Fixed anion

When the extraction of the hydrophilic counteranion from the aqueous solution into the membrane bulk is negligible (cation permselectivity preserved), the concentration of the complex cation in the membrane bulk Cb, is equal to that of the fixed anionic sites, X, in the membrane matrix, due to the electroneutrality condition within the membrane bulk ... 

Fig. 6.2 Concentration distribution of cations c+, anions c and fixed anions in a cationexchanging membrane. The bathing solutions have electrolyte concentrations cx and c2. (According to K. Sollner)...

Takamatsu et al. studied the diffusion of water into the acid as well as mono-, di-, and trivalent salt forms of 1155 and 1200 EW samples."pj e gravimetric uptakes of membranes immersed in distilled liquid water versus time were determined. Three approximate diffusion formulas were applied to the data, and all yielded essentially the same result. The log D versus 1/7 plots, over the range 20—81 °C, yielded activation energies of 4.9 and 13.0 kcal/mol for the acid and K+ forms, respectively. Diffusion coefficients of various mineral cations that permeated from aqueous electrolytes were considerably smaller than that of water. Also, log Z7was seen to be proportional to the quantity q a, where q is the charge of the cation and a is the center-to-center distance between the cation and fixed anion in a contact ion pair. 

Nafion is a copolymer of poly(tetrafluoroethylene) and polysulfonyl fluoride vinyl ether. It has fixed anions, which are sulfonic acid sites, and consequently, by electroneutrality, the concentration of positive ions is fixed. Furthermore, the transference number of protons in this system is 1, which greatly simplifies the governing transport equations, as seen below. There can be different forms of Nafion in terms of the positive counterion (e.g., proton, sodium, etc.). Most models deal only with the proton or acid form of Nafion, which is the most common form used in polymer-electrolyte fuel cells due to its high proton conductivity. 

To estimate the limiting value t (i) and to introduce the molal fixed charge concentration X, expressed in equivalents of univalent fixed anions per kg of water sorbed by the membrane, we have treated the ion concentrations in the membrane as being governed by a Donnan distribution. 

NMR titrations (of anion into ligand at fixed pH) and pH-potentiometric titrations (of pH at fixed anion ligand ratios) provide comparable values of the stability constants for binding of mononegative oxoanions by protonated R3Bm, R3F, and R3P hosts [15,20,21] Table 2. The weak complexation at hexaprotonated levels for tetrahedral monoanionic oxoanions makes it difficult to obtain reliable data for protonation levels below 5. This has however been achieved for nitrate with the cleft binding host R3P as well as for Re O4 with the most basic cryptand R3Bm. 

Figure 2.11. Ion-exchange chromatography. For clarity, anions in solution required for electroneutrality are not shown. F", fixed anion C+, counterion S+, solute cation.

Ionic liquids with discrete anions have a fixed anion structure but in the eutectic-based liquids at some composition point the Lewis or Bronsted acid will be in considerable excess and the system becomes a solution of salt in the acid. A similar scenario also exists with the incorporation of diluents or impurities and hence we need to define at what composition an ionic liquid is formed. Many ionic liquids with discrete anions are hydrophilic and the absorption of water is found sometimes to have a significant effect upon the viscosity and conductivity of the liquid [20-22], Two recent approaches to overcome this difficulty have been to classify ionic liquids in terms of their charge mobility characteristics [23] and the correlation between the molar conductivity and fluidity of the liquids [24], This latter approach is thought by some to be due to the validity of the Walden rule... 

In the case of materials that contain mobile positive ions included in a fixed anionic framework, for example, zeolites [28], jumps of mobile charge carriers between localized sites in a framework of charges of different signs occurs, creating polarization. In general, this is a slow process. 

For a series of cations and a fixed anion this is given by... 

The Donnan potential can also be regarded as a special case of a diffusion potential. We can assume that the mobile ions are initially in the same region as the immobile ones. In time, some of the mobile ions will tend to diffuse away. This tendency, based on thermal motion, causes a slight charge separation, which sets up an electrical potential difference between the Donnan phase and the bulk of the adjacent solution. For the case of a single species of mobile cations with the anions fixed in the membrane (both assumed to be monovalent), the diffusion potential across that part of the aqueous phase next to the membrane can be described by Equation 3.11 n — El = (u- — u+)/(u + w+)](i 77F)ln (c11/ 1) that we derived for diffusion toward regions of lower chemical potential in a solution. Fixed anions have zero mobility (u = 0) hence (u — u+)/(u — u+) here is —uJu+> or —1. Equation 3.11 then becomes En — El = — (RT/F) In (cll/cl)> which is the same as the Nernst potential (Eq. 3.6) for monovalent cations [—In = In (cVc11)]. 

It should be acknowledged that Risen utilized the concept of the ionic domains in ionomers (Nafion sulfonates, sulfonated linear polystyrene) as microreactors within which transition metal partides can be grown and utilized as catalysts (23-25). Transition metal (e.g. Rh, Ru, Pt, Ag) cations were sorbed by these ionomers from aqueous solutions and preferentially aggregated within the pre-existing clusters of fixed anions. Then, the ionomers were dehydrated, heated and reduced to the metallic state with Hg. Risen discussed the idea of utilizing ionomeric heterophasic morphology to tailor the size and size distributions of the incorporated metal particles. The affected particle sizes in Nafion were observed, by electron microscopy, to be in the range of 25-40 A, which indeed is of the established order of cluster sizes in the pre-modified ionomer. 

ILs are composed of organic cations and weakly coordinating anions and have considerably low melting points (<100°C) [8]. Figure 9.2 shows the most-often studied structures of such cations and anions [2]. The most widely used cations are imidazolium, pyridinium, ammonium, and phosphonium, but new cations for application in ILs are constantly discovered as well. Common IL anions may be grouped into two major categories one is composed of adjustable aluminum chloride anions, while the other is composed of fixed anions, such as hydrophilic CL, Br , L, N03, ... 

The free energy of a "vesicle" containing the water molecules and the mobile cations is calculated. The cations are shown to build a layer of charges at equilibrium the fixed anions coat the vesicle as densely as they can. 

We call N the number of fixed anions coating the vesicle. Here we consider only the case of electrically neutral vesicles, with no coions, so that N is also the number of mobile cations inside the vesicle. We introduce a reduced radius x = p/R, where p is the distance from the center. T(x) is the distribution function of the cations T(x) dx is the probability of finding a cation between x and x + dx. The volume density probability y(x) is related to T(x) by... 

The increase of urinary citrate after alkali administration provides a means of eliminating the excess of cations without parallel increase in the elimination of fixed anions citrate would thus play for the economy of fixed anions a role which is similar to that postulated for ammonia in the case of the fixed cations (012). 

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