Efficient Strategy for Determining the Atomic-Resolution Structure of

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Article Cite This: Macromolecules XXXX, XXX, XXX−XXX

Efficient Strategy for Determining the Atomic-Resolution Structure of Micro- and Nanocrystalline Solids within Polymeric Microbeads: Domain-Edited NMR Crystallography Jiri Brus,* Jiri Czernek, Martin Hruby, Pavel Svec, Libor Kobera, Sabina Abbrent, and Martina Urbanova

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Institute of Macromolecular Chemistry, Academy of Sciences of the Czech Republic, Heyrovsky sq. 2, 162 06 Prague 6, Czech Republic S Supporting Information *

ABSTRACT: Precise structural analysis of multiphase polymeric nanocomposites remains a challenge even in the presence of highquality X-ray diffraction data. This contribution thus addresses our attempt to formulate a combined analytical strategy for obtaining the atomic-resolution structure of multicomponent polymeric solids with complex nanodomain architecture. In this strategy, through the application of T1-filtered solid-state NMR spectroscopy, the individual components are successively distinguished and selected, and the corresponding 1H, 13C, and 15N isotropic chemical shifts are explicitly assigned. Thereafter, using an automated protocol allowing for processing and statistical analysis of large data sets, the experimentally determined NMR parameters are systematically compared with those DFT-calculated for the representative set of crystal structure predictions. Particular attention is devoted to the analysis of NMR parameters of hydrogen-bonded protons which are responsible for molecular packing. As a result of this search, the structures of micro- and nanosized crystallites dispersed in the polymeric matrix are determined and independently verified by the measurements of through-space dipolar couplings. The potential of this strategy is demonstrated on injectable polyanhydride microbeads consisting of a mixture of microcrystalline decitabine and nanocrystalline sebacic acid, both incorporated in the semicrystalline polymeric matrix of poly(sebacic acid). Through the synergistic interplay between the measurements, calculations, and the statistical analysis, we have developed an integrated approach providing structural information that is challenging to elucidate using conventional diffraction approaches. This combination of experimental and theoretical approaches enables one to determine the structural arrangements of molecules in situations which are not tractable by conventional spectroscopic techniques.

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INTRODUCTION For over 60 years, nanomaterials have consistently attracted the attention of the scientific community. In the field of nanomedicine, a recent effort toward optimizing the therapeutic efficacy of newly discovered active compounds has resulted in the development of original supramolecular systems that execute multiple functions, thereby providing not only targeted drug delivery and temporal protection but also the combined advantages of solid and liquid dosage forms.1−3 However, the true potential of these systems has not been entirely utilized. In addition to the formulation of cutting-edge supramolecular synthetic procedures, advancing these materials calls for precise structural analysis of individual elements and a description of the mutual relations between them. This is a stringent requirement, as these systems exist at the borderline between crystalline and amorphous solids, for which highquality diffraction data are inherently unavailable.2,4,5 This contribution thus addresses our attempt to formulate an efficient experimental−computational strategy for obtaining deep insight into the structure of complex polycrystalline composites with micro- and nanodomain architecture. To © XXXX American Chemical Society

determine the atomic-resolution structure of these systems, we apply a procedure based on NMR crystallography6−8 extended to describe the component-selective data. This strategy is based on the combined application of domain-selective solidstate NMR spectroscopy (ss-NMR), crystal structure prediction (CSP), and density functional theory (DFT) based calculations of NMR chemical shifts.6−8 This combination of experimental and theoretical approaches enables one to determine the structural arrangements of molecules in situations which are not tractable by conventional spectroscopic techniques. Its applications should be of particular importance for systems in which phase transformations can occur, and new polymorphic forms can be spontaneously created under the influence of the matrix environment. The proposed method, which employs the confluence of computational data with measured NMR parameters, thus provides for a way to distinguish between alternative candidate structures Received: February 21, 2018 Revised: June 18, 2018

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DOI: 10.1021/acs.macromol.8b00392 Macromolecules XXXX, XXX, XXX−XXX

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Macromolecules exclusively existing in the composite assembles and to select the ones that are the most compatible with available information. The potential of this combined analytical approach, which has never been previously applied for the structure elucidation of nanostructured composites, is highlighted using the recently developed9 biodegradable, injectable polyanhydride microbead formulation of decitabine (5-aza-2′-deoxycytidine, DAC), an archetypal DNA methyltransferase inhibitor used as an efficient therapeutic for epigenetic cancer therapy. In this innovative drug-delivery formulation, which was developed to circumvent the problem of hydrolytic lability of the active compound, a mixture of microcrystalline domains of decitabine and nanodomains of sebacic acid (SA) is embedded in the semicrystalline matrix of poly(sebacic acid-co-1,4-cyclohexane-dicarboxylic acid) (PSA-co-PCH) carrier (for details of the synthesis see ref 9 and Supporting Information SI1).

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EXPERIMENTAL SECTION

Solid-State NMR Spectroscopy. Solid-state-NMR spectra were measured at 11.7 T on a Bruker Avance III HD 500 US/WB NMR spectrometer (Karlsruhe, Germany, 2013). For explicit determination of isotropic chemical shifts, the following techniques were used: (i) 1 H NMR with DUMBO homodecoupling,10 (ii) 13C and 15N CP/ MAS and 13C CPPI/MAS NMR,11,12 (iii) 2D 1H−13C FSLG HETCOR NMR,13 (iv) 2D NOESY-type 1H−1H spin-diffusion NMR with DUMBO homodecoupling,14 and (v) 2D DQ/SQ 1H−1H DUMBO MAS NMR15 with SPC5 DQ recoupling.16 1H−13C dipolar profiles were obtained using the well-established 2D 1H−13C Lee− Goldburg cross-polarization experiments.17,18 To suppress unwanted coherences, the T1(1H) filter consisting of a 180° (1H) pulse followed by a short delay was used. Frictional heating19,20 of the spinning samples was compensated for by active cooling. For all of the experimental details, see Supporting Information SI2. Density Functional Theory Calculations. The periodic structures of the candidate polymorphs were generated using the Polymorph Predictor module of the Materials Studio Package21 as described in our previous work.22 The selected structures were subjected to the full geometrical optimization using the PW DFT approach with the periodic boundary conditions imposed, as implemented in the CASTEP 6.1 suite of codes.23−25 The resulting geometries served as the input for the NMR chemical shielding predictions, which were performed by applying the GIPAW method26,27 implemented in the CASTEP-NMR module.25 The RPBE28 and PBE29 functionals were employed in the CASTEP calculations of DAC and SA, respectively. The chemical shielding data were then used to evaluate the agreement between the theoretical and measured values through the protocol described previously.22 For further details see Supporting Information SI3.

Figure 1. (a) Micrograph and schematic representation of the DAC/ PSA-co-PCH microbeads and (b) 13C MAS and CP/MAS NMR spectra of PSA-co-PCH copolymer (blue spectra) and the DAC/PSAco-PCH microbeads (red spectra). The 13C CP/MAS NMR spectrum of the reference polymorphic form DAC-I is demonstrated as well (black spectrum).

are incorporated into the polymer matrix, the mobile polymer fraction disappears because it is transformed into a hindered amorphous phase (broad signals in the 13C MAS NMR spectrum) and a secondary β-crystalline phase (the narrow 13C CP/MAS NMR signals at 34.5, 33.7, and 25.3 ppm; Figure 1b, red spectra). The spatially restricted, residual dynamics of polymer segments in the amorphous phase of DAC/PSA-co-PCH microbeads is demonstrated in 1H−13C dipolar profiles (Figure 2a,b) obtained using the well-established 2D 1H−13C Lee− Goldburg cross-polarization experiments.17,18 Whereas the highly mobile polymer segments in the amorphous phase of neat PSA-co-PCH copolymer are characterized by a very narrow 1H−13C dipolar profile with a splitting of ca. 3 kHz (Figure 2b, blue spectrum), the polymer chains in the amorphous phase of DAC/PSA-co-PCH microbeads are characterized by broad nearly featureless profiles with the splitting of ca. 15 kHz (Figure 2b, red spectrum). This finding thus indicates restricted segmental dynamics with a broad distribution of motional modes, when PSA-co-PCH polymer chains in the amorphous phase are not completely immobilized adopting combined static and dynamic disorder. In contrast,

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RESULTS AND DISCUSSION Structural Complexity of Polymeric Microbead Formulations. In nanocomposites, the complex pathways of reversible processes with low activation energy can induce unexpected structural transformations of individual components. Consequently, also the structure of the synthesized polyanhydride microbeads of decitabine (DAC/PSA-co-PCH), the size of which ranges from 50 to 300 μm (Figure 1a), is exceedingly complex. Even neat PSA-co-PCH copolymer consists of two vastly different phases. While strong 13C CP/ MAS NMR resonances reflect the prevailing α-crystalline phase (Fα, blue spectra, Figure 1b), narrow signals detected in the single-pulse 13C MAS NMR spectrum indicate the coexistence of highly mobile polymer chains in a residual amorphous phase. When the microcrystalline domains of DAC B

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and PSA-co-PCH polymer matrix are different, their micro/ nanosegregation occurred.4,30−32 This finding is further supported by the absence of corresponding decitabine-polymer correlation signals in the 1H−1H CRAMPS spin-diffusion spectra measured with long mixing times (1−10 ms; Figure 2c and Supporting Information SI4). In addition to their multicomponent character, DAC/PSAco-PCH microbeads are difficult to structurally characterize because of the extensive polymorphism of decitabine (DAC), as at least five modifications of decitabine have been found.33,34 Moreover, various phase transformations and molecular reorganization induced by the polymer matrix can result in the formation of structures exclusively existing in composite assembles. In our particular case, the comparison of the recorded 13C CP/MAS NMR chemical shifts with the previously reported reference NMR data22 (Figure 1b) indicates the presence of a yet undescribed crystal modification of decitabine, which we denote for the sake of clarity as DACX. Further, due to the low content of DAC-X microcrystals surrounded by the semicrystalline polymer matrix, many of the X-ray reflections overlap and hence the crystal structure determination process using X-ray powder diffraction data (XRPD) becomes very challenging. Consequently, structural analysis of this multicomponent polycrystalline system at the atomic-resolution level calls for the application of an alternative approach based on NMR crystallography that in principle allows for determination of crystal structures from 1H NMR chemical shifts only.6,7 Domain Selection by T1-Filtered ss-NMR Spectroscopy. To date, determination of crystal structures utilizing exclusively the analysis of isotropic NMR chemical shifts has mostly been applied to the structural elucidation of crystallographically uniform organic solids.6−8,22,35−39 We believe, however, that the true potential of this approach of NMR crystallography lies in the structural description of complex polycrystalline composites with micro- or nanodomain architecture for which direct crystal structure refinement using XRPD data does not typically lead to satisfactory structure solutions. Successful application of this variant of NMR crystallography preferably requires explicit assignment of NMR signals. Previously, it has been found out that only “unambiguously” assigned chemical shifts can be used for the crystal structure determination. It has been demonstrated that unambiguous signal assignment increases the robustness of the structure selection process and considerably enhances the potential to discriminate among candidate structures.6−8 However, in the complex organic solids consisting of many different components and domains the corresponding 1H NMR resonances are often overlapping and the resulting spectra exhibit insufficient resolution. Particularly, if the carrier matrix considerably prevails over the active compounds, the characteristic spectroscopic markers are no longer observed, as they are hidden under the strong signals of excipients. Fortunately, solid-state NMR spectroscopy offers a range of experimental techniques enabling selective suppression or enhancement of the required signals. For polymeric composites, the T1- and T2filtered experiments, which are sensitive to differences in segmental dynamics, are particularly convenient techniques.40−45 This is given by the fact that local motions in even highly crystalline polymers efficiently reduce 1H spin− lattice relaxation times T1(1H), which then tend to be several seconds only. In contrast, low-molecular-weight crystalline

Figure 2. (a) 2D 1H−13C PILGRIM spectrum of the DAC/PSA-coPCH microbeads; (b) 1H−13C dipolar profiles extracted for aromatic CH(6) group of crystalline decitabine (154.7 ppm), CH2 group of crystalline PSA (35.7 ppm), and hindered amorphous PSA (29.3 ppm). For comparison the dipolar profile recorded for free amorphous phase of neat PSA-co-PCH matrix is also displayed as blue spectrum. (c) 2D 1H−1H CRAMPS spin-diffusion correlation spectrum of DAC/PSA-co-PCH microbeads measured with a 10 ms mixing time. Empty boxes underline the absence of decitabinepolymer correlation signals.

the 1H−13C dipolar splitting recorded for crystalline decitabine and crystalline components of the polymer matrix reaches the value of ca. 22−23 kHz, which is close to the limit expected for rigid C−H segments in CH and CH2 groups.17,18 These findings thus reflect differences in molecular mobility which can be associated with heterogeneous micro/nanosegregated nature of DAC/PSA-co-PCH microbeads. Existence of micro/nanosegregated domains in the prepared microbeads is, however, clearly documented by distinct differences in T1(1H) spin−lattice relaxation times between the polymer matrix and decitabine molecules (T1(1H) = 1.3 and 55 s, respectively). Previously, using a range of twocomponent solids,4,31,32 differences in 1H relaxation times between individual components have been demonstrated to indicate their micro/nanosegregation. This follows from the fact that 1H−1H spin diffusion, which is generally very rapid in organic solids, is not able to equilibrate nuclear spin properties of 1H nuclei in all parts of the phase-separated heterogeneous systems. Typically, 1H magnetization is transferred over a distance of approximately 1.1−1.2 nm during 1 ms.30 In the measurements of T1(1H) spin−lattice relaxation times, the relevant times of 1H spin diffusion are in the range of several seconds. Consequently, 1H magnetization can be effectively transferred over several hundred nanometers. Therefore, as the T1(1H) spin−lattice relaxation times of decitabine molecules C

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Figure 3. T1-filtered 1H DUMBO and 13C CP/MAS NMR spectra of DAC/PSA-co-PCH microbeads measured at various τf delays, panels a and b, respectively; T1(1H) inversion−recovery relaxation of PSA-co-PCH and DAC-X components of DAC/PSA-co-PCH microbeads (c); representation of T1-filtered 1H−13C HETCOR pulse sequence (d); 2D 1H−13C FSLG HETCOR NMR spectra of DAC/PSA-co-PCH microbeads measured with 70 and 150 μs CP mixing times (e); 2D 1H−1H SQ/SQ NMR spectrum of DAC/PSA-co-PCH microbeads measured with a 25 μs spin-diffusion period; and 2D 1H−1H DQ/SQ DUMBO NMR spectrum of DAC/PSA-co-PCH microbeads measured with a 40 μs recoupling period (f).

components (T1(1H) = 55 and 1.3 s for DAC-X and PSA-coPCH, as directly determined for the investigated microbeads, respectively), makes it possible to apply a proton T1(1H) relaxation filter. In the most simple arrangement, this filter consists of a single 180°(1H) pulse and a short delay, both placed at the beginning of a pulse sequence (Figure 3d). Subsequently, when applying this T1(1H)-filter the 1H magnetization of PSA-co-PCH copolymer passes through the zero point at τf = 0.9 s (Figure 3c), thus leaving the corresponding T1(1H)-filtered 1H DUMBO and 13C CP/MAS

compounds often exhibit much longer relaxation times reaching up to several hundreds of seconds. As a variety of different relaxation filters and editing techniques can be applied,40−45 the appropriate experimental conditions enabling efficient suppression of the unwanted signals can often be readily attained. As expected, for the DAC/PSA-co-PCH microbeads, the 1H NMR signals of DAC-X are strongly overlapped with the signals of PSA-co-PCH copolymer matrix (Figure 3a). However, the different relaxation behavior of these two main D

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compared. The procedure proposed here thus allows for efficient narrowing down of the batch of possible crystal structure predictions and automatic selection of the most suitable candidates. When searching for the NMR-consistent crystal structure of microcrystalline decitabine existing in DAC/PSA-co-PCH microbeads 32 DAC polymorphs selected previously from the batch of ca. 300 crystal structure predictions were considered.22 For all of these, the PW DFT geometrical optimizations and the GIPAW predictions of the NMR data were performed using the RPBE (“revised PBE”) DFT exchange-correlation functional28,29 while adopting the “Fine” level of settings of the CASTEP package (for all computational details, see Supporting Information SI3). The NMR chemical shieldings obtained in this manner, together with the assigned chemical shifts, are used by the above-mentioned software. Below, the application of the polymorph-selection procedure to the case of DAC-X dispersed in a PSA-co-PCH matrix is highlighted. First, the linear regression of the σ and δ data for all the 1H and 13C nuclei is performed. Then, the structures are screened in two loops, which accordingly employ the value of one standard deviation of the correlations of the proton, 1H (all) r.m.s.d., and carbon, 13C (all) r.m.s.d. To ensure that all suitable candidates are captured in the first selection step, the structures are selected with both 13C (all) and 1H (all) r.m.s.d. values less than the relatively high thresholds values set to 2.5 and 0.8 ppm (Figure 4a,b). If the number of possible candidates selected is too large, then the threshold limits can be reduced. For the preselected candidates, analogous linear regressions are performed for the 1H species directly bound to carbon atoms, and the corresponding 1H (CH) r.m.s.d. values are determined. In this case, the threshold limit indicating potential candidates is reduced to 0.5 ppm (Figure 4c). As exchangeable OH and NH sites involved in hydrogenbonding networks are particularly important in crystal formation, we suggest analyzing their 1H and 15N isotropic chemical shifts separately and determining the corresponding 1 H (OH/NH) and 15N r.m.s.d. values. When 15N and 1H (OH/NH) r.m.s.d. values are small (Table 1), it is practically guaranteed that the candidate structure represents the most appropriate polymorph (i.e., fortuitous reproduction of the experimental chemical shifts is highly improbable). However, due to the limited number of the corresponding sites in the crystalline decitabine the 1H r.m.s.d. values determined only for NH/OH protons, as well as the 15N r.m.s.d. values, are not sufficiently robust to be directly included among the key criteria for selecting the most appropriate crystal structure. Rather we consider them as auxiliary criteria. Therefore, to further reduce the set of models and thus to identify the most appropriate NMR-consistent crystal structure, the theoretical prediction of the corresponding 2D heteronuclear correlation (HETCOR) spectrum is performed for the directly bound proton-to-carbon pairs in the remaining candidate structures. The level of agreement with the measured HETCOR peak positions is then established, thereby providing the value of covariance, s(CH), between the two data sets (Figure 4d).48−50 In the final step, the most appropriate structure is chosen from among the candidates that have met all the above-mentioned criteria based on the lowest value of covariance.22 Overall, considering all of the obtained NMR statistical parameters below the thresholds accepted as indicators of the

NMR spectra of DAC/PSA-co-PCH microbeads free of the signals from the polymer matrix (Figure 3a,b, red spectra). Analogous modification of correlation experiments (Figure 3d) then provides 2D spectra which are relatively more easily interpreted (Figure 3e,f). In this way, explicit assignment of the 1 H and 13C NMR signals of DAC-X was achieved (Supporting Information SI5 and Table S1). Particular attention was then devoted to the identification of the amino (7.25; 7.81 ppm) and hydroxyl (4.5; 5.0 ppm) protons, which represent crucial species responsible for hydrogen bonding and molecular cluster formation. Automated Processing of NMR Parameters. In the next step, the experimentally determined 1H, 13C, and 15N NMR chemical shifts are systematically compared with the NMR parameters DFT-calculated for the set of predicted crystal structures. In general, and regardless of the system investigated, when searching for the most appropriate crystal structures best describing unknown molecular arrangements, it is necessary to generate a representative set of crystal structure predictions. This collection may consist of up to several thousand suggestions.6−8 The reliability of this approach has already been verified using a range of organic crystalline compounds.6−8 In this context, we have recently applied and extended this methodology to reconstruct the complete crystal structure of decitabine polymorphic form I (DAC-I) from isotropic 1H NMR chemical shifts and 1H−13C correlation signals. This way we found out specific threshold limits of statistical NMR parameters (root-mean-square deviation, r.m.s.d.) required to identify the most appropriate (correct) models of decitabine crystal structures (1.9 and 0.5 ppm for 13 C and 1H r.m.s.d.) and formulated a procedure allowing us to discriminate inconsistencies resulting from the long-range symmetry operations.22 Specifically, the applied computational approach employs fully periodic structures from a batch of computer-predicted polymorphs21 and subjects them to full geometrical optimization conducted using a plane-wave (PW) DFT-based strategy.23−25 For the PW DFT geometries, the isotropic NMR chemical shieldings, σ, are computed by applying the gaugeincluding projector augmented wave (GIPAW) technique26,27 within the CASTEP25 suite of codes. These values for the 1H, 13 C, and 15N nuclei are then used in the statistical evaluation of the similarity between the experimental (corresponding NMR chemical shifts, δ) and theoretical data sets. Based on the results, selection of the final structure(s) is performed. Importantly, the present approach is general in the following sense: first, any other suitable procedures can be used to generate the coordinates of polymorphs,46 and second, other available methods47 may be used to predict the σ values. In addition, this computational protocol can also be easily extended to nuclei and/or solid-state NMR parameters other than those considered here. Moreover, the procedure for selecting the optimal polymorph from the data mentioned above has now been automated (the software POSEL, POLymorph SELector, is described in Supporting Information SI3 and can be obtained upon contacting the corresponding author), allowing it to be run immediately with different inputs. This way, thus the data sets consisting of a large number of model structures and NMR experimental parameters can be processed. Bear in mind that in some cases several hundred crystal structure predictions are analyzed and a broad range of NMR parameters is systematically E

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Table 1. Root-Mean-Square Deviations of Linear Correlations between the 1H, 13C, and 15N NMR Chemical Shieldings Calculated for the Selected Structure of Decitabine and the Corresponding Chemical Shifts Measured for the Dispersed DAC-X (DAC-X)exp vs (CSP#1)cal DFT functional NMR similarity parameters 13

C(all) r.m.s.d, ppm 1 H(all) r.m.s.d., ppm 1 H(CH) r.m.s.d., ppm 1 H(OH/NH) r.m.s.d., ppm 15 N r.m.s.d., ppm s(CH) covariance, ppm2

PBE

RPBE

1.94 0.53 0.52 0.34 3.11 0.054

1.92 0.43 0.48 0.16 4.20 0.21

selected model CSP#1 must still be considered just one of several possible NMR-consistent candidates. In practice, other predictions consistent with the experimental NMR parameters may exist depending on the size of the pool of models generated by the polymorph predictor. Generally, we must also admit that some suitable models may have been lost in the preselection step, during which the initial set of CSPs containing up to several hundred models was narrowed down according to the relative lattice energies.22 Consequently, the energetic criterion can be also taken into account, although previously only weak correlation was found between the correct crystal structure selection and the corresponding lattice energy.6−8 Therefore, using the RPBE method28 we calculated the lattice energy for the predicted structure of DAC-X and the reference structure of X-ray structure of DACI22 and compared them. This way, we found out that the lattice energy of DAC-X is increased by ca. 15 kJ/mol relative to the lattice energy of DAC-I. Although the obtained value is still in the acceptable limit of relative energies expected for physically realistic polymorphs (ca. 20−30 kJ/mol),7,51,52 the observed increase may indicate certain inconsistencies between the predicted model and the real structure. As the insufficient resolution of the labile protons remains a critical factor, and the inconsistencies in the long-range molecular packing must also be taken into account,22 because NMR parameters are primarily sensitive to the local arrangements only, a verification of the selected crystal structure using experimental parameters other than the isotropic chemical shifts is of particular interest. In NMR spectroscopy, the most straightforward route to determine 3D molecular structure utilizes the measurement of dipole−dipole interactions, e.g., 1 H−15N/14N dipolar couplings, which possess outstanding advantages, as they are accessible without isotopic enrichment and reflect the strength of hydrogen bonding. Variable-contact-time experiments monitoring the evolution of 1H−15N cross-polarization (CP) are an ideal choice for comparing the strength of 1H−15N dipolar couplings.53 Figure 5a shows the 1H−15N CP build-ups recorded for the N3 and N5 nitrogen sites of DAC-X (DAC/PSA-co-PCH microbeads) and of the reference system DAC-I. These dependences and the corresponding CP rate constants, TIS(DAC-X) = 8.0 and 9.0 ms and TIS(DAC-I) = 4.5 and 5.5 ms for N3 and N5, respectively, thus reflect significant differences in the strength of the 1H−15N dipolar interactions. In general, the strength of dipolar couplings is sensitive to the interatomic distance and molecular dynamics. However,

Figure 4. Comparison of the assigned experimental chemical shifts and the GIPAW-RPBE-predicted chemical shieldings, represented in terms of the r.m.s.d. values of the respective linear regressions: panels a and b describe all carbon and hydrogen atoms, 13C (all) and 1H (all), respectively; panel c describes 1H species directly bound to carbon atoms, 1H (CH). Panel d shows the values of the covariance, s(CH). The final NMR-consistent crystal structure corresponding to the DAC-X dispersed in PSA-co-PCH is presented in panel e. The bars in red color demonstrate gradual selection of the models which can be considered as potential candidates of the most appropriate crystal structure.

most appropriate structures (Table 1), we identified just one NMR-consistent candidate (CSP#1) in the set of predicted models (Figure 4e). Importantly, the 1H(OH/NH) r.m.s.d. values obtained for exchangeable protons are also very low, ca. 0.2 ppm, thereby providing additional support that the proposed hydrogen-bonding motif is consistent with the experimental data. These findings are further supported by the fact that the obtained values are comparable to those previously determined for the X-ray refined polymorphic form DAC-I (Supporting Information SI6, Table S2, and Figure S9). In addition, those values are only slightly dependent on the DFT functional employed in the calculations as both RPE and PBE functionals were tested (Table 1). Independent Experimental Verification. Despite the very good agreement with the experimental NMR data, the F

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of this H-bonding motif and much longer N3···H and N5···H distances reaching 2.7 and 2.4 Å, respectively (Figure 5c). These experimental findings, derived from the evolution of the 1H−15N CP, are consistent with the 15N NMR spectra (both predicted and experimental, Figure 5b), which nicely reproduce changes in the magnetic shielding at the nitrogen atoms. The significant decrease in hydrogen-bonding strength observed in DAC-X is also in accordance with the predicted Hirshfeld surfaces (Figures 5c). Intermolecular contacts shorter than van der Waals distances marked as red spots clearly involve nitrogen atoms N3 and N5 in the molecular cluster of DAC-I. In the related fingerprint plot, these N···H contacts are highlighted as narrow spikes showing their significance in the crystal packing (blue spikes, Figure 5d, right). In contrast, the corresponding fingerprint plot of DACX showed no such close N···H contacts in the molecular packing of DAC-X; instead, only insignificant projection was found (blue surface in Figure 5d, left). These findings thus indicate that the local, previously unreported structural motifs and arrangements of molecular clusters in the crystalline domains of DAC-X were determined correctly. Selection and Structure Determination of Nanocrystalline Components. The same domain-selective approach of NMR crystallography can be successively applied to inspect the structure of other crystalline phases present in the investigated composites. By optimizing the specific experimental parameters of the T1 filters individual components can be step-by-step selected according to their dynamical and spin-relaxation behavior. The corresponding spectral parameters then can be explicitly determined. This way, by using the saturation recovery 1H T1-filter, two sets of narrow signals corresponding to α- and β-crystalline fractions of the polymeric matrix are enhanced in the 13C CP/ MAS and 1H−13C HETCOR NMR spectra of DAC/PSA-coPCH microbeads (Figure 6a). From the 1H−13C correlation pattern which includes the nonprotonated carbonyl carbons resonating at ca. 169 ppm the high-intensity Fα signals were attributed to the crystalline fraction of poly(sebacic acid) (PSA). Because of the narrower 1H projections and the clear correlation with the carbon and proton of the COOH carboxyl group resonating at ca. 181 and 12 ppm, respectively, the less intensive Fβ signals were assigned to the residual fraction of crystalline monomeric sebacic acid (SA). Interestingly, the observed efficient selection of the residual fraction of crystalline monomeric SA indicates relatively fast 1 H spin−lattice relaxation. Precise measurements of 1H T1 spin−lattice relaxation times in DAC/PSA-co-PCH microbeads then revealed that relaxation times of crystalline sebacic acid and polymeric PSA matrix are equal (they reach the same value of T1(1H) = 1.3 s). In contrast, the 1H spin−lattice relaxation time determined for neat microcrystalline SA is considerably longer ca. T1(1H) = 38 s. The observed substantial shortening of the relaxation time for SA crystallites in DAC/PSA-co-PCH microbeads thus reflects fast and efficient equilibration of 1H magnetization driven by the 1H−1H spin diffusion from the PSA matrix. The phenomenon then indicates that the crystallites of SA present in the matrix of PSA-co-PCH reach relatively small dimensions. To approximately quantify the scale of these dispersed crystallites, we monitored 1H−1H spin-diffusion process54,55 and calculated the maximum diffusive path length over which 1 H magnetization is effectively transferred.56−59 In the most simple expression, the maximum diffusive path length (L)

Figure 5. 1H−15N CP build-up curves (a); predicted and experimental 15N CP/MAS NMR spectra (b); Hirshfeld surfaces (c); and the corresponding fingerprint plots (d), all for DAC-X and the reference system DAC-I. The 15N CP/MAS NMR spectra and the build-up curves were measured for DAC/PSA-co-PCH microbeads and the reference DAC-I system.

segmental motions and the corresponding motional averaging of dipolar couplings can be neglected for crystalline decitabine. This assumption is clearly evidenced by the experimentally determined 1H spin−lattice relaxation times (T1(1H)), which for DAC-I and DAC-X reach up to 60 and 55 s, respectively. The observed very long relaxation times thus rule out the motions with the potential to reduce dipolar couplings. The absence of considerable molecular dynamics in DAC-X microcrystals is further supported by the unreduced onebond 1H−13C dipolar coupling constant of ca. 22 kHz determined for CH(6) aromatic group (Figure 2), which is a typical value for the completely rigid organic solids.17,18 Consequently, the observed increase in 1H−15N CP rate constant can be exclusively explained by the increase in N···H interatomic distances and weakening of N···H hydrogenbonding interactions in the DAC-X polymorphic form in comparison with those in the reference system DAC-I. While the N···H hydrogen-bonding motif is essential for the crystal packing of the polymorphic form DAC-I, as reflected by the short N3···H and N5···H distances (1.8 and 1.9 Å, respectively), the selected model CSP#1 predicts the absence G

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facts were subsequently used for generating the set of CSPs of SA. In this context also the known X-ray structure (CCSD 159745) was considered.60 In the next step, the DFTcalculated NMR parameters were compared with the experimental 1H−13C HETCOR NMR data, and as a result of this search, we identified the polymorph of SA dispersed in the PSA matrix after gradually decreasing the threshold limits down to ca. 0.5 and 0.1 ppm for the 13C and 1H r.m.s.d. values, respectively. As demonstrated in Figure 6b, the lowest 13C(all) and 1H(all) r.m.s.d. values (0.49 and 0.07 ppm, respectively) clearly point to the most stable monoclinic P21/c form of sebacic acid (CCSD 159745).60 The next most preferred predictions, CSP#16(SA) and CSP#37(SA), slightly differs in hydrogen-bonding motifs, as demonstrated in Figure 6c. Thus, we have confirmed the ability of the proposed domain-editing approach to determine the crystal structure of not only microcrystalline domains but also nanosized crystallites dispersed in a crystalline polymeric matrix. As all of the models adopted the same all trans conformation, the obtained results revealed that isotropic chemical shifts are sufficiently sensitive to changes in the molecular packing. This finding thus opens a way toward the structure refinement of the crystal structures of synthetic polymers for which a limited amount of spectroscopic data is usually available.

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CONCLUSIONS Determination of the atomic-resolution structure of microscale composites with nanodomain architecture remains a challenge even in the presence of high-quality diffraction data. To overcome this problem we explored a combination of domainselective solid-state NMR techniques with DFT calculations and spectral data processing and formulated the combined analytical strategy for monitoring the atomic-resolution structure of polycrystalline multicomponent systems whose domains are incorporated in the semicrystalline matrix. In this strategy, by applying T1-filtered NMR experiments, the individual components differing in segmental dynamics are consistently selected in a step-by-step manner and the corresponding isotropic chemical shifts are explicitly determined. In the next step, with an automated protocol that allows the processing and statistical analysis of large sets of model structures and NMR data, the experimentally determined NMR parameters are systematically compared with those DFT-calculated for the representative set of crystal structure predictions. In this way, the representative set of CSPs is gradually narrowed down. As a result of this search, the crystal structures of micro- and nanosized crystallites dispersed in the polymeric matrix are determined. An independent verification of the selected structures can be attained by measuring the 1H−15N and 1H−1H dipole−dipole interactions, as they are accessible without isotopic enrichment and faithfully reflect the strength of hydrogen bonding. Using the proposed strategy an intricate hierarchical structure of novel microbead formulations of decitabine was efficiently probed. On the basis of differences in nuclear-spin relaxation the investigated polyanhydride microbeads were spectroscopically decomposed into individual constituents revealing the presence of a crystalline polymeric matrix that is accompanied by the partly immobilized amorphous phase, microcrystallites of decitabine, and nanoscaled crystallites of sebacic acid. Atomic-resolution structure of the both types of dispersed crystallites was then successfully determined (Figure 7).

Figure 6. 2D 1H−13C HETCOR NMR spectrum of the DAC-X/PSAco-PCH microbeads measured with a short repetition delay and CP mixing time (a); comparison of the GIPAW-RPBE-predicted 13C and 1 H chemical shieldings with the corresponding chemical shifts in terms of the r.m.s.d. values 13C (all) and 1H (all) of the related linear regressions (b); X-ray structure and CSP#16 of SA (c).

obtained with the 1H−1H spin-diffusion in three dimensions over the time (Ti) is described using the following relation, L = (6DTi)1/2, where D is the spin-diffusion coefficient (0.3−0.8 nm2 ms−1) and Ti is the spin−lattice relaxation time T1(1H).4,56−59 Consequently, by using the upper and lower limit of spin-diffusion coefficients the determined equilibrated value of T1(1H) relaxation time (1.3 s) reflects maximum diffusive pathways ranging from 50 to 80 nm. This way, the presence of a secondary fraction of nanoscaled crystallites of SA is clearly confirmed. It is also shown that the size of the corresponding crystallites is typically about 100 nm, not exceeding ca. 200 nm. Subsequently when searching for the atomic-resolution structure of these nanocrystalline domains of sebacic acid, the 1H−13C correlation pattern was analyzed first. Although the molecule of SA consists of 10 carbon atoms, the correlation pattern contains only a half of the expected 13C NMR signals. This observation thus indicates that the corresponding molecular segments adopt a highly symmetric all trans conformation, and it is obvious that the crystal unit cell of SA consists of a single symmetry-independent molecule. These H

DOI: 10.1021/acs.macromol.8b00392 Macromolecules XXXX, XXX, XXX−XXX

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Macromolecules Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank the Czech Science Foundation (Grant No. GA16-04109S) and the Ministry of Education, Youth and Sports of the CR within the National Sustainability Program I (NPU I), Project LO1507 POLYMAT, for their financial support. We are grateful to Dr. Michal Hušaḱ (University of Chemistry and Technology, Prague) for the technical assistance with Materials Studio calculations. Computational resources were partially provided under the program LM2010005 and in the Center CERIT Scientific Cloud, part of the Operational Program Research and Development for Innovations, Reg. No. CZ.1.05/3.2.00/08.0144. M.H. and P.S. thank the Ministry of Education, Youth and Sports of the CR within the Project No. LM2015064 ERIC, for their financial support.

Figure 7. Schematic representation of the determined structures of the key components of injectable polyanhydride microbeads of decitabine (DAC/PSA-co-PCH).

Regarding the future perspectives, when this procedure is applied, it is clearly important to preselect the representative set of CSPs, which will be involved in the DFT optimization and statistical evaluation. As a nearly countless number of structural models can be rapidly generated, a method allowing reliable preselection to narrow down the search is of particular interest. To avoid the problem of losing suitable models, we are currently working on the procedure based on a systematic search through a set of models based on experimentally defined specific interatomic distances (distance restraints). As the obtained results also opened a route toward the structure refinement of synthetic polymers with a limited amount of spectroscopic data available, finding a procedure for the reliable generation of a representative set of CSPs of synthetic polymers is thus of paramount importance. This contribution thus demonstrates the synergy effects of the proposed combination of several experimental and computational procedures, which considerably extends the NMR crystallography approach into the area of intricate mixtures and nanostructured composites in micro- and nanosized forms.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.8b00392. Materials and synthesis; experimentally determined 1H, 15 N, and 13C isotropic chemical shifts; details of computational procedures; similarity measures for the reference system; and complete parameters of solid-state NMR experiments (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Telephone: +420 296 809 350. Fax: +420 296 809 410. ORCID

Jiri Brus: 0000-0003-2692-612X Martin Hruby: 0000-0002-5075-261X Libor Kobera: 0000-0002-8826-948X I

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