Ionic solutions permittivity

Employing the additivity approximation, we find dielectric response of a reorienting single dipole (of a water molecule) in an intermolecular potential well. The corresponding complex permittivity jip is found in terms of the hybrid model described in Section IV. The ionic complex permittivity A on is calculated for the above-mentioned types of one-dimensional and spatial motions of the charged particles. The effect of ions is found for low concentrated NaCl and KC1 aqueous solutions in terms of the resulting complex permittivity e p + Ae on. The calculations are made for long (Tjon x) and rather short (xion = x) ionic lifetimes. 

This mention of a family of solvents with particular physical properties prompt us to remark that there are other solvents with special physical quantities requiring some modifications in the methodological formulation of basic PCM. We cite, among others, liquid crystals in which the electric permittivity has an intrinsic tensorial character, and ionic solutions. Both solvents are included in the IEF formulation of the continuum method [20] which is the standard PCM version. 

The present evidence is thus that kinetic effects may account for half or more of permittivity decreases of ionic solutions and this may be an important factor in determing the amplitude of the Y dispersion in conducting biopolymer solutions and lead to revisions in estimated nature and amount of bound water. The effect may also have some bearing on dielectric properties of cell interiors and membranes if these have appreciable conductances. It would seem premature to attempt definitive answers to such questions until the relative importance of static and kinetic effects in presumably simpler ionic solutions has been better established experimentally in comparison with theory which treats them self-consistently. 

The permittivity of ionic solutions, is less than that of the pure solvent and decreases linearly with an increase in concentration. The reason for this has already been discussed (Section 2.12.1) water dipoles held by the very strong local field of an ion cannot orient against the weak applied field used in measuring the dielectric constant. The average is therefore decreased. 

The operator Le has a different form according to the model we are using to describe the system. We report here the expression for three important cases, namely the linear infinite isotropic dielectric, the linear infinite anisotropic dielectric (with homogeneous tensorial permittivity c), and the infinite ionic solutions in the linearized Poisson-Boltzmann formulation ... 

The first result to be stressed is that, with the lEF approach, it is possible to reduce to an ASC form problems which are generally treated by resorting to 3D numerical techniques. Dielectrics with a tensorial permittivity c have been thus far treated by a combined Boundary Element - Finite Element Method (BEM/FEM) [36] and ionic solutions using Finite Difference (FD) approaches. 

On the contrary, by applying the lEF method, we have only to define the apparent charges spread on the cavity surface also for dielectric with a tensorial permittivity or for the ionic solutions, exactly as for the simple isotropic case. The basic relationships (18) can be written in the following form ... 

TABLE 2.12 Ionic Static Permittivity Decrements, 5uj/dm mol" [130] and Surface Tension Increments, dff/dc/mN-m" -moP -dm year, in Aqueous Solutions at 20-30°C... 

Debye and Hiickel devised a theory for the activity coefficients of ionic solutes. Their theory begins with the expression for the force between a pair of ions in Eq. (6.4-19), assuming a constant value of the permittivity of the solvent. It is also assumed that the centers of two ions cannot approach each other more closely than some distance of closest approach, called a. The solution is assumed to behave like an ordinary dilute solution except for the effects of the electrostatic forces. 

The actual value of the double-layer capacitance depends on many variables including electrode type, electrochemical potential, oxide layers, electrode surface heterogeneity, impurity adsorption, media type, temperature, etc. [1, pp. 45-48]. Capacitance of the double layer also largely depends on the intermolecular structure of the analyzed media, such as the dielectric constant (or high-frequency permittivity), concentration and types of conducting species, electron-pair donicity, dipole moment, molecular size, and shape of solvent molecules. Systematic correlation with dielectric constant is lacking and complex, due to ionic interactions in the solution. In ionic aqueous solutions with supporting electrolyte ("supported system") the values of -10-60 pF/ cm are typically experimentally observed for thin double layers and solution permittivity e - 80. The double-layer capacitance values for nonpolar dielec-... 

For 1% cells in the suspension the permittivity increment becomes AEp 25 (Figme 7-7), a value that is two to five orders of magnitude lower than typical values of permittivity increments observed in experimental dielectric studies of cellular colloidal dispersions [12]. Experimental assessment of the dielectric data in ionic solutions is further complicated by the masking effects of interfacial polarization at the electrode/solution interfaces that often become apparent below -1-10 kHz. 

Hess B, Hohn C. (2006) Modeling multibody effects in ionic solutions with a concentration dependent dielectric permittivity. Phys Kev Lett 96 1478011-1478014. 

Meanwhile, the R-R coupling (see Sect. 2.2) has evidently found general acceptance as the main reaction path for the electropolymerization of conducting polymers The ionic character of the coupling species explains why polar additives such as anions or solvents with high permittivity accelerate the rate of polymerization and function as catalysts. Thus, electropolymerization of pyrrole is catalyzed in CHjCN by bromide ions or in aqueous solution by 4,5-dihydro-1,3-benzenedisulfonic acid The electrocatalytic influence of water has been known since the work... 

In aqueous electrolyte solutions the molar conductivities of the electrolyte. A, and of individual ions, Xj, always increase with decreasing solute concentration [cf. Eq. (7.11) for solutions of weak electrolytes, and Eq. (7.14) for solutions of strong electrolytes]. In nonaqueous solutions even this rule fails, and in some cases maxima and minima appear in the plots of A vs. c (Eig. 8.1). This tendency becomes stronger in solvents with low permittivity. This anomalons behavior of the nonaqueous solutions can be explained in terms of the various equilibria for ionic association (ion pairs or triplets) and complex formation. It is for the same reason that concentration changes often cause a drastic change in transport numbers of individual ions, which in some cases even assume values less than zero or more than unity. 

When the relative permittivity of the organic solvent or solvent mixture is e < 10, then ionic dissociation can generally be entirely neglected, and potential electrolytes behave as if they were nonelectrolytes. This is most clearly demonstrated experimentally by the negligible electrical conductivity of the solution, which is about as small as that of the pure organic solvent. The interactions between solute and solvent in such solutions have been discussed in section 2.3, and the concern here is with solute-solute interactions only. These take place mainly by dipole-dipole interactions, hydrogen bonding, or adduct formation. 

The mobility depends on both the particle properties (e.g., surface charge density and size) and solution properties (e.g., ionic strength, electric permittivity, and pH). For high ionic strengths, an approximate expression for the electrophoretic mobility, pc, is given by the Smoluchowski equation ... 

Avogadro s number I = Ionic strength E = Permittivity of the solution... 

A further problem is that ion association, that is, the tendency of oppositely charged ions to form pairs or larger aggregates in solution, becomes increasingly important as the temperature rises unless the density is kept constant this is because ion association is inversely related to the dielectric constant (relative permittivity) of the medium, which is correlated with density for a given solvent. Helgeson and co-workers have attacked these problems theoretically for aqueous solutions up to 1000 °C.28 For our purposes, it is enough to note that quantitative treatment of ionic reactions in sub- and supercritical aqueous solutions is extremely difficult at present, and likely to remain so for some time. 

The electrostatic part of the ionic solvation energy, AGei (kj rriol ), corresponds to the difference between the electrostatic free energy of an ion in vacuo and that of the ion in a solution of relative permittivity eP It is roughly given by the Born equation ... 

In the above sections, we considered electrolytes that are ionophores.10 Iono-phores, like sodium chloride, are ionic in the crystalline state and are expected to dissociate into free ions in dilute solutions. In fact, in high-permittivity solvents (er>40), ionophores dissociate almost completely into ions unless the solutions are of high concentration. When an ionophore is completely dissociated in the solution, its molar conductivity A decreases linearly with the square root of the concentration c (<10 2 M) ... 

With the decrease in permittivity, however, complete dissociation becomes difficult. Some part of the dissolved electrolyte remains undissociated and forms ion-pairs. In low-permittivity solvents, most of the ionic species exist as ion-pairs. Ion-pairs contribute neither ionic strength nor electric conductivity to the solution. Thus, we can detect the formation of ion-pairs by the decrease in molar conductivity, A. In Fig. 2.12, the logarithmic values of ion-association constants (log KA) for tetrabutylammonium picrate (Bu4NPic) and potassium chloride (KC1) are plotted against (1 /er) [38]. 

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