Conductive-system dispersion

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. 

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. 

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 ... 

Composite materials. It has been shown that composite electrolyte systems composed of polymers such as PEO, Li salts such as Lil, and dispersed micronic and submicronic alumina (A1203) particles provide Li+ ion conducting systems of improved properties (e.g., higher conductivity, high Li+ transference number, higher stability) [388-389],... 

Experimental studies by Dukhin et al [14] showed that the specific electric conductance of disperse system depends on the frequency of applied field. These findings can be explained by changes in polarization effects at high frequencies. 

In heterogeneous systems, an interfacial polarisation is Created due to the space charges. This polarisation corresponds to the electron motion inside conductive charges, dispersed in an insulated matrice (Maxwell-Wagner Model). In fact, this phenomenon will appear as soon as two materials I and 2 are mixed so that c7]/ei C2le.2 with a conductivity and e dielectric constant at zero frequency [ 123]. 

The new non-equilibrium thermodynamic theory of heterogeneous polymer systems [37] is aimed at giving a basis for an integrated description for the dynamics of dispersion and blending processes, structure formation, phase transition and critical phenomena. Our new concept is derived from these more general non-equilibrium thermodynamics and has been worked out on the basis of experiments mainly with conductive systems, plus some orienting and critical examples with non-con-ductive systems [72d]. The principal ideas of the new general non-equilibrium thermodynamical theory of multiphase polymer systems can be outlined as follows. 

R. E. DeLaRue, Electric conductivity of dispersed systems, Master s thesis, University of California, Berkeley, 1955. 

The mixing of neutral polymers with particles of conductive substances like metals or carbon black for the purpose of modifying the electrical conductivity of polymers has been demonstrated in many works. Electric conduction in such composite materials is achieved due to contacts between the conductive particles dispersed in the polymeric matrix. In order to obtain continuous conductive paths in such a system the quantity of the additive has to be relatively large. However, the presence of these additives has an undesirable effect on the mechanical properties of the composite. ... 

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. 

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

Santhosh P, Manesh KM, Gopalan A, Lee K-P (2007) Novel amperometric carbon monoxide sensor based on multi-wedl carbon nanotubes grafted with polydiphenylamine-fabrication and performance. Sens Actuators B 125 92-99 Shai K, Wagner J (1982) Enhanced ionic conduction in dispersed solid electrolyte systems (DSES) and/or multiphase systems Agl-Al Oj, Agl-SiO, Agl-Ely ash, and Agl-AgBr. J Sohd State Chem 42 107-119 Shimizu Y, Yamashita N (2000) Solid electrolyte CO sensor using NASICON and perovskite-type oxide electrode. Sens Actuators B 64 102-106... 

Uvarov N, lusupov V, Sharama V, Shukla K (1992) Effect of morphology and particle size on the ionic conductivities of composite solid electrolytes. Solid State Ionics 51 41-52 Uvarov NF, Ponomareva VG, Lavrova GV (2010) Composite solid electrolytes. Russ J Electrochem 46(7) 722-733 Vaidehi N, Akila R, Shukla A, Jacob KT (1986) Enhanced ionic conduction in dispersed sohd electrolyte systems CaFj-AljO, and CaF -CeO. Mater Res Bull 21 909-916... 

Expressions for the Flux j and Mechanistic Indicators for Microheterogeneous Catalysis at Conducting Polymer/Dispersed Microparticle Composite Systems... 

The first effective conductivity detector to be described was that of Martin and Randall (8). Improved cell designs have been described by Harlan (9), Sjoberg (10) and more stable and sensitive electronic circuits for use with conductivity detectors have been discussed by Avinzonis and Fritz (11) and Berger (12). Scott et al. (13) inserted electrodes in the walls of a column to monitor changes in band dispersion along a chromatogra Mc column by conductivity measurement. More recently, Keller (14) described a bipolar electrical conductivity detector and Kourilova et al. (15) described a conductivity system with a detecting cell of only 0.1 jil volume. 

It was shown that the shape of the complex conductivity spectra of the investigated PEC systems can be divided into two classes those with x > 0.50 and those with x < 0.50 [47]. In Fig. 6a it is obvious that, for comparable dc conductivities, the dispersive regime begins earlier on the frequency scale for PEC with X > 0.50 than for the other PEC. In all materials with x > 0.50, a shoulder occurs in the conductivity spectra, roughly between 0.1 kHz and 10 kHz. An analogous behavior is hardly detectable for x < 0.50. The real part of the permittivity shows higher values, and e decays more rapidly with increasing frequency, for x > 0.50 than for x < 0.50. An analysis of the exact shape of the real part of the dynamic conductivity will be described in Sect. 3.4. 

Summerfield S (1985) Universal low-frequency behavior in the ac hopping conductivity of dispersed systems. Philos Mag B 52 9-22... 

In early 1939, Winslow began experimental research on the electric-field-induced viscosity increase in a suspension system made from solid semi-conducting particulates dispersed into a low viscosity and very high insulation oil. He first got a patent in 1947 [5] and then in 1949 reported his results in J. Appl. Phys.[64]. He found that a several hundred gram per square centimeter shear force eould be obtained under an electric field... 

Fridce HA (1924) A mathematical treatment of the electrk conductivity of disperse systems. Phys Rev 24 12-15... 

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