**1. Introduction**

Oral administration is a preferred route for drug delivery in many cases because of it is easy, convenient, and safe for most patients. However, many new drug candidates with low solubility fail to reach the target bioavailability via oral administration [1]. One effective approach to enhance the solubility of poorly water-soluble drugs is to keep the drugs in their amorphous form [2–4]. Compared to crystals, amorphous solids are inherently in the higher-energy state and thus their dissolution is more energy favorable [5]. However, the higher-energy of amorphous solids can also cause phase instability and drive them towards crystallization, causing the loss of their advantages being amorphous.

A common approach to improve the stability of the amorphous drugs is to disperse them into polymeric materials to yield kinetically stable amorphous solid dispersions [6–16]. To obtain a better insight into the physical stability of amorphous pharmaceutical solids, it is of special importance to investigate the key physicochemical properties governing the crystallization and phase separation. In the past few decades, key thermodynamic and kinetic properties of amorphous solids have been extensively studied, including configurational entropy, structural relaxation, secondary relaxation, surface molecular diffusion, etc. [17–20]. These thermodynamic and kinetic properties have attracted wide attentions because they are considered important parameters for predicting the physical stability of amorphous pharmaceutical solids.

Unique properties of crystalline and amorphous solids have been extensively investigated by several established and emerging techniques including polarized light microscope

**Citation:** Wang, Y.; Wang, Y.; Cheng, J.; Chen, H.; Xu, J.; Liu, Z.; Shi, Q.; Zhang, C. Recent Advances in the Application of Characterization Techniques for Studying Physical Stability of Amorphous Pharmaceutical Solids. *Crystals* **2021**, *11*, 1440. https://doi.org/10.3390/ cryst11121440

Academic Editors: Carlos Rodriguez-Navarro, Duane Choquesillo-Lazarte and Alicia Dominguez-Martin

Received: 9 October 2021 Accepted: 19 November 2021 Published: 23 November 2021

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combined with a hot stage, surface grating decay, thermal analysis, broadband dielectric spectroscopy, and solid-state nuclear magnetic resonance (NMR). In this article, we will review the recent advances and highlight the applications of these characterization techniques. Moreover, we will also briefly discuss the limitations, challenges, and future development trends of these characterization techniques, and the aim is to provide a reference of current tools for developing robust amorphous pharmaceutical formulations.
