Free energy of elasticity

For the free energy of elastic deformation of network chains, Fel, the following expression of the classical theory of rubber elasticity can be used [21] ... 

Gaussian chains (Flory 1953), the Gibbs free energy of elastic deformation AGw scales with the deformation ratio as... 

The mean values of the chain end-to-end vectors are displaced affinely with the macroscopic extension in the James-Guth theory (James and Guth 1943). The fluctuations of the junctions are independent of the deformation of the sample. As a consequence, the end-to-end vectors are deformed not affinely. The free energy of elasticity of the free-fluctuation limit is... 

Let us consider first the case of a nematic film in which the initial undisturbed orientation of the director is throughout parallel to the glass plates. The magnetic field H is now applied perpendicular to the director and to the plates (fig. 3.4.1(a)). For this geometry, n = (cos, 0,sin, H = (0,0,7/) and G = (O,O, fa sin0). The free energy of elastic deformation (3.3.6) reduces in this case to... 

The free energy of elastic deformation per unit volume is given by (3.2.7). 

Making use of (5.8.1), and assuming the layers to be incompressible, the free energy of elastic distortion may be written in the form... 

The approach is based on a combination of the linear viscoelastic theory with elements of the elasticity theory developed by Erman, Floiy and Monnery in which the free energy of elasticity, AA i, is considered as a sum of the phantom component, AApj, and a component of steric entanglements determined by interlacing chains andjunctions. ... 

Figure 12 The dependence of the total free energy (b) and its additive components (a) free energy of non-Coulomb interactions F,d, free energy of elastic deformation Pei, and free energy contribution of translational entropy of counterions firansi on the swelling ratio for uncharged (i) and weakly charged (ii) gels.

The first term is the free energy of elastic deformations of gel... 

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