A quantitative model to evaluate solubility relationship of polymorphs from their thermal properties

Area of Science:

• Physical Chemistry
• Materials Science
• Pharmaceutical Sciences

Background:

• Polymorphism significantly impacts drug solubility and bioavailability.
• Accurate prediction of solubility ratios between polymorphic forms is crucial for drug development.
• Existing methods for determining solubility ratios can be complex and time-consuming.

Purpose of the Study:

• To develop a thermodynamic model for estimating the solubility ratio of two polymorphic forms.
• To enable prediction of solubility ratios at any temperature based on free energy differences.
• To provide a practical tool for compounds with low solubility.

Main Methods:

• Model derivation using melting/transition temperatures and heats of fusion/transition.
• Inclusion of heat capacity (Cp) for rigorous derivation.
• Validation using differential scanning calorimetry (DSC) data from various drug polymorphs.
• Comparison of model-predicted solubility ratios with experimental values.

Main Results:

• The full thermodynamic model accurately predicts solubility ratios.
• Simplified working equations (without Cp) show errors of 10% or less, indicating practical applicability.
• A correction factor of 1.1 is recommended for enantiotropic systems to account for transition temperature inconsistencies.

Conclusions:

• A model based on free energy changes successfully predicts drug polymorph solubility ratios from thermal properties.
• The model establishes a thermodynamic link between free energy differences and equilibrium solubilities.
• The approach offers a rapid and practical method for evaluating relative polymorph solubility using DSC.