Describing Ion Exchange at Membrane Electrodes for Ions of Different Charge

Abstract

It is well‐documented in the literature that the Nikolsky‐Eisenman equation cannot accurately describe the equilibrium of ion exchange at membrane electrodes for ions of different charge. Despite this, unfortunately, it is still widely used owing to the complexity of the more rigorous formalism developed by Bakker et al. in 1994. Here, different available approaches are presented in a unified manner and compared. This includes two different approximations that are equally appropriate for cases of low level of interference where the extent of ion‐exchange is comparatively small, one of which is introduced here for the first time. The comparison also considers the permutated form of the Nikolsky‐Eisenman equation, where the primary ion is treated as the interfering ion and vice versa. As the permutated form gives a deviation from the thermodynamic model that is opposite that of the regular Nikolsky‐Eisenman equation, the two can be combined to give a semi‐empirical equation that is surprisingly close to the thermodynamic model and that comprises a single equation for any charge combination. The different choices presented here may be helpful to solve more complex theoretical problems, as for example in the modeling of the time dependence of the electrode response by numerical simulation where the interfacial step condition is a unique and difficult feature of the calculation.

Potentiometric Sensing

“…This group proposed to modify the established calculation protocol and termed it an interface equilibria-triggered time-dependent diffusion model. 49 52 It included Nikolsky-Eisenman equation and its permutated form, the most rigorous self-consistent model, which is however mathematically complex, and two different approximations valid for cases of low level of interference. One of these approximations was introduced for the first time.…”

“…It is well established that the Nikolsky-Eisenman equation does not adequately describe this case. The authors compared and analyzed five different approaches to describe this problem . It included the Nikolsky-Eisenman equation and its permutated form, the most rigorous self-consistent model, which is however mathematically complex, and two different approximations valid for cases of low level of interference.…”

“…Top: monovalent primary and divalent interfering ion. Bottom: divalent primary and monovalent interfering ion . To average, the second Nikolsky-Eisenman equation is written to treat the interfering ion as the primary one as vice versa.…”

A Scientific Journey with Ionophore-based Sensors

“…Calculated potential response of a monovalent ion-selective electrode exhibiting interference from a divalent ion, based on the two semi-empirical Nikolskii-Eisenman Eqns. (3) and (4) (which are inconsistent), the thermodynamically sound description (Equilibrium Model), and the behavior calculated from computing the average of Eqns (3) and (4) (Average), which better agrees with the thermodynamic model [14].…”

“…It gives guidance to develop ion sensors for a given application, such as in clinical 3) and ( 4) (which are inconsistent), the thermodynamically sound description (Equilibrium Model), and the behavior calculated from computing the average of Eqns ( 3) and (4) (Average), which better agrees with the thermodynamic model. [14] an unlikely potentiometric response to heparin in physiological levels of NaCl with seemingly simple ion-selective membranes containing tridodecylammonium chloride. [21] At the time it was not clear why heparin should give a response, as its polysaccharide backbone is already hydrophilic, the high anionic charge (about -70) should render extraction into an organic phase in high saline concentration impossible.…”