Condition of electro-neutrality

Reciprocal salt mixtures. In a binary system there are three kinds of ions, e.g. A+, B+/X . However, only the amount of two of these three constituents can be independently changed because of the constraint given by the condition of electro-neutrality... 

This equation can apply to all ions under the condition of electro-neutrality. 

The Donnan potential can be calculated from the condition of electro-neutrality of the system ... 

The first, second, and third terms on the right-hand side of Equation (12.12) respectively, represent the three governing transport mechanisms of species diffusion, migration, and eonvection. Combining Equations (12.11) and (12.12) with the condition of electro-neutrality (E ZhCh =0) gives ... 

Preliminaries. In the previous chapter we dealt with locally electro-neutral time-dependent electro-diffusion under the condition of no electric current in a medium with a spatially constant fixed charge density (ion-exchangers). It was observed that under these circumstances electrodiffusion is equivalent to nonlinear diffusion with concentration-dependent diffusivities. 

We shall begin with a recapitulation of the conditions under which the local electro-neutrality approximation is expected to hold or, at least, to be consistent. Furthermore, we shall postulate using intuitive arguments the conditions of conjugation for the locally electro-neutral transport variables at the surfaces of discontinuity of N(x). (Some asymptotic justification for these conditions will be provided in the next chapter.)... 

Anomalous rectification [3]. Our aim in this section is to show that under certain conditions development of a nonequilibrium space charge may yield, besides the punch through, some additional effects, unpredictable by the locally electro-neutral formulations. We shall exemplify this by considering two parallel formulations—the full space charge one and its locally electro-neutral counterpart. It will be observed that inclusion of the space charge into consideration enables us to account for the anomalous rectification effect that could not be predicted by the locally electro-neutral treatment. Physical motivation for this study is as follows. 

Surface of gold electrodes was modified with thiol SAM and further reacted with PAMAM dendrimers by electrostatic interaction [148], Then, Prussian Blue (PB) was anchored on the surface of electrodes. The surface coverage of PB at acidic condition is improved on the dendrimer-modified electrodes as compared with that on naked electrodes. Moreover, the stability of electrodes at neutral pH increases on dendrimer-modified electrodes, while PB film is not formed on naked electrodes at the condition of neutral pH. It is suggested that, in the stable PB-dendrimer composite films prepared on thiolated gold electrode surfaces, the uptake of PB takes place inside the dendrimer and PB molecules retain their electrocatalytic properties for the electro-oxidation due to the permeability and hosting properties of dendrimer. 

At T > x , the network is in the very expanded state. The size of the chain between two junction points, R, is proportional to m R = aRo ma/oj as it is for fully str died chain. The reason for such an essential expamion is the osmotic presuie of counto- ions which originates from their translational entropy. From the entropy consideration counter ions would like to leave the network, however, this is forbidden due to the condition of total electro-neutrality. This effect was for the first time described in Ref. 7]. 

There are alternative algebraic functions. Instead of writing the electro-neutrality equation, we can derive a relation called the proton condition. If we made our solution from pure H2O and HB, after equilibrium has been reached the number of excess protons must be equal to the numtier of proton deficiencies. Excess of deficiency of protons is counted with respect to a zero level reference condition representing the species that were added, that is, H2O and HB. The number of excess protons is equal to [H ] the number of proton deficiencies must equal [B ] -I-[OH ]. This proton condition gives, as in equation iva, [H" ] = [B ] -f lOH-]. 

A precursor step to solving the electrical potentials within the electrolyte is carried out, whereby electro-neutrality is enforced at the solid-electrolyte interface via the adjustment of all solid-containing interface cells. These potentials are held as Dirichlet boundary conditions and the final electrical potential field throughout the electrolyte is calculated using... 

Therefore, one cannot proceed with the KB theory. Sometimes, this rendering of the KB theory impossible, is attributed to the long-range interactions between the ionic solutes. However, the KB theory does not require any specific behavior of the intermolecular interactions. The KB theory can be applied for ionic solutions without any restriction on the type of interactions. The apparent impossibility of obtaining an inverse of the matrix B is not due to any special electro-neutrality condition, but is a result of mismatch of the KBIs, Ga(g, defined in different ensembles. To clarify the situation, we consider the following two examples... 

To see this, we first note that though it is true that for ionic species, equations (4.123)-(4.126) can result from the electro-neutrality conditions, the conditions themselves are not necessarily a result of the electric charge neutrality. They arise from the closure condition with respect to the fragments A and B. Thus, for a solute S dissociating into two neutral fragments A and B, as in (4.118) not necessarily ionic species as in (4.121), we still have the following conservation relations ... 

To summarize, for ionic solutions, one can either adopt the view that the system is a two-component mixture and use the KB theory for a two non-ionic species, say water and salt [as has been done by Friedman and Ramanathan (1970) and by Chitra and Smith (2002)], where the system is open with respect to the water and the salt (as a single entity). In this view, there is no place for ion-ion correlations hence the electro-neutrality condition is irrelevant. In this view only correlations between neutral molecules are meaningful. Or we can view the system as water, cation, and anion - but in this case one must open the system with respect to each of the species individually (hence allow also charged fluctuations in the system). In this case, the KBI are meaningful, but the thermodynamic quantities such as V, or fi/(,/6Nj are not available. In the second view, the ion-ion correlations do enter into the KB theory, but again the electro-neutrality condition is irrelevant. 

An actual research topic is to also capture the electrical stimulation. In this case the influence of the local change of the concentrations and the electric potential - in the solution phase - on the unknowns in the gel phase has to be considered. In Avci et al. (Avci 2008), the electro-neutrality condition is substituted by an equation for the electric potential. So the electric potential may be used as an additional degree of freedom. 

Another possibility consists in grafting neutral and reticulated polymers onto the walls of the cell so as to reduce the siuface electric charge drastically and to increase the viscosity of the interfacial layer for eliminating electro-osmosis. This type of processing has been the subject of extensive studies to determine the nature, the structure, and the molecular weight of the most effective polymers [37-39]. But, the maintenance of its efficiency must be evaluated according to the variations of the experimental conditions, because electro-osmosis can be restored by the adsorption on the polymer of an ionic compound of the immersing liquid. In particular, Creux [40] has shown that pH and hydrocarbon additives can affect the efficiency of hydropolymers but not that... 

Chemical equilibrium in a closed system at constant temperature and pressure is achieved at the minimum of the total Gibbs energy, min(G) constrained by material-balance and electro-neutrality conditions. For aqueous electrolyte solutions, we require activity coefficients for all species in the mixture. Well-established models, e.g. Debye-Htickel, extended Debye-Hiickel, Pitzer, and the Harvie-Weare modification of Pitzer s activity coefficient model, are used to take into account ionic interactions in natural systems [15-20]. 

The general validity of the electro-neutrality condition requires that in a closed system no net generation or net consumption of free electrons will take place. In the presence of ionizing radiation, free electrons are produced whose concentration is compensated for by unusual atomic valency states with respect to equilibrium considerations, therefore, this effect can be ignored. As long as the FP in the above formula stands for the most easily oxidizable or reducible species in the system, the equation ( 2 V-V ) = 0 is valid. A single crystallite of the UO2 material can... 

In the present model. Equation (12.23) is solved for two anions Al(OH)4 and OH , and the concentration of cation, K is deduced with the electro-neutrality condition stated before from the known concentrations ofAl(OH)4 andOH The production terms (5,) forOH andAl(OH)4, evaluated using Faraday s law, respectively are ... 

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