Effects of Ion Transport on the Potential Response of Ionophore-Based Membrane Electrodes: A Theoretical Approach

Determination of Single-Ion Partition Coefficients between Water and Plasticized PVC Membrane Using Equilibrium-Based Techniques

An experimentally simple method for the direct determination of single-ion partition coefficients between water and a PVC membrane plasticized with o-NPOE is suggested. The method uses the traditional assumption of equal single-ion partition coefficients for some reference cation and anion, in this case tetraphenylphosphonium (TPP⁺) and tetraphenylborate (TPB^-). The method is based on an integrated approach, including direct study of some salts' distribution between water and membrane phases, estimation of ion association constants, and measurements of unbiased selectivity coefficients for ions of interest, including the reference ones. The knowledge of distribution coefficients together with ion association constants allows for direct calculation of the multiple of the single-ion partition coefficients for the corresponding cation and anion, while the knowledge of unbiased selectivity coefficients together with ion association constants allows for immediate estimation of the single-ion partition coefficients for any ion under study, if the corresponding value for the reference ion is known. Both potentiometric and extraction studies are inherently equilibrium-based techniques, while traditionally accepted methods such as voltammetry and diffusion are kinetical. The inner coherent scale of single-ion partition coefficients between water and membrane phases was constructed.

Physically Tailoring Ion Fluxes by Introducing Foamlike Structures into Polymeric Membranes of Solid Contact Ion-Selective Electrodes

Transmembrane ion fluxes have earlier been identified as a source of potential instability in solid contact ion-selective electrodes (SC-ISEs). In this work, foamlike structures were intentionally introduced into a potassium-sensitive plasticized poly(vinyl chloride) ion-selective membrane (ISM) near the membrane|solid contact interface by controlling the temperature during membrane deposition. Foamlike structures in the ISM were shown to be effective at physically tailoring the transport of ions in the ion-selective membrane, greatly reducing the flux of interfering ions from the sample to the membrane|solid contact interface. The drifts during a conventional water layer test were hence able to be greatly mitigated, even with SC-ISEs incorporating a relatively hydrophilic poly(3,4-ethylenedioxythiophene) doped with poly(styrenesulfonate) (PEDOT:PSS) solid contact. In solutions with a high background concentration of interfering ions, equilibrated ion-selective electrodes with foamlike membranes were able to reproduce their initial potentials within 0.6 mV uncertainty (n = 3) from 0 to 18 h. This was achieved despite sensor exposure to solutions exceeding the selectivity limit of the ISEs in 3 h intervals, allowing improvement of the potential reproducibility of the sensors. Since the introduction of foamlike structures into ISM is linked to temperature-controlled membrane deposition, it is envisaged that the method is generally applicable to all solid contact ion-selective electrodes that are based on polymeric membranes and require membrane deposition from the cocktail solution.

Steady-State and Transient Performance of Ion-Sensitive Electrodes Suitable for Wearable and Implantable Electro-chemical Sensing

Traditional Potentiometric Ion-selective Electrodes (ISE) are widely used in industrial and clinical settings. The simplicity and small footprint of ISE have encouraged their recent adoption as wearable/implantable sensors for personalized healthcare and precision agriculture, creating a new set of unique challenges absent in traditional ISE. In this paper, we develop a fundamental physics-based model to describe both steady-state and transient responses of ISE relevant for wearable/implantable sensors. The model is encapsulated in a generalized Nernst formula that explicitly accounts for the analyte density, time-dynamics of signal transduction, ion-selective membrane thickness, and other sensor parameters. The formula is validated numerically by self-consistent modeling of multispecies ion-transport and experimentally by interpreting the time dynamics and thickness dependence of thin-film solid-contact and graphene-based ISE sensors for measuring soil nitrate concentration. These fundamental results will support the accelerated development of ISE for wearable/implantable applications.

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.

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.

A highly selective lead-sensitive electrode with solid contact based on ionic liquid

A new polyvinylchloride membrane sensor for Pb(2+) with solid contact based on ionic liquid has been prepared. The electrode shows a Nernstian response for lead ions over a wide concentration range (1×10(-8) to 1×10(-1) mol L(-1)) and the slope of 29.8 mV/decade. The limit of detection is 4.3×10(-9) mol L(-1). It has a fast response time of 5-7 s and can be used for 4 months without any divergence in potential. The proposed sensor is not pH sensitive in the range 3.5-7.3 and shows a very good discriminating ability towards Pb(2+) ion in comparison with some alkali, alkaline earth, transition and heavy metal ions. It was successfully applied as an indicator electrode in potentiometric titration of lead ions with K(2)CrO(4) and for direct determination of Pb(2+) ions in real sample solution.

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.

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.

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.

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

A simple but powerful numerical simulation for analyzing the electrochemical behavior of ion-selective membranes and liquid junctions is presented. The computer modeling makes use of a finite-element procedure in the space and time domains, which can be easily processed (e. g., with MS Excel software) without the need for complex mathematical evaluations. It leads to convincing results on the dynamic evolution of concentration profiles, potentials, and fluxes in the studied systems. The treatment accounts for influences of convection, flow, or stirring in the sample solution that act on the boundary diffusion layer and it is even capable of including the effects of an electrolyte flow through the whole system. To minimize the number of arbitrary parameters, interfacial reactions are assumed to be near local equilibrium, and space-charge influences are considered via phase-boundary potential differences. The applicability of the computer simulation is demonstrated for different ion-selective membranes as well as for liquid junctions. The numerical results are in excellent agreement with experimental data.

Dysprosium(III) Ion-Selective Electrochemical Sensor Based on 6-Hydrazino-1,5-diphenyl-6,7-dihydropyrazolo[3,4-d]pyrimidine-4(5H)-imine

A Dy(III) ion-selective electrode based on 6-hydrazino-1,5-diphenyl-6,7-dihydropyrazolo[3,4-d]pyrimidine-4(5H)-imine (HDDPI) as an excellent sensing material was developed. The sensor exhibits a Nernstian behavior (a slope of 19.6 ± 0.3 mV per decade) over a wide concentration range (from 1.0 × 10-1 to 8.0 × 10-7 M Dy) with a detection limit of 4.2 × 10-7 M. The sensor response is independent of pH of the solution in the pH range 3.5-8.3. The sensor possesses the advantages of short conditioning time, fast response time (<10 s) and in particular, good selectivity and sensitivity to the dysprosium ion in the presence of a variety of cations, including alkali, alkaline earth, transition and heavy metal ions. The sensor also showed a great enhancement in selectivity coefficients for dysprosium ions, in comparison with the formerly mentioned dysprosium sensors. The electrode can be used for at least 10 weeks without any considerable divergence in the potentials. The proposed electrode was successfully used as an indicator electrode in potentiometric titration of Dy(III) ions with EDTA. The membrane sensor was also used in the determination of concentration of F- ions in some mouth washing solutions and in the Dy3+ recovery from solution.

Modern potentiometry

For most chemists, potentiometry with ion-selective electrodes (ISEs) primarily means pH measurements with a glass electrode. Those interested in clinical analysis might know that ISEs, routinely used for the determination of blood electrolytes, have a market size comparable to that of glass electrodes. It is even less well known that potentiometry went through a silent revolution during the past decade. The lower detection limit and the discrimination of interfering ions (the selectivity coefficients) have been improved in many cases by factors up to 10(6) and 10(10), respectively, thus allowing their application in fields such as environmental trace analysis and potentiometric biosensing. The determination of complex formation constants for lipophilic hosts and ionic guests is also covered in this Minireview.

Selectivity enhancement of anion-responsive electrodes by pulsed chronopotentiometry

A large and robust selectivity improvement of ion-selective electrodes is presented for the measurement of abundant ions. An improvement in selectivity by more than two orders of magnitude has been attained for the hydrophilic chloride ions measured in a dilute background of the lipophilic ions perchlorate and salicylate in a pulsed chronopotentiometric measurement mode. This is attributed to a robust kinetic discrimination of the dilute lipophilic ions in this measuring mode, which is not possible to achieve in classical potentiometry. Maximum tolerable concentrations of the interfering ions are found to be on the order of 30 microM before causing substantial changes in potential. As an example of practical relevance, the robust detection of chloride in 72 microM salicylate (reflecting 1:10 diluted blood) with a detection limit of 0.5 mM chloride is demonstrated. Corresponding potentiometric sensors did not give a useful chloride response under these conditions.

Approaches to Improving the Lower Detection Limit of Polymeric Membrane Ion-Selective Electrodes

More than ten different approaches for improving the lower detection limit of polymeric membrane ion-selective electrodes have been suggested during the recent years. In this contribution, their principles are briefly summarized with a focus to their general practical applicability. The methods that are the most rugged and the easiest to implement in a routine laboratory will be highlighted.

Dynamic diffusion model for tracing the real-time potential response of polymeric membrane ion-selective electrodes

A numerical solution for the prediction of the time-dependent potential response of a polymeric-based ion-selective electrode (ISE) is presented. The model addresses short- and middle-term potential drifts that are dependent on changes in concentration gradients in the aqueous sample and organic membrane phase. This work has important implications for the understanding of the real-time response behavior of potentiometric sensors with low detection limits and with nonclassical super-Nernstian response slopes. As a model system, the initial exposure of membranes containing the well-examined silver ionophore O,O' '-bis[2-(methylthio)ethyl]-tert-butylcalix[4]arene was monitored, and the large observed potential drifts were compared to theoretical predictions. The model is based on an approximate solution of the diffusion equation for both aqueous and organic diffusion layers using a numerical scheme (finite difference in time and finite elements in space). The model may be evaluated on the basis of experimentally available parameters and gives time-dependent information previously inaccessible with a simpler steady-state diffusion model. For the cases studied, the model gave a very good correlation with experimental data, albeit with lower than expected diffusion coefficients for the organic phase. This model may address numerous open questions regarding the response time and memory effects of low-detection-limit ion-selective electrodes and for other membrane electrodes where ion fluxes are relevant.

Rotating Disk Potentiometry for Inner Solution Optimization of Low-Detection-Limit Ion-Selective Electrodes

The extent of optimization of the lower detection limit of ion-selective electrodes (ISEs) can be assessed with an elegant new method. At the detection limit (i.e., in the absence of primary ions in the sample), one can observe a reproducible change in the membrane potential upon alteration of the aqueous diffusion layer thickness. This stir effect is predicted to depend on the composition of the inner solution, which is known to influence the lower detection limit of the potentiometric sensor dramatically. For an optimized electrode, the stir effect is calculated to be exactly one-half the value of the case when substantial coextraction occurs at the inner membrane side. In contrast, there is no stir effect when substantial ion exchange occurs at the inner membrane side. Consequently, this experimental method can be used to determine how well the inner filling solution has been optimized. A rotating disk electrode was used in this study because it provides adequate control of the aqueous diffusion layer thickness. Various ion-selective membranes with a variety of inner solutions that gave different calculated concentrations of the complex at the inner membrane side were studied to evaluate this principle. They contained the well-examined silver ionophore O,O' '-bis[2-(methylthio)ethyl]-tert-butylcalix[4]arene, the potassium ionophore valinomycin, or the iodide carrier [9]mercuracarborand-3. Stir effects were determined in different background solutions and compared to theoretical expectations. Correlations were good, and the results encourage the use of such stir-effect measurements to optimize ISE compositions for real-world applications. The technique was also found to be useful in estimating the level of primary ion impurities in the sample. For an iodide-selective electrode measured in phosphoric acid, for example, apparent iodide impurity levels were calculated as 5 x 10(-10) M.

Plasticizer-free polymer containing a covalently immobilized Ca2+-selective ionophore for potentiometric and optical sensors

A derivative of a known Ca2+-selective ionophore, ETH 129, was synthesized to contain a polymerizable acrylic moiety (AU-1) and covalently grafted into a methyl methacrylate-co-decyl methacrylate polymer matrix. The polymer containing AU-1 was prepared via a simple one-step homogeneous polymerization method. It exhibited mechanical properties suitable for the fabrication of plasticizer-free ion-selective membrane electrodes and bulk optode films by solvent-casting and spin-coating techniques, respectively. The segmented sandwich membrane technique was utilized to assess the binding constant of free and covalently bound ionophores to calcium and to study their diffusion coefficients in the membrane phase. Diffusion was greatly diminished for the bound ionophore. This was confirmed in ion-selective electrode membranes containing no calcium ions in the inner solution, which should normally show apparent super-Nernstian response slopes in dilute calcium solutions. The response slope was Nernstian down to submicromolar concentration levels, indicating slow mass transport of calcium in the membrane. Optical-sensing films with the new copolymer matrix, unblended and blended with PVC-DOS, also confirmed that covalently bound ionophores are fully functional for maintaining selective ion extraction and binding properties of the sensing membrane.

Improving the Detection Limit of Anion-Selective Electrodes: An Iodide-Selective Membrane with a Nanomolar Detection Limit

The lower detection limit and the selectivity behavior of anion-selective electrodes (ISEs) are improved by using optimized inner solutions and membrane compositions. With a membrane based on the recently described ionophore [9]mercuracarborand-3, a detection limit of 2 x 10(-9) M has been achieved for iodide. Nevertheless, the improvements are less pronounced than in the case of cation ISEs. This is mainly due to the fact that so far no anion ISE is known with the extremely high selectivities of cation ISEs. If the membrane does not contain an ionophore, leaching of the ion exchanger from the membrane into the sample is also a relevant limiting factor except for ion exchangers of very high lipophilicity.

Rational design of potentiometric trace level ion sensors. A Ag+-selective electrode with a 100 ppt detection limit

Submicromolar to picomolar lower detection limits have recently been obtained with various polymer membrane ion-selective electrodes by minimizing biases due to ion fluxes through the membrane. For the best performance, the compositions of the membrane and inner solution should be optimized for each application. Given the number of parameters to be adjusted, it has been difficult to find the best parameters for a target sample. In this paper, a much simplified and more practical steady-state model of zero-current ion fluxes is derived, which is based on measurable parameters. The model allows one to predict achievable lower detection limits for a membrane with given selectivities. It can also be used to predict the optimal composition of the inner filling solution for the measurement of samples with a known, typical ionic background. Selectivity coefficients of monovalent and divalent analyte ions required for desired detection limits in drinking water are calculated. As an application of the proposed general recipe, a silver-selective electrode is developed on the basis of the ionophore O,O''-bis[2-(methylthio)ethyl]-tert-butylcalix[4]arene. With the predicted optimal composition of the inner electrolyte, its lower detection limit is found to be 10(-9) M or 100 ppt Ag+ with an ionic background of 10(-5) M LiNO3, which is very close to the expected value.