Main

Crystallinity, a property of hard matter, underpins a wide variety of existing modern technologies, which include semiconductors and lasers1,2,3,4. The regular arrangement of molecules in crystal lattices is required for new high-strength industrial components and the development of emerging gas-adsorption and sequestration technologies5,6,7,8. Crystalline materials, however, are commonly hard and brittle, and when they are struck or bent they typically crack, shatter or deform irreversibly1,9,10,11,12. Such mechanical responses limit the use of these materials in practical applications, particularly in flexible electronics and optical devices2. Crystals that could be reversibly and repeatedly bent—characteristics normally associated with soft matter—are extremely attractive for use in myriad engineering applications that require materials in which properties can be tuned through external stimuli5,13,14,15,16.

Recently, there have been several reports of organic molecular crystals that exhibit plastic (irreversible) bending1,9,10,11,12. Here we describe single crystals that display significant elastic flexibility. Acicular crystals of bis(acetylacetonato)copper(II) ([Cu(acac)2]) (Fig. 1a), a classic coordination compound17, are so flexible they can be repeatedly and reversibly twisted and bent without losing crystallinity (Supplementary Movie 1). They can even be tied into a knot (Fig. 1b). Through synchrotron X-ray measurements, we have mapped the changes in crystal structure that occur when these crystals are bent and determined the mechanism that allows elastic flexibility with atomic resolution.

Figure 1: Crystal structure of [Cu(acac)2].
figure 1

a, Chemical structure of [Cu(acac)2]. b, A [Cu(acac)2] crystal tied (reversibly) in an overhand knot. c, The crystal structure of unbent [Cu(acac)2] viewed along the [010] (top right) and [] (bottom right) directions as determined by face indexing.

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Results and discussion

The crystal structure of [Cu(acac)2] (Fig. 1c) was first reported in 196918 and is isomorphous (monoclinic, P21/n) between 100–298 K (refs 19 –23). The [Cu(acac)2] molecules are planar and stack closely together along the crystallographic b axis. The mean planes of the molecules within each stack are exactly parallel and inclined with a dihedral angle of 48.7° from the (010) plane. This supramolecular stacking is facilitated by π–π interactions of delocalized electronic systems24,25 and by relatively strong Cu–π interactions26. The dominant supramolecular connectivity (π–π and Cu–π) is one-dimensional with only weak dispersive interactions that propagate in other directions. Face indexing confirmed the relationship between the crystal packing and the crystal morphology. The crystal faces coincide with the crystallographic (101) and () planes, as shown in Fig. 1c. The longest metric dimension of the crystals coincides with the crystallographic b axis (that is, [010]). These crystals can be repeatedly bent along the [010] direction and the (101) and () faces (which are not equivalent under the symmetry of the monoclinic space group P21/n). Removal of the force bending the crystals results in the crystals quickly returning to their original shape with no signs of breaking or cracking (Supplementary Movie 1; Fig. 2). Single-crystal X-ray diffraction experiments both before and after bending showed no loss of crystallinity (Supplementary Table 7). When bent, however, Bragg peaks in the diffraction pattern were broadened (Fig. 3a), which indicates the loss of long-range order because of differences in the molecular separations induced by bending.

Figure 2: Mechanical properties of single crystals of [Cu(acac)2].
figure 2

a, Nanoindentation tests performed on the () and (101) faces of [Cu(acac)2] crystals show anisotropic mechanical properties (top) and a picture of a crystal with the three imprints from the indenter after measurement (bottom). b, Tensile stress–strain curve of [Cu(acac)2] (top) and a picture of a crystal during a tensile test (bottom). c, Flexural stress–strain curve of [Cu(acac)2] (top) and a picture of a crystal in a three-point bending test (bottom). The reversibility of the elastic region was proved by bending and unbending a crystal twice in the elastic region before continuing the test until plastic deformation commenced.

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Figure 3: Structure changes in [Cu(acac)2] crystals during flexure.
figure 3

a, A crystal of [Cu(acac)2] bent into a loop and diffraction patterns obtained with a wide (100 μm) beam from both a straight part of the crystal and a bent part of the crystal. The Bragg peaks from the bent part are significantly broadened. b, A bent crystal as mounted at the Australian Synchrotron MX2 beamline and a view of the structural deformation on the elongated (left) and compressed (right) areas of the crystal. Arrows indicate the dimension changes of the crystal in the [010] (orange), [101] (green) and [01] (red) directions. c, Deformation (ε) along the natural crystal directions and volume variation (ΔV/V) from the outside (left) to the inside (right) of a bent crystal determined with a 7.5 μm beam.

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Mechanical characterization

The flexibility of the crystals was characterized with a suite of mechanical techniques. The surface hardness and elastic moduli of the [Cu(acac)2] crystals were measured using nanoindentation (Fig. 2a). The hardness of the (101) face was found to be in the range 200–240 MPa with an elastic modulus between 4.8 and 6.9 GPa. The hardness of the () face was 380–400 MPa and the elastic modulus 11.3–13.8 GPa, significantly larger than that of the (101) face. These values are typical of molecular materials and metal organic frameworks27.

We then measured the tensile elasticity of the crystals by stretching four individual single crystals (Fig. 2b). The crystals could be stretched up to 4.4% of their length before breaking. The slopes of the stress–strain curves indicate an elastic modulus between 210 and 550 MPa and the tensile strength (point of fracture) was determined to be 8.0–22 MPa. This tensile strength is slightly less than that for polyethylene (20–45 MPa) (ref. 8).

The crystals were then subjected to flexural contortion (that is, bending) via three-point bend tests (Fig. 2c). To demonstrate the elastic flexibility of the material, a crystal was bent twice with a stress of 15 MPa (which gave an elastic modulus of 8 GPa) and then the strain released (Fig. 2c, bottom). The crystal was then bent a third time and the strain was increased until plastic deformation commenced (60 MPa). In total, six other crystals were also subjected to flexural stress–strain measurements and the results were similar (Supplementary Section 4). Once again, the clear (initial) linear relationship between stress and strain indicates an elastic flexibility with a flexure modulus in the range 2–8 GPa. This is comparable to the elasticity observed in soft materials, such as nylon (2–5 GPa) (ref. 8).

Microfocus X-ray diffraction

To determine the structural mechanism that permits this remarkable flexibility, microfocus synchrotron X-ray diffraction was employed. A crystal was bent into a loop, mounted on the diffractometer and oriented such that the trajectory of the X-ray beam was perpendicular to the plane of the loop of the crystal (Fig. 3b). An incremental line map was recorded across the crystals from the outside to the inside of the loop at ∼5 µm intervals. At each interval, 20 diffraction images were recorded to allow the determination of the crystal structure at that position in the crystal. The data-acquisition method is illustrated in Supplementary Movie 2, which shows the trajectory of the line map and the median diffraction image collected at each interval. No phase change was observed throughout the linear map. These mapping experiments demonstrate that the [010] axis of the crystal is significantly elongated (1.5%) on the outside of the bent crystal and significantly compressed on the inside of the bent crystal (1.9%). The opposite relationship was observed for the crystal dimensions orthogonal to the length of the crystal. The [101] direction becomes 1.3% shorter on the outside of the loop and expands on the inside section of the loop (1.7%). Similarly, although with much less magnitude, there is contraction in the [] direction (0.3% shorter) on the outside of the loop and expansion (up to 0.4% longer) on the inside of the loop. Overall, the total variations of length from the inside to the outside of the loop in these different directions are 3.4% [010], 3.0% [101] and 0.7% []. The deformation is not isotropic. Most of the crystal deformation occurs along the [010] and [101] directions (that is, in the () plane), and deformation occurs to a smaller extent along []. This result is consistent with the nanoindentation measurements by which the (101) face was confirmed to be mechanically softer and more elastic than the () face. Notably, there is almost no change to the overall volume of the unit cell on the inside of the loop compared to the outside (<0.2%). The density of crystal packing also, therefore, remains essentially unchanged by bending (Fig. 3c).

Mechanism of elastic flexure

Changes in position of the molecules within the crystal lattice with bending were then examined. Although the individual molecules of [Cu(acac)2] were found to be identical throughout the sample, the refined crystal structures at each position in the bent crystal showed significant differences in the arrangement of the molecules with respect to each other. The mean planes of the molecules are approximately orthogonal to the () plane and the molecules rotate towards planarity with the (010) face as a function of compression (inside the loop); rotation in the opposite direction occurs with elongation (outside the loop). Importantly though, the distances between the planar [Cu(acac)2] molecules do not change (Supplementary Figs 22–24); rather, the molecules rotate in response to the mechanical stress. This rotation of the molecules facilitates the compression in the [010] direction as well as a simultaneous expansion in the [101] and [] directions. We compiled the structures from outside the loop and from inside the loop into an animation (Supplementary Movie 2) that demonstrates the change in orientation of the molecules that occurs from outside the loop to inside it, along with the changes to the unit-cell shape to provide a visual representation of the supramolecular mechanism that facilitates elastic bending in these crystals. During elastic bending and/or stretching, the local molecular rearrangements required are very small, but when added together for the vast numbers of molecules in a single crystal they facilitate significant levels of elastic contortion.

The ability of crystals to bend flexibly has wide-ranging implications. For example, the loss of translational symmetry means a crystal that is bent (or twisted) is no longer strictly a crystal in the sense that it has lost its long-range order15,28. Instead, the ‘unit cells’ of the bent crystal are related by movement along an arc rather than by regular translation. Furthermore, the changes in orientation of molecules within different parts of the bent crystal also must influence the physical properties of the crystal. The broadening of Bragg peaks observed for bent crystals of [Cu(acac)2] (Fig. 3a) illustrates this point. In this case, bending the crystal results in a loss of centrosymmetry on the macroscale, but it is approximately maintained locally, which may enable temporary and reversible second-order nonlinear optical properties. Similarly, the application of mechanical force to a magnetic material could lead to spin-state switching and the associated magnetic and optical changes.

Recently, it has been postulated that for a molecular crystal to bend elastically, two criteria must be met. First, the molecules must be connected isotropically by relatively ‘weak and dispersive’ intermolecular interactions and, second, that there must be corrugated crystal packing in which the molecules are interlocked to prevent slippage and consequential plastic deformation29,30,31. Our results show that this is not correct. The intermolecular interactions in [Cu(acac)2] crystals are anisotropic with relatively strong π stacking in one dimension and only dispersive interactions in the others. Furthermore, the molecules are not interlocked. Instead, our results indicate more generally that for elastic bending to occur the molecules must be able to reorganize reversibily to allow compression of the crystal along the interior of the arc with subsequent expansion in orthogonal directions (and vice versa along the exterior of the arc). In [Cu(acac)2], the relatively large area of π-electron density allows sufficient reorientation (rotation) of the molecules without breaking the overall continuity of the crystal packing. In contrast, in molecular crystals that display plastic deformation, it is more energetically favourable for certain planes of molecules in the crystal to slip past each other when subjected to strain than it is for the distances between the planes to expand or contract11,12,29,30,31. In [Cu(acac)2], we observe no evidence of plastic deformation below 1% strain, but infer that a similar mechanism of slippage is responsible for the plastic deformation that occurs at higher strain values.

The simple mechanism of flexing in [Cu(acac)2] suggests that elastic flexibility will be evident in a much wider array of molecular crystalline materials than previously anticipated. Accordingly, we postulated that it may be possible to control further the mechanical properties of crystals by tuning the strength and type of supramolecular interactions present between molecular materials of this type. Indeed, preliminary investigations into subtly modified crystals (that is, those that are chemically similar to [Cu(acac)2]), such as bis(3-bromo-2,4-pentanedione)copper(II), bis(3-chloro-2,4-pentanedione)copper(II), bis(benzoylacetonato)copper(II), bis(acetylacetonato)palladium(II) and bis(3-chloro-2,4-pentanedione)palladium(II) also reveal remarkable elastic flexibility (Supplementary Figs 25–29).

Conclusion

We have reported an elastically flexible crystal of a coordination compound, and determined the mechanism of flexibility with atomic precision. In addition to the fundamental interest that surrounds the crystalline state, stimuli-responsive materials, such as this one, are enticing as they could enable the design of a range of new hybrid materials that fall between the boundaries of what have typically been regarded as the limitations of hard and soft matter.

Methods

Synthesis of bis(acetylacetonato)copper(II)

The complex was prepared from acetylacetone and copper(II) nitrate hemi(pentahydrate) following the method of Holtzclaw and Collman32. Blue acicular crystals were grown by dissolving the complex in chloroform and allowing the solvent to evaporate slowly. Elemental analysis, found: C, 45.80; H, 5.39%; calculated for C10H14O4Cu: C, 45.88; H, 5.39%.

Nanoindentation

Nanoindentation measurements were performed using a Hysitron TI 950 TriboIndenter system33 with a Berkovich indenter (three-sided pyramidal indenter with a tip radius of approximately 100 nm, and 142.3° total included angles). Indentation was performed under the load-control setting with a 10 s loading period and a 10 s unloading period. The flat areas on a crystal's surface suitable for indentation were identified by the on-board optical microscope. To determine truly representative values for the elastic modulus and hardness, the indentation was repeated on a number of sites on a single crystal, and several crystals were tested in the same way for each face. Further details are given in Supplementary Information.

Tensile stress

Tensile stress was measured using a Tytron 250 Microforce Testing System with a displacement resolution of 0.1 µm and a load resolution of 1 µN. The tests were conducted in the displacement controlled mode at a rate of 5 mm min–1. The samples were fixed with the 250 N mechanical clamp grip and double-sided tape was placed between the grips and the sample to minimize slippage during testing. During the mechanical testing, load (F) and displacement (d) were recorded in real time. Further details are given in Supplementary Information.

Three-point bend tests

Three-point bend tests were conducted at room temperature using an Instron Model 5543 universal testing machine with a capacity of a 5 N load cell and a three-point bending apparatus with a 15 mm span. A crosshead speed of 2 mm min–1 was adopted. The individual and average results for six [Cu(acac)2] crystals were determined. Further details are given in Supplementary Information.

Synchrotron X-ray studies

Synchrotron crystal structures were recorded at the Australian Synchrotron MX beamlines. All the measurements were performed at 100(2) K and with the wavelength λ = 0.7108 Å. A full data collection was performed at the MX1 beamline with a beam cross-section (full-width at half-maximum (FWHM)) of 120 by 120 µm. Mapping studies were performed at the MX2 beamline using a microcollimator that produced a beam cross-section of 7.5 by 11.25 µm (FWHM). Data acquisition was performed using Blu-Ice (ref. 34). Data integration and reduction was performed using the XDS package35. Using the Olex2 graphical interface36, the structures were solved with ShelXT (ref. 37) and refined with ShelXL (ref. 38).

Data availability

The data supporting the findings of this study are available within the article and its Supplementary Information files, or from the corresponding authors on reasonable request. The X-ray crystal structure data have been deposited with the Cambridge Crystallographic Data Centre (CCDC) and are available free of charge from https://www.ccdc.cam.ac.uk/structures/, under the reference numbers CCDC 1529008 to 1529042. CCDC 1529008 contains the crystal structure of unbent [Cu(acac)2] at 100(2) K. CCDC 1529009–1529024 contain the results of mapping studies on crystal 1 (structures a–p). CCDC1529025–1529042 contain the results of the mapping studies on crystal 2 (structures a–r). Full experimental details and crystallographic analysis are given in Supplementary Information.

Additional information

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