Models for the Complex Permittivity of Dielectric Sorbent-Sorbate Systems

3 Models for the Complex Permittivity of Dielectric Sorbent-Sorbate Systems 

Let us consider again a sorption system consisting on a sorbent-sorbate phase and a sorptive gas located between the plates or cylinders of a capacitor, Fig. 6.8. This system is an electric network which for small applied voltages (U(t)) can be interpreted as a Linear Passive System (LPS). That is a stimulus (U(t)) applied to the system creates a response, the electric current I(t), which is linearly related to U(t). However it may exhibit a phase shift and also lead to energy dissipation, i. e. Ohmian heat which, as a consequence of the Second Law of Thermodynamics at finite ambient temperature, never can completely be reverted again to electric energy. Linear Passive Systems can be found quite frequently in Physics. A mathematical theory of such systems has been developed by H. Kdnig and J. Meixner in the 1960 s, [6.27] and later on extended and applied to various stochastic processes, i. e. statistical physics by J. U. Keller, [6.28]. 

As the theory of LPS provides a fairly general and physically sound basis to develop models for the dielectric behavior of sorbent-sorbate systems, we here will present some of its main results. These then are used to develop an electric network model which includes the well-known Debye model of dielectric materials as a special case [6.24]. Another approach to model dielectric properties of solid sorption systems has been discussed by Coelho in [6.29], which however will not be considered here. 

Any voltage (U(t)) apphed externally to the material-filled capacitor. Fig. 6.8, will create a current (I(t)), which generally speaking is a functional of the voltage (U(t)). Hence we have a relation 

The functional (L) is assumed to have very general properties, as follows  

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