Surface anchoring energy polar

Various types of surface-anchor interactions are responsible for the adsorption of a dispersant to the particle surface. These include ionic or acid/base interactions sulphonic acid, carboxylic acid or phosphate with a basic surface (e.g., alumina) amine or quaternary with an acidic surface (e.g., silica) H-bonding surface esters, ketones, ethers, hydroxyls multiple anchors-polyamines and polyols (H-bond donor or acceptor) or polyethers (H-bond acceptor). Polarizing groups (e.g., polyurethanes) can also provide sufficient adsorption energies and, in nonspecific cases, lyophobic bonding (via van der Waals attractions) driven by insolubility (e.g., PMMA). It is also possible to use chemical bonding, for example by reactive silanes. 

Here, the quantities JVo, Wa and Wp stand for the isotropic, azimuthal, and polar anchorings, respectively. The unit vectors % and point along the NP symmetry axis and perpendicular to it. W is integrated over the particle surface, neglecting its end parts. The resulting surface-anchoring Ifee-energy penalty is... 

When the liquid crystal director n is aligned along the direction specified by the polar angle G and azimuthal angle (p, the anisotropic part of the surface energy - referred to as the anchoring energy function - of the liquid crystal isfs=fs G,(p). When G = Gg and

[Pg.38]

It should be noted that there is currently some discrepancy between the values of the flexoelectric coefficients derived by various methods even for the same material, in particular, in MBBA. This may be caused by difficulties in calculating the real values of the anchoring energy of the molecules to the surface, or by not allowing for the sinrface polarization of the nematic liquid crystal caused by the polar nature of its molecules [189]. 

In general, the elastic term includes the elasticity related to the reorientation of the director (nematic moduli T ), and to a change in the tilt angle (coefficients a, b, c, etc., of the Landau expansion see e.g. Eq. (10)). The corresponding expression for gj is very complex and may be found in Pikin [7]. The surface energy includes both the dispersion and the polar terms of the anchoring energy Wg. Below we consider a few rather simple cases. 

In a chiral compound, the liquid crystalline structure itself possesses a polarity which interacts with the surface. At the surface of a smectic C liquid crystal, the ferroelectric polarization P points preferably either towards or away from the surface, depending on the material [104, 105]. Conversely, if the surface director of a chiral nematic liquid crystal is tilted, a polarization (dependent on the tilt angle) is created perpendicular to the tilt plane [106]. In principle, the presence of this polarization makes a contribution to the anchoring energy this chiral contribution is, however, too small to be measured [107]. 

We consider a nematic cell located between the two planes located at X3 = 0 and Xs= as illustrated schematically in FIGURE 1. The easy directions at the top and bottom substrate surfaces are denoted by the unit vectors and e , respectively. Generally the Rapini-Papoular energy has been written as a linear combination of a polar angle anchoring energy... 

The surface anchoring en gy is geno-ally expressed as a sum of independent terms gse(0) and gs4(< >) for the polar and azimuthal angles. A new approach in which the anchoring energy is written as a two-dimensional function 0,4) has been prqiosed thew ically and investigated. The coupling... 

D. Shenoy, L. Beresnev, D. Holt, and R. Shashidhar, Tuning polar anchoring energy through chemical modification of photodimerized surfaces. Applied Physics Letters 80, 1538 (2002). 

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