Crystal morphology and structure

As many as 12 trisubstituted imidazoles (Fig. 1) bearing at least one halogen atom and capable of forming N–H⋯N hydrogen bond chains were synthesized, and their structure-property relationships were explored at both the mechanical and electrical levels. The trisubstituted imidazoles were crystallized at room temperature from Me 2 CO/H 2 O mixtures by slow evaporation of the more volatile solvent. The resulting crystals were characterized (Supplementary Tables 1 and 2, and Supplementary Figs 1–5) by single-crystal X-ray diffraction, allowing us to identify a group of isostructural compounds 1–8 displaying very different crystal morphologies (Fig. 1). Whereas the symmetrically substituted imidazoles 2, 3 and 5 formed needle-like crystals, the symmetrically chlorinated imidazoles 1 and 4, as well as the unsymmetrically substituted compounds 6, 7, and 8 behaved quite differently. Remarkably, the crystals of these compounds exhibited substantial natural distortions, sometimes appearing as spirals making multiple full turns. Both experimental and theoretical methods were employed in order to understand the observed unusual morphologies.

Figure 1: Macroscopic characterization of haloimidazole crystals. A library of trisubstituted haloimidazoles, 1–12, from which isostructural compounds 1–8 (optical microscopy images shown) were chosen for investigation of their mechanical and electrical properties. The scale bars are 500 μm. Full size image

The crystallographic data reveal that all compounds 1–8 crystallize in the orthorhombic Ama2 space group (Laue group mm2) with a short c-axis of ca. 4 Å, a situation which is characteristic of small halogenated aromatic compounds27,28. A thorough analysis of their crystal structures reveals highly anisotropic intermolecular interactions which, in previous reports21,29, have been identified as a distinctive feature of plastic crystals. The crystal packing (Fig. 2) is governed by three types of interactions of different strengths, namely N–H⋯N hydrogen bonds (2.84–2.97 Å) linking imidazole molecules in infinite chains extending in the a-axis direction, electrostatic interactions leading to the stacking of the chains one above the other along the c-axis to form sheets with the interchain distance between the imidazole rings in the range of 3.79–4.42 Å, and halogen–halogen interactions (Type II, see below) holding these sheets altogether. The anisotropy of the crystal packing forces translates itself to the crystal microstructure. Images obtained by scanning electron microscopy (SEM) reveal (Fig. 3) the layered structures of the crystals of 1 in the dimension perpendicular to the bc planes.

Figure 2: Crystal structure of 1–8. Intermolecular interactions present in the crystal structure of 1 which is used as a representation for all compounds 1–8. (Top) N–H⋯N hydrogen bonds linking imidazole molecules in infinite chains extending along the a-axis. (Bottom) Crystal packing along the a-axis showing both the position of electrostatic interactions as well as halogen bonds. A black dotted line represents the 2-fold screw axis (black triangle). α represents the angle between two consecutive molecules in the N–H⋯N chain. is a polarization vector. Full size image

Figure 3: Scanning electron microscopy. SEM images depicting the microstructure of distorted crystals of 1. The scale bars are 60 (a), 300 (Ba), 50 (Bb), 10 (Bc), 100 (c), 100 (d), 100 (e) and 40 μm (f). Full size image

Computational analysis of intermolecular interactions

Since we suspected that the ability of the trisubstituted haloimidazole crystals to become deformed during growth might arise from weak halogen–halogen contacts21,22,29, these interactions were investigated computationally. Identifying bond critical points in imidazoles 1, 2 and 4 by Atoms in Molecules (AIM) analysis30,31,32,33,34 suggests that only halogen–halogen contacts between the molecules related by a 2-fold screw axis (m 1 and m 4 , and m 4 and m 3 in Fig. 4a and Supplementary Fig. 6) are essential, and that the strength of the interaction increases with the growth in the atomic radius of the halogen (Supplementary Note 1 and Supplementary Table 3). The geometric parameters of these essential contacts, θ 1 and θ 2 angles (Supplementary Table 4), allow us to classify them as Type II halogen–halogen interactions35 (|θ 1 −θ 2 |≥30°) which, according to the IUPAC definition36, are true halogen bonds (Supplementary Note 2). To assess the role of these interactions in the structure, the ellipticity (ɛAIM) and the dissociation energies (DEG) of the bonds were compared with those in hexachlorobenzene C 6 Cl 6 (Fig. 4b and Supplementary Table 5), which is known29 to form plastic crystals that are easily deformable under the influence of external mechanical forces. According to this analysis, the fragment of C 6 Cl 6 solid-state structure shown in Fig. 4b has only two true halogen bonds, with the rest of halogen–halogen interactions being attributed to close packing. Hence, the weakness of these intermolecular interactions explains (Fig. 4c) the ease with which the stacks of C 6 Cl 6 molecules can glide past each other to alleviate strain37, resulting in the plastic deformation of the crystals.

Figure 4: Computational analysis of intermolecular interactions. Representative fragments of the solid-state structures of 4 (a) and hexachlorobenzene (b) showing bond paths (dashed lines) obtained by AIM analysis. Blue lines denote significant interactions whose existence was confirmed by the AIM method, along with their ellipticity, (a.u.), and dissociation energies, DEG (kcal mol−1), values. Green colour denotes imidazole rings, and red colour denotes benzene rings. (c) A schematic representation of the process responsible for the plastic deformation observed for C 6 Cl 6 crystals. Full size image

In contrast, the presence of one-dimensional infinite chains composed of imidazole molecules interconnected by hydrogen bonds prevents the gliding between the individual stacks, consistent with the absence of plasticity. In those cases where the halogen bonds are sufficiently weak, as in imidazoles possessing chlorine atoms in positions 4 and 5, the energetic cost of rotation of imidazole rings about the N–H⋯N bonds during crystal growth appears to be low, resulting in a change of α dihedral angle (Fig. 2) and a local loss of periodicity. This misalignment, which alternatively can be thought of as the dislocation along the 2-fold screw axis (Fig. 2), induces a slight curvature of the halogen-layered sheets, leading to crystal curving on the macroscopic scale. Similar arguments can be used to rationalize the curved crystal morphology observed in the case of 2,4-dibromo-5-methylimidazole (8), where the density of halogen bonds holding the sheets altogether is lower on account of the presence of the 5-Me substituent, even despite the stronger Br⋯Br bonds. Although other experimental factors, such as temperature and rate of crystallization are known to influence the density of crystalline defects, and are also likely to affect the crystal curvature, they were not investigated.

Molecular mobility in the solid state

While the formation of curved crystals appears to indicate the ease with which the haloimidazole molecules can be displaced during the crystal growth, it was also of interest to find out whether the molecular mobility is retained in the solid state. Hence, we performed electric permittivity measurements on a few selected (1, 2 and 3) 4,5-dihalo-2-methylimidazoles. Since the molecules possess permanent dipole moments, the dynamic processes in the crystals can be expected to reveal themselves under the influence of an alternating electric field, provided sufficient space is available in the crystal lattice. Indeed, relaxation processes were observed (Fig. 5a–c) in the frequency range between 200 Hz and 2 MHz for all three compounds under investigation, as suggested by dispersion and absorption on ɛ′(T) and ɛ′′(T) curves, respectively. The processes are well described by the Cole–Cole or Havriliak–Negami equations38 (Supplementary Tables 6 and 7), and the parameters derived from these equations allowed us to estimate the activation energies E a , which were found (Supplementary Figs 7–9) to be in the 2.5–53 kcal mol−1 range. A plausible rationale for the observed relaxation behaviour in the solid state is that certain molecular motions are not fully restrained by the immediate surroundings (Fig. 5d and Supplementary Note 3) of the haloimidazole molecules. The measurements were performed on pelleted samples containing large numbers of randomly oriented crystals. The calculated activation energies show no simple correlation with the expected strengths of the halogen bonds. Rather, the observed dielectric response should be used as a qualitative proof for the existence of substantial molecular mobility in the crystals. Thus, it appears that, while the curved crystal shape is primarily determined by the strength of the halogen bonds, the dynamic processes in the crystal are independent of their morphology, and were observed in both curved (1) and regular (2 and 3) crystals. This realization leads us to the conclusion that the possible electrical properties (see below) arising from the non-centrosymmetric crystal structure of these haloimidazole systems should persist regardless of the morphological effects that dictate the crystal shape.

Figure 5: Molecular mobility in the solid state. (a–c) Temperature dependence of the real, ɛ′(T), and imaginary, ɛ′′(T), parts of the complex electric permittivity measured for 1, 2 and 3, respectively. The colour gradient depicts the change in frequency from the lowest (blue) to the highest (red). (d) The closest neighbours to a molecule of 3 in the crystal lattice and the comparison of its molecular structure at 100 and 250 K. Intermolecular interactions are marked with dashed lines. Due to the presence of a mirror plane, protons of NH and CH 3 groups are disordered between two positions with 0.5 site occupancy factors. Full size image

Flexible mixed crystals

The pursuit of more dynamic morphological properties led us to explore mixed crystal systems. The halogen bonding influence on crystal shape, as well as the molecular mobility of haloimidazoles in the solid state, appeared to us to be convenient handles for tuning the morphology and mechanical properties of the crystals. We proposed that the halogen bonded network of trihaloimidazoles 4–7 could be disturbed in a controlled manner with the Me groups of 4,5-dihalo-2-methylimidazoles 1 and 2 through co-crystallization (Fig. 6a and Supplementary Table 8), preventing crystal distortion during growth. Indeed, with some tuning of the component ratio, co-crystallization resulted in the formation of 1–4 cm long straight needles (Fig. 6b), even in those cases where individual compounds (1, 4, and 7) gave curved crystals. According to single-crystal X-ray diffraction (Fig. 6c, Supplementary Figs 10 and 11, and Supplementary Table 9), the samples prepared by co-crystallization are not true co-crystals, but rather are mixed crystals (solid solutions) maintaining the ratio of components used for crystallization. As an additional proof of the structural composition of the mixed crystals (1·5, 1·6, 1·7, 2·5, 2·6, 2·7), and the consistency of the imidazole ratio throughout the crystallization batch, we performed a series of HPLC experiments (Supplementary Fig. 12, Supplementary Tables 10–15) with five randomly selected crystals from each batch. Perhaps the most significant attribute of these mixed crystals is the fact that aside from their different morphologies, they were also found to be substantially more flexible than the crystals of pure imidazoles (Fig. 6b, Supplementary Videos S1–S3, and Supplementary Fig. 13). Thus, when taken out of the crystallization dish using a toothpick, and pressed against a glass slide, the crystals can be bent many times without breaking, provided that the applied force does not exceed a certain limit. The elastic properties are most visible to the naked eye if the crystal thickness does not exceed 50 μm, and under optimum circumstances the opposite ends of the elastic needle can be forced to touch without breaking the crystals. The solid solutions were analysed with a nanoindentation technique, and determined to be gel-like from their measured hardness, supporting the flexibility observations (Supplementary Table 16). To assess the extent of the structural changes occurring in elastic crystals, we performed an X-ray diffraction study of a crystal that had been exposed to multiple bending/relaxation cycles. Since no elongation of X-ray diffraction peaks was observed, and the peaks could be indexed to the unit cell identical to that of the crystal before bending, it can be assumed that the molecules regain their original positions in the crystal lattice upon withdrawal of the applied bending force.

Figure 6: Flexibility of haloimidazole mixed crystals. (a) The pattern used for preparing a library of haloimidazole solid solutions. (b) Crystalline needles of a solid solution grown from a Me 2 CO/H 2 O mixture and their elastic properties. (c) Asymmetric parts of the mixed crystals unit cell marked with solid lines and symmetrical equivalents marked with dotted lines. Stoichiometric ratios in which components were mixed are presented in parentheses. Occupancy factors of disordered atoms are also given. Thermal ellipsoids are shown at 50% probability. (d) SEM images of flexible solid solution crystals and (e) the mechanism of a crystal deformation. X⋯X contacts are not shown for the sake of clarity. The scale bar in d is 100 μm. Full size image

On the basis of crystal indexing data and SEM imaging (Fig. 6d), we were able to propose a mechanism for the observed crystal flexibility. Attaching bent elastic crystals to carbon tape used as the SEM substrate, followed by fracturing the mechanically strained crystals, allowed us to acquire SEM images clearly demonstrating the exposed layers in the crystal (Supplementary Fig. 14) corresponding to the N–H⋯N chains expanding in the a-axis direction. Thus, it seems likely that it is the facile slippage of the imidazole chains past each other in the ab plane—distorting electrostatic interactions between imidazole rings in the c-axis direction—that confers flexibility upon the mixed crystals (Fig. 6e). The ability of the crystals to deform elastically in response to the bending force appears to be a function of the X⋯X halogen bonds wherein the potential wells seems to be wide enough to allow the bonds become strained/relaxed without being broken. When the external force is removed, the bonds regain their original position, causing the crystal to bounce back and adopt its original shape.

Piezoelectric and ferroelectric properties

Initial electromechanical experiments (Fig. 7) for determining the piezoelectric nature of the materials were carried out using Piezoresponse Force Microscopy (PFM) as the method of choice to characterize the electromechanical behaviour of these systems while simultaneously defining the topographical orientation of the substrate. The oscillation of the conductive cantilever in contact with a piezoelectric system is captured by both the amplitude and the phase of the collective material and the cantilever system. While the amplitude allows us to examine the magnitude of the piezoelectric response, the phase gives us information on the sequence of the mechanical oscillation that is related to the orientation of the polarization, allowing us to identify domain structures. More specifically, the piezoelectric coefficient, d, is related linearly39 to the spontaneous polarization, P s , permittivity, ɛ, electrostrictive coefficient, Q, by equation (1)

Figure 7: Piezoelectric properties and polarization domain structure of 2. Piezoresponse Force Microscopy (PFM) images (a–j) and schematic representation of the domain structure (k): (a) 3D image of the topography in b with the colourmap of the long axis lateral phase (d) demonstrating the one-to-one correspondence, and the molecular arrangement in the crystallographic ac plane. (c) Lateral amplitude of the long axis of the crystal. (d) Lateral phase of the long axis response. (e) Topography image of the large crystal of 2. (f) Lateral amplitude of the long axis of the crystal. (g) Lateral phase of the long axis response. (h) Topography image of the same crystalline needle. Vertical amplitude (i) and vertical phase (j) response of the crystal. (k) 3D schematic representation of the domain structure in the crystal imaged by PFM. The scale bars in b–d are 470 nm and 1 μm in e–j. Full size image

As ferroelectricity is defined by the switchable polarization under the influence of an external electric field, PFM hysteresis loop measurement is a tool that could probe the ferroelectricity if all the potential artefacts are taken care of. Since the cantilever has only two degrees of freedom—vertical bending and lateral torsion—with which to probe the piezoelectric motion of the sample, physical alignment of either the long or short in-plane axes of the crystalline needle with the torsion of the cantilever, was performed by rotating the sample through 90 degrees in order to obtain the alternate axis.

Since the crystal face indexing of 1–8 and solid solutions of these molecules differs in regards to the position of the crystallographic a and b axes (Supplementary Figs 5 and 11), we investigated the electromechanical properties of two types of crystals: one with the widest (010) face (crystals of 2) and the other with the widest (100) face (mixed crystals 2·7 and crystals of 8). Figure 7a shows the three-dimensional (3D) topography image of the analysed crystal of 2 (Fig. 7b) along with crystallographic directions obtained from the X-ray crystal face indexing. As can be observed, there is a strong amplitude response along the long axis of the crystal (Fig. 7c) and a uniform lateral phase (Fig. 7d). The piezoelectric response along the short axis (Supplementary Fig. 15) is effectively zero, in contrast to the in-plane long axis which is aligned with the primary crystallographic polar axis (c-axis in Ama2 space group). By ramping the applied drive amplitude and monitoring the response of the material, the piezoelectric properties were probed (Supplementary Fig. 16) quantitatively. A linear piezoelectric response is obtained predominantly along the long axis, with a slight piezoelectric response along the vertical dimension as well. Accounting for the background signal, calibrating the vertical deflection signal, and estimating the lateral deflection sensitivity (as described in the Supplementary Note 4, Supplementary Figs 17–20 and Supplementary Table 17), the vertical piezoelectric and long axis lateral effective piezoelectric coefficients for 2 were roughly estimated to be 0.12 and 2.6 pm V−1, respectively; however, these values may be underestimated as a result of unavoidable friction and slip between the cantilever and the sample40,41. When larger crystals of 2 were analysed, we started to see polarization domain structures with opposite directions as shown in Fig. 7e–k. Both out-of-plane and in-plane piezoresponse, however, did not show any polarization switching characteristics, indicative of piezoelectricity without ferroelectricity or ferroelectric polarization pinned by charged defects.

Interestingly, this situation changed when the crystals with the crystallographic a-axis perpendicular to the widest face were probed. The molecular arrangement along the a direction is presented in Fig. 2 (bottom). For mixed crystals of 2·7, we were able to switch the lateral piezoresponse by applying a vertical field, which implies polarization switching by external electric field (Fig. 8a–g). This strongly suggests that sample 2·7 possesses ferroelectric properties along the polar axis (c-axis) of the crystal. Figure 8f,g and Supplementary Fig. 21 show the vertical and lateral piezoresponse hysteresis loops measured using both pulse and continuous modes (or ‘on’ and ‘off’ modes), respectively42. The cantilever–sample interaction is strong (Supplementary Fig. 21), even though we used stiff cantilevers with high aspect ratio tip, probably due to the large voltage that was applied in an attempt to switch the polarization. In such cases, hysteresis loops obtained by pulse dc mode provide a clearer picture for identifying switchable polarization. Figure 8f,g presents such loops and shows that only the lateral piezoresponse can be switched from one direction to the other upon application of the external electric field, whereas the vertical piezoresponse cannot be switched within the voltage range of 200 V.

Figure 8: Polarization domain and piezoresponse hysteresis loops of 2·7. Piezoresponse Force Microscopy (PFM) images (a–d) and schematic representation of the domain structure (e): (a) Vertical amplitude and (b) phase of the crystal. (c) Lateral amplitude and (d) phase of the long axis response of the crystal. (e) 3D schematic representation of the domain structure in the crystal imaged by PFM. (f) Lateral amplitude and phase and (g) vertical amplitude and phase hysteresis loops obtained by a pulse dc mode. The scale bars in a–d are 10 μm. Full size image

Both vertical and lateral PFM were used to confirm the presence of the ferroelectric and piezoelectric properties in single-component crystals of 8, which exhibit the same axes orientation as 2·7. The crystals of 8 exhibited an even weaker vertical piezoresponse than sample 2·7, indicating greater alignment of the polarization along the long axis of the crystal. As shown in Fig. 9a,b, the lateral PFM images showed a similar in-plane polarization domain structure to sample 2. In addition, the piezoresponse hysteresis loop measurement indicated switchable in-plane polarization (Fig. 9c,d) by external electric field in 8, similar to sample 2·7, as well as prototypical polymer ferroelectrics19. Although the mobility of molecules about the N–H⋯N hydrogen bonds—that is postulated in this work as an explanation for both the natural distortion of crystals and the observed relaxation processes—might also explain the ease of the lateral piezoresponse switching when an external field is applied along N–H⋯N chains, the precise molecular mechanism of the switching still needs to be evaluated in greater detail.