Membrane-solution interface

In concentrated electrolytes the electric current appHed to a stack is limited by economic considerations, the higher the current I the greater the power consumption W in accordance with the equation W = P where is the electrical resistance of the stack. In relatively dilute electrolytes the electric current that can be appHed is limited by the abflity of ions to diffuse to the membranes. This is illustrated in Eigure 4 for the case of an AX membrane. When a direct current is passed, a fraction (t 0.85-0.95) is carried by anions passing out of the membrane—solution interface region and... 

McLaughlin, S., Electrostatic potentials at membrane-solution interfaces, Curr. Topics. Membr. Transport 9, 71-144 (1977). 

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 A0D 4 = 0p — 0(1) and A0D 2 = 0(2) — 0q are established at both surfaces of the membranes (x = p and jc = q). A liquid junction potential, A0l = 0q — 0P, due to ion diffusion is formed within the membrane. Thus... 

Fig. 6 The electrical potential, ij/, profile across a lipid bilayer. The transmembrane potential, Aij/, is due to the difference in anion and cation concentrations between the two bulk aqueous phases. The surface potential, ij/s, arises from charged residues at the membrane-solution interface. The dipole potential, J/d, results from the alignment of dipolar residues of the lipids and associated water molecules within the membrane...

PBP model considers the membrane potential as a sum of the potentials formed at the membrane-solution interfaces (phase boundary potentials), and generally neglects any diffusion potential within the membrane ... 

An inner filling solution and internal reference electrode are used in macro ISEs due to a very good stability of the potential at the inner membrane-solution interface in such a setup (see Fig. 4.4). However, the presence of a solution inside a sensor could be a serious limitation for development of microelectrodes and may be undesired for a variety of other reasons, including ionic fluxes in the membrane and limited temperature range of sensor operation. There are several requirements for such an inner contact. First of all, a reversible change of electricity carriers ions-electrons must take place at the membrane-substrate interface. The potential of the electrochemical reaction, ensuring this transfer, has to be constant, stable, and must not depend on the sample composition. At last, the substrate must not influence the membrane analytical performance. 

FIGURE 10.1 A schematic diagram for a typical electrode system for potentiometric pH measurements. A potential is established on the pH sensitive membrane-solution interface of a pH electrode that responds to the activity or concentration of hydrogen ions in the solution. The reference electrode has a very stable half-cell potential. The cell potential, which is proportional to the pH in the test solution, is measured using a high input impedance voltmeter between the pH electrode and the reference electrode. 

Kasianowicz, J., Benz, R. and McLaughlin, S. (1987). How do protons cross the membrane solution interface Kinetic studies on bilayer membranes exposed to the protonophore S-13 (5-chloro-3-tert-butyl-2 -chloro-4 -nitrosalicylanilide), J. Membr. Biol., 95, 73-89. 

Another way around the problem of pressure-driven flow in the single-phase membrane was presented by Meyers.He worked around the problem by allowing for a discontinuity in pressure at the membrane/solution interface, even though the electrochemical potential of all soluble species is continuous. He argued that additional mechanical stresses compressing the membrane should be indistinguishable from the thermodynamic pressure, and thus, the thermodynamic pressure might be discontinuous at the interface. 

The rate of the charge-transfer reaction across the membrane/solution interface, leading to charging of the electrical double layer at this interface [87]. 

The preferential sorption-capillary flow mechanism of reverse osmosis does that. In the NaCl-H20-cellulose acetate membrane system, water is preferentially sorbed at the membrane-solution Interface due to electrostatic repulsion of ions in the vicinity of materials of low dielectric constant (13) and also due to the polar character of the cellulose acetate membrane material. In the p-chlorophenol-water-cellulose acetate membrane system, solute is preferentially sorbed at the interface due to higher acidity (proton donating ability) of p-chlorophenol compared to that of water and the net proton acceptor (basic) character of the polar part of cellulose acetate membrane material. In the benzene-water-cellulose acetate membrane, and cumene-water-cellulose acetate membrane systems, again solute is preferentially sorbed at the interface due to nonpolar... 

Preferential Sorption at Membrane-Solution Interfaces and Solute Separation In Reverse Osmosis... 

The solute-solvent-polymer (membrane material) interactions, similar to those governing the effect of structure on reactivity of molecules (20,21,22,23,24) arise in general from polar-, sterlc-, nonpolar-, and/or ionic-character of each one of the three components In the reverse osmosis system. The overall result of such interactions determines whether solvent, or solute, or neither is preferentially sorbed at the membrane-solution Interface. 

With particular reference to reverse osmosis systems involving cellulose acetate membranes and aqueous solutions, the membrane material has both polar and nonpolar character, and the solvent, of course, is polar. When these two components of the reverse osmosis system are kept constant, preferential sorption at the membrane-solution interface, and, in turn, solute separation in reverse osmosis, may be expected to be controlled by the chemical nature of the solute. If the latter can be expressed by appropriate quantitative physicochemical parameters representing polar-, steric-, nonpolar-, and/or ionic-character of the solutes, then one can expect unique correlations to exist between such parameters and reverse osmosis data on solute separations for each membrane. Experimental results confirm that such is indeed the case (18). 

When the acidity or the basicity of the solute molecule is high enough to stretch the OH or OD bond to the point of rupture, then the molecule dissociates into ions in solution. Therefore the dissociation constants also serve as a measure of acidity or basicity of solute molecules, especially those which are subject to significant ionization. Since the coulombic forces causing repulsion of ions at membrane-solution interfaces extend to distances farther than those involved in the polar hydrogen bonding repulsions of nonionized solutes at such interfaces, one would expect that a dissociated molecule to be repelled and, in... 

The parameters AVg (acidity), AVg (basicity), pK, and Zo represent properties of solute in the bulk solution phase. If reverse osmosis separation is governed by the property of solute in the membrane-solution interface, the existence of unique correlations between data on reverse osmosis separations and those on the above parameters, means that the property of solute in the bulk solution phase and the corresponding property of solute in the membrane-solution interface are also uniquely related. This leads one to the development of interfacial free energy parameters (-AAG/RT) for both nonionized solute molecules and dissociated ions in solution for reverse osmosis systems where water is preferentially sorbed at the membrane-solution interface. 

The relevance of LSC data to reverse osmosis stems from the physicochemical basis (adsorption equilibrium considerations) of liquid-solid chromatography (52), and the principle that the solute-solvent-membrane material (column material) Interactions governing the relative retention times of solutes in LSC are analogous to the interactions prevailing at the membrane-solution Interface under reverse osmosis conditions. The work already reported in several papers on the subject (53-58) indicate that the foregoing principle is valid, and hence LSC data offer an appropriate means of characterizing interfacial properties of membrane materials, and understanding solute separations in reverse osmosis. 

Gibbs adsorption equation is an expression of the natural phenomenon that surface forces can give rise to concentration gradients at Interfaces. Such concentration gradient at a membrane-solution Interface constitutes preferential sorption of one of the constituents of the solution at the interface. By letting the preferentially sorbed Interfacial fluid under the Influence of surface forces, flow out under pressure through suitably created pores in an appropriate membrane material, a new and versatile physicochemical separation process unfolds itself. That was how "reverse osmosis" was conceived in 1956. 

For thin membranes the ionic fluxes may become large at rather low values of E. Thus large displacements from the equilibrium state must be considered to occur at the membrane-solution interfaces. The same effect has to be expected for slow interfacial reactions. A more detailed discussion of this kinetic domain is given in Ref. 55. 

Below we present a well-known calculation of membrane potential based on the classical Teorell-Meyer-Sievers (TMS) membrane model [2], [3]. The essence of this model is in treating the ion-selective membrane as a homogeneous layer of electrolyte solution with constant fixed charge density and with local ionic equilibrium at the membrane/solution interfaces. In spite of the obvious idealization involved in the first assumption the TMS model often yields useful results and represents in fact the main tool for practical membrane calculations. We shall return to TMS once again in 4.4 when discussing the electric current effects upon membrane selectivity. In the case of our present interest, the simplest TMS model of membrane potential for a 1,2 valent electrolyte reads... 

Here Ci, C2 are the cation concentrations in both compartments. The conjugation conditions (3.4.6) express the continuity of the ionic electrochemical potentials at the membrane/solution interfaces. 

The appropriate standard set of boundary and conjugation conditions at the membrane/solution interfaces is as follows... 

K. S. Spiegler, Polarization at ion exchange membrane-solution interfaces, Desalination, 9 (1971), pp. 367. 

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