Electrolytes, symmetric

Valleau J P, Cohen L K and Card D N 1980 Primitive model electrolytes. II. The symmetrical electrolyte J. Chem. Phys. 72 5942... 

To conclude this section let us note that already, with this very simple model, we find a variety of behaviors. There is a clear effect of the asymmetry of the ions. We have obtained a simple description of the role of the major constituents of the phenomena—coulombic interaction, ideal entropy, and specific interaction. In the Lie group invariant (78) Coulombic attraction leads to the term -cr /2. Ideal entropy yields a contribution proportional to the kinetic pressure 2 g +g ) and the specific part yields a contribution which retains the bilinear form a g +a g g + a g. At high charge densities the asymptotic behavior is determined by the opposition of the coulombic and specific non-coulombic contributions. At low charge densities the entropic contribution is important and, in the case of a totally symmetric electrolyte, the effect of the specific non-coulombic interaction is cancelled so that the behavior of the system is determined by coulombic and entropic contributions. 

A. L. Kholodenko, A. L. Beyerlein. Theory of symmetric electrolyte solutions Field theoretic approach. Phys Rev A 54 3309-3324, 1986. 

The commonly used method for the determination of association constants is by conductivity measurements on symmetrical electrolytes at low salt concentrations. The evaluation may advantageously be based on the low-concentration chemical model (lcCM), which is a Hamiltonian model at the McMillan-Mayer level including short-range nonelectrostatic interactions of cations and anions [89]. It is a feature of the lcCM that the association constants do not depend on the physical... 

For symmetric electrolytes i=l for 1 2 electrolytes (e.g., Na2S04), 1 3 electrolytes (AICI3), and 2 3 electrolytes ([Al2(S04)3], the corresponding valnes of A, are 1.587, 2.280, and 2.551. Mean ionic activity coefficients of many salts, acids, and bases in binary aqneons solutions are reported for wide concentration ranges in special handbooks. 

For symmetrical electrolytes, of, e.g., type 1 1, such a liquid-liquid interface, in equilibrium, is described by the standard Galvani potential, usually called the distribution potential. This very important quantity can be expressed in the three equivalent forms, i.e., using the ionic standard potentials, or standard Gibbs energies of transfer, and employing the limiting ionic partition coefficients [3] ... 

For solutions of simple electrolytes, the surface excess of ions can be determined by measuring the interfacial tension. Consider the valence-symmetrical electrolyte BA (z+ = —z = z). The Gibbs-Lippmann equation then has the form... 

If this equation is employed for a solution of a single valence-symmetrical electrolyte (z+ = z = z), then... 

This theory of the diffuse layer is satisfactory up to a symmetrical electrolyte concentration of 0.1 mol dm-3, as the Poisson-Boltzmann equation is valid only for dilute solutions. Similarly to the theory of strong electrolytes, the Gouy-Chapman theory of the diffuse layer is more readily applicable to symmetrical rather than unsymmetrical electrolytes. 

The charge density of specifically adsorbed ions (assuming that anions are adsorbed specifically while cations are present only in the diffuse layer) for a valence-symmetrical electrolyte (z+ = — z = z) is... 

Consider the simple case where both sides of the membrane are in contact with a solution of symmetrical electrolyte BA in a single solvent and the membrane is permeable for only one ionic species. In equilibrium its electrochemical potential (Eq. (3.1.5)) in both solutions adjacent to the membrane has the same value. Thus,... 

However some problems must be addressed prior to the use of Equation (3.66) from the data generated above. The first problem is that the ions in the diffuse layers must be included in the estimation of k. This becomes essential as soon as the particle-particle interactions become significant and so Equations (3.62) to (3.65) should contain a volume fraction dependence of k of the form given by Russel,30 for example for a symmetrical electrolyte ... 

S. Fevine and A. Suddaby Simplified Forms for Free Energy of the Double-Layers of Two Plates in a Symmetrical Electrolyte. Proc. Phys. Soc. A 64, 287 (1951). 

In the above equations, h is the film thickness, n is the munber concentration of z z symmetrical electrolyte and is the surface potential. The surface potential is the potential at the interface of stem and diffuse layers and is usually replaced by the zeta potential of the droplet determined from electrophoretic measurements. When the interface has an adsorbed layer of globular proteins, it may be reasonable to assume that the shear plane is located at the interface of protein layer. When xp > 2L, the disjoining pressure 11 / can be evaluated by replacing with potential and taking as (jCf - 2L,). 

The solution of the linearized Poisson-Boltzmann equation around cylinders also requires numerical methods, although when cylindrical symmetry and the Debye-Hiickel approximation are assumed the equation can be solved. The solution, however, requires advanced mathematical techniques and we will not discuss it here. It is nevertheless useful to note the form of the solution. The potential for symmetrical electrolytes has been given by Dube (1943) and is written in terms of the charge density a as... 

FIG. 11.5 Fraction of double-layer potential versus distance from a surface according to the Debye-Hiickel approximation, Equation (37) (a) curves drawn for 1 1 electrolyte at three concentrations and (b) curves drawn for 0.001 M symmetrical electrolytes of three different valence types. 

Field saturation. Consider a particle occupying a convex open domain CR3 (or ft2) with a smooth boundary du>, charged to the electric potential > 0, at equilibrium with an infinite solution of a symmetric electrolyte of a given average concentration. (Properties described below are directly generalizable to an arbitrary electrolyte or electrolyte mixture.)... 

The question to be discussed is whether saturation of the electric field (asserted by Proposition 2.1) implies saturation of the interparticle force of interaction. Consider for definiteness repulsion between two symmetrically charged particles in a symmetric electrolyte solution. In the onedimensional case (for parallel plates) the answer is known—the force of repulsion per unit area of the plates saturates. (This follows from a direct integration of the Poisson-Boltzmann equation carried out in numerous works, primarily in the colloid stability context, e.g., [9]. Recall that again in vacuum, dielectrics, or an ionic system with a linear screening, the appropriate force grows without bound with the charging of the particles.)... 

Consider the following simplest prototype problem for stationary electrodiffusion of a univalent symmetric electrolyte through a bipolar ion-exchange membrane with an antisymmetric piecewise constant fixed charge density XN(x). 

In 1962 Fuoss and Onsager began a revision of their treatment of the conductance of symmetrical electrolytes. In their first paper they considered the potential of total force in the second, the relaxation field in the third, electrophoresis and in the fourth, the hydrodynamic and osmotic terms in the relaxation field (1,2,3,4). In 1965 Fuoss, Onsager, and Skinner (5) combined the results of the four papers and formulated a general conductance equation ... 

Because so much of the behavior of suspensions is determined or modified by charge associated with the solid phases, ZPC may be inferred from a wide variety of experiments involving pH as a master variable. For example, coagulation and sedimentation rates are maximum at the ZPC, and anion and cation exchange capacities (measured with nonspecific, symmetrical electrolytes) are equal and minimum at the ZPC. More direct and less ambiguous are electrophoresis and streaming potential, in any of their modifications. One can estimate the IEP(s) by measuring adsorption of H+ and OH" if one is certain that no specific adsorption of other species occurs. 

A single symmetrical electrolyte of charge number z mil be assumed. This assumption facilitates the derivation while losing little owing to the relative unimportance of co-ion charge number. 

For an aqueous solution of a symmetrical electrolyte at 25°C, equation (7.6) becomes... 

We now discuss an asymptotic methodology of calculating the preferential interaction coefficient of nucleic acids. Assume that the electric potential of a cylindrical polyion satisfies the nonlinear PB equation. The polyion is immersed in an aqueous solution containing symmetric electrolytes. If y ze i/kBT denotes the reduced potential, where / is the actual potential, then the preferential interaction coefficient can be expressed in terms of the surface potential yfl[65-67, 77, 78]... 

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