Orientational free energy

On the basis of an Onsager cavity (23) model of dielectrics applied to a polar solute with an intrinsic dipole movement /xr° in its rth electronic state, Mazurenko gives an equation for the orientational free energy of the solute molecule in a pure polar solvent environment, which can be identified as equivalent to u/jlpe chem, thus 2... 

Even if simple expressions for the directional field are not available, it is possible to draw certain conclusions about the other thermodynamic functions from (4.2). The orientational free energy Fi<>0 leads to the following additional contributions to the entropy, internal energy and heat capacity at constant volume... 

The sign of the anisotropies and Xa governs the behavior of the liquid crystal in an electric (E) or a magnetic field (H) field via an electromagnetic contribution, fem, to the orientational free energy density ... 

Any spatial distortion of n leads to elastic restoring torques, which are determined in the standard continuum description of nematics (exclusively used in this review) by three elastic constants Ki (splay), K2 (twist) and Ks (bend). In addition, the electric field E gives rise to an electric torque on the director. The balance of these torques, reflected in the resulting equilibrium director configuration, corresponds to the minimum of the orientational free energy J- n). For positive dielectric anisotropy (ca = — x) the dielectric torque (oc is destabihzing in the pla-... 

For the orientational free energy, we employ the conventional molecular field theory of Maier and Saupe [66], or its extension by McMillan [67], which includes both orientational ordering of the mesogenic cores and translational ordering of their centers of mass. It is given by... 

Clearly, a free energy of binding computed with (9), (10) and (13) refers to a highly restricted state of the dissociated ligand. In order to convert such a free energy to a free energy relative to a normal standard state with volume per molecule Vg and no restriction on the molecular orientation, the following term must be added... 

Figure 2 Examples of overlayer structures with appropriate notation, (a) fee (100) p(2X2) (b) fee (100) c(2X2) (c) fee (111) p(73 X 73>R30< (d) bee (110 ) p(2 X 1) and bee (110) p(1 X 2). The two orientations for the unit mesh in (d) are both possible because of the symmetry of the substrate they have the same free energy and are called degenerate.

Crystals have spatially preferred directions relative to their internal lattice structure with consequences for orientation-dependent physico-chemical properties i.e., they are anisotropic. This anisotropy is the reason for the typical formation of flat facetted faces. For the configuration of the facets the so-called Wullf theorem [20] was formulated as in a crystal in equihbrium the distances of the facets from the centre of the crystal are proportional to their surface free energies. ... 

Fig. 10. Free energy versus relative extension (r/lmax) for a dumbbell oriented in a longitudinal velocity gradient...

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