Conductivity electrical

In electrical conductors such as metals, the attraction between the outer electrons and the nucleus of the atom is weak the outer electrons can move readily and, since an electric current is essentially a flow of electrons, metals are good conductors of electricity. In electrical insulators (or dielectrics), electrons are strongly bonded to the nucleus and are not free to move. The electrical properties of Group IV carbides are shown in Table 

Electrical Resistitoty at20 C Compound (pf xm) Hall Constant at20°C lO cmVA-s Magnetic Susceptibility 10 emu/mol 

As shown in the above table, the Group IV carbides (and Groups V and VI carbides as well) are good electrical conductors and have an electrical resistivity only slightly higher than that of the parent metals, reflecting the metallic character of these compounds. The nitrides and especially the borides have even lower resistivity. The large spread in the reported values may be attributed to differences in composition and the presence of defects and impurities. 

The magnetic susceptibility is strongly affected by the metal-to-carbon ratio, and the values listed here are extrapolated to stoichiometric composition. 

High conductivity of solvent mixture formed from chemically non-interacting components may be related to the properties of only one or both components. Very high conductivity of mineral acids, carboxylic acids, some complexes of acids with amines, stannous chloride, and some tetraalkylammonium salts increases conductivity of their mixtures with other solvents.  

Normal practice does not often deal with mixed solvents of such high conductivity. Therefore, the theory of concentration dependence of conductivity of binary solvents is briefly discussed here.  

Two basic factors which influence conductivity of binary solvent mixture are viscosity and permittivity. The influence of these factors on specific conductivity is quantitatively considered in empirical equation  

K conductivity (symbols without index belong to the mixture properties, index 1 belongs to 

Concentration dependencies of permittivity, viscosity, density (molar volume) and conductivity described here permit to select with certainty the composition of mixed solvent, characterized by any value of mentioned properties. 

Electrical conductivity measurements have been reported on a wide range of polymers including carbon nanofibre reinforced HOPE [52], carbon black filled LDPE-ethylene methyl acrylate composites [28], carbon black filled HDPE [53], carbon black reinforced PP [27], talc filled PP [54], copper particle modified epoxy resins [55], epoxy and epoxy-haematite nanorod composites [56], polyvinyl pyrrolidone (PVP) and polyvinyl alcohol (PVA) blends [57], polyacrylonitrile based carbon fibre/PC composites [58], PC/MnCli composite films [59], titanocene polyester derivatives of terephthalic acid [60], lithium trifluoromethane sulfonamide doped PS-block-polyethylene oxide (PEO) copolymers [61], boron containing PVA derived ceramic organic semiconductors [62], sodium lanthanum tetrafluoride complexed with PEO [63], PC, acrylonitrile butadiene [64], blends of polyethylene dioxythiophene/ polystyrene sulfonate, PVC and PEO [65], EVA copolymer/carbon fibre conductive composites [66], carbon nanofibre modified thermotropic liquid crystalline polymers [67], PPY [68], PPY/PP/montmorillonite composites [69], carbon fibre reinforced PDMS-PPY composites [29], PANI [70], epoxy resin/PANI dodecylbenzene sulfonic acid blends [71], PANI/PA 6,6 composites [72], carbon fibre EVA composites [66], HDPE carbon fibre nanocomposites [52] and PPS [73]. 

Electrical conductivity is easily determined by measuring the impedance of the sample in the low frequency range (see Section 22.6.3), but at a frequency above the range in which errors arise owing to electrode polarization effects. For example, measurement of the electrical conductivity of cream, which can be carried out by measuring the impedance between a pair of stainless steel or platinum electrodes immersed in the cream sample, should be done at a frequency of 105 Hz or higher (Lawton and Pethig, 1993). 

The general principles of the measurement of rheological properties of milk fat and fat-based products are described in Section 22.4.9. The measurement of other product-specific functional properties, either ingredient properties or end use properties is described in the following. 

The electrical conductivity of carbon blacks is inferior to that of graphite, and is dependent on the type of production process, as well as on the specific surface area and structure. Since the limiting factor in electrical conductivity is generally the transition resistance between neighbouring particles, compression or concentration of pure or dispersed carbon black plays an important role. Special grades of carbon black are used to equip polymers with antistatic or electrically conductive properties. Carbon blacks with a high conductivity and high adsorption capacity for electrolyte solutions are used in dry-cell batteries. 

The electrical conductivity of coal is generally discussed in terms of specific resistance, p (units of p are ohm-centimeters), and is defined as the resistance of a block of coal 1 cm long and having a 1 cm cross section. Substances having a specific resistance greater than approximately 1 x 10 ohm-cm are classified as insulators while those with a specific resistance of less than 1 ohm-cm are conductors materials between these limits are semiconductors. 

Electrical conductivity depends on several factors, such as temperature, pressure, and moisture content of the coal. The electrical conductivity of coal is quite pronounced at high temperatures 

Source Baughman, G.L., Synthetic Fuels Data Handbc  

Coal is considered to be a semiconductor since the specific resistance of bituminous coal ranges from 1 X 10 ° to 1 X 10 ohm-cm. Anthracite has values ranging from 1 to 1 x 10 ohm-cm but exhibits some directional dependence (anisotropy). 

The conductivity of coal is explained in part by the partial mobility of electrons in the coal structure lattice which occurs because of unpaired electrons (free radicals) (Chapter 10). Mineral matter in coal may have some influence on electrical conductivity. The conductivities of coal mac-erals show distinct differences fusains conduct electricity much better than clarains, durains, and vitrains. 

The electrical conductivity of water is based on the presence of ions. It can be regarded as a non-specific yardstick for the content or the concen- 

A simple continuous method for determining the content of dissociable substances, particularly in the case of measurements to be repeated regularly at specified intervals, is important not only for systematic but also for intermittent checking on water and its content of dissolved mineral substances. 

In the structure of an electrical field in water, the anions migrate to the positively charged anode, the cations migrate to the negatively charged cathode. At constant temperature, the electrical conductivity of a given water is a function of its concentration of ions. 

Electrical conductivity is expressed as the reciprocal of electrical resistance in ohm (Q), in relation to a water cube of edge length 1 cm at 20 C (specific electrical conductivity). It is given in Siemens (S = 0 per cm (S cm M. Q 

Good distilled water should have values below 0.3 x 10 S cm  

The electrical conductivity of aluminium is around two-thirds that of copper, which it is replacing in many electrical applications. Overhead power transmission lines made of aluminium or aluminium alloy of the Almelec type, on the market in France since 1927 [2] are used throughout the world. Aluminium bars and tubes are also widely used in connecting stations for high- and medium-voltage outdoor networks. 

Aluminium is used for protecting underground and undersea telephone cables and for the construction of sulphur hexafluoride (SFg) insulated, sealed converters, where it provides protection from electrical or magnetic fields (hardening). 

The electrical conductivity of molten salts is again an important feature and has been reported for many salts. The methodology has been described many years ago by Tomlinson [261] and by Sundheim [262] and much more recently by Nunes et al. [263]. The critically compiled conductance data in [214] and many of the subsequently reported data are in terms of the specific conductance k, which like the viscosity follows an Arrhenius-type expression  

The conductance increases with the temperature, so that the minus sign before the activation energy for the conductance should be noted, contrary to the positive values of numerator of the exponent for the viscosity. The equivalent conductance of the molten salt, which is the product of the specific conductance with the molar volume of the molten salt, also follows an Arrhenius-type expression  

Values of A a and Ba are listed in Table 3.19 as far as they are known or could be derived from reported specific conductance data [214] by means of the molar volumes and their temperature dependence in Tables 3.13 and 3.14. The derived equivalent conductivities at the corresponding temperature of lAT are also recorded in this Table as far as the relevant data are known. Else, the values of and Bk are shown in Table 3.19 in parentheses. Some of the values recorded in Table 3.19 appear to be unreliable for instance the low values of the equivalent conductivities of the lanthanide chlorides from samarium onwards contrast with the much larger values of the lighter salts, and the fluctuations within the series with the atomic number are also suspect. 

Whereas generally diminishes as the size of the ions increases, Ba increases in this direction, Fig. 3.7. 

The conductivity of molten salts has been related to the existence of free volume in the melt [268] and it was argued that the Arrhenius activation energy Ba should be lower than the corresponding one for ion diffusion in the melt (see below), Bd as was in fact found. This would explain why the conductivity does not adhere to the Nemst-Einstein relation A = F D+ + D-)/RT for the diffusion or to Stokes law as mentioned above. The significant structure theory in this case [160] specifies that only the solid-like particles contribute to the conductivity. Their number per unit volume is where Fsd is the molar volume of the solid 

Total electrical conductivity in a solid (G,) is defined as the sum of conductivity contributions from each of the charge carriers present in that solid  

The charge carrier may be electronic (either electrons, e, or holes, h) or atomic (cation or anion defects). Each of the partial conductivities is given by the expression  

In cases where ionic and elctronic conduction occur together, (case of mixed conduction)  

At high temperatures and low oxygen partial pressures, ceria behaves as an n-type semiconductor and electrons liberated following reduction are the primary charge carriers. The reaction which leads to non-stoichiometry is  

The extremely open structure of the fluorite assembly tolerates a high level of atomic disorder, which may be introduced either by reduction or by doping. On reduction, both vacancies and electrons are present, thus giving rise to a large 

The phenomenological equation for electrical conduction is Ohm s law, which first appeared in Die galvanische kette mathematisch bearbeitet (the galvanic circuit investigated mathematically), the 1827 treatise on the theory of electricity by the Bavarian mathematician Georg Simon Ohm (1789-1854). Ohm discovered that the current through most materials is directly proportional to the potential difference apphed across the 

What current density vector y (units Am ) is produced by the application of an electric field of 10 V/m along the [1 1 1] direction of the crystal What is the angle between y and El What is the magnitude of a-along the [111]  

From the form of Eq. 6.21, it is seen that the components of y are given by  

The components of the electric field vector E now need to be found along the three mutually perpendicular axes (x, y, z), which are simply the projections of the vector on the axes for this, direction cosines are used. The vector E is directed along [111], which is the body diagonal. The body diagonal runs from the origin with Cartesian coordinates (xt, Yu Zi) = (0, 0, 0) to the opposite corner of the unit cell, in this case with Cartesian coordinates (X2, Y2. Z2) = (a, b, c) = (5.10, 6.25, 2.40). So, the direction cosines are given by  

With the construction of a unit vector along E using the direction cosines as its components along thex, y, and z directions, the vector E can be expressed as  

Independent of the mechanism of motion, electrical conductivities can always be described by Eq. (7.4) as 

For given electron and hole densities Ce and Ch as determined by the dopant content, the temperature dependence Tei(T) just reflects the temperature dependence of the electric mobilities i/ei,e and j/ei,h- For a hopping motion with varying hopping distances theories predict a temperature dependence of the mobility and, thus, of the electric conductivity as given by the equation 

Applying an external pressure lowers the distances between the monomers and thus will, in tendency, raise the interdomain jump rates. One therefore expects an increase in the conductivity Fig. 7.20 shows that this is indeed found. 

A modest increase in electrical conductivity is observed when an insulating thermoplastic is loaded with an ICP at low concentrations. As the concentration of the ICP increases, a sudden increase in electrical conductivity occurs around the percolation threshold. The percolation threshold is a narrow concentration range where a conductive network of ICP is formed within the insulating phase [60]. 

The electrical conductivity of polyacetylene/ PE composites, prepared by polymerization of acetylene in low density PE films impregnated with a Ti(OBu)y EtjAl Ziegler-Natta catalyst, increased with higher polyacetylene content [61]. An ultimate conductivity of 10 S cm was obtained with a percolation threshold of just 2%. 

Chen et al. (1995) observed a difference in the percolation threshold for polypyrrole/ PE composites prepared by a solvent method and with a melting technique [58]. The solvent method involved dissolving both PE and polypyrrole in toluene at about 100°C, while the melting method involved 

Polyblend fiber composites of polyaniline, doped with dodecylbenzene-sulfonic acid, and PE exhibited a conductivity of 2 S cm with 40 wt % polyaniline composition, but the percolation threshold was 10%. Hoiser et al. (2001) also obtained polyaniline/ PE blends with conductivities in the range lO to lO S cm and a percolation threshold of 10% [45]. Blends of polyaniline doped with camphor sulfonic acid and ultra high molecular weight PE displayed a percolation threshold of 5% with the conductivity being about 10 S cm [47]. The conductivity of extruded polyaniline/ PE blends increased from 3.38 x 10 to 1.19 x lO S cm as the polyaniline varied from 5 to 20 wt % [23]. No percolation threshold was observed up to 20 wt % loading as the polyaniline used to prepare the blends was not doped by any added acids, as had been the case in other studies. 

ICPs like polyaniline are gaining recognition for their use as solid antioxidants [62]. Their antioxidant activity, characterized by their free radical scavenging capacity, is attributed to their ability to switch between reduced and oxidized states. The reduced units of the ICP chains get oxidized in contact with free radicals and the free radicals in turn are neutralized by gaining electrons from the ICPs. Thus, the ICPs act as solid antioxidants. 

In [19], we studied the electrical conductivity (AC) of CMC and its CMC-Cu(II) complex. Moreover, the role of carboxymethyl content (DS) of CMC and origin of Cu(II) ion on semiconductor behavior 

From Figs. 7A-7.6, it is clear that the shape of the plots have more or less similar trends in behavior. For all investigated samples, the values of resistivity lie within the range 10 to 10 Q cm, and these values decreased with increasing temperature. This meant that we were dealing with a behavior often observed in semiconductor compounds, which varies experimentally according to the Arrhenius equation [33, 34], 

The observed increase in the values of the activation energies, in the high-temperature region [second peak] means that the samples were converted from low to high semiconductor materials. 

In other words, it was motivated by the semiconductor behavior of the materials. However, due to the combined effect of the conduction mechanism and the number of metal and chelating groups, the decreased in activation energy was observed. 

4 Applications of Cellulose Derivative-Metal Complexes for Paper Production (Functional Paper Sheets) 

Some measurements of this property have been made in a range of electrically conducting polymers. These include epoxy resin/polyaniline-dodecylbenzene sulfonic acid blends [38], polystyrene-black polyphenylene oxide copolymers [38], semiconductor-based polypyrroles [33], titanocene polyesters [40], boron-containing polyvinyl alcohol [41], copper-filled epoxy resin [42], polyethylidene dioxy thiophene-polystyrene sulfonate, polyvinyl chloride, polyethylene oxide [43], polycarbonate/acrylonitrile-butadiene-styrene composites [44], polyethylene oxide complexes with sodium lanthanum tetra-fluoride [45], chlorine-substituted polyaniline [46], polyvinyl pyrolidine-polyvinyl alcohol coupled with potassium bromate tetrafluoromethane sulfonamide [47], doped polystyrene block polyethylene [38, 39], polypyrrole [48], polyaniline-polyamide composites [49], and polydimethyl siloxane-polypyrrole composites [50]. 

A current of intensity I is applied between two electrodes and the electrical resistance R of the adhesive strip, measured with an ohm-meter, provides the volume resistivity by the relation py = Rhwjl. 

Silver-filled inks Silver-filled polyimides Silver-filled epoxies Graphite 

Low-end silver epoxies Graphite-filled coatings Polyamide Oxide-filled epoxies Unfilled epoxies Dielectric polymers Poly(tetrafluoroethylene) 

Liquid phosgene is a poor electrical conductor. The specific conductivity of re-distilled technical material (of unspecified purity) was measured as 7 x 10 S m at 25 C [736]. 

Zhang et al. studied the effect of conductive network formation in a polymer melt on the conductivity of MWNT/TPU composite systems (91). An extremely low percolation threshold of 0.13 wt% was achieved in hot-pressed composite film samples, whereas a much higher CNT concentration (3-4 wt%) is needed to form a conductive network in extruded composite strands. This was explained in terms of the dynamic percolation behavior of the CNT network in the polymer melt. The conductivity of extruded strand showed a hopping resistivity dominated behavior at low concentrations and a dynamic percolation induced network dominated behavior at higher concentrations. It was shown that a higher temperature can reduce the filler concentration required for the dynamic percolation to take effect. 

The conductivity of a soil is precisely the specific conductivity at 25°C of a water extract obtained at a definite soil water ratio. The electrical conductivity is measure on an electrical conductivity bridge and is normally reported in mmhos cm k A fairly quantitative estimate of the soluble salt content of solutions extracted from the soils can be made from their electrical conductance. Soil extracts obtained using high water to soil ratios are as less accurate measure of the solute content of the soil since more salts may be removed than are ever present in the soil, at field moisture contents. Usually soil water ratio of 1 2.5 or 1.5 is used for routine measurement. Thus the soil water ratio employed must be specified with the analysis. 

The cell constant k of a conductance cell is determined by measurement of the electrical conductance C of a standard KCl solution usually 0.0 IM KCl solution and use of equation. 

C is the conductance of the standard solution measured in a given cell (mmhos). 

The measured conductance C of a test solution in mmhos multipled by the cell constant( ) gives the specific conductance, L mmhos/cm of the test solution, i.e. L = 

For soil classification purpose the conductivity of saturation extracts of soils is required. However, extraction of solution from a saturated paste is very difficult process. As an approximation, the conductivity of the water extracts from a 1 2.5 soikwater suspension is determined and the conductivity of the saturation extract is calculated as EC (saturation extract) = E.C (1 2.5 extract) x 250/saturation percentage. 

This Structural feature has been shown to be a necessary condition for electrical conductivity in these materials, although the mixed mode of stacking is generally considered to be the thermodynamically preferred one (Shaik 1982). Proof of the relative stability of the mixed and segregated stack motifs, and a recipe for obtaining crystals of the latter, came with the discovery of a pair of polymorphic 1 1 complexes of 6-II with 6-III (Bechgaard etal. 1977 Kistenmacher etal. 1982). The red, transparent, mixed-stack form of the complex is a semiconductor, while the black, opaque structure with segregated stacks is a conductor (Fig. 6.2). 

This finding demonstrated that the presence of segregated stacks is a necessary condition for electrical conductivity. Reflecting the relative stabilities for the two stacking modes noted above, crystals of the red semiconductor form are obtained from a thermodynamic or equilibrium crystallization equimolar solutions of the donor and acceptor in accetonitrile are mixed and allowed to evaporate slowly. On the other hand, crystals of the black form are obtained from a kinetic or non-equilibrium crystallization hot equimolar solutions of the donor and acceptor in (the same) acetonitrile solvent are mixed and cooled rapidly. Some microcrystals of the resulting black powder are then used as seeds to obtain larger crystals of the segregated stack black form. 

Non-equilibrium crystallization methods, in particular electrochemical techniques, have become standard procedure for obtaining crystals of organic conductors, in part because of the ability to control and reproduce the crystallization conditions 

As an exampie of the type of variation observed, the p and k phases can be compared (Fig. 6.3) aiong with the schematic packing motifs of other poiymorphic forms. The former, apparentiy favoured by thermodynamic crystaiiization conditions (e.g. iow current density) is a centrosymmetric triciinic structure with one formuia unit of the sait in the unit ceii. The symmetry arguments require that the anion iie on a 

The prototypical N-I system is formed by tetrathafulvalene (TTF) 6-1 and chloranil (CA) 6-VI, although others have also been reported (Katan and Koenig 1999). The 

Another difference in properties between ionic and covalent compounds is electrical conductivity. No solid compound will conduct electricity, because the particles are not free to move. They are locked into the lattice. 

If you melt the compound, or dissolve it in water, the particles become free to move. You can dip a positive and a negative electrode into the melt or the solution and see if it conducts. What you find is that covalent compounds do not conduct electricity, whereas ionic ones do. Once again this result is not unexpected, since covalent compounds are composed of neutral molecules which will not be attracted to the electrodes, whereas ionic compounds are made up of charged ions which will be attracted to them. 

Conduction in metals causes no chemical change, because only electrons move (see Section 2.3.3). 

Only conducts when molten or in solution, and is alwa)fs broken up when conducting 

Partially filled bands of collective-electron states support metallic conductivity. The electrical conductivity is defined as the ratio of current density J = nev to electric field strength, E, where n is the number of carriers of charge e per unit volume and v is their average velocity. Since the average force on a charged particle is eE = m v/r, where r is the mean time between collisions and m is the effective mass, it follows that 

It should be possible to extrapolate the Heitler-London-Heisenberg description of the outer electrons from the case where the electrons are localized (R Rc) to the collective-electron case (R Re), since there is nothing in this description that requires that the electrons 

The significance of these considerations for the magnetic susceptibility of the collective d electrons, given no localized electrons simultaneously present, is the following  

Compounds with the Ni2In and Cu2Sb structure illustrate the situation for cation/anion ratio 1. 

Next to the dispersion degree, the conductivity is affected by the distribution of nanotubes. As shown for a composite with 0.875 wt% MWCNTs in polycarbonate, rmder suitable pressing conditions, due to the formation of secondary agglomerates, the electrical conductivity increased several orders of magnitude (see Section 5.4.1). Since the formation of the secondary agglomerates is time dependent, Zhang et al introduced the expression 

The percolation takes place if the critical volume fraction of secondary nanotube agglomerates Vy ggg is reached. According to classical percolation theory, the conductivity increase can be described with power law behavior (Eq. 5.9) with cr the plateau value of conductivity and the critical exponent (see also Appendix). 

The former considerations have shown that the conductivity of polymer-carbon nano-tube composites can be significantly raised by annealing at high temperatures. However, 

Experiment Injection velocity (mm/s) Melt temperature (°C) Holding pressure 2 wt%/5 wt% (bar) Mold temperature (°C) 

Since the formation of the nanotube network is strongly related to the flow of the melt, the electrical conductivity of injection molded parts can exhibit local variations [46]. Thus, next to the choice of the injection molding parameters, the electrical properties depend on the design parameters of the mold as gate position and shape, for instance. Such kind of investigations and the development of corresponding models are the topic of actual research activities. Some first results can be found in [67]. 

In many composites, conducting fillers (carbon black, carbon nanotubes, or metal nanoparticles) are added to make material conductive. The relationship between composite morphology and electrical conductivity has been studied extensively, especially in the context of carbon black filled polymers [156-162]. It is well known that the dependence of conductivity on the loading of conductive filler, pp, can be described on the basis of percolation theory there is some threshold filler loading below which there is no conductive pathway through the system and conductivity is zero above the threshold, conductivity grows very rapidly as  

composites with high-aspect-ratio carbon nanotubes become conductive at filler loadings of less than 1 vol.%, while composites with spherical particles like carbon black begin to conduct at much higher loadings ( 15 vol.%). 

The percolation threshold can be further reduced, and conductivity increased, if one makes use of the concept of double percolation, first theoretically studied by Levon, Margolina, and Patashinsky [164], and experimentally observed by Sumita and coworkers [161], as well as other researchers [157, 158, 162] for the dispersion of carbon black in binary polymer blends. To obtain double percolation, one needs to have a ternary system, with two phase-separating polymers and conducting filler with strong affinity to one of the polymers (we denote it as A, and the second polymer as B). Then, the system could be conducting if (i) filler loading in the A-domain is above percolation threshold and (ii) the volume fraction of the filled A-domains is above 

As already mentioned, another way of reducing percolation threshold is to use high-aspect-ratio particles, for example, carbon nanotubes instead of carbon black. 

The all-valence band diagram of Fig. 15-14 still leads to the prediction that the n band is half filled. Many texts make the point that metallic conductivity results when there are empty MOs immediately above the Fermi energy in a bulk solid, so we should consider whether or not polyacetylene is a metallic conductor. This leads us into the topic of electrical conductivity in one-dimensional periodic systems. 

If the first empty levels are separated from the Fermi level by a modest energy gap (on the order of kBT, where k is Boltzmann s constant, 1.38 x 10-23 jK-i), then a small population of electrons will exist in the empty orbitals at thermal equilibrium. This allows electrical conductivity (though typically much lower than that normal for metals) which increases with temperature—the situation in intrinsic semiconductors. If the gap is large, no conductivity occurs except at extreme voltages and the material is an insulator. 

The above discussion is based on a free-particle wavefunction. In real materials the potential along a coordinate is not constant, so the band stmcture becomes more complicated than the parabola of Fig. 15-1. Also, charge-density adjustments occur that tend to screen out the applied field. However the basic requirement for metallic conductivity continues to be the absence of a gap between the highest fllled and lowest empty MOs. Therefore, if the n band of polyacetylene really is partly fllled, pure 

We now reconsider our assumption of uniform C-C bond lengths. Since the molecules leading up to polyacetylene (butadiene, hexatriene, etc.) have alternating long and short C-C bonds, it is reasonable to ask whether this variation disappears completely in the limit of the infinite polymer. 

The band diagram undergoes a marked change in appearance when we change from a one-atom to a two-atom unit cell, quite aside from the fact that we have two bond distances. To show this, we will first work out the two-atom unit cell band diagram for equal bond lengths. 

Consider a suspension of Vp identical spherical soft particles in a general electrolyte solution of volume V. We define the macroscopic electric field in the suspension (E), which differs from the applied electric field E. The field (E) may be regarded as the average of the gradient of the electric potential (= in the 

The electric field E) is different from the applied field E and these two fields are related to each other by continuity of electric current, namely. 

We obtain Ci for the lo y potential case and substitute the result into Eq. (23.8), giving 

That is, in this limit the conductivity equals that in the absence of the particles so that spherical polyelectrolytes do not contribute to the conductivity. 

Finally, we derive an approximate conductivity formula for the important case where 

Given the versatility of this technique one can expect a remarkable surge of new studies in the near future. The few alrea published (see Chap. Ill) certaiidy testify to the enormous potential of further research. 

The above observations are obviously not intended as a rejection of this very useful technique. We shall have numerous opportunities to underline the important contributions made by its judicious exploitation. Perhaps the most interesting application of conductivity in cationic polymerisation relates to measurements in model systems such as the study of the self-ionisation of initiators, the interactions of Lewis acids with cocatalysts, and of course the extent of dissociation of stable carbenium salts. 

We feel that, provided one is aware of the pitfalls which beset an uncritical usage of this technique, and therefore interprets its results with due caution, it is always beneficial to have a pair of electrodes in a polsmerising soluticxi. Some of the information obtained might in fact help in unravelling the mechanism under study. 

The free electron in both the unsubstituted and substituted bis(phthalocyaninato)lutetium(III) complexes is associated with the extensive u-system of the phthalocyanine macrocycles. The individual [PciLu] units can be considered nominally as [Lu Pc2 ]. There remains 

The electric studies were later extended by the same authors to [ (Ci2H250)8Pc 2Lu], and the oxidised species [ (Ci2H250)8Pc 2Lu] -[Bp4] , obtained by oxidation of the parent compound with nitrosyl tetrafluoroborate. The electrical properties were determined in the 

Van de Craats et al. used the pulse-radiolysis time resolved microwave conductivity (PR-TRMC) technique to study the charge-transport properties of [ (Ci2H250)gPc 2Lu]. Their results showed an increase in charge carrier mobility at the crystalline solid to Col mesophase 

Only very few conductivity measurements have been performed on metal-lomesogens other than metallophthalocyanine complexes. Godquin-Giroud et al. demonstrated a conductivity of the order of 10 S cm for the copper(II) complex of the /3-diketone bis(3,4-nonyloxybenzoyl)methane in a hexagonal columnar phase.  

ll-hexakis(heptyloxy)triphenylene (HAT7) with 1% w/w of tri-phenylene-capped gold nanoparticles. 

Like Nickel Oxide, Ohms thwart Current. From 

For reasons that will become clear shortly, a prerequisite for diffusion and electrical conductivity is the presence of point and electronic defects. Consequently, this chapter and the preceding one are intimately related, and one goal of this chapter is to make that relationship clear. 

In many ceramics, diffusion and electrical conductivity are inextricably linked for two reasons. The first is that ionic species can be induced to migrate under the influence of a chemical potential gradient (diffusion) or an electric 

There are no known exceptions to this rule for cation membranes. The few exemptions for anions can be explained by higher hydration and by smaller ion-exchange constants for the corresponded counterions. 

Ion-permeable membranes are changing ionic forms during eleclrodialysis. The electrical conductivity of ion-permeable membrane containing two ion species 1 and 2 can be calculated as the average between two extreme values. One of them is based on the model of parallel independent movement of two types of ions /m) and another one is based on the model of successive ion movement from one fixed charge to another [2]  

The membranes in different ionic forms may have very different degrees of swelling. In this case the values X m and X2 , have to be adjusted to accommodate a decrease in fast-moving ion mobility and an increase in slow-moving ion mobility. 

The electric conductivity of this system can be described by the following formula [3]  

The total fraction of gel area (/] in the pressed through the model s parameters  

Diffusion phenomena rely on the Pick s law that states the relationship between the flux Ji and the concentration gradient V Ci of a diffusing species i  

When considering planar diffusion along one dimension x), Eq. (8.9) reduces to 

For non-steady-state conditions, the Pick s second law establishes the relationship between the concentration gradient dCijdx of the species i and the rate of its concentration change dCt/dt due to its flux  

Solution to this equation with appropriate initial and boundary conditions leads to the determination of the oxygen transport parameters. 

Sasaki-SiC 97) Sasaki-PBN 97) Graphite Silicon carbide Alumina Silicon nitride Boron nitride Quartz 

Viscosity is also available by measuring the half-width value of oscillation Avi/2 under microgravity, as shown by [101]. 

This proposal of a new technique will assure measurement of electrical conductivity under undercooled conditions. 

---

An fuel-air mixture explosion can be initiated by a sudden discharge of static electricity. Yet, while flowing in systems, a fluid develops an electrical charge which will take as long to dissipate as the fluid is a poor conductor. The natural electrical conductivity of jet fuel is very low, on the order of a few picosiemens per meter, and it decreases further at low temperature. 

It is believed that to avoid any risk of explosion, the electrical conductivity of jet fuel should fall between 50 and 450 pS/m. This level is attained using anti-static additives which are metallic salts (chromium, calcium) added at very low levels on the order of 1 ppm. 

Hydrocarbons generally have very low electrical conductivities and manipulation of these fluids creates electrostatic charges that can result in fire or explosions. This problem is encountered with gasoline and kerosene. 

Nearly all reservoirs are water bearing prior to hydrocarbon charge. As hydrocarbons migrate into a trap they displace the water from the reservoir, but not completely. Water remains trapped in small pore throats and pore spaces. In 1942 Arch/ e developed an equation describing the relationship between the electrical conductivity of reservoir rock and the properties of its pore system and pore fluids. 

Secondly it can be observed that as water is displaced by (non conductive) oil in the pore system the conductivity (C() of an oil bearing reservoir sample decreases. As the water saturation (SJ reduces so does the electrical conductivity of the sample, such that ... 

The intensity of the magnetic field produced by eddy current is depended on electrical conductivity and magnetic permeability of the studied area. In case of a uniform structure, when the conductivity of the material is high, the intensity of the induced magnetic field is big and signal received by probe Hp is small. 

Attention should be given in the fact, that penetration of eddy currents in residual austenite will be slightly deeper than in the martensite structure of steel, as austenite shows low electrical conductivity. The signal originatimg from the austenite structure will be amplified in effect of the influence of the structure found at greater depth. There will be no error as the method of measurement is compartable and the samples made for reference purposes will have the same structure as the studied part. 

A magnetic probe should be realized in a material of a high magnetic permeability and a low electric conductivity. 

We showed that the impedance variation of low frequency probes is influenced by the coating depth. Consequently, the tempering increase and the surface processing decrease the permeability and the electrical conductivity. 

Let us consider a domain U e R, representing the three-dimensional flaw imbedded in a homogeneous conductive media, with electric conductivity uo and permeability The flawed region D is assumed to be inhomogeneous, and characterized by the relative real conductivity ... 

Maximum gap between the eddy-current converter and the expected surface- 10mm Inspected surface electrical conductivity- 0.5-r60MS/m. 

Blocks have been prepared of 7075-T6 aluminum alloy 20 mm thick, with electrical conductivity of 1.89x10 S/m. The discontinuity has been machined by milling at a width of 0.2 mm. 

Dislocation theory as a portion of the subject of solid-state physics is somewhat beyond the scope of this book, but it is desirable to examine the subject briefly in terms of its implications in surface chemistry. Perhaps the most elementary type of defect is that of an extra or interstitial atom—Frenkel defect [110]—or a missing atom or vacancy—Schottky defect [111]. Such point defects play an important role in the treatment of diffusion and electrical conductivities in solids and the solubility of a salt in the host lattice of another or different valence type [112]. Point defects have a thermodynamic basis for their existence in terms of the energy and entropy of their formation, the situation is similar to the formation of isolated holes and erratic atoms on a surface. Dislocations, on the other hand, may be viewed as an organized concentration of point defects they are lattice defects and play an important role in the mechanism of the plastic deformation of solids. Lattice defects or dislocations are not thermodynamic in the sense of the point defects their formation is intimately connected with the mechanism of nucleation and crystal growth (see Section IX-4), and they constitute an important source of surface imperfection. 

In many crystals there is sufficient overlap of atomic orbitals of adjacent atoms so that each group of a given quantum state can be treated as a crystal orbital or band. Such crystals will be electrically conducting if they have a partly filled band but if the bands are all either full or empty, the conductivity will be small. Metal oxides constitute an example of this type of crystal if exactly stoichiometric, all bands are either full or empty, and there is little electrical conductivity. If, however, some excess metal is present in an oxide, it will furnish electrons to an empty band formed of the 3s or 3p orbitals of the oxygen ions, thus giving electrical conductivity. An example is ZnO, which ordinarily has excess zinc in it. 

Another important accomplislnnent of the free electron model concerns tire heat capacity of a metal. At low temperatures, the heat capacity of a metal goes linearly with the temperature and vanishes at absolute zero. This behaviour is in contrast with classical statistical mechanics. According to classical theories, the equipartition theory predicts that a free particle should have a heat capacity of where is the Boltzmann constant. An ideal gas has a heat capacity consistent with tliis value. The electrical conductivity of a metal suggests that the conduction electrons behave like free particles and might also have a heat capacity of 3/fg,... 

Examples of even processes include heat conduction, electrical conduction, diflfiision and chemical reactions [4], Examples of odd processes include the Hall effect [12] and rotating frames of reference [4], Examples of the general setting that lacks even or odd synnnetry include hydrodynamics [14] and the Boltzmaim equation [15]. 

Figure Bl.19.40. The scanning ion-conductance microscope (SICM) scans a micropipette over the contours of a surface, keepmg the electrical conductance tlirough the tip of the micropipette constant by adjusting the vertical height of the probe. (Taken from [211], figure 1.)...

Two major sources of ultrasound are employed, namely ultrasonic baths and ultrasonic immersion hom probes [79, 71]- The fonuer consists of fixed-frequency transducers beneath the exterior of the bath unit filled with water in which the electrochemical cell is then fixed. Alternatively, the metal bath is coated and directly employed as electrochemical cell, but m both cases the results strongly depend on the position and design of the set-up. The ultrasonic horn transducer, on the other hand, is a transducer provided with an electrically conducting tip (often Ti6A14V), which is inuuersed in a three-electrode thenuostatted cell to a depth of 1-2 cm directly facing the electrode surface. 

Hamilton D C, Mitchell A C and Nellis W J 1986 Electrical conductivity measurements in shock compressed liquid nitrogen Shock M/aves in Condensed Matter (Proc. 4th Am. Phys. Soc. Top. Conf.) p 473... 

Polymeropoulos E E and Sagiv J 1978 Electrical conduction through adsorbed monolayers J. Chem. Phys. 69 1836-47... 

In a defect-free, undoped, semiconductor, tliere are no energy states witliin tire gap. At 7"= 0 K, all of tire VB states are occupied by electrons and all of the CB states are empty, resulting in zero conductivity. The tliennal excitation of electrons across tire gap becomes possible at T > 0 and a net electron concentration in tire CB is established. The electrons excited into tire CB leave empty states in tire VB. These holes behave like positively charged electrons. Botli tire electrons in the CB and holes in tire VB participate in tire electrical conductivity. 

In tenns of the carrier mobility, the electrical conductivity c of an n type semiconductor can be written as... 

Liquid ammonia (p. 216). like water, is very slightly dissociated, and shows a very small electrical conductance ... 

---