Planar anchoring energy

Fig. 7.9. Planar anchoring can allow for a lying helix structure but the elastic energy, especially in regions of opposite twist (marked by an arrow), leads to relaxation into the deformation-free standing helix texture. ...

At the free interface, Wh is the homeotropic anchoring energy and 9 the actual angle between n and the normal to the film. On the substrate, Wy is the planar anchoring energy and 9y the actual angle between n and the normal. 

AB diblock copolymers in the presence of a selective surface can form an adsorbed layer, which is a planar form of aggregation or self-assembly. This is very useful in the manipulation of the surface properties of solid surfaces, especially those that are employed in liquid media. Several situations have been studied both theoretically and experimentally, among them the case of a selective surface but a nonselective solvent [75] which results in swelling of both the anchor and the buoy layers. However, we concentrate on the situation most closely related to the micelle conditions just discussed, namely, adsorption from a selective solvent. Our theoretical discussion is adapted and abbreviated from that of Marques et al. [76], who considered many features not discussed here. They began their analysis from the grand canonical free energy of a block copolymer layer in equilibrium with a reservoir containing soluble block copolymer at chemical potential peK. They also considered the possible effects of micellization in solution on the adsorption process [61]. We assume in this presentation that the anchor layer is in a solvent-free, melt state above Tg. The anchor layer is assumed to be thin and smooth, with a sharp interface between it and the solvent swollen buoy layer. 

The modem chemist could not reasonably have expected either planar or pyramidal CH4 to be potentially isolable molecules, i.e. to be potential energy surface minima, and indeed as we have seen calculation indicates that they are not (and the inversion transition state for tetrahedral methane is not planar Chapter 1). Consider however the simple artifice of anchoring the basal bonds of pyramidal methane to a... 

The theoretical analysis of ffexodomains in planar nematics, which is briefly reviewed in the following, exploits the balance of torques by minimizing the total free energy E n). If not otherwise stated, an assumption of strong anchoring of the director n at the confining plates is used i.e. the director at the boundaries remains parallel to no x, irrespective of director distortions in the bulk of the nematic layer. 

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