Conductive-system dispersion response

Conductive-system dispersive response may be associated with a distribution of relaxation times (DRT) at the complex resistivity level, as in the work of Moynihan, Boesch, and Laberge [1973] based on the assumption of stretched-exponential response in the time domain (Eq. (118), Section 2.1.2.7), work that led to the widely used original modulus formalism (OMF) for data fitting and analysis, hi contrast, dielectric dispersive response may be characterized by a distribution of dielectric relaxation times defined at the complex dielectric constant or permittivity level (Macdonald [1995]). Its history, summarized in the monograph of Bbttcher and Bordewijk [1978], began more than a hundred years ago. Until relatively recently, however, these two types of dispersive response were not usually distinguished, and conductive-system dispersive response was often analyzed as if it were of dielectric character, even when this was not the case. In this section, material parameters will be expressed in specific form appropriate to the level concerned. 

Since conductive-system dispersive response may be transformed and shown graphically at the complex dielectric level, and dielectric dispersion may be presented at the complex resistivity level, frequency-response data alone may be insufficient to allow positive identification of which type of process is present, since there may be great similarity between the peaked dispersion curves that appear in plots of p"(co) and of e"(co) or of e"(cd) = e"((o) - (otjcoev). Here, e is the permittivity of vacuum. This quantity has usually been designated as b, as in other parts of this book. Its designation here as f avoids ambiguity and allows clear distinction between it and e(0) = e (0) = o, the usage in the present section. 

Conductive-system dispersive response involving mobile charge may be conceptually associated with the effects of three processes ... 

Conductive-system dispersion (CSD) usually involves thermally activated conduction extending to zero frequency plus an always-present bulk dielectric constant, usually taken to be frequency-independent in the experimental range. Dielectric-system dispersion (DSD) often involves dielectric-level response with only weak temperature dependence, and it may or may not involve a non-negligible frequency-independent leakage resistivity, pc = Pdc = po= 1/ob- There may be cases where separate processes lead to the simultaneous presence within an experimental frequency range of both types of dispersion, but this is rare for most solid electrolytes. Further complications are present when conduction involves both mobile ionic and electronic charges, neither of whose effects are negligible (Jamnik [2003]). Here only ionic, dipolar, and vibronic effects will be further considered, with the main emphasis on conductive rather than on dielectric dispersion. 

Analysis of Dispersed, Conducting-System Frequency-Response Data, J. Non-Cry St. Solids 197, 83-110. 

When the OMF approach is used to fit experimental data, a fatal flaw appears, one that invalidates any conclusions based on such fitting results. For good data, aU CMF fits yield closely the same estimates of % and Pic, independent of the inunit-tance level for the data. This is not the case, however, for OMF fits. They lead to inconsistent results such that fits of the data in M(co) or M"((o) form yield characteristically large values of Pw, usually falling in the range 0.45 < Pio 0.55 for midrange temperatures and concentrations, while fits of the same data in yield values close to 1/3. As mentioned earlier, since has no effect on must yield the same estimates, and OMF and CMF fits are then equivalent. A table of such comparisons and further discussion of OMF problems appear in Macdonald [2004] and make it evident that the OMF treatment of d as an intrinsic part of the K1 dispersive conductive-system model is incorrect. 

In this study, both the normal mode relaxation of the siloxane network and the MWS processes arising from the interaction of the dispersed nanoclay platelets within the polymer network have been observed. Although it is routine practice to observe the primary alpha relaxation of a polymeric system at temperatures below Tg, in this work it is the MWS processes associated with the clay particles within the polymer matrix that are of interest. Therefore, all BDS analyses were conducted at 40°C over a frequency range of 10 to 6.5x10 Hz. At these temperatures, interfacial polarization effects dominate the dielectric response of the filled systems and although it is possible to resolve a normal mode relaxation of the polymer in the unfilled system (see Figure 2), MWS processes arising from the presence of the nanoclay mask this comparatively weak process. 

Unsteady-State Analysis Including Axial Dispersion. As in the previous unsteady-state analysis, the effects of placental barrier tissue oxygen consumption are neglected in this study. For the unsteady-state analysis of the model in which axial dispersion was included, one study was conducted. This study involved placing a step change on the maternal blood velocity to a new maternal blood velocity of 0.125 times the normal in an attempt to determine the effects of axial dispersion on the system at low maternal blood velocities. The discussion of this study is divided into the following two parts first, the effect of axial dispersion on the response of the fetal blood end capillary oxygen concentration, and second, the effect on the transient axial profiles. 

In the trimer series, the hydrophobic domains in the fluorescence data reflect isocyanurate associations. The hydrophobe associations responsible for effective thickening occur at higher concentrations. Probe studies similar to those conducted in oxyethylene-oxypropylene block polymers (12, 13) are warranted. The difference of importance to the rheology of dispersed systems is likely related to the cohesiveness of the surfactant hydrophobe interaction (21). 

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