Dielectric increment frequency

When an alternating electric field of small amplitude is applied, we can measure the chemically induced complex dielectric increment (e )ch = ( )ch — i(e")ch [i = (— 1)1/2] as a function of frequency to. It can be shown (124) that t is then given by... 

The case of DNA in the double helix form is of especial interest because dipoles along the oppositely directed helical strands cancel to leave little or no resultant dipole moment. The observed dielectric increments, i.e., excess of permittivity over that of solvent water,are very large, however, and reach a static value only at audio or subaudio frequencies, showing the necessity of some mechanism of considerable charge displacements which develop slowly. 

The same mechanism must in prindple apply to globular proteins. However, because of the small dimensions of these biopolymers the dielectric increments are of comparatively small magnitude. Furthermore, their dispersion falls in the same frequency range as that of the rotational polarization mechanism of permanent dipole moments. Since the latter is apparently predominant, it would be difficult to distinguish the coimterion effect. 

In the same frequency range, the dispersion of the dielectric increment Ae of solution can be observed. The curves of dielectric dispersion almost coincide with the dispersion curves for EB (Fig. 59) so that both mechanisms of molecular motion are identical and are represented by dispersion Eq. (81) for kinetically rigid mol ules. 

The experimental errors in the capacity and conductivity readings in the low frequency region are summarized in Table I. In the last column, the magnitude of the error in the dielectric constant is shown. The error of 21.42 at 50 c.p.s. in the dielectric constant seems large however, the total dielectric increment is so large that this error is not really serious. 

The dielectric increment at low frequencies is given by the following expression ... 

The dielectric properties of polystyrenesulfonic acid membranes in their H form have also been studied over the frequency range of 10 -10 Hz, with H O content and temperature as parameters. It was concluded that the presence of water in the membrane gives rise to a specific, water induced relaxation process which is characterized by high dielectric constant, loss, and dielectric increment, Ae . 

The dielectric spectra of aqueous protein solutions exhibit anomalous dielectric increments where the value of the static dielectric constant of the solution is significantly larger than that of pure water. A typical experimental result illustrating the dielectric increment is shown in Figure 8.3, where the real part of the frequency-dependent dielectric constant of myoglobin is evident. Both the increment at zero frequency and the overall shape of this curve have drawn a lot of attention. 

Dielectric relaxation results are proven to be the most definitive to infer the distinctly different dynamic behavior of the hydration layer compared to bulk water. However, it is also important to understand the contributions that give rise to such an anomalous spectrum in the protein hydration layer, and in this context MD simulation has proven to be useful. The calculated frequency-dependent dielectric properties of an ubiquitin solution showed a significant dielectric increment for the static dielectric constant at low frequencies but a decrement at high frequencies [8]. When the overall dielectric response was decomposed into protein-protein, water-water, and water-protein cross-terms, the most important contribution was found to arise from the self-term of water. The simulations beautifully captured the bimodal shape of the dielectric response function, as often observed in experiments. 

Note that the critical relaxation time is predicted to depend upon the square of the particle radius, as observable. This bound-ion-layer model of Schwarz was remarkably successful in several ways. The magnitude of the dielectric increment and its frequency shift with particle radius were reasonably in agreement with observation. Despite this welcome advance in the understandings of dispersions, the Schwarz theory deliberately excluded the possibility of bound counterion exchange with the surrounding medium. It also neglected any contribution to the particle polarizability that arises from the distortion of the outer or surrounding portions of the diffuse double layer. 

Whole blood exhibits P-, y-, and 6-dispersion, but curiously enough it exhibits no a-dispersion (Foster and Schwan, 1989). The 3-dispersion has a dielectric increment of approximately 2000 centered at approximately 3 MHz (hematocrit 40%). Erythrocytes in suspension have a frequency-independent membrane capacitance with very low losses (Schwan, 1957). The impedance of lysed erjrthrocytes in suspension shows two clearly separated single relaxation frequencies (Debye dispersions). The a-dispersion is in the lower kilohertz range, and the p-dispersion is in the lower MHz range (Schwan, 1957 Pauly and Schwan, 1966). 

FIGU RE 3.13 Real part of the dielectric increment (relative to the vacuum permittivity cq) of ethylceUulose (Aquacoat ) latex particles as a function of frequency, in 1 mmol/1 sodium salicylate (A) logarithmic derivative technique (A) standard electrode-separation procedure. 

FIGURE 3.18 Frequency dependence of the relative dielectric increment of 265-nm radius polystyrene spheres in 0.1 nunol/1 KCl solution. Symbols experimental data soUd line classical calculation dashed line DSL calculation. In both calculations, the zeta potential used was the one best-fitting simultaneously electrophoretic mobility and dielectric dispersion data. 

Figure 4 shows typical variations of the dielectric relaxation with water content as recorded along a line stretched across I( /o) and directed towards the 100% water vertex of the pseudo-ternary phase diagram, that is for systems characterized with a fixed ratio of combined surface-active agents to hexadecane and enriched gradually with water. While dielectric relaxation phenomena are hardly detectable at low water contents, systems characterized with higher water contents exhibit striking dielectric relaxations, the dielectric increment (e - e ) increasing drastically as p approaches the critical value corresponding to the transparent-to-turbid transition. The increase in (G - e ) results from the drastic increase in the low frequency permittivity whose variations with p are plotted in Figure 5a. While at low water contents, increases slowly and almost linearly with p, it displays a divergent behavior in the vicinity of the border line F. Simi-...

These fluorocyanopolymers were dielectrically characterized in a wide range of frequencies and temperatures. The dominating relaxation process detected in these materials is the a-relaxation, associated with the dynamic glass transition. A VFTH temperature dependence of the relaxation times was found for these fluorocyanopolymers. The polarity-dielectric constant relationship has been established. Actually, the inclusion of CN group into fluorinated units enhances the dielectric increment and makes them potential candidates for film capacitors. 

Figure 2 The dielectric increment Ae of monodispersed anionic polystyrene latex particle of a mean diameter 156 nm dispersed in 10 MNaCl aqueous solution vs. frequency. The particle volume fraction is 1.9 vol%. Ac was...

Experimental data by addition of 1, 3.5, 8 and 15 mol% of C to A are presented in Figs. 30 and 31 [158]. There is a clear evidence for the existence of mixed associates. A chemical variation of the components results a stronger (B/C) or weaker (B/D) increase of the dielectric increment Ay depending on the overall dipole moment in the direction of the molecular long axis (Fig. 32) [159]. The relaxation frequencies do not depend on the concentration but depend on the chemical structure of the associates (Fig. 33). 

Figure 32. Dielectric increment of the low frequency relaxation for different mixtures [159].

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). 

Here e , is the high frequ y limit of s, So is the static dielectric constant (low frequency limit of s ). So - Soo = A is the dielectric increment, fR is the relaxation frequency, a is the Cole-Cole distribution parameter, and P is the asymmetry parameter. The relaxation frequency is related to the relaxation time by fa = (27It) A simple exponential decay of P (oc,P = 0) is characterised by a single relaxation time (Debye-process [1]), P = 0 and 1 < a < 0 describe a Cole-Cole-relaxation [2] with a symmetrical distribution function of t whereas the Havriliak-Negami equation (EQN (4)) is used for an asymmetric distribution of x [3]. The symmetry can be readily seen by plotting s versus s" as the so-called Cole-Cole plot [4-6]. 

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