Energy bulk distortion

The first term is related to the bulk distortion energy, determined by the elastic deformation and external bulk field interactions. The second term is the surface contribution of the limiting surface D. The actual director field can be obtained by minimizing the energy. In a simple sandwich cell geometry (see Figure 4.27), the director (n(r)) can be expressed with the tilt angle as Q = cos (n k)> where k is the unit vector of the surface normal. 

Brooks [10] assumed the crystal is isotropic and considered the formation of a vacancy as an equivalent to creating new surface, equal to the area of one unit cell, being approximately the spherical surface of the atomic volume. He also assumed that the surface tension of the hole would shrink the vacancy size by distorting the rest of the crystal elastically. Then, the for atomic vacancy formation inside a bulk solid equals the minimum of the sum of the increased surface energy and distortion energy,... 

There is no reason why the distortion parameter should not contain an entropy as well as an energy component, and one may therefore write 0 = 0q-sT. The entropy of adsorption, relative to bulk liquid, becomes A5fi = sexp(-ca). A critical temperature is now implied, Tc = 0o/s, at which the contact angle goes to zero [151]. For example, Tc was calculated to be 174°C by fitting adsorption and contact angle data for the -octane-PTFE system. 

Returning to more surface chemical considerations, most literature discussions that relate adhesion to work of adhesion or to contact angle deal with surface free energy quantities. It has been pointed out that structural distortions are generally present in adsorbed layers and must be present if bulk liquid adsorbate forms a finite contact angle with the substrate (see Ref. 115). Thus both the entropy and the energy of adsorption are important (relative to bulk liquid). The... 

In crystals with the LI2 structure (the fcc-based ordered structure), there exist three independent elastic constants-in the contracted notation, Cn, C12 and 044. A set of three independent ab initio total-energy calculations (i.e. total energy as a function of strain) is required to determine these elastic constants. We have determined the bulk modulus, Cii, and C44 from distortion energies associated with uniform hydrostatic pressure, uniaxial strain and pure shear strain, respectively. The shear moduli for the 001 plane along the [100] direction and for the 110 plane along the [110] direction, are G ooi = G44 and G no = (Cu — G12), respectively. The shear anisotropy factor, A = provides a measure of the degree of anisotropy of the electronic charge... 

Coefficients K, Ki and in the expression for the distortion-Gibbs energy density, g, of a bulk nematic liquid crystal, with... 

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