Electric Field in an Electrolyte

Fig. 4.2. The migration of ions resulting from a gradient of electrostatic potential (i.e., an electric field) in an electrolyte. The electric field is produced by the application of a potential difference between two electrodes immersed in the electrolyte. The directions of increasing electrostatic potentials and of ionic migration are shown below the diagram.

Fig. 4 An ideally polarizable cylinder subjected to a nonuniform E)C electric field in an electrolyte with thin double layers (a) field lines and the DEP force, typically directed down the field gradient, (b) Streamlines of ICEO flow and the ICEP velocity, which always directed opposite to the DEP force [4]...

Full evaluation of equation (2.4) thus requires knowledge of the charge distribution at the electrode - electrolyte interface, a problem that has been explored in various works.For example, Dickinson and Compton recently used numerical modelling to solve the Poisson - Boltzmann equation, which describes the electric field in an electrolyte solution under thermodynamic equilibrium, for hemispherical electrodes. The simulations revealed a transition between two classical limits a planar double layer as predicted by the Gouy - Chapman model and the spherical double layer associated with a point charge (Coulomb s Law). This is illustrated in Fig. 2.2, in which the dimensionless charge density, Q ( FrqjRTEQEg) is plotted as a function of the dimensionless hemispherical electrode radius,... 

Fig. 4.45. A geometric representation of the electric field In an electrochemical system in which plane-parallel electrodes are immersed in an electrolyte so that they extend up to the walls of the rectangular insulating container. The equipotential surfaces are parallel to the electrodes.

From the beginning of free solution electrophoresis, band broadening from thermal effects was foreseen as the main problem restricting its development [6]. The energy generated as heat by application of an electric field to an electrolyte solution in a column raises the solution temperature, but more critically, results in a radial... 

Ire boundary element method of Kashin is similar in spirit to the polarisable continuum model, lut the surface of the cavity is taken to be the molecular surface of the solute [Kashin and lamboodiri 1987 Kashin 1990]. This cavity surface is divided into small boimdary elements, he solute is modelled as a set of atoms with point polarisabilities. The electric field induces 1 dipole proportional to its polarisability. The electric field at an atom has contributions from lipoles on other atoms in the molecule, from polarisation charges on the boundary, and where appropriate) from the charges of electrolytes in the solution. The charge density is issumed to be constant within each boundary element but is not reduced to a single )oint as in the PCM model. A set of linear equations can be set up to describe the electrostatic nteractions within the system. The solutions to these equations give the boundary element harge distribution and the induced dipoles, from which thermodynamic quantities can be letermined. 

For electrolytic solutions, migration of charged species in an electric field constitutes an additional mechanism of mass transfer. Thus the flux of an ionic species Nj in (g mol)/(cm s) in dilute solutions can be expressed as... 

Transport numbers are intended to measure the fraction of the total ionic current carried by an ion in an electrolyte as it migrates under the influence of an applied electric field. In essence, transport numbers are an indication of the relative ability of an ion to carry charge. The classical way to measure transport numbers is to pass a current between two electrodes contained in separate compartments of a two-compartment cell These two compartments are separated by a barrier that only allows the passage of ions. After a known amount of charge has passed, the composition and/or mass of the electrolytes in the two compartments are analyzed. Erom these data the fraction of the charge transported by the cation and the anion can be calculated. Transport numbers obtained by this method are measured with respect to an external reference point (i.e., the separator), and, therefore, are often referred to as external transport numbers. Two variations of the above method, the Moving Boundary method [66] and the Eiittorff method [66-69], have been used to measure cation (tR+) and anion (tx ) transport numbers in ionic liquids, and these data are listed in Table 3.6-7. 

Incomplete Dissociation into Free Ions. As is well known, there are many substances which behave as a strong electrolyte when dissolved in one solvent, but as a weak electrolyte when dissolved in another solvent. In any solvent the Debye-IIiickel-Onsager theory predicts how the ions of a solute should behave in an applied electric field, if the solute is completely dissociated into free ions. When we wish to survey the electrical conductivity of those solutes which (in certain solvents) behave as weak electrolytes, we have to ask, in each case, the question posed in Sec. 20 in this solution is it true that, at any moment, every ion responds to the applied electric field in the way predicted by the Debye-Hiickel theory, or does a certain fraction of the solute fail to respond to the field in this way In cases where it is true that, at any moment, a certain fraction of the solute fails to contribute to the conductivity, we have to ask the further question is this failure due to the presence of short-range forces of attraction, or can it be due merely to the presence of strong electrostatic forces ... 

One important stracture in molecules are polar bonds and, as a result, polar molecules. The polarity of molecules had been first formulated by the Dutch physicist Peter Debye (1884-1966) in 1912, as he tried to build a microphysical model to explain dielectricity (the behaviour of an electric field in a substance). Later, he related the polarity of molecules to the interaction between molecules and ions. Together with Erich Hiickel he succeeded in formulating a complete theory about the behaviour of electrolytes (Hofimann, 2006). The discovery of the dipole moment caused high efforts in the research on physical chemistry. On the one hand, methods for determining the dipole momerrt were developed. On the other hand, the correlation between the shape of the molectrle and its dipole moment was investigated (Estermanrr, 1929 Errera Sherrill, 1929). 

The first study on the oxidation of arylmethanes used this reaction as a model to show the general advantages of electrochemical micro processing and to prove the feasibility of an at this time newly developed reactor concept [69]. Several limits of current electrochemical process technology hindered its widespread use in synthetic chemistry [69]. As one major drawback, electrochemical cells stiU suffer from inhomogeneities of the electric field. In addition, heat is released and large contents of electrolyte are needed that have to be separated from the product. 

From the physical point of view there cannot exist, under equilibrium conditions, a measurable excess of charge in the bulk of an electrolyte solution. By electrostatic repulsion this charge would be dragged to the phase boundary where it would be the source of a strong electric field in the vicinity of the phase. This point will be discussed in Section 3.1.3. 

The description of the properties of this region is based on the solution of the Poisson equation (Eqs 4.3.2 and 4.3.3). For an intrinsic semiconductor where the only charge carriers are electrons and holes present in the conductivity or valence band, respectively, the result is given directly by Eq. (4.3.11) with the electrolyte concentration c replaced by the ratio n°/NA, where n is the concentration of electrons in 1 cm3 of the semiconductor in a region without an electric field (in solid-state physics, concentrations are expressed in terms of the number of particles per unit volume). 

A further electrokinetic phenomenon is the inverse of the former according to the Le Chatelier-Brown principle if motion occurs under the influence of an electric field, then an electric field must be formed by motion (in the presence of an electrokinetic potential). During the motion of particles bearing an electrical double layer in an electrolyte solution (e.g. as a result of a gravitational or centrifugal field), a potential difference is formed between the top and the bottom of the solution, called the sedimentation potential. 

The basic requirements of electrophoresis are a semi-conducting medium and an electric field. The semi-conducting medium can be a paper soaked in an electrolyte or a gel placed in an electrolyte. In the case of CE, it is a capillary filled with an electrolyte or a gel. The electric field is generated by applying a voltage difference over the capillary. 

Semiconductor - Electrolyte Interlace The electric field in the space charge region that may develop at the semiconductor electrolyte interface can help to separate photogenerated e /h 1 couples, effectively suppressing recombination. When a semiconductor is brought into contact with an electrolyte, the electrochemical potential of the semiconductor (corresponding to the Fermi level, Ey of the solid [50]) and of the redox couple (A/A ) in solution equilibrate. When an n-type semiconductor is considered, before contact the Ey of the solid is in the band gap, near the conduction band edge. After contact and equilibration the Ey will... 

In general, an electronic conductor which is used to introduce an electric field or electric current is called an electrode. In electrochemistry, an electronic conductor immersed in an electrolyte of ionic conductor is conventionally called the electrode. Since the function of an electrode to provide electric current does not work in isolation but requires the presence of an electrolyte in contact with the electrode, the term of "electrode" is defined as a combination of an electronic conductor and an ionic electrolyte. Usually, an electrode is used in the form of its partial inunersion in an electrolyte as shown in Fig. 4-1 (a). It is, however, more common to define the electrode in the form of complete immersion in the electrolyte as shown in Fig. 4—1 (b). 

There is a modest increase in the electrical conductance with an increase in the electric-field gradient, an effect that operates with both strong and weak electrolytes (the first Wien effect). More important in the present context is the marked increase in electrical conductance of weak electrolytes when a high-intensity electric field is applied (second Wien effect). The high field promotes an increase in the concentration of ion pairs and free ions in the equilibrium... 

Light absorption causes formation of an electron/hole (e h ) pair in the interfacial region of the solid and, in the presence of an electric field (e. g. when the solid is held in an electrolyte), the electrons migrate inwards towards the bulk of the solid and the holes move towards the surface and react with the FeOH groups, i.e. the charges separate. The surface reaction is, Fe-OH + hye Fe(OH)s where s = surface and hvB is a hole. A feature of the iron oxides is electron/hole pair recombination - many electrons recombine with the holes and are neutralized - which decreases the photo-activity of the solid. The extent of recombination depends to some extent on the pH of the solution and its effect on the proportion of FeOH groups at the surface (see Chap. 10 and Zhang et al., 1993). 

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