Free energy distortion

In the one-constant approximation, the distortion free energy per unit volume is... 

The distortion free energy density can be expanded around its equiUbrium value go, but, in the simplest case, only quadratic components are held ... 

The director now has x and z components and 0(z) is measirred from the x-axis to the director in the xz plane. Calculation of the distortion free energy proceeds as before. 

The advantage of this approach is that the onset of failure is defined by a single parameter, the distortional free energy, while that the former method of Nagdi and Murch and Crochet required the determination of three new parameters in addition to those needed to describe constitutive behavior. 

The distortion free energy density is then the difference in free energies given by Eq. (86) between the distorted and undistorted states, that is ... 

The SmC phase possesses a mirror symmetry plane (the z-x plane) and a two-fold rotation axis along they axis. With these two symmetries the distortion free energy density (up to second order) takes the following form ... 

In the case of completely asymmetric hypothetical fluid nematic liquid crystals, this means that "only" 45 elastic constants are needed. However, as has been shovm by Frank (see Appendix C.l), in the case of nonchiral and nonpolar nematic liquid crystals of uniaxial symmetry, the distortion free energy, in general, can be written as... 

In the limit of small distortions aVn 1 a molecular size), the distortion free energy density approaches zero, which means that F can be expressed in powers of Viz. 

Taking into account (C.5), we can write the distortion-free energy as ... 

With these, and by utilizing the well-known operator identity, ax b x c) = b a c) - c a b), we can rewrite the distortion-free energy density in coordinate independent tensorial form as ... 

In general, more than one form of deformation will be induced by an applied external field. If all three forms of deformation are created, the total distortion free-energy density is given by... 

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... 

As for crystals, tire elasticity of smectic and columnar phases is analysed in tenns of displacements of tire lattice witli respect to the undistorted state, described by tire field u(r). This represents tire distortion of tire layers in a smectic phase and, tluis, u(r) is a one-dimensional vector (conventionally defined along z), whereas tire columnar phase is two dimensional, so tliat u(r) is also. The symmetry of a smectic A phase leads to an elastic free energy density of tire fonn [86]... 

A phase itself, the amplitude of the density modulation is constant and twist and splay distortions are forbidden, thus the expression for the free energy density simplifies to equation (C2.2.10). 

The evaluation of the elastic free energy AFei rests on the assumption that the root-mean-square distance between the ends of the chain is distorted by the same factor a representing the linear expansion of the spatial distribution. As in the treatment of the swelling of network... 

Smaller values of the activation free energy, Fa, due to the distortion of the shape of the free energy surfaces. 

Smaller values of the activation free energy due to (i) the distortion of the shape of the free energy surfaces and (ii) the increase of the resonance splitting, AJF, of the potential free energies for the classical subsystem due to the increased overlapping of the wave functions of the quantum particles. 

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