Threshold field strength

All sorts of biological particles of different effective complex dielectric constants behave similarly in an electrolyte medium. Figure 5 illustrates this fact. Neumann and Rosenheck s (AO) results on chromaffin vesicles are combined with E. coli data obtained by Sher and erythrocyte data obtained by Sher and silicon particles (full circles), also by Sher (A5). The total material fits convincingly the solid line of slope -1.5 which is demanded by the theoretical requirement that particle volume must be inversely related to the square of the threshold field strength mentioned above and discussed in greater detail elsewhere (Schwan and Sher (5A)). 

Figure 5. Threshold field strength values as a function of particle size (49).

Fig. 9.26 The nonlinear conductivity of (Fa)2PFe-and (Per)2PFe crystals. The threshold field strengths Fj lie at about 1 V/cm and 0.1 V/cm. Inset the differential resistance and the noise voltage of a (Fa)2PFe crystal as well as the noise voltage from a reference resistance of the same value (see text). After [39].

If, usually above a threshold field strength, the field-induced processes involve massive structural changes (beyond polarization, elongation, and reorientation) such as phase transition or percolation of the system, then the relaxation signals may become more complex, and An t) cannot be described by Eq. (16). Such behavior is easily recognized, for instance, from the nonmonotonic course of the forward relaxation or from the stretched exponential nature of the reverse relaxation. The analysis of such signals is, of course, more problematic, and the use of results of additional experiments is necessary for their interpretation. 

Our task now is to find the threshold field strength for the distortion and the distribution of the director n(z) over the cell thickness above the threshold. This time we shall take an initial homeotropic alignment, case (b) in Fig. 11.15. In its modem form, the theory was developed by Saupe [16]. 

A distinctive feature of (5.55) is that it predicts the threshold field strength, not the threshold voltage. This is because of the particular distribution of the charge studied by Turnbull [105] and illustrated in Fig. 5.19(a). The space charge is concentrated near the electrodes at a depth approximately equal to the Debye screening length... 

J/m. Shao et al. [103] have found a similar field-induced phase transition, namely a stabilization of the SmA phase with respect to the TGBa phase due to an electric field. The threshold field strength of this transition is decreasing with increasing temperature, and the transition is irreversible. Thus, it has been proposed for optical storage applications. 

The optical pattern of the perturbed state in the high frequency (/>/,) region is characterized by periodic parallel striations of a much shorter period (a few micrometers) than the Williams domains [23]. Above the threshold, these striations move, and bend and give rise to what has been called a chevron pattern (Fig. 5) [8-12,17,23-26]. In this regime, the threshold is determined by a critical field rather than a critical voltage. The threshold field strength increases with the square root of the frequency. The spatial periodicity of the chevron pattern is also frequency dependent it is... 

Table 2. The effect of an ether linkage position on the threshold field strength.

Example 3.8. Determine the threshold field strength for lead at 3.7 K, assuming that the parabolic rule for the transition curve is valid. 

Figure 3.24 shows a threshold field strength for lead of 600 G at 3.7 K. Thus, the parabolic relationship adequately represents the transition curve for lead. 

For this series a rather strong influence of the number of carbon atoms in the flexible spacer on the nematic orientation was reported. Increasing n from 5 to 9 produced an increase in the threshold field strength from 4 to 15 kG for a 1-min orientation time. No evidence of alignment was observed after 200 min for the polyester with A2 = 12. Hardouin suggested that... 

Figure 11 Orientation angie of the microstructure with respect to the field direction as function of the electric field strength. A value of 90° corresponds to cylinders oriented parallel to the substrate, whereas 0° corresponds to cylinders oriented normal to the substrate, that is, parallel to the field direction. The shaded region denotes a range in electric field strengths where both parallel and perpendicular cylinder alignment is observed. Et is the threshold field strength, above which full alignment parallel to the applied field is observed. Reproduced with permission from Thurn-Albrecht, T. DeRouchey, J. Russell, T. P. Jaeger, J. M. Macromolecules 2000, 33, 3250. " ...

---