Rod-shaped molecules, mesogens, in the smectic phase show a translational order as well as orientational order as discussed in the Liquid Crystal Phases section. In the smectic C phase, the periodic spacing of the mesogens along one axis, we will use the z axis, causes them to form layers in the x-y plane. The director of each planar layer is tilted at an angle q from the normal. This angle is temperature dependent if a smectic C to smectic A transition occurs with increasing temperature.
When the molecule is chiral, successive smectic C layers show a gradual change in the direction of tilt, such that the director precesses about the z axis from layer to layer, always lying on the surface of a hypothetical cone of angle 2q as illustrated in the animation on the left. The angle around the circle of precession is known as the azimuthal angle. This creates a helical structure in the chiral smectic C (SmC*) mesophase with the pitch being the distance along the z axis needed to reach the same molecular orientation.
In addition to producing this helical structure, chirality results in a spontaneous molecular polarization, shown by the blue arrow in the animation on the left. This polarization vector is perpendicular to the molecule and contained in the layer plane. Therefore, all possible directions for the vector are tangent to the circle of intersection of the cone with the plane. A bulk SmC* sample, free to develop its helical structure, will not show ferroelectric behavior since the spontaneous polarization will average to zero over one pitch (since polarization vectors go around an entire circle and cancel each other out). This is often referred to as the helielectric phase. To see the top view of the polarization vector of each layer of one pitch showing the polarization vector going through a full circle, click the button labeled "Cycle through layers." Click on a layer to see a top view of its polarization vector only. Typically, the pitch includes many layers in such a material.
Clark and Lagerwall (Clark and Lagerwall, 1980) proposed a way to suppress the helix and developed the surface stabilized ferroelectric liquid crystal (SSFLC) arrangement shown below. The helix is constrained by using a cell gap that is less than the helical pitch. Interaction forces between the liquid crystal and the bounding plates unwind the intrinsic helix. Symmetry arguments show that this boundary condition also causes the molecular orientation for each layer to be the same and the material exhibits ferroelectric behavior. The director is favored to lie in the plane of the bounding plates. Because of this condition and the fact that the director is constrained to be at a certain angle from the normal to the layer (i.e. to lie on the intersection of a cone and the bounding plate), there are two stable states. The polarization vector, therefore, must be normal to the bounding plates and its two states are in opposite directions. These two states are shown in the diagram below. The up state is shown by the green molecule, while the down state is shown by the dotted line. Note how both states lie along the cone and are in the plane of the bounding plate.
Electro-optical effects are achieved by applying an electric field that induces changes in the director orientation. Since the polarization vector is coupled to the director, it is also switched between the two stable states by the electric field. This process is known as the Clark-Lagerwall effect (Clark and Lagerwall, 1980) and is illustrated for a layer of mesogens in a schematic representation of a thin film of SSFLC material shown in the animation below, where the switching layer is the rightmost one. The two stable states are shown more plainly for the upper mesogen only, for clarity in the diagram. Click on the button to change states.
This animation contains other mesogens (left and middle layers) which do not yet respond to the E-field. They are representative of the many mesogens contained in a SSFLC which are interacting and still must quickly and smoothly make the transition from one stable state to the other in a coordinated way. Clark and Lagerwall explained this process by modeling the switching of successive layers in terms of a domain wall motion, where the electric field switches the director between the two stable states that are separated by the domain wall. This wall is schematically represented by the separations between the right-hand layer which switches and the adjacent one which does not yet "feel" that reversal in the electric field and therefore does not switch in a similar way.
The next animation demonstrates the motion of this domain wall through an SSFLC in a simplified schematic. Such a domain wall model provides a means for the two states to coexist and is energetically preferable to a sudden switch of the entire film in response to the application of an electric field below a certain threshold value. The movement of the domain wall is shown by clicking on the play button below the sample. As the domain wall moves the molecules and their director and polarization vector are switching to the opposite state moving initially in this case from left to right in the figure and back upon the reversal of the electric field. Bistability is accomplished by the two symmetric states and is what gives the SSFLC an inherent erasable memory that can be used in either polarization direction. What this means is that both states can exist at the same time without an applied electric field (electric field only needed to switch states). Clark and Lagerwall (1980) report that the critical parameter in this switching process is the product of the voltage pulse amplitude and pulse width, ranging from 25 Vmsec to 800 Vmsec. In this simplified animation, only the top surface molecules are shown. However, there are many molecules stacked on top of each other (as in diagram above) and they move from the stable position on one side of the z axis to the other as switching takes place. More specifically, the surface molecules would not change exactly with the bulk when the field is applied.
The geometry discussed is known as a bookshelf geometry because the smectic layers are ordered one right next to the other, like books in a bookshelf. However, they are not necessarily perpendicular to the bounding plates, in other words they are tilted. In fact, x-ray experiments and texture analysis show the bookshelf structure most often has an internal chevron structure, as illustrated on the right. The tilt of the layers changes in relation to temperature and the tilt shrinks the layer thickness. This is one example of the production complications.
