Single wall carbon nanotubes (SWNTs) that are found as close-packed arrays in crystalline ropes have been studied by using Raman scattering techniques with laser excitation wavelengths in the range from 514.5 to 1320 nanometers. Numerous Raman peaks were observed and identified with vibrational modes of armchair symmetry (n, n) SWNTs. The Raman spectra are in good agreement with lattice dynamics calculations based on C-C force constants used to fit the two-dimensional, experimental phonon dispersion of a single graphene sheet. Calculated intensities from a nonresonant, bond polarizability model optimized for sp2 carbon are also in qualitative agreement with the Raman data, although a resonant Raman scattering process is also taking place. This resonance results from the one-dimensional quantum confinement of the electrons in the nanotube.

We demonstrate the use of individual single-walled carbon nanotubes (SWNTs) as nanoelectrodes for electrochemistry. SWNTs were contacted by nanolithography, and cyclic voltammetry was performed in aqueous solutions. Interestingly, metallic and semiconducting SWNTs yielded similar steady-state voltammetric curves. We clarify this behavior through a model that considers the electronic structure of the SWNTs. Interfacial electron transfer to the SWNTs is observed to be very fast but can nonetheless be resolved due to the nanometer critical dimension of SWNTs. These studies demonstrate the potential of using a SWNT as a model carbon nanoelectrode for electrochemistry.

We present a theoretical description of the kinetics of electrochemical charge transfer at singlewalled carbon nanotube (SWNT) electrodes, explicitly taking into account the SWNT electronic band structure. SWNTs have a distinct and low density of electronic states (DOS), as expressed by a small value of the quantum capacitance. We show that this greatly affects the alignment and occupation of electronic states in voltammetric experiments and thus the electrode kinetics. We model electrochemistry at metallic and semiconducting SWNTs as well as at graphene by applying the Gerischer-Marcus model of electron transfer kinetics. We predict that the semiconducting or metallic SWNT band structure and its distinct van Hove singularities can be resolved in voltammetry, in a manner analogous to scanning tunneling spectroscopy. Consequently, SWNTs of different atomic structure yield different rate constants due to structure-dependent variations in the DOS. Interestingly, the rate of charge transfer does not necessarily vanish in the band gap of a semiconducting SWNT, due to significant contributions from states which are a few kBT away from the Fermi level. The combination of a nanometer critical dimension and the distinct band structure makes SWNTs a model system for studying the effect of the electronic structure of the electrode on electrochemical charge transfer.

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