Thermodynamics and forces in charged solid insulators

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A thermodynamic framework is a powerful method to synthesise our knowledge on the material properties. This is done by introducing fields and related properties of the vacuum. The thermodynamic description of the medium is achieved by adding two new variables to the classical description (temperature T, deformation E, composition /spl gamma//spl infin/). These variables are the polarisation P for the matter and the Maxwell (or mean) electric field E for the vacuum if the free energy is used as thermodynamic potential to characterize the system. Then, the expression of the matter free energy depends on the polarisation P and the vacuum related term that only depends on E must be added: f/sub vol/(T, /spl epsiv/, /spl gamma//sub /spl alpha//, P, E)=f/sub vol/(T, /spl epsiv/, /spl gamma//sub /spl alpha//, P)+ 1/2 /spl epsiv//sub 0/E/sup 2/. From the thermodynamic potential the physical quantities (entropy, energy, chemical potentials, stresses) are obtained as usual using partial derivatives. The mechanical forces that a dielectric can support are deduced after having added the Maxwell electric tensor: /spl sigma//sub el/=/spl epsiv//sub 0/(E/spl otimes/D- 1/2 E.D /spl delta/) where /spl delta/ is the unit tensor, D=/spl epsiv//sub 0/E+P and /spl otimes/ the tensor product. The equation giving the evolution toward the equilibrium is also obtained. It is governed by the associated thermodynamic force: A/sub P/=/spl delta/f/sub vol///spl delta/P-E. Then partial equilibrium between the matter and the electric field is considered. We show that at the polarisation equilibrium: /spl delta/f/sub vol///spl delta/P=E and a new internal variable D=/spl epsiv//sub 0/E+P (displacement field) must be substituted in replacement of E and P while the value of the thermodynamic potential remains unchanged f/sub eq/(-, D)=f/sub vol/(-, P, E).