Conductivity and mobility

The conductivity of a solution is a result of the movement of all ions in solution under the influence of an electric field. 

The current, /, that passes between two parallel electrodes of area A is related to the flux of charge j, and to the potential difference between them, A0, by 

Therefore, for the solution (which contains various ions) the measured conductivity, k, is given by 

As can be seen, the measurement of the conductivity of an electrolyte solution is not species selective. Individual ionic conductivities can be calculated only if the conductivity (or mobility) of one ion is known this in the case of a simple salt solution containing one cation and one anion. If various ions are present, calculation is correspondingly more difficult. Additionally, individual ionic conductivities can vary with solution composition and concentration. 

We next consider the relation between mobility and diffusion coefficient. This arises because a concentration gradient is also a chemical potential gradient. For a sufficiently dilute solute, i, 

---

The differentiation between whether delocalized (band theory) conductivity or diffusionlike hopping conductivity best explains experimental conductivity results is not always easy in practice but can be made by a comparison of the theoretical expressions for electrical conductivity and mobility of the charge carriers in a solid. 

TABLE 7.1 Electrical Conductivity and Mobility of Charge Carriers in Metals, Band-like Semiconductors, and Hopping Semiconductors... 

Baildown tests have been used for decades during the initial or preliminary phases of LNAPL recovery system design to determine adequate locations for recovery wells and to evaluate recovery rates. Baildown tests involve the rapid removal of fluids from a well with subsequent monitoring of fluid levels, both the LNAPL-water (or oil-water) interface and LNAPL-air (or oil-air) interface, in the well with time. Hydrocarbon saturation is typically less than 1, and commonly below 0.5, due to the presence of other phases in the formation (i.e., air and water). Since the relative permeability decreases as hydrocarbon saturation decreases, the effective conductivity and mobility of the LNAPL is much less than that of water, regardless of the effects induced by increased viscosity and decreased density of the LNAPL. 

Table 2.2. Conductivities and mobilities of some ions in water at infinite...

Section 7.2 agrees quite well with the theoretical estimates of Eq. (7.99). The conductivity and mobility data therefore seem to be consistent with a sharp mobility edge and with the theoretical calculations of Furthermore, the uncertainty principle broadening of Ef, is less than kT at the normal measurement temperatures and so is not a significant effect. 

The proton is indeed anomalous in its conductance and mobility. These properties do not vary with temperature in the expected, regular way. There is not the expected near-sameness for hydronium and deuterium ion mobilities. The conductance of protons in aqueous-non-aqueous media is wholly dependent on the mole-fraction of water present. 

The authors state that while the above definition is used widely, other authors have defined tortuosity as 1/T, T, and l/T as these forms are frequently encountered in expressions for ionic conductivity and mobility through tortuous membranes. Experimental measurement of liquid membrane support tortuosity is described by Bateman et al. 

It should be realized thatand just express the properties ofthe conductivity and mobility from which they are derived, and using them in the Fick s law Jc = —D c is at best a crude approximation. On the other hand they contain information about interparticle correlations that result from carrier-carrier interactions. A useful quantity that gauge the importance of such correlations is the Haven ratio... 

In most books on electrochemistry k and Uj are used as symbols for conductivity and mobility, respectively. In order to have the same symbols throughout this book, we are using here those which were introduced in the solid state physics chapter). 

The relationship between ionic conductivity and Onsager s theory can now be presented in terms of the electrochemical potential. By expressing the force leading to the transport of ions in terms of the gradient of jr,-, one finds important relationships between the diffusion coefficients of the ions, and the molar conductivity and mobility. Furthermore, when the force has the correct Newtonian units, one is also in a position to calculate the rate of entropy production. On the basis of the thermodynamics of irreversible processes, the relationship between the flux of ion i and the force Vp,- is... 

Conductivity and Mobility of neariy-free Charge Carriers 223... 

Paasch, G., Lindner, T, and Scheinert, S. 2002. Variable range hopping as possible origin of a universal relation between conductivity and mobility in disordered organic semiconductors. Synthetic Metals 132 97-104. 

The electrical properties of the homogeneous alloys (Hall effect, conductivity, thermoelectric power) were studied at room temperature on electrically homogeneous samples prepared under identical conditions. The measurements showed that the alloys in systems 1 through 5 have n-type conduction while those in system 6 have p-type conduction. Extrinsic conduction and a high carrier density have been established for the alloys in all the systems. The electrical conductivity and mobility (Fig. 2) decrease monotonically with an increase in the content of A B component in the solution. The thermoelectric power and the effective mass of the electrons have low values and vary little with the composition. 

Rupturing cells threaten physical safety and reduce cycle life. Precautions must be taken with aqueous electrolyte systems to restrict the voltage window to avoid rupture. As a result, the potential window for most aqueous systems is limited to about 1 V. The low voltage stability of aqueous electrolytes greatly restricts the energy and power density possible in an ES. Conversely, the higher ionic conductivity and mobility of aqueous electrolytes seen in Table 4.7 translates into the best possible capacitance for an ES and lower internal cell resistance. The low internal resistance allows quick response time. 

Ionic Atmosphere and Mobility Due to electrostatic forces, an ion is always surrounded by many other ions of opposite charge which form an ionic atmosphere. The ionic atmosphere can affect the conductance and mobility of the central ion in... 

Figure 1. (a) The density of states of a-SiHv after Fritzsche s synthesis of the experimental data. (d) A sketch of the microscopic conductivities and mobilities for the conduction and valence bands. 

In Fig. (lb) are shown the corresponding microscopic conductivities and mobilities. However, to complete the correspondence between... 

In the preceding chapters we have looked at temperature dependencies of concentrations of electronic defects and point defects, and we have looked at the conductivity and mobility of thermally activated diffusing species. In the following we consider the charge carrier mobilities of electrons and holes in some more detail. For instance for an intrinsic electronic semiconductor (where n=p) we can from Eq. 6.29 in combination with Eqs. 6.23 and 6.24 write an expression for... 

The multitude of transport coefficients collected can thus be divided into self-diffusion types (total or partial conductivities and mobilities obtained from equilibrium electrical measurements, ambipolar or self-diffusion data from steady state flux measurements through membranes), tracer-diffusivities, and chemical diffusivities from transient measurements. All but the last are fairly easily interrelated through definitions, the Nemst-Einstein relation, and the correlation factor. However, we need to look more closely at the chemical diffusion coefficient. We will do this next by a specific example, namely within the framework of oxygen ion and electron transport that we have restricted ourselves to at this stage. 

A large number of other experimental methods are available for the investigation of ion solvation and complexation processes. Some are related to the determination of motion inside the solution and enable the estimation of the effective volume of the moving solvated ion and, consequently, the solvation number. The motion may be spontaneous (e.g. diffusion), mechanically produced (e.g. viscosity) or electrically produced (e.g. conductivity). Conductivities and mobilities, which are closely related, provide a measure of the resistance of the complexed ions to motion through the solvent. Other methods include extraction, chromatography and isotopic dilution. 

At this point it is appropriate to say a few words on the conduction of current through solutions. As is well known, the current is carried through the solution by ions which differ from each other in their mobility. The conductance of a solution (which is the reciprocal resistance) is proportional to the number of ions in the solution and to some function of their mobility. To find this relationship between conductance and mobility let us start with Ohm s law... 

So far we discussed transport phenomena in organic materials at low values of electric fields F, at which the conductivity and mobility of charge carriers are independent of the applied electric field. However, at high electric fields the carrier mobility and the conductivity in organic disordered materials depend strongly on... 

Properties such as formation of ion pairs, viscosity, conductivity, and mobility are important factors to describe the efficiency of ion transport. Dielectric relaxation spectroscopy (DRS) [529] is a method that has not been applied for studying electrolytes related to lithium ion batteries. This group anticipates that this situation... 

---