Surface anchoring energy Rapini-Papoular

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 expression for the sur ce energy can also be predicted for other shapes of the sur ce energy which are different from the Rapini-Papoular energy type, for example the elliptic type, Legendre expansion [14], and so oa Thwe is presently a widespread intwest in the inclusion of the surface elastic moduli Kb and K24 in the theory to allow for novel contributions to the surfrice anchoring energy to be taken into account [23] (see Datareview 5.3). 

The contribution of the confining surface to the free energy depends strongly on the characteristics of the substrate. In the case where the surface induces a preferred orientation v of the director at the boundary, the intrinsic interactions orient the whole sample and the sample is aligned. Any deviation of the director at the surface from the induced orientation increases the free energy, and the term added to (4.3) is the Rapini-Papoular surface anchoring term [10]... 

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