Ionic self-diffusion

In binary ion-exchange, intraparticle mass transfer is described by Eq. (16-75) and is dependent on the ionic self diffusivities of the exchanging counterions. A numerical solution of the corresponding conseiwation equation for spherical particles with an infinite fluid volume is given by Helfferich and Plesset [J. Chem. Phy.s., 66, 28, 418... 

Ionic self-diffusion coefficient, mVs [Eqs. (16-73), (16-74)] Fractional approach to equilibrium Volumetric flow rate, mVs Enthalpy, J/mol ... 

Table II. Ionic Self-Diffusion Coefficients in 1200 EW Nafion (7)...

Diffusion coefficients provide two kinds of information. First, their absolute magnitudes, combined with membrane sodium ion concentrations, are useful indicators of the temperature dependence of ionic self-diffusion and thereby they yield the activation energy for diffusion. They thereby provide insight into the nature of the diffusion mechanism (16). When activation energies are measured for various types of related membranes, the influence of different membrane structural design features can thus be separated and determined directly. 

Much less is known about micellar charge and counterion binding in the case of bile salts. Based on the result of ionic self-diffusion measurements [20,163,173], conductance studies [17,18,187], Na, and Ca activity coefficients [16,19,144,188,189] and NMR studies with Na, Rb and Cs [190], a number of generalities can be made. Below the operational CMC, all bile salts behave as fully dissociated 1 1 electrolytes, yet interionic effects between cations and bile salt anions decrease the equivalent conductance of very dilute solutions [17,18,187]. With the onset of micelle formation, counterions become bound to a small degree values at this concentration are about < 0.07-0.13 and are not greatly influenced by the species of monovalent alkali cations [163,190]. At concentrations above the CMC, values remain relatively constant to 100 mM in the case of C and this... 

Saito Y, Yamamoto H, Nakamura O, Kageyama H, Ishikawa H, Miyoshi T, Matsuoka M (1999) Determination of ionic self-diffusion coefficients of lithium electrolytes using the pulsed field gradient NMR. J Power Sources 81-82 772-776... 

Three types of experiments have been employed to evaluate these ionomer films in solution environments sorption of water and electrolyte, ionic self-diffusion, and electrical conductance measurements. 

Ionic Self-Diffusion in Aqueous Solutions The inherent movement of ions in the absence of an external field is their self-diffusion, but a directional concentration gradient at finite concentration (a gradient of chemical potentials) causes directional diffusion of ions. The limiting ionic self-diffusion coefficients are generally obtained from the limiting conductivities... 

The molar conductivity may be determined, in addition to its direct determination from the specific conductivity k and the molar volume T (asA = kV), also from the ionic self-diffusion coefficients, obtained fi om NMR measurements as mentioned above, according to the Nemst-Einstein equation A = F (D+ +D-)/RT, with results in fair agreement with the directly determined values according to Tokuda et al. [80, 352, 374]. Ionic self-diffusion coefficients can be estimated from molecular d5mamics simulations and can then be transformed into the molar conductivity, as applied in [365, 387, 388], showing fair agreement with experimental values.. 

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