Relaxation time conductivity

DGEBA Oligomer T (°C) Mw Viscosity Relaxation time Conductivity ... 

Figure 4. Circuit diagrams for a material exhibiting a) a relaxation process with a single relaxation time and induced polarization, b) a relaxation process with a single relaxation time, conduction and induced polarization and c) a distribution of relaxation times and induced polarization.

For many years the petroleum industry has defined nonconductive liquids as having conductivities less than 50 pS/m. A higher value of 100 pS/m is used here to address the higher dielectric constants of certain flammable chemicals in relation to petroleum products. For example the dielectric constant of ethyl ether is 4.6 versus 2.3 for benzene from Eq. (2-3.2), ethyl ether therefore has the same relaxation time at a conductivity of 100 pS/m as benzene at a conductivity of 50 pS/m. It is the relaxation time, not the conductivity alone, that determines the rate of loss of charge hence the same logic that makes 50 pS/m appropriate for identifying nonconductive hydrocarbons makes 100 pS/m appropriate for identifying nonconductive chemical products. 

ESR can detect unpaired electrons. Therefore, the measurement has been often used for the studies of radicals. It is also useful to study metallic or semiconducting materials since unpaired electrons play an important role in electric conduction. The information from ESR measurements is the spin susceptibility, the spin relaxation time and other electronic states of a sample. It has been well known that the spin susceptibility of the conduction electrons in metallic or semimetallic samples does not depend on temperature (so called Pauli susceptibility), while that of the localised electrons is dependent on temperature as described by Curie law. 

Figure 8. Example of microwave conductivity transient map PMC relaxation time map taken from a 20- m thin silicon wafer onto which 11 droplets of zeolith suspension were deposited and dried. Reduced lifetimes are clearly observed in the region of droplets. For color version please see color plates opposite this page.

The dramatic slowing down of molecular motions is seen explicitly in a vast area of different probes of liquid local structures. Slow motion is evident in viscosity, dielectric relaxation, frequency-dependent ionic conductance, and in the speed of crystallization itself. In all cases, the temperature dependence of the generic relaxation time obeys to a reasonable, but not perfect, approximation the empirical Vogel-Fulcher law ... 

An accurate calculation of the heat conductivity requires solving a kinetic equation for the phonons coupled with the multilevel systems, which would account for thermal saturation effects and so on. We encountered one example of such saturation in the expression (21) for the scattering strength by a two-level system, where the factor of tanh((3co/2) reflected the difference between thermal populations of the two states. Neglecting these effects should lead to an error on the order of unity for the thermal frequencies. Within this single relaxation time approximation for each phonon frequency, the Fermi golden rule yields, for the scattering rate of a phonon with Ha kgT,... 

An entirely different type of transport is formed by thermal convection and conduction. Flow induced by thermal convection can be examined by the phaseencoding techniques described above [8, 44, 45] or by time-of-flight methods [28, 45]. The latter provide less quantitative but more illustrative representations of thermal convection rolls. The origin of any heat transport, namely temperature gradients and spatial temperature distributions, can also be mapped with the aid of NMR techniques. Of course, there is no direct encoding method such as those for flow parameters. However, there are a number of other parameters, for example, relaxation times, which strongly depend on the temperature so that these parameters can be calibrated correspondingly. Examples are described in Refs. [8, 46, 47], for instance. 

Thermal Conductivity and Relaxation Times for Various Densities" at Zb = 2... 

Debye and Falkenhagen predicted that the ionic atmosphere would not be able to adopt an asymmetric configuration corresponding to a moving central ion if the ion were oscillating in response to an applied electrical field and if the frequency of the applied field were comparable to the reciprocal of the relaxation time of the ionic atmosphere. This was found to be the case at frequencies over 5 MHz where the molar conductivity approaches a value somewhat higher than A0. This increase of conductivity is caused by the disappearance of the time-of-relaxation effect, while the electrophoretic effect remains in full force. 

Although relaxation measurements have been widely used in nuclear magnetic resonance studies of solid catalysts and adsorbed molecules, they have not found such favor in similar ESR work. Relaxation phenomena, however, do play a very important role in any magnetic resonance experiment, whether or not this aspect of the problem is studied. In fact, the temperature at which most ESR experiments are conducted is dictated by the relaxation process. Furthermore, even qualitative data on relaxation times can be used as supporting evidence in the identification of a paramagnetic species. 

Experimental measurement of Hall mobility produces values of the same order of magnitude as the drift mobility their ratio r = jij/l may be called the Hall ratio. If we restrict ourselves to high-mobility electrons in conducting states in which they are occasionally scattered and if we adopt a relaxation time formulation, then it can be shown that (Smith, 1978 Dekker, 1957)... 

Using the known thermal conductivity data [46] of the wafers, their internal thermal relaxation time was estimated to be less than 1 ms, i.e. much shorter than C/G. Such estimate was confirmed by the fact that, within the experimental errors, a single discharge time constant r was always observed. 

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