Mathematical modelling of controlled drug release from polymer micro-spheres : incorporating the effects of swelling, diffusion and dissolution via moving boundary problems

Controlled drug delivery is a key topic in modern pharmacotherapy, where controlled drug delivery devices are required to prolong the period of release, maintain a constant release rate, or release the drug with a predetermined release profile. In the pharmaceutical industry, the development process of a controlled drug delivery device may be facilitated enormously by the mathematical modelling of drug release mechanisms, directly decreasing the number of necessary experiments. Such mathematical modelling is difficult because several mechanisms are involved during the drug release process. The main drug release mechanisms of a controlled release device are based on the device’s physiochemical properties, and include diffusion, swelling and erosion. In this thesis, four controlled drug delivery models are investigated. These four models selectively involve the solvent penetration into the polymeric device, the swelling of the polymer, the polymer erosion and the drug diffusion out of the device but all share two common key features. The first is that the solvent penetration into the polymer causes the transition of the polymer from a glassy state into a rubbery state. The interface between the two states of the polymer is modelled as a moving boundary and the speed of this interface is governed by a kinetic law. The second feature is that drug diffusion only happens in the rubbery region of the polymer, with a nonlinear diffusion coefficient which is dependent on the concentration of solvent. These models are analysed by using both formal asymptotics and numerical computation, where front-fixing methods and the method of lines with finite difference approximations are used to solve these models numerically. This numerical scheme is conservative, accurate and easily implemented to the moving boundary problems and is thoroughly explained in Section 3.2. From the small time asymptotic analysis in Sections 5.3.1, 6.3.1 and 7.2.1, these models exhibit the non-Fickian behaviour referred to as Case II diffusion, and an initial constant rate of drug release which is appealing to the pharmaceutical industry because this indicates zeroorder release. The numerical results of the models qualitatively confirms the experimental behaviour identified in the literature. The knowledge obtained from investigating these models can help to develop more complex multi-layered drug delivery devices in order to achieve sophisticated drug release profiles. A multi-layer matrix tablet, which consists of a number of polymer layers designed to provide sustainable and constant drug release or bimodal drug release, is also discussed in this research. The moving boundary problem describing the solvent penetration into the polymer also arises in melting and freezing problems which have been modelled as the classical onephase Stefan problem. The classical one-phase Stefan problem has unrealistic singularities existed in the problem at the complete melting time. Hence we investigate the effect of including the kinetic undercooling to the melting problem and this problem is called the one-phase Stefan problem with kinetic undercooling. Interestingly we discover the unrealistic singularities existed in the classical one-phase Stefan problem at the complete melting time are regularised and also find out the small time behaviour of the one-phase Stefan problem with kinetic undercooling is different to the classical one-phase Stefan problem from the small time asymptotic analysis in Section 3.3. In the case of melting very small particles, it is known that surface tension effects are important. The effect of including the surface tension to the melting problem for nanoparticles (no kinetic undercooling) has been investigated in the past, however the one-phase Stefan problem with surface tension exhibits finite-time blow-up. Therefore we investigate the effect of including both the surface tension and kinetic undercooling to the melting problem for nanoparticles and find out the the solution continues to exist until complete melting. The investigation of including kinetic undercooling and surface tension to the melting problems reveals more insight into the regularisations of unphysical singularities in the classical one-phase Stefan problem. This investigation gives a better understanding of melting a particle, and contributes to the current body of knowledge related to melting and freezing due to heat conduction.

Adsorption and dissociation of ammonia borane outside and inside single-walled carbon nanotubes : A density functional theory study

Amonia borane (AB) has been identified as a potential candidate highcapacity hydrogen storage material. This work probes the adsorption and dissociation of AB inside and outside single-walled carbon nanotubes (SWCNTs) within the framework of density functional theory. The dissociation barriers of AB have been calculated and compared with that of the isolated AB molecule. On the basis of the present calculations, no notable improvement results from SWCNT confinement; on the contrary, the dissociation barrier slightly increases with respect to isolated AB.

Adsorption of carbon dioxide and nitrogen on single-layer aluminum nitride nanostructures studied by density functional theory

The adsorption of carbon dioxide and nitrogen molecules on aluminum nitride (AlN) nanostructures has been explored using first-principle computational methods. Optimized configurations corresponding to physisorption and, subsequentially, chemisorption of CO2 are identified, in contrast to N2, for which only a physisorption structure is found. Transition-state searches imply a low energy barrier between the physisorption and chemisorption states for CO2 such that the latter is accessible and thermodynamically favored at room temperature. The effective binding energy of the optimized chemisorption structure is apparently larger than those for other CO2 adsorptive materials, suggesting the potential for application of aluminum nitride nanostructures for carbon dioxide capture and storage.

The effect of Fe doping on adsorption of CO2/N2within carbon nanotubes : a density functional theory study with dispersion corrections

An ab initio density functional theory (DFT) study with correction for dispersive interactions was performed to study the adsorption of N2 and CO2 inside an (8, 8) single-walled carbon nanotube. We find that the approach of combining DFT and van der Waals correction is very effective for describing the long-range interaction between N2/CO2 and the carbon nanotube (CNT). Surprisingly, exohedral doping of an Fe atom onto the CNT surface will only affect the adsorption energy of the quadrupolar CO2 molecule inside the CNT (20–30%), and not that of molecular N2. Our results suggest the feasibility of enhancement of CO2/N2 separation in CNT-based membranes by using exohedral doping of metal atoms.

Half metallicity in finite-length zigzag single walled carbon nanotube : A first-principle prediction

We predict here from first-principle calculations that finite-length (n,0) single walled carbon nanotubes (SWCNTs) with H-termination at the open ends displaying antiferromagnetic coupling when n is greater than 6. An opposite local gating effect of the spin states, i.e., half metallicity, is found under the influence of an external electric field along the direction of tube axis. Remarkably, boron doping of unpassivated SWCNTs at both zigzag edges is found to favor a ferromagnetic ground state, with the B-doped tubes displaying half-metallic behavior even in the absence of an electric field. Aside of the intrinsic interest of these results, an important avenue for development of CNT-based spintronic is suggested.

CO2 capture and gas separation on boron carbon nanotubes

Concern about the increasing atmospheric CO2 concentration and its impact on the environment has led to increasing attention directed toward finding advanced materials and technologies suited for efficient CO2 capture, storage and purification of clean-burning natural gas. In this letter, we have performed comprehensive theoretical investigation of CO2, N2, CH4 and H2 adsorption on B2CNTs. Our study shows that CO2 molecules can form strong interactions with B2CNTs with different charge states. However, N2, CH4 and H2 can only form very weak interactions with B2CNTs. Therefore, the study demonstrates B2CNTs could sever as promising materials for CO2 capture and gas separation.

Addition of diazomethane to armchair single-walled carbon nanotubes and their reaction sequences : A computational study

The sidewall additions of diazomethane to (n, n), n = 3–10 armchair single-walled carbon nanotubes (SWCNTs) on two different orientations of C–C bonds have been studied using the ONIOM(B3LYP/6-31G(d):PM3) approach. The binding energies of SWCNTs complexes with CH2N2, CH2 and their transition-state structures were computed at the B3LYP/6-31G(d) level. The effects of diameters of armchair SWCNTs on their binding energies were studied. Relative reactivities of all the SWCNTs and their complexes based on their frontier orbital energies gaps are reported.

Structural and electronic properties of diazonium functionalized (4, 4) single walled carbon nanotube : an ab initio study

In this work, ab initio density functional theory (DFT) calculations are performed to study the structural and electronic properties of diazonium reagent functionalized (4, 4) single-walled carbon nanotube (SWCNT). We find the aryl group covalently bonds with SWCNT and prefers to be perpendicular to the side wall of nanotube. It has a rotational barrier of 0.35 eV around the formed aryl-tube bond axis and should be thermodynamically stable at room temperature. Additionally, new peaks appeared around the Fermi energy in the density of state (DOS) due to the weak band dispersion. Increasing of the coverage of the functional group will result in significant upshift of the Fermi level.

Atomic hydrogen diffusion in novel magnesium nanostructures : the impact of incorporated subsurface carbon atoms

Ab initio Density Functional Theory (DFT) calculations are performed to study the diffusion of atomic hydrogen on a Mg(0001) surface and their migration into the subsurface layers. A carbon atom located initially on a Mg(0001) surface can migrate into the sub-surface layer and occupy a fcc site, with charge transfer to the C atom from neighboring Mg atoms. The cluster of postively charged Mg atoms surrounding a sub-surface C is then shown to facilitate the dissociative chemisorption of molecular hydrogen on the Mg(0001) surface, and the surface migration and subsequent diffusion into the subsurface of atomic hydrogen. This helps rationalize the experimentally-observed improvement in absorption kinetics of H2 when graphite or single walled carbon nanotubes (SWCNT) are introduced into the Mg powder during ball milling.

Catalytic effects of subsurface carbon in the chemisorption of hydrogen on a Mg(0001) surface: an ab-initio study

Ab initio density functional theory (DFT) calculations are performed to explore possible catalytic effects on the dissociative chemisorption of hydrogen on a Mg(0001) surface when carbon is incorporated into Mg materials. The computational results imply that a C atom located initially on a Mg(0001) surface can migrate into the subsurface and occupy an fcc interstitial site, with charge transfer to the C atom from neighboring Mg atoms. The effect of subsurface C on the dissociation of H2 on the Mg(0001) surface is found to be relatively marginal: a perfect sublayer of interstitial C is calculated to lower the barrier by 0.16 eV compared with that on a pure Mg(0001) surface. Further calculations reveal, however, that sublayer C may have a significant effect in enhancing the diffusion of atomic hydrogen into the sublayers through fcc channels. This contributes new physical understanding toward rationalizing the experimentally observed improvement in absorption kinetics of H2 when graphite or single walled carbon nanotubes (SWCNT) are introduced into the Mg powder during ball milling.

Structure character in small-carbon-cluster deposition on diamond surface

Experimentally, hydrogen-free diamond-like carbon (DLC) films were assembled by means of pulsed laser deposition (PLD), where energetic small-carbon-clusters were deposited on the substrate. In this paper, the chemisorption of energetic C2 and C10 clusters on diamond (001)-( 2×1) surface was investigated by molecular dynamics simulation. The influence of cluster size and the impact energy on the structure character of the deposited clusters is mainly addressed. The impact energy was varied from a few tens eV to 100 eV. The chemisorption of C10 was found to occur only when its incident energy is above a threshold value ( E th). While, the C2 cluster was easily to adsorb on the surface even at much lower incident energy. With increasing the impact energy, the structures of the deposited C2 and C10 are different from the free clusters. Finally, the growth of films synthesized by energetic C2 and C10 clusters were simulated. The statistics indicate the C2 cluster has high probability of adsorption and films assembled of C2 present slightly higher SP3 fraction than that of C10-films, especially at higher impact energy and lower substrate temperature. Our result supports the experimental findings. Moreover, the simulation underlines the deposition mechanism at atomic scale.

Children exposure assessment to ultrafine particles and black carbon: The role of transport and cooking activities

An accurate evaluation of the airborne particle dose-response relationship requires detailed measurements of the actual particle concentration levels that people are exposed to, in every microenvironment in which they reside. The aim of this work was to perform an exposure assessment of children in relation to two different aerosol species: ultrafine particles (UFPs) and black carbon (BC). To this purpose, personal exposure measurements, in terms of UFP and BC concentrations, were performed on 103 children aged 8-11 years (10.1 ± 1.1 years) using hand-held particle counters and aethalometers. Simultaneously, a time-activity diary and a portable GPS were used to determine the children’s daily time-activity pattern and estimate their inhaled dose of UFPs and BC. The median concentration to which the study population was exposed was found to be comparable to the high levels typically detected in urban traffic microenvironments, in terms of both particle number (2.2×104 part. cm-3) and BC (3.8 μg m-3) concentrations. Daily inhaled doses were also found to be relatively high and were equal to 3.35×1011 part. day-1 and 3.92×101 μg day-1 for UFPs and BC, respectively. Cooking and using transportation were recognized as the main activities contributing to overall daily exposure, when normalized according to their corresponding time contribution for UFPs and BC, respectively. Therefore, UFPs and BC could represent tracers of children exposure to particulate pollution from indoor cooking activities and transportation microenvironments, respectively.

Cobalt-doped cadmium selenide colloidal nanowires

Co2+-doped CdSe colloidal nanowires with tunable size and dopant concentration have been prepared by a solution–liquid–solid (SLS) approach for the first time. These doped nanowires exhibit anomalous photoluminescence temperature dependence in comparison with undoped nanowires.

From rights to responsibilities : reconceptualising carbon sequestration rights in Australia

Biosequestration of carbon in trees, forests and vegetation is a key method for mitigating climate change in Australia. To facilitate this, all States have enacted legislation for carbon sequestration rights, separating commercial rights in carbon from ownership of the land, trees and vegetation in which the carbon is sequestered. Ownership of carbon sequestration rights under state law is a prerequisite for the issue of carbon credits to proponents of ‘eligible sequestration offsets projects’ under the Carbon Credits (Carbon Farming Initiative) Act 2011 (Cth) (‘Carbon Farming Act’). This article examines the extent to which current State carbon sequestration rights support the offsets regime established by the Carbon Farming Act. The Commonwealth Act is concerned with allocating responsibilities to ensure the maintenance of the carbon sequestration, while the State Acts confer commercial rights in the carbon and leave the responsibilities to be allocated by private agreements. The carbon sequestration rights as defined by state laws do not confer the rights of access and management over land that a project proponent needs in order to discharge its responsibilities to maintain the carbon sequestration.

Crime and the commodification of carbon

Carbon will be the world's biggest market. Barclays was the first UK bank to set up a dedicated carbon trading desk to help clients, and Barclays Capital is the most active player in the emissions trading market having traded 300 million tonnes as at February 2007. (Barclays, 2007: 1)