Simple Maxwell-Wagner model

Another model of experimental interest concerns the case of a highly conductive shell around practically non-conductive material. It may be applied to macromolecules or colloidal particles in electrolyte solution which usually have counterion atmospheres so that the field may displace freely movable ionic charges on their surfaces. The resulting dielectric effect turns out to be equivalent to a simple Maxwell-Wagner dispersion of particles having an apparent bulk conductivity of... 

Inspection of Figure 4.1.9 suggests that Eq. (20) generates spectra that are similar to those of simple RC circuits. This is indeed the case. In fact, Bonanos and Lilley [1981] showed that the Maxwell-Wagner model is formally identical to the two-element circuit of Figure 4.1.1, but with values of gi, g2, Ci, and C2 that can be expressed as rather complicated functions of Oi, [Pg.218]

Maxwell model A mechanical model for simple linear viscoelastic behavior that consists of a spring of Young s modulus E) in series with a dashpot of coefficient of viscosity (ri). It is an isostress model (with stress 8), the strain (e) being the sum of the individual strains in the spring and dashpot. This leads to a differential representation of linear viscoelasticity as stress relaxation and creep with Newtonian flow analysis. Also called Maxwell fluid model. See stress relaxation viscoelasticity. Maxwell-Wagner efifect See dielectric, Maxwell-Wagner effect. 

Figure 3.9 Equivalent circuits for the Maxwell—Wagner effect in a simple dielectric model, (a) The slabs in series, and the resistors cause the interface to be charged, (b) The slabs...

Interfacial or Maxwell-Wagner polarization is a special mechanism of dielectric polarization caused by charge build-up at the interfaces of different phases, characterized by different permittivities and conductivities. The simplest model is the bilayer dielectric [1,2], (see Fig. 1.) where this mechanism can be described by a simple Debye response (exponential current decay). The effective dielectric parameters (unrelaxed and relaxed permittivities, relaxation time and static conductivity) of the bilayer dielectric are functions of the dielectric parameters and of the relative amount of the constituent phases ... 

Conducting particles held in a nonconducting medium form a system which has a frequency-dependent dielectric constant. The dielectric loss in such a system depends upon the build-up of charges at the interfaces, and has been modeled for a simple system by Wagner [8], As the concentration of the conducting phase is increased, a point is reached where individual conducting areas contribute and this has been developed by Maxwell and Wagner in a two-layer capacitor model. Some success is claimed for the relation... 

Table 7 gives a summary of qualitative performances and problems encountered for simple shear and uniaxial elongational flows, using the Wagner and the Phan Thien Tanner equations or more simple models as special cases of the former. Additional information may also be found in papers by Tanner [46, 64]. All equations presented hereafter can be cast in the form of a linear Maxwell model in the small strain limit and therefore are suitable for the description of results of the linear viscoelasticity in the terminal zone of polymer melts. 

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