Membrane potential equilibrium theory

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... 

Earlier, Gavach et al. studied the superselectivity of Nafion 125 sulfonate membranes in contact with aqueous NaCl solutions using the methods of zero-current membrane potential, electrolyte desorption kinetics into pure water, co-ion and counterion selfdiffusion fluxes, co-ion fluxes under a constant current, and membrane electrical conductance. Superselectivity refers to a condition where anion transport is very small relative to cation transport. The exclusion of the anions in these systems is much greater than that as predicted by simple Donnan equilibrium theory that involves the equality of chemical potentials of cations and anions across the membrane—electrolyte interface as well as the principle of electroneutrality. The results showed the importance of membrane swelling there is a loss of superselectivity, in that there is a decrease in the counterion/co-ion mobility, with greater swelling. 

This theory of an equilibrium of one species between each side of the membrane was formulated by Donnan in 1925 and from then until 1955, it reigned as the theory of membrane potentials. Its demise came when radiotracer measurements showed that all relevant ions (e.g., K+, Na+, and Cl ) permeated more than a dozen actual biological membranes, although each ion had a characteristic permeability coefficient in each membrane (Hodgkin and Keynes, 1953). 

Both Equations (7.27) and (7.28) predict zero current at AT = V a, as illustrated in Figure 7.6. Note that the current-voltage curve does not go through the point (0,0). The outward current is positive only when the membrane voltage exceeds the equilibrium voltage. For all membrane potential values below Vjva, the current is inward. Ionic current through membranes can be further understood in terms of the theory of electro-diffusion. For a mathematical treatment of the subject, see [102],... 

Donnan EG. Theory of membrane equilibrium and membrane potential in the presence of non-dialysing electrol3des A contribution to physical-chemical physiology. Z Elektrochem. Angewandte Phys. Chem. 1911 17 572-581. 

In order to explain this transmembrane potential, a number of authors have proposed membrane potential theories. Historically, the first membrane potential theory for biological systems was the use of the concept of the Donnan membrane equilibrium. 

Fixed Charge Theory. As a result of combining the above two theories, a fixed charge membrane theory was developed by Teorell and Meyer and Sievers. The theory includes the equilibrium of the electrochemical potentials of ions at the membrane boundaries and the diffusion of ions in the membrane. Therefore, the total membrane potential E is composed of three separate potential differences Eo corresponds to the first transition region between the solution (o) and membrane phases, difl corresponds to the ion diffusion potential in the membrane, and corresponds to the other transition region between membrane and the solution (i) phases (see Figure 26B). Thus, the transmembrane potential is... 

The membrane potential in biology came to prominence in the days in which electrode phenomena were treated exclusively in terms of equilibrium thermodynamics. Between 1892 (Nernst ) and 1911 (Donnan " ), three treatments were given of membrane potentials. They form such a durable part of electrochemistry, not because of their importance per se, or even of their direct relevance to biological phenomena, but because one of them was the origin of the best-known of bioelectrochemical theories, the Hodgkin-Huxley-Katz mechanism for the passage of electricity through nerves. 

Membrane phenomena cover an extremely broad field. Membranes are organized structures especially designed to perform several specific functions. They act as a barrier in living organisms to separate two regions, and they must be able to control the transport of matter. Moreover, alteration in transmembrane potentials can have a profound effect on key physiological processes such as muscle contraction and neuronal activity. In 1875, Gibbs stated the thermodynamic relations that form the basis of membrane equilibria. The theory of ionic membrane equilibrium was developed later by Donnan (1911). From theoretical considerations, Donnan obtained an expression for the electric potential difference, commonly known as the membrane potential between two phases. 

In the applications it is however rarely possible to apply the Donnan theory for ideal systems, at least if more than qualitative results are wanted. From the eq. (115, 116, 117 and 118) it is possible to determine the charge on the colloid in three independent ways. This means, that two relations between the three phenomena (distr. of ions, membrane potential, osmotic pressure) should exist. Now usually, when the osmotic pressure is calculated either from analytical data or from the membrane potential it is found to be too low (Hahmarsten effect ). This clearly indicates the need for a more exact treatment of the Donnan equilibrium, in the first place the introduction of activity coefficients. 

Concentration of Electrolyte Myer and Sievers"" applied the Donnan equilibrium to charged membranes and developed a quantitative theory of membrane selectivity. They expressed this selectivity in terms of a selectivity constant, which they defined as the concentration of fixed ions attached to the polymer network. They determined the selectivity constant of a number of membranes by the measurement of diffusion potentials. Nasini etal and Kumins"" extended the measurements to paint and varnish films. 

Otherwise it has been shown that the accumulation of electrolytes by many cells runs at the expense of cellular energy and is in no sense an equilibrium condition 113) and that the use of equilibrium thermodynamic equations (e.g., the Nemst-equation) is not allowed in systems with appreciable leaks which indicate a kinetic steady-state 114). In addition, a superposition of partial current-voltage curves was used to explain the excitability of biological membranes112 . In interdisciplinary research the adaptation of a successful theory developed in a neighboring discipline may be beneficial, thus an attempt will be made here, to use the mixed potential model for ion-selective membranes also in the context of biomembrane surfaces. 

In conclusion, it should be mentioned that extraction parameters (the equilibrium constants of exchange reactions and ion-pair stabilities) were introduced into the theory of ion-selective electrodes in [2, 31,33, 34, 35,69]. The theory of ISEs with a liquid membrane and a diffusion potential in the membrane was extended by Buck etal. [11, 13, 14, 73, 74] and Morf [54]. 

Equality (1.20) is of primary importance because of the following reason. It is customary in most ionic transport theories to use the local electroneutrality (LEN) approximation, that is, to set formally e = 0 in (1.9c). This reduces the order of the system (1.9), (l.lld) and makes overdetermined the boundary value problems (b.v.p.s) which were well posed for (1.9). In particular, in terms of LEN approximation, the continuity of Ci and ip is not preserved at the interfaces of discontinuity of N, such as those at the ion-exchange membrane/solution contact or at the contact of two ion-exchange membranes or ion-exchangers, etc. Physically this amounts to replacing the thin internal (boundary) layers, associated with N discontinuities, by jumps. On the other hand, according to (1-20) at local equilibrium the electrochemical potential of a species remains continuous across the interface. (Discontinuity of Cj, ip follows from continuity of p2 and preservation of the LEN condition (1.13) on both sides of the interface.)... 

Sep. 5,1870, Colombo, Ceylon (British Empire), now Sri Lanka - Dec. 16,1956, Canterbury, Kent, UK). Donnan was a British chemist who greatly contributed to the development of colloid chemistry, physical chemistry, and electrochemistry [i—iii]. In different periods of his life, he was working with van t - Hoff, -> Ostwald, F. W., and Ramsay. In electrochemistry, he studied (1911) the electrical potential set-up at a semipermeable membrane between two electrolytes [iv], an effect of great importance in living cells [v], Donnan is mostly remembered for his theory of membrane equilibrium, known as - Donnan equilibrium. This equilibrium results in the formation of - Donnan potential across a membrane. 

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