Our understanding of the "long range" electrodynamic, electrostatic, and polar interactions that dominate the organization of small objects at separations beyond an interatomic bond length is reviewed. From this basic-forces perspective, a large number of systems are described from which one can learn about these organizing forces and how to modulate them. The many practical systems that harness these nanoscale forces are then surveyed. The survey reveals not only the promise of new devices and materials, but also the possibility of designing them more effectively.

We investigate the van der Waals-London dispersion interactions between a single-walled carbon nanotube immersed in water and interacting with three different objects: an optically isotropic planar substrate, an optically anisotropic planar substrate, and another single-walled carbon nanotube of identical chirality. These interactions were derived from ab initio optical properties and an appropriate formulation of the Lifshitz theory. We derive two analytically tractable limits for the van der Waals interaction: the far limit at separations much larger than the cylinder radius, and the near or Derjaguin limit where surface-cylinder separation is much smaller than the radius. We investigate in detail the effect of relative geometry and the relative separation on the magnitude of the dispersion interaction.

Optical dispersion spectra at energies up to 30 eV play a vital role in understanding the chirality-dependent van der Waals London dispersion interactions of single wall carbon nanotubes (SWCNTs). We use one-electron theory based calculations to obtain the band structures and the frequency dependent dielectric response function from 0-30 eV for 64 SWCNTs differing in radius, electronic structure classification, and geometry. The resulting optical dispersion properties can be categorized over three distinct energy intervals (M, π, and σ, respectively representing 0-0.1, 0.1-5, and 5-30 eV regions) and over radii above or below the zone-folding limit of 0.7 nm. While π peaks vary systematically with radius for a given electronic structure type, σ peaks are independent of tube radius above the zone folding limit and depend entirely on SWCNT geometry. We also observe the so-called metal paradox, where a SWCNT has a metallic band structure and continuous density of states through the Fermi level but still behaves optically like a material with a large optical band gap between M and π regions. This paradox appears to be unique to armchair and large diameter zigzag nanotubes. Based on these calculated one-electron dielectric response functions we compute and review Van der Waals -London dispersion spectra, full spectral Hamaker coefficients, and van der Waals -London dispersion interaction energies for all calculated frequency dependent dielectric response functions. Our results are categorized using a new optical dielectric function classification scheme that groups the nanotubes according to observable trends and notable features (e.g. the metal paradox ) in the 0-30 eV part of the optical dispersion spectra. While the trends in these spectra begin to break down at the zone folding diameter limit, the trends in the related van der Waals -London dispersion spectra tend to remain stable all the way down to the smallest single wall carbon nanotubes in a given class. IntroductionSince their discovery in 1993 by the Iijima and the Bethune groups 1,2 , single wall carbon nanotubes (SWCNTs) have received enthusiastic attention. Their intriguing mechanical and electrical properties make them ideal for a wide range of applications, from metal oxide semiconductor field effect transistors (MOSFETs) to novel drug delivery systems 3-8 and have inspired strong scientific and industrial interest 1,[9][10][11][12][13][14][15] . The area that has arguably received the most attention and focus is † Electronic Supplementary Information (ESI) available: [details of any supplementary information available should be included here]. See ) * In the context of the dielectric response functions of CNTs, we denote the SWCNT with a mnemonic [n,m, type] rather then the standard but equivalent (n,m), when we want to invoke its type explicitly in order to help the reader organize the voluminous information and in order to be consistent with our previous publications. Of course the two designations, together with the simple (n-m)/3 = integer rule to...

We derive the complete form of the van der Waals dispersion interaction between two infinitely long anisotropic semiconducting/insulating thin cylinders at all separations. The derivation is based on the general theory of dispersion interactions between anisotropic media as formulated in Munday et al. ͓Phys. Rev. A 71, 042102 ͑2005͔͒. This formulation is then used to calculate the dispersion interactions between a pair of single-walled carbon nanotubes at all separations and all angles. Nonretarded and retarded forms of the interactions are developed separately. The possibility of repulsive dispersion interactions and nonmonotonic dispersion interactions is discussed within the framework of the formulation.

The van der Waals-London dispersion (vdW-Ld) spectra are calculated for the [9,3,m] metallic and [6,5,s] semiconducting single wall carbon nanotubes (SWCNTs), graphite, and graphene (a single carbon sheet of the graphite structure) using uniaxial optical properties determined from ab initio band structure calculations. The [9,3,m], exhibiting metallic optical properties in the axial direction versus semiconducting optical properties in the radial direction, highlights the strong anisotropic nature of metallic SWCNTs. Availability of both efficient ab initio local density band structure codes and sufficient computational power has allowed us to calculate the imaginary parts of the frequency dependent dielectric spectra, which are then easily converted to the required vdW-Ld spectra for Hamaker coefficient calculations. The resulting Hamaker coefficients, calculated from the Lifshitz quantum electrodynamic theory, show that neither graphite nor graphene are accurate model materials for estimating the Hamaker coefficients of SWCNTs. Additionally, Hamaker coefficients were calculated between pure radial-radial, radial-axial, and axial-axial components of both SWCNTs. Analysis of these coefficients reveals that the vdW-Ld interactions will depend on both chirality and the particular orientation between neighboring SWCNTs. The minimization of energy, with respect to orientation, predicts that vdW-Ld alignment forces will arise as a result of the anisotropic optical properties of SWCNTs.

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.

A complete form of the van der Waals dispersion interaction between an infinitely long anisotropic semiconducting/insulating thin cylinder and an anisotropic half space is derived for all separations between the cylinder and the half space. The derivation proceeds from the theory of dispersion interactions between two anisotropic infinite half spaces as formulated in Phys. Rev. A 71, 042102 ͑2005͒. The approach is valid in the retarded as well as nonretarded regimes of the interaction and is coupled with the recently evaluated ab initio dielectric response functions of various semiconducting/insulating single wall carbon nanotubes, enables the authors to evaluate the strength of the van der Waals dispersion interaction for all orientation angles and separations between a thin cylindrical nanotube and the half space. The possibility of repulsive and/or nonmonotonic dispersion interactions is examined in detail.

Van der Waals-London dispersion interaction framework for experimentally realistic carbon nanotube systems A system's van der Waals-London dispersion interactions are often ignored, poorly understood, or crudely approximated, despite their importance in determining the intrinsic properties and intermolecular forces present in a given system. There are several key barriers that contribute to this issue: 1) lack of the required full spectral optical properties, 2) lack of the proper geometrical formulation to give meaningful results, and 3) a perception that a full van der Waals-London dispersion calculation is somehow unwieldy or difficult to understand conceptually. However, the physical origin of the fundamental interactions for carbon nanotube systems can now be readily understood due to recent developments which have filled in the missing pieces and provided a complete conceptual framework. Specifically, our understanding is enhanced through a combination of a robust, ab-initio method to obtain optically anisotropic properties out to 30 electron Volts, proper extensions to the Lifshitz's formulations to include optical anisotropy with increasingly complex geometries, and a proper methodology for employing optical mixing rules to address multibody and multi-component structures. Here we review this new framework to help end-users understand these interactions, with the goal of better system design and experimental prediction. Numerous examples are provided to show the impact of a material's intrinsic geometry, including optical anisotropy as a function of that geometry, and the effect of the size of the nanotube core and surfactant material present on its surface. We'll also introduce some new examples of how known trends in optical properties as a function of [n, m] can result in van der Waals interactions as a function of nanotube classification, radius, and other parameters. The concepts and framework presented are not limited to the nanotube community, and can be equally applied to other nanoscale or even biological systems.