Diffusion of an electrolyte

I.2. Interdiffusion. If a membrane separates two solutions with two different counter-ions, but the same co-ion, interdiffusion of ions takes place. The mathematical treatment of these bi-ionic systems is about the same as of the diffusion of an electrolyte across a membrane (52, 54). 

Consider the simple diffusion of an electrolyte in the absence of an external electric field. The diffusion occurs because of a concentration gradient. The situation shown in Fig. 31.12(a) illustrates the initial condition of an electrolytic solution over which there is a layer of pure water. We assume that initially the boundary between the two layers is sharp. Suppose that the ion moves more rapidly than the ion. Then we soon have the situation illustrated in Fig. 31.12(b). In the first few moments of the process the positive ions outdistance the negative ions. An electrical double layer forms, with an associated electric field. The effect of this electric field is to speed up the slower ion and to slow down the faster ion. The system quickly adjusts so that both ions move, in the same direction with the same velocity. If this adjustment did not occur, large departures from electrical neutrality would occur because of the difference in velocity between the positive and negative ions. Correspondingly enormous electric potential differences would develop in the direction of diffusion. In fact, the potential difference that develops and that equalizes the velocities of the ions is rather small (< 100 mV) it is the diffusion potential and is responsible for the liquid junction potential that was described in Section 17.18. 

Diffusivities of Electroljrtes. Dilute Solutions, The diffusion of an electrolyte is complicated by the dissociation of the molecule into ions. Conductivity measurements indicate that the various ions have different mobilities, and consequently it might be assumed that the various ions might diffuse at different rates. This would lead, however, to high local concentrations of positively and negatively charged ions, and the electrostatic forces resulting would slow down the fast ions and speed up the slow. As a result, the ions actually diffuse at equal speeds, and the solution remains electrically neutral. Since the ions are smaller than the undissociated molecules, they diffuse at greater rates. 

For complete dissociation, Nemst (20) showed that at infinite dilution the diffusivity of an electrolyte is related to the ionic mobilities in the following manner ... 

Consider the diffusion of an electrolyte A Yfr in a dilute solution without any applied electrical field. In order to show that the diffusion coefficient expression (3.1.107) is to be used for the electrolyte as a whole or for any of the ions, we start with the flux expressions for the two charged species in a stagnant medium. Here the unknown diffusion potential is to be eliminated. Define the molar concentrations of positively charged and negatively charged ions in solution as C+ andC (gmol/cm ), respectively. 

The interaction of an electrolyte with an adsorbent may take one of several forms. Several of these are discussed, albeit briefly, in what follows. The electrolyte may be adsorbed in toto, in which case the situation is similar to that for molecular adsorption. It is more often true, however, that ions of one sign are held more strongly, with those of the opposite sign forming a diffuse or secondary layer. The surface may be polar, with a potential l/, so that primary adsorption can be treated in terms of the Stem model (Section V-3), or the adsorption of interest may involve exchange of ions in the diffuse layer. 

The investigations of interfacial phenomena of immiscible electrolyte solutions are very important from the theoretical point of view. They provide convenient approaches to the determination of various physciochemical parameters, such as transfer and solvation energy of ions, partition and diffusion coefficients, as well as interfacial potentials [1-7,12-17]. Of course, it should be remembered that at equilibrium, either in the presence or absence of an electrolyte, the solvents forming the discussed system are saturated in each other. Therefore, these two phases, in a sense, constitute two mixed solvents. 

When the pore bottom is covered by an oxide, the change of applied potential occurs almost completely in the oxide due to the very high resistance of the oxide. The rate of reactions is now limited by the chemical dissolution of the oxide on the oxide covered area. When the entire pore bottom is covered with an oxide the rate of reaction is the same on the entire surface of the pore bottom. As a result, the bottom flattens and the condition for PS formation disappears. The change of oxide coverage on the pore bottom can also occur when diffusion of the electrolyte inside deep pores becomes the rate limiting process. Since the current at which formation of an oxide occurs increases with HF concentration, a decreased HF concentration at pore bottom due to the diffusion effect can result in the formation of an oxide on the pore bottom of a deep pore at a condition that does not occur in shallow pores. 

The presence of water does not only create conditions for the existence of an electrolyte, but it acts as a solvent for the dissolution of contaminants [10], Oxygen plays an important role as oxidant element in the atmospheric corrosion process. The thickness of the water layer determines the oxygen diffusion toward the metallic surface and also the diffusion of the reaction products to the outside interface limited by the atmosphere. Another aspect of ISO definition is that a metallic surface is covered by adsorptive and/or liquid films of electrolyte . According to new results, the presence of adsorptive or liquid films of electrolyte perhaps could be not in the entire metallic surface, but in places where there is formed a central anodic drop due to the existence of hygroscopic particles or substances surrounded by microdrops where the cathodic process takes place. This phenomenon is particularly possible in indoor conditions [15-18],... 

Dialysis may be described as the fractional diffusion of solids from one side of a semi-permeable membrane to the other side under a concentration gradient Electrolysis is die process of local or spatial separation of the ions of an electrolyte and the transfer of their respective charges, ie the decompn of a compd by an elec current... 

There are several ways in which the solvent-supporting electrolyte system can influence mass transfer, the electrode reaction (electron transfer), and the chemical reactions that are coupled to the electron transfer. The diffusion of an electroactive species will be affected not only by the viscosity of the medium but also by the strength of the solute-solvent interactions that determine the size of the solvation sphere. The solvent also plays a crucial role in proton mobility water and other protic solvents produce a much higher proton mobility because of fast solvent proton exchange, a phenomenon that does not exist in aprotic organic solvents. 

Therefore, an additional expression is required to evaluate the three coefficients, Lu,Ln, and L22. Such a relation may be obtained from the diffusion of the electrolyte. In this case, there is no electric current in the system, and the total transport of charge must vanish... 

Consider a solution of an electrolyte MX to which a certain amount of radioactive M ions are added in the form of the salt MX. Further, suppose that the tracer ions are not dispersed uniformly throughout the solution instead, let there be a concentration gradient of the tagged species so that its diffusion flux Jp is given by Fick s first law... 

For aqueous solutions at room temperature, the order of magnitude of the diffusion coefficient of most of the common simple ions (Na, iC, CIO4) is 10 cm s . Suppose now that a capillary tube containing a solution of an electrolyte is brought into contact vertically and very gently with a capillary of pure water about how far would the electrolyte diffuse into the capillary of water in 24 hr ... 

An archetypal MEA consists of an electrolyte membrane sandwiched between two catalyst layers and two gas diffusion layers (GDLs) as shown in Fig. 1. The fuel and oxidant gases diffuse through the GDL to react in the catalyst layer between the electrode and electrolyte. The catalyst, typically Pt or Pt based alloy, are nanoparticles residing on carbon particles. In addition to its primary purpose as the center of reactivity, the catalyst must participate in the effective adsorption of the reactants, conduction of the electrons to/from the electrode and diffusion of protons to/from... 

The kinetic Monte Carlo (KMC) simulation method focuses on the state-to-state dynamic transitions and neglects the short-time system fluctuations. This approximation allows much longer timescales to be reached, without chemically relevant compromise in the resolution of the simulation, especially for solid-state systems. This is particularly important, since the diffusion of an oxygen ion on the surface of a YSZ electrolyte (among defect sites) requires approximately 1 ps, and the adsorption of one molecular oxygen onto the YSZ at 0.01 atm pressure requires approximately 0.5 ps [32]. Thus, deterministic simulation methods, like MD, are not easily able to capture this behavior, so other methods must be employed. 

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