Calculating van der Waals-London Dispersion Spectra and Hamaker Coefficients of Carbon Nanotubes in Water from Ab Initio Optical Properties

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

New Perspectives on van Der Waals-London Interactions of Materials. From Planar Interfaces to Carbon Nanotubes

The drive towards nanoscale assembly necessitates an accurate understanding of all the fundamental forces present in a given system to ensure the greatest chance of success. The van der Waals - London dispersion (vdW-Ld) interaction is the universal, long range, interaction that is present in all materials systems. However, scientists and engineers often either ignore or crudely approximate the vdW-Ld interactions because the calculations often appear impractical due to the 1) lack of the required full spectra optical properties and 2) lack of the proper geometrical formulation to give meaningful results. These two barriers are being actively eliminated by the introduction of robust ab initiocodes that can calculate anisotropic full spectral optical properties and by proper extensions to the Lifshitz vdW-Ld formulation that take into account anisotropic spectral optical properties as well as novel geometries. These new capabilities are of broad utility, especially in the biological community, because of the difficulty in experimental determination of full spectral optical properties of nanoscale, liquid phase biomolecules. Here we compare 3 levels of complexity of vdW-Ld interactions (optically isotropic planar, optically anisotropic planar, and optically anisotropic solid cylinder) as well as calculate and compare a variety of Hamaker coefficients relevant to these systems. For the latter two, more complex, cases, we use the ab initiooptical properties of single wall carbon nanotubes (SWCNTs). Our results show the effects of strong optical anisotropy upon the overall vdW-Ld interaction strength as well as the presence of strong dispersion-driven torques in both anisotropic cases, which can play a role in CNT alignment with other CNTs and also preferred CNT alignment directions with optically anisotropic substrates[1, 2]

Van Der Waals-London Dispersion Interaction Framework for Experimentally Realistic Carbon Nanotube Systems

A system\u27s 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\u27s formulations to include optical anisotropy with increasingly complex geometries, and a proper methodology for employing optical mixing rules to address multi-body 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\u27s 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\u27ll 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

Graded Interface Models for More Accurate Determination of van Der Waals-London Dispersion Interactions across Grain Boundaries

Attractive van der Waals–London dispersion interactions between two half crystals arise from local physical property gradients within the interface layer separating the crystals. Hamaker coefficients and London dispersion energies were quantitatively determined for Σ5 and near-∑13 grain boundaries in SrTiO3 by analysis of spatially resolved valence electron energy-loss spectroscopy (VEELS) data. From the experimental data, local complex dielectric functions were determined, from which optical properties can be locally analyzed. Both local electronic structures and optical properties revealed gradients within the grain boundary cores of both investigated interfaces. The results show that even in the presence of atomically structured grain boundary cores with widths of less than 1nm, optical properties have to be represented with gradual changes across the grain boundary structures to quantitatively reproduce accurate van der Waals–London dispersion interactions. London dispersion energies of the order of 10% of the apparent interface energies of SrTiO3 were observed, demonstrating their significance in the grain boundary formation process. The application of different models to represent optical property gradients shows that long-range van der Waals–London dispersion interactions scale significantly with local, i.e., atomic length scale property variations

Dispersion Interactions between Optically Anisotropic Cylinders at All Separations: Retardation Effects for Insulating and Semiconducting Single-Wall Carbon Nanotubes

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 (2005)]. 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

Optically Anisotropic Infinite Cylinder above an Optically Anisotropic Half Space: Dispersion Interaction of a Single-Walled Carbon Nanotube with a Substrate

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 (2005). 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

Long Range Interactions in Nanoscale Science

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

Local Optical Properties, Electron Densities, and London Dispersion Energies of Atomically Structured Grain Boundaries

Quantitative analysis of spatially resolved valence electron energy-loss spectra shows strong physical property contrasts for Σ5 and near Σ13 grain boundaries in Fe-doped SrTiO3, resulting in London dispersion interaction energies of 14 to 50mJ/m2 between the adjacent grains. The determination of local physical properties of grain boundary cores and the appreciable contribution of long-range London dispersion to interface energies provides new information on formation and control of interfaces in materials

Nonadditivity in van Der Waals Interactions within Multilayers

Working at the macroscopic continuum level, we investigate effective van der Waals interactions between two layers within a multilayer assembly. By comparing the pair interactions between two layers with effective pair interactions within an assembly we assess the significant consequences of nonadditivity of van der Waals interactions. This allows us to evaluate the best numerical estimate to date for the Hamaker coefficient of van der Waals interactions in lipid-water multilamellar systems