(M0930-01-03) A Bivariate Glass Transition Temperature/Molar Volume Empirical Model Predicts Mechanically-Induced Disordering with High Accuracy

Purpose: Unanticipated mechanically-activated transformations of organic materials pose potential practical and regulatory implications associated with their occurrence. Previous research on milling-induced disordering potential suggested that physicochemical properties could be used to predict whether or not a small molecule organic crystal would become amorphous following continuous impact milling. A bivariate empirical model combining the glass transition temperature (T_g) and molar volume (M_V) correctly grouped 17 materials according to their potential to become fully disordered (1). In this research the materials library was expanded to 32 materials, increasing the diversity of the T_g and M_v. The previously constructed bivariate model was tested for robustness and an updated boundary was determined for the expanded dataset.

Methods: Predictions of disordering potential were made for 15 crystalline materials, using the previously developed bivariate model. To compare with the model, ~2 g of each material was extensively cryomilled at 77 K in alternating 2 min grinding/cooling cycles for up to a total of 5 h. Complete disordering after comminution was confirmed or refuted using interpretations of Powder X-ray Diffraction (PXRD) and Differential Scanning Calorimetry (DSC) data for milled materials. Univariate and multivariate logistic regression were performed using an α threshold of 0.05 to identify updated model equations. Regression outcome coded as 1 corresponded with materials that were experimentally and predicted to completely disorder on cryomilling and outcome coded as 0 corresponded with materials that were experimentally and predicted to be resistant to complete disordering on impact milling.

Results: The present work expanded the dataset from 17 to 32 materials, capturing molecules having T_g values ranging between -44 °C (ibuprofen) to 109 °C (D-trehalose), and M_V values from 100 cm³/mol (xylitol) to 519 cm³/mol (itraconazole). Univariate logistic regressions of g(T_g) and g(M_V) were evaluated using all materials in the larger dataset, and showed that both were highly significant with respect to disordering behavior. Values of 𝑝 < 0.0001; 𝜒² = 21.16 for g(T_g) and 𝑝 < 0.0001; 𝜒² = 17.86 for g(M_V) reaffirmed that these materials properties continued to capture information important for predictions of mechanically-induced disordering. Figure 1A shows the original bivariate empirical model, including materials from the expanded dataset. Although library expansion nearly doubled the number of materials evaluated, only ketoprofen was misclassified by the published model g(T_g, M_v), retaining high prediction accuracy (97%). Figure 1B shows the updated bivariate model with 32 materials, where the classification boundary was recalibrated. A second misclassification (tolbutamide) resulted; nonetheless, the prediction accuracy of the updated g(T_g, M_v) model remained high (94%), as shown in Figure 2. Overall, the materials that were completely disordered by cryomilling had, on average, a higher T_g (58.49 ± 29.77 °C) and higher M_V (247.23 ± 91.38 cm³/mol) relative to materials that were resistant to disordering, which had lower T_g (2.50 ± 26.21 °C) and lower M_V (142.79 ± 40.41 cm³/mol).

Conclusion: Evaluation of the empirical bivariate model with an expanded dataset confirmed complete disordering potential can be predicted with 97% accuracy using easily obtainable materials properties (T_g and M_V). Even after model recalibration to accommodate dataset expansion, the prediction accuracy remained high (94%). Behavioral misclassifications by empirical models are expected as the size of a dataset size is increased. The robustness of g(T_g, M_V) appears to be related to aspects of molecular mobility, molecular complexity, and strength of intermolecular interactions, captured by these variables, therefore, it was not surprising that these materials properties were important for determining disordering potential.

References: 1) Lin Y, Cogdill RP, Wildfong PLD. Informatic calibration of a materials properties database for predictive assessment of mechanically activated disordering potential for small molecule organic solids. J Pharm Sci. 2009;98(8):2696-708.

Figure 1: Bivariate plots of the joint distribution of Tg and MV where circle represents complete disordering observed and diamonds represents material resistant to disordering. A) The classification boundary from the model developed by Lin et al. (1). The black data points represent the original 17 materials, while red and green points represent the new materials (n = 15) added here that test the previously established model. b) The updated bivariate empirical model with a classification boundary recalibrated with the expanded dataset (n = 32).

Figure 2: Illustration of the experimental disordering potential for 32 materials; (0 = Resistant to Complete Disordering; 1 = Complete Disordering). Red and green bars indicate correct classification (grey bars reflect incorrect classification) by the recalibrated bivariate model resulting in 94% prediction accuracy.