Characteristic relaxation frequency

Freezing of a dipolar liquid is accompanied by a rapid decrease in its electric permittivity [8-10]. Following solidification, dipole rotation ceases and the electric permittivity is almost equal to n, where n is refractive index, as it arises from deformation polarisation only. Investigation of the dynamics of a confined liquid is possible from the frequency dependences of dielectric properties, which allows both the determination of the phase transition temperature of the adsorbed substance and characteristic relaxation frequencies related to molecular motion in particular phases. 

The elasticities and viscosities calculated from the oscillations as a function of the concentration are given in Figures 9 and 10. The two proteins show a completely different behaviour. The concentration dependencies for j -CS are fully in line with what we would expect for a slightly soluble surfactant. At fixed frequency, the elasticity increases while the viscosity decreases. This behaviour is observed for systems with a characteristic relaxation frequency larger than the applied frequency. Note, there is a peculiarity at the concentration where the isotherm shows a kink in the slope. 

There is a duality in the electrical properties of tissue. Tissue may be regarded as a conductor or a dielectric. In frequencies of 100 kHz or less, most tissues are predominantly electrolytic conductors. Therefore, we start Chapter 2 with a look at electrolytes. Bulk electrolyte continuity is broken in two important ways by electrode metal plates and by cell membranes. This break in continuity introduces capacitive current flow segments. At the electrodes, electric double layers are formed in the electrolyte the cell interiors are guarded by membranes. With high-resolution techniques, it is possible to extract important capacitive (i.e., dielectric) properties even at low frequencies, such as 10 Hz. At higher frequencies, such as 50 kHz, the dielectric properties of tissue (discussed in Chapter 3) may dominate. At the highest frequencies, tissue properties become more and more equal to that of water. Pure water has a characteristic relaxation frequency of approximately 18 GHz. 

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. 

The time constant and characteristic relaxation frequency can be defined in more than one way ... 

Characteristic times and relaxation frequencies of FLCs can be measured by plotting the Cole-Cole diagrams (see Chapter 2) [32, 46-49]. The dielectric response of the smectic A, near the phase transition, into smectic C phase is approximately one order of magnitude weaker than the corresponding response of the ferroelectric phase. The only contribution to the smectic A response is made by the soft mode with characteristic relaxation frequency [46-48]... 

According to the Rouse terminal relaxation time theory [14], a polymer solution always has a corresponding characteristic relaxation frequency Ochar)- Here, the codur is the (0.79 corresponding to the point of maximum curvature of the flow curve. Therefore the calculated M is believed to be the peak MW (Mp). Mp indicates the maximum probability of... 

Table 15.1 Values of the ionic conductivity, characteristic relaxation frequency and glass transition temperature for DHP with different Li content at room temperature...

Therefore, our electrical measurements (Figs 15.3a and b) clearly confirm that only ions (LF or Na ) appear to be mobile in the structure of the DHP. In addition, the characteristic relaxation frequency,/o, was extracted from these data, as indicated in Figs 15.3(a) and (b).The characteristic relaxation frequency (/o) is also shown in the log/(Hz) versus -Z" curve, where the part of the curve that indicates high frequency corresponds to a bulk relaxation phenomenon and the plateaued regions are related to <7. ... 

Note the displacements of/o and a with increasing lithium and sodium content, suggesting that there is some kind of interaction between lithium/ sodium ions and the DPH matrix. In addition, a comparison of the characteristic relaxation frequencies of the two ions (Figs 15.3c and d and Tables... 

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