Shape programming lines of concentrated Gaussian curvature

Liquid crystal elastomers (LCEs) can undergo large reversible contractions along their nematic director upon heating or illumination. A spatially patterned director within a flat LCE sheet thus encodes a pattern of contraction on heating, which can morph the sheet into a curved shell, akin to how a pattern of growth sculpts a developing organism. Here we consider, theoretically, numerically and experimentally, patterns constructed from regions of radial and circular director, which, in isolation, would form cones and anticones. The resultant surfaces contain curved ridges with sharp V-shaped cross-sections, associated with the boundaries between regions in the patterns. Such ridges may be created in positively and negatively curved variants and, since they bear Gauss curvature (quantified here via the Gauss-Bonnet theorem), they cannot be flattened without energetically prohibitive stretch. Our experiments and numerics highlight that, although such ridges cannot be flattened isometrically, they can deform isometrically by trading the (singular) curvature of the V angle against the (finite) curvature of the ridge line. Furthermore, in finite thickness sheets, the sharp ridges are inevitably non-isometrically blunted to relieve bend, resulting in a modest smearing out of the encoded singular Gauss curvature. We close by discussing the use of such features as actuating linear features, such as probes, tongues and limbs, and highlighting the similarities between these patterns of shape change and those found during the morphogenesis of several biological systems.F.F. and M.W. were supported by the EPSRC [grant number EP/P034616/1]. M.W. is grateful for support from the ELBE Visiting Faculty Program, Dresden. D.D. was supported by the EPSRC Centre for Doctoral Training in Computational Methods for Materials Science [grant no. EP/L015552/1]. J.S.B. was supported by a UKRI “future leaders fellowship” [grant number MR/S017186/1]. This material is partially based upon work supported by the National Science Foundation under Grant DMR 2041671

Magnetic polydomain liquid crystal elastomers–synthesis and characterisation

Although liquid crystal elastomers (LCE) are a fascinating class of materials with interesting thermomechanical properties of their own, the aim is to enhance their performance or add new features, e.g. response to external stimuli. The generally weak response of organic materials can be significantly intensified by mixing nano-sized magnetic particles into the host polymer matrix. An alternative approach is chemically coupling the nanoparticles to the elastomer. We achieved this by bonding functionalised magnetic nanoplatelets to the backbone of a main-chain LCE and obtained polydomain magnetic liquid crystal elastomers. We measured the magnetisation curves in samples, which were exposed to either small or large magnetic fields–their response being a consequence of partial particle reorientation or magnetic moment flipping. In contrast to the samples, which were exposed to small magnetic field and in which the remanent magnetisation can be reset to zero by heating the sample, the samples with flipped magnetisation within the platelets cannot be reversed into the original state. Coupling of magnetic and mechanical properties shows a slight magneto-elastic response at elevated temperatures and a significant inverse magneto-elastic effect: the magnetisation caused by mechanical stretching is almost equal to the magnetisation caused by an external magnetic field

Shape programming lines of concentrated Gaussian curvature

Liquid crystal elastomers (LCEs) can undergo large reversible contractions along their nematic director upon heating or illumination. A spatially patterned director within a flat LCE sheet thus encodes a pattern of contraction on heating, which can morph the sheet into a curved shell, akin to how a pattern of growth sculpts a developing organism. Here we consider, theoretically, numerically and experimentally, patterns constructed from regions of radial and circular director, which, in isolation, would form cones and anticones. The resultant surfaces contain curved ridges with sharp V -shaped cross-sections, associated with the boundaries between regions in the patterns. Such ridges may be created in positively and negatively curved variants and, since they bear Gauss curvature (quantified here via the Gauss-Bonnet theorem), they cannot be flattened without energetically prohibitive stretch. Our experiments and numerics highlight that, although such ridges cannot be flattened isometrically, they can deform isometrically by trading the (singular) curvature of the V angle against the (finite) curvature of the ridge line. Furthermore, in finite thickness sheets, the sharp ridges are inevitably non-isometrically blunted to relieve bend, resulting in a modest smearing out of the encoded singular Gauss curvature. We close by discussing the use of such features as actuating linear features, such as probes, tongues and grippers. We speculate on similarities between these patterns of shape change and those found during the morphogenesis of several biological systems.F.F. and M.W. were supported by the EPSRC [grant number EP/P034616/1]. M.W. is grateful for support from the ELBE Visiting Faculty Program, Dresden. D.D. was supported by the EPSRC Centre for Doctoral Training in Computational Methods for Materials Science [grant no. EP/L015552/1]. J.S.B. was supported by a UKRI “future leaders fellowship” [grant number MR/S017186/1]. This material is partially based upon work supported by the National Science Foundation under Grant DMR 2041671

Distinctive features of pretransitional behaviour between nematic phases as revealed by DDM

Pretransitional behaviour, with strong softening of the bend or splay elastic constants, is characteristic of two of the nematic to nematic phase transitions reported in the last decade. Such softening is strongly reflected in the pretransitional behaviour of the thermally excited director fluctuations. Here we give a comprehensive overview of the cross-Differential Dynamic Microscopy (c-DDM) method and its application to the investigation of thermal director fluctuations and phase transitions. For this, we build on the potentialities of the method for the investigation of the standard nematic phase of E7 to compare with the pretransitional behaviour of the nematic to twist bend nematic phase transition as well as the nematic to ferroelectric nematic transition

Optical second harmonic generation in a ferromagnetic liquid crystal.

A comparative experimental investigation of the dependence of second harmonic generation (SHG) on an applied external voltage between a standard nematic liquid crystalline material and an analogue ferromagnetic nematic liquid crystalline material was performed by using a fundamental optical beam at an 800 nm wavelength. For the ferromagnetic material, the dependence of SHG on an applied magnetic field was also examined. Three different polarization combinations of the fundamental and the second harmonic radiation were analysed. The SHG signal observed in the former material is attributed to a combination of electric field-induced SHG (EFISHG) and flexoelectric deformation-induced SHG, while the SHG signal observed in the latter material is attributed solely to flexoelectric deformation-induced SHG. The obtained dependences of the SHG signal on the associated optical retardation show that, in the most favourable polarization combination, the two contributions generate about the same effective nonlinear optical susceptibility

Ferroelectric-Ferroelastic Phase Transition in a Nematic Liquid Crystal.

Ferroelectric ordering in liquids is a fundamental question of physics. Here, we show that ferroelectric ordering of the molecules causes the formation of recently reported splay nematic liquid-crystalline phase. As shown by dielectric spectroscopy, the transition between the uniaxial and the splay nematic phase has the characteristics of a ferroelectric phase transition, which drives an orientational ferroelastic transition via flexoelectric coupling. The polarity of the splay phase was proven by second harmonic generation imaging, which additionally allowed for determination of the splay modulation period to be of the order of 5-10 microns, also confirmed by polarized optical microscopy. The observations can be quantitatively described by a Landau-de Gennes type of macroscopic theory

Introducing the azocinnamic acid scaffold into bent-core liquid crystal design: A structure–property relationship study

A series of bent-core liquid crystals possessing the azocinnamoyl unit in both elongating side arms was synthesized. The chain length was kept fixed for each molecule (C12H25), whereas the substituents at the central and outer rings were varied. The LC phases were assigned by polarizing optical microscopy, differential scanning calorimetry and X-ray diffraction. The investigated compounds are suitably diverse to reveal some aspects of the relationship between molecular structure and the mesomorphic properties. Namely, non-substituted parent compound is crystalline only and the methyl group in position 2 or the chlorine atom in position 4 of the central ring suppresses LC phase formation. Introduction of the strong electron-withdrawing nitro group between the side arms on the central ring leads to a B7 phase. Compounds possessing a bromine atom or two chlorine atoms in the neighbourhood of the ester groups form LC phases typical for rod-like molecules, namely a nematic – smectic phase sequence. The results are compared with those reported for the azobenzoyl analogues