Relaxation Maxwell-Wagner

The specific carrier-wave amplitudes (field intensities) which have been found to be effective in producing Ca ion efflux are discussed in terms of tissue properties and relevant mechanisms. The brain tissue is hypothesized to be electrically nonlinear at specific field intensities this nonlinearity demodulates the carrier and releases a 16 Hz signal within ljie tissue. The 16 Hz signal is selectively coupled to the Ca ions by some mechanism, perhaps a dipolar-typ +(Maxwell-Wagner) relaxation, which enhances the efflux of Ca ions. The hypothesis that brain tissue exhibits a slight nonlinearity for certain values of applied RF electric field intensity is not testable by conventional measurements of e because changes... 

We would expect intuitively that tan 0 emd the Deborah number De are related, since both refer to the ratio between the rates of an imposed process and that (or those) of the system. The exact shape of this relationship depends on the number and nature(s) of the releixation process(es). So let us anticipate [3.6.4 la] for the loss tangent of a monolayer in oscillatory motion, which describes a special case of [3.6,12], namely -tan0 = t]°(o/K°. Here, (o is the imposed frequency, equal to the reciprocal time of observation, t(obs) =< . The quotient K° /t]° also has the dimensions of a time in fact it is the surface rheological equivalent of the Maxwell-Wagner relaxation time in electricity, (Recall from sec. 1.6c that for the electrostatic case relaxation is exponential ith T = e/K where e e is the dielectric permittivity and K the conductivity of the relaxing system. In other words, T is the quotient between the storage and the dissipative part.) For the surface rheological case T therefore becomes The exponential decay that is required for such a... 

Equation (3) shows that the real part of the Clausius-Mossotti factor goes to a low frequency co = 0) limiting value of (o -cr )/(o +2cr ), i.e. it depends on the conductivity of the particle and the medium. At high frequency ( oo) the limiting value is 6p-6m)l Sp+2 m) and the polarization is dominated by the permittivity of the particle and the medium. From Eq. (4), the imaginary part of the Clausius-Mossotti factor is zero at both low and high frequencies at the Maxwell-Wagner relaxation frequency /mw " it has a value of p- m)l pF2 m) - (Jp-(Jm)l... 

ICPs behave like traditional metals existing in mesoscopic particle sizes. The Maxwell-Wagner relaxation found in both cases could be facilitated by the anisotropic (bipolar) structure. 

The erythrocyte and erythrocyte ghost suspensions are very similar systems. They differ in their inner solution (in the case of erythrocytes it is an ionic hemoglobin solution in the case of ghosts it is almost like the surrounding solution they were in while they were sealed). The cell sizes in a prepared suspension depend both on the ion concentration in the supernatant and in the cell interior (70). Thus, the dielectric spectra of erythrocytes and erythrocyte ghost suspensions have the same shape, which means that there are no additional (except Maxwell-Wagner) relaxation processes in the erythrocyte cytoplasm thus, the singleshell model (Eq. 89) can be applied. 

The angular frequency comw = 2w/mw = 1/tmw is the Maxwell-Wagner relaxation... 

At still higher frequencies, the Maxwell-Wagner relaxation (o) tt>Mw) will be observable for those frequencies, ions cannot rearrange back and forth around the particle as fast as required by the field. 

Assuming (as it is reasonable) that for conditions in which the approximation ko 5> 1 is valid, the dynamic mobility also contains the (1 — Cq) dependence displayed by the static mobility (Equation (3.37)), one can expect a qualitative dependence of the dynamic mobility on the frequency of the field as shown in Figure 3.14. The first relaxation (the one at lowest frequency) in the modulus of u can be expected at the a-relaxation frequency (Equation (3.55)) as the dipole coefficient increases at such frequency, the mobility should decrease. If the frequency is increased, one finds the Maxwell-Wagner relaxation (Equation (3.54)), where the situation is reversed Re(Cg) decreases and the mobility increases. In addition, it can be shown [19,82] that at frequencies of the order of (rj/o Pp) the inertia of the particle hinders its motion, and the mobility decreases in a monotonic fashion. Depending on the particle size and the conductivity of the medium, the two latter relaxations might superimpose on each other and be impossible to distinguish. 

Schwan [12] and Asami [13] offered expressions describing experimentally observed kHz range incremental increases in permittivity Ae due to the Maxwell-Wagner relaxation (also known as "P-relaxation") process for biological cellular colloids ... 

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