Modelling the stability of ternary solid dispersions

Abstract

This thesis provides a mathematical analysis of the stability of some ternary solid dispersions using thermodynamic theory. Solid dispersions have been developed to improve the solubility of poorly soluble drugs. Traditional solid dispersions typically consist of two components - a drug and a hydrophilic polymer, the purpose of the polymer being to improve the solubility of the drug when administered orally. More recently, ternary dispersions (that is, systems with three components) have been developed. Ternary dispersions provide an extra degree of freedom to enable system designers to optimize both the stability and solubility properties of the dispersion. Unstable dispersions may phase separate, thereby limiting their shelf life. In this thesis, I mathematically model ternary solid dispersions with a view to identifying parameter regimes that lead to favourable and unfavourable stability properties for the dispersion. A systematic study of this kind has hitherto been lacking in the literature. The methodology used is as follows. The solid dispersions are modelled using Flory- Huggins solution theory, a well-established thermodynamic model in polymer science for polymer blends. The stability properties of the dispersions are determined by constructing phase diagrams using the Gibbs free energy of mixing. The phase diagrams determine whether a particular ternary composition is stable or unstable or metastable. The requisite numerical calculations to construct the diagrams are carried out by programs that I wrote using the mathematical packages MAPLE and MATLAB. Thermodynamic theory determines the broad character of the ultimate state of the mixture, but yields no information on how the mixture evolves to that state, or what the detailed character of the final state is for unstable compositions. To address these issues, a partial differential equations model is developed to describe the dispersion mixture evolution, and some simulations of this model are also presented. A few notable results are as follows. For polymer-polymer-drug ternary systems, it is found that for desirable stability properties to be possible, the two polymers need to be compatible (in a sense that has been described quantitatively). Also, the stability behaviour can be finely dependent on the asymmetry between how the two polymers interact with the drug. Closed loops of immiscibility are shown to be theoretically possible. For polymer-surfactant-drug ternary systems, it is shown that the stability behaviour can be sensitive to the character of the interaction between the polymer and the surfactant, and the molecular weight of the surfactant. Numerous other predictions are made.