Maxwell-Wagner theory

Finally, attempts are made on a theoretical basis to explain the unusually large dielectric increments and relaxation times of DNA. The discussion is limited to ionic-type polarizations in this report. The available theories, such as the Maxwell-Wagner theory 29) and the surface conductivity treatment, are reviewed and analyzed. These theories do not explain the dielectric relaxation of DNA satisfactorily. Finally, the counter ion polarization theory is described, and it is demonstrated that it explains most reasonably the dielectric relaxation of DNA. 

This is the well known Maxwell-Wagner theory of spherical suspensions (29). According to this theory, the dielectric increment of a spherical suspension is determined solely by the dielectric constant and the conductivities of the particle and the solvent. 

The dielectric constant of the wet resin is according to the Maxwell-Wagner theory ... 

The dielectric constant at 20°C increased from 3.39 to 3.84 due to the 1.7 %wt. moisture (2.0 %v.). The calculated increase of the dielectric constant from 3.39 to 3.60 is only about 50 % of the total effect. The Maxwell-Wagner theory thus seems to describe roughly the frequency/temperature location of the dielectric loss maximum due to absorbed moisture. However, it does not adequately describe the increase of the dielectric constant due to the moisture uptake from the air. A possible reason for this discrepancy might be that one of the assumptions does not hold, viz. that the conductivity of the resin matrix is negligibly small. 

In Section 7.5, we analyze the double layer charge in a solution as a function of the perpendicular distance from the solid surface. No double layer formations are considered in the Maxwell—Wagner theory (Section 3.5.1). However, in wet systems and in particular with a high volume fraction of very small particles, the surface effects from counter-ions and double layers usually dominate. This was shown by Schwan et al. (1962). By dielectric spectroscopy, they determined the dispersion for a suspension of polystyrene particles (Figure 3.10). Classical theories based on polar media and interfacial Maxwell—Wagner theory could not explain such results the measured permittivity decrement was too large. The authors proposed that the results could be explained in terms of surface lateral) admittance. 

Two other approaches have been taken to modelling the conductivity of composites, effective medium theories (Landauer, 1978) and computer simulation. In the effective medium approach the properties of the composite are determined by a combination of the properties of the two components. Treating a composite containing spherical inclusions as a series combination of slabs of the component materials leads to the Maxwell-Wagner relations, see Section 3.6.1. Treating the composite as a mixture of spherical particles with a broad size distribution in order to minimise voids leads to the equation ... 

Maxwell-Wagner Dispersion.—Macroscopic heterogeneities of the complex permittivity must always result in an apparent overall dielectric dispersion, even if the above-discussed orientation effect cannot occur. We may investigate this for the case of spherical particles of radius a and complex permittivity eg which are suspended in a medium with complex permittivity eg. It follows from electrostatic theory that the presence of one such sphere is equivalent to a dipole moment given by... 

Maxwell-Wagner Type Theory. If a sphere with a dielectric constant 2 and conductivity k2 is suspended in a medium with a dielectric constant i and a conductivity kh the dielectric constant of the suspension may be expressed by the Maxwell equation (11),... 

Exceedingly large losses at low frequencies above 150°C are attributed to Maxwell-Wagner-Sillars (NWS) polarizations arising from conduction mismatches at the structural interfaces between a continuous matrix of amorphous polycarbonate and a crystalline or densified second phase. Provided that the discontinuous phase tends towards a two-dimensional aspect and has a conductivity less than that of the matrix, theory predicts substantial NWS losses even with a low concentration of the discontinous phase [37]. 

The first original derivation of mixture formula for spherical particles was performed by Maxwell (18) and was later extended by Wagner (19). This Maxwell-Wagner (MW) theory of intorfacial polarization usually can be successfully applied only for dilute dis persions of spherical particles. The dielectric permittiv ity of such a mixture can be expressed by flic well-known relationship ... 

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... 

However, the Maxwell-Wagner-Sillats (Grossman and Isatd, 1970) equation predicts as a complete solution of the Wagner-Raleigh theory for a system of one spherical particle uniformly distributed in another... 

Figure 1-6). Maxwell-Wagner, Helmholtz, Gouy-Chapman, Stem, and Gra-hame theories have been used to describe the interfacial and double layer dynamics [9]. 

Maxwell-Wagner interfacial polarization theory explains relaxations in a double layer of colloidal particles as a result of ionic species current conductance in parallel with capacitance. As a result of these processes in the double layer of a colloidal particle, the particle interface is charged by conductivity. 

Wagner KW (1914) Electricity of the dielectric behaviour on the basis of the Maxwell theory. Arch J Elektrotech 2 371-387... 

Maxwell [68] first addressed the dielectric behavior of dispersions with spherical particles covered with shells. Pauly and Schwan [72] subsequently extended Maxwell s treatment for obtaining the frequency dependence of the dielectric constant of the systems. Maintaining the same procedure as used in Wagner s theory, the dielectric constant of those systems can be expressed as ... 

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