Empirical prediction of electronic potentials of single-walled carbon nanotubes with a specific chirality (n,m).

The determination of the electronic states of single-walled carbon nanotubes (SWNTs) with a specific chirality has been a central issue in the science of SWNTs. Here we present the empirical equations with fitting parameters for the determination of the reduction and oxidation potentials of SWNTs for a wide range of diameters and chiral angles. In these equations, a distinct chirality family dependence of the reduction potentials is observed, while the oxidation potentials show a simple diameter dependence nearly proportional to the inversed nanotube diameter. Based on observations of the asymmetric chirality dependence between the reduction and oxidation potentials, the Fermi levels of the SWNTs were revealed to have a definite chirality family dependence, which indicates that the work functions of the SWNTs with small diameters deviate from the values for the large diameter SWNTs and graphene. We also performed quantum chemical calculations to compare the experiment to the calculations.

Observation of negative and positive trions in the electrochemically carrier-doped single-walled carbon nanotubes.

Understanding of electronic and optical features of single-walled carbon nanotubes (SWNTs) has been a central issue in science and nanotechnology of carbon nanotubes. We describe the detection of both the positive trion (positively charged exciton) and negative trion (negatively charged exciton) as a three-particle bound state in the SWNTs at room temperature by an in situ photoluminescence spectroelectrochemistry method for an isolated SWNT film cast on an ITO electrode. The electrochemical hole and electron dopings enable us to detect such trions on the SWNTs. The large energy difference between the singlet bright exciton and the negative and positive trions showing a tube diameter dependence is determined by both the exchange splitting energy and the trion binding energy. In contrast to conventional compound semiconductors, on the SWNTs, the negative trion has almost the same binding energy to the positive trion, which is attributed to nearly identical effective masses of the holes and electrons.

Strong micro-dielectric environment effect on the band gaps of (n,m)single-walled carbon nanotubes.

The electronic states of carbon nanotubes are one of the most fundamental properties of the nanotubes. We now describe the finding that the band gaps of (n,m)SWNTs are strongly affected by the change in microdielectric environments around the isolated nanotubes. In situ photoluminescence (PL) spectroelectrochemistry of the films containing 15 isolated (n,m)single-walled carbon nanotubes (SWNTs) cast on ITO electrodes in organic solvents including DMSO, acetonitirile, DMF, THF, and chloroform was completed and then the oxidation and reduction potentials, and band gaps (ΔE(electr)) of the (n,m)SWNTs in the solvents were determined. We have discovered that the ΔE(electr) of the (n,m)SWNTs become greater as the solvent dielectric constants decreased, which is in sharp contrast to the optical band gaps (ΔE(opt)) that show virtually no solvent dependence. Such a strong solvent dependence of the electrochemical band gaps is due to the difference in the solvation energy of the charged SWNTs produced during the electrochemical processes. The ΔE(electr) of both mod types of the SWNTs, mod = 1 and mod = 2, linearly increased versus the reciprocal of the tube diameter, which agrees with the theory. Moreover, the states of the π-electrons in the SWNTs were evaluated from the dependence of the band gaps on the diameter of the SWNTs. Furthermore, the states of the π-electrons on the sidewalls of the SWNTs were evaluated using the γ(0) values, a parameter representing the measure of the stability or the degree of delocalization of π-electrons in the sidewall of the SWNTs, and revealed that the γ(0) values of the mod = 1 and mod = 2 SWNTs increased with a decrease in the dielectric constants of the solvents in the range of 38-79. This study has enabled us to understand the essential electronic properties of the carbon nanotubes.