Equilibria Donnan uptake

First, assume that the surface charge on the membrane particles does not interact with the mobile protons (no proton release or uptake). An ion step will result in an increase in the double-layer capacitances of the particles and consequently in a decrease of the surface potentials fr, because the charge densities remain constant. The ISFET will measure a transient change in the mean pore potential. As a result of the potential changes, an ion redistribution will take place and the equilibrium situation is re-established. The theoretical maximum ion step response is the change in the mean pore potential. This is comparable with the Donnan model where the theoretical maximum is determined by the change in the Donnan potential at the membrane solution interface. 

Soil scientists and physical chemists tend to view this situation somewhat differently. The former see it as the acid-base reaction (Eq. [11]) at the surface the latter, as an equilibrium uptake of anion and cation of acid HA or base B (see Eq. [12]) regulated by the Donnan potential and followed by the respective reaction (Paterson and Rahman, 1985)... 

Summary. We have shown that ion transport in "Nafion" per-fluorinated membrane is controlled by percolation, which means that the connectivity of ion clusters is critical. This basically reflects the heterogeneous nature of a wet membrane. Although transport across a membrane is usually perceived as a one-dimensional process, our analysis suggests that it is distinctly three-dimensional in "Nafion". (Compare the experimental values of c and n with those listed in Table 7.) This is not totally unexpected since ion clusters are typically 5.0 nm, whereas a membrane is normally several mils thick. We have also uncovered an ionic insulator-to-conductor transition at 10 volume % of electrolyte uptake. Similar transitions are expected in other ion-containing polymers, and the Cluster-Network model may find useful application to ion transport in other ion containing polymers. Finally, our transport and current efficiency data are consistent with the Cluster-Network model, but not the conventional Donnan equilibrium. 

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