**2. Combination of Polarized Light Microscope and Hot Stage**

Polarized light microscope is one of the most widely used techniques in characterizing nucleation [21–23], crystal growth [24,25], polymorphic transition [26], and phase separation [27] of amorphous pharmaceutical solids. In recent studies, polarized light microscopy was often combined with a hot stage to extend its experimental temperature range and achieve the goal of precise temperature control. Prior to investigating the nucleation and crystal growth processes, amorphous drug was firstly prepared by the melting-quenching method using a hot stage for precisely controlling the temperature. The drugs prepared by the melt-quenching method are confirmed to be amorphous by the absence of birefringence under the polarized light microscope.

Cai and co-workers systemically investigated the crystal growth behaviors of a classical antifungal drug griseofulvin as a function of temperature by a polarized light microscope equipped with a hot stage [24]. As shown in Figure 1, growth morphologies of griseofulvin crystals exhibit strong temperature dependence, producing faceted coarse crystals near the melting point (*T*m), fiber-like fine crystal near the glass transition temperature (*T*g), and even finer compact spherulites below *T*g [24]. In addition, the velocity of crystal growth of griseofulvin could also be measured by recording the advancing growth front of the crystal into the supercooled liquid or glass as a function of time [24]. In the supercooled liquid, the rate of crystal growth decreases with the temperature decreasing near *T*m while it increases with the temperature further decreasing near *T*g. This bell-shaped curve of crystal growth rate vs. temperature is mainly attributed to the competition between the negative dependence of the thermodynamic driving force and the positive dependence of the bulk molecular diffusion on the temperature. For some small-molecule drugs, one fast crystal growth mode termed as glass-to-crystal (GC) growth, is activated as the temperature decreases near or below *T*g, with a rate orders of magnitude faster than those predicted by bulk diffusion controlled modes [24,28]. Several models have been proposed to explain the GC growth; however, its mechanism remain imperfectly understood. In a very recent model, voids and free surface is proposed to be continuously created by fracture, leading the fast GC growth by taking advantage of the fast surface mobility.

For the crystal growth in drug–polymer binary systems, one interesting phenomenon, polymer enrichment as a function of temperature and polymer concentration, could be observed at the advancing growth front of crystal using polarized light microscopy combined with a hot stage [29,30]. Visual observations can directly provide a reasonable explanation for the fact that the increase of global molecular mobility alone is insufficient to account for the accelerating effects of a low-*T*<sup>g</sup> polymer—e.g., poly (ethylene oxide) (PEO)—on the crystal growth of small-molecule drug griseofulvin and indomethacin [31,32]. In addition to the high global molecular mobility, PEO enrichment at the growth front could also accelerate the mass transport of drug molecules entering the crystalline phase by the high segmental mobility of PEO [29,30]. Moreover, polymer enrichment could also be one of the key factors rendering the selective effect of polymer on the crystal growth of different drug polymorphs [30]. In a very recent study, Zhang et al. found that the extent of the accelerating effect of PEO on the crystal growth of indomethacin polymorphs is very consistent with the concentration of PEO enrichment at the crystal–liquid interface [30]. They proposed that distinct drug–polymer distribution at the growth front of indomethacin polymorphs strongly affects the mass transport of drug molecules and the energy barrier, thus leading to the selective accelerating effects of PEO on crystal growth of indomethacin polymorphs [30].

**Figure 1.** Bulk crystal growth morphologies of GSF as a function of temperature from 210 ◦C to 60 ◦C, (**a**) 210 ◦C, (**b**) 130 ◦C, (**c**) 100 ◦C, (**d**) 90 ◦C, (**e**) 80 ◦C, and (**f**) 60 ◦C. Adapted from the [24] with the permission. Copyright © 2016 American Chemical Society.

Apart from studying crystal growth behaviors, polarized light microscope combined with hot stage can be used to explore the nucleation of amorphous pharmaceutical solids [21–23]. According to the different kinetics of nucleation and crystal growth, studies on drug nucleation can be mainly defined as one-stage method and two-stage method [21–23]. One-stage method can be used to determine the number of nucleation events per unit volume for the drug systems showing both fast nucleation and fast crystal growth behaviors. Herein, individual nucleation is allowed to grow to the observable size for some time *t*<sup>0</sup> in the supercooled liquid. The size and growth rates of the crystal are measured by using the combined technology of polarized light microscope and hot stage. On the basis of the crystal size (radius *r*) and growth rate (*u*), the birth time *t* of individual nucleus as a function of time can be calculated as

$$t = t\_0 - r/u$$

In general, drug nucleation follows a steady rate after an induction period, followed by a slower rate due to the decreased available liquid volume for nucleation.

If a drug crystal grows relatively slow, one-stage method is not suitable, and two-stage method needs to be applied for this situation. Unlike one-stage method, two-stage method is briefly summarized as a two-step process consisting of a nucleation step at a relatively low temperature and then quickly switch to an elevated temperature to allow the nuclei grow to visible dimensions under a polarized microscope. The temperature selected for crystal growth is required to ensure the rapid growth of nuclei but meanwhile prevent the formation of new nuclei.

Huang et al. compared the crystal nucleation rates of four polyalcohols exhibiting the similar kinetics of crystal growth on the *T*/*T*<sup>g</sup> scale [21]. On the same scale of *T*/*T*g, nucleation rates of these four polyalcohols are vastly different, indicating the fundamentally different mechanisms of nucleation [21]. In a recent study, Yao et al. compared the inhibitory effects of polymer on the crystal nucleation and growth via polarized light microscope combined with a hot stage [22]. Interestingly, the inhibitory effects of polymer on the crystal nucleation rates are similar to those on the crystal growth [22]. At a given temperature, the ratios between the rates of nucleation and growth are nearly identical, and are independent of the concentration and molecular weight of the polymer [22]. Moreover, in a very recent study, Zhang et al. found that the accelerating effects of low-*T*g polymer (PEO) on crystal

nucleation and growth of fluconazole are also approximately the same [23]. Based on these studies, both the crystal nucleation and growth were proposed to be molecular mobilitylimited processes [22,23]. Herein, dissolved polymer in the amorphous matrix acts as a mobility modifier, imposing similar degrees of inhibitory and accelerating effects on the crystal nucleation and growth [22,23].

One important nucleation phenomenon, termed as cross-nucleation, could also be observed under a polarized light microscope, in which another polymorph nucleates on the early nucleating polymorph [33]. Compared to the early nucleating polymorph, the newly nucleated polymorph could be less or more thermodynamically stable [34]. This interesting nucleation behavior is quite different from the classical Ostwald's law of stages, would lead to the ineffectiveness of the seeding method for obtaining the required polymorph. The newly nucleated polymorph always exhibits a faster or same crystal growth rate as the initial polymorph. If the frequency of cross-nucleation is sufficiently high, thesurface of the early nucleating polymorph will eventually be occupied by the cross-nuclei of newly nucleated polymorph.

Polarized light microscope combined with hot stage can also be used to obtain highquality single crystals [35,36]. For instance, high-quality single crystals of the metastable form II of griseofulvin, was obtained from the melt under a polarized light microscope equipped with a hot stage [35]. Large and faceted single crystals of griseofulvin form II were observed after a rapid growth at 200 ◦C in the presence of 10% *w*/*w* PEO, which is reported to effectively accelerate the crystal growth [35]. Single-crystal X-ray diffraction analysis as a function of temperature revealed that griseofulvin form II exhibited an anomalously large coefficient of thermal expansion [35]. In a recent study, a creative strategy of cultivating single crystal was developed for rapidly obtaining the desired polymorph from the melt microdroplets near *T*<sup>m</sup> [35]. Herein, a hot stage was used to control the temperature near *T*m, at which the secondary nucleation was effectively inhibited to avoid the formation of polycrystals. Meanwhile, polarized microscope was used to monitor the growth of single crystals until a proper size was reached. In addition, polarized light microscope combined with hot stage can also be applied into the downstream processing of the preparation of amorphous pharmaceutical formulations [37].Yang et al. used this combined technique to analyze the microstructure and state of the samples at various temperature, facilitating the determination of temperature range for amorphous drug formulations during the hot melt extrusion process [37].
