Ion-Selective Electrodes: Selectivity Coefficients for Interfering Ions of the Opposite Charge Sign

The way upper limits of detection (LODs) are typically reported in the ion-selective electrode (ISE) literature is unfortunately outdated. It is well understood that the upper LOD of a polymeric-membrane ISE is limited by Donnan failure, that is, the transfer of primary ions along with interfering ions of the opposite charge sign (commonly referred to as counterions) from the sample into the sensing membrane. However, it is often difficult to compare upper LODs for ISEs from different sources. The majority of publications on ISEs describe Donnan failure for one type of counterion only, making it impossible for end users to predict the interference for other counterions. Moreover, linear ranges for ISEs based on different ionophores cannot be compared to one another when Donnan failure was reported for different counterions. To this end, we introduce here selectivity coefficients, <i>K</i>_{<i>I</i>,<i>X</i>}^potX, for interfering counterions. Using this new concept, the primary ion activity at which Donnan failure occurs can be readily predicted from measured <i>K</i>_{<i>I</i>,<i>X</i>}^potX values by the use of the uncomplicated expression <i>a</i>_X^{<i>z</i>_<i>I</i>/<i>z</i>_<i>x</i>}/<i>K</i>_{<i>I</i>,<i>X</i>}^potX. Consistent with the intuition that many ISE users have for conventional selectivity coefficients, large <i>K</i>_{<i>I</i>,<i>X</i>}^potX values are characteristic for counterions that interfere strongly. We show experimentally that trends as predicted by the phase boundary model for Donnan failure, such as the effects of counterion hydrophobicity and ionophore complex stability, are often accurately predicted with the <i>K</i>_{<i>I</i>,<i>X</i>}^potX approach. However, there are notable exceptions when the underlying assumptions made by users do not apply, such as when counterions unexpectedly form aggregates with other species in the sensing membranes. The empirically measured <i>K</i>_{<i>I</i>,<i>X</i>}^potX coefficients enable the discovery of such phenomena, opening a rational path to improving upper LODs and, thereby, linear response ranges.