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

机译:多组分碳纳米管之间范德华-伦敦色散相互作用的光谱混合配方

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摘要

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, and∕or 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.
机译:在研究具有表面活性剂涂层,管内管和/或较大芯尺寸的碳纳米管(CNT)的范德华斯-伦敦色散(vdW-Ld)相互作用时,必须认识到空间变化的光学特性。解决这些径向相关的光学特性的理想方法是在圆柱坐标系中具有类似于层平面几何结构的解析附加层解决方案。然而,这样的表述不存在,或者看起来很难被精确地获得。对于最终用户而言,最佳和最实用的选择是获取许多组件的光谱,并使用光谱混合配方,以创建有效的固态圆柱光谱,以用于远距离范围。 “接触”处的近极限状态主要由最外层的光学特性决定,因此不需要光谱混合。具体而言,我们结合使用轴向平行电容器和径向布鲁格曼有效介质。然后,我们分析了使用这种混合配方对有效vdW-Ld光谱的影响以及在近端和远端限制区域中小直径和大直径单壁CNT(SWCNT)产生的Hamaker系数。我们还测试了[16,0,s + 7,0,s]多层CNT(MWCNT)的光谱,并通过混合其[16,0,s]和[7,0,s] SWCNT创建了有效的MWCNT光谱组件,以证明相邻层之间存在非线性耦合效应。尽管本文主要针对纳米管,但提出的策略,实施和分析适用于任何需要解决特定Lifshitz配方中空间变化的光学特性的系统。

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