Ion-exchanger Membranes in .NET

Integrated DataMatrix in .NET Ion-exchanger Membranes
Ion-exchanger Membranes
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Ion-exchanger membranes with fixed ion-exchanger sites contain ion conductive polymers (ionomers) the properties of which have already been described on p. 128. These membranes are either homogeneous, consisting only of a polyelectrolyte that may be chemically bonded to an un-ionized polymer matrix, and heterogeneous, where the grains of polyelectrolyte are incorporated into an un-ionized polymer membrane. The electrochemical behaviour of these two groups does not differ substantially. All ion-exchanger membranes with fixed ion-exchanger sites are porous to a certain degree (in contrast to liquid membranes and to membranes of ion-selective electrodes based on solid or glassy electrolytes, such as a single crystal of lanthanum fluoride). 6.2.1 Classification of porous membranes Depending on the pore size, porous membranes can be divided into three groups: (a) Membranes with wide pores are simply diaphragms limiting flow and diffusion of the solutions with which the membrane is in contact. When the diaphragm contains cylindrical pores with identical radii r and a density N per unit area, then, in the ideal case, the material flux of the
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416 ith component of the solution through the diaphragm is given as Jt = c,/v - N^jzDXRTy^i-y1 (6.2.1)
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where c, is the concentration of the ith component, D, is its diffusion coefficient, j z is its electrochemical potential and 7V is the volume flux of U the solution:
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y =d ^ = Njtr^dy1 ^
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(6.2.2)
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where dh is the mechanical permeability (permeability per unit pressure gradient), rj is the viscosity of the solution, d is the thickness of the membrane and P is the hydrostatic pressure. Equation (6.2.1) follows directly from Eq. (2.3.23) and (2.5.23). (b) Fine-pore membranes (r = 1-100 nm) selectively affect the character of transport. These are often called semipermeable membranes the permeability of the membrane is different for different components of the solution as a result of the properties of the membrane itself (rather than as a result of different mobilities of the components of the solution). The walls of the pores of ion-exchanger membranes are electrically charged and contain an aqueous solution. The contents of the electrolyte components in the pores depends on the electric charge on the pore walls and concentration of the electrolyte in contact with the membrane. The electrical double layer formed inside the pores results in the counterions (=gegenions, ions with opposite charge to the fixed ions on the membrane wall) having a greater concentration in the pores than ions with the same charge as the fixed ions (coions). When the solution is dilute and the pores so narrow that the diffuse electrical layer has an effective thickness comparable with the pore radius, then the gegenions are present in a clear excess over the coions (see Fig. 6.1). In the extreme case, the electrical diffuse layers completely fill the pores, which then contain only counterions and the membrane is permeable only for these ions, the transport number of counterion being T, = 1. Such a membrane is termed permselective. On the other hand, if the electrolyte is more concentrated and the pores wider, then the excess of the counterions over the coions eventually becomes negligible. (c) Microporous membranes have such small pore radii that mass is transported by an exchange process between the dissolved species and the solvent particles. This structure is characteristic, for example, for amorphous polymer films below the glass transition temperature. The porosity is a result of irregular coiling of segments of the polymer chains. These membranes are used to separate mixtures of gases and liquids (these are not electrochemical membranes) and to desalinate
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Fig. 6.1 Distribution of cations and anions in pores of a cation-exchanger membrane depends on pore radius which decreases in the sequence A B C. In case C the membrane becomes permselective. (According to K. Sollner)
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water by hyperfiltration. They must be very thin for transport to occur at all and must simultaneously be mechanically strong. 6.2.2 The potential of ion -exchanger membranes The distribution of electric potential across the membrane and the dependence of the membrane potential on the concentration of fixed ions in the membrane and of the electrolyte in the solutions in contact with the membrane is described in the model of an ion-exchanger membrane worked out by T. Teorell, and K. H. Meyer and J. F. Sievers. This theory will be demonstrated on a membrane with fixed univalent negative charges, with a concentration in the membrane, cx. The pores of the membrane are filled with the same solvent as the solutions with which the membrane is in contact that contain the same uni-univalent electrolyte with concentrations cx and c2. Conditions at the membrane-solution interface are analogous to those described by the Donnan equilibrium theory, where the fixed ion X~ acts as a non-diffusible ion. The Donnan potentials A 0 D 1 = 0 P 0(1) and A0 D 2 = 0(2) 0 q are established at both surfaces of the membranes (x = p and x = q). A liquid junction potential, A0 L = 0 q 0 P , due to ion diffusion is formed within the membrane. Thus The Donnan equilibrium condition (6.1.9) gives
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(6.2.4)
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(For simplicity, the effect of the activity coefficients is neglected; it should be recalled that the membrane is not completely impermeable for anions so that neither c_ p nor c_ q is equal to zero.) These relationships and the electroneutrality condition in the membrane
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yield the expressions for the surface concentrations at the membrane:
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(6.2.5)
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When the expressions (6.2.5) are substituted into the Henderson equation (2.5.34) A0 L is obtained. Both contributions A$ D are calculated from the Donnan equation. From Eq. (6.2.3) we obtain, for the membrane potential,
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