Local dielectric coefficient

The effect of a variable local dielectric coefficient based on Eqs. [385]-... 

Figure 47 The potential profiles for the systems of Figure 46 with (circles) and without (no circles) the local dielectric coefficient correction.

Chernenko has investigated the effect of a counterion-induced dielectric decrement on the solution of the Gouy-Chapman equation. Sansom et al. have studied the effect of a local dielectric coefficient in an ion channel pore (in the absence of ions), and others have analyzed cylindrical models of Kozak and co-workers and Frahim and Diekmann have... 

The Helmholtz capacitance may be described by Ch = e o/d, where e is the local value of the dielectric coefficient and d is the Stem layer thickness. Under conditions where e is independent of surface charge density, we can identify two domains of nearly constant capacitance under varying surface charge densities (i.e., pH). When Cq Ch (at high ionic strength), C == Ch when Cq Ch (lower ionic strength), C Cq. When the surface potential is small, for example, less than 25 mV, then Cq = eeox = 2.3 (25°C) (equation... 

As mentioned before, the ions are modelled as point charges embedded in the center of a hard sphere where the sphere has the same dielectric coefficient as the surrounding medium. This approach replaces the polarization charges induced around the source charge from the surface of the sphere to the position of the source charge localized on it. The error made by this assumption was... 

The first term in Equation 11.1 is the Coulomb integral, 3b apj apj gj f e total charges on atoms k and I e is the local dielectric constant is the distance between atoms k and 1 Cf-a is the coefficient of atomic orbitals (a) in molecular orbital (r), where r refers to the molecular orbitals on one molecule and s refers to those on the other and Ef and Eg are the energies of the molecular orbitals. 

It is known that the value of dielectric constant is a function of the local electric field. Since the electric field near the interface is not a constant, but a function of distance from it, the further refinement of EDL theory and potential profile at the BLM interface should include this positional dependency of dielectric coefficient. The local value of this coefficient is of course a measure of the influence of uncharged species such as water or lipid molecules on the interaction between charges in their vicinity. The dielectric coefficient of bulk aqueous electrolyte at... 

The dramatic change in the local movement of polymer chains at Tg leads to large changes in a host of physical properties. These properties include density, specific heat, mechanical modulus, mechanical energy absorption, dielectric coefficients, acoustical properties, viscosity, and the rate of gas or liquid diffusion through the polymer, to name a few. Any of these properties can be used, at least in a crude manner, to determine T ... 

The state of an adsorbate is often described as mobile or localized, usually in connection with adsorption models and analyses of adsorption entropies (see Section XVII-3C). A more direct criterion is, in analogy to that of the fluidity of a bulk phase, the degree of mobility as reflected by the surface diffusion coefficient. This may be estimated from the dielectric relaxation time Resing [115] gives values of the diffusion coefficient for adsorbed water ranging from near bulk liquids values (lO cm /sec) to as low as 10 cm /sec. 

The expression for the excess Gibbs energy is built up from the usual NRTL equation normalized by infinite dilution activity coefficients, the Pitzer-Debye-Hiickel expression and the Born equation. The first expression is used to represent the local interactions, whereas the second describes the contribution of the long-range ion-ion interactions. The Bom equation accounts for the Gibbs energy of the transfer of ionic species from the infinite dilution state in a mixed-solvent to a similar state in the aqueous phase [38, 39], In order to become applicable to reactive absorption, the Electrolyte NRTL model must be extended to multicomponent systems. The model parameters include pure component dielectric constants of non-aqueous solvents, Born radii of ionic species and NRTL interaction parameters (molecule-molecule, molecule-electrolyte and electrolyte-electrolyte pairs). 

We shall now discuss the depression of the static permittivity of water by the addition of eiectrolyte solutes, which is a phenomenon of some importance in the understanding of the hydration sheath of the ions. It is essentially a dielectric saturation phenomenon the strong electric fields in the neighbourhood of the ions produce a non-linear polarization, which renders the local water moleodes ineffective as regards orientation in the applied field. It is possible to make estimates of the extent of hydration, or hydration number , of water molecules considered to be bound irrotationally to the average ion these estimates are in reasonable agreement with hydration numbers estimated on the basis of activity coefficients, entropies, mobilities, and viscosities. The hydration number must be distinguished from the number of water molecules actually adjacent to the ion in the first or second layers of hydration (the hydration sheath) it does not follow that all of these molecules can be considered to be attached to the ion as it moves in the solution. 

---