Purpose: Flory-Huggins solution theory is widely used to predict the thermodynamic phase behavior of drug-excipient mixtures as a function of drug/excipient concentration and temperature. Data from the melting point depression of the drug in the presence of an excipient and the interaction parameter of drug and excipient at room temperature are the basis of Flory-Huggins theory. The value of drug-excipient interaction parameter (χdrug-excipient) at room temperature can be calculated by two methods, i.e. Hildebrand and Hansen solubility approaches. The Hildebrand solubility approach considers the total energy of a substance as its cohesive energy density whereas Hansen solubility approach considers the total energy of a substance as the sum of the dispersive, polar and hydrogen-bonding forces. The values of the interaction parameter obtained using these two approaches differ from each other that, in turn, affect the predicted thermodynamic phase diagram. The purpose of the present study therefore was to investigate the effect of the values of interaction parameter obtained using Hildebrand and Hansen solubility approaches on the drug-excipient thermodynamic phase diagram.
Indomethacin was used as a model drug, and Aqoat® (HPMCAS), Kollidon® VA64 and Kolliphor® P188 were used as polymeric excipients for the study. The physical mixtures of indomethacin and each polymeric excipient in the ratio of 95:05, 90:10, 85:15, 80:20 and 75:25, respectively were prepared by gentle trituration using a mortar and pestle. The melting point depression of the drug in the physical mixtures was determined using a DSC at a heating rate of 5°C/min from 40° to 180°C with nitrogen as purge gas. The end-point of melting endothermic peak was calculated from the intercept of the endothermic peak and the post-melting baseline. The value of the interaction parameter at a higher temperature (melting point of the drug) was calculated from the melting point depression data. The solubility parameter, δt, of the drug and the polymeric excipients was calculated individually according to Hoftyzer and Van Krevelen group contribution method. The value of the interaction parameter at 25°C was calculated according to Hildebrand and Hansen solubility approaches. Once the values of the interaction parameter at room temperature and at higher temperatures were calculated, the drug-excipient thermodynamic phase diagrams were constructed according to Flory-Huggins theory.
The values of total solubility parameter, δt, of indomethacin, HPMCAS, Kolliphor® P188 and Kollidon® VA64 were found to be 27.98, 25.68, 22.06 and 23.04 MPa0.5, respectively. The difference in the values of total solubility parameter among the materials demonstrates that indomethacin will have higher miscible in HPMCAS followed by that in Kollidon® VA64 and Kolliphor® P188. Also, the values of interaction parameter calculated at 25°C using Hildebrand as well as Hansen’s approaches show that the degree of interaction between indomethacin and HPMCAS will be higher as compared to the other two polymers. The temperature-independent entropic contribution and the temperature-dependent enthalpic contribution to the drug-polymer miscibility were determined by plotting the value of the interaction parameter as a function of absolute temperature data according to the first-order relationship. The entropic and enthalpic contribution to the value of interaction parameter increased with an increase in the molecular weight of the polymeric excipient. This can be attributed to the molecular mobility of the polymer at higher temperature; a polymer with larger molecular weight will have lower mobility compared to lower molecular weight polymers. Also, the enthalpic and entropic contribution to indomethacin-HPMCAS was significantly higher when calculated using the Hansen approach rather than that calculated using the Hildebrand approach. This was due to the fact that Hansen solubility approach hypothesizes that all three types of intermolecular forces affect the value of interaction parameter whereas Hildebrand approach hypothesizes that only the cohesive energy of a substance impacts the value of interaction parameter. This results in a significant error in the prediction of the value of interaction parameter between indomethacin and HPMCASaccording to Hildebrand approach since HPMCAS has higher polar and hydrogen-bonding forces and lesser dispersion forces. This error in prediction can be observed in the thermodynamic phase diagram of indomethacin-HPMCAS system which shows a negative Gibbs’ free energy suggesting complete miscibility even at 10°C. On the other hand, the thermodynamic phase diagrams constructed using the Hansen approach show better predictability of indomethacin-HPMCAS miscibility at all temperatures. Thus, from the phase diagrams of the three systems, it can be inferred that indomethacin-HPMCAS has the lowest Gibbs’ free energy at room temperature at a maximum drug loading of 50% v/v.
The ability of Flory-Huggins theory to predict the thermodynamic phase diagrams depends on the method used to calculate the value of interaction parameter at 25°C. Of the two approaches studied, Hansen method was found to better predict the value of interaction parameter at 25°C. The thermodynamic phase diagrams constructed using this approach will serve as a powerful preformulation tool in the formulation of solid dispersions using hot-melt extrusion.
Saurabh Mishra– Student, St. John's University, New York
Hemanth Mamidi– St. Johns University
Bhagwan Rohera– St. Johns University
Bhagwan Rohera– St. Johns University
Saurabh Maheshwari Mishra– Student, St. John's University, Jamaica