**4. Solid-State Nuclear Magnetic Resonance (NMR)**

Solid-state nuclear magnetic resonance (SS-NMR) has also been introduced into the pharmaceutical field for studying the dynamics and phase composition of amorphous solid dispersions [54,55]. In addition, crystalline and amorphous drug generally exhibit different spectra of SS-NMR [37,56]. Compared to the crystalline form, 13C peaks of amorphous drug are much broader, which is mainly attributed to the disordered molecular packing [56]. SS-NMR spectroscopy could provide diverse and critical information of complex amorphous dispersions from the atomic level, which is barely realized by other existing methods [54]. One main application of SS-NMR is to study the site-specific molecular mobility of amorphous solids by measuring the spin–lattice relaxation times and their spin–spin relaxation [57]. Herein, the spin–lattice relaxation times of rare nuclei consist of the static and rotating frame form (*T*<sup>1</sup> and *T*1ρ) [57]. *T*<sup>1</sup> and *T*1<sup>ρ</sup> relaxations (e.g., 13C) could provide pure dynamic information including the most kinds of local motions [57]. Moreover, relaxations representing the primary and secondary molecular motions can

be identified from the spin–lattice relaxation in the SS-NMR [58]. Herein, *T*<sup>1</sup> relaxation generally represents the secondary molecular relaxations due to its sensitivity towards the local and rapid motions [58]. *T*1<sup>ρ</sup> relaxation could be affected by the slower molecular motions of amorphous solid, which is associated with the primary relaxation [58]. For instance, in the case of pharmaceutical polymer methylcellulose and polyvinylpyrrolidone, *T*1<sup>ρ</sup> relaxation originates from the motions of polymer backbone. For comparison, *T*<sup>1</sup> relaxations come from the local dynamics originated from the side chain motions.

High resolution 13C SS-NMR could be used to investigate the hydrogen bonding interactions of amorphous pharmaceutical solids [59]. With the aid of SS-NMR, Yuan et al. quantitatively studied the hydrogen bonding interactions in amorphous indomethacin with and without the presence of poly (vinylpyrrolidone) (PVP) and poly(vinylpyrrolidone-covinyl acetate) (PVPVA) [59]. For the pure amorphous indomethacin system, 13C SS-NMR revealed that its hydrogen bonding interaction consists of three main types including disordered carboxylic acid chains, carboxylic acid cyclic dimer, and the carboxylic acid hydrogen bonded to the amide carbonyl (Figure 4) [59]. This self-interaction of indomethacin could be disrupted once indomethacin formed a solid dispersion with the addition of polymer [59]. The extent of drug–polymer hydrogen bonding interactions increase with the increase in polymer concentration. For comparison, the carboxylic dimers between two indomethacin molecules could not be observed any more as the polymer concentration increased to 50% *w*/*w*. In a recent study, Sarpal et al. used the SS-NMR technique to compare the molecular interactions in amorphous ketoconazole (KET), KET binary dispersions, and KET ternary dispersions [60]. A detailed 13C SS-NMR deconvolution study showed that binary KET and poly (acrylic acid) (PAA) system exhibits higher prevalence of ionic and hydrogen bonds in comparison with its ternary system containing hydroxypropyl methyl cellulose (HPMC) [60].

**Figure 4.** CPMAS 13C spectrum of the carboxylic acid of amorphous indomethacin. Simulated peaks are shown in red, yellow, and blue to illustrate the various hydrogen bonds. Adapted from the [59] with the permission. Copyright © 2015 American Chemical Society.

In recent studies, two-dimensional (2D) ss-NMR was also developed to identify the type and strength of various drug–polymer interactions in ASDs with enhanced sensitivity and resolution [61,62]. Lu et al. used 2D 1H-19F ss-NMR to investigate the molecular interaction between the difluorophenyl group of posaconazole and the hydroxyl group of

hydroxypropyl methylcellulose acetate succinate (HPMCAS) in the ASD. For hydrogen bond patterns, they proposed that the hydroxyl groups of HPMCAS act as acceptors while the fluorine or difluorophenyl rings of posaconazole act as donors [62]. Moreover, a 19F-13C rotational echo and double resonance technique was used to measure the atomic distance, and it revealed the close proximity between 13C of the hydroxyl group and 19F of posaconazole at 4.3 Å [62].

Moreover, the miscibility between drug and polymer can also be investigated using the *T*<sup>1</sup> and *T*1<sup>ρ</sup> relaxation times obtained from 1H SS-NMR [59,63–67]. At present, measuring the *T*<sup>g</sup> using differential scanning calorimetry (DSC) is the most widely used approach for determining the miscibility of amorphous solids. Generally, a single *T*g between those of drug and polymer indicates a miscible system, while two separated *T*gs suggest a phase-separated system. However, *T*<sup>g</sup> is sometimes not a reliable indicator of system miscibility, as some studies reported that phase-separated system could exhibit a single *T*<sup>g</sup> and vice versa [63]. Moreover, the miscibility assessed by *T*<sup>g</sup> generally has a detection limit of 20–30 nm, meaning that a two-phase system with smaller domain size would be indistinguishable by DSC. For comparison, SS-NMR is suggested to be a more accurate technique, which could measure the drug–polymer miscibility for small domain sizes.

For the miscibility measurement using SS-NMR, length scale of 1H spin diffusion is important and could be calculated by

$$\langle \mathbb{L} \rangle = \sqrt{6Dt}$$

Herein, *t* represents the relaxation time, *D* represents the spin diffusion coefficient and is typically assumed as 10−<sup>12</sup> cm2/s for the organic solids. The length scale of spin diffusion is ca. 20–50 nm for a typical *T*<sup>1</sup> value as 1–5 s. For a typical *T*1<sup>ρ</sup> as 5–50 ms, the length scale is ca. 2–5 nm. It is expected that three scenarios might occur depending on the domain size. A common *T*<sup>1</sup> and *T*1<sup>ρ</sup> values could be obtained for drug and polymer for the domain size smaller than 2–5 nm. If the domain size is 5–20 nm, *T*<sup>1</sup> values of drug and polymer are the same while *T*1<sup>ρ</sup> values are different. If both the *T*<sup>1</sup> and *T*1<sup>ρ</sup> values of drug and polymer are different, the domain size is larger than 20–50 nm. Pham et al. used the SS-NMR cross-polarization hetero-nuclear correlation technique to investigate the spin diffusion effects of the amorphous pharmaceutical solids, facilitating the detection of the drug–polymer molecular interaction and phase separation [64]. Litvinov et al. investigated the phase behavior of miconazole-poly(ethylene glycol)-g-vinyl alcohol (PEG-g-PVA) solid dispersions by a combination of modulated DSC, XRPD, and SS-NMR [63]. In their work, miconazole (10% *w*/*w*) was identified to form the amorphous nanocluster with ~1.6 nm average cluster size in the amorphous matrix of PEG-g-PVA, indicating the miscibility at the molecular level [65].

Sarpal et al. compared the phase homogeneity of felodipine ASDs doped with PVP, PVPVA, and poly(vinylacetate) (PVAc) by measuring the 1H T1 and T1ρ of drug and polymer [66]. Better compositional homogeneity was observed in felodipine-PVP and felodipine-PVPVA ASDs compared to felodipine-PVAc ASD. 13C ss-NMR was also used to investigate the strength and extent of drug–polymer hydrogen bonding interactions, and it revealed a ranking of PVP > PVPVA > PVAc [66]. The results also suggested that hydrogen bonding interaction in ASDs could impact system phase homogeneity [66]. Recently, an 1H double-filtering SS-NMR technique with 1H spin diffusion and 13C detection was developed to provide the highest-resolution quantification of molecular miscibility and homogeneity of amorphous solid dispersions [68]. However, spectrum acquisition typically requires one week for obtaining sufficient signal-to-noise ratio, therefore, low-field and benchtop NMR techniques are to be developed to shorten the acquisition times, which would make SS-NMR a useful technique for capturing structural evolution that occurs within a short time period [69].
