Diffusion potential Donnan phase

In order to obtain the membrane potential, any potential differences present in adhering liquid films must be taken into account, such in addition to the Donnan potentials. It should be observed that the splitting up of the membrane potential in diffusion potential, phase-boundary potentials and film potentials has met with opposition (49,121). 

The Donnan potential can also be regarded as a special case of a diffusion potential. We can assume that the mobile ions are initially in the same region as the immobile ones. In time, some of the mobile ions will tend to diffuse away. This tendency, based on thermal motion, causes a slight charge separation, which sets up an electrical potential difference between the Donnan phase and the bulk of the adjacent solution. For the case of a single species of mobile cations with the anions fixed in the membrane (both assumed to be monovalent), the diffusion potential across that part of the aqueous phase next to the membrane can be described by Equation 3.11 n — El = (u- — u+)/(u + w+)](i 77F)ln (c11/ 1) that we derived for diffusion toward regions of lower chemical potential in a solution. Fixed anions have zero mobility (u = 0) hence (u — u+)/(u — u+) here is —uJu+> or —1. Equation 3.11 then becomes En — El = — (RT/F) In (cll/cl)> which is the same as the Nernst potential (Eq. 3.6) for monovalent cations [—In = In (cVc11)]. 

Thus the Donnan potential can also be regarded as a diffusion potential occurring as the mobile ions tend to diffuse away from the immobile charges of opposite sign, which remain fixed in the Donnan phase (Fig. 3-8). 

The simple Donnan model has limitations that are comparable to those of the GC model. The assumption that d,D = 0 just outside the hypothetical membrane is reasonable as long as the particle size is much larger than For particle sizes that are of the order of the hypothetical membrane can be thought at about a distance from the particle surface to incorporate the diffuse layer ions in the Donnan phase [25]. Ultimately this leads to a value of Vd that is larger than the void volume inside the particles and an average Donnan potential that is somewhat lower than the potential without this correction. The magnitude of the differences will depend on... 

In general, the chemical potentials of the cation are not equal in a given solution and in the membrane. At equilibrium the electrochemical potentials of the cation must be equal in the two phases. As a result, a potential difference called the Donnan potential is established at each interface. Moreover, the concentration of the cation on the left-hand side of the membrane is not always the same as that on the right and the cation diffuses from the location of high concentration to the one where it is lower. The non-equilibrium diffusion process gives rises to a diffusion potential. 

There are two important types of liquid membranes used in analytical applications. One type involves an ion-exchanging system dissolved in a hydrophobic solvent, usually of low permittivity. The other type makes use of an ionophore or neutral complexing agent dissolved in a similar solvent. In both systems, Donnan potentials are established on either side of the membrane but a diffusion potential is absent because of the mobility of the solute in the liquid phase. More details about the functioning of these membranes are given in this section. 

However, it was recognized (29 30) that equation (1) is an over-simplification since, in addition to the Donnan phase boundary potential, it should include a term to allow for diffusion phenomena arising from the fact that the membrane is more permeable to counter ion A than to co-ion Y ... 

Freed of other restrictions, a mobile ion may be expected to diffuse down any concentration gradient that exists between porous solid and liquid. In the particular case of ion exchange, there is an additional requirement that the resin and liquid phases should remain electrically neutral. Any tendency for molecules to move in such a way as to disturb this neutrality will generate a large electrostatic potential opposing further movement, known as the Donnan potential. 

In view of the potentially important effect of the Donnan equilibrium of charged species in similar systems, for example, two-phase aqueous polymer systems (29,30), it is important to note that several observations indicate that this effect is not a dominant one in the diffusion cell experiments (24). Specifically, (i) relatively small differences in the partitioning of cytochrome-c were observed to accompany the substitution of different salt types, and (ii) the PEO concentration in the PEO-rich compartment is an order of magnitude smaller than that encountered in typical two-phase aqueous polymer systems. As a result, the effective electrical potential difference across the membrane was estimated to be 0.2mV or less (24). 

We have assumed that the sample solution has been dialysed against a solvent v/hich contains a neutral salt of 1-1 type having a common counter-ion with the polyelectrolyte solution until the Donnan membrane equilibrium is attained. Moreover, we have also assumed that the diffusion coefficient of the polyion is so small that the chemical potentials of the simple ions are always equal throughout the entire solution at every moment during the diffusion process. That is, the diffusion process proceeds under conditions such that the Donnan equilibrium condition between the polymer phase and the solvent phase is always maintained. Then,... 

When a nondiffusible component (e.g., protein) is at dialysis equilibrium in a medium containing two or more diffusible components, then the molalities of the diffusible components on the two sides of the dialysis membrane are not necessarily the same (e.g., due to Donnan effects, preferential binding, etc.). But, though at equilibrium the mass ratios of the diffusible components may differ, the chemical potentials, p, of each component are equal in the two phases. Then, a plot of the densities of a series of solutions vs. C2 yields another limiting slope, namely (Bp/Bci). ... 

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