Ionic equilibria, electric field effects

Besides electric field effects, ion association within the polymer films plays an important role in the dynamics of electron hopping within the films. (Extensive ion association might be expected due to the high ion content and the low dielectric permittivity that prevails in the interiors of many redox polymers.) According to the model that includes ion association, the sharp rise in the apparent diffusion coefiicient as the concentration of the redox couple in the film approaches saturation is an expected consequence of the shift in the ionic association equilibrium to produce larger concentrations of the oxidized form of the redox couple, which is related to rapid electron acceptance from the reduced form of the couple [176]. 

The outer layer (beyond the compact layer), referred to as the diffuse layer (or Gouy layer), is a three-dimensional region of scattered ions, which extends from the OHP into the bulk solution. Such an ionic distribution reflects the counterbalance between ordering forces of the electrical field and the disorder caused by a random thermal motion. Based on the equilibrium between these two opposing effects, the concentration of ionic species at a given distance from the surface, C(x), decays exponentially with the ratio between the electro static energy (zF) and the thermal energy (R 7). in accordance with the Boltzmann equation ... 

At high field strengths a conductance Increase Is observed both In solution of strong and weak electrolytes. The phenomena were discovered by M. Wien (6- ) and are known as the first and the second Wien effect, respectively. The first Wien effect Is completely explained as an Increase In Ionic mobility which Is a consequency of the Inability of the fast moving Ions to build up an Ionic atmosphere (8). This mobility Increase may also be observed In solution of weak electrolytes but since the second Wien effect Is a much more pronounced effect we must Invoke another explanation, l.e. an Increase In free charge-carriers. The second Wien effect Is therefore a shift in Ionic equilibrium towards free ions upon the application of an electric field and is therefore also known as the Field Dissociation Effect (FDE). Only the smallness of the field dissociation effect safeguards the use of conductance techniques for the study of Ionization equilibria. 

The energy dissipation of a system containing free charges subjected to electric fields Is well known but this Indicates a non-equilibrium situation and as a result a thermodyanmlc description of the FDE Is Impossible. Within the framework of interionic attraction theory Onsager was able to derive the effect of an electric field on the Ionic dissociation from the transport properties of the Ions In the combined coulomb and external fields (2). It is not improper to mention here the notorious mathematical difficulty of Onsager s paper on the second Wien effect. 

Mobility — The (ionic or electric) mobility u of an ion is given by the drift velocity v (the velocity of an ion at equilibrium between the accelerating effect of the electric field and the decelerating effect of the viscous medium (Stokes friction)) of an ion and the effective electric field E v... 

To get the main idea of the charge effect on adsorption kinetics, it is sufficient to consider an aqueous solution of a symmetric (z z) ionic surfactant in the presence of an additional indifferent symmetric (z z) electrolyte. When a new interface is created or the equilibrium state of an interfacial layer disturbed a diffusion transport of surface active ions, counterions and coions sets in. This transport is affected by the electric field in the DEL. According to Borwankar and Wasan [102], the Gouy plane as the dividing surface marks the boundary between the diffuse and Stem layers (see Fig. 4.10). When we denote the surfactant ion, the counterion and the coion, respectively, with the indices / = 1, 2 and 3, the transport of the ionic species with valency Z/ and diffusion coefficient A, under the influence of electrical potential i, is described by the equation [2, 33] ... 

The model must deal with the situation encountered when the electrodes are coated with a polymer and ionic leakage eventually causes failure. Ionic species and molecules diffuse to the electrodes as migration takes place under the effect of the electric field, the latter governed by the electrolytic process. Before steady state is attained, there is a transient period during which the incoming diffused species and the migration component establish concentration profiles and an equilibrium ionic concentration at the electrodes. 

Particles dispersed in an aqueous medium invariably carry an electric charge. Thus they are surrounded by an electrical double-layer whose thickness k depends on the ionic strength of the solution. Flow causes a distortion of the local ionic atmosphere from spherical symmetry, but the Maxwell stress generated from the asymmetric electric field tends to restore the equilibrium symmetry of the double-layer. This leads to enhanced energy dissipation and hence an increased viscosity. This phenomenon was first described by Smoluchowski, and is now known as the primary electroviscous effect. For a dispersion of charged hard spheres of radius a at a concentration low enough for double-layers not to overlap (d> 8a ic ), the intrinsic viscosity defined by eqn. (5.2) increases... 

We have implicitly allowed the friction coefficients to be independent of the magnitude and the nature of applied forces, that is to say these coefficients are completely defined by the equilibrium properties of the solution as shown for example by Bearman for self-diffusion processes in binary liquid solutions [14]. Nevertheless, for ionic solutions polarization effects resulting from the application of an external field of forces may give rise to distorted ionic atmospheres and the identification of a unique interaction parameter in electrical and self-diffusion processes becomes questionable. However, it has been proved that as far as polyelectrolytes are concerned, the perturbation of the counter-ion distribution with respect to the equilibrium situation is fairly small despite the high polarizability of polyelectrolyte solutions [18]. Moreover, linear forces - fluxes relations have usually been reported from experimental investigations and for both polyelectrolyte and pure salt solutions electrical and self-diffusion determinations have led to nearly identical frictional parameters [19-20]. The friction model might therefore be used with confidence as long as systems not too far from equilibrium are concerned. 

In an electric field, the mobility of each ion is reduced because of the attraction or drag exerted by its ionic atmosphere. Similarly, the magnitudes of colligative properties are reduced. This explains why, for example, the value of i for 0.010 m NaCl is 1.94 rather than 2.00. What we can say is that each type of ion in an aqueous solution has two "concentrations." One is called the stoichiometric concentration and is based on the amount of solute dissolved. The other is an "effective" concentration, called the activity, which takes into account interionic attractions. Stoichiometric calculations of the type presented in Chapters 4 and 5 can be made with great accuracy using stoichiometric concentrations. However, no calculations involving solution properties are 100% accurate if stoichiometric concentrations are used. Activities are needed instead. The activity of an ion in solution is related to its stoichiometric concentration through a factor called an activity coefficient. Activities were introduced in Chapter 13. In Chapter 15 their importance in chemical equilibrium will be discussed in more detail. 

Reactions at surface functional groups are typically modeled via surface com-plexation models (SCMs), which are simply equilibrium chemical models modified to correct for surface electrostatic effects. SCMs model acid-base reactions at surface functional groups via intrinsic equilibrium constants and ionic solutirai species concentrations corrected to account for the electric field around the interface. Thus, the effective equilibrium constants account for both chemical and electrostatic effects, and continuously change as surface charging progresses. 

Membrane phenomena cover an extremely broad field. Membranes are organized structures especially designed to perform several specific functions. They act as a barrier in living organisms to separate two regions, and they must be able to control the transport of matter. Moreover, alteration in transmembrane potentials can have a profound effect on key physiological processes such as muscle contraction and neuronal activity. In 1875, Gibbs stated the thermodynamic relations that form the basis of membrane equilibria. The theory of ionic membrane equilibrium was developed later by Donnan (1911). From theoretical considerations, Donnan obtained an expression for the electric potential difference, commonly known as the membrane potential between two phases. 

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