Splay-bend Nematic Phase Research Articles

Splay-bend nematic phases of bent colloidal silica rods induced by polydispersity

Liquid crystal (LC) phases are in between solids and liquids with properties of both. Nematic LCs composed of rod-like molecules or particles exhibit long-range orientational order, yielding characteristic birefringence, but they lack positional order, allowing them to flow like a liquid. This combination of properties as well as their sensitivity to external fields make nematic LCs fundamental for optical applications e.g. liquid crystal displays (LCDs). When rod-like particles become bent, spontaneous bend deformations arise in the LC, leading to geometric frustration which can be resolved by complementary twist or splay deformations forming intriguing twist-bend (NTB) and splay-bend (NSB) nematic phases. Here, we show experimentally that the elusive NSB phases can be stabilized in systems of polydisperse micron-sized bent silica rods. Our results open avenues for the realization of NTB and NSB phases of colloidal and molecular LCs.

Coupling between splay deformations and density modulations in splay-bend phases of bent colloidal rods.

Using a grand-canonical Landau-de Gennes theory for colloidal suspensions of bent (banana-shaped) rods, we investigate how spatial deformations in the nematic director field affect the local density of twist-bend and splay-bend nematic phases. The grand-canonical character of the theory naturally relates the local density to the local nematic order parameter S. In the splay-bend phase, we find S and hence the local density to modulate periodically along one spatial direction. As a consequence the splay-bend phase has the key symmetries of a smectic rather than a nematic phase. By contrast we find that S and hence the local density do not vary in space in the twist-bend phase, which is therefore a proper nematic phase. The theoretically predicted one-dimensional density modulations in splay-bend phases are in agreement with recent simulations.

A generalized density-modulated twist-splay-bend phase of banana-shaped particles

In 1976, Meyer predicted that bend distortions of the nematic director field are complemented by deformations of either twist or splay, yielding twist-bend and splay-bend nematic phases, respectively. Four decades later, the existence of the splay-bend nematic phase remains dubious, and the origin of these spontaneous distortions uncertain. Here, we conjecture that bend deformations of the nematic director can be complemented by simultaneous distortions of both twist and splay, yielding a twist-splay-bend nematic phase. Using theory and simulations, we show that the coupling between polar order and bend deformations drives the formation of modulated phases in systems of curved rods. We find that twist-bend phases transition to splay-bend phases via intermediate twist-splay-bend phases, and that splay distortions are always accompanied by periodic density modulations due to the coupling of the particle curvature with the non-uniform curvature of the splayed director field, implying that the twist-splay-bend and splay-bend phases of banana-shaped particles are actually smectic phases.

Biaxiality-driven twist-bend to splay-bend nematic phase transition induced by an electric field.

Although the existence of the twist-bend (NTB) and splay-bend (NSB) nematic phases was predicted long ago, only the former has as yet been observed experimentally, whereas the latter remains elusive. This is especially disappointing because the NSB nematic is promising for applications in electro-optic devices. By applying an electric field to a planar cell filled with the compound CB7CB, we have found an NTB-NSB phase transition using birefringence measurements. This field-induced transition to the biaxial NSB occurred, although the field was applied along the symmetry axis of the macroscopically uniaxial NTB Therefore, this transition is a counterintuitive example of breaking of the macroscopic uniaxial symmetry. We show by theoretical modeling that the transition cannot be explained without considering explicitly the biaxiality of both phases at the microscopic scale. This strongly suggests that molecular biaxiality should be a key factor favoring the stability of the NSB phase.

Shaping colloidal bananas to reveal biaxial, splay-bend nematic, and smectic phases.

Understanding the impact of curvature on the self-assembly of elongated microscopic building blocks, such as molecules and proteins, is key to engineering functional materials with predesigned structure. We develop model "banana-shaped" colloidal particles with tunable dimensions and curvature, whose structure and dynamics are accessible at the particle level. By heating initially straight rods made of SU-8 photoresist, we induce a controllable shape deformation that causes the rods to buckle into banana-shaped particles. We elucidate the phase behavior of differently curved colloidal bananas using confocal microscopy. Although highly curved bananas only form isotropic phases, less curved bananas exhibit very rich phase behavior, including biaxial nematic phases, polar and antipolar smectic-like phases, and even the long-predicted, elusive splay-bend nematic phase.

Controlling the curvature

Liquid Crystals Molecular chirality is often required to make chiral liquid crystalline phases, but liquid crystallinity has also been obtained using curved elongated rods known as bent-core or banana-shaped molecules. Fernandez-Rico et al. developed a method to controllably alter the curvature of the rods using ultraviolet light and a photoresponsive polymer (see the Perspective by Godinho). From a single starting batch can come a family of rods with different curvatures but similar overall rod thickness, length, and length distribution. The researchers explored a range of liquid crystalline phases, including the splay-bend nematic phase that was predicted more than 40 years ago. Science , this issue p. [950][1]; see also p. [918][2] [1]: /lookup/doi/10.1126/science.abb4536 [2]: /lookup/doi/10.1126/science.abd3548

A new flexoelectric mode in twist-bend nematic liquid crystals

Mesogenic dimers in the twist-bend nematic phase exhibit much higher flexoelectric polarization than in their uniform nematic phase. In order to theoretically investigate this data, we extend the symmetry based linear elastic theory of the twist-bend nematic phase developed in Phys. Rev. E 92, 030501(R) 2015, by including flexoelectricity under the action of an external electric field perpendicular to the helical axis. We show that at the nematic towards twist-bend nematic transition, a new flexoelectric mode becomes active. Consequently, the present model predicts the increase of the effective flexoelectric coefficient when the system is entering the twist-bend nematic phase. The influence of the flexoelectric coupling on the equilibrium wavevector and the spontaneous heliconical tilt angle are investigated. The electroclinic coefficient is calculated. Finally we argue that the helix could be unwound giving rise to a splay-bend nematic phase.

Biaxial, Twist-bend, and Splay-bend Nematic Phases of Banana-shaped Particles Revealed by Lifting the “Smectic Blanket”

We perform an extensive computational study on the phase behavior of hard banana-shaped particles, and show that biaxial, twist-bend, and splay-bend nematic phases are metastable with respect to a smectic phase for a system of hard bent spherocylinders. However, if the smectic phase is destabilized-either by polydispersity in the particle length or by curvature in the particle shape-stable biaxial, twist-bend, and splay-bend nematic phases are obtained. This provides a unified and consistent picture on the subtle role of particle shape on the phase behavior of bent rods.

Nonlinear nematic elasticity

The nonlinear elastic properties of nematic liquid crystals have acquired new interest with the recent experimental observation of bulk modulated nematic phases which are composed by achiral molecules. We extend the Oseen-Zocher-Frank's elastic theory for nematic liquid crystals by including gradients of the nematic strain tensor in the elastic deformation energy. The invariants of the elastic tensor fields, up to the fourth order in the nematic director spatial derivatives, are calculated. An alternative approach that consists in the extension of the linear elastic energy to higher powers of the nematic strain tensor, as in classical elasticity of solids, is also developed. The twist-bend nematic modulated phase is investigated by both approaches and the results are critically compared. The conical angle of the twist-bend phase is calculated as function of the elastic constants. Surface-like effects are considered. Finally, we demonstrate that a splay-bend nematic phase with small oscillations of the nematic director around an axis is prohibited.

^{13}C NMR study of the director distribution adopted by the modulated nematic phases formed by liquid-crystal dimers with odd numbers of atoms in their spacers.

The orientational order of the molecules in the bent mesogen CB6OCB has been studied throughout the range of temperature stability of both the N_{U} and N_{TB} liquid-crystal phases by ^{13}C NMR spectroscopy. These spectra provide local order parameters for the para axes of both of the nonequivalent cyanobiphenyl groups and show how they change on entering the twist-bend nematic phase. A key feature of the order parameters is a weak, but clear maximum in the temperature variation of the order parameter prior to the N_{TB} phase. This suggests that the directors in both the N_{U} and N_{TB} phases are tilted with respect to the magnetic field of the spectrometer. Significantly the conformational states of the spacer are comparable in both phases, although the low temperature nematic is chiral but not that at high temperature. It is proposed that the higher temperature, tilted phase could be the splay-bend nematic phase.

Modulated nematic structures induced by chirality and steric polarization.

What kind of one-dimensional modulated nematic structures (ODMNS) can form nonchiral and chiral bent-core and dimeric materials? Here, using the Landau-de Gennes theory of nematics, extended to account for molecular steric polarization, we study a possibility of formation of ODMNS, both in nonchiral and intrinsically chiral liquid crystalline materials. Besides nematic and cholesteric phases, we find four bulk ODMNS for nonchiral materials, two of which, to the best of our knowledge, have not been reported so far. These two structures are longitudinal (N_{LP}) and transverse (N_{TP}) periodic waves where the polarization field being periodic in one dimension stays parallel and perpendicular, respectively, to the wave vector. The other two phases are the twist-bend nematic phase (N_{TB}) and the splay-bend nematic phase (N_{SB}), but their fine structure appears more complex than that considered so far. The presence of molecular chirality converts nonchiral N_{TP} and N_{SB} into new N_{TB} phases. Surprisingly, the nonchiral N_{LP} phase can stay stable even in the presence of intrinsic chirality.