullerenes in the neighborhood of the Γ symmetric point These results show that the presence of the pentagonal faces in the fullerene family hinders the smooth convergence of their VDOS to the bulk graphene one. These findings hint that pentagonal impurities in graphene can have far more important implications on its vibrational properties than expected

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