Katchalsky’s theory

Katchalsky s Theory. Suppose there is a gel swelling in an aqueous solution. At equilibrium, the chemical potentials of the wat in the gel and in the external solution... 

The merit of Katchalsky s approach is that it allows us to calculate the salt absoq)tion without knowing the form of the activity coefficient of the free ions in the gel explicitly. But, Katchalsky s theory does not consider counterion condensation. Tlie interactions between various charge species are over-simplified. 

New Expression for Salt Partitioning. As mentioned before, Katchalsky s theory does not consider the counterion condensation. We will show later that die counterion condensation theories alone, both linear and nonlinear theories, cannot account for all the non-ideality of the Donnan equilibrium. Therefore, we seek an expression that can combine both contributions. We follow a similar approach of Katchalsky by writing die Donnan equOibrium as ... 

Figure 4. Comparison of expaimental salt abswption with Aeoretical predictions based on ideal Donnan equilibrium (Cal-I), Katchalsky s theory (Cal-K), and our...

It should be further noted that these authors accounted for the concentration dependence by Lifson and Katchalsky s theory for a rodlike model (ST). The foot that the experimental data are explainable simultaneously by this theory and the cube-root relation su ests that the relation may be derived from the theory. 36 Adv. Polymer Set, VoL 7... 

Theoretically, Equation (20) and (21) should permit the evaluation of both the equilibrium swelling q and the salt accumulation (p-a)/2 from the known data of the external solution. In Katchalsky s work, however, instead of solving the two equations simultaneously, tiiey substituted the experimental swelling ratios into the equation (21) and deduced from it the salt accumulation data. Then they compared the deduced salt accumulation with experiments and found they agreed well. They concluded that their theory worked well. However, we found that equation (20) could not predict the correct swelling if the salt absorption is substituted into it... 

For highly diluted solutions, the results of Manning s theory agree with the results of Lifson and Katchalsky [cf. (46) and (47)]. For example, Manning [106] gives for the osmotic coefficient of an aqueous solution of a single polyion where the counterions have the (absolute) charge munber zq ... 

In the absence of gradients of salt concentration and temperature, flows of water and electric current in bentonite clay are coupled through a set of linear phenomenological equations, derived from the theory of irreversible thermodynamics (Katchalsky and Curran, 1967), making use of Onsager s Reciprocal Relations (Groenevelt, 1971) ... 

Based on Donnan s [18, 19] and Onsager s [41, 42] fundamental works, the theories for Donnan dialysis systems were developed [20-26, 32-36]. The BAHLM system could be considered as two DD systems, operating in consecutive order, continuously in one module (see Fig. 6.2) the first is composed of feed/LM and the second is composed of LM/strip compartments, separated by ion-exchange membranes. Therefore, the Kedem-Katchalsky equations [43, 44] can be applied to our case ... 

A. Katchalsky and P.F. Curran, Nonequilibrium Thermodynamics in Biophysics, Harvard University Press, Cambridge, MA, 1965, Ch. 12 S.R. de Groot and P. Mazur, Non-equilibrium Thermodynamics, North-Holland Publishers, Amsterdam, 1962 H. Kimizuka, Membrane Permeation of Ions, Basic Theory of Irreversible Thermodynamics, Kyoritsu Shuppan, Tokyo, 1988. 

Flory PJ (1953) Principles of polymer chemistry. Cornell University Press, Ithaca Freed KF (1987) Renormalization group theory of macromolecules. Wiley, New York Freed KF, Dudowicz J, Stukalin EB, Douglas JF (2010) General approach to polymer chains confined by interacting boundaries. J Chem Phys 133 094901 Fuoss RM, Katchalsky A, Lifson S (1951) The potential of an infinite rod-like molecule and the distribution of the counter ions. Proc Natl Acad Sci USA 37 579-589 Golestanian R, Kardar M, Liverpool TB (1999) Collapse of stiff polyelectrolytes due to counterion fluctuations. Phys Rev Lett 82 4456-4459 Guggenheim FA (1952) Mixtures. The Clarendon Press, Oxford... 

Penetration of a substance is measured by the permeability coefficient, P, which could be converted to a measurable diffusional coefficient, D, if Pick s law applied strictly. In the more complex situation of a membrane barrier, Kedem and Katchalsky (1958, 1961) have shown that under rigidly controlled conditions there exist at least three parameters which must be considered when characterizing the behavior of a membrane toward a particular solute (1) the interaction between membrane and solvent (2) the interaction between solute and membrane and (3) the interaction between solute and solvent. The reflection coefficient, (T, measures relative rates of solute and solvent permeabilities in the system (Staverman, 1952) and is therefore a measure of semipermeability. Lp is the mechanical coefficient of filtration or pressure filtration coefficient, and co is the solute mobility or solute diffusional coefficient. In the case of living membranes, conditions such as volume flow, osmotic gradients, and cell volume can be manipulated in order to measure the phenomenological coefficients cr, o>, and Lp. Detailed discussions of the theories, methods, and problems involved in such... 

Manning s values for (j) are equal to those of the Lifson-Katchalsky theory at infinite dilution. 

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