Dynamic and microscopic X-ray characterization of a compound chevron layer in electroclinic liquid crystals

The local layer structure of surface stabilized electroclinic liquid crystals has been analysed by time-resolved synchrotron X-ray microdiffraction. At a low applied electric field, the initial bookshelf structure starts to respond above a threshold voltage. With a low to medium applied field of triangular form, the layer structure transforms reversibly between the bookshelf (low field) and the compound chevron (high field), in which the vertical and horizontal chevrons alternate along the layer. When the horizontal chevron component appears, a stripe texture can be seen in an optical micrograph. With increasing field, the horizontal chevron becomes a dominant structure while the vertical chevron still remains. The layer spacing changes in correlation with the chevron angle during the field application. At high field, surface molecules partly rearrange, resulting in alignment deterioration at the interface. The layer response time for an a.c. square wave field is of the order of a few µs to ten µs, which is close to the optical response. The appearance of the compound chevron is discussed in conjunction with the anchoring effect.     

Dynamic and microscopic X‐ray characterization of a compound chevron layer in electroclinic liquid crystals

The local layer structure of surface stabilized electroclinic liquid crystals has been analysed by time‐resolved synchrotron X‐ray microdiffraction. At a low applied electric field, the initial bookshelf structure starts to respond above a threshold voltage. With a low to medium applied field of triangular form, the layer structure transforms reversibly between the bookshelf (low field) and the compound chevron (high field), in which the vertical and horizontal chevrons alternate along the layer. When the horizontal chevron component appears, a stripe texture can be seen in an optical micrograph. With increasing field, the horizontal chevron becomes a dominant structure while the vertical chevron still remains. The layer spacing changes in correlation with the chevron angle during the field application. At high field, surface molecules partly rearrange, resulting in alignment deterioration at the interface. The layer response time for an a.c. square wave field is of the order of a few µs to ten µs, which is close to the optical response. The appearance of the compound chevron is discussed in conjunction with the anchoring effect.     

Smectic C* layer directional instabilities in cells with twist geometry

We have investigated the formation and structure of horizontal chevrons, as well as the reorientation dynamics of smectic layers under applied asymmetric electric fields in cells with a twist geometry. The tilted layer structure of horizontal chevron domains is found to be rotated by an angle approximately equal to the twist angle alpha, as compared with parallel rubbed substrates, alpha = 0°. The time of horizontal chevron formation decreases slightly with increasing twist angle. The smectic layer reorientation under application of time-asymmetric electric fields is found to be enhanced for reorientation into the direction of twist, while it is hindered for reorientation out of the direction of layer twist. Increasing the twist angle results in a basically linear increase/decrease in the reorientation velocity, depending on field asymmetry direction. The electro-optic behaviour of twist cells with inclined smectic layers is outlined and compared with measurements performed on cells with monostable, parallel anchoring conditions.     

Smectic C* layer directional instabilities in cells with twist geometry

We have investigated the formation and structure of horizontal chevrons, as well as the reorientation dynamics of smectic layers under applied asymmetric electric fields in cells with a twist geometry. The tilted layer structure of horizontal chevron domains is found to be rotated by an angle approximately equal to the twist angle alpha, as compared with parallel rubbed substrates, alpha = 0°. The time of horizontal chevron formation decreases slightly with increasing twist angle. The smectic layer reorientation under application of time-asymmetric electric fields is found to be enhanced for reorientation into the direction of twist, while it is hindered for reorientation out of the direction of layer twist. Increasing the twist angle results in a basically linear increase/decrease in the reorientation velocity, depending on field asymmetry direction. The electro-optic behaviour of twist cells with inclined smectic layers is outlined and compared with measurements performed on cells with monostable, parallel anchoring conditions.     

Dielectric versus optical response of chevron ferroelectric liquid crystals

Dielectric and optical methods to investigate the response of surface-stabilized ferroelectric liquid crystals (SSFLCs) of the chevron structure are examined and compared in the case of the azimuthal mode of collective relaxation processes. It is found that the variation of an effective (averaged over the chevron cell volume) dielectric permittivity tensor under the influence of a weak alternating external electric field is approximately equivalent to the transformation of this tensor as a consequence of the rotation of the laboratory frame around the axis perpendicular to the smectic plane about a small angle. Then, using an analytic solution of the equation of motion describing the azimuthal rotation of molecules, it is shown that both of the analysed approaches to calculate and measure the response of SSFLCs yield consistent results for these rotational dynamic processes. This allows the calculation of the spontaneous polarization of the unit volume of chevron slabs, provided that the pretilted azimuthal angle (in the absence of an applied electric field) within the smectic plane is known.     

Time resolved X-ray diffraction studies of electric field induced layer motion in a chevron geometry smectic A liquid crystal device

Small angle time-resolved X-ray diffraction was used to monitor the behaviour of the smectic layers during the electric field induced planar to homeotropic transition in a smectic A cell possessing a chevron layer geometry. The liquid crystal material used was S3, from Merck Ltd, and was sandwiched in a 15 mum parallel plate device. The main features of the transition are the cooperative rotation of layers and the creation of an asymmetric chevron structure during the early stages of switching. The time scale for the planar-to-homeotropic transition in the device is approximately 5 s, at a temperature of 3 C below the nematic-to-smectic A phase transition and for an applied electric field of 2 V mum -1 (rms).     

Dielectric versus optical response of chevron ferroelectric liquid crystals

Dielectric and optical methods to investigate the response of surface‐stabilized ferroelectric liquid crystals (SSFLCs) of the chevron structure are examined and compared in the case of the azimuthal mode of collective relaxation processes. It is found that the variation of an effective (averaged over the chevron cell volume) dielectric permittivity tensor under the influence of a weak alternating external electric field is approximately equivalent to the transformation of this tensor as a consequence of the rotation of the laboratory frame around the axis perpendicular to the smectic plane about a small angle. Then, using an analytic solution of the equation of motion describing the azimuthal rotation of molecules, it is shown that both of the analysed approaches to calculate and measure the response of SSFLCs yield consistent results for these rotational dynamic processes. This allows the calculation of the spontaneous polarization of the unit volume of chevron slabs, provided that the pretilted azimuthal angle (in the absence of an applied electric field) within the smectic plane is known.     

Horizontal chevron domain formation and smectic layer reorientation in SmC* liquid crystals stabilized by polymer networks

The influence of a polymer network, stabilizing an initial texture of horizontal chevron geometry, on the in-plane smectic C* layer reorientation process is studied for different applied electric field conditions. As expected, the reorientation of smectic layers is strongly slowed down and eventually suppressed by the network, even at rather low monomer concentrations. Polymer network formation in a uniformly reoriented smectic layer state reveals that the network acts in two ways: first it gives a biased elastic torque counteracting a field of such symmetry as to cause a change from the templated layer direction; second it introduces an increased effective viscosity counteracting the reorientation in both directions. The behaviour of samples stabilized by two different kinds of polymer networks, created in between the smectic layers (intra-layer) and across them (inter-layer), is then investigated and discussed.     

Horizontal chevron domain formation and smectic layer reorientation in SmC* liquid crystals stabilized by polymer networks

The influence of a polymer network, stabilizing an initial texture of horizontal chevron geometry, on the in-plane smectic C* layer reorientation process is studied for different applied electric field conditions. As expected, the reorientation of smectic layers is strongly slowed down and eventually suppressed by the network, even at rather low monomer concentrations. Polymer network formation in a uniformly reoriented smectic layer state reveals that the network acts in two ways: first it gives a biased elastic torque counteracting a field of such symmetry as to cause a change from the templated layer direction; second it introduces an increased effective viscosity counteracting the reorientation in both directions. The behaviour of samples stabilized by two different kinds of polymer networks, created in between the smectic layers (intra-layer) and across them (inter-layer), is then investigated and discussed.     

The realignment of an achiral smectic C chevron structure with applied field

This is the second of two papers describing the study of a conventional display cell filled with an achiral smectic C phase. In our first paper we described the X-ray diffraction study of the smectic layer alignment in the cell in its initial ‘off’ state. The mesogen used has positive dielectric anisotropy and the cell surfaces were treated conventionally to give a parallel homogeneous alignment. The X-ray results were interpreted in terms of a complex threecomponent chevron pattern with two outer arms and a central, tilted bookshelf region. This paper concerns the change in optical texture of the cell as the applied field is increased. There is a sequence of reversible texture changes before the final irreversible breakdown of the structure. The optical data are consolidated by electro-optic and field-dependent X-ray data. We interpret the changes in optical texture in terms of a sequence of four distinct realignment processes as the field is increased: (1) re-alignment of the molecules within the existing layer structure by rotation of the director around the smectic C cones; (2) growth of the two outer chevron arms at the expense of the central bookshelf region; (3) a progressive modification of the domain structure; (4) an abrupt, drastic, irreversible re-alignment at high field with complete breakdown of the original chevron structure to a quasi-homeotropic structure.     

The realignment of an achiral smectic C chevron structure with applied field

This is the second of two papers describing the study of a conventional display cell filled with an achiral smectic C phase. In our first paper we described the X-ray diffraction study of the smectic layer alignment in the cell in its initial 'off' state. The mesogen used has positive dielectric anisotropy and the cell surfaces were treated conventionally to give a parallel homogeneous alignment. The X-ray results were interpreted in terms of a complex threecomponent chevron pattern with two outer arms and a central, tilted bookshelf region. This paper concerns the change in optical texture of the cell as the applied field is increased. There is a sequence of reversible texture changes before the final irreversible breakdown of the structure. The optical data are consolidated by electro-optic and field-dependent X-ray data. We interpret the changes in optical texture in terms of a sequence of four distinct realignment processes as the field is increased: (1) re-alignment of the molecules within the existing layer structure by rotation of the director around the smectic C cones; (2) growth of the two outer chevron arms at the expense of the central bookshelf region; (3) a progressive modification of the domain structure; (4) an abrupt, drastic, irreversible re-alignment at high field with complete breakdown of the original chevron structure to a quasi-homeotropic structure.     

Molecular director and layer response of chevron surface stabilized ferroelectric liquid crystals to low electric field

Recent papers on chevron surface stabilized ferroelectric liquid crystal cells claim that the chevron layer structure can be reversibly uprighted by application of the low to moderate electric fields typically employed to produce director reorientation. In this paper we show, using optical microscopy and X-ray scattering, that there is no significant change in the smectic layer thickness or chevron layer structure of our chevron surface stabilized ferroelectric liquid crystal cells under typical director switching conditions. Furthermore, we present arguments, based on the known elastic properties of smectics, that there is not likely to be a significant elastic layer response to these levels of applied electric field in any surface stabilized ferroelectric liquid crystal cell with anchored layers. Both the switching and observed continuous optical response to applied field can be understood on the basis of electric field induced reorientation of a non-uniform molecular director distribution. We further show that the typically observed broad distribution of layer orientations about the mean chevron structure arises from localized layering defects.     

Microsecond studies of layer motion in a ferroelectric liquid crystal device

Small angle X-ray scattering has been employed to study dynamically the layer motion in a ferroelectric liquid crystal device on application of low electric fields. Microsecond time resolution was achieved and the use of an area detector in the experiment allowed the examination of layer motion in two orthogonal planes. The X-ray data show that during switching the chevron structure adopted by the layers distorts, implying a variation in the chevron angle. A rotation of the layers in the plane of the device is also observed, coincident in time with the change in chevron angle. The motion of the layers takes place on a ten microsecond time scale and the angular rotation of the layers is approximately 1°.     

Microsecond studies of layer motion in a ferroelectric liquid crystal device

Abstract

Small angle X-ray scattering has been employed to study dynamically the layer motion in a ferroelectric liquid crystal device on application of low electric fields. Microsecond time resolution was achieved and the use of an area detector in the experiment allowed the examination of layer motion in two orthogonal planes. The X-ray data show that during switching the chevron structure adopted by the layers distorts, implying a variation in the chevron angle. A rotation of the layers in the plane of the device is also observed, coincident in time with the change in chevron angle. The motion of the layers takes place on a ten microsecond time scale and the angular rotation of the layers is approximately 1°.     

The mountain defect. A new kind of planar defect in surface stabilized smectic C liquid crystals

A new kind of planar chevron defect, which we call the 'mountain defect' due to its mountain-shaped appearance under the microscope, is observed in chevron surface stabilized smectic C liquid crystal cells for both chiral (ferroelectric) and achiral materials. Polarized optical microscopy investigations reveal that this kind of defect, which can either appear spontaneously and grow slowly over days, weeks and months or can be induced by applying an electric field or mechanical distortion, mediates change in the chevron interface position, separating chevron domains of differing chevron interface position. The full three dimensional layer structure of this defect and its relation with other commonly seen line defects in such cells, like zig-zag walls and field lines, will be presented. The formation of this kind of defect indicates that chevron structure is not necessarily a stable structure in these cells.     

Director reorientation dynamics in chevron ferroelectric liquid crystal cells

We present sample numerical solutions of the equation of motion that governs the dynamics of molecular orientation in ferroelectric liquid crystal cells with chevron layer structure. We show that the chevron structure significantly influences the director field, the chevron interface providing surface stabilization on a plane interior to the FLC layer. Assuming non-polar nematic-like elasticity in the vicinity of the chevron interface, we have modelled the effects of applied field on cells with purely non-polar cell boundary interactions that have uniform director orientation at zero field, and on cells in which the cell walls are strongly polar and the zero-field states are splayed. The simulations with strongly polar surfaces give bistable operation with the two states having fixed orientations at the FLC-solid surfaces, different orientation of P at the chevron interface, and P splayed in either the upper or lower portion of the cell. A monostable state can arise when the chevron interface is asymmetric, i.e. located away from the middle of the cell. Experimental results on asymmetric chevron cells qualitatively confirm the calculated switching scenario.     

On the dynamics of ferro- and antiferro-electric liquid crystals

In this work, a set of Landau-Ginzburg equations to investigate the dynamic properties of ferro- and antiferro-electric smectic phases is formulated on the basis of the elastic continuum theory of compressible smectics. In the present framework, the polarization electric field is consistently taken into account through the Poisson equation as seen in our previous work. As a practical application, a few numerical results are presented for the surface-stabilized geometry with inclined and chevron layer structures. An asymmetric bistable switching is found to be achieved in the chevron layer structure under an alternating external field. In an inclined layer structure, however, a symmetric switching is found to be possible. In addition, it is first presented from a theoretical standpoint that the compressible smectic layer structure may be drastically deformed in the chevron and inclined layer structures with a sufficiently large external field.     

On the dynamics of ferro- and antiferro-electric liquid crystals

Abstract

In this work, a set of Landau–Ginzburg equations to investigate the dynamic properties of ferro- and antiferro-electric smectic phases is formulated on the basis of the elastic continuum theory of compressible smectics. In the present framework, the polarization electric field is consistently taken into account through the Poisson equation as seen in our previous work. As a practical application, a few numerical results are presented for the surface-stabilized geometry with inclined and chevron layer structures. An asymmetric bistable switching is found to be achieved in the chevron layer structure under an alternating external field. In an inclined layer structure, however, a symmetric switching is found to be possible. In addition, it is first presented from a theoretical standpoint that the compressible smectic layer structure may be drastically deformed in the chevron and inclined layer structures with a sufficiently large external field.     

Characterization of focal conics in chiral smectic C liquid crystals by X-ray microdiffraction

Focal conics consisting of an ellipse and a hyperbola in chiral smectic C liquid crystals aligned in surface-stabilized cells of medium thickness (about 25 µm cell gap) were characterized in relation to the chevron structure by synchrotron X-ray microdiffraction. The focal conic texture is embedded in the chevron structure with a relatively sharp interface. The deformed layer of the focal conics is a kinked bookshelf consisting of a few slightly bent segments for small focal conics, whereas it is a bookshelf layer for large focal conics. Around the focus of the ellipse toward the hyperbola, a complicated layer structure appears, although the core region of small layer curvature has been hardly observed within the present experimental sensitivity. The broad and narrow walls of a zigzag defect in the same cell are analyzed for comparison.     

Quasi-mesoscopic model for ferroelectric switching in the chevron geometry

We present a theory of ferroelectric liquid crystal switching which combines elements of standard macroscopic continuum theories with mesoscopic Landau-de Gennes chevron theories. The macroscopic elements of the theory apply in the chevron arms, and are subject to a boundary condition at the chevron interface. This boundary condition can be derived from an anchoring energy associated with the director discontinuity at the chevron tip. The anchoring energy, which corresponds to the degree to which the cone mismatch condition is not satisfied, is calculated using the mesoscopic Landau-de Gennes theory. In the combined theory the frequently used cone-matching condition emerges as a thick cell limit. We are able to calculate a free energy associated with the imposition of a field on particular configurations. There follows a switching phase diagram determining the conditions for thresholdless and bistable switching. We further show that the time dependence of the switching process is determined by the slower bulk relaxation dynamics rather than by the fast chevron surface dynamics.