Orienting the Liquid Crystals

66 4. LiquidCrystals for MicrowaveApplications

4.2. Orienting theLiquidCrystals 67

For the energy stored in magneticfield applies:

wmag = ¹

2_{H B}^∗ = ¹

2_H ^↔_{μ H}^∗ _(4.15)

and, analog to (4.14):

wmag =_μ⊥|^H|²+_Δμ n_{H (4.16)}

The last term in Eq. (4.14) and (4.16) depends on the orientation of the field vector relative to the director n. Since the terms related to the external fields in Eq. (4.11) (w_f,el and w_f,mag) have a negative sign, the system will tend to maximize them, in order to minimize the overall energy per unit volume. The minimum of w_f is thus achieved when thefield vectors (_{Eand H} respectively) are aligned with the directorn.

Orientation with a Magnetic Field

Is an external magnetic field applied to a liquid crystal volume, in the light of the pre-sented energy considerations, the director will tend to rotate and align as much as pos-sible with the field lines, minimizing the overall free energy of the system.

Orientation with a magnetic field is practical for experimental purposes, when the real-ization of metallic electrodes to apply an electric field for the orientation is not always possible or impairs the RF properties of the DUT. In this case the DUT containing the liquid crystal can be inserted between the pole shoes of an electromagnet, for operation with εr,⊥ for instance, and then either the pole shoes or the DUT can be rotated with 90^◦ to obtain operation with ε_r,. For a functional device however, the usage of bulky permanent magnets or electromagnets is not reasonable because of size and weight, and solutions must be sought to control the director orientation with an electricfield.

Orientation with an Electric Field

Based on the same energy considerations, when an external electric field is applied to the liquid crystal, the molecules will rotate as well until the director is parallel with the electric field lines.

The reorientation of the LC molecules in an electrostatic field is also known under the name Fréedericksz-effect. The reorientation begins as soon as a threshold voltage is ex-ceeded (Fréedericksz-transition). For the case of an LC volume enclosed between two

68 4. LiquidCrystals for MicrowaveApplications

parallel electrodes, the threshold voltage can be expressed with the formula:

U_th= ^Eth d =_π

K

Δε , (4.17)

with E_th the threshold electric field intensity, d the distance between the electrodes and K an LC specific elastic constant. Is the voltage increased above the threshold, the molecules will start to rotate from their initial state. Eventually a saturation state is reached, when they are parallel to the electric field lines. The orientation with electric field is schematically presented in Fig. 4.5 for the case of a parallel plate capacitor.

The reorientation with an electric field is naturally the preferred choice for practical applications. In the case of microstrip reflectarrays this reorientation method is very suitable, since the topology of a microstrip reflectarray unit cell resembles that of a parallel plate capacitor. The ground will provide a common potential, and suitable voltages will have to be provided to the microstrip elements, under the assumption that the substrate between them is replaced by liquid crystal. The only problem that has to be carefully taken into consideration is the interference caused by the voltage control lines to the RFfield radiated by the cell.

n n n

U=0 U=U_{t h} U>>U_{t h}

=

r

e

e

e =

e

Figure 4.5: Orientation of the liquid crystal molecules by applying an electric field. The relative permittivity seen by a RF wave propagating through the LC changes continuously.

Orientation with an Orientation Layer

When a nematic LC is in contact with another phase, an interface is created. At this interface, the nematic order is disturbed and the orientation of the LC molecules is determined by the adjoining surface and its properties. This phenomenon is called surface anchoring[Pen00].

Depending on the tilt angle α ( the angle between the director and boundary surface) the alignment of nematic LC can be categorized as follows:

(a) α =₀^◦ - planar (parallel) alignment: director parallel to the boundary surface

(b) α = ₉₀^◦ - homeotropic (perpendicular) alignment: director perpendicular to the

4.2. Orienting theLiquidCrystals 69

Figure 4.6: Illustrative orientation of a rod-like liquid crystal molecule by use of a poly-imide layer with corrugations.

boundary surface

(c) 0^◦ <_α <₉₀^◦ - tilted alignment

Surface treatments can further be divided into two major groups: mechanical treatment and deposition of substances that assist the alignment. In this work mechanical treat-ment has been used, owing to the relatively simple processing and also to the existing know how in our group.

Rubbing the boundary surface in one direction to obtain homogeneous alignment of the molecules is one of the most widely used techniques, in research laboratories as well as in the industry. First, a very thin polyimide layer (with typical thickness between 100-300 nm) is deposited by spin coating on the surface and cured by backing in two steps. The technological details are given in Appendix A2. Fine, parallel corrugations are applied into this layer through mechanical rubbing in one direction (for instance with a textile material). These corrugations, together with the chemical interaction between polyimide and the LC molecules will cause the orientation of the directorn along the rubbing direction, with an angle of approximately 0^◦ with respect to the surfaces, as illustrated in Fig. 4.6.

Switching times

A drawback of liquid crystals for applications where speed is a requirement are the switching times. Switching times are a measure for the time interval characterizing the transition from one equilibrium state to another, when external fields are applied or removed. For instance, using the example of the parallel plate capacitor from the previous subsection, one can define two switching times, a Δton for the transition from εr,⊥ to εr, when the DC electric field is applied, and a Δt_{o f f} for the inverse transition when the electricfield is removed.

70 4. LiquidCrystals for MicrowaveApplications

For these switching times following formulas are valid [Tar92]:

Δt_on ∝ γd² Δε

U_c²−^U_th^{2 Δto f f ∝} γd²

ΔεU_th² (4.18)

withγthe rotational viscosity of the LC molecules,U_c the control voltage,U_ththe Fréed-ericksz threshold voltage and dthe distance between the electrodes.

The rotational viscosity and the dielectric anisotropy are material dependent, therefore only an optimization of LCs with respect to these two parameters could improve the switching times. However, the switching times are directly proportional with the square of the liquid crystal layer thickness, which means that they could be reduced by design-ing devices with LC layers that are as thin as possible.

In [Mue05a] switching times of a finline phase shifter with a LC layer thickness of d=127μm were measured. For Δton the values were in the order of 10⁻²s, whereas for Δto f f the values were in the range 5-15 s. These values have to be dramatically improved for time-sensitive applications.