Elastic Gibbs energy

The elastic Gibbs energy introduced in Chapter 4 must be extended to include the swelling deformation, since the volume of the network will now change. The deformation ratio for isotropic swelling is defined as = V/ Vq, where Vq is the volume of the dry rubber. The elastic Gibbs energy is then ... 

These g values are defined per unit volume. Let us now put in the interface energy previously left out. If V = 4/3-7rr3 is the volume of the nucleus, the net Gibbs energy change is (neglecting elastic misfit energies)... 

Often, however, it is more realistic to abandon the model of a discontinuous interface. Segregation of impurities and other point defects, as well as elastic and electric fields, broaden the interface region. For this extended boundary, we can formulate j the Gibbs energy of Eqn. (10.1) as (< = A,B) j... 

In a foregoing section, we mentioned that field forces (e,g., of the electric or elastic field) can cause an interface to move. If they are large enough so that inherent counterforces (such as interface tension or friction) do not bring the boundary to a stop, the interface motion would continue and eventually become uniform. In this section, however, we are primarily concerned with boundary motions caused by chemical potential changes. From irreversible thermodynamics, we know that the dissipated Gibbs energy of the discontinuous system is T-ab, where crb here is the entropy production (see Section 4.2). Since dG/dV = dG/dV = crb- T/ A < ), we have with Eqn. (4.8) at the boundary b... 

Let us assume that the martensite particle has grown in the form of an oblate spheroid, the volume of which is (4-n/3with c as the semi-thickness of the spheroid. The total Gibbs energy change for the formation of this particle includes a chemical, an elastic, and an interface energy term. It can be appropriately written as... 

Following the derivation in Section 11.3.3, the Gibbs energy of elasticity depends on the effective chain content Ve in the cross-linked system before cross-linking as well as on the expansion factor a = ax = oLy = az. From Equation (11-34), the following is obtained with = -TASei ... 

In a somewhat reduced approach, the elastic Gibbs free energy of a ferroelectric crystal is given (Uchino 1995) by ... 

Without loss of generality, let us choose the model of the new phase as a Hne (strictly stoichiometric) intermediate phase with composition C = Ci = 0.5, and exclude the elastic contributions to the Gibbs energy. The parent phase in the vicinity of the phase transition points will be described by the ideal solution law and will be also denoted as the a-phase. In fact, the model of regular solution would be more reasonable since the existence of intermediate phases usually correlates with negative mixing energy. Yet, for simpHcity, below we restrict ourselves to the... 

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