Facile investigation of reversible nanostructure changes in exible crystals

Detailed investigation of macroscopic deformation and nanoscopic structural changes in exible organic crystals pose challenges for investigators. Herein, applied stress and subsequent relaxation of elastic organic crystals resulted in reversible macroscopic crystal deformation. X-ray diffraction with a curved jig revealed reversible nanoscopic structural changes in the crystal structure under the bending stress and relaxation. The crystal lattice changed quantitatively under the applied macroscopic stress-strain (%). This method enables quantitative monitoring of the dynamic nanoscopic structural changes in detail associated with crystal deformation through the use of standard laboratory X-ray diffraction analysis. Importantly, the developed method offers a way of quantitatively measuring reversible structural changes, without synchrotron X-ray analysis. Moreover, the analysis derives Poisson’s ratio, i.e., the ratio of the change in the width per unit width of materials. It is important in materials science, normally has a positive value in the range of 0.2–0.5. However, the crystals show not only the "Poisson effect" but also the unusual "negative Poisson effect". This novel approach for investigation generates unprecedented opportunities for understanding dynamic nanostructure changes in exible organic crystals.

Spatially resolved X-ray diffraction measured at different regions of a bent elastic crystal from the outer part of an elongated arc to the inner contracted arc is an effective method of structural investigation, as reported by Clegg and McMurtrie. 15 In the case of uorescent elastic organic crystals, deformationinduced uorescence changes also enable intermolecular packing information to be predicted from spatially resolved emission spectra. 16 Raman spectroscopy is also effective for tracking changes in intermolecular interactions. 17,18 However, synchrotron X-ray analysis is necessary to characterize nanoscopic structural changes associated with crystal bending deformation in detail, 15 which limits the accessibility of such measurements. In addition, there are currently no simple readily accessible methods to quantitatively determine the degree of a nanoscopic change with respect to the amount of deformation (strain, %).
Here, we examine a uorescent donor-acceptor elastic organic crystal based on the screening of cyano-βoligo(phenylenevinylene)s. To develop a simple measurement of the nanoscopic structural changes with respect to curvature (strain, %), the diffraction patterns at the crystal interface were examined. Onedimensional (1D) X-ray diffraction (XRD) analysis, which is readily accessible, was used to determine the degree of nanoscopic structural change with respect to the macroscopic deformation amount (%) calculated from the stress-strain owing to the crystal bending curvature. Quantitative deformation and nanoscopic changes revealed that the crystal cell unit had a negative Poisson effect. 23 This is the rst time a mechanical deformation phenomenon has been reported for an organic crystalline material.

Results And Discussion
Fabrication of elastic organic crystals. Synthesis of β-COPVs was performed by Knoevenagel condensation of aryl dicarboxaldehyde with aryl acetonitrile in the presence of a strong base. 24 As a result of screening, an elastic organic crystal based on the molecule with a methoxyphenylene core and bromophenyl end groups (Fig. 1a) was obtained from 4-bromobenzyl cyanide and 2,5-dimethoxybenzene-1,4-dicarboxaldehyde. 25 Reddish orange-colored needle-like crystals were grown from 1,2-dichloroethane ( Fig. 1b). The optical properties, i.e., UV-vis absorption (λ abs ) and emission (λ em ) wavelengths, full-width half-maximum (FWHM), absolute uorescence quantum yield (Φ F ), uorescence lifetime (τ), and radiative (k r ) and nonradiative (k nr ) decay rate constants, were measured from solution and crystals. The β-COPV with methoxy groups on the phenylene core exhibited charge transfer (CT) interactions. UV-vis absorption spectrum showed two peaks corresponding to π-π* and CT transitions (Fig. 1c). The emission spectrum of the crystal was red-shifted compared with that in CH 2 Cl 2 (ca. +100 nm) owing to formation of an intermolecular donor-acceptor system and a more planar π-system (Fig. 1c). The compound had a higher quantum yield (Φ F ) in its crystal form (Φ F = 0.95) than in CH 2 Cl 2 solution (Φ F = 0.41) owing to suppression of nonradiative processes from the excited state. Moreover, the emission spectrum of the crystal was very narrow, with a FWHM of 65 nm, which was much smaller than that in solution (74 nm). When compared with the solution results (e.g., CH 2 Cl 2 : k r = 1.86 × 10 8 s − 1 , k nr = 2.68 × 10 8 s − 1 ), the crystal had a comparable k r of 2.38 × 10 8 s − 1 but a much smaller k nr of 0.12 × 10 8 s − 1 . The suppression of k nr likely contributed to the enhanced Φ F of the crystal. These results suggest that the desired intermolecular interactions in crystal produced e cient and low-energy emission.
The crystal structure of the molecule is shown in Fig. 2 (triclinic, space group = P-1). The torsion angle (θ) between the core Ar 1 and terminal Ar 2 units is 19.37° (Figs. 2a and 2b). The packing of the molecules has a slip-stacked assembly along the a-axis that results in close π-π-stacking interactions (l p = 0.3651 nm) (Fig. 2c). The center-to-center distance of the molecular planes (l s ) is 0.2798 nm. The bril lamella morphology originates from the slip-stacked molecular packing wires through the self-assembly of planar molecules (Fig. 2c).
Elastic bending for macroscopic deformation. Individual crystals were mechanically tested to assess their elastic properties ( Fig. 3a and Supplementary Video S1). A single crystal (thickness: 168 µm, width: 320 µm, length: 12 mm) was xed to a metal pin with adhesive. Figure 3b and Video 1 show the mechanical bending-relaxation performance of the crystal. Bending stress was applied by pushing the crystal with a glass plate. The straight crystal bent under an applied stress in the c direction and then recovered its original shape upon releasing the stress. Notably, the reversible bending-relaxation of the crystal could be repeated many times (Figs. 3b-l). This mechanical behavior clearly indicates that the crystal is an elastic (bendable) organic single crystal. The crystal bending angle exceeded 70° (Fig. 3k). The elastic organic crystals did not exhibit slipping between the planes and on visual inspection there was no detectable change in the angle between the ends of the crystals. Thus, the crystal underwent elongation at the outside and contraction at the inside of the bend (Supplementary Fig. S1). The elastic strain (ε n ) of the crystal in the c-direction was estimated from the curvature of the bent crystal and the equation ε n = d/2r, where d corresponds to the width of the (001) plane (d = 168 µm) and r is the radius.
The values of ε n were 1.02%, 1.19%, 1.40%, 1.70%, and 2.80% (Figs. 3c, 3 g, 3i, and 3 k). In contrast, the crystal did not bend under an applied stress in the b-direction, i.e., the elasticity was limited to one direction (directional-speci c elasticity). Figure 3m schematically illustrates the elastic bending test using a pair of tweezers and a needle. The crystal bent without breaking when the (001) plane was face-up and the bent crystal quickly recovered its original straight shape without any breaking or crack formation upon withdrawal of the force (Figs. 3n and 3o). In contrast, under elastic bending, when the (010) plane was face-up the crystal was brittle (Figs. 3p and 3q). In this case, the in exible crystal fractured. This direction-depended elasticity is related to anisotropy of the molecular arrangement in the crystal (Fig. 2c).
X-ray analysis of nanoscopic structural changes. To link the directivity of the crystal to its crystal structure, one-dimensional (1D) X-ray diffraction (XRD) analysis of the crystal was performed with an original set-up ( Supplementary Fig. S2). Patterns derived from the lamellar structure for the c-axis were detected when the crystal was positioned parallel to the substrate (Fig. 4a). The Bragg equation was used to calculate the length of the original crystal (010) face up to be 12.367 Å (7.12°), which corresponds to one lamellar layer in the c-direction (Fig. 4b). Thus, the face parallel to the substrate is the (001) face. To determine the changes in the structure induced by bending and relaxation, 1D XRD analysis of the front and back of the straight (original and relaxed) and bent crystal was conducted by performing measurements with the crystal set at different curvatures (Fig. 4a). The elastic strain (ε n ) of the crystal in the c-direction was also estimated from the width of the (001) plane (d = 168 µm) and the radius (r = 3, 5, and 7 mm) of the curved jigs. Upon bending (ε n = 1.2%), the patterns at the front of the crystal shifted to a lower angle (7.04°), which corresponded to a distance of 12.556 Å (Fig. 4b). The patterns returned to their original positions upon releasing the stress. Upon re-bending (ε n = 1.68%), the patterns shifted to an even lower angle (6.98°, 12.657 Å). Recovery of the pattern upon relaxation was also observed. In the case of a greater bending (ε n = 2.8%), a further shift to a low angle was observed at the front of the crystal (6.94°, 12.723 Å). Furthermore, the patterns from the back of the bent crystal (ε n = 0.84%), shifted to a higher angle (7.18°, 12.303 Å). These analyses point to a change of the lamellar distance in the c-direction, d 0 → d x upon bending (Fig. 4c).
Plots of strain (%) from curvature [Δε (100) ] against the degree of change, Δε (001) , from XRD results, and ε n showed a correlation between strain and the change of lamellar distance (Fig. 4d). Hence, the elongation or contraction in the a-direction induced elongation or contraction in the c-direction, respectively (Fig. 4e). The calculated Poisson's ratio, v, is de ned as the ratio of the change in the width per unit width of materials (plastics, metals), to the change in its length per unit length, as a result of strain. Typically, v values are in the range of 0.2-0.5 associated with a contraction of the width of a material when it is stretched (Fig. 4f). Here, the v value of the cell unit (001) can be estimated from the a-axis elongation, as calculated from the bending strain and the variation ratio of c-axis: v (001) = − Δε (001) / Δε (100) . 16 Notably, the v (001) value of this crystal was approximately − 1.0 (Fig. 4d). A negative value of Poisson's ratio (negative Poisson effect) represents an unusual deformation mode in material science, 18 but characteristic examples are based on molecularly dense and well-organized organic crystals.
To investigate the applicability of this method to other crystals, similar measurements were performed for an elastic 9,10-dibromoanthracence crystal. A reversible peak shift occurred as the shape changed from straight to bent (Supplementary Fig. S3a). Importantly, the degree of change in the peak shifts of [Δε (001) ] and [Δε (100) ] changed with the curvature. In this crystal, contraction of the c-axis occurred rather than elongation of the a-axis. However, because elongation of the c-axis occurred with respect to contraction for a-axis, the behavior was different from that of the elastic β-COPV crystal (Supplementary Figs. S3b and S3c). Hence, this crystal showed a typical Poisson effect with a v (001) value of 0.23-0.25.

Conclusion
A simple method is developed for quantitative investigation of reversible nanoscopic structural changes in exible crystals. Mechanically reversible bending deformation causes a nanoscopic structural change in an elastic organic crystal based on the novel π-conjugated molecule, β-COPV. The nanoscopic lattice structure in a crystal changed under the applied macroscopic stress-strain (%). This method enables the nanoscopic structural changes associated with crystal bending deformation to be quantitative analyzed with readily available X-ray equipment. Notably, the calculated Poisson's ratio of the crystal for the (001) face was approximately − 1.0, which is unusual among common materials (approximately 0.2-0.5). Hence, this material showed a negative Poisson effect, suggesting the mechanical characteristics of a dense and well-organized organic crystal structure. Similarly, deformation and structural changes were observed for 9,10-dibromoanthracence crystals, which should a showed normal Poisson effect (approximately 0.24). This work opens new avenues for structural investigations of exible crystals. This is simple method that will be of great utility to researchers who cannot readily access synchrotron X-ray diffraction facilities.