Thermodynamics and forces in charged solid insulators

摘要

Thermodynamic framework is a powerful method to synthesise our knowledge on the material properties, but do not suffer the less step away. Compared to the neutral matter, dielectric thermodynamic has the difficult task to tackle with distantinteraction effects. This is overcome by introducing fields and related properties of the vacuum (energetic as stress).The thermodynamic description of the medium is achieved by adding two new variables to the classical description (temperature T deformation 250L? compositionγ{sub}α,...) These variables are the polarization 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 characterized 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 beadded.f{sub}(vol)(T,ε,γ{sub}α,P, E) = f{sub}(vol)(T,ε,γ{sub}α,P) +1/2ε{sub}0E{sup}2 From the thermodynamic potential the physical quantities (entropy energy, chemical potentials, stresses) are obtained as usually using partial derivatives. Themechanical forces that a dielectric can support are deduced after having added Maxwell electric tensor: σ{sub}(el)=ε{sub}0(E&D-1/2E.Dδ) whereδ is the unit tensor, D=ε{sub}0E+P and & the tensor product.The equation giving the evolution toward the equilibrium are also obtained; noticeably for the polarisation P. It is governed by the associated thermodynamic force: Ap=&f{sub}(vol)/&P-E.Then partial equilibrium between the matter and the electric field is considered We show that at the polarisation equilibrium:&f{sub}(vol)/&P=Eand a new internal variable D (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)Furthermore the electric field is given byE=&f{sub}(eq)/&DThe previous results are illustrated with expressing the electro-mechanical term of the linear polarisation: Δf{sub}(vol)(matter) = P{sup}2/2Kwhere a priori K=K(T,ε). Then, the classical expressions are recovered, noticeably for the polarisation equilibrium:P=KE.In the case of a linear dependence of K inεand for an isotropic medium:K=K{sub}0+1ε+α{sub}2 trερ, whereα{sub}1 etα{sub}2 are the classical electrostriction coefficients. The corresponding polarisation stresses are deduced (or electromechanical stresses at the polarisation equilibrium): σ{sub}(el-mec)=1/2(α{sub}1ExE + α{sub}2 E{sup}2δ) From these stresses and the Maxwell tensor are deduced the electrical force and the electromechanical force that are suffered by any matter element in a homogeneous dielectric: f= -1/4(α1 +2α{sub}2 gradE{sup}2 +(1-α{sub}1/2ε{sub}0)ρ{sup}(ext) where ext are the extinsic charges.We applied the thermodynamic procedure for evaluating the forces in a plane capacitor. The procedure is also applied for recovering the expression of the polaron energy. Also, in a model of continuous matter the energy components (total energy, activation energy) of the charge trapping by an ion are analysed.