Computer Simulation of Ion-Selective Membrane Electrodes and Related Systems by Finite-Element Procedures

Selective Ion Capturing via Carbon Nanotubes Charging

We present a phenomenon consisting of the synergistic effects of a capacitive material, such as carbon nanotubes (CNTs), and an ion-selective, thin-layer membrane. CNTs can trigger a charge disbalance and propagate this effect into a thin-layer membrane domain under mildly polarization conditions. With the exceptional selectivity and the fast establishment of new concentration profiles provided by the thin-layer membrane, a selective ion capture from the solution is expected, which is necessarily linked to the charge generation on the CNTs lattice. As a proof-of-concept, we investigated an arrangement based on a layer of CNTs modified with a nanometer-sized, potassium-selective membrane to conform an actuator that is in contact with a thin-layer aqueous solution (thickness of 50 μm). The potassium ion content was fixed in the solution (0.1–10 mM range), and the system was operated for 120 s at −400 mV (with respect to the open circuit potential). A 10-fold decrease from the initial potassium concentration in the thin-layer solution was detected through either a potentiometric potassium-selective sensor or an optode confronted to the actuator system. This work is significant, because it provides empirical evidence for interconnected charge transfer processes in CNT–membrane systems (actuators) that result in controlled ion uptake from the solution, which is monitored by a sensor. One potential application of this concept is the removal of ionic interferences in a sample by means of the actuator to enhance precision of analytical assessments of a charged or neutral target in the sample with the sensor.

Integration of an Aerosol-Assisted Deposition Technique for the Deposition of Functional Biomaterials Applied to the Fabrication of Miniaturised Ion Sensors

Ion-selective electrodes are at the forefront of research nowadays, with applications in healthcare, agriculture and water quality analysis among others. Despite multiple attempts of miniaturization of these polyvinyl chloride (PVC) gel-based ion sensors, no ion-sensing devices with a thickness below the micrometer range, and operating using open circuit potential, have been developed so far. This work reports the causes of this thickness limitation in potassium-selective sensors. Highly homogeneous ion-sensing films were fabricated by a method based on aerosol assisted chemical vapour deposition, leading to smooth surfaces with 27 ± 11 nm of roughness. Such homogeneity allowed the systematic study of the performance and ionic diffusion properties of the sensing films at sub-micrometer scales. Sensitivities below the Nernst response were found at low thicknesses. The nature of this reduction in sensitivity was studied, and a difference in the superficial and bulk compositions of the films was measured. An optimal configuration was found at 15 µm, with a good selectivity against Na+ (KK+, Na+ = -1.8) a limit of detection in the range of 10-4 M and esponse time below 40 s. The stability of sensors was improved by the deposition of protective layers, which expanded the lifespan of the ion sensors up to 5 weeks while preserving the Nernst sensitivity.

Kinetic Description of the Membrane-Solution Interface for Ion-Selective Electrodes

The theoretical models for ISEs almost exclusively assume thermodynamic equilibrium at the membrane/solution-phase boundary. In this report, we present a new, congruent model which combines first-order reaction kinetics of ion-exchange at the phase boundary and diffusional mass transport in the adjoining phases in the continuity equation. The influence of the rate constant in the new kinetic model has significant impact on the predicted transients corresponding to instantaneous change in the sample solution composition. The simulated transients generated with the new model coincide with the transients recorded in common potentiometric experiments, e.g., with transients recorded upon step change in the primary or interfering ion concentrations. The simulated transients also align well with previously published transients representing special cases of potentiometry (e.g., super-Nernstian response, non-Nernstian responses in the presence of highly interfering ions). The implementation of the kinetic model for simulating the transients in the water layer test also resulted in a better agreement with the experiments compared to the previous models.

Overcoming of One More Pitfall in Boundary Element Calculations with Computer Simulations of Ion-Selective Electrode Response

Computer simulations of ion-selective membrane electrodes using diffusion layer models based on finite-differences principle for calculating diffusion processes in both phases and taking into account the local ion exchange equilibrium at the interface are successfully used for clarifying and even predicting the influence of different diffusion factors on several time-dependent characteristics of electrodes. It is shown here that a well-established approach based on the assumption of the constant concentration of the interfering ion in the sample solution fails for solutions containing strongly interfering ions where the concentration of the interfering ion in the boundary layer of the solution can be far lower in comparison with its concentration in the bulk. The limitation is demonstrated by a drastic discrepancy between experimental and calculated curves for the dependence of potential on time. This limitation can be overcome by taking into account the change of the interfering ion concentration in the boundary layer in accordance with the electroneutrality condition. A good agreement between simulation results and experimental data is demonstrated.

Application of the interface equilibria-triggered dynamic diffusion model of the boundary potential for the numerical simulation of neutral carrier-based ion-selective electrodes response

It is shown that a simple dynamic diffusion model of the boundary potential based on a separate, step-by-step, account of ion transfer across the membrane/aqueous solution interface and the diffusion processes within both phases which was proposed earlier for describing the response of ionophore-free membranes, can be successfully used for ionophore-based membranes as well. The model makes it possible to carry out both separate and joint account of the effects of co-extraction, transmembrane transport and ion exchange on the boundary potential and retains robustness in all the variants studied. The model adequately describes the ionophore-based electrode response over the entire range of concentrations and allows one to clearly demonstrate the dependence of lower detection limit on such parameters as the diffusion coefficients and the concentration of electroactive substances in the membrane phase, the thickness of the diffusion layer in the sample solution, the duration of the measurement, and the composition of the internal reference solution. The results of numerical simulation are in good agreement with the experimental data presented in the literature. As all the factors of influence considered above can easily be regulated in more or less wide limits, but at the same time, an estimation of their cumulative effect is not always possible on an intuitive level, the present model can be of practical interest for justifying the ways of optimizing the design of the ISE and the algorithm for performing measurements in solving specific analytical problems.

Agarose hydrogel containing immobilized pH buffer microemulsion without increasing permselectivity

A heterogeneous pH buffer based on a colloidal emulsion containing ion-exchanger and lipophilic base is described that can be integrated into hydrogels without affecting their ion-exchange properties. Each sphere works on the basis of reversible ion-exchange of hydrogen ions with solution cations, acting as a pH buffer while staying removed from solution in the nonpolar core of the spheres. The ion-exchange mechanism is supported by titration experiments in aqueous emulsion, showing that the nature and concentration of the exchanging solution cations influences the buffer action, with increasing lipophilicity moving the equilibrium to lower pH values. Agarose gels with entrapped pH buffer emulsions and mounted in a transport cell are shown by zero current potentiometry to exhibit negligible permselective properties above an ionic strength of 1mM, a behavior no different from unmodified agarose, with an observed ion-exchanger concentration of 7mM in dry agarose. This suggests that such pH buffers do not give rise to substantial ion-exchange properties of the gel material. In a first attempt to control the pH in the vicinity of an electrode surface by this approach, the emulsion was entrapped in an agarose gel in direct contact with a pH electrode, demonstrating the ability to buffer such gel films.

Theory of the formation of the electric double layer at the ion exchange membrane-solution interface

This work aims to extend the study of the formation of the electric double layer at the interface defined by a solution and an ion-exchange membrane on the basis of the Nernst-Planck and Poisson equations, including different values of the counter-ion diffusion coefficient and the dielectric constant in the solution and membrane phases. The network simulation method is used to obtain the time evolution of the electric potential, the displacement electric vector, the electric charge density and the ionic concentrations at the interface between a binary electrolyte solution and a cation-exchange membrane with total co-ion exclusion. The numerical results for the temporal evolution of the interfacial electric potential and the surface electric charge are compared with analytical solutions derived in the limit of the shortest times by considering the Poisson equation for a simple cationic diffusion process. The steady-state results are justified from the Gouy-Chapman theory for the diffuse double layer in the limits of similar and high bathing ionic concentrations with respect to the fixed-charge concentration inside the membrane. Interesting new physical insights arise from the interpretation of the process of the formation of the electric double layer at the ion exchange membrane-solution interface on the basis of a membrane model with total co-ion exclusion.

Potentiometric investigation of protonation reactions at aqueous-aqueous boundaries within a dual-stream microfluidic structure

The laminar flow regime prevailing in pressure-driven flow through a Y-shaped microfluidic channel was utilized to create a stable boundary between two aqueous liquids. Transverse transport of ions between these two liquids gave rise to a diffusion potential, which was monitored by measurement of the open circuit potential. In this report, the influence on the cross-channel potential distribution of protonation reactions occurring in the boundary zone between the two co-flowing liquids is presented. The proton source was present in one of the co-flowing streams, and an uncharged proton acceptor was present in the other aqueous stream. The time-dependent transport equation for diffusion and migration was augmented by chemical reaction terms and was solved for all species present in both streams as a theoretical basis for the analysis. Within this model, the system was assumed to be homogeneous along the channel height, and effects of nonuniform velocity profiles were neglected. A reduction in potential by several millivolts was predicted for a protonation reaction occurring close to the boundary between the two aqueous streams, provided that the mobility of the protonated species was lower than the mobility of the co-cation in the background electrolyte (alkali metal cation in this case). The magnitude of the decrease in the potential was greater for protonated molecules with lower mobility or if the mobility of the background electrolyte cation was increased. Experimental results are presented for imidazole and D-histidine as proton acceptors present in 10 mM KCl, 10 mM NaCl, or 10 mM CsCl solution and co-flowing with a stream of 10 mM hydrochloric acid, which served as the proton source. Decreases in measured potential, in line with the predicted diminished potential, were obtained.

Theoretical Treatment and Numerical Simulation of Potential and Concentration Profiles in Extremely Thin Non-Electroneutral Membranes Used for Ion-Selective Electrodes

The applicability of extremely thin non-electroneutral membranes for ion-selective electrodes (ISEs) is investigated. A theoretical treatment of potential and concentration profiles in space-charge membranes of << 1 μm thickness is presented. The theory is based on the Nernst-Planck equation for ion fluxes, which reduces to Boltzmann's formula at equilibrium, and on the Poisson relationship between space-charge density and electric field gradient. A general solution in integral form is obtained for the potential function and the corresponding ion profiles at equilibrium. A series of explicit sub-solutions is derived for particular cases. Membrane systems with up to three different ion species are discussed, including trapped ionic sites and co-extracted ions. Solid-contacted thin membranes (without formation of aqueous films at the inner interface) are shown to exhibit a sub-Nernstian response. The theoretical results are confirmed by numerical simulations using a simplified finite-difference procedure based on the Nernst-Planck-Poisson model, which are shown to be in excellent agreement.

Generalized Selectivity Description for Polymeric Ion-Selective Electrodes Based on the Phase Boundary Potential Model

A generalized description of the response behavior of potentiometric polymer membrane ion-selective electrodes is presented on the basis of ion-exchange equilibrium considerations at the sample-membrane interface. This paper includes and extends on previously reported theoretical advances in a more compact yet more comprehensive form. Specifically, the phase boundary potential model is used to derive the origin of the Nernstian response behavior in a single expression, which is valid for a membrane containing any charge type and complex stoichiometry of ionophore and ion-exchanger. This forms the basis for a generalized expression of the selectivity coefficient, which may be used for the selectivity optimization of ion-selective membranes containing electrically charged and neutral ionophores of any desired stoichiometry. It is shown to reduce to expressions published previously for specialized cases, and may be effectively applied to problems relevant in modern potentiometry. The treatment is extended to mixed ion solutions, offering a comprehensive yet formally compact derivation of the response behavior of ion-selective electrodes to a mixture of ions of any desired charge. It is compared to predictions by the less accurate Nicolsky-Eisenman equation. The influence of ion fluxes or any form of electrochemical excitation is not considered here, but may be readily incorporated if an ion-exchange equilibrium at the interface may be assumed in these cases.

Interpretation of chronopotentiometric transients of ion-selective membranes with two transition times

Passing currents through ion-selective membranes has contributed to the development of a variety of novel methods. In this work, chronopotentiometric (CP) transients with two transition times (breakpoints) are presented for the first time, with the theoretical interpretation of such voltage transients. The validity of our theory has been confirmed in experiments utilizing ETH 5294 chromoionophore-based pH sensitive membranes with and without lipophilic background electrolyte and ETH 5234 ionophore-based calcium selective membranes in which the ionophore forms 3:1 complexes with Ca(2+) ions. The conditions under which two breakpoints can be identified in the chronopotentiometric voltage transients are discussed.Spectroelectrochemical microscopy (SpECM) is used to show that the two breakpoints in the CP curves emerge approximately when the free ionophore and ion-ionophore complex concentrations approach zero at the opposite membrane-solution interfaces. The two breakpoint times can be utilized to follow simultaneously the concentration changes of the free ionophore, the ion-ionophore complex, and the mobile anionic sites in cation-selective membranes. In membranes with known composition, the time instances where breakpoints occur can be used to estimate the free ionophore and the ion-ionophore complex diffusion coefficients.

Memory Effects of Ion-Selective Electrodes: Theory and Computer Simulation of the Time-Dependent Potential Response to Multiple Sample Changes

A straightforward theoretical description of the time-dependent response of ion-selective membrane electrodes to multiple sample changes is presented. The derivation makes use of an approximation for the ion fluxes in the membrane, and of the superposition of partial fluxes induced by the step-changes. The general theory allows for any number of samples and ions. It is applied for the analysis of memory effects that reflect the influence of preceding samples on subsequent measurements. Various phenomena are discussed, including super-, near-, or sub-nernstian responses, shifts of apparent reference potentials, and potential dips with domains of reversed slopes. The theoretical results agree well with virtual experiments based on computer simulation.

Limitations of current polarization for lowering the detection limit of potentiometric polymeric membrane sensors

Ion fluxes across polymeric ion-selective membranes are a decisive parameter dictating the lower detection limit of potentiometric ion sensors. An applied current was earlier proposed to counteract such fluxes and reduce the detection limit to ultratrace levels. So far, however, the method has not been used in practical situations since the correct current amplitude requires prior knowledge of the sample composition. This paper explores the use of the stir effect to evaluate the optimal current by theory and experiments. It is shown that the traditionally used steady-state model assuming a uniform distribution of ion exchanger in the membrane, fixed with time, violates the electroneutrality condition. A modified steady-state model is introduced that allows for a concentration tilt of the ion exchanger and predicts that a stir effect can indeed be utilized to find the optimal current. Ideally, by choosing the optimal current and very long measurement times, the thermodynamic detection limit might be obtained. However, in practice the stir effect declines at low concentrations and the conditions are far from steady state. Therefore, the improvement of the lower detection limit achievable by galvanostatic control is only about 1 order of magnitude. A numerical finite-difference approximation is shown to trace the experimental potential responses of silver-selective electrodes well and to reproduce the stir effect adequately, even for different conditioning protocols. The stir effect is successfully used to improve the detection limit of electrodes with ill-optimized inner solutions; however, significant improvements beyond what is commonly feasible by chemical optimization does not seem to be easily achievable. The results indicate that with conventional membranes the possibility of improving the detection limit by current polarization is much more limited than assumed so far.

Theory and Computer Simulation of the Time-Dependent Selectivity Behavior of Polymeric Membrane Ion-Selective Electrodes

A theoretical treatment of the time-dependent potential response of ion-selective electrodes to sample solutions containing primary and interfering ions is presented. The theory accounts for the influence of ion fluxes in the electrode membrane and the contacting aqueous sample layer and describes the variations in the apparent selectivity behavior as a function of the measuring time. The applicability of the theory is demonstrated by comparing predicted response curves with results of virtual experiments based on computer simulation. A close and convincing agreement was achieved for a large series of different examples, which confirms that the new theory can be successfully applied for general cases.