EIS simulations for ion-selective site-based membranes by a numerical solution of the coupled Nernst–Planck–Poisson equations

Computer simulation of ion-selective membrane electrodes and related systems by finite-difference procedures

“…On the other hand, the observable effects of space-charge regions in real experiments on ISEs are usually very small, apart from fast acmeasurements as applied for the study of complex impedance spectra [21,25]. The reason is that space charge, as a rule, is restricted to the nanometer domain, in accordance with the respective Debye length [6].…”

“…The resulting net charge concentrations are usually well below the range of the total ion concentrations, except for extremely thin membranes [6,31]. A further limitation of space-charge approaches is their need for highly involved, implicit mathematical procedures, which may become a critical factor [22,24,25]. Even more seriously, none of the earlier attempts of simulating ISEs accounted for the presence of a stagnant solution film adhering to the electrode.…”

“…Buck also pioneered a more general treatment that accounts for space-charge influences according to the Poisson equation [21]. Recently, Lewenstam's group presented a new version of this space-charge approach and reported different applications to membranes and liquid junctions [22,24,25].…”

“…A series of numerical simulations have been reported in the past for membranes of ion-selective electrodes [18][19][20][21][22][23][24][25], for liquid junctions of reference electrodes [22,24] and for diffusion layers of other electrode systems [26][27][28][29]. In an early contribution, Buck's group introduced digital simulations for investigating the electrical behavior of membranes based on liquid ionexchangers [18,19].…”

Comparison of different approaches to the description of the detection limit of ion-selective electrodes

“…The first NPP model implementation where the method of lines (MOL) [11] was used was presented in [12,13]. Later on, MOL extensions of the NPP model for an arbitrary number of layers were developed and implemented in C++ [14] or in MathCad [9] and Matlab [15] scripts.…”