Yue Chan

Hydrogen storage inside graphene-oxide frameworks

In this paper, we use applied mathematical modelling to investigate the storage of hydrogen molecules inside graphene-oxide frameworks, which comprise two parallel graphenes rigidly separated by perpendicular ligands. Hydrogen uptake is calculated for graphene-oxide frameworks using the continuous approximation and an equation of state for both the bulk and adsorption gas phases. We first validate our approach by obtaining results for two parallel graphene sheets. This result agrees well with an existing theoretical result, namely 1.85 wt% from our calculations, and 2 wt% arising from an ab initio and grand canonical Monte Carlo calculation. This provides confidence to the determination of the hydrogen uptake for the four graphene-oxide frameworks, GOF-120, GOF-66, GOF-28 and GOF-6, and we obtain 1.68, 2, 6.33 and 0 wt%, respectively. The high value obtained for GOF-28 may be partly explained by the fact that the benzenediboronic acid pillars between graphene sheets not only provide mechanical support and porous spaces for the molecular structure but also provide the higher binding energy to enhance the hydrogen storage inside graphene-oxide frameworks. For the other three structures, this binding energy is not as large in comparison to that of GOF-28 and this effect diminishes as the ligand density decreases. In the absence of conflicting data, the present work indicates GOF-28 as a likely contender for practical hydrogen storage.

Metallofullerenes in Composite Carbon Nanotubes as a Nanocomputing Memory Device

Here, we investigate a hybrid carbon nanostructure, which comprises two single-open host nanotubes of the same radius and joined by another single-open nanotube, which is centrally located between the host nanotubes but has a smaller radius. A metallofullerene is then enclosed inside the structure to represent a bit information and is originally located inside one of the host nanotubes. The geometric parameters, such as the radii of nanotubes and fullerene radius are purposely chosen so that the metallofullerene cannot enter the central nanotube without additional energy. By applying an external electrical field, the metallofullerene can overcome the energy barrier and pass from one end to the other end to form a two-state fullerene shuttle memory device. The key geometric parameters are provided for a range of fullerenes, including C60, C 80, and C100, noting that we assume most metallofullerenes take the form M@C60, M@C80, and M@C100, where M denotes a metal atom or ion located noncovalently inside the fullerene Cn.

Ion selectivity using membranes comprising functionalized carbon nanotubes

In this paper, we use applied mathematical modelling to investigate the transportation of ions inside functionalized carbon nanotubes, and in particular the transport of sodium and chloride ions. This problem is important for future ion transport and detection, and also arises in ion diffusion inside complex biological channels. Some important future applications of the system for a solvent are ultra-sensitive biosensors and electrolytes for alkaline fuel cells. We model the interactions between the ions and the nanotube by the Lennard-Jones potential and the interactions between the ions and the functional group by the Coulomb potential, while the atomic interactions between the ions is modeled by both the Lennard-Jones and Coulomb potentials. We further assume that the carbon atoms, the charge of the functional group, and the ions are all evenly distributed on the surface of the nanotube, the entry of the nanotube and the envisaged ionic surface, respectively, so that we may use the continuous approximation to calculate the corresponding potential energies. For nanotubes located in salt water, the molecular effects arising from the bulk solution can be extracted from MD simulation studies. Assuming that the solvent is absent, we first determine the acceptance radii for the sodium or chloride ion entering the nanotube, both with and without a functional group, and we then determine the equilibrium positions of two identical ions inside the nanotube. Finally, the transportation time of an intruding ion through the nanotube is deduced from the total axial force. In the presence of a solvent, the molecular effects arising from the bulk solution are examined and we establish that the presence of a solvent stabilizes the selectivity of the ions.

Mechanical model for a collagen fibril pair in extracellular matrix

In this paper, we model the mechanics of a collagen pair in the connective tissue extracellular matrix that exists in abundance throughout animals, including the human body. This connective tissue comprises repeated units of two main structures, namely collagens as well as axial, parallel and regular anionic glycosaminoglycan between collagens. The collagen fibril can be modeled by Hooke’s law whereas anionic glycosaminoglycan behaves more like a rubber-band rod and as such can be better modeled by the worm-like chain model. While both computer simulations and continuum mechanics models have been investigated for the behavior of this connective tissue typically, authors either assume a simple form of the molecular potential energy or entirely ignore the microscopic structure of the connective tissue. Here, we apply basic physical methodologies and simple applied mathematical modeling techniques to describe the collagen pair quantitatively. We found that the growth of fibrils was intimately related to the maximum length of the anionic glycosaminoglycan and the relative displacement of two adjacent fibrils, which in return was closely related to the effectiveness of anionic glycosaminoglycan in transmitting forces between fibrils. These reveal the importance of the anionic glycosaminoglycan in maintaining the structural shape of the connective tissue extracellular matrix and eventually the shape modulus of human tissues. We also found that some macroscopic properties, like the maximum molecular energy and the breaking fraction of the collagen, were also related to the microscopic characteristics of the anionic glycosaminoglycan.

Force-extension formula for the worm-like chain model from a variational principle

Stiff polymers, such as single-stranded DNA, unstructured RNA and cellulose, are all basically extremely long rods with relatively short repeating monomers. The simplest model for describing such stiff polymers is called the freely jointed chain model, which treats a molecule as a chain of perfectly rigid subunits of orientationally independent statistical segments, joined together by perfectly flexible hinges. A more realistic model that incorporates the entropic elasticity of a molecule, called the worm-like chain model, has been proposed by assuming that each monomer resists the bending force. Some force-extension formulae for the worm-like chain model have been previously found in terms of interpolation and numerical solutions resulting from statistical mechanics. In this paper, however, we adopt a variational principle to seek the minimum energy configuration of a stretched molecule by incorporating all the possible orientations of each monomer under thermal equilibrium, i.e., constant temperature. We determine a force-extension formula for the worm-like chain model analytically. We find that our formula suggests new terms such as the free energy and the cut-off force of a molecule, which define a clear transition from the entropic regime to the enthalpic regime and the fracture of the molecule, respectively. In addition, we predict two possible phase changes for a stretched molecule, i.e., from a super-helix to a soliton and then from a soliton to a vertical twisted line. We show theoretically that a molecule must undergo at least one phase change before it is fully stretched into its total contour length. This new formula is used to fit recent experimental data and shows a good agreement with some current literature that uses a statistical approach. Finally, an instability analysis is adopted to investigate the sensitivity of the new formula subject to small changes in temperature.

Mathematical modeling and simulations on massive hydrogen yield using functionalized nanomaterials

In this paper, we adopt the mathematical modeling and MD simulation to investigate the possibility of using functionalized nanomaterials, in particular carbon nanotubes and graphene to yield hydrogen from an acidic solution by the mean of reverse osmosis. Positively charged nanomaterials are found to be a necessary condition for such phenomenon to happen. For hydrogen chloride acid under certain external forces, only hydrogen ions could gain sufficient work done to overcome the energy barrier induced by the functionalized nanomaterials, resulting in sole hydrogen ions in the permeate side. Hydrogen could then be produced from hydrogen ions by a chemical reduction. Our numerical results indicate that for the two proposed nanomaterials, functionalized graphene turns out to be the better candidate for the current purpose.

Spiral motion of carbon atoms and C60 fullerenes inside single-walled carbon nanotubes

In this paper, we investigate the motion of a carbon atom and a C60 fullerene inside a carbon nanotube. The pairwise molecular energy between molecules arising from the van der Waals forces is approximated by performing surface integrals. In the absence of any thermal fluctuations, the carbon atom or the C60 molecule will oscillate in an axial direction inside the carbon nanotube. However, any thermal fluctuations will tend to induce a spiral-like motion of the atom or the C60 molecule. Our results also indicate that the thermal fluctuations reduce the general oscillatory frequency for the C60 molecule inside the nanotube due to the energy dissipation during the unstable spiral motion.

Restricted Three Body Problems at the Nanoscale

In this paper, we investigate some of the classical restricted three body problems at the nanoscale, such as the circular planar restricted problem for three C60 fullerenes, and a carbon atom and two C60 fullerenes. We model the van der Waals forces between the fullerenes by the Lennard–Jones potential. In particular, the pairwise potential energies between the carbon atoms on the fullerenes are approximated by the continuous approach, so that the total molecular energy between two fullerenes can be determined analytically. Since we assume that such interactions between the molecules occur at sufficiently large distance, the classical three body problems analysis is legitimate to determine the collective angular velocity of the two and three C60 fullerenes at the nanoscale. We find that the maximum collective angular velocity of the two and three fullerenes systems reach the terahertz range and we also determine the stationary points and the points which have maximum velocity for the carbon atom, for the carbon atom and the two fullerenes system.

Modelling and MD simulations on ultra-filtration using graphene sheet

In this paper, we investigate the ion rejection of salt water using graphene sheet as a semi-permeable membrane. Both the mathematical modeling and MD simulations will be performed to determine the acceptance conditions for a water molecule or a sodium ion permeating into the membrane. Chloride ion is always blocked by the graphene due to the fact that the ionic size of the chloride ion is larger than the pore size of the graphene leaving the sieve of water and sodium ions which depends on the strength of the external forces. In particular, certain ranges of the external forces will be theoretically deduced for the complete desalination, which turn out to depend intimately on the size of the permeate container and the hydraulic force acting among salt water. In this paper, we reduce the multi-body system into several two-body systems and reduce the 3D problem into degenerated 1D problems using the continuous approximation, where the molecular interactions between the water molecule or the sodium ion and the graphene could be determined in terms of surface integrals. Given the force fields between the intruder and the membrane, MD simulations could be used to investigate the time evolution of the system and compare with the theoretical results deduced by the present mathematical model. We confirm the computational results given by Tanugi and Grossman (Nano Lett 12:3602–3608, 2012). Moreover, our approach is computationally rapid and generates inductive results for more engineering applications.

A carbon atom orbiting around the outside of a carbon nanotube

In this paper, we examine a carbon atom orbiting around the outside of a (6,6) carbon nanotube, where the orbiting phenomena is assumed to arise only from the van der Waals interactions between the carbon atom and the atoms on the surface of the carbon nanotube. We model the van der Waals forces utilizing the Lennard-Jones potential and assume that the carbon atoms are uniformly distributed over the surface of the carbon nanotube, so that a discrete sum of the atomic potential energy between the carbon atom and the molecule can be approximated by a line integral. The circular orbiting frequency of the system can be estimated by investigating the minimum energy configuration of the effective potential energy. An instability calculation is performed to ensure that the circular orbit remains stable, and the classification of the atompsilas possible loci is determined numerically. We find that the circular orbiting frequency of the proposed system reaches the gigahertz regime, which suggests that such a system has potential to be utilized as an ideal device in future technological development. We also briefly show that the results obtained from the above system can be extended to a fullerene orbiting around the outside of a carbon nanotube without conceptual difficulties, but with increased mathematical complexity.