Ionic motion, effective potential

At the shear plane, fluid motion relative to the particle surface is 2ero. For particles with no adsorbed surfactant or ionic atmosphere, this plane is at the particle surface. Adsorbed surfactant or ions that are strongly attracted to the particle, with their accompanying solvent, prevent Hquid motion close to the particle, thus moving the shear plane away from the particle surface. The effective potential at the shear plane is called the 2eta potential, It is smaller than the potential at the surface, but because it is difficult to determine 01 To usual assumption is that /q is effectively equal to which can be... 

The individual ionic activities must be estimated by use of the Debye-HUckel theory. However, Eq. (4.8.3) shows that the cationic and anionic contributions tend to cancel out. Hence, except for a truly unusual situation in which a particular ratio a(B)/a(A) exceeds a factor of ten, and/or where t/ z for a particular species is very large compared to all others, the emf remains well below the value of RT/F = 0.0592 V at room temperature. Thus, junction potentials tend to be small compared to most emfs developed by cells. The effect may be further reduced by use of salt bridges that contain cations and anions of comparable mobility, so as to compensate for the tendency to develop internal emfs. The effect is also attenuated by employing parchment, agar-agar gels, or collodion to impede unbalancing ionic motion across the junction. In any event, junction potentials of the type described here tend to be small. 

An elementary discussion of the neglected terms is given in [1.32]. Equation (1.8) is an equation for a wave function of the ions alone. The essential point is that for the ionic motion, an effective potential energy function... 

At finite concentrations this formula needs modifying in two ways. In the first place, diffusion is governed by the osmotic pressure, or chemical potential, gradient (not, strictly, by the concentration gradient), so that the mean activity coefficient of the electrolyte must be taken into account. In the second place, ionic atmosphere effects must be allowed for. In diffusion, unlike conductance, the two ions are moving in the same direction, and the motion causes no disturbance of the symmetries of the ionic atmospheres there is therefore no relaxation effect. There is a small electrophoretic effect, however, the magnitude of which for dilute solutions has been worked out by Onsager, and the most accurate measurements support the extended formula based on these corrections. 

These three terms represent contributions to the flux from migration, diffusion, and convection, respectively. The bulk fluid velocity is determined from the equations of motion. Equation 25, with the convection term neglected, is frequently referred to as the Nemst-Planck equation. In systems containing charged species, ions experience a force from the electric field. This effect is called migration. The charge number of the ion is Eis Faraday s constant, is the ionic mobiUty, and O is the electric potential. The ionic mobiUty and the diffusion coefficient are related ... 

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. 

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