Electrical conductivity, description

Following the general trend of looldng for a molecular description of the properties of matter, self-diffusion in liquids has become a key quantity for interpretation and modeling of transport in liquids [5]. Self-diffusion coefficients can be combined with other data, such as viscosities, electrical conductivities, densities, etc., in order to evaluate and improve solvodynamic models such as the Stokes-Einstein type [6-9]. From temperature-dependent measurements, activation energies can be calculated by the Arrhenius or the Vogel-Tamman-Fulcher equation (VTF), in order to evaluate models that treat the diffusion process similarly to diffusion in the solid state with jump or hole models [1, 2, 7]. 

The Mechanism of Electrical Conduction. Let us first give some description of electrical conduction in terms of this random motion that must exist in the absence of an electric field. Since in electrolytic conduction the drift of ions of either sign is quite similar to the drift of electrons in metallic conduction, we may first briefly discuss the latter, where we have to deal with only one species of moving particle. Consider, for example, a metallic bar whose cross section is 1 cm2, and along which a small steady uniform electric current is flowing, because of the presence of a weak electric field along the axis of the bar. Let the bar be vertical and in Fig. 16 let AB represent any plane perpendicular to the axis of the bar, that is to say, perpendicular to the direction of the cuirent. 

This equation is identical to the Maxwell [236,237] solution originally derived for electrical conductivity in a dilute suspension of spheres. Hashin and Shtrikman [149] using variational theory showed that Maxwell s equation is in fact an upper bound for the relative diffusion coefficients in isotropic medium for any concentration of suspended spheres and even for cases where the solid portions of the medium are not spheres. However, they also noted that a reduced upper bound may be obtained if one includes additional statistical descriptions of the medium other than the void fraction. Weissberg [419] demonstrated that this was indeed true when additional geometrical parameters are included in the calculations. Batchelor and O Brien [34] further extended the Maxwell approach. 

In general case the solution describing the development of the process according to the scheme (2.114) is very bulky. Indeed, description of kinetics of the change in electric conductivity during adsorption of H-atoms would need the studies of behavior of dynamic system on the plane of the following type ... 

Cuevas JC, Heurich J, Pauly F, Wenzel W, Schon G (2003) Theoretical description of the electrical conduction in atomic and molecular junctions. Nanotechnology 14(8) R29-R38... 

Berlin YA, Ratner MA (2005) Intra-molecular electron transfer and electric conductance via sequential hopping unified theoretical description. Radiat Phys Chem 74 124—131... 

Direct measurement of concentration fluctuations for liquid flow in packed and fluidized beds have been made by Hanratty et al. (H4), Prausnitz and Wilhelm (P12), Cairns (Cl), and Cairns and Prausnitz (C4). Detailed descriptions of electrical conductivity probes used for measurement of these fluctuations have been given by Prausnitz and Wilhelm (Pll) and Lamb et al. (LI). 

The example selected here shows the techniques developed by Szwarc s group (Bhattacharyya, Lee, Smid and Szwarc, 1965). They eschewed completely the use of taps and in each experiment the electrical conductivity and the optical absorption of the solution were measured this actually involves the same combination of devices as the Pask-Nuyken and Holdcroft-Plesch reactors described in Section 3.2.2. The description of the procedure is taken almost verbatim from the original publication, whose conciseness cannot be bettered. 

Conductivity requires a charge carrier. There are two types of charge carriers we will consider electrons and ions. The structural descriptions of Chapter 1 will be helpful in determining the primary type of charge carrier within a material, if any. In subsequent sections, we explore the molecular origins of each type of conductivity, investigate the important parameters that cause conductivity to vary in materials, and describe additional electrical conduction phenomena that have revolutionized our lives. 

Unlike direct measurements of electrical conductivity of DNA [34, 35], chemical and photochemical experiments provide detailed data on how the CT efficiency depends on the DNA sequence and the local structure of an oligomer [5-9]. The latter experiments rely on intercalated or covalently bound chromophores which may affect the DNA structure. In the following, we will not discuss this effect of the chromophore although we realize that it may be important for a complete description of the systems used in those experiments. Rather, we will focus on a better understanding of the CT through unperturbed DNA fragments. 

This chapter consists of two sections, one being a general discussion of the stable forms of the elements, whether they are metals or non-metals, and the reasons for the differences. The theory of the metallic bond is introduced, and related to the electrical conduction properties of the elements. The second section is devoted to a detailed description of the energetics of ionic bond formation. A discussion of the transition from ionic to covalent bonding in solids is also included. 

Equations (1.194) and (1.195) can be accepted, within reason, because both the chemical equilibrium constants and the hole mobility for semiconductors have an Arrhenius-type temperature dependence. It has been shown, by a least-square fitting of the electrical conductivity data of Maruenda et al. to eqn (1.193), that 85 per cent of the data points are within 1.5 per cent of the calculated values, as shown in Fig. 1.58. This indicates that the model proposed here gives an accurate description of the data. The fitting parameters are listed in Table 1.5. 

As has been well established, piezoelectricity in a non-polar crystal is brought about by the internal strain in the crystal. The internal strain means the displacement of atoms which is not affine to the deformation of crystal lattice. In the case of a polymer film which is not electrically conductive and where the charges are possibly embedded, a description of piezoelectricity can be reached by considering not only the internal strain in the lattice but also the displacement of these charges which is not affine to the average deformation of the whole system. 

POLAR. Descriptive of a molecule in which the positive and negative electrical charges are permanently separated, as opposed to non-polar molecules in which the charges coincide, Polar molecules ionize in solution and impart electrical conductivity. Water, alcohol, and sulfuric acid are polar in nature most hydrocarbon liquids are not. Carboxyl and hydroxyl groups often exhibit an electric charge, The formation of emulsions and the action of detergents are dependent on tills behavior,... 

This picture, by the way, finds a most important application in the description of bonding in metals. Take, for instance, sodium, with one electron per atom for four orbitals. It is quite clear that here there is a vast excess of orbitals over electron pairs, and electrons in solid sodium, as in all metals, are effectively delocalized over the whole metal crystal. This idea can account satisfactorily for the electrical conductivity of metals. A more detailed discussion of metals would go beyond the space available here. 

Another troublesome borderline area is that between ionic solids and three-dimensional polymers. The distinction cannot be made from the structure alone. Electrical conductivity in the molten state does not, as already mentioned, necessarily demonstrate the presence of ions in the solid state and such a test is inapplicable where, as often happens, the substance sublimes or decomposes before melting. There can rarely be any objective means of assigning a compound to one category or the other. We are often persuaded towards one description on aesthetic grounds. For example, the structure of sodium chloride cannot easily be rendered in terms of localised, electron-pair bonds (but this is true also of many unequivocally covalent compounds). Its structure is eminently plausible for an array of cations and anions, however. 

The attenuation of the amplitudes along the propagation path in our wave description enters through the imaginary part —i 2 of the complex dielectric function i = eq — i 2. The latter translates into a complex refractive index h = n — ik. Both result from the electrical conductivity term a. The corresponding attenuation of the Poynting vector in our system, which we assume to respond in a linear way to field perturbations, accordingly shows... 

Within a one-electron description (i.e., U = 0, U being the on-site Coulomb repulsion [2,3], regular conducting TCNQ chains with p = electron per molecular site correspond to quarter-filled electronic bands. Consequently, the Fermi wave vector is in this case kF = n/4d, d being the spacing parameter between adjacent sites, and the chains are metallic. This is the case, for instance, for MEM(TCNQ)2 and TEA(TCNQ)2. Note that in these two salts the cations MEM+ and TEA+ are diamagnetic and do not participate in electrical conduction. 

Conductometry paved the way for the development of the ion-pair concept [3]. The oldest experimental evidence of ion-pairing was obtained from colligative properties and electrical conductivity measurements. It is generally accepted that electroneutral ion-pairs do not contribute to solution conductivity. Conductometry is now a reliable and well established technique even in low millimolar concentration ranges, but the full description of conductance in the presence of ion-pairing is anon-trivial task. To date the most accepted equation was developed by Fuoss and Hsia [92] and expanded by Fernandez-Prini and Justice [93] ... 

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