Identifying and characterising flexible crystals

Abstract

Mechanically flexible single crystals are emerging as a useful class of materials due to their unique combination of crystallinity and molecular-scale responses to applied mechanical stress. In this tutorial review, we suggest best practice approaches to the identification and characterisation of these fascinating materials. These approaches can be applied in crystals that show either plastic or elastic flexibility, or a combination of the two. In particular, we highlight that the molecular mechanism of flexibility that occurs when a crystal is subject to mechanical stress varies from system to system and so it is impossible to infer the nature of movement that will occur merely from crystal packing analysis. Understanding the structural changes that occur when a crystal is subject to mechanical stress is essential for developing their utility in a wide range of applications, particularly in optoelectronics, waveguides and piezoelectrics.

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Atiqur Rahman

Atiqur Rahman received his BSc (Hons) in Chemistry from Kirori Mal College, University of Delhi and his MSc in Chemistry from Indian Institute of Technology Delhi. He is currently pursuing a joint PhD at IIT Delhi and The University of Queensland under the supervision of Professor Sajesh P. Thomas and Professor Jack K. Clegg. His doctoral research focuses on the structural origins of mechanical flexibility and piezoelectricity in molecular crystals, with an emphasis on structural perturbations induced by bending and high-pressure conditions, employing synchrotron-based micro-focused X-ray diffraction and high-pressure crystallographic techniques.

John C. McMurtrie

Professor John C. McMurtrie completed his BSc (Hons) at Macquarie University before moving to The University of New South Wales for his doctoral. He then completed a postdoctoral appointment at the University of Sydney (2003–2004). John was appointed Lecturer in Inorganic Chemistry at Queensland University of Technology in 2004 where he remains, now as a Professor of Inorganic Chemistry.

Sajesh P. Thomas

Sajesh P. Thomas earned his MSc in Chemistry from Mahatma Gandhi University, Kottayam and his Bachelor's degree from Kasaragod Government College, Kerala. He completed his PhD in 2014 from the Indian Institute of Science, Bangalore, under the guidance of Prof. T. N. Guru Row, focusing on charge density and crystal engineering studies of pharmaceutical solids. Following his doctorate, he conducted postdoctoral research with Prof. Mark A. Spackman at the University of Western Australia, Perth, and later held a Marie-Curie fellowship with Prof. Bo B. Iversen at Aarhus University, Denmark. He is currently an Associate Professor in the Department of Chemistry at the Indian Institute of Technology Delhi, where he leads Materials and Quantum Crystallography Lab (MQCL). His research interests include quantum crystallography and crystal engineering of pharmaceutical solids and soft piezoelectric materials.

Jack K. Clegg

Professor Jack K. Clegg studied Chemistry, History and German graduating with a Bachelor of Liberal Studies (Honours) and a University Medal from the University of Sydney. He went on to complete a PhD in Chemistry (2008) and a Bachelor of Laws (2009) from the same institution graduating with the Convocation Medal. After completing his studies he won a Marie Curie Fellowship to conduct research at the University of Cambridge. Jack returned to Australia to join The University of Queensland in 2012. In 2018 Jack was awarded the Malcolm McIntosh Prize for Physical Scientist of the Year.

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Key learning points

1. Molecular crystals undergo two types of mechanical deformation—elastic (reversible) and plastic (irreversible)—each led by different structural features and intermolecular interactions.

2. Elastic flexibility is often driven by anisotropic interaction topologies and reversible molecular reorientations, whereas plasticity is facilitated by low-energy slip systems (often slip planes).

3. μ-XRD and μ-Raman mapping provide insight into structural changes and local internal stress distribution across the elastically bent crystals.

4. Mechanical deformation affects a range of material properties, including fluorescence, conductivity, and thermal behaviour, highlighting the multifunctionality of flexible crystals.

5. Classical models like Euler–Bernoulli theory are limited due to anisotropic and inhomogeneous deformations in crystals.

6. Flexible molecular crystals are promising for next-gen technologies such as piezoelectric actuators and reconfigurable waveguides.

Introduction

Molecular crystals have applications in optoelectronics,¹ sensors,² waveguides,^3,4 wearable devices⁵ and bioimplantable devices. Traditionally, due to the prevalence of crystalline minerals in our environment, the common perception of all crystals is that they are hard, brittle materials which crack or break in response to mechanical stress. This perception has curtailed the applications of crystals in many areas where some degree of flexibility is desired. Over the last decade, observations that molecular crystals can display notable elastic and plastic flexibility,^6–15 or other emerging properties such as thermosalience^16–18 or self-healing,^19–25 is leading to the use of these crystals in flexible electronics, flexible field effect transistors, and wearable devices.

The molecular scale structural changes that occur upon deformation in turn affect various physical properties, such as melting points,²⁶ electronic conductivity²⁷ and magnetic ordering temperatures.²⁸ Additionally, variations in photophysical properties, including fluorescence emission and fluorescence lifetime,²⁹ have also been reported in deformed crystals, highlighting the potential of flexible crystals for future research and development.

This tutorial review aims to summarise the best-practice approaches to understand crystals with notable mechanical flexibility. The steps that need to be undertaken, consistent with the scientific method, include: 1) identifying that a crystal is flexible and qualitatively establishing the type(s) of flexibility it displays, 2) characterising the flexibility both in terms of quantifying the flexibility and establishing the molecular mechanisms that underpin it, and 3) using this knowledge to generate new understanding for the design of functional materials.

Identifying flexibility in crystals

Mechanical flexibility in numerous materials such as metals, wood and polymers has been employed for millennia and underpins many technologies that have supported the development of society as we know it today. In contrast, crystalline materials are generally thought of as brittle, leading to them being overlooked in many engineering applications despite their other attractive properties. Over the last twenty years, there has been an increasing number of flexible crystals discovered, including organic⁶ and metal–organic molecular crystals³⁰ and coordination polymers.³¹ In many early examples, the mechanical flexibility of the crystals was discovered serendipitously while mounting samples for single-crystal X-ray diffraction.³²

The flexible responses of materials can be divided into two broad categories: (i) materials (“beams” in an engineering context) which return to their original shape after mechanical deformation are termed “elastically flexible” (Fig. 1a), and (ii) beams which undergo irreversible (permanent) deformation are termed “plastically flexible”† (Fig. 1b). All crystals display some degree of elasticity with plastic deformation or breakage only occurring beyond the elastic limit. In some cases, crystals in which significant elasticity is observed before plasticity is observed (i.e. where the elastic limit is large enough and shape of the crystal is suitable) have been described as “elasto-plastic” crystals, which are thus a sub-class of plastically flexible crystals.

Fig. 1 (a) Elastically bent [Cu(acac)₂] crystal tied into a knot and (b) plastically bent 4-trifluoromethyl phenyl isothiocyanate crystal.

It is well established that elastically deformed (bent) beams (or crystals) contract on the inner arc of a bend and are elongated on the outer arc, generating both compressive and expansive strain in the material (and concomitant changes in unit cell) (Fig. 2a). Plastic deformation, instead, results from the slippage of planes throughout a beam, resulting in defects, but no net strain or change in unit cell dimensions within the material (Fig. 2b).^33,34 Indeed, micro-focused diffraction studies on elastically flexible crystals have revealed that the strain arising from deformation results in molecular reorientations and reorganisation to accommodate the lattice contraction and expansions without resulting in significant bond-length changes.^30,35–37 Similar studies in plastically flexible crystals confirm that no significant changes in unit-cell parameters occur.

Fig. 2 (a) Deformation in unit cell parameters in the elastically flexible bis(3,5-heptanedionato)copper(II) crystal demonstrates linear variation from the inner arc to the outer arc. (b) No systematic linear trend reported in the unit cell deformation percentage in the plastically bent crystal, highlighting increased crystal mosaicity and crystal defects.

The most straightforward way to qualitatively identify if a crystal is flexible is to simply perform a three-point bending test by using forceps (two-points) to hold a crystal while bending the crystal by applying force against the crystal from the opposite direction using a needle or probe (third-point) while observing it under a microscope. If the crystal can be bent without breaking and returns to its original shape, then it is qualitatively elastic; if the crystal bends and remains permanently so, it is qualitatively plastically flexible (although until the elastic limit is reached, it is elastic). It is also important to confirm that the object being bent is actually a single crystal and diffraction experiments should be used to confirm this before the crystal is deformed – the crystal should be face-indexed at the same time. It is generally helpful if the purity of the material in question has been established as impurities within crystals can effect mechanical behaviour.³⁸

It will be far easier to observe flexible responses in a sample if the crystals are acicular in habit because of the intrinsic relationship between strain and cross-sectional surface area (see discussion below); just because a crystal is block-shaped does not mean it does not have interesting mechanical properties, they will just be difficult to observe visually and alternate crystallisation methods may need to be trialled. Similarly, if crystals can only be prepared that are too small for manipulation with forceps, then more sophisticated methods will be required, for example, nanoindentation or atomic force microscopy.³⁹

Characterising elastic responses

Quantification of elasticity

The mechanical behaviour of a material under an applied force is characterised by Young's modulus (Y), defined as the ratio of stress (σ) to strain (ε). Here, stress is the force per unit area (σ = F/A) applied to the material, while strain represents the relative change in length (ε = Δl/l₀), indicating how much the material deforms under the applied force. A constant (linear) stress-to-strain ratio indicates elastic (reversible) deformation. The point at which the relationship ceases to be linear is termed the elastic limit, at which point the material will either undergo irreversible deformation (e.g., plastic deformation) or fracture (or both).
The relationship between stress and strain underscores the importance of the thickness of a crystal when subject to deformation. As strain is inversely related to the cross-sectional area of the sample, a thinner crystal can be deformed more than a thicker crystal of the same material under equivalent stress. It should be noted, however, that the above relationship is simplified by assuming isotropicity; in most molecular (anisotropic) crystals, the complete elastic tensors are required to understand the stress–strain relationship under an applied load (within the elastic limit). The elastic tensor is a 2nd order and fourth-rank tensor represented by a 6 × 6 matrix that describes the deformation of materials under applied stress (Fig. 3a). Determining elastic tensors experimentally^40,41 is challenging as it requires significantly large and well-defined crystal faces.⁴² The elastic tensor of a crystal can be readily calculated from the crystal structure using quantum periodic calculations.^{29,32,37,43–45} The tensor can be plotted to allow the visualisation of the stress–strain relationship in different crystallographic directions (Fig. 3b).⁴⁶ In addition, the anisotropy index can also be calculated from the tensor value for comparison to measured values described below.

Fig. 3 (a) Stiffness matrix for an anisotropic material represented by a 6 × 6 matrix and 21 independent coefficients. (b) 3D representation of Young's modulus from the elasticity tensor calculated for the elastically flexible acenaphthoquinone crystal.

Various experimental techniques can be used to quantify the behaviour of a crystal. These include three or four-point bending and tensile mechanical testing, which are commonly used in engineering,^47,48 nano-indentation⁴⁹ or atomic-force microscopy^50,51 (AFM). How each of these techniques can be employed on flexible crystals has recently been described.⁶ While mechanical testing gives additional information that cannot be obtained from either nanoindentation or AFM, sufficiently large crystals (several cm in length) are required. Nanoindentation or AFM can be employed on very small samples; on the other hand, it can also be used to investigate the properties of different faces of a crystal.

If these techniques are not readily available, it is possible to qualitatively estimate the strain in an elastically bent crystal using optical microscopy.^52,53 This measurement has exceptionally high uncertainty and is based on Euler–Bernoulli beam theory, which correlates the elastic strain in a bent beam with its thickness and radius of curvature. This approach employs several assumptions, and it relies on measurements of the thickness and curvature of a beam, which are inherently uncertain when optical microscopy is employed alone. The assumptions of Euler–Bernoulli beam theory include i) that the planar cross-sections normal to the bending axis remain planar, ii) that they remain normal to the neutral axis, and iii) that there is no change in the cross-sectional shape/size of the beam when bent. Recently, X-ray studies have shown that cross-sectional areas of crystals change significantly when bent even at low strains highlighting the complexities of using this technique for anisotropic materials.^30,35–37 Thus, strains measured in this way provide only a qualitative estimation and need to be verified by an alternate measurement; strains reported by using this technique should be considered sceptically, especially where no evidence of single crystallinity or elasticity is provided. If this approach is to be employed then significant care should be taken and reproducible tools such as FLεX, which employs computer vision tools to eliminate measurement errors should be used.⁵⁴

Three-point bending and tensile tests are used to calculate the strain and study the material's behaviour under applied load. A qualitative measurement of elastic strain can be obtained from the three-point bending test, which can estimate the elastic strain. Nanoindentation and atomic force microscopy are the two techniques that have been exploited to measure the elastic modulus, hardness, flexural strain, etc. However, these tests do not provide any details of compressive and expansive strain in the inner and outer arc of an elastically flexible crystal. At the atomic scale, μ-XRD mapping offers a detailed understanding of strain in terms of deformation in unit cell parameters from one edge of the bent crystal to another edge. However, this method necessitates a high-energy μ-focused X-ray beam (radius less than 10 μm) and a crystal of suitable size. Additionally, mounting an elastically bent crystal for mapping studies is relatively difficult. The accessible wedges of useful diffraction also limit data quality when studying structural perturbations.⁵⁵

The mechanisms of bending

When a crystal is bent, either elastically or plastically, changes occur on the molecular scale as a response to the strain. While plastic deformation arises from slippage between layers, different mechanisms can arise under elastic deformation. In molecular crystals, the magnitude of potential energy stored in the crystal under modest elastic strain is similarly modest (often ∼1 kJ mol⁻¹ or less)⁵⁶ – far less than the amount of energy released when a covalent bond is formed and thus significant changes of length or angle are more likely to occur in comparatively weak intramolecular (supramolecular) bonds rather than the stronger covalent interactions. Thus, molecular responses to elastic strain generally lead to some form of reversible movement between molecules with respect to each other on the molecular level rather than changes in bond lengths or angles, while irreversible movement occurs in plastic deformation. This molecular movement is referred to as the mechanism of bending. Determining the mechanism of bending is fundamental to generating understanding about the origin of flexibility in crystals and their potential applications. While there are several methods now available to investigate the mechanisms of bending, including spectroscopic and computational approaches, the gold standard remains X-ray diffraction.⁵⁷

Computational approaches

Early approaches to determine the mechanism of bending in crystals focused purely on comparative analysis of crystal packing to infer the effects that strain could have on the crystal structures of flexible crystals. This approach led to several hypotheses about requirements for particular features to be present in crystal packing arrangements for elastic flexibility to occur, including “corrugation”, “criss-cross”, “slip-stacked” or “interlocked” arrangements, to minimise plastic deformation. It is now clear, however, that particular crystal packing arrangements are not required.⁶ The nature, directionality, and relative strength of intermolecular interactions, instead are fundamentally important to the mechanism of bending. Energy framework analysis⁵⁸ is a very efficient way of identifying important intermolecular interactions in a crystal packing and their relative strengths, which underpins the resulting mechanisms.^32,56,59 This analysis does not give direct evidence of the mechanism of elastic bending. Similarly, efficient calculations can be used to identify potential slip planes if plastic deformation is observed, which can then be related to the mechanism.⁶⁰ For instance, in the elastically flexible crystal [Cu(acac)₂], energy framework analysis of the three dominant supramolecular dimers revealed significant anisotropy in the interaction energy topology, with distinct variations in interaction strengths along different crystallographic directions (Fig. 4a).⁵⁶ In plastically bending fumaronitrile crystals, the same approach identifies much weaker interactions that enable molecular slippage during deformation (Fig. 4b).³²

Fig. 4 Energy frameworks of (a) elastically flexible Cu(acac)₂ crystal, highlighting the magnitude of different intermolecular interactions, (b) plastically flexible fumaronitrile crystal.

More complicated calculations can be used to provide better insight into the mechanisms of bending. For example, periodic dispersion corrected density functional theory has been used to simulate the structural changes that might occur in the inner and outer arc of the bent crystals.⁶¹ These uniaxial pressures, both positive and negative, mimic the compressive and expansive strain, respectively, to approximate a molecular-scale understanding of mechanical flexibility (Fig. 5).²⁹ Structural changes, including unit cell length variation along the bending direction, molecular reorientation, and changes in intermolecular interactions such as π⋯π stacking, can be observed.⁶² These optimised geometries were then used to further investigate the variations in photophysical properties, such as band structure and HOMO–LUMO gaps, which correlated well with variations in fluorescence emission spectra and fluorescence lifetime measured at the bent crystal region of an elastically bent crystal.

Fig. 5 Structural changes upon elastic bending in the acenaphthoquinone crystal simulated using periodic quantum chemical calculations.

Spectroscopic approaches

Raman spectroscopy. Raman mapping is one of the tools that has been employed to understand changes in intermolecular interactions upon bending. The vibrational frequency shifts associated with the local internal stress developed in response to applied mechanical force can be studied by spectral mapping of the bent crystal region from one arc to another using a micro-focused laser. For example, μ-Raman spectra of plastically bendable hexachlorobenzene crystals at different positions throughout the deformed region showed no significant frequency shift in the unpolarised Raman spectra.⁶⁵ Similarly, plastic bending in a 1D coordination polymer and elasto-plastic bending in 2,4-dichloro-6-[(6-methylpyridin-2-ylimino)methyl]phenol crystals demonstrated no change in characteristic vibrational modes.^63,66 In these cases, the lack of any significant shift in vibrational modes indicates that the applied stress is accommodated via molecular slippage, a characteristic deformation mechanism of plastically flexible crystals. In a recent investigation, a blue shift in the inner arc and a red shift in the outer arc of the bend in characteristic vibrational modes (C=O stretching and C–C, C–O, C–H bending) were observed in elastically flexible dimethyl 5-(hexylcarbamoyl)isophthalate crystal (Fig. 6a).⁶⁴ The frequency shifts in the inner arc were understood using a steepening of the interatomic potential wells model, suggesting changes in the intermolecular interactions. These shifts were correlated with the shift observed under high pressure, allowing for an estimate of the local internal stress difference (∼2 GPa) experienced by the molecule between the inner arc and the outer arc (Fig. 6b). Although finite element analysis has been used to calculate stress distribution in bent crystals,⁶³ this study represents the first experimental approach combining μ-Raman mapping with high-pressure Raman to provide a direct estimate of the local internal stress developed due to bending.⁶⁴

Fig. 6 Vibrational frequency shifts in the C=O stretching modes observed under two conditions: (a) during crystal bending, collected via micro-Raman mapping, and (b) under hydrostatic compression, measured using high-pressure Raman spectroscopy.

Spatially resolved fluorescence studies

Photoluminescence properties are sensitive to the structural changes at the molecular and intermolecular scale, as they originate from electronic transitions in materials. These properties, such as shifts in emission wavelength,^67–69 intensity changes/quantum yield,^70,71 and lifetime,^29,51 vary with a subtle alteration in crystal packing. Confocal fluorescence microscopy allows spectral variation with nano-scale spatial resolution to be probed. The shifts in emission spectra and variation in fluorescence lifetime can thus give insight into the structural changes that occur upon bending (Fig. 7a and b), such as slipping of π–π stacks, H and J-aggregates, and variation in the extent of π–π overlap. Contrasting results, however, have been reported; one case reported a red shift in the inner arc,²⁹ while another showed blue shifts.^72,73 The contradictory trends in spectral shifts from one compound to another thus need to be correlated with additional experimental evidence. These shifts have been rationalised based on variation in π⋯π interaction distance, sliding of molecular planes between π⋯π interactions, and variation in such π⋯π interactions (Fig. 7c).

Fig. 7 Systematic variation in fluorescence emission spectra (a) and fluorescence lifetime (b), reported in the elastically flexible acenaphthoquinone crystal from the outer arc to the inner arc. (c) Hirshfeld surface analysis mapped on expanded geometry and compressed geometry simulated using periodic quantum chemical calculations, demonstrating variation in the strength of intermolecular interaction.

Single crystal diffraction

Although computational and spectroscopic studies provide some insight into the mechanisms of bending in molecular crystals, they do not provide a comprehensive understanding of the structural changes. Single crystal diffraction, on the other hand, can directly measure the changes in crystal structure that occur when a crystal is bent either plastically or elastically. To satisfactorily map these changes a micro-focused (synchrotron), beam is required, and a robust method to measure the data has to have been established.^30,55,74,75

μ-Focus diffraction studies on elastically bent crystals demonstrated a systematic contraction in unit cell parameters in the inner arc and expansion in the outer arc (Table 1), consistent with the theoretical expectations, which are accompanied by variations in intermolecular distances and changes in molecular orientations. The unit cell parameters show the most pronounced variations along the bending direction, whereas other directions display comparatively minor and often contrasting changes (see the indicatrix plot comparison in Fig. 8). A systematic study on several elastically bent derivatives of bis(2,4-pentanedionato)copper(II) reveals distinct structural changes facilitating mechanical flexibility in each case.³⁶

Table 1 μ-XRD mapping on flexible molecular crystals and respective structural changes (the arrows ↑ and ↓ represent the increase and decrease in the corresponding values of the geometrical parameters)

Compound name	Flexibility	Unit cell length along the bending direction		Mean plane distances		Mean plane angle
		Inner arc	Outer arc	Inner arc	Outer arc	Inner arc	Outer arc
Bis(2,4-pentanedionato)copper(II)	Elastic^36	↓	↑	No change		↓	↑
Bis(3,5-heptanedionato)copper(II)	Elastic^36	↓	↑	↓	↑	↓	↑
Bis(4,6-noneanedionato)copper(II)	Elastic^36	↓	↑	↓	↑	No change
cis-Aquabis(glycinato)copper(II)	Elastic^37	↓	↑	—	—	—	—
4-Trifluoromethyl phenyl isothiocyanate	Plastic^76	No significant change		—	—	—	—
2,4-Dichloro-6-[(6-methylpyridin-2-ylimino)methyl]phenol	Elasto-plastic^53	↓	↑	↓	↑	↓	↑
Cocrystal of caffeine, 4-chloro-3-nitrobenzoic acid, and methanol solvate	Elastic^35	↓	↑	↓	↑	↓	↑
Hexachlorobenzene	Plastic^65	No significant change		—	—	—	—
N-(5-Bromosalicylidene)-1-aminopyrene	Elastic^77	↓	↑	—	—	—	—
Cu-Triazolate	Plastic^78	No significant change		—	—	—	—

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Fig. 8 (a–c) Variation in the mechanism of bending in aliphatic derivatives of [Cu(acac)₂] crystals (from left to right: molecular structure, indicatrix plot, variation in interplanar distances and molecular orientations in the inner and outer arc, and bending mechanism facilitating elastic deformation).

With the variation in the side chain from methyl to propyl groups, the mechanism of elastic bending changes from molecular rotation to compression and expansion of the mean plane distance (π–π stacking distance). Crystals with an ethyl group in the side chain deform via both mechanisms, involving changes in the π–π stacking distance as well as molecular reorientation (Fig. 8). The results clearly demonstrate that there is no universal mechanism of bending. μ-XRD mapping of the elastically bent organic molecular crystal 2,4-dichloro-6-[(6-methylpyridin-2-ylimino)methyl]phenol⁵³ and a cocrystal of caffeine with 4-chloro-3-nitrobenzoic acid³⁵ have shown that molecular reorientation and variations in intermolecular distances are key factors supporting flexibility. To advance our understanding and develop a conclusive unified theory, exploring more examples of flexible crystals, such as systems that lack π–π stacking and non-planar molecular structures, would be worthwhile. Mapping these systems can provide valuable insights and enhance our overall understanding of the mechanisms of deformation in flexible crystals.

New understanding

Flexible crystals undergo compressive and expansive strain, which allows bent crystals to regain their undeformed shape. Understanding the origin of restoring force at the atomic scale in elastically flexible crystals is crucial for their efficient use in flexible electronics and other real-world applications. Extracting molecular-scale insights into the restoring force in an elastically bent crystal is challenging when using other quantitative analyses, such as elastic modulus. A recent study reported the role of weak intermolecular interactions in the context of elastic flexibility in [Cu(acac)₂] crystal.⁵⁶ The three key intermolecular interactions in [Cu(acac)₂] (π–π, CH–π, and CH–O interactions) were found to each change in energy across the bent crystal region from the compressed arc to the expanded arc (Fig. 9) resulting in different amounts of stored potential energy in each interaction. These findings highlight the role of π–π interaction energies in accommodating expansive strain on the outer arc, while CH–π and CH–O interactions restore compressive strain on the inner arc of the elastically bent crystal.

Fig. 9 Variation in interaction energy with compression and expansion along the bending axis in three majorly contributing dimers in [Cu(acac)₂].

To experimentally verify the calculated energies, the authors prepared single crystal cantilevers.⁵⁶ Long needle-shaped crystals were fixed at one end to a glass slide, while metallic balls of varying masses (12.5–110 times the mass of the crystals) were attached to the free end. The crystals were able to repeatedly lift these steel balls against gravity showing the calculated potential energy was reasonable. The bent crystals were estimated to be capable of lifting 30 times their own weight 1 m in the air.

Applications

Flexible piezoelectric molecular crystals

Piezoelectricity – the phenomenon of interconversion between mechanical energy and electrical energy in non-centrosymmetric crystalline materials, discovered by Pierre Curie and Jacques Curie in 1880,⁷⁹ finds emerging interest in numerous real-world applications such as energy harvesting devices, biomedical implants, sensors, and wearable devices. Commercially used piezoelectric materials, such as ceramics and metal oxides, are renowned for their exceptional piezoelectric response. However, their mechanical brittleness poses significant durability challenges that cannot be overlooked. To address this, various strategies such as thin film fabrication, integration with flexible substrates, and encapsulation into soft materials have been employed, resulting in a lowering of the bulk response. Combining piezoelectricity and mechanical flexibility, a relatively rare property, can provide another alternative to enhance the usefulness of these materials.

Piezoelectric responses in elastically flexible halogenated imidazole crystals that crystallise in a non-centrosymmetric space group is now well established.⁸⁰ Recently, elastically bendable N,N′-bis(4-nitrophenyl)methanediamine crystals have been used in energy harvesting devices.⁵² Flexible piezoelectric crystals based on small molecules have not yet been extensively studied.⁴⁵ Most flexible molecular crystals reported to date crystallise in centrosymmetric space groups, which limit the potential for piezoelectric applications.⁶

Flexible electronics

Molecular crystals have gained significant attention for their electronic applications owing to their unique combination of mechanical flexibility and long-range order compared to thin films and polymers, which offers enhanced charge carrier mobility,⁶¹ increased electrical conductivity²⁷ and tunable optoelectronic properties.²⁹ This mechanical compliance enables their integration into flexible field-effect transistors (FETs),⁶¹ waveguides^3,81 and photodetectors. Recent studies using μ-PL mapping and fluorescence lifetime imaging have revealed that bending-induced strain can significantly tune the electronic and photophysical properties.²⁹ These property changes, reversible in the case of elastic flexibility, can be extended to design strain-sensitive optoelectronic devices. Furthermore, flexible crystals can be integrated with substrates such as PDMS (polydimethylsiloxane) or other stretchable polymers to create composite systems.⁸² Plastically flexible crystals, due to their ability to undergo irreversible shaping, also find potential in applications where mechanical adaptability is required during fabrication or deployment. However, the scalability of flexible crystals, environmental stability, and integration with existing device fabrication processes need to be addressed. Nevertheless, the combination of mechanical compliance and high-performance electronic properties positions flexible molecular crystals as a key material class for the future of stretchable and wearable electronics.

Conclusions

Mechanically flexible molecular crystals have emerged as a fascinating class of materials with tremendous potential in flexible electronics, waveguides, sensors, and piezoelectric devices. This tutorial review has outlined the key differences between elastic and plastic flexibility in crystals, emphasizing the structural mechanisms underpinning each type. System dependency associated with the mechanism of elastic flexibility discussed here can aid in understanding the variation in physical properties in molecular systems when they are bent. Experimental methods such as μ-XRD, μ-Raman, and μ-PL have provided valuable insights into the atomic-scale structural perturbations of these materials under mechanical stress. A deep understanding of bending mechanisms, strain quantification methods, and their correlations with photophysical and electronic properties reveals that flexibility is not merely a structural curiosity but a functional attribute. Future directions suggest utilizing these crystals in practical applications, particularly in fields that demand resilience and adaptability.

Conflicts of interest

There are no conflicts to declare.

Data availability

All data is available in the cited publications.

Acknowledgements

S. P. T. thanks DST-SERB for a Startup Research Grant (SRG/2022/001852). A. R. thanks UGC for the Junior Research Fellowship and UQIDRA for a research fellowship. The University of Queensland and Queensland University of Technology are thanked for their support.

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Footnote

† Plastically flexible crystals in general should not be confused with “plastic crystals” which are crystals composed of molecules that are nearly spherical in shape with very weak interactions between them. “Plastic crystals” are often observed to undergo plastic deformation and thus can be considered a sub-class of the more broad category of plastically flexible crystals.

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