Surface ordering parameter

In addition, the square of the surface order parameter is proportional to the chemical reactivity profile of the twin domain wall interface at the surface (Locherer et al. 1996, Houchmanzadeh et al.(1992). Intuitively, one would expect the chemical reactivity of the surface to be largest at the centre of the twin domain wall, falling off as the distance from the centre of the wall increases. Contrary to the expected behaviour, a more complex behaviour is found. The reactivity, a monotonic function of Q, is expected to fall off as the distance from the centre of the wall increases, but only after if has reached a maximum of a distance of - 3 IF from the centre of the domain wall. If such a structure is expected to show particle adsorption (e.g. in the MBE growth of thin films on twinned substrates) we expect the sticking coefficient to vary spatially. In one scenario, adsorption may be enhanced on either side of the wall while being reduced at the centre. The real space topography of the surface is determined by both sources of relaxation-twin domain wall and the surface. These are distinct and, when considered separately, the wall... 

Fig. 67. Order parameter profiles m(z)/mt, associated with surface-induced disorder. The coordinate z measures the distance from the surface (z = 0). is the bulk correlation length and mu the bulk order parameter. If ease (a) persists up to the first-order transition temperature Tc, this means the surface stays ordered up to 7 c, while case (b) shows surface induced disordering a layer of thickness L gets disordered already at T <71, and as T — Tc the (delocalized) interface at mean position z = L from the surface advances into the bulk, fJ(7 ) -+ oo as T - Tc, and the surface order parameter mj = m(z = 0) then vanishes continuously, mj a (1 - T/Tc). From Dasch et al. (1988).

We now consider the interface between a vacuum and a system that undergoes a first-order (i.e., discontinuous) order-disorder transition in the bulk at a temperature Tc. Due to missing neighbors at a surface, we expect that the order parameter at temperatures T < Tc is slightly reduced in comparison with its bulk value (fig. 67). If this situation persists up to T > T, such that both the bulk order parameter < >(z oo) and the surface order parameter 4> = z = 0) vanish discontinuous the surface stays ordered up to Tc, a situation that is not of very general interest. However, it may happen (Lipowsky, 1982, 1983, 1984, 1987 Lipowsky and Speth, 1983) that the surface region disorders somewhat already at T < Tc, and this disordered layer grows as T T and leads to a continuous... 

The surface order parameter is temperature independent if the W2 term in the denominator prevails. In this case, So is determined completely by the short range interactions between the liqnid crystal and substrate. Otherwise, it increases with decreasing temperature on approaching the transition into the liqnid crystal phase. 

A good fit of (2.14) to the experimental data is obtained by varying only two parameters, Sq and the temperature independent contribution C. The value obtained for Sq is 0.08 0.03 and does not vary with temperature in the whole temperature range of about 15 K above Tni- It is larger than the surface order parameter of the same liquid crystal in contact with inorganic Anopore membrane, but still considerably smaller than the bulk nematic value at the transition temperature. This indicates that only a partial orientational wetting takes place in the isotropic phase of the PDLC material and that the... 

In general, the ellipticity coefficient is temperature dependent because of the temperatm e dependence of the correlation length (T) and the surface order parameter 5q(T). It increases by approaching the isotropic-nematic phase transition from above. By measuring ps(T) one can therefore directly determine the product T)Sq T), and, if we assume a power law dependence of (T), the temperature dependence of the nematic order parameter at the surface Sq T) can be extracted. 

The surface order parameter So shows very interesting features. Fig. 10.5 illustrates the calculated dependence of So on temperature with parameters of a liquid crystal 5CB. The different curves correspond to the different values of the surface potential. According to the positive sign of the surface potential W, we see an expected increase in the orientational order in the surface nematic phase (negative values of T-Tni). Further, the increasing potential W shifts the N-I transition point to higher temperatures. At W = W, the phase transition at the surface disappears and the surface order parameter becomes a continuous functimi of temperature. For high values of the surface potential, the orientational order at the interface remains finite even at temperatures well above the N-I transition point in the bulk. 

Some solid surfaces induce disorder in nematic liquid crystals. It means that the order parameter at the interface is lower than the bulk value. For instance, evaporated SiO layers of a certain thickness due to their roughness decrease the order parameter of MBBA from the bulk value Sb 0.6 down to So 0.1-0.2. In some cases, the surface order parameter may be equal to zero (surface melting). 

This theory employed a purely macroscopic point of view and used a continuum theory which had been modified to include a surface order parameter Qij and an easy axis. 

In order to make a more qualitative discussion, it will be necessary to find a method to measure the coefficients k and Att, which determine the value of a, and to measure the surface order parameter S . Furthermore, the direction of the easy axis must be determined for the oblique evaporated surface exactly... 

The TIR and ATR effects are not the only possible phenomena which are useful in studying the surface properties such as the director orientation at the boundaries, the surface order parameter, the anchoring energy, etc. Such useful techniques as Brewster angle measurements [215] and ellipso-metric studies [216] should also be mentioned. But the discussion of these methods is beyond the firamework of this book. 

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