Free Debye-Huckel electrostatic

When A > A the ions are free and the Debye-Huckel theory applies. When A < A the two ions tend to approach each other and form an ion-pair, and there is no contribution to the electrostatic energy from the interaction between an ion and its atmosphere. 

This is the electrostatic energy arising from ions approaching within a of each other. When subtracted from the free energy functional above the corrected Debye Huckel equation becomes... 

The electrostatic term, AFgiggtrostatiC is the change in electrostatic free energy when the protein goes from the crystalline state to the solution state. Melander and Horvath have expressed this term by combining the proper terms from the Debye-Huckel and Kirkwood theories (7). This term is always positive, and is responsible for salTing in. 

These techniques can also be developed further to deal with Stern layer problems. Note that for Z) the effective capacitance distance D is reduced by a factor (1 —0.62y/alD). If image effects are included, it can be shown that (when the zwitterions are immersed in a high dielectric medium e = 80, adjacent to a hydrocarbon surface s = 2), image effects can virtually double the electrostatic energy so that the two effects may partially cancel out. Nonetheless the observation that is reduced from the intuitive capacitance form is of some interest, as it is known that for ionic micelles use of Debye-Huckel theory (at low salt equivalent to the capacitance form) gives results for the repulsive free energy too large by a factor of 2. 

Debye-Huckel theory A theory to explain the nonideal behaviour of electrolytes, published in 1923 by Peter Debye (1884-1966) and Erich HUckel (1896- ). It assumes that electrolytes in solution are fully dissociated and that nonideal behaviour arises because of electrostatic interactions between the ions. The theory shows how to calculate the extra free energy per ion resulting from such interactions, and consequently the activity coefficient. It gives a good description of nonideal electrolyte behaviour for very dilute solutions, but cannot be used for more concentrated electrolytes. 

If the electrostatic (Helmholtz) free enei, pel, of the system is approximately evaluated in terms of ionically screened (Debye-HUckel) potentials of the type r exp(-Kr), summed over all pairs of chaises on the same polyion (thus neglecting interactions betwen polyions), one finds ... 

Michaeli and Overbeek used the Debye-Huckel approach to estimate the enthalpy of the PE-PE and PE-solvent interaction [23]. In this model, the Flory entropy is used as the entropic term of the PE chain, and the electrostatic free enthalpy is calculated from the electrostatic energy of a strong PE [23]. By thermodynamic considerations, Michaeli and Overbeek showed that for small univalent counterions no coacervation (complex-formation between PE) occurs... 

As is clear from the above discussion, the definition of ion-binding is not unique. It depends on our assumption on the state of free ions. Sometimes, it is assumed that the free ions are the same as the ions in simple salt solutions at the same concentration. Sometimes, the electrostatic interaction between polyion and free counterions is taken into account. In the case, the so-called Debye-Huckel approximation may be assumed as the charge density is lowered with ion-binding. 

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