RESISTENCIA A LA TRACCIÓN DE LA FORMULACIÓN DE PEBD VIRGEN CON MATERIAL DEGRADADO

The rod-like shape of the molecules, coupled with the degree of ordering, gives rise to anisotropies within the NLC. The LC has mechanical anisotropy (viscosity and elastic forces), as well as electromagnetic anisotropies (optical birefringence and dielectric anisotropy).

3.3.1 Viscosity

The viscosity of LCs depends on the orientation of the director in relation to the flow direction. The three viscosities, sometimes called the Miesowicz coefficients are called r|i (director perpendicular to the flow and parallel to the velocity gradient),r|2 (director parallel to the flow), and r|3 (director perpendicular to the flow and perpendicular to the velocity gradient). r\ \ is much greater than the other two [Collings & Hird, 1998, p. 18]. These will not be discussed further here.

3.3.2 Birefringence (Optical Anisotropy)

NLCs are biréfringent. The birefringence (An) is related to the order parameter, so as the thermotropic LC is heated towards its isotropic phase, the birefringence reduces. An example o f this is shown in Figure 3-2, but the exact variation in refractive indices with temperature is individual to the particular LC.

Chapter 3 Liquid crystals

1.7- - ne

s: g •a

c Nem atic phase

1.6— yi iso D > O eg Isotropic phase no 1.5— 60 50 8 0. 30 40 70 Figure 3-2 Change in birefringence of a typical nematic LC with

temperature. After [Pelzl et al. 1975]

Temperature (degrees C)

It can be seen from Figure 3-2 that the principal refractive indices and have different temperature dependencies. In this particular case, decreases strongly with increasing temperature, but there is only a slight change in with temperature. The birefringence disappears suddenly at the clearing temperature [Demus et al., 1998, p. 132]

3.3.3 Changes in a LC with application of an electric field (dielectric

anisotropy)

NLCs have a different dielectric constant perpendicular and parallel {s/j) to the director. This dielectric anisotropy {As=sif-£j) leads to a reorientation of the director when an electric field, E is applied along the z axis [de Gennes & Prost, 1993, p.l34]. As for birefringence, the dielectric anisotropy is highly temperature dependent, and this is shown in (Figure 3-3).

30~~ D ielectric con stan t 10“ ' 140 120

Tem perature (d eg rees C)

Figure 3-3 Change in Dielectric Constant of the Nematic Phase

of 4-aminobenzonitrile with temperature. After [Schadt

1972].

The similarities between Figure 3-2 and Figure 3-3 are not surprising, as the two indices of refraction o f a LC equal the square root of the corresponding relative permittivities.

3.3.4 Energetic Anisotropy

When an electric field is applied to a NLC, the director reorientates itself so it assumes the position of minimum free energy This means that the molecules attempt to rotate to align themselves with the applied electric field. However, the viscosity and elastic forces within the LC compete with the electric field to keep the director in its ‘resting’ position. The director position that results depends upon the relative effects of the external electric field and these internal forces which are present in the LC. In a NLC these elastic forces are splay, twist and bend and are defined as;

Splay= '/2 K ,[V -n] ^ Twist= K ;[n ( V x n ) ] ' Bend=H K jin x ( V x n ) |,2 equation 3-2

where V -n = div n and V x n = cu rl n [Yeh & Gu, 1999, p.404]. In these equations n is the vector representing the director orientation and n is the unit vector along this direction.

" A similar effect occurs on the application of a magnetic field, because of the anisotropy of the magnetic susceptibilities parallel and perpendicular to the director.

Chapter 3 Liquid crystals

Splay

T w ist B end

Figure 3-4 Principle deformations in liquid crystals (after [Collings & Patel 1997, p. 10])

Ki, K], and K3 are the respective Frank elastic constants which describe the ‘stiffness’ of the LC, and are generally different from each other [Collings & Patel, 1997, p.9]. (n a n d -n are indistinguishable [deGennes & Prost 1993, p. 100]). Combining these it is seen that if the director has the unit vector n the free energy per unit volume (Fv) of a non-chiral nematic liquid crystal can be written as [deGennes & Prost 1993, p. 102]:

Fv = 1/2 K i[ V- n] ^ + '/2 K2[ n • ( VX n )]‘ + 16 K31 n x ( V x n) equation 3-3

In an unswitched twisted nematic LC (see s. 3.4.2 below), splay and bend equate to zero, so twist is the only elastic force present [Collings & Hird, 1998, p.32]. The behaviour of the director in a TNLCD is governed by the combination of the electric field applied and the elastic forces. The Freedericksz transition occurs when the force exerted by the electric field is greater than the forces that keep the twisted structure. At this point the twist begins to straighten (see below).

3.4

Liquid Crystai Dispiays

The anisotropies of the NLC, coupled with its fluidity, are used in LCDs. The dielectric anisotropy means that applying an electric field can change the orientation o f the director, and the optical anisotropy means that the material is biréfringent. The optic axis depends on the director orientation, and this can therefore be varied by the application of an external electric field. The polarisation of incident (polarised) light can therefore be changed (s.2.4.2). If the display is viewed through crossed (or parallel) polarisers this polarisation change is converted to an intensity change. There are several types of LC which are used in displays. The only type that will be covered in this thesis is the twisted nematic LCD. A comparison between the twisted nematic LCD and a parallel aligned nematic spatial light modulator will be made at the end o f this chapter (s.3.5).

3.4.1 Alignment layers

For the LC to be useful in a display, the molecules must be oriented in the required direction. This is usually achieved by treating the surface of the container (the LC cell), so that the molecules have a particular orientation. This ensures a single domain, and so reduces the scattering seen in an unaligned sample. In the device studied in this thesis, the inside surfaces of the glass cells are treated with polyimide, which is then mechanically rubbed to produce tiny grooves in the surface. When the LC cell is then filled with LC, the nematic molecules align along the rubbing direction. Much work has been done on explaining how a NLC aligns on a rubbed alignment layer (e.g. [Chung et al., 2000]). One theory is that it is energetically unfavourable for the long LC molecules to be distorted, so they lie along the grooves. The alignment layer also controls the pretilt; in the TNLCD, to avoid an ambiguity of twist direction, it is necessary to anchor the LC molecules to the substrate so that they are tilted slightly away from, rather than being in the plane of, the substrate. This tilt away from the substrate (the pretilt) leads to one twist sense of rotation being preferred rather than the other. The size of this pretilt angle depends on the exact monomer structure of the polyimide alignment layer [Stohr & Samant, 1999].

Alignment layers are used in two areas in this thesis: firstly in the LCD as described above, and secondly to pattem the LC polymer when making a test security mark. The making of the security marks will be described in Chapter 8.

Chapter 3 Liquid crystals

3.4.2 The twisted nematic liquid crystal display

A TNLCD is formed by aligning the director so that it twists through 90°, like a spiral staircase, from one surface of the cell to the other. This is shown in Figure 3-5 below.