Modeling of the effect of diffusion processes on the response of ion-selective electrodes by the finite difference technique: Comparison of theory with experiment and critical evaluation

Potentiometric Sensing

“…The obvious advantage of this material is its hydrophobicity, large capacitance and good solubility in the membrane matrix. [47][48][49] It was found that in some cases the earlier model shows principal limitations that may lead to failure of the calculations. 47 The authors studied the influence of the boundary conditions and simulation parameters to find a solution for this problem.…”

“…[47][48][49] It was found that in some cases the earlier model shows principal limitations that may lead to failure of the calculations. 47 The authors studied the influence of the boundary conditions and simulation parameters to find a solution for this problem. 48 The reason for the failure is that mass transport does not account for concentration changes at both sides of the phase boundary, just at one.…”

Description of the Effects of Non‐ion‐exchange Extraction and Intra‐membrane Interactions on the Ion‐selective Electrodes Response within the Interface Equilibria‐triggered Model

“…Numerical simulations in some cases provide information on the influence of various factors upon the response of ISEs much faster and cheaper than experimental measurements . In this regard, dynamic diffusion models that use a relatively simple mathematical apparatus based on solving the Fick diffusion equations by the finite difference method under the assumption of fast kinetics of the interface transfer, thus allowing to calculate the time dependences of the concentration profiles of potential‐determining components in the solution and membrane phases, seem very promising for routine use . These models are based on splitting the membrane and the diffusion layer of the sample solution into a number of elementary layers which are thin enough to assume that the concentration profiles of the components between the midpoints of the adjacent layers are linear.…”

“…A simple and, in our opinion, universal solution to this problem was proposed in the framework of the interface equilibria‐triggered (IET) dynamic diffusion model, according to which each calculation cycle for an instant of time t begins with recalculation of equilibrium concentrations of each component in rather thin near‐boundary layers. To perform this recalculation, the concentrations of the corresponding components in near‐boundary layers attained at the previous instant of time t–δt as the result of diffusion are used and interphase and intra‐phase equilibrium constants together with material balance and electroneutrality conditions in these layers are taken into account . The obtained corrected values of concentrations are then used to recalculate the concentrations of each component in all other elementary layers of the membrane and in the aqueous diffusion layer (from the first layer to the last one) taking into account diffusion processes.…”

“…This model has proven its operability and high predictive efficiency for both ion exchanger‐based and neutral carrier‐based electrodes for all realistic scenarios of the electrode functioning, making it possible to carry out both separate and joint accounting of the effects of ion exchange processes, co‐extraction at the membrane/sample solution interface and transmembrane transfer from the internal solution to the external one on the ISE response . Due to the separate, step‐by step, account of local equilibria at the interface and diffusion processes within each phase the algorithm of calculating is relatively simple and the model is rather flexible.…”