C13NMR Chemical Shift of Single-Wall Carbon Nanotubes

Abstract

We compute the magnetic shielding tensor within the London approximation and estimate the Knight shift of single-wall carbon nanotubes. Our results indicate that high resolution 13 C NMR should be able to separate the metallic and insulator character of the nanotubes since a 11 ppm splitting is predicted from the respective resonances. As a model for disorder, bending, and defects in these structures, we investigate the magnetic response of nanotubes with finite size. We get a small line broadening coming from an intrinsic length dependent resonance effect. The nanotube packing is also studied and leads to a 20 ppm broadening which disappears under experimental high-resolution conditions. DOI: 10.1103/PhysRevLett.86.3160 PACS numbers: 76.60.Cq, 71.15.Ap, 75.20. -g Nuclear magnetic resonance (NMR) has been proved to be a useful tool to study the dynamics and electronic structure of fullerene [1] and nanotube [2,3] materials. In spite of this experimental relevance, for a refined characterization of carbon materials, not much theoretical work is available about infinite sp 2 -like carbon objects due to the intrinsic diamagnetic divergence in the graphite susceptibility at T 0 K [4]. Moreover, the change of magnetic properties when going to low dimensional graphitic nanostructures is still not well understood. In particular, single-wall carbon nanotubes (SWNTs), which can be seen as long rolled graphene sheets, have attracted a lot of attention as promising materials for nanotechnology applications and composites. These particular quasi-1D structures, with finite-size effects as a one dimensional quantum box [5,6], show interesting correlations between geometry and electronic properties [7]. Of course, the magnetic response is affected by this interplay, as shown in magnetic susceptibility [8] and magnetotransport [9]. In this Letter, we aim to understand the microscopic mechanisms which contribute to the NMR spectra of SWNTs, by performing a detailed theoretical study of the magnetic response of perfect and isolated tubes as a function of temperature.By measuring the shift of the Larmor frequency of the nuclear spin, NMR in solids gives information about the chemical environment and the metal-like properties of a compound. The NMR shift which represents the perturbation of the applied field due to the electrons consists of a sum of two tensorial contributions: the shielding tensor $ s , which is the contribution of orbital electronic magnetism, and the Knight shift $ K , which is a Fermi contact effect of electron spin which appears uniquely in metals. The chemical shift anisotropy tensor $ d is measured experimentally by comparing to a standard reference asThe $ s tensor can be separated in two parts: the London ring-current (RC) contribution ( $ s RC ) and the Pople correction [11]. The first part is an effect of the interatomic electronic current, and the second one is a local intraatomic part that can be written as a function of the hybridization of the carbon atom [12].Whereas the Knight shift (in metalli...

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