Electrical relaxation

R = factor for electrical relaxation D = dielectric constant of medium F = factor for size of spheres and = zeta potential. 

Changes in polarization may be caused by either the input stress profile or a relaxation of stress in the piezoelectric material. The mechanical relaxation is obviously inelastic but the present model should serve as an approximation to the inelastic behavior. Internal conduction is not treated in the theory nevertheless, if electrical relaxations in current due to conduction are not large, an approximate solution is obtained. The analysis is particularly useful for determining the signs and magnitudes of the electric fields so that threshold conditions for conduction can be established. 

Finally, there is the extremely important group of relaxation methods for determining T. These can be based on either mechanical (sometimes thermomechanical) or electrical relaxations occurring within the material, and, although they do not always give results that are completely consistent with those obtained by the static mechanical tests already mentioned, they are considered very reliable and are widely used. 

In the non-steady state experiment, however, transient currents may be observed which correspond to interfacial processes not arising from chemical changes at the electrode (non-Faradaic processes), but rather from the electrical relaxation of the electrochemical interface. 

A persistent question regarding carbon capacitance is related to the relative contributions of Faradaic ( pseudocapacitance ) and non-Faradaic (i.e., double-layer) processes [85,87,95,187], A practical issue that may help resolve the uncertainties regarding DL- and pseudo-capacitance is the relationship between the PZC (or the point of zero potential) [150] and the point of zero charge (or isoelectric point) of carbons [4], The former corresponds to the electrode potential at which the surface charge density is zero. The latter is the pH value for which the zeta potential (or electrophoretic mobility) and the net surface charge is zero. At a more fundamental level (see Figure 5.6), the discussion here focuses on the coupling of an externally imposed double layer (an electrically polarized interface) and a double layer formed spontaneously by preferential adsorp-tion/desorption of ions (an electrically relaxed interface). This issue has been discussed extensively (and authoritatively ) by Lyklema and coworkers [188-191] for amphifunctionally electrified... 

Weleiams, M. L. The temperature dependence of mechanical and electrical relaxation in polymers. J. Phys. Chem. 59, 95 (1955). 

Figure 6.21. Relaxation map for observations on mechanical and electrical relaxation in xAgl (l-x)AgP03 glasses. Inset Low frequency portion of thin film transmission IR spectra for 0.5Agl 0.5AgP03 glass (After, Liu, Angell, 1986).

Jain and Huang (1994) have argued that since M" is calculated as (coGCo)/(G + co C ), (Co is the vacuum equivalent capacitance and C is the actual capacitance), the undesirable effects arising from the use of blocking electrode is suppressed. Further, measurements over only a limited range of frequency is needed (a few decades on either side of Xdx = CG) in order to study the electrical relaxation, when modulus formalism is used. 

It is interesting to note that the stretched exponential function was first used by Kohlrausch in his studies on electrical relaxation of leyden jar (a glassy ionic material) in 1847 (cited by Ngai, 1996). 

Mechanical relaxation experiments reveal that relaxation of shear moduli are similar to those of electrical moduli (chapter 7). In general mechanical relaxation spectra (G or E) exhibit a higher value of FWHM compared to M (electrical relaxation spectra). The mechanical relaxation data can also be collapsed on to master plots, which suggests that they obey time temperature superposition principle. There is therefore a parallel theoretical basis for the phenomenon. 

To and p being relaxation parameters and 0 < / 1. This empirical function has found theoretical justification thanks to a general model for relaxation phenomena developed by Ngai [132a and b]. This function has been used by several authors to describe electric relaxation phenomena in ionic conductors [133] and also mechanical phenomena relaxation in polymers [134]. Using the Williams and Watts decay function it is possible to show that the expression of M (co ) becomes ... 

G. Williams and D. K. Thomas, Phenomenological and Moleculsu Theories of Dielectric and Electrical Relaxation of Materials, Application Note Dielectrics 3, Novocontrol GmbH, 1998. 

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