Local electric field at the emitting surface of a carbon nanotube

Abstract

We present a method for the calculation of the local electric field at the surface of a nanoscopic emitting structure. The method is here applied to carbon nanotubes (NT) where symmetry makes the application of the method easier. The NT is simulated as a cylindrical array of touching spheres, each sphere representing an atom of the tube. The electrostatic potential is written as a linear combination of the potentials produced by each of the spheres. We calculate the local electric field and the corresponding enhancement factor γ for both open and closed nanotubes. For a closed NT we find for γ a simple polynomial expression in terms of the ratio of the height h of the tube to its radius R, which for h/R<40 reduces to a frequently quoted formula of γ. For an open single-wall NT we find that γ is three times greater than that of a single-wall NT of the same h/R. As the thickness of the wall increases this difference diminishes. From these results one may deduce a possible explanation as to why in some experiments a closed NT emits more current than a corresponding open one while in other experiments the opposite holds true.

Atomistic modeling of metal surfaces under electric fields: Direct coupling of electric fields to a molecular dynamics algorithm

“…Although the slope of the linear dependence is high, it is less than the unity as given in Ref. [33]: The analytical model by Kokkorakis et al [34] gives the simplified formula| F max |/| F ex | = a 0 + 0.72r tip /h tip , and those based on finite-element calculations Edgcombe and Valdrè [30] derive a similar but sublinear dependence. These formulas give approximately the same slope of 0.72, which can be a good probe testing for our Laplace solver.…”

“…The generally accepted concept of the electric field linearly enhancing with the aspect ratio of a metal protrusion on a metal surface [33] was verified in many articles [30][31][32]34]. Although the different calculations give slightly different fitting functions to describe the dependence, the main conclusion of a significant growth of the field on a protrusion seems to be a strong tendency in all models.…”

Electric Field Enhancement Factors Around a Metallic, End-Capped Cylinder

“…There exist a number of reports about calculations of γ for emitters like CNT (i.e., long conducting cylinders closed with a hemisphere). 8,11,12 Forbes et al 9 made a critical review of these studies and found that all approximations to cylindrical emitters with shapes which are commensurate with analytically solvable models (e.g., floating sphere model, semi-ellipsoid on the plane) give poor results compared to the numerical simulations for the exact cylindrical surface. It is, however, clear from all these studies that γ has an almost linear dependence on L/R.…”

High-Order Quadratures for the Solution of Scattering Problems in Two Dimensions

“…High aspect ratio field enhancement at the tip of a charged point or projection is a well-known phenomenon, and it may be possible to take advantage of this effect by forming electrodes with arrays of carbon nanotubes (CNTs), bio-compatible metal nanowires, or other high-aspect ratio nanoscale structures for delivery of nanoelectropulses to biological systems. For example, following the analysis of Kokkorakis et al [19], a 5 volt potential on a single CNT can produce electric fields of 20 MV/m or higher over distances within a few nanometers of the tip of the tube, depending on the system geometry and the dielectric environment. Not only does this simplify the pulse generator engineering problem, but the nanometer dimensional scale of these novel electrodes also makes possible the very highly localized application of these new stimuli so that we may envision pulse exposures involving only small regions of the cell -individual organelles or nanometer-size compartments in the cytoplasm or isolated domains of the cell membrane.…”