Low-frequency dielectric dispersion

Baur and Stockmayer (13) have recently observed a low frequency dielectric dispersion zone in liquid poly(propylene) oxide which is dependent upon molecular weight in the manner of Eqs. (2.8) and (2.9). Due to the method of synthesis of their samples, there are only infrequent reversals of dipolar sense along the chain, and the model discussed above... 

Schwarz, G. (1962) A theory of the low-frequency dielectric dispersion of spherical colloidal particles in electrolyte solution, Journal of Physical Chemistry 66, 2636-2642... 

Einolf, C. W. Carstensen, E. L. Low-frequency dielectric dispersion in suspensions of ion-exchange resins. J. Phys. Chem. 1971, 75, 1091-1099. 

State conduction and other dielectric results have been reported by Morgan and Pethig (1986), who concluded that the low-frequency dielectric dispersion had to be associated with interactions between ions and metal electrodes. 

One of the most characteristic problems in the measurement of low frequency dielectric dispersion is that the ratio between the resistive and capacitive component of Z (tu) is very large. In other words, the phase angle is high. Therefore, accurate measurements of the latter component require an extremely powerful phase-sensitive detector. A second, nagging, problem, is electrode polarization, which may become particularly troublesome at low co. There are two options to avoid, or suppress, electrode polarization ... 

For a particle diameter of about 1 fim, x 2 x l(F cm-, and g a 0.2, a Asg of ca. 3SOOO is obtained at room temperature. The dispersion occurs in the low-frequency range of 1—10 kHz, in quantitative agreement with the relaxation time given by (46). There can be little doubt that the still more remarkable low-frequency dielectric dispersion of biological cells and tissue is also due to such counterion-polarization effects. 

Integrated electrosurface investigations, which include measurements of the mobile charge ct , by means of low-frequency dielectric dispersion (Lyklema et al. 1983) and electrokinetic charge by electrophoresis were applied by many groups in the world for particle surface... 

Biopolymers are both polar and ionic in character. They exhibit features characteristic of both polymeric solutes and of colloidal particles, giving complex behaviors difficult to describe simply. Enormous responses can occur at low frequencies. Minakata, Imai, and Oosawa have studied theory and experiment for solutions of the polyelectrolyte, tetra-JV-butylammonium polyacrylate (BU4NPA). They observed two low-frequency dielectric dispersion peaks, one at about 100,000 Hz, the other at about 1000 Hz. They suggest that the former is due to a bulk-bulk, Maxwell-Wagner process and that the later and slower process is... 

Martinsen, 0.G., Grimnes, S., Karlsen, J., 1998a. Low frequency dielectric dispersion of microporous membranes in electrolyte solution. J. Colloid Interface Sci. 199, 107—110. 

The last equation demonstrates that the starting point for the solution of the problem is the calculation of ci(double layer (this makes low-frequency dielectric dispersion [LFDD] measurements a most valuable electrokinetic technique). Probably, the first theoretical treatment is the one due to Schwarz [61], who considered only surface diffusion of counterions (it is the so-called surface diffusion model). In fact, the model is inconsistent with any explanation of dielectric dispersion based on double-layer polarization. The generalization of the theory of diffuse atmosphere polarization to the case of alternating external fields and its application to the explanation of LFDD were first achieved by Dukhin and Shilov [20]. A full numerical approach to the LFDD in suspensions is due to DeLacey and White [60], and comparison with this numerical model allowed to show that the thin double-layer approximations [20,62,63] worked reasonably well in a wider than expected range of values of both and ku [64]. Figure 3.12 is an example of the calculation of As. From this it will be clear that (i) at low frequencies As can be very high and (ii) the relaxation of the dielectric constant takes place in the few-kHz frequency range, in accordance with Equations (3.56) and (3.57). 

Sengwa, R.J., Soni, A., 2006. Low-frequency dielectric dispersion and microwave dielectric properties of dry and water-saturated limestraies of the Jodhpur region. Geophysics 71 (5), 269-277. 

One such phenomenon is the low-frequency dielectric dispersion (LFDD) of suspensions. This is the denomination given to the frequency dependence of the permittivity of dispersed systems for applied electric field frequencies close to characteristic frequencies of relaxation (typically in the kHz to MHz range) in the electrical double layer. A significant effect has been reported of the properties of the medium, of the particle, and of their interface on the relaxation pattern of the permittivity, in particular number of relaxations observed, natural frequencies, and amplitudes of those relaxations. This explains the increased interest in the determination of the permittivity of colloidal systems during the last decade or so [19-26]. In this contribution, we will show results that clearly demonstrate that the presence of the SPs affects the amplitude and characteristic frequency of the LFDD far more than could be explained by simple considerations of accumulation of effects. 

Delgado, A.V., Arroyo, F.J., Gonzalez-Caballero, R, Shilov, V.N., and Borkovskaya, Y.B. 1998. The effect of the concentration of dispersed particles on the mechanisms of low-frequency dielectric dispersion (LFDD) in colloidal suspensions. Colloids Surf. A 140 139-149. 

Maxwell-Wagner polarization (20-23) arises in heterogeneous specimens containing domains of different conductivity and/or dielectric constant. This phenomenon can be distinguished by low-frequency impedance dispersions that extend over several decades of frequency. In addition, the magnitude and frequency dependence of Maxwell-Wagner polarization is related to spatial fluctuations of dielectric... 

Native DNA. The dielectric dispersion of salmon testes DNA is shown in Figure 1. It is obvious that the dielectric constant of a DNA solution rises far above the dielectric constant of water and is still increasing at 50 c.p.s. Unless we have an entirely different measurement technique, we cannot hope to extend the frequency toward the lower frequency region. Thus at present it is not possible to obtain the complete dispersion curve to estimate the low frequency dielectric constant. 

When referring to a Debye dispersion, it should be kept in mind that Debye s theory applies exclusively to rotational polarization of molecules with permanent dipoles, without net charge transfer (33, 90). The occurrence of an appreciable ionic transfer complicates the picture, as in ice doped with ionic impurities. A further complicating factor is aging. Steinemann observed that thin crystals (0.1 to 0.2 cm.) showed a decrease of both the low-frequency dielectric constant and the low-frequency conductivity, suggesting difiusion of impurity (HF) out of the sample into the electrodes. Thicker samples (of the order of 1 cm.) were not affected. 

Various difficulties with the form of e(w) or the procedure used by NINHAM and PARSEGIAN may arise when conductors or very small particles are examined. In the first case, nonlocal dispersion has not been adequately treated in van der Waals theory in general, but even if the nonlocal effects could be ignored, interband transitions may need to be accommodated. LANDAU and LIFSHITZ [5.50] propose the form e(o)) = 4iria)/a, where a is the conductivity, for the very low-frequency dielectric permeability of conductors. Small particles and clusters also must be treated with caution if they are metallic due to surface-scattering and size quantization effects [5.59]. 

Pb(Mg /iNb2/i)0i (LB Number LB-dk). This crystal exhibits a broad ferroelectric phase transition with an average transition temperature of — 8°C determined by the maximum of the low-frequency dielectric constant. A marked frequency dispersion of the... 

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). 

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