Ultrafast Magic Angle Spinning Research Articles

Resolving Structures of Paramagnetic Systems in Chemistry and Materials Science by Solid-State NMR: The Revolving Power of Ultra-Fast MAS.

Ultra-fast magic-angle spinning (100+kHz) has revolutionized solid-state NMR of biomolecular systems but has so far failed to gain ground for the analysis of paramagnetic organic and inorganic powders, despite the potential rewards from substantially improved spectral resolution. The principal blockages are that the smaller fast-spinning rotors present significant barriers for sample preparation, particularly for air/moisture-sensitive systems, and are associated with low sensitivity from the reduced sample volumes. Here, we demonstrate that the sensitivity penalty is less severe than expected for highly paramagnetic solids and is more than offset by the associated improved resolution. While previous approaches employing slower MAS are often unsuccessful in providing sufficient resolution, we show that ultra-fast 100+kHz MAS allows site-specific assignments of all resonances from complex paramagnetic solids. Combined with more reliable rotor materials and handling methods, this opens the way to the routine characterization of geometry and electronic structures of functional paramagnetic systems in chemistry, including catalysts and battery materials. We benchmark this approach on a hygroscopic luminescent Tb3+ complex, an air-sensitive homogeneous high-spin Fe2+ catalyst, and a series of mixed Fe2+/Mn2+/Mg2+ olivine-type cathode materials.

Crystal structure validation of verinurad via proton-detected ultra-fast MAS NMR and machine learning.

The recent development of ultra-fast magic-angle spinning (MAS) (>100 kHz) provides new opportunities for structural characterization in solids. Here, we use NMR crystallography to validate the structure of verinurad, a microcrystalline active pharmaceutical ingredient. To do this, we take advantage of 1H resolution improvement at ultra-fast MAS and use solely 1H-detected experiments and machine learning methods to assign all the experimental proton and carbon chemical shifts. This framework provides a new tool for elucidating chemical information from crystalline samples with limited sample volume and yields remarkably faster acquisition times compared to 13C-detected experiments, without the need to employ dynamic nuclear polarization.

Performance of the cross-polarization experiment in conditions of radiofrequency field inhomogeneity and slow to ultrafast magic angle spinning (MAS).

In this paper, we provide an analytical description of the performance of the cross-polarization (CP) experiment, including linear ramps and adiabatic tangential sweeps, using effective Hamiltonians and simple rotations in 3Dspace. It is shown that radiofrequency field inhomogeneity induces a reduction in the transfer efficiency at increasing magic angle spinning (MAS)frequencies for both the ramp and the adiabatic CPexperiments. The effect depends on the ratio of the dipolar coupling constant and the sample rotation frequency. In particular, our simulations show that for small dipolar couplings (1 ) and ultrafast MAS (above 100 ) the transfer efficiency is below 40 % when extended contact times up to 20 are used and relaxation losses are ignored. New recoupling and magnetization transfer techniques that are designed explicitly to account for inhomogeneous radiofrequencyfields are needed.

Multiple acquisitions in a single scan: exhausting abundant 1H polarization at fast MAS

Proton-detected solid-state NMR spectroscopy is emerging as a unique tool for atomic characterization of organic solids due to the boost of resolution and sensitivity afforded by the combined use of high magnetic field and ultrafast magic angle spinning (MAS). Here, we proposed a new set of proton-detected solid-state NMR sequences that hybrid multi-dimensional 1H–1H homonuclear chemical shift correlation (HOMCOR) and two-dimensional 1H–13C heteronuclear chemical shift correlation (HETCOR) sequences into a single experiment, enabling the simultaneous acquisition of multidimensional HOMCOR and HETCOR spectra and thus significant time savings. Based on the core idea of exhausting 1H polarization in each transient scan, we firstly demonstrated that 3D 1H multiple-quantum (MQ) HOMCOR sequence can be combined with 2D HETCOR sequence into a single experiment, leading to the simultaneous acquisition of a 3D 1H MQ HOMCOR and a 2D 1H–13C HETCOR spectrum. Besides, we also showed that 2D 1H/1H double-quantum/single-quantum (DQ/SQ) and single-quantum/single-quantum (SQ/SQ) HOMCOR sequence can be simultaneously combined with HETCOR sequence either, and thus three spectra can be simultaneously obtained from one experiment, including 2D 1H DQ/SQ, 2D 1H SQ/SQ and 2D 1H–13C HETCOR spectra. Since there is only one recycle delay in each experiment, experimental time is substantially reduced compared to separate acquisition of each multi-dimensional solid-state NMR spectrum. Furthermore, those new sequences can be implemented on any standard solid-state spectrometer with only one receiver. Thus, we foresee that these approaches can be valuable for the study of a broad range of molecular systems, including polymers, pharmaceuticals, covalent-organic frameworks (COF) and so on.

New Development in Understanding Drug-Polymer Interactions in Pharmaceutical Amorphous Solid Dispersions from Solid-State Nuclear Magnetic Resonance.

Pharmaceutical amorphous solid dispersions (ASDs) represent a widely used technology to increase the bioavailability of active pharmaceutical ingredients (APIs). ASDs are based on an amorphous API dispersed in a polymer, and their stability is driven by the presence of strong intermolecular interactions between these two species (e.g., hydrogen bond, electrostatic interactions, etc.). The understanding of these interactions at the atomic level is therefore crucial, and solid-state nuclear magnetic resonance (NMR) has demonstrated itself as a very powerful technique for probing API-polymer interactions. Other reviews have also reported exciting approaches to study the structures and dynamic properties of ASDs and largely focused on the study of API-polymer miscibility and on the identification of API-polymer interactions. Considering the increased use of NMR in the field, the aim of this Review is to specifically highlight recent experimental strategies used to identify API-polymer interactions and report promising recent examples using one-dimensional (1D) and two-dimensional (2D) experiments by exploiting the following emerging approaches of very-high magnetic field and ultrafast magic angle spinning (MAS). A range of different ASDs spanning APIs and polymers with varied structural motifs is targeted to illustrate new ways to understand the mechanism of stability of ASDs to enable the design of new dispersions.

Heteronuclear decoupling with rotor-synchronized phase-alternated cycles.

A new heteronuclear decoupling pulse sequence is introduced, dubbed ROtor-Synchronized Phase-Alternated Cycles (ROSPAC). It is based on a partial refocusing of the coherences (spin operator products or cross-terms) [Filip et al., J. Mag. Reson. 176, 2 (2005)] responsible for transverse spin-polarization dephasing, on the irradiation of a large pattern of radio-frequencies, and on a significant minimization of the cross-effects implying 1H chemical-shift anisotropy. Decoupling efficiency is analyzed by numerical simulations and experiments and compared to that of established decoupling sequences [swept-frequency two-pulse phase-modulated (TPPM), TPPM, small phase incremental alternation (SPINAL), refocused Continuous-wave (CWApa), and Rotor-Synchronized Hahn-Echo pulse train (RS-HEPT)]. It was found that ROSPAC offers good 1H offset robustness for a large range of chemical shifts and low radio-frequency (RF) powers, and performs very well in the ultra-fast magic-angle spinning (MAS) regime, where it is almost independent from RF power and permits it to avoid rotary-resonance recoupling conditions (v1 = nvr, n = 1, 2). It has the advantage that only the pulse lengths require optimization and has a low duty cycle in the pulsed decoupling regime. The efficiency of the decoupling sequence is demonstrated on a model microcrystalline sample of the model protein domain GB1 at 100kHz MAS at 18.8T.

Pink and White Noise in Resting EEG: A Marker for Behavioural Activation and Inhibition?

1H-detected solid-state nuclear magnetic resonance (NMR) experiments are recorded on both intact and trypsin-cleaved sedimented measles virus (MeV) nucleocapsids under ultra-fast magic-angle spinning. High-resolution 1H,15N-fingerprints allow probing the degree of molecular order and flexibility of individual capsid proteins, providing an exciting atomic-scale complement to electro microscopy (EM) studies of the same systems.

Sensitivity-Enhanced Solid-State NMR Detection of Structural Differences and Unique Polymorphs in Pico- to Nanomolar Amounts of Brain-Derived and Synthetic 42-Residue Amyloid-β Fibrils.

Amyloid-β (Aβ) fibrils in neuritic plaques are a hallmark of Alzheimer's disease (AD). Since the 42-residue Aβ (Aβ42) fibril is the most pathogenic among different Aβ species, its structural characterization is crucial to our understanding of AD. While several polymorphs have been reported for Aβ40, previous studies of Aβ42 fibrils prepared at neutral pH detected essentially only one structure, with an S-shaped β-sheet arrangement (e.g., Xiao et al. Nat. Struct. Mol. Biol. 2015, 22, 499). Herein, we demonstrate the feasibility of characterizing the structure of trace amounts of brain-derived and synthetic amyloid fibrils by sensitivity-enhanced 1H-detected solid-state NMR (SSNMR) under ultrafast magic angle spinning. By taking advantage of the high sensitivity of this technique, we first demonstrate its applicability for the high-throughput screening of trace amounts of selectively 13C- and 15N-labeled Aβ42 fibril prepared with ∼0.01% patient-derived amyloid (ca. 4 pmol) as a seed. The comparison of 2D 13C/1H SSNMR data revealed marked structural differences between AD-derived Aβ42 (∼40 nmol or ∼200 μg) and synthetic fibrils in less than 10 min, confirming the feasibility of assessing the fibril structure from ∼1 pmol of brain amyloid seed in ∼2.5 h. We also present the first structural characterization of synthetic fully protonated Aβ42 fibril by 1H-detected 3D and 4D SSNMR. With procedures assisted by automated assignments, main-chain resonance assignments were completed for trace amounts (∼42 nmol) of a fully protonated amyloid fibril in the 1H-detection approach. The results suggest that this Aβ42 fibril exhibits a novel fold or polymorph structure.

Decoherence optimized tilted-angle cross polarization: A novel concept for sensitivity-enhanced solid-state NMR using ultra-fast magic angle spinning

Ultra-fast magic-angle spinning (UFMAS) at a MAS rate (ωR/2π) of 60 kHz or higher has dramatically improved the resolution and sensitivity of solid-state NMR (SSNMR). However, limited polarization transfer efficiency using cross-polarization (CP) between 1H and rare spins such as 13C still restricts the sensitivity and multi-dimensional applications of SSNMR using UFMAS. We propose a novel approach, which we call decoherence-optimized tilted-angle CP (DOTA CP), to improve CP efficiency with prolonged lifetime of 1H coherence in the spin-locked condition and efficient band-selective polarization transfer by incorporating off-resonance irradiation to 1H spins. 13C CP-MAS at ωR/2π of 70–90 kHz suggested that DOTA CP notably outperformed traditional adiabatic CP, a de-facto-standard CP scheme over the past decade, in sensitivity for the aliphatic-region spectra of 13C-labeled GB1 protein and N-formyl-Met-Leu-Phe samples by up to 1.4- and 1.2-fold, respectively. 1H-detected 2D 1H/13C SSNMR for the GB1 sample indicated the effectiveness of this approach in various multidimensional applications.

Selectively Enhanced 1H-1H Correlations in Proton-Detected Solid-State NMR under Ultrafast MAS Conditions.

Proton-detected solid-state NMR has emerged as a powerful analytical technique in structural elucidation via 1H-1H correlations, which are mostly established by broadband methods. We propose a new class of frequency-selective homonuclear recoupling methods to selectively enhance 1H-1H correlations of interest under ultrafast magic-angle spinning (MAS). These methods, dubbed as selective phase-optimized recoupling (SPR), can provide a sensitivity enhancement by a factor of ∼3 over the widely used radio-frequency-driven recoupling (RFDR) to observe 1HN-1HN contacts in a protonated tripeptide N-formyl-Met-Leu-Phe (fMLF) under 150 kHz MAS and are successfully utilized to probe a long-range 1H-1H contact in a pharmaceutical molecule, the hydrochloride form of pioglitazone (PIO-HCl). SPR is not only highly efficient in frequency-selective recoupling but also easy to implement, imparting to it great potential to probe 1H-1H contacts for the structural elucidation of organic solids such as proteins and pharmaceuticals under ultrafast MAS conditions.

Towards Accurate Predictions of Proton NMR Spectroscopic Parameters in Molecular Solids.

The factors contributing to the accuracy of quantum-chemical calculations for the prediction of proton NMR chemical shifts in molecular solids are systematically investigated. Proton chemical shifts of six solid amino acids with hydrogen atoms in various bonding environments (CH, CH2 , CH3 , OH, SH and NH3 ) were determined experimentally using ultra-fast magic-angle spinning and proton-detected 2D NMR experiments. The standard DFT method commonly used for the calculations of NMR parameters of solids is shown to provide chemical shifts that deviate from experiment by up to 1.5 ppm. The effects of the computational level (hybrid DFT functional, coupled-cluster calculation, inclusion of relativistic spin-orbit coupling) are thoroughly discussed. The effect of molecular dynamics and nuclear quantum effects are investigated using path-integral molecular dynamics (PIMD) simulations. It is demonstrated that the accuracy of the calculated proton chemical shifts is significantly better when these effects are included in the calculations.

Quantifying Pharmaceutical Formulations from Proton Detected Solid-State NMR under Ultrafast Magic Angle Spinning

Probing form conversions of active pharmaceutical ingredients in solid dosages is critical for understanding the physicochemical stability of drug substances in formulations. The multicomponent and low drug loading nature of drug products often results in challenges to quantify the phase stability, at a low detection limit and with the chemical resolution that differentiate drug molecules and excipients, for routine laboratory techniques. Recent advancement of ultrafast magic angle spinning (UF-MAS) enables proton-detected solid-state nuclear magnetic resonance (ssNMR) techniques to characterize pharmaceutical materials with enhanced resolution and sensitivity. This study demonstrates one of the first documented cases implementing 60 kHz UF-MAS techniques to quantify the minor content of pioglitazone free base (PIO-FB) in a binary system with its hydrochloride salt (PIO–HCl) and a multicomponent formulation with typical excipients. One-dimensional 1H methods can unambiguously differentiate the two forms and exhibit a limit of detection at 1.77% (w/w). Moreover, we extended it to a two-dimensional 1H–1H correlation for minimizing peak overlap and successfully quantifying approximately 2.0% (w/w) PIO-FB in a multicomponent formulation. These results have demonstrated that 1H ssNMR as a novel method to quantify solid dosages at a higher resolution and faster acquisition than conventional 13C techniques.

Understanding Molecular Interactions in Rafoxanide-Povidone Amorphous Solid Dispersions from Ultrafast Magic Angle Spinning NMR.

In solid dosage formulations, probing intermolecular interactions between active pharmaceutical ingredients (APIs) and polymeric excipients, which have a mechanistic impact on physical stability as well as bioavailability, remains a challenge. In recent years, solid-state NMR spectroscopy has been demonstrated to be a powerful tool to provide structural details with an atomic resolution of therapeutic organic compounds and formulation products. However, conventional 13C-detected techniques often suffer from poor resolution and low sensitivity due to the disordered structure of certain materials such as amorphous pharmaceuticals and 13C natural abundance, hindering in-depth investigations. In this study, we utilize the magic angle spinning (MAS) technique with ultrafast speeds (UF-MAS: νR = 60 and 110 kHz) and demonstrate the enabled methods with 1H detection to study the amorphous molecular complex of rafoxanide and povidone in the solid state. The downfield shift of the RAF amide proton, resolved under UF-MAS, and its correlations with aliphatic protons of PVP, serve as strong evidence of the existence of intermolecular hydrogen bonding. Two-dimensional (2D) 1H-detected 1H{13C} and 1H-1H correlation experiments, interestingly, exhibit distinct API-polymer interactions in the spray-dried amorphous solid dispersions (ASDs), utilizing aqueous and organic cosolvents and organic solvents mixtures. The rich intermolecular interactions in the aqueously prepared ASDs presumably contribute to the physical stability, and the interactions are retained in the solution state to maintain supersaturation for an enhanced dissolution profile. This study presents the first application of UF-MAS NMR characterization of therapeutic solid dosages at a spinning frequency of 110 kHz and uncovers the molecular mechanisms of solvent-mediated pharmaceutical dispersions.

Multi-receiver solid-state NMR using polarization optimized experiments (POE) at ultrafast magic angle spinning.

Ultrafast magic angle spinning (MAS) technology and 1H detection have dramatically enhanced the sensitivity of solid-state NMR (ssNMR) spectroscopy of biopolymers. We previously showed that, when combined with polarization optimized experiments (POE), these advancements enable the simultaneous acquisition of multi-dimensional 1H- or 13C-detected experiments using a single receiver. Here, we propose a new sub-class within the POE family, namely HC-DUMAS, HC-MEIOSIS, and HC-MAeSTOSO, that utilize dual receiver technology for the simultaneous detection of 1H and 13C nuclei. We also expand this approach to record 1H-, 13C-, and 15N-detected homonuclear 2D spectra simultaneously using three independent receivers. The combination of POE and multi-receiver technology will further shorten the total experimental time of ssNMR experiments for biological solids.

High-resolution proton-detected MAS experiments on self-assembled diphenylalanine nanotubes enabled by fast MAS and high magnetic field

The advent of ultrahigh magnetic field and fast magic-angle-spinning (MAS) probe technology has led to dramatically enhanced spectral resolution and sensitivity in solid-state NMR spectroscopy. In particular, proton-based multidimensional solid-state NMR techniques have become feasible to investigate the structure and dynamics at atomic resolution, due to the increased chemical shift span and spectral resolution. Herein, the benefits of faster MAS and higher magnetic field are demonstrated on a self-assembled diphenylalanine (Phe-Phe) nanomaterial. Proton-detected 2D 1H/1H single-quantum/single-quantum (SQ/SQ) correlation, double-quantum/single-quantum (DQ/SQ) correlation, and 1H chemical shift anisotropy/chemical shift (CSA/CS) correlation spectra obtained at two different spinning speeds (60 and 100 kHz) and two different magnetic fields (600 and 900 MHz) are reported. The dramatic enhancement of proton spectral resolution achieved with the use of a 900 MHz magnetic field and 100 kHz MAS is remarkable and enabled the measurement of proton CSA tensors, which will be useful to better understand the self-assembled structures of Phe-Phe nanotubes. We also show through numerical simulations that the unaveraged proton-proton dipolar couplings can result in broadening of CSA lines, leading to inaccurate determination of CSA tensors of protons. Thus, our results clearly show the insufficiency of a 600 MHz magnetic field to resolve 1H spectra lines and the inability of a moderate spinning speed of 60 kHz to completely suppress 1H–1H dipolar couplings, which further justify the pursuit of ultrahigh magnetic field beyond 1 GHz and ultrafast MAS beyond 100 kHz.

Molecular packing of pharmaceuticals analyzed with paramagnetic relaxation enhancement and ultrafast magic angle pinning NMR

Understanding the relationship between the structure and the physicochemical attributes of crystalline pharmaceuticals requires high-resolution molecular details. Solid-state nuclear magnetic resonance (ssNMR) spectroscopy is an indispensable tool for analyzing molecular structures, but often experiences challenges of low spectral resolution and sensitivity, particularly in the characterization of unlabeled pharmaceutical materials. Besides, the relatively long spin-lattice relaxation times in pharmaceutical crystals result in time-consuming data collections. In this study, we utilize ultrafast magic angle spinning (UF-MAS) of the sample at 60 and 110 kHz to enable proton and fluorine spectroscopies for probing the structural details of crystalline posaconazole. Paramagnetic relaxation enhancement (PRE), obtained by doping Cu(ii) ions into the crystalline lattice and coating on particle surface, is implemented to shorten the spin-lattice relaxation time for speeding up the ssNMR acquisition. Our results demonstrate a remarkably improved 1H and 19F resolution and sensitivity, which enables multi-dimensional 1H-1H and heteronuclear 1H-19F correlations. In combination with density functional theory (DFT) calculations of chemical shifts, molecular details of posaconazole are established in terms of 1H and 19F networks for identifying "head-to-tail" and "head-to-head" intermolecular packings, with presumably critical contacts that stabilize the crystalline structure. The PRE and UF-MAS techniques enable the high-resolution structure characterization of fluorinated drug molecules in pharmaceutical formulations at natural abundance.

Exploiting heterogeneous time scale of dynamics to enhance 2D HETCOR solid-state NMR sensitivity.

Multidimensional solid-state NMR spectroscopy plays a significant role in offering atomic-level insights into molecular systems. In particular, heteronuclear chemical shift correlation (HETCOR) experiments could provide local chemical and structural information in terms of spatial heteronuclear proximity and through-bond connectivity. In solid state, the transfer of magnetization between heteronuclei, a key step in HETCOR experiments, is usually achieved using cross-polarization (CP) or insensitive nuclei enhanced by polarization transfer (INEPT) depending on the sample characteristics and magic-angle-spinning (MAS) frequency. But, for a multiphase system constituting molecular components that differ in their time scales of mobilities, CP efficiency is pretty low for mobile components because of the averaging of heteronuclear dipolar couplings whereas INEPT is inefficient for immobile components due to the short T2 and can yield through-space connectivity due to strong proton spin diffusion for immobile components especially under moderate spinning speeds. Herein, in this study we present two 2D pulse sequences that enable the sequential acquisition of 13C/1H HETCOR NMR spectra for the rigid and mobile components by taking full advantage of the abundant proton magnetization in a single experiment with barely increasing the overall experimental time. In particular, the 13C-detected HETCOR experiment could be applied under slow MAS conditions, where a multiple-pulse sequence is typically employed to enhance 1H spectral resolution in the indirect dimension. In contrast, the 1H-detected HETCOR experiment should be applied under ultrafast MAS, where CP and heteronuclear nuclear Overhauser effect (NOE) polarization transfer are combined to enhance 13C signal intensities for mobile components. These pulse sequences are experimentally demonstrated on two model systems to obtain 2D 13C/1H chemical shift correlation spectra of rigid and mobile components independently and separately. These pulse sequences can be used for dynamics based spectral editing and resonance assignments. Therefore, we believe the proposed 2D HETCOR NMR pulse sequences will be beneficial for the structural studies of heterogeneous systems containing molecular components that differ in their time scale of motions for understanding the interplay of structures and properties.

Protonated Nitrogen Structure in 15N-Labeled Model Coal Investigated by Solid-State 1H–15N Double-CP NMR Experiments under Ultrafast Magic-Angle Spinning

The nitrogen structure in coals has been focused on as a key factor for reducing NOx. Solid-state nuclear magnetic resonance (NMR) with high spectral resolution can be an effective tool for analyzi...

Line narrowing in 1H NMR of powdered organic solids with TOP-CT-MAS experiments at ultra-fast MAS.

The residual broadening observed in 1H spectra of rigid organic solids at natural abundance under 111 kHz magic angle spinning (MAS) is typically a few hundred Hertz. Here we show that refocusable and non-refocusable interactions contribute roughly equally to this residual at high-fields (21.14 T), and suggest that the removal of the non-refocusable part will produce significant increase in spectral resolution. To this end, we demonstrate an experiment for the indirect acquisition of constant-time experiments at ultra-fast MAS (CT-MAS) which verifies this hypothesis. The combination of this experiment with the two-dimensional one pulse (TOP) transformation reduces the experimental time to a fraction of the original cost while retaining the narrowing effects. Results obtained with TOP-CT-MAS at 111 kHz MAS on a sample of β-AspAla yield up to 30% higher resolution spectra than the equivalent one-pulse experiment, in less than 10 min.

Molecular Interactions in Posaconazole Amorphous Solid Dispersions from Two-Dimensional Solid-State NMR Spectroscopy.

Molecular interactions between the active pharmaceutical ingredient and polymer have potentially substantial impacts on the physical stability of amorphous solid dispersions (ASDs), presumably by manipulating molecular mobility and miscibility. However, structural details for understanding the nature of the molecular contacts and mechanistic roles in various physicochemical and thermodynamic events often remain unclear. This study provides a spectroscopic characterization of posaconazole (POSA) formulations, a second-generation triazole antifungal drug (Noxafil, Merck & Co., Inc., Kenilworth, NJ, USA), at molecular resolution. One- and two-dimensional (2D) solid-state NMR (ssNMR) techniques including spectral editing, heteronuclear 1H-13C, 19F-13C, 15N-13C, and 19F-1H polarization transfer, and spin correlation and ultrafast magic angle spinning, together with the isotopic labeling strategy, were utilized to uncover molecular details in POSA ASDs in a site-specific manner. Active groups in triazole and difluorophenyl rings exhibited rich but distinct categories of interactions with two polymers, hypromellose acetate succinate and hypromellose phthalate, including intermolecular O-H···O═C and O-H···F-C hydrogen bonding, π-π aromatic packing, and electrostatic interaction. Interestingly, the chlorine-to-fluorine substituent in POSA, one of the major structural differences from itraconazole that could facilitate binding to the biological target, offers an additional contact with the polymer. These findings exhibit 2D ssNMR as a sensitive technique for probing sub-nanometer structures of pharmaceutical materials and provide a structural basis for optimizing the type and strength of drug-polymer interactions in the design of amorphous formulations.