Duangkamon Baowan

Encapsulation of TiO 2 nanoparticles into single-walled carbon nanotubes

Nanostructures such as carbon nanotubes and titanium dioxide (TiO2) offer the means to create novel nanoscale devices and technologies. The question as to whether or not TiO2-nanoparticle (TiO2-NP) can be encapsulated in a single-walled carbon nanotube (SWNT) depends on the physical and chemical interactions between the TiO2-NP and the SWNT. Motivated by nanoscale encapsulation research and nanoscale delivery systems, we present a simple but useful model to study the system comprised of an SWNT encapsulated with TiO2-NP under various conditions. Using the well-known Lennard-Jones (6-12) potential for both cylindrical- and spherical-shaped TiO2- NP, analytical expressions are obtained for calculating the potential energy, the encapsulating energy and the force distribution and other quantities. In particular, the suction force experienced by an SWNT located near an open end of a

Energetics of liposomes encapsulating silica nanoparticles

Nanoparticles may be taken up into cells via endocytotic processes whereby the foreign particles are encapsulated in vesicles formed by lipid bilayers. After uptake into these endocytic vesicles, intracellular targeting processes and vesicle fusion might cause transfer of the vesicle cargo into other vesicle types, e.g., early or late endosomes, lysosomes, or others. In addition, nanoparticles might be taken up as single particles or larger agglomerates and the agglomeration state of the particles might change during vesicle processing. In this study, liposomes are regarded as simple models for intracellular vesicles. We compared the energetic balance between two liposomes encapsulating each a single silica nanoparticle and a large liposome containing two silica nanoparticles. Analytical expressions were derived that show how the energy of the system depends on the particle size and the distance between the particles. We found that the electrostatic contributions to the total energy of the system are negligibly small. In contrast, the van der Waals term strongly favors arrangements where the liposome snugly fits around the nanoparticle(s). Thus the two separated small liposomes have a more favorable energy than a larger liposome encapsulating two nanoparticles.

Junctions between a boron nitride nanotube and a boron nitride sheet

For future nanoelectromechanical signalling devices, it is vital to understand how to connect various nanostructures. Since boron nitride nanostructures are believed to be good electronic materials, in this paper we elucidate the classification of defect geometries for combining boron nitride structures. Specifically, we determine possible joining structures between a boron nitride nanotube and a flat sheet of hexagonal boron nitride. Firstly, we determine the appropriate defect configurations on which the tube can be connected, given that the energetically favourable rings for boron nitride structures are rings with an even number of sides. A new formula E = 6+2J relating the number of edges E and the number of joining positions J is established for each defect, and the number of possible distinct defects is related to the so-called necklace and bracelet problems of combinatorial theory. Two least squares approaches, which involve variation in bond length and variation in bond angle, are employed to determine the perpendicular connection of both zigzag and armchair boron nitride nanotubes with a boron nitride sheet. Here, three boron nitride tubes, which are (3, 3), (6, 0) and (9, 0) tubes, are joined with the sheet, and Eulers theorem is used to verify geometrically that the connected structures are sound, and their relationship with the bonded potential energy function approach is discussed. For zigzag tubes (n,0), it is proved that such connections investigated here are possible only for n divisible by 3.

Zigzag and spiral configurations for fullerenes in carbon nanotubes

The success or otherwise of nanoscale devices hinges on a correct understanding of the physical effects at this scale. Research in nanotechnology is predominantly through either experimentation using electron and atomic force microscopy or through large-scale computation using molecular dynamics simulation. In this paper, we employ elementary mechanical principles and classical modelling procedures to investigate the packing of C60 fullerene chains inside a single-walled carbon nanotube by utilizing the Lennard–Jones potential function and the continuum approximation. Such assemblies are often referred to as nanopeapods. We examine both zigzag and spiral chain configurations inside (10, 10), (16, 16) and (20, 20) carbon nanotubes and we obtain analytical expressions in terms of hypergeometric functions for the potential energy for such configurations. We find that for a (10, 10) tube, the C60 fullerene chain is formed linearly along the tube axis. In the case of both (16, 16) and (20, 20) tubes, both zigzag and spiral configurations are more clearly evident along the tube. In particular, the resulting pattern obtained for the zigzag chain is entirely consistent with a specific angular spacing for the spiral pattern.

Continuum modelling of gigahertz nano-oscillators

Fullerenes and carbon nanotubes are of considerable interest throughout many scientific areas due to their unique and exceptional properties, such as low weight, high strength, flexibility, high thermal conductivity and chemical stability. These nanostructures have many potential applications in nano-devices. One concept that has attracted much attention is the creation of nano-oscillators, which can produce frequencies in the gigahertz range, for applications such as ultra-fast optical filters and nano-antennae. In this paper, we provide the underlying mechanisms of the gigahertz nano-oscillators and we review some recent results derived by the authors using the Lennard-Jones potential together with the continuum approach to mathematically model three different types of nano-oscillators including double-walled carbon nanotube, C60-nanotube and C60-nanotorus oscillators.

Relating elasticity and graphene folding conformation

Variational calculus is employed to determine the folding behaviour of a single graphene sheet. Both the elastic and van der Waals energies are taken into account, and from these considerations the shape of the curve is determined. By prescribing that the separation distance between the folded graphene in the parallel region is 3.32 A, an arbitrary constant arising by integrating the Euler–Lagrange equation is determined, and the full parametric representations for the folding conformation are derived. Using typical values of the bending rigidity in the range of 0.800–1.60 eV, the shortest stable folded graphene sheets are required to be at least 6.5–10 nm in length.

A continuous model for the joining of two fullerenes

The successful design of many novel nano-electronic devices will require a thorough understanding of the geometric joining issues of certain nano-structures. In this paper, we adopt a continuous approach and we employ the calculus of variations to model the nanostructure obtained by the joining of two fullerenes. We model the fullerenes as spheres and we assume symmetric defects on both fullerenes so that the three-dimensional problem is axially symmetric and can therefore be reduced to a problem in two dimensions. We propose two models depending upon the curvature of the join profile which can be either positive or both positive and negative. However, there is at present no experimental or simulation data to verify the theoretical connecting structures predicted by this study.

Modelling of carbon dioxide: methane separation using titanium dioxide nanotubes

The separation of carbon dioxide (CO2) and methane (CH4) mixture is of considerable interest in order to purify natural gas, and one suggestion is that titanium dioxide (TiO2) nanotubes might be exploited to separate a gaseous mixture of methane and carbon dioxide. In this study, we employ both Coulomb’s law and the Lennard–Jones potential to determine the total energy of adsorption CO2 and CH4 into a TiO2 nanotube. The CH4 is a nonpolar molecule, and therefore the Coulombic interaction may be neglected. The total energy of the systems is evaluated utilizing the continuous approximation, which assumes that the two gas molecules are spheres of certain radii, while the tube is modelled as a cylinder. Further, both electrostatic and van der Waals potentials are determined and expressed in the exact analytical formulae. The numerical results predict that a single molecule of CO2 or CH4 can be encapsulated into the tube. On assuming both gases may form clusters with the same proportion of atom species, a cluster of CO2 will not be adsorbed into the tube when its radius exceeds 3.32Å. On the other hand, a cluster of CH4 can be encapsulated into an appropriate radius of TiO2 nanotube. These results indicate that TiO2 nanotubes may be useful in the purification of CH4.

Force Distribution for Double-Walled Carbon Nanotubes

Advances in technology have led to the creation of many nano-scale devices and carbon nanotubes are representative materials to construct these devices. Double-walled carbon nanotubes with the inner tube oscillating can be used as gigahertz oscillators and form the basis of possible nano-electronic devices. Such gigahertz oscillating devices made from carbon nanotubes might be instrumental in the micro-computer industry, which is predominantly based on electron transport phenomena. There are many experiments and molecular dynamics simulations which show that a wave is generated on the outer cylinder by the oscillation of the carbon nanotubes and that the frequency of this wave is also in the gigahertz range. However, conventional applied mathematical modelling techniques are generally lacking. In order to analyse and model such devices, it is necessary to estimate accurately the resultant force distribution due to the inter-atomic interactions. Here, we find the van der Waals force using the Lennard-Jones potential to calculate the oscillation frequency using Newtons second law for double-walled carbon nanotubes of any length of the inner and the outer tubes, 2L1 and 2L2, respectively. These results are based on work by the present authors derived in (Baowan and Hill).

Three model shapes of Doxorubicin for liposome encapsulation

Targeted drug delivery provides a possible method for the transfer of drug molecules into cancer cells. Liposomes together with a drug, such as Doxorubicin (DOX) inside the liposomes, can be formed as a nano-capsule. In this study, we are interested in finding a favorable size of liposome and an appropriate shape of DOX cluster: sphere, cylinder or ellipsoid. Using mathematical modeling, the interaction energy of the system is obtained from the Lennard-Jones potential and the continuum assumption which assumes that discrete atomic structure can be replaced by an average atomic density spread over a surface. The numerical results show that the spherical shape gives the lowest energy at the equilibrium configuration amongst the three shapes. In the case of equivalent surface areas, the spherical shape gives the energy lower than −4,000 kJ/mol at the equilibrium while the energies for the other cases do not come close to this level. Further in the case of a liposome of 50 nm in radius, the sphere of radius 49.726 nm, equivalent to 31,072 nm2 surface area, gives the minimum energy at −6,642 kJ/mol. However, an equivalent cylindrical shape is not possible due to geometric constraints. The lowest minimum energy for the ellipsoid occurs for equal major and minor axes, namely for the spherical case. The results presented here are a first step in the design and implementation of a drug molecule for a targeted drug delivery system.