Dielectric critical frequency

Some time ago we measured the dielectric dispersion of a plant virus particle and found a critical frequency in the kHz region, therefore in a region that may well correspond to the eventual maximum of your ultrasonic absorption. We were able to describe the mechanism leading to this dispersion in terms of the rotation of the complete virus particle and of the motion of associated (or bound) counterions on the elongated surface of the particle. 

Fig. 38. Helix-coil transition of a PBLG sample (Mw = 59000) in a DCA-CHa3 mixture (70 30) detected by ORD ( ) and by dielectric dispersion (O). (+) (US). Here d and e represent the quantities defined by Eq. (E-6) and Eq. (E-7), respectively, and tj f. denotes the critical frequency of the dispersion corrected for solvent viscosity...

By measuring the static dielectric constant of solutions of polar polymers in nonpolar solvents, one may calculate a statistical mean dipole of the macromolecule. With polar solvents interesting information can be obtained concerning the interaction between polymer and solvent molecules. Finally the study of relaxation phenomena, including the accurate determination of the critical frequencies may lead us to a better knowledge of the statistical unit and of its interaction with its environment. 

Do these critical frequencies associated with reproduction processes (or their ranges) correspond to the frequency of the dielectric loss peaks of... 

The dependences of the threshold of the Kapustin-Williams domains [68] and the critical frequency [79] on physical parameters are in good agreement with the theoretical estimations (5.43). Only a certain correction of (5.43) is needed to explain the variation of critical frequency for different substances [79]. However, the anisotropic dielectric regime of the electrohydrodynamic instability in homogeneously oriented nematic hquid crystals seems not to have been observed in experiment yet. 

The basic EW theory elucidated here has been directly extended to analyze electrocapillary effects under AC electric fields as well. For instance, if the AC frequency corresponds to a time scale that is less than the hydrodynamic response time of the droplet (typically 0.01 s for mm-sized droplets), the droplet shape and contact angle evolution can be described by employing instantaneous quasiequilibrium considerations in accordance with Eq. (13). On the other hand, for higher frequencies, the droplet response depends only on the r.m.s value of the applied voltage, so long as the liquid can be treated as a perfect conductor. However, beyond a critical frequency (a>c), the dissolved ions cannot follow the applied field and therefore, cannot screen the electric field from the interior of the liquid [2]). Far beyond a>c, the droplet behaves like a dielectric, and is effectively actuated by dielectrophoresis mechanisms. For homogeneous bulk liquids, a>c (Ti/si, where <7 and are the conductivity and permittivity of the liquid, respectively. For a t)fpical aqueous solution (such as NaCl, with cr 0.1 Sm ), o)c 10 s However, for demineralised water (tr 10 Sm ), a>c can be as low as 10 s . ... 

Many relaxation processes influence the dielectric spectra of FLCs. Apart from the usual l.f. and h.f. modes characterizing the reorientations of molecules around their principal axes, the Sm C phase shows at least two collective processes. One collective mode, the Goldstone mode (GM), is associated with the fluctuations of the azimuthal angle (the cone motion) it is observed in Sm C phase at low frequencies and is not an activated process. The second mode, the soft mode (SM), is connected with the tilt fluctuations its critical frequency falls in the kilohertz range, from ca. 50 to ca. 500 kHz. The soft mode shows a decrease of frequency in Sm A phase on approaching the transition Sm A -Sm C, but it survives to the lower temperature phase. In special conditions (e.g., after applying an appropriate strength of the bias field ) yet another collective mode can be observed (domain mode). 

Main quantities characterizing the properties of FLCs (the values of the tilt angle d, the spontaneous polarization P, the dielectric constant , the critical frequencies for particular collective modes) depend on intermolecular interactions caused by the chirality of molecules. " Thus the ferroelectricity of LCs must be sensitive to the intermolecular distance it must then be pressure dependent. The pressure studies of FLCs have been undertaken in a few labora-tories. - ... 

The dielectric spectroscopy of anisotropic fluids started in the 1970s by the extension of the Debye model from isotropic media (described in Appendix D) to uniaxial systems based on statistical mechanical Kubo formalism/ but no quantitative estimates about the critical frequencies or the susceptibilities were obtained. Quantitative estimates were given first on molecules with dipole moments along the long axis/ then for general dipole directions using the rotational Brownian picture in Maier-Saupe mean-field potential. This theory was subsequently refined in the 1990s.i ... 

The value of the relaxation time is based on dielectric constant studies of Oncley (140) at 25 , who showed that the protein underwent anomalous dispersion and conformed nicely to the simple Debye curve, exhibiting a single critical frequency ve — 1.9 X 10 cycles sec"S a low frequency dielectric increment of -f 0.33 g. liter and a high frequency increment of —0.11 g." liter. The data just presented have been discussed by Oncley (141) and by Wyman and Ingalls (241) with the aid of their nomograms. It appears from their analyses that the facts might reasonably well be reconciled with the assumption either of oblate ellipsoids with p = 3 and A = 0.3 — 0.4 or of prolate ellipsoids with p = H and = 0.3 — 0.4. On the assumption of prolate ellipsoids, however, it would be necessary to assume that there was no component of the electric moment parallel to the long axis (axis of revolution). In either case the two dielectric increments correspond to an electric moment of about 500 Debye units (140). 

The response times for both field- and conduction-induced phenomena can be changed by the presence of a second voltage source whose frequency is above some critical cutoff frequency, while the main source has a frequency less the critical frequency. For dynamic scattering, the critical frequency is /c, which is inversely proportional to the dielectric relaxation time of the fluid. For an applied frequency / > /c, the conduction torques do not affect the fluid and, through... 

For field-effect materials, the critical cutoff frequency occurs only in materials that have positive dielectric anisotropy at low frequencies. Above the critical frequency, the dielectric anisotropy is negative. Several materials have been developed with a critical frequency as low as a few kHz at As with dynamic scattering, the ap-... 

The two-frequency approach can also be used with field-effect materials. Bucher, Klingbiel, and Van Meter have shown that the low-frequency threshold voltage for the twisted nematic effect is increased by the superposition of a signal whose drive frequency is greater than the critical frequency where the dielectric anisotropy becomes negative. They claim that... 

ER effect is dependent on the distance between the adjacent particles. This parameter increases for highly concentrated suspensions of well-dispersed, small, closely packed particles. TTiese ERF modifications result in smaller particle-to particle distances, higher effective "surface area," and higher dielectric constant of created microcapacitors, according to Eqs. 7-1 through 7-5. For a critical frequency at 10 kFlz the value for the contact capacitance becomes Qontxct 100-1000 pF/cm exceeding the base oil capacitance by a factor of 100-1000. 

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