Nernst-Planck-Poisson Model for the Description of Behaviour of Solid-Contact Ion-Selective Electrodes at Low Analyte Concentration Jerzy J. Jasielec, a Grzegorz Lisak, a Michal Wagner, a Tomasz Sokalski, a Andrzej Lewenstam* a, b a Process Chemistry Centre, c/o Centre for Process Analytical Chemistry and Sensor Technology (ProSens), bo Akademi University, Biskopsgatan 8, 20500 bo-Turku, Finland b AGH – University of Science and Technology, Faculty of Material Science and Ceramics, Al. Mickiewicza 30, 30059 Cracow, Poland *e-mail: andrzej.lewenstam@abo.fi Received: July 12, 2012 Accepted: October 10, 2012 Published online: December 5, 2012 Abstract All-solid-state electrodes are increasingly being used in clinical, industrial and environmental analysis. This wide range of applications requires deep theoretical description of such electrodes. This work concentrates on the devel- opment of a numerical tool for the qualitative prediction of electrochemical behaviour for solid-contact ion-selec- tive electrodes at low analyte concentrations. For this purpose, a general approach to the description of electro-dif- fusion processes, namely the Nernst-Planck-Poisson (NPP) model, was applied. The results obtained from this model are verified by experimental data of lead(II)-selective electrodes based on a polymeric PVC membrane with polybenzopyrene doped with Eriochrome Black T used as the solid contact. Keywords: Potentiometry, Ion-selective electrodes, Solid contact, Response, Nernst-Planck-Poisson model, Electrodiffusion DOI: 10.1002/elan.201200353 1 Introduction Owing to several advantages, potentiometric sensors are broadly used in clinical and environmental analysis. In- strumentation and sensors are relatively cheaper and more user-friendly than other analytical techniques. Moreover, the potentiometric measurements do not change the samples chemical composition [1]. The aspect of lowering of the detection limit of ion-selec- tive electrodes (ISEs) has been an issue of interest for all types of potentiometric sensors. The first trials were per- formed with solid-state membrane electrodes [2–4]. Later, electrodes with polymeric membranes and inner filling so- lution were used [5,6]. More recently, solid-contact ion-se- lective electrodes (SC ISEs) with polymer membranes were applied [7–10]. In the latter electrodes, the inner filling so- lution is deliberately replaced with an intermediate layer between electrically conducting substrate and the solvent polymeric membrane [11]. The materials frequently used for this purpose are conducting polymers (CPs). Owing to their mixed conductivity, CPs serve as the elements that un- block faradaic charge transfer at the contact interfaces and thus adequately act as ion-to-electron transducers [12–14]. Applications of various conducting polymers as the SCs are extensively presented in the literature. Among them the most popular are: polypyrrole (PPy), poly(3-octyltiophene) (PEDOT) and polyaniline (PANI) [15]. In respect of lower- ing the detection limit, the removal of inner filling solution may bring advantages in reducing transmembrane ion fluxes from the inner compartment to the sample solution as well as allowing miniaturization [7,16]. Much effort is being put into developing a sensor which would operate at nanomolar concentrations. In par- ticular, the determination of heavy metals is one of the major interests [17–19]. Understanding the processes involved in the response of ISEs at low analyte concentration is crucial in environ- mental analysis. Theoretical modelling brings new insight into those processes. Ideally, a tool which would predict the behaviour of a particular system is needed. There are many models describing the response of ISEs, but they differ in generality and idealization level. Among them, the Nernst-Planck-Poisson (NPP) model offers the most complete and universal description of membranes and related systems [1]. Since the first application of the NPP model to mem- brane electrochemistry was presented in 1978 [20], an ap- proach dedicated to the general description of ISE behav- iour was developed [21–25]. In the mentioned papers, the authors describe the ISE potential as the effects of diffu- sion and migration taking place only in an ion-selective membrane. The extension of the NPP model to a two-layer system made it possible to simulate the processes occurring in SPECIAL ISSUE Electroanalysis 2013, 25, No. 1, 133 – 140  2013 Wiley-VCH Verlag GmbH &Co. KGaA, Weinheim 133 Full Paper