Exploring carbon catenoids and their applications for encapsulation of carbon nanostructures.

Carbon nanostructures of various shapes are among materials that have been extensively studied due to their unique chemical and physical properties. In this paper, we propose a new geometry of carbon nanostructures known as molecular carbon catenoid to compare with theoretical catenoid found from minimising the Willmore energy functional. Since applications of this structure include electron and molecular transport, this paper mathematically models the energetic behaviour of an atom and a spherical molecule entering a catenoid using the Lennard-Jones potential and a continuum approach.

Catalytic effect of graphene on the inversion of corannulene using a continuum approach with the Lennard-Jones potential.

The catalytic effect of graphene on the corannulene bowl-to-bowl inversion is confirmed in this paper using a pair-wise dispersion interaction model. In particular, a continuum approach together with the Lennard-Jones potential are adopted to determine the interaction energy between corannulene and graphene. These results are consistent with previous quantum chemical studies, which showed that a graphene sheet reduces the barrier height for the bowl-to-bowl inversion in corannulene.

Modeling Ultrafast Transport of Water Clusters in Carbon Nanotubes.

Carbon nanotubes can be used as ultrafast liquid transporters for water purification and drug delivery applications. In this study, we mathematically model the interaction between water clusters and carbon nanotubes using a continuum approach with the Lennard-Jones potential. Since the structure of water clusters depends on the confining material, this paper models the cluster as a cylindrical column of water molecules located inside a carbon nanotube.

Continuum Modeling with Functional Lennard-Jones Parameters for Methane Storage inside Various Carbon Nanostructures.

Methane capture and storage are of particular importance for the development of new technology to reduce the effects of climate change and global warming. Carbon-based nanomaterials are among several porous nanomaterials proposed as potential candidates for methane storage. In this paper, we adopt a new continuum approach with functional Lennard-Jones parameters to provide interaction energies for methane inside carbon nanostructures, namely fullerenes, nanotube bundles, and nanocones.

Correction: Modelling locust foraging: How and why food affects group formation.

[This corrects the article DOI: 10.1371/journal.pcbi.

Modelling locust foraging: How and why food affects group formation.

Locusts are short horned grasshoppers that exhibit two behaviour types depending on their local population density. These are: solitarious, where they will actively avoid other locusts, and gregarious where they will seek them out. It is in this gregarious state that locusts can form massive and destructive flying swarms or plagues.

Exploring Nonlinear Diffusion Equations for Modelling Dye-Sensitized Solar Cells.

Dye-sensitized solar cells offer an alternative source for renewable energy by means of converting sunlight into electricity. While there are many studies concerning the development of DSSCs, comprehensive mathematical modelling of the devices is still lacking. Recent mathematical models are based on diffusion equations of electron density in the conduction band of the nano-porous semiconductor in dye-sensitized solar cells.

Continuum Modelling for Interacting Coronene Molecules with a Carbon Nanotube.

The production of single dimensional carbon structures has recently been made easier using carbon nanotubes. We consider here encapsulated coronene molecules, which are flat and circular-shaped polycyclic aromatic hydrocarbons, inside carbon nanotubes. Depending on the radius of the nanotube, certain specific configurations of the coronene molecules can be achieved that give rise to the formation of stacked columns or aid in forming nanoribbons.

Mechanics and dynamics of lysozyme immobilisation inside nanotubes.

Lysozyme is an enzyme often used as an antibacterial agent in food industries and biochemical and pharmaceutical laboratories. Immobilisation of lysozyme by encapsulating in a nanotube has received much interest as it can enhance stability of the enzyme in ambient condition. Experimentally, various types of nanotubes have been proposed as a host for lysozyme.

Conformation of graphene folding around single-walled carbon nanotubes.

The low bending rigidity of graphene facilitates the formation of folds into the structure. This curvature change affects the reactivity and electron transport of the sheet. One novel extension of this is the intercalation of small molecules into these folds.

Modeling interactions between C₆₀ antiviral compounds and HIV protease.

Fullerenes have generated a great deal of interest in recent years, due to their properties and potential applications in many fields, including medicine. In this paper, we study an antiviral fullerene compound which may be used to treat the human immunodeficiency virus (HIV). We formulate a mathematical model which can describe the interaction energy between the C[Formula: see text] antiviral compounds and the HIV.

Comment on "Equilibrium conformation of polymer chains with noncircular cross section".

In this Comment, we point out that the Euler-Lagrange equations, which are referred to as the general equilibrium equations by Zhao et al. [Phys. Rev.

Modelling peptide nanotubes for artificial ion channels.

We investigate the van der Waals interaction of D,L-Ala cyclopeptide nanotubes and various ions, ion-water clusters and C(60) fullerenes, using the Lennard-Jones potential and a continuum approach which assumes that the atoms are smeared over the peptide nanotube providing an average atomic density. Our results predict that Li(+), Na(+), Rb(+) and Cl(-) ions and ion-water clusters are accepted into peptide nanotubes of 8.5 Å internal diameter whereas the C(60) molecule is rejected.

Modeling encapsulation of acetylene molecules into carbon nanotubes.

Polyacetylene is a well-known conductive polymer and when doped its conductivity can be altered by up to 12 orders of magnitude. However, due to entropy effects a polyacetylene chain usually suffers from distortions and interchain couplings which lead to unpredictable changes in its conducting property. Encapsulating a polyacetylene chain into a carbon nanotube can resolve these issues.

Oscillation of carbon molecules inside carbon nanotube bundles.

In this paper, we investigate the mechanics of a nanoscaled gigahertz oscillator comprising a carbon molecule oscillating within the centre of a uniform concentric ring or bundle of carbon nanotubes. Two kinds of oscillating molecules are considered, which are a carbon nanotube and a C(60) fullerene. Using the Lennard-Jones potential and the continuum approach, we obtain a relation between the bundle radius and the radii of the nanotubes forming the bundle, as well as the optimum bundle size which gives rise to the maximum oscillatory frequency for both the nanotube-bundle and the C(60)-bundle oscillators.

Comment on "General equilibrium shape equations of polymer chains".

In this Comment, we point out that the Euler-Lagrange equations, which are referred to as the general equilibrium shape equations presented by Zhang et al. [Phys. Rev.

Continuum modelling for carbon and boron nitride nanostructures.

Continuum based models are presented here for certain boron nitride and carbon nanostructures. In particular, certain fullerene interactions, C(60)-C(60), B(36)N(36)-B(36)N(36) and C(60)-B(36)N(36), and fullerene-nanotube oscillator interactions, C(60)-boron nitride nanotube, C(60)-carbon nanotube, B(36)N(36)-boron nitride nanotube and B(36)N(36)-carbon nanotube, are studied using the Lennard-Jones potential and the continuum approach, which assumes a uniform distribution of atoms on the surface of each molecule. Issues regarding the encapsulation of a fullerene into a nanotube are also addressed, including acceptance and suction energies of the fullerenes, preferred position of the fullerenes inside the nanotube and the gigahertz frequency oscillation of the inner molecule inside the outer nanotube.