Local control of electric current driven shell etching of multiwalled carbon nanotubes

We report on a novel method for local control of shell engineering in multiwalled carbon nanotubes (MWNTs) using Joule-heating induced electric breakdown. By modulating the heat dissipation along a nanotube, we can confine its thinning and shell breakdown to occur within localized regions of peak temperatures, which are distributed over one-half of the NT length. The modulation is achieved by using suitably designed nanomachined heat sinks with different degrees of thermal coupling at different parts of a current-carrying nanotube. The location of electric breakdown occurs precisely at the regions of high temperatures predicted by the classical finite-element model of Joule heating in the MWNT. The experiments herein provide new insight into the electric breakdown mechanism and prove unambiguously that shell removal occurs due to thermal stress, underpinning the diffusive nature of MWNTs. The method demonstrated here has the potential to be a powerful tool in realizing MWNT bearings with complex architectures for use in integrated nanoelectromechanical systems (NEMS). In addition, the breakdown current and power in the nanotubes are significantly higher than those observed in nanotubes without heat removal via additional heat sinks. This indicates future avenues for enhancing the performance of MWNTs in electrical interconnect and nanoelectronic applications. PACS  73.63.Fg; 65.80.+n     

The Weierstrass mean

Theorem.Let the sequences {e _i ⁽ⁿ⁾ },i=1, 2, 3,n=0, 1, 2, ...be defined by where the e ⁽⁰⁾ s satisfy and where all square roots are taken positive. Then where the convergence is quadratic and monotone and where The discussions of convergence are entirely elementary. However, although the determination of the limits can be made in an elementary way, an acquaintance with elliptic objects is desirable for real understanding.     

The many limits of mixed means

The sequences introduced by Carlson (1971) are variants of the Gauss arithmetic geometric sequences (which have been elegantly discussed by D. A. Cox (1984, 1985)). Given (complex)a ₀,b ₀ we define

CHEMILUMINESCENCE FROM THE OXIDATION OF AUXIN DERIVATIVES

Abstract— The thiophenyl ester of indole-3-acetic acid and indole-3-acetonitrile produce chemiluminescence in aerated dimethylsulfoxide in the presence of potassium t -butoxide. The emitter is the aromatic aldehyde. In the case of acetonitrile, the other product expected from the cleavage of an intermediate dioxetane, cyanate/isocyanate, has also been identified. Other auxins also chemiluminesce under similar conditions, but the emitters have not been properly identified.
These systems are models for the peroxidase catalyzed oxidation of indole-3-acetic acid to indole-3-carboxaldehyde and as such support the earlier inference (Vidigal et al , 1975) that the excited aldehyde is generated in the enzymic process.
An additional result is the observation of an exciplex between excited indole-3-carboxaldehyde and the thiophenylester of indole-3-acetic acid. This appears to be the first case of chemical generation of an exciplex by a route other than radical ion reaction, presumably by the dioxetane route.