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.

Quantitative evaluation of polymer gel dosimeters by broadband ultrasound attenuation

Ultrasound has been examined previously as an alternative readout method for irradiated polymer gel dosimeters, with authors reporting varying dose response to ultrasound transmission measurements. In this current work we extend previous work to measure the broadband ultrasound attenuation (BUA) response of irradiated PAGAT gel dosimeters, using a novel ultrasound computed tomography system.

Reconstructing 3D x-ray CT images of polymer gel dosimeters using the zero-scan method

In this study x-ray CT has been used to produce a 3D image of an irradiated PAGAT gel sample, with noise-reduction achieved using the ‘zero-scan’ method. The gel was repeatedly CT scanned and a linear fit to the varying Hounsfield unit of each pixel in the 3D volume was evaluated across the repeated scans, allowing a zero-scan extrapolation of the image to be obtained. To minimise heating of the CT scanner’s x-ray tube, this study used a large slice thickness (1 cm), to provide image slices across the irradiated region of the gel, and a relatively small number of CT scans (63), to extrapolate the zero-scan image. The resulting set of transverse images shows reduced noise compared to images from the initial CT scan of the gel, without being degraded by the additional radiation dose delivered to the gel during the repeated scanning. The full, 3D image of the gel has a low spatial resolution in the longitudinal direction, due to the selected scan parameters. Nonetheless, important features of the dose distribution are apparent in the 3D x-ray CT scan of the gel. The results of this study demonstrate that the zero-scan extrapolation method can be applied to the reconstruction of multiple x-ray CT slices, to provide useful 2D and 3D images of irradiated dosimetry gels.

Deformation and failure of graphene sheet and graphene-polymer interface

With a monolayer honeycomb-lattice of sp2-hybridized carbon atoms, graphene has demonstrated exceptional electrical, mechanical and thermal properties. One of its promising applications is to create graphene-polymer nanocomposites with tailored mechanical and physical properties. In general, the mechanical properties of graphene nanofiller as well as graphene-polymer interface govern the overall mechanical performance of graphene-polymer nanocomposites. However, the strengthening and toughening mechanisms in these novel nanocomposites have not been well understood. In this work, the deformation and failure of graphene sheet and graphene-polymer interface were investigated using molecular dynamics (MD) simulations. The effect of structural defects on the mechanical properties of graphene and graphene-polymer interface was investigated as well. The results showed that structural defects in graphene (e.g. Stone-Wales defect and multi-vacancy defect) can significantly deteriorate the fracture strength of graphene but may still make full utilization of corresponding strength of graphene and keep the interfacial strength and the overall mechanical performance of graphene-polymer nanocomposites.

Thermal transport in graphene-polymer nanocomposites

Graphene-polymer nanocomposites have attracted considerable attention due to their unique properties, such as high thermal conductivity (~3000 W mK-1), mechanical stiffness (~ 1 TPa) and electronic transport properties. Relatively, the thermal performance of graphene-polymer composites has not been well investigated. The major technical challenge is to understand the interfacial thermal transport between graphene nanofiller and polymer matrix at small material length scale. To this end, we conducted molecular dynamics simulations to investigate the thermal transport in graphene-polyethylene nanocomposite. The influence of functionalization with hydrocarbon chains on the interfacial thermal conductivity was studied, taking into account of the effects of model size and thermal conductivity of graphene. The results are considered to contribute to development of new graphene-polymer nanocomposites with tailored thermal properties.

Measuring the mechanical properties of ground ophthalmic polymer surfaces using nanoindentation

This work is motivated by the need to efficiently machine the edges of ophthalmic polymer lenses for mounting in spectacle or instrument frames. The polymer materials used are required to have suitable optical characteristics such high refractive index and Abbe number, combined with low density and high scratch and impact resistance. Edge surface finish is an important aesthetic consideration; its quality is governed by the material removal operation and the physical properties of the material being processed. The wear behaviour of polymer materials is not as straightforward as for other materials due to their molecular and structural complexity, not to mention their time-dependent properties. Four commercial ophthalmic polymers have been studied in this work using nanoindentation techniques which are evaluated as tools for probing surface mechanical properties in order to better understand the grinding response of polymer materials.

trans-Polyacetylene on sodium and cesium mordenites: a resonance Raman spectroscopic study

Sodium and cesium mordenite (denoted NaM and CsM, respectively) were investigated as potential catalysts for the synthesis of polyacetylene ((CH) x). Both were successful in initiating polymerization of purified gaseous acetylene at room temperature as evidenced by Raman spectroscopic studies. The polyacetylene synthesised in this way exhibited resonance enhancement of the polyene skeletal vibrations. trans-Polyacetylene, but no cis-(CH) x, was detected. As no apparent coloration of the NaM and CsM substrates accompanied the formation of trans-(CH) x it was concluded that only small quantities of the polymer were present. The number of conjugated double bonds was estimated from the frequencies of the Raman active C-C and C=C stretching vibrations, and it was shown that the trans-(CH) x formed on CsM has a distribution of conjugation lengths ranging from less than 6 to at least 30 double bonds. The polyacetylene formed on NaM was significantly shorter and was produced in lower yields than that synthesized on CsM. "Sliced" resonance excitation profiles of polyacetylene formed on CsM were obtained using nearly 40 different excitation wavelengths and these confirmed that the adsorbed trans-(CH) x was composed of segments having a distribution of conjugated lengths. The architecture of the mordenite pore system permitted only a single polymer molecule per channel, thereby preventing cross-linking. Raman spectroscopic studies of the effects of exposure to air revealed that progressive oxidative degradation occurred with a reduction in the number of conjugated double bond

Bond strength of steel hollow sections using carbon fibre reinforced polymer composites

This research was a step forward in developing bond strength of CFRP strengthened steel hollow sections under tension loads. The studies have revealed the ultimate load carrying capacity of the CFRP strengthened steel hollow sections and the stress distribution for different orientations of the CFRP sheet at different layers. This thesis presents a series of experimental and finite element analysis to determine a good understanding of the bond characteristics of CFRP strengthened steel hollow sections.

Polymer nanocarrier system for endosome escape and timed release of siRNA with complete gene silencing and cell death in cancer cells

An influenza virus-inspired polymer mimic nanocarrier was used to deliver siRNA for specific and near complete gene knockdown of an osteoscarcom cell line (U-2SO). The polymer was synthesized by single-electron transfer living radical polymerization (SET-LRP) at room temperature to avoid complexities of transfer to monomer or polymer. It was the only LRP method that allowed good block copolymer formation with a narrow molecular weight distribution. At nitrogen to phosphorus (N/P) ratios of equal to or greater than 20 (greater than a polymer concentration of 13.8 μg/mL) with polo-like kinase 1 (PLK1) siRNA gave specific and near complete (>98%) cell death. The polymer further degrades to a benign polymer that showed no toxicity even at polymer concentrations of 200 μg/mL (or N/P ratio of 300), suggesting that our polymer nanocarrier can be used as a very effective siRNA delivery system and in a multiple dose administration. This work demonstrates that with a well-designed delivery device, siRNA can specifically kill cells without the inclusion of an additional clinically used highly toxic cochemotherapeutic agent. Our work also showed that this excellent delivery is sensitive for the study of off-target knockdown of siRNA.

Flexural and shear bond characteristics of thin layer polymer cement mortared concrete masonry

This paper presents an experimental investigation of the flexural and shear bond characteristics of thin layer polymer cement mortared concrete masonry. It is well known that the bond characteristics of masonry depend upon the mortar type, the techniques of dispersion of mortar and the surface texture of concrete blocks; there exists an abundance of literature on the conventional 10 mm thick cement mortared masonry bond; however, 1-4 mm thick polymer cement mortared masonry bond is not yet well researched. This paper reports a study on the examination of the effect of mortar compositions, dispersion methods and unit surface textures to the flexural and shear bond characteristics of thin layer mortared concrete masonry. A non-contact digital image correlation method was adopted for the measurement of strains at the unit-mortar interface in this research. All mortar joints have been carefully prepared to ensure achievement of the desired thin layer mortar thickness on average. The results exhibit that the bond strength of thin mortar layered concrete masonry with polymer cement mortar is higher than that of the conventional masonry; moreover the unit surface texture and the mortar dispersion methods are found to have significant influence on the flexural and shear bond characteristics. From the experimental results, a correlation between the flexural and the shear bond strengths has been determined and is presented in this paper.

Multi-wall carbon nanotube coating of fluorine-doped tin oxide as an electrode surface modifier for polymer solar cells

A controlled layer of multi-wall carbon nanotubes (MWCNT) was grown directly on top of fluorine-doped tin oxide (FTO) glass electrodes as a surface modifier for improving the performance of polymer solar cells. By using low-temperature chemical vapor deposition with short synthesis times, very short MWCNTs were grown, these uniformly decorating the FTO surface. The chemical vapor deposition parameters were carefully refined to balance the tube size and density, while minimizing the decrease in conductivity and light harvesting of the electrode. As created FTO/CNT electrodes were applied to bulk-heterojunction polymer solar cells, both in direct and inverted architecture. Thanks to the inclusion of MWCNT and the consequent nano-structuring of the electrode surface, we observe an increase in external quantum efficiency in the wavelength range from 550 to 650 nm. Overall, polymer solar cells realized with these FTO/CNT electrodes attain power conversion efficiency higher than 2%, outclassing reference cells based on standard FTO electrodes.

Probing the effect of charge transfer enhancement in off resonance mode SERS via conjugation of the probe dye between silver nanoparticles and metal substrates

The charge transfer-mediated surface enhanced Raman scattering (SERS) of crystal violet (CV) molecules that were chemically conjugated between partially polarized silver nanoparticles and optically smooth gold and silver substrates has been studied under off-resonant conditions. Tyrosine molecules were used as a reducing agent to convert silver ions into silver nanoparticles where oxidised tyrosine caps the silver nanoparticle surface with its semiquinone group. This binding through the quinone group facilitates charge transfer and results in partially oxidised silver. This establishes a chemical link between the silver nanoparticles and the CV molecules, where the positively charged central carbon of CV molecules can bind to the terminal carboxylate anion of the oxidised tyrosine molecules. After drop casting Ag nanoparticles bound with CV molecules it was found that the free terminal amine groups tend to bind with the underlying substrates. Significantly, only those CV molecules that were chemically conjugated between the partially polarised silver nanoparticles and the underlying gold or silver substrates were found to show SERS under off-resonant conditions. The importance of partial charge transfer at the nanoparticle/capping agent interface and the resultant conjugation of CV molecules to off resonant SERS effects was confirmed by using gold nanoparticles prepared in a similar manner. In this case the capping agent binds to the nanoparticle through the amine group which does not facilitate charge transfer from the gold nanoparticle and under these conditions SERS enhancement in the sandwich configuration was not observed.

Atomistic simulation of interfacial behaviour in graphene-polymer nanocomposites

Graphene–polymer nanocomposites have promising properties as new structural and functional materials. The remarkable mechanical property enhancement in these nanocomposites is generally attributed to exceptional mechanical property of graphene and possible load transfer between graphene and polymer matrix. However, the underlying strengthening and toughening mechanisms have not been well understood. In this work, the interfacial behavior of graphene-polyethylene (PE) was investigated using molecular dynamics (MD) method. The interfacial shear force (ISF) and interfacial shear stress (ISS) between graphene and PE matrix were evaluated, taking into account graphene size, the number of graphene layers and the structural defects in graphene. MD results show that the ISS at graphene-PE interface mainly distributes at each end of the graphene nanofiller within the range of 1 nm, and much larger than that at carbon nanotube (CNT)-PE interface. Moreover, it was found that the ISS at graphene-PE interface is sensitive to the layer number.

Dry powder inhaler formulations-effect of polymer carrier size on the drug dispersion

Background The size of the carrier influences the aerosolization of drug from a dry powder inhaler (DPI) formulation. Currently, lactose monohydrate particles in a variety of sizes are preferably used in carrier based DPI formulations of various drugs; however, contradictory reports exist regarding the effect of the size of the carrier on the dispersion of drug. In this study we examined the influence of the intrinsic particle size of the polymeric carrier on the aerosolization of a model drug salbutamol sulphate (SS). Methods Four different sizes (20–150 lm) of polymer carriers were fabricated using solvent evaporation technique and the dispersion of SS particles from these carriers was measured by a Twin Stage Impinger (TSI). The size and morphological properties of polymer carriers were by laser diffraction and SEM, respectively. Results The FPF from these carriers was found to be increasing from 5.6% to 21.3% with increasing the carrier size. The FPF was found to be greater (21%) with the highest particle size of the carrier (150 lm). Conclusions The aerosolization of drug was dependent on the size of polymer carriers. The smaller size of the carrier resulted in lower FPF which was increased with increasing the carrier size. For a fixed mass of drug particles in a formulation, the mass of drug particles per unit area of carriers is higher in formulations containing the larger carriers, which leads to an increase in the dispersion of drug due to the increased mechanical forces occurred between the carriers and the device walls.

Effect of chemical conjugation of L-leucine to chitosan on the dispersibility and drug release of a dry powder inhaler nanoparticle formulation

Purpose: This study investigated the effect of chemical conjugation of the amino acid L-leucine to the polysaccharide chitosan on the dispersibility and drug release pattern of a polymeric nanoparticle (NP)-based controlled release dry powder inhaler (DPI) formulation. Methods: A chemical conjugate of L-leucine with chitosan was synthesized and characterized by Infrared (IR) Spectroscopy, Nuclear Magnetic Resonance (NMR) Spectroscopy, Elemental Analysis and X-ray Photoelectron Spectroscopy (XPS). Nanoparticles of both chitosan and its conjugate were prepared by a water-in-oil emulsification – glutaraldehyde cross-linking method using the antihypertensive agent, diltiazem (Dz) hydrochloride as the model drug. The surface morphology and particle size distribution of the nanoparticles were determined by Scanning Electron Microscopy (SEM) and Dynamic Light Scattering (DLS). The dispersibility of the nanoparticle formulation was analysed by a Twin Stage Impinger (TSI) with a Rotahaler as the DPI device. Deposition of the particles in the different stages was determined by gravimetry and the amount of drug released was analysed by UV spectrophotometry. The release profile of the drug was studied in phosphate buffered saline at 37 ⁰C and analyzed by UV spectrophotometry. Results: The TSI study revealed that the fine particle fractions (FPF), as determined gravimetrically, for empty and drug-loaded conjugate nanoparticles were significantly higher than for the corresponding chitosan nanoparticles (24±1.2% and 21±0.7% vs 19±1.2% and 15±1.5% respectively; n=3, p<0.05). The FPF of drug-loaded chitosan and conjugate nanoparticles, in terms of the amount of drug determined spectrophotometrically, had similar values (21±0.7% vs 16±1.6%). After an initial burst, both chitosan and conjugate nanoparticles showed controlled release that lasted about 8 to 10 days, but conjugate nanoparticles showed twice as much total drug release compared to chitosan nanoparticles (~50% vs ~25%). Conjugate nanoparticles also showed significantly higher dug loading and entrapment efficiency than chitosan nanoparticles (conjugate: 20±1% & 46±1%, chitosan: 16±1% & 38±1%, n=3, p<0.05). Conclusion: Although L-leucine conjugation to chitosan increased dispersibility of formulated nanoparticles, the FPF values are still far from optimum. The particles showed a high level of initial burst release (chitosan, 16% and conjugate, 31%) that also will need further optimization.