Ionic species, diffusion coefficient

Based on the competing needs of these factors, an electrolyte with some diffusivity of reactants is needed. For the PEFC, the diffusivity has been correlated from experimental data for 1100-EW Nafion, the most well-studied polymer electrolyte. Other electrolyte polymers should have similar trends, but actual values change with EW values. In general, low-EW polymers that absorb more water will have higher gas-phase species diffusion coefficients than higher EW electrolytes. Transport properties in the polyflourosulfonic acid (PFSA) based membranes such as Nafion are generally dependent on the water sorption in the membrane. For dry membranes, ionic conductivity and water mobihty are very low. As water sorption is increased, the membrane swells, and particularly at over 60% RH,... 

The diffusion of metal ions in vitreous siUca has not been studied as extensively as that of the gaseous species. The alkaU metals have received the most attention because their behavior is important in electrical appHcations. The diffusion coefficients for various metal ions are Hsted in Table 5. The general trend is for the diffusion coefficient to increase with larger ionic sizes and higher valences. 

For an ion to move through the lattice, there must be an empty equivalent vacancy or interstitial site available, and it must possess sufficient energy to overcome the potential barrier between the two sites. Ionic conductivity, or the transport of charge by mobile ions, is a diffusion and activated process. From Fick s Law, J = —D dn/dx), for diffusion of a species in a concentration gradient, the diffusion coefficient D is given by... 

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 ... 

First, when a large excess of inert elec trolyte is present, the electric field will be small and migration can be neglected for minor ionic components Eq. (22-19) then applies to these minor components, where D is the ionic-diffusion coefficient. Second, Eq. (22-19) apphes when the solution contains only one cationic and one anionic species. 

From the molecular point of view, the self-diffusion coefficient is more important than the mutual diffusion coefficient, because the different self-diffusion coefficients give a more detailed description of the single chemical species than the mutual diffusion coefficient, which characterizes the system with only one coefficient. Owing to its cooperative nature, a theoretical description of mutual diffusion is expected to be more complex than one of self-diffusion [5]. Besides that, self-diffusion measurements are determinable in pure ionic liquids, while mutual diffusion measurements require mixtures of liquids. 

If species 1 is a tracer for species 2, D,2 is termed the tracer diffusion (or self-diffusion) coefficient of species 2,D. Thus, for three ionic species the tracer diffusion coefficients can be obtained from consideration of a three-component (four-species) system in which one species is a tracer for another. 

The diffusive and convective terms in Eq. (20-10) are the same as in nonelectrolytic mass transfer. The ionic mobility Uj, (g mol cm )/(J-s), can be related to the ionic-diffusion coefficient D, cmVs, and the ionic conductance of the ith species X, cmV(f2-g equivalent) ... 

The terms in Eq. (6) include the gravitational constant, g, the tube radius, R, the fluid viscosity, p, the solute concentration in the donor phase, C0, and the penetration depth, The density difference between the solution and solvent (ps - p0) is critical to the calculation of a. Thus, this method is dependent upon accurate measurement of density values and close temperature control, particularly when C0 represents a dilute solution. This method has been shown to be sensitive to different diffusion coefficients for various ionic species of citrate and phosphate [5], The variability of this method in terms of the coefficient of variation ranged from 19% for glycine to 2.9% for ortho-aminobenzoic acid. 

The aqueous diffusivities of charged permeants are equivalent to those of uncharged species in a medium of sufficiently high ionic strength. The product DF(r/R) is the effective diffusion coefficient for the pore. It is implicit in k that adsorption of the cations does not occur, so that the fixed surface charges on the wall of the pore are not neutralized. Adsorption is more likely to occur with multivalent cations than with univalent ones. 

Reactions in solution proceed in a similar manner, by elementary steps, to those in the gas phase. Many of the concepts, such as reaction coordinates and energy barriers, are the same. The two theories for elementary reactions have also been extended to liquid-phase reactions. The TST naturally extends to the liquid phase, since the transition state is treated as a thermodynamic entity. Features not present in gas-phase reactions, such as solvent effects and activity coefficients of ionic species in polar media, are treated as for stable species. Molecules in a liquid are in an almost constant state of collision so that the collision-based rate theories require modification to be used quantitatively. The energy distributions in the jostling motion in a liquid are similar to those in gas-phase collisions, but any reaction trajectory is modified by interaction with neighboring molecules. Furthermore, the frequency with which reaction partners approach each other is governed by diffusion rather than by random collisions, and, once together, multiple encounters between a reactant pair occur in this molecular traffic jam. This can modify the rate constants for individual reaction steps significantly. Thus, several aspects of reaction in a condensed phase differ from those in the gas phase ... 

In general, only the two fastest species have to be taken into consideration and all other ones may be neglected. The second fastest species are rate controlling since these limit the motion of the fastest ones. In general, electrons (or holes) and the fastest moving ionic species have to be considered in electrodes. For the combined motion, the proportionality constant between the flux and the concentration gradient is called the chemical diffusion coefficient D ... 

The chemical diffusion coefficient may be expressed by the diffusivity of the mobile species i, the transference number and the variation of the activity of the mobile component as a function of its concentration according to Eqns (8.26) and (8.27), if the transference numbers of other ionic species are negligibly small. 

In these equations is the partial molal free energy (chemical potential) and Vj the partial molal volume. The Mj are the molecular weights, c is the concentration in moles per liter, p is the mass density, and z, is the mole fraction of species i. The D are the multicomponent diffusion coefficients, and the are the multicomponent thermal diffusion coefficients. The first contribution to the mass flux—that due to the concentration gradients—is seen to depend in a complicated way on the chemical potentials of all the components present. It is shown in the next section how this expression reduces to the usual expressions for the mass flux in two-component systems. The pressure diffusion contribution to the mass flux is quite small and has thus far been studied only slightly it is considered in Sec. IV,A,6. The forced diffusion term is important in ionic systems (C3, Chapter 18 K4) if gravity is the only external force, then this term vanishes identically. The thermal diffusion term is impor-... 

Ionic radii in the figure are measured by X-ray diffraction of ions in crystals. Hydrated radii are estimated from diffusion coefficients of ions in solution and from the mobilities of aqueous ions in an electric field.3-4 Smaller, more highly charged ions bind more water molecules and behave as larger species in solution. The activity of aqueous ions, which we study in this chapter, is related to the size of the hydrated species. 

Diffusion. The rate of self-diffusion of a metal solute species has been used to infer the degree of aggregation of the solute species, in accordance with the postulate that the diffusion coefficient is inversely proportional to the square root of the ionic weight of the solute. An example is the study of isopolytungstates by Anderson and Saddington (1). However, Baker and Pope (6) showed that two heteropolyions, of essentially the same structure, yet differing in ionic weight by about 1000 units, have essentially the same diffusion coefficients. Thus the interpretation of diffusion data in most cases needs to be reconsidered. 

Introduction of room-temperature ionic liquids (RTIL) as electrochemical media promises to enhance the utility of fuel-cell-type sensors (Buzzeo et al., 2004). These highly versatile solvents have nearly ideal properties for the realization of fuelcell-type amperometric sensors. Their electrochemical window extends up to 5 V and they have near-zero vapor pressure. There are typically two cations used in RTIL V-dialkyl immidazolium and A-alkyl pyridinium cations. Their properties are controlled mostly by the anion (Table 7.4). The lower diffusion coefficient and lower solubility for some species is offset by the possibility of operation at higher temperatures. 

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