Diffusion ionic solutions

Liquid Junction Potentials A liquid junction potential develops at the interface between any two ionic solutions that differ in composition and for which the mobility of the ions differs. Consider, for example, solutions of 0.1 M ITCl and 0.01 M ITCl separated by a porous membrane (Figure 11.6a). Since the concentration of ITCl on the left side of the membrane is greater than that on the right side of the membrane, there is a net diffusion of IT " and Ck in the direction of the arrows. The mobility of IT ", however, is greater than that for Ck, as shown by the difference in the... 

Thermal motion of the ions in the EDL was included in the theories developed independently by Georges Gouy in Erance (1910) and David L. Chapman in England (1913). The combined elfects of the electrostatic forces and of the thermal motion in the solution near the electrode surface give rise to a diffuse distribution of the excess ions, and a diffuse EDL part or diffuse ionic layer with a space charge Qy x) (depending on the distance x from the electrode s surface) is formed. The total excess charge in the solution per unit surface area is determined by the expression... 

For hydrophilic and ionic solutes, diffusion mainly takes place via a pore mechanism in the solvent-filled pores. In a simplistic view, the polymer chains in a highly swollen gel can be viewed as obstacles to solute transport. Applying this obstruction model to the diffusion of small ions in a water-swollen resin, Mackie and Meares [56] considered that the effect of the obstruction is to increase the diffusion path length by a tortuosity factor, 0. The diffusion coefficient in the gel, )3,i2, normalized by the diffusivity in free water, DX1, is related to 0 by... 

Diffusion in solution is the process whereby ionic or molecular constituents move under the influence of their kinetic activity in the direction of their concentration gradient. The process of diffusion is often known as self-diffusion, molecular diffusion, or ionic diffusion. The mass of diffusing substance passing through a given cross section per unit time is proportional to the concentration gradient (Fick s first law). 

The surface sites and complexes lie in a layer on the mineral surface which, because of the charged complexes, has a net electrical charge that can be either positive or negative. A second layer, the diffuse layer, separates the surface layer from the bulk fluid. The role of the diffuse layer is to achieve local charge balance with the surface hence, its net charge is opposite that of the sorbing surface. Double layer theory, applied to a mixed ionic solution, does not specify which ions make up the diffuse layer. 

The compact and diffuse layers act as two capacitors in series. In between the Cd Zf parallel circuit and the counter electrode, the resistance of the ionic solution consists of two parts, one for the solution between the working... 

An adsorbed layer of water molecules at the interface separates hydrated ions from the solid surface. The interfacial electric double layer can be represented by a condenser model comprising three distinct layers a diffuse charge layer in the ionic solution, a compact layer of adsorbed water molecules, and a diffuse charge layer in the solid as shown in Fig. 5-8. The interfacial excess charge on the... 

Differentiating Eqn. 5—3 with respect to the potential, we obtain the differential electric capacity, Ci = (3oM/d oHP), of the diffuse layer in an aqueous ionic solution of z-z valence as shown in Eqn. 5-4 ... 

Further, the thicknesses of the diffuse and space charge layers depend on the potentials Ma and i sc across the respective layers for the space charge layer the thickness, dgc, is expressed, to a first approximation, by dsc = 2Lox (eA /kT)- [Memming, 1983]. The Debye length, Ld, is about 100 nm in usual semiconductors with impurity concentrations in the order of 10 cm and is about 10 nm in dilute 0.01 M ionic solutions. 

The structure of the double layer can be altered if there is interaction of concentration gradients, due to chemical reactions or diffusion processes, and the diffuse ionic double layer. These effects may be important in very fast reactions where relaxation techniques are used and high current densities flow through the interface. From the work of Levich, only in very dilute solutions and at electrode potentials far from the pzc are superposition of concentration gradients due to diffuse double layer and diffusion expected [25]. It has been found that, even at high current densities, no difficulties arise in the use of the equilibrium double layer conditions in the analysis of electrode kinetics, as will be discussed in Sect. 3.5. 

Certain complications arise when solutions containing both non-diffusible and (inevitably) diffusible ionic species are considered. Gibbs predicted and later Donnan demonstrated that when the non-diffusible ions are located on one side of a semipermeable membrane, the distribution of the diffusible ions is unequal when equilibrium is attained, being greater on the side of the membrane containing the non-diffusible ions. This distribution can be calculated thermodynamically, although a simpler kinetic treatment will suffice. 

When dealing with currents in ionic solutes, one must take into account the finite diffusion of ions within the electrolyte. As mentioned in Section 6.21, Fick s83 second law of diffusion states that the time-dependence of the concentration profile in a one-dimensional planar system Co(x,t) depends linearly on the derivative of the concentration gradient ... 

How can this concept be used to calculate diffusion coefficients in ionic solutions First one has to remember that for diffusion in one direction. 

The Nemst-Planck equation is conventionally applied to measure iontophoretic flux and arises from the theoretical development of Eq. 1 to define the flux of an ionic solute /, across a membrane (a) by simple diffusion due to the solute concentration gradient and (b) as a result of the electric potential difference across the membrane (electrochemical transport) [68-70]. 

In real cells, multiple transmembrane pumps and channels maintain and regulate the transmembrane potential. Furthermore, those processes are at best only in a quasi-steady state, not truly at equilibrium. Thus, electrophoresis of an ionic solute across a membrane may be a passive equilibrative diffusion process in itself, but is effectively an active and concentra-tive process when the cell is considered as a whole. Other factors that influence transport across membranes include pH gradients, differences in binding, and coupled reactions that convert the transported substrate into another chemical form. In each case, transport is governed by the concentration of free and permeable substrate available in each compartment. The effect of pH on transport will depend on whether the permeant species is the protonated form (e.g., acids) or the unprotonated form (e.g., bases), on the pfQ of the compound, and on the pH in each compartment. The effects can be predicted with reference to the Henderson-Hasselbach equation (Equation 14.2), which states that the ratio of acid and base forms changes by a factor of 10 for each unit change in either pH or pfCt ... 

Water dynamics is slowed down by the electric field of the cation, as revealed by diffusion coefficient reduced by a factor of two, compared with pure SPC/E water [132]. A reduction of D of water in ionic solutions is also observed experimentally, with values, determined with the tracer technique, ranging from 1.22 10-5 cm /s for Li+ to 0.52 and 0.53 10 5 cm /s for Fe3+ and Al3+, respectively [206]. 

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