Spectral mixing formulations for van der Waals–London dispersion interactions between multicomponent carbon nanotubes

Abstract

Recognition of spatially varying optical properties is a necessity when studying the van der Waals-London dispersion (vdW-Ld) interactions of carbon nanotubes (CNTs) that have surfactant coatings, tubes within tubes, andor substantial core sizes. The ideal way to address these radially dependent optical properties would be to have an analytical add-a-layer solution in cylindrical coordinates similar to the one readily available for the plane-plane geometry. However, such a formulation does not exist nor does it appear trivial to be obtained exactly. The best and most pragmatic alternative for end-users is to take the optical spectra of the many components and to use a spectral mixing formulation so as to create effective solid-cylinder spectra for use in the far-limit regime. The near-limit regime at "contact" is dominated by the optical properties of the outermost layer, and thus no spectral mixing is required. Specifically we use a combination of a parallel capacitor in the axial direction and the Bruggeman effective medium in the radial direction. We then analyze the impact of using this mixing formulation upon the effective vdW-Ld spectra and the resulting Hamaker coefficients for small and large diameter single walled CNTs (SWCNTs) in both the near- and far-limit regions. We also test the spectra of a [16,0,s+7,0,s] multiwalled CNT (MWCNT) with an effective MWCNT spectrum created by mixing its [16,0,s] and [7,0,s] SWCNT components to demonstrate nonlinear coupling effects that exist between neighboring layers. Although this paper is primarily on nanotubes, the strategies, implementation, and analysis presented are applicable and likely necessary to any system where one needs to resolve spatially varying optical properties in a particular Lifshitz formulation.

Long range interactions in nanoscale science

“…Test calculations on several ceramic crystals showed that the calculated Hamaker coefficients using theoretical spectra do not differ much from those obtained using experimental spectra ͑Ahuja et al, 2004͒. Recently this approach has been applied to obtain Hamaker constants for both metallic and semiconducting single-wall carbon nanotubes ͑SWCNT͒ and multiwall carbon nanotubes ͑MWCNT͒ of different chiralities with considerable success ͑Rajter, Rajter et al, 2008͒. In Figs. 2 and 3 we show Љ͑͒ and the corresponding vdW-Ld spectra properties of ͓6,5,s͔ and ͓9,3,m͔ SWCNTs. It is important to capture all of these interband transitions, out to at least 30 eV, because all areas are adding to the overall summations and can shift the magnitude of the resulting Hamaker coefficients.…”

Dispersion interactions between optically anisotropic cylinders at all separations: Retardation effects for insulating and semiconducting single-wall carbon nanotubes

“…Several experimental procedures have exploited the differences among these properties in order to separate SWCNTs by chirality ͑see Ref. 2 and references therein͒. In order to separate a polydisperse solution of SWCNTs into monodisperse fractions of one chirality reliably, one needs to understand the detailed features of the interactions between constituent SWCNTs.…”

Optically anisotropic infinite cylinder above an optically anisotropic half space: Dispersion interaction of a single-walled carbon nanotube with a substrate

“…Taking into account the finite thickness of the wall would require a more careful modeling of its effective dielectric response 3 and thus introduce additional parameters that would complicate the understanding of the retardation effects in van der Waals-dispersion interactions between this SWCNT and the half space, which is our primary aim in this article. Also, once the surface-to-surface separation between a SWCNT and the half space is greater than approximately two SWCNT outer diameters, 3 this approximation turns out to work quite well. In the case the ͑6,5͒ SWCNT, this would mean greater than 1.5 nm.…”

“…2,3 Several experimental procedures have been proposed to exploit the differences between these properties in order to separate SWCNTs by chirality ͑see Ref. 3 and references therein͒. Different separation mechanisms have been suggested and tested 4 but we are still some way off to separate a nanotube mixture into its single chirality components.…”

“…2,3 Several experimental procedures have been proposed to exploit the differences between these properties in order to separate SWCNTs by chirality ͑see Ref. 3 and references therein͒.…”