Temperature dependence of the conductivity

The temperature dependence of the conductivity in polymer electrolytes has often been taken as indicative of a particular type of conduction mechanism In particular, a distinction is generally made between systems which show an Arrhenius type of behaviour and those which present a curvature in log a or log aT inverse temperature plots. In the latter case, empirical equations derived from the free-volume theory have 

Similarities between the PEO/H3PO4 and PEO/alkali salt systems have been pointed out i . The data for the amorphous PEO, O.42H3PO4 composition, which corresponds to the maximum of conductivity (Fig. 20.2), have been reproduced by the VTF equation with A = 2, T = 224 K and , = 0.05 eV whereas the x = 0.66 semi-crystalline composition exhibits Arrhenius behaviour.  

The PVA, O.42H3PO4 composition also shows Arrhenius-like behaviour and this is interpreted as due to the presence of a separate H3PO4/H2O conducting phase rather than to a transport mechanism linked to polymer motions. 

In all the other systems (Table 20.2), curvature has been observed in the log aT vs (lOOO/T) plots, as illustrated in Fig. 20.5 and reported in 

NMR and QNS studies of the polymer and anion dynamics are likely to provide a more direct approach to the understanding of the conduction mechanisms in these systems .  

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In Fig.. I we present the temperature dependence of the conductance for one of the CNTs, measured by means of a three-probe technique, in respectively zero magnetic field, 7 T and 14 T. The zero-field results showed a logarithmic decrease of the conductance at higher temperature, followed by a saturation of the conductance at very low temperature. At zero magnetic field the saturation occurs at a critical temperature, = 0.2 K, which shifts to higher temperatures in the presence of a magnetic field. 

Typical magnetoconductance data for the individual MWCNT are shown in Fig. 4. At low temperature, reproducible aperiodic fluctuations appear in the magnetoconduclance. The positions of the peaks and the valleys with respect to magnetic field are temperature independent. In Fig. 5, we present the temperature dependence of the peak-to-peak amplitude of the conductance fluctuations for three selected peaks (see Fig. 4) as well as the rms amplitude of the fluctuations, rms[AG]. It may be seen that the fiuctuations have constant amplitudes at low temperature, which decrease slowly with increasing temperature following a weak power law at higher temperature. The turnover in the temperature dependence of the conductance fluctuations occurs at a critical temperature Tc = 0.3 K which, in contrast to the values discussed above, is independent of the magnetic field. This behaviour was found to be consistent with a quantum transport effect of universal character, the universal conductance fluctuations (UCF) [25,26]. UCFs were previously observed in mesoscopic weakly disordered... 

So, despite the very small diameter of the MWCNT with respeet to the de Broglie wavelengths of the charge carriers, the cylindrical structure of the honeycomb lattice gives rise to a 2D electron gas for both weak localisation and UCF effects. Indeed, both the amplitude and the temperature dependence of the conductance fluctuations were found to be consistent with the universal conductance fluctuations models for mesoscopic 2D systems applied to the particular cylindrical structure of MWCNTs [10]. 

The experiments [2] yielded also a considerable temperature dependence of the conductivities - including solid phases too [3]. Hence, we are going to consider now the T dependence of the conductivity for the liquid alloys. 

Metals and semiconductors are electronic conductors in which an electric current is carried by delocalized electrons. A metallic conductor is an electronic conductor in which the electrical conductivity decreases as the temperature is raised. A semiconductor is an electronic conductor in which the electrical conductivity increases as the temperature is raised. In most cases, a metallic conductor has a much higher electrical conductivity than a semiconductor, but it is the temperature dependence of the conductivity that distinguishes the two types of conductors. An insulator does not conduct electricity. A superconductor is a solid that has zero resistance to an electric current. Some metals become superconductors at very low temperatures, at about 20 K or less, and some compounds also show superconductivity (see Box 5.2). High-temperature superconductors have enormous technological potential because they offer the prospect of more efficient power transmission and the generation of high magnetic fields for use in transport systems (Fig. 3.42). 

Therefore, the temperature dependence of the conductivity of complexes (LiX)o, igy/MEEP (X=CF3C00, SCN, SO3CF3, BF4) were also compared. The highest conductivity was obtained with BF4, and the activation energies for ion transport were found to be similar, suggesting that the mechanism for ion motion is independent on the salt. The lithium transport number, which varies from 0.3 to 0.6, depending on the complexed salt, does not change with concentration. 

Similarly, the temperature dependence of the conductivity of (triflate salts)o 25/MEEP complexes (the cations being Sr, Na, Li, Ag) has been studied. It was shown that the conductivity increases in the order Sr[Pg.204]

The temperature dependence of the conductivity can be described by the classical Arrhenius equation a = a"cxp(-E7RT), where E is the activation energy for the conduction process. According to the Arrhenius equation the lna versus 1/T plot should be linear. However, in numerous ionic liquids a non-linearity of the Arrhenius plot has been reported in such a case the temperature dependence of the conductivity can be expressed by the Vogel-Tammann-Fuller (VTF) relationship a = a°cxp -B/(T-T0), ... 

In addition, Janczak [26] studied the conductivity property of complex 3 with a polycrystalline sample, and the results show that the conductivity is in the range 2.7 -2.8 x 10-2Q-1cm-1 at room temperature. Very weak temperature dependence of the conductivity and a metallic-like dependence in conductivity are observed in the range 300-15 K. Ibers and co-workers [70] investigated the electrical conductivity of partially oxidized complex 82 with a suitable single crystal and the results indicate its semiconductor nature (Ea = 0.22eV). 

Horita et al. [97] studied the electrochemical polarization performance of Laj x SrxCo03 (x = 0.2, 0.3, 0.4) cathodes on (La, Sr) (Gd, Mg)03, LSGM electrolyte. With an increase of Sr content in LSC, the conductivity increases above 1400 Scm-1 (for x = 0.3, 0.4). The temperature dependence of the conductivity shows metallic behavior, especially above x = 0.3. The polarization activity for the 02 reduction increases with the Sr content in LSC. The cathodic polarization curves at the porous... 

Another semiconducting fulleride salt, [Ru(bpy)3](C5o)2 with bpy = 2,2 -bipyridine, crystallizes on the Pt electrode surface out of dichloromethane solutions saturated with [Ru(bpy)3]PF5 within a few minutes [79]. The NIR spectra of benzonitrile solutions of this salt demonstrate that the only fulleride anion present is 55 . The temperature dependence of the conductivity is typical for a semiconductor, with the room temperature conductivity being 0.01 S cm and the activation energy 0.1 kj mol (0.15 eV). It was postulated that there is an electronic overlap between the two ions of this salt leading to a donation of electron density from the 55 to the ligand orbitals in the [Ru(bpy)3] " AI 0.7) [79]. 

The effect of the addition of water and molecular solvents such as propylene carbonate, N-methylformamide, and 1-methylimidazole on the conductivity of [C4Cilm][Br] and [C2Cilm][BF4] was measured at 298 K [211]. The mixture of the IL and the molecular solvent or water showed a maximum on the conductivity/mole fraction IL curves. The maximum for nonaqueous solvents was at the level of approximately 18-30 mScm at low mole fraction of the IL and the maximum for water was at level approximately 92-98 mScm [211]. The conductivity of a mixture of these two ILs depends monotonically on the composition. The temperature dependence of the conductivity obeys the Arrhenius law. Activation energies, determined from the Arrhenius plot, are usually in the range of 10-40 kj mol / The mixtures of two ILs or of an IL with molecular solvents may find practical applications in electrochemical capacitors [212]. 

In NiO a metal-insulator transition has been observed under very high pressure (2.5Mbar) (Kawai and Mochizuki 1971) the conductivity at room temperature dropped abruptly by about 106. Nothing was determined regarding the temperature dependence of the conductivity, or the change of volume. 

The temperature dependence of the conductivity of the various classes of polymer electrolyte discussed above is summarized in the Arrhenius plots in Fig. 7.23. While a wide choice of materials is now available, it is important to note that improvements in conductivity are generally accompanied by losses in chemical stability and by increases in reactivity towards the lithium metal electrode. Successful development of rechargeable LPBs is therefore likely to be linked to the use of the so-called dry polymer electrolytes, namely pure PEO-LiX systems. This necessarily confines the operation of LPBs to above ambient temperatures. This restriction does not apply to lithium ion cells. 

The intrinsic band gap is too great to account for the observed conductivities and the presence of PtIV impurities, which create acceptor levels within the band gap, has been found in related systems.6 The temperature dependence of the conductivity as given by... 

Raman and Mossbauer studies.97 Thus the compounds are partially oxidized and should be more correctly expressed as [M(DPG)2KIs)o.2 with the nickel in a formal oxidation state of 2.20.97 The electrical conductivity in the Ni atom chain direction is 10-2 fi 1 cm-1, 105 times that of the unoxidized parent compound.97 98 The temperature dependence of the conductivity indicates that the compound is a semiconductor with AE = 0.19+0.01 eV. Table 3 indicates that changing the halide has little effect on the conductivity but that the Ni complex is more conducting than the Pd analogue. 

Single crystals of all these compounds behave as molecular metals at room temperature, but the temperature dependence of the conductivities vary significantly from one another (Figure 10). 

Figure 10 Temperature dependence of the conductivity for Ni(PC)I, Ni(TBP)I and Ni(TATP)I (reproduced with permission from Struct. Bonding (Berlin), 1982, 50, 1)...

The first term on the right-hand side of Eq. (4.39) indicates chemical relaxation, while the remaining terms are physical effects, such as changes of ionic mobility and density due to pressure and temperature changes. The temperature change can be eliminated by using a reference cell filled with a nonrelaxing solution with the same temperature dependence of the conductivity as the sample cell (Knoche and Wiese, 1974). 

The temperature dependence of the conductivity behavior of the nanoparticle films predicted that electronic conduction occurred via an electron hopping mechanism. 

A full model of the charge transport in the electrolyte would require the detailed description of the ionic transport processes inside the electrolyte. However, for the orientating study pursued in this contribution, it seems more appropriate to choose a simpler model that is able to describe the temperature dependence of the electrolyte qualitatively. The temperature dependence of diffusion coefficients in molten electrolytes can be described by an Arrhenius function [1]. Therefore, the temperature dependence of the conductivity is assumed to be of an Arrhenius type, as suggested in [6]. 

Sheppard46 has studied the temperature dependence of the conductivity in a homologous series of DBEGA resins with n in the range from 0 to 12. The data are shown plotted in Arrhenius fashion in Fig. 28, with the solid lines representing the fit of the WLF Equation to the data. Similar temperature dependences of the conductivity have been reported in fully-cured epoxy systems 24,86 . In both cases, and just as with the dipolar mobility, the driving force behind the observed temperature dependence is the mobility of the polymer as determined by the difference T — Tg. There are, however, differences in detail between the temperature dependences of the dipolar mobility and the conductivity. The first is that the C, constant Sheppard obtained for the conductivity is completely independent of the molecular... 

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