Conductivity curves

Conductivity curves (A versus c ) of salts in solvents of low-permittivity commonly show a weakly temperature-dependent minimum around 0.02 molL-1 followed by a strongly temperature-dependent maximum at about 1 mol L 1. According to Fuoss and Kraus [101,102] the increase of conductivity behind the minimum is due to the formation of new charge carriers from the ion pairs. They assume that coulombic forces suffice to form bilateral cationic [C+A-C+] and anionic [A C+A ] triple ions in solvents of low-permittivity ( <15) if the ions have approximately equal radii. 

Fig. 1.14. The qualitative profile of dependencies of equilibrium values of electric conductivity (curve /) and the tangent of inclination angle of VAC Ps (curves 2, 3) as a function of concentration of chemisorbed acceptors 2 - Inoj) 4co > a/2 3 - Inob co < o/2...

The diversity of EEP reactions on a solid surface can be illustrated by the survey if interaction between excited atoms of mercury and zinc oxide [186]. When atoms of Hg get to an oxidized surface of ZnO at room temperature, an increase in the semiconductor electrical conductivity take place (Fig. 5.3, curve 2). The electrical conductivity change signal is irreversible, and in case of an increase in the temperature, after the Hg flux is disabled, an additional increase in the electrical conductivity (curves 3 and 4) takes place. One can logically suppose that we are dealing here with partial reduction of zinc oxide according to the scheme... 

Fig. 3 Energy diagram for an M-A-M diode showing elastic and inelastic tunneling processes (top). The HOMO (n) and LUMO (71 ) orbital energies and a few vibrational levels are indicated. Applied bias energy (eV) is just sufficient to allow inelastic tunneling with excitation of the first vibrational level, eV = hv. Also shown (bottom) are the I(V) curve, conductance- / curve, and the IETS spectrum that would result from both elastic processes and the first inelastic channel. (Reproduced by permission of the American Chemical Society from [19])...

With diethyl ether and with anisole it was found [65, 67] that a sharp minimum in the specific conductivity curve, at an [ether]/[AlCl3] ratio of unity, was flanked by maxima, and that these were accompanied by a well defined maximum, and two minima, respectively, in the DP curve (see Figure 7). 

A more detailed investigation (EtCl, -78.5°) with ethanol [68] showed again a very striking antibatic correlation between DP and specific conductivity in the neighbourhood of [EtOH]/[AlCl3] = 1, with a very sharp peak in the DP curve and a corresponding sharp minimum in the conductivity curve. It was also shown that when the complex EtOH A1C13 was used as catalyst, the plots of conductivity and of 1/DP (after the subtraction of an... 

In this manner the number of ions is decreased and the conductivity curve shows an inflection In DMF and DMSO even a flat maximum is found, which is followed by a flat minimum. Upon further addition of the donor the red color disappears and the conductivity increases steadily, since ionization according to Eq. (1) is now predominating. 

The inflection is hardly pronounced for D = HMPA since the donor is strong and formation of [Snl6 ]2 takes place only to a small extent. The flat maximum in the conductivity curve for D = TBP is due to a physical effect a decrease in e and an increase in viscosity. There is no inflection for THF and the solution remains red even at high donor contents of the solution, since autocomplex species are the most stable entities in this system. 

The conductivity curve is analogous to that of the system HMPA-FeCl3 and the conductivities are lower than those in the presence of PhjPOCl, which is a weaker donor than Ph3PO (Fig. 13). This observation is interpreted by analogy to the HMPA-FeCl3 system. The autocomplex formation... 

In the HMPA-SbCls system the conductivity curve is similar to that in the HMPA-SnI4 system. Since SbCl5 is much more difficult to ionize, autocomplex formation is more likely than simple ionization ... 

With the U-Type systems (i.e. with the low chain alcohols) the trends in the conductivity - curve are consistent with percolative conduction originally proposed to explain the behaviour of conductance of conductor-insulator composite materials (27). In the latter model, the effective conductivity is practically zero as long as the conductive volume fraction is smaller than a critical value called the percolation threshold, beyond which k suddenly takes a non-zero value and rapidly increases with increase of Under these conditions. 

The increase in conductivity is due to increase in dissolved surfactant, and this increase continues until all the crystallites dissolve. The peak in specific conductance is attained when the microemulsion is formed and the specific conductance levels off. The plateau of Figure 6 is often referred to as a "percolation threshold" (] ) and is reached when there is a disordered interspersion capable of bicontinuous structures ( ). Further addition of methanol results in a lowering of conductivity explained by the solution eventually approaching the conductivity of methanol. This is the region of molecular dispersion. These conductivity curves are similar to those observed by Lagues and Santerey (13) on a system of water, cyclohexane, sodium dodecylsulfate and 1-pentanol. 

Such a temperature-time-conductance curve for a vacuum-sintered sample is shown in Fig. 5. A sample, pretreated at 100°C as described above, was heated to 125°C at time zero. The conductance changes as a function of time were followed for 160 minutes (point B), and then the temperature was suddenly raised to 150°C. The time-dependent conductance changes proved to be quite reversible, contrary to the irreversible decrease of conductance with increasing temperature for samples kept in an oxygen atmosphere. 

Stockmann found that tempering zinc oxide in a hydrogen atmosphere at 250°C increased its conductivity and changed the shape of the resulting time-temperature-conductivity curve. The effect of hydrogen on zinc oxide will be discussed in the next section. 

The conductivity curve for the hydrogen sulphate ion calculated by means of this equation is shown in Fig. 2. It may be seen that it predicts a much smaller decrease in the equivalent conductivity than... 

F. W. Kiister and R. Kremann detected two irregularities in the conductivity curve of soln. containing 25 and 50 per cent, of HNOa ... 

The inversion from one form to the other was supposed to explain the maximum attained by the conductivity curve, Fig. 33. H. Gorke showed that there is no need for this hypothesis to explain the facts. The salt prepared at the low temp, may have a trace of impurity, say barium hydroxide, which accelerates the reduction, and that prepared at the higher temp, may be an acid salt or contain a trace of phosphoric acid which retards the reduction. H. Burgarth, H. Remy, and T. M. Lowry discussed the electronic structure of phosphorous acid—vide supra, phosphoric acid. 

Fig 3 DTA curve (solid line) and pyrolysis (thermal conductivity) curve (dashed line) for Tetryl... 

Fig. 3. Conductivity curves of the copolymerization of 2-hydroxy-4-(2,3-epoxypropoxy)benzophenone (0.5 mol/1) with phthalic anhydride (0.5 mol/1) in o-xylene at 120 °C initiated by various initiators.57) 1 — tri-n-hexylamine (0.025 mol/1) 2 - tri-n-hexylamine (0.025 mol/1) and cyclohexanol (0.025 mol je 1) 3 — tri-n-hexylamine (0.025 mol/1) and benzoic acid (0.025 mol/1) 4 — hexadecyltrimethyl-ammonium bromide (0.005 mol/1)...

From experiments made at several frequencies, the conductivity curve is built up by superimposing the curves s"s0co versus time in the regions where they are independent of frequency (Kranbuehl et al, 1986 Wasylyshyn and Johari, 1997). Figure 6.10 displays the obtained conductivity, a, versus reaction time for both epoxy systems (a) and (b). Cure temperatures, T , are higher than Tg for case (a) and lower than Tg for case (b). The initial conductivity, a0, increases with temperature. Conductivities are higher for system (a) than for system (b) and vary over 3 and 6 decades, respectively, during reaction. 

Now let us discuss the particular situation of STS experiments [32,33,35, 36]. Here we concentrate mainly on the dependence on the tip-to-molecule distance [33]. When the tip (left lead in our notations) is far from the molecule, the junction is strongly asymmetric rR approximately symmetric rR rR and r] 0.5, and the conductance curve is of the type shown in Fig. 30. We calculated the transformation of the conductance from the asymmetric to symmetric case (Fig. 32). It is one new feature appeared in asymmetric case due to the fact that we started from a finite parameter r] = 0.2 (in the Fig. 31 77 = 0), namely a single peak at negative voltages, which is shifted to smaller voltage in the symmetric junction. The form and behavior of this peak is in agreement with experimental results [33]. 

Figure 2. Membrane capacitance (Curve 1) and conductance (Curve 2) at different...

Figure 3. Membrane capacity (Curve I) and conductivity (Curve 2) of squid giant axon at various frequencies. Note anomalous behavior at low frequencies.

The authors pointed out the similarity of the conductivity curves (Fig. 4) and viscosity curves (Fig. 14) which they observed. The shapes of both curves may be explained in the same way, namely by the formation and disappearance of... 

Recently Swinarski and Dembinski [51] and Swinarski and Piotrowski [52], have examined the viscosities of the three component solutions HN03-H2S04-H20. The diagram in Fig, 14 shows the results of these investigations, in terms of changes in viscosity with increase in HN03 content. The authors pointed out a similarity between the viscosity curve they obtained and the electric conductivity curve (see Fig. 4, p. 18). 

Figure 21. Temperature variation of the CO gap in Ndo.25Lao.25Cao.5-Mn03 (closed circles) and NdojSro.JvlnCb (closed triangles). Inset shows a typical tunneling conductance curve (from Araliaj et al.40). Shaded region represents the coexistence regime.

The electrical resistivity of Na W03, Li WOs, and K WOg has been measured at 300° K. The range of x values was 0.25 < x < 0.9. All resistivities were characteristic of a metal and lie on a single curve. Extrapolation of the conductivity curve to zero conductivity indicated that the tungsten bronzes should be semiconductors for x < 0.25. The resistivities measured for tungsten bronzes with x < 0.25 showed semiconducting behavior. The resistivity of Li WOg exhibited an anomalous peak in the p vs. T curve. The Hall coefficient of Li0 37WO3 indicated one free electron per alkali atom, as previously found for Na WOg. The Seebeck coefficient of Na WOg depended linearly on x 2/3, as expected from free electron theory. The implications of these and other data are discussed. 

If c or V is known and a is determined by one of the experimental methods mentioned in Section 1.10, K can be calculated by these equations. These equations are often referred to as Ostwald s dilution law, as they express the correlation between dilution and the degree of dissociation. As the latter is proportional to the molar conductivity of the solution, the above correlation describes the particular shapes of the conductivity curves shown in Fig. 1.3. 

One consequence of the modified defect chemistry being restricted to the boundary is readily seen in Fig. 27. Unlike in the case of homogeneous doping, in heterogeneous doping the transition from interstitial to vacancy type does not show up as a knee in the conductivity curves, since, as soon as the boundary zone becomes less conductive, the bulk which is in parallel, dominates.113... 

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