Electroneutrality field

The occurrence of a reaction at each electrode is tantamount to removal of equal amounts of positive and negative charge from the solution. Hence, when electron-transfer reactions occur at the electrodes, ionic drift does not lead to segregation of charges and the building up of an electroneutrality field (opposite to the applied field). Thus, the flow of charge can continue i.e., the solution conducts. It is an ionic conductor. 

When charges of opposite sign are spatially separated, a potential difference develops. This potential difference between two unit volumes at Xj and x, opposes the attempt at charge segregation. The faster-moving positive ions face strong opposition from the electroneutrality field and they are slowed down. In contrast, the slower-... 

The picture of the development of the electroneutrality field raises a general question concerning the flow or drift of ions in an electrolytic solution. Is the flux of one ionic species dependent on the fluxes of the other species In the diffusion experiment just discussed, is the diffusion of positive ions affected by the diffusion of negative ions The answer to both these questions is in the affirmative. 

Without doubt, the ionic flows start off as if they were completely independent, but it is this attempt to assert their freedom that leads to an incipient charge separation and the generation of an electroneutrality field. This field, which is dependent on the flows of all ionic species, curtails the independence of any one particular species. In this way, the flow of one ionic species is coupled to the flows of the other species. 

When, however, the flux of the species i is affected by the flux of the species j through the electroneutrality field, then another modification (see Section 4.5.3) of the... 

The development of an electroneutrality field introduces an interaction between flows and makes the flux of one species dependent on the fluxes of all the other species. To treat situations in which there is a coupling between the drift of one species and that of another, a general formalism will be developed. It is only when there is zero coupling or zero interaction that one can accurately write the Nemst-Planck flux equation... 

Once the interaction (due to the electroneutrality field) develops, a correction term is required, i.e.. 

The important step in the derivation of the diffusion potential is the statement that under conditions of steady state, the electroneutrality field sees to it that the quantity of positive charge flowing into a volume element is equal in magnitude but opposite in sign to the quantity of negative charge flowing in (Fig. 4.82). That is. 

There is, however, another method of deriving the diffusion potential. One takes note of the fact that when a steady-state electroneutrality field has developed, the system relevant to a study of the diffusion potential hangs together in a delicate balance. The diffusion flux is exactly balanced by the electric flux the concentrations and the electrostatic potential throughout the interphase region do not vary with time. (Remember the derivation of the Einstein relation in Section 4.4.) In fact, one may turn a blind eye to the drift and pretend that the whole system is in equilibrium. 

As the present system is essentially an electronic conductor (electronic transference number, tei 1) over the entire range of the present concern, as is clearly seen from Figure 10.17, the local electroneutrality field will be negligible. Hence, the diffusion of each type of ionic defect proceeds in the respective sublattices with no mutual coupling or... 

Ion-selective bulk membranes are the electro-active component of ion-selective electrodes. They differ from biological membranes in many aspects, the most marked being their thickness which is normally more then 105 times greater, therefore electroneutrality exists in the interior. A further difference is given by the fact that ion-selective membranes are homogeneous and symmetric with respect to their functioning. However, because of certain similarities with biomembranes (e.g., ion-selectivity order, etc.) the more easily to handle ion-selective membranes were studied extensively also by many physiologists and biochemists as model membranes. For this reason research in the field of bio-membranes, and developments in the field of ion-selective electrodes have been of mutual benefit. 

First, when a large excess of inert electrolyte is present, the electric field will be small and migration can be neglected for minor ionic components Eq. (20-16) then applies to these minor components, where D is the ionic-diffusion coefficient. Second, Eq. (20-16) applies when the solution contains only one cationic and one anionic species. The electric field can be eliminated by means of the electroneutrality relation. 

This part will be concerned with the properties of electrolytes (liquid or solid) under ordinary laboratory conditions (i.e. in the absence of strong external electric fields). The electroneutrality condition (Eq. 1.1.1) holds with sufficient accuracy for current flow under these conditions ... 

It is characteristic for the actual diffusion in electrolyte solutions that the individual species are not transported independently. The diffusion of the faster ions forms an electric field that accelerates the diffusion of the slower ions, so that the electroneutrality condition is practically maintained in solution. Diffusion in a two-component solution is relatively simple (i.e. diffusion of a binary salt—see Section 2.5.4). In contrast, diffusion in a three-component electrolyte solution is quite complicated and requires the use of equations such as (2.1.2), taking into account that the flux of one electrically charged component affects the others. 

Electroneutral substances that are less polar than the solvent and also those that exhibit a tendency to interact chemically with the electrode surface, e.g. substances containing sulphur (thiourea, etc.), are adsorbed on the electrode. During adsorption, solvent molecules in the compact layer are replaced by molecules of the adsorbed substance, called surface-active substance (surfactant).t The effect of adsorption on the individual electrocapillary terms can best be expressed in terms of the difference of these quantities for the original (base) electrolyte and for the same electrolyte in the presence of surfactants. Figure 4.7 schematically depicts this dependence for the interfacial tension, surface electrode charge and differential capacity and also the dependence of the surface excess on the potential. It can be seen that, at sufficiently positive or negative potentials, the surfactant is completely desorbed from the electrode. The strong electric field leads to replacement of the less polar particles of the surface-active substance by polar solvent molecules. The desorption potentials are characterized by sharp peaks on the differential capacity curves. 

Field effects in electron hopping derive from the fact that electron motion is accompanied by the displacement of positive electroinactive ions in the same direction and/or negative electroinactive ions in the reverse direction so as to maintain electroneutrality. The analysis of these effects thus associates equations (4.22) and (4.23), depicting electron hopping, with equations like (4.27), which describes the concomitant motion of the electroinactive ions. Similarly, in terms of fluxes, equations (4.25) and (4.26) should be associated with equation (4.28). 

This means that the motions of the two species are coupled and show the same transport rate because of electroneutrality. The fastest species move ahead and generate an electrical field in such a way that the faster species are slowed down and the slower ones are accelerated. 

In the favourable case of low concentrations of highly mobile electronic species, both electrons and ions diffuse under the influence of concentration gradients. The electrons move ahead of the ions and in this way generate an internal electrical field in which the ions are accelerated and the electrons are slowed down in order to tnaintain electroneutrality. If... 

The very peculiar molar ratio 0.4 DDAB to 0.6 oleate, which gives rise to the narrow size distribution, is really noteworthy. This molar ratio corresponds closely to electroneutrality (this is not at 50 50 molarity, due to the relatively high pK of oleate carboxylate in the bilayer) and suggests that small mixed vesicles with an approximately equal number of positive and negative charges may enjoy particular stability. More detailed studies are needed, and this indicates the richness of the unexplored in the field of vesicles. This is shown in its fullness in the next section on the matrix effect, which is also an unexpected phenomenon and one that may have implications for the origin of early cell. 

Figure 26-25 Stacking of anions and cations at opposite ends of the low-conductivity sample plug (zone) occurs because the electric field in the sample plug is much higher than the electric field in the background electrolyte. Time increases from panels a to d. Electroneutrality is maintained by migration of background electrolyte ions, which are not shown.

The region extending from the phase boundary out to about 3 nm is quite unlike the solution beyond. Generalizations valid elsewhere in the solution do not necessarily apply here. In this inner zone, the so-called double-layer region [9], we may encounter a violation of the electroneutrality condition (see Sect. 4.1) and large electric fields. Concentrations may be enhanced or depleted compared with the adjacent solution. 

If the cations of variable valency (e.g., Fe2+/Fe3 + ) are present in not too low concentrations, the crystals will be semiconductors. In non-equilibrium vermiculites, the internal electric field is then strongly influenced by their electronic conductivity, as explained in Section 4.4.2. If we start with an equilibrium crystal and change either pH, ae, aor a, (where i designates any other component), coupled transport processes are induced. The coupling is enforced firstly by the condition of electroneutrality, secondly by the site conservation requirements in the T-O-T blocks (Fig. 15-3), and thirdly by the available free volume in the (van der Waals) interlayer. It is in this interlayer that the cations and the molecules are the more mobile species. However, local ion exchange between the interlayer and the relatively rigid T-O-T blocks is also possible. 

In an extrinsic semiconductor, containing only one type of dopant, there are equal densities of mobile charges (electrons in the n-type and holes in the jp-type) and ionized dopant atoms (positively charged for the n-type and negatively charged for the jp-type). For simplicity, we restrict this discussion to a jp-type extrinsic semiconductor. The condition of electroneutrality applies only in the absence of an external electric field. 

What happens when the dimensions are furthermore reduced Initially, an enhanced diffusive mass transport would be expected. That is true, until the critical dimension is comparable to the thickness of the electrical double layer or the molecular size (a few nanometers) [7,8]. In this case, diffusive mass transport occurs mainly across the electrical double layer where the characteristics (electrical field, ion solvent interaction, viscosity, density, etc.) are different from those of the bulk solution. An important change is that the assumption of electroneutrality and lack of electromigration mass transport is not appropriate, regardless of the electrolyte concentration [9]. Therefore, there are subtle differences between the microelectrodic and nanoelectrodic behaviour. 

---