Teorell-Meyer-Sievers

Finally, in 3.4 we present a calculation of membrane potential in terms of the classical Teorell-Meyer-Sievers (TMS) [2], [3] model of a charged permselective membrane. In spite of its extreme simplicity, this calculation yields a practically useful result and is typical for numerous membrane computations, some more of which will be touched upon subsequently in Chapter 4. 

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... 

For comparison, we present in Fig. 5.3.2 some numerical results for the following non-locally-electro-neutral generalization of the classical Teorell-Meyer-Sievers (TMS) model of membrane transport (see [11], [12] and 3.4 of this text). 

X.L.Wang, T. Tsuru, S.-I. Nakao and S. Kimura, Electrolyte transport through nanofiltration membranes by the Space Charge Model and the comparison with Teorell-Meyer-Sievers model. /. Membr. Sci., 103 (1995)117. 

In ion-selective electrode potentiometry, the cell potential reflects the dependence of the membrane potential on the primary ion activity (concentration). According to the Teorell-Meyer-Sievers (TMS) theory, the sum of... 

The electrical potential difference at both sides of a membrane separating two solutions of the same electrolyte but different concentrations (Ci, C2) is called membrane potential (AOm). The Teorell-Meyer-Sievers (or TMS) theory [37, 38] assumes the membrane potential can be considered as the sum of three terms associated with two different contributions ... 

In ISE potentiometry, the cell potential reflects the dependence of the membrane potential on the primary ion activity (concentration). According to the Teorell-Meyer-Sievers (TMS) theory, the membrane potential is the sum of three potential contributions namely the phase boundary potentials generated by ion-exchange processes at both interfaces, ((()i - c )n, i) and (([)n, 2 4>2). and the inter membrane diffusion potential, (c )ni i - <[)ni,2). If the membrane composition is constant and there are no concentration gradients within the membrane, then the membrane diffusion potential is zero and the membrane potential can be described by phase boundary potentials (see Figure 10.3b). This approach is also used to treat the response of ISE made with a range of membranes. 

Concentration- or Dialysis Potential. The refined formula of Meyer, Sievers and Teorell for the concentration potential has been experimentally tested by several investigators. G. Manecke and K. F. Bonhoeffer (89) and K. F. Bonhoeffer and U. Schindewolf (21) found that for external concentrations smaller than appr. x/3 of the concentration at fixed charged groups the general trend of the potential with the external concentration was as indicated by the formula of K. H. Meyer and J. F. Sievers (97) [equation (44)]. Above this value there are deviations. 

M.S.T.-model = Meyer-Sievers-Teorell-model (see Introduction, sec. 1). 

Many researchers have derived improved equations concerning the membrane potential after Meyer-Sievers-Teorell e.g. Bonhoeffer,10 Schlogl-Helfferich,11 Nagasawa-Kobatake.12... 

The most popular theoretical description of the potentiometric behavior of ion-selective membranes makes use of the three-segmented membrane model introduced by Sollner53), Teorell 30,54), and Meyer and Sievers 31-5S). In this model the two phase boundaries and the interior of the membrane are treated separately. Here, the... 

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. 

The search for models of biological membranes among porous membranes continued in the twenties and thirties. Here, Michaelis [67] and Sollner (for a summary of his work, see [90] for development in the field, [89]) should be mentioned. The existence and characteristics of Donnan membrane equilibria could be confirmed using this type of membrane [20]. The theory of porous membranes with fixed charges of a certain sign was developed by Teorell [93], and Meyer and Sievers [65]. 

Different versions of the above calculations, carried out for particular ionic contexts, form the basis of numerous studies of the ion-selective membrane transport, starting with classical papers by Teorell [7], and Meyer and Sievers [8]. Without attempting to give a full or merely fair account of all these studies, we shall mention here just a typical few Schlogl [5] (arbitrary number of ions in a monopolar membrane), Spiegler [9] (am-bipolar ionic transport in a unipolar membrane and solution layers adjacent to it — concentration polarization), Oren and Litan [10], Brady and Turner [11], Rubinstein [12] (multipolar transport in a unipolar membrane and the adjacent solution layers—effects of concentration polarization upon... 

Taking for the diffusion potential the Henderson diffusion potential and adding the two Donnan potentials one gets the well-known formula of K. H. Meyer (97, 98), J. F. Sievers (97, 98) and T. Teorell (168). 

For the interpretation of the parameters that influence the membrane potential a general three-segment model of Teorell [17], Meyer and Sievers [18] (TMS model) is often used (Figure 4). The membrane potential (Equation 1) is given by the potential of the (inner) reference solution (O ) minus the potential of the sample solution ([Pg.196]

T. Teorell, An attempt to formulate a quantitative theory of membrane permeability, Proc. Soc. Exptl. Biol. Med., 1935, 33, 282 K.H. Meyer and J.-F. Sievers, La permeabilite des membranes I. Theorie de la permeabilite ionique, Helv. Chim. Acta, 1936,19, 649, 665. 

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... 

Earlier studies on theoretical thin membranes were continued by Teorell [S] and Meyer and Sievers [6], who in their theory attempted to interpret the behavior of practical, thick membranes, in contact on both sides with solutions containing the sort of ion which can produce a membrane potential. This initiated further research and many workers studied the perm-selective properties of ion-selective electrode membranes. As a result, ion transport across thick ion-selective membranes was considered as the basic concept of the theory of ion-selective electrodes. This theory was further elaborated by Eisenmann, Simon, and Buck. 

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