Relaxation and Dispersion

This time dependence may be characterized by introducing the concept of relaxation. It was first used by Maxwell in connection with elastic forces in gases. Later, Debye used it referring to the time required for dipolar molecules to orient themselves. Instead of applying a sinusoidal AC measuring signal and measure (e.g., admittance and phase shift). 

It is often stated that all electrical properties of biological materials are due to relaxation phenomena. However, the concept of relaxation is not so meaningful with frequency independent DC conductance the conductance is constant with time and does not relax. When DC voltage is switched on, the current starts immediately. 

Impedance theory and relaxation theory often do not include resonance phenomena, as these are usually not found in macro tissue samples in the frequency range from pHz to MHz. 

Dispersion (frequency dependence according to the laws of relaxation) is the correspondent frequency domain concept of relaxation permittivity as a function of frequency. Even if the concept of relaxation is linked with step functions, it can of course be studied also with sine waves. An ideal step function contains all frequencies, and dispersion can be analyzed with a step function followed by a frequency (Fourier) analysis of the response signal or with a sinusoidal signal of varying frequency. 

As we shall see in the next section, in a simple case of a single dispersion with a single relaxation time constant, there will be one permittivity level at low frequencies (time for complete relaxation) and a second lower level at higher frequencies (not sufficient time for the relaxation process studied). It will be a transition zone characterized by a frequency window with a characteristic center frequency. Therefore dispersion in relaxation theory often has a somewhat more precise meaning than just frequency dependence. Simple dispersions are characterized by a permittivity with two different frequency independent levels, and a transition zone around the characteristic relaxation frequency. In biomaterials, such levels may be found more or less pronounced. 

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