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.

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.

Improved detection limits and sensitivities of potentiometric titrations.

Zero-current ion fluxes through polymer membranes of ion-selective electrodes (ISEs) may lead to biased endpoints of potentiometric titrations. The bias is eliminated, and the sensitivity of the end-point detection is improved through reducing transmembrane ion fluxes by an appropriate choice of the inner solution. Surprisingly, ISE membranes that have a significant primary ion flux toward the inner solution show much larger sensitivities than expected by titration theory; however, depending on the experimental conditions, their application may bias the endpoint. With the optimal systems, endpoint detection is now possible with total sample concentrations below 10(-6) M, as demonstrated by the titration of EDTA with a Pb2+ solution.

A novel formalism to characterize the degree of unsaturation of organic molecules.

The existing formalism to calculate the degree of unsaturation from the molecular formula of organic molecules cannot be applied to charged and/or disconnected species. Moreover, the calculated value depends on the assumed formal valence of each of the elements. In this work, we introduce a new formalism that eliminates these problems. The suggested property, degree of unsaturation, can be calculated from the molecular formula as well as from any structural representation of a molecule corresponding to that molecular formula.

Potentiometric polymeric membrane electrodes for measurement of environmental samples at trace levels: new requirements for selectivities and measuring protocols, and comparison with ICPMS.

It is here established that potentiometric polymeric membrane electrodes based on electrically neutral ionophores are useful analytical tools for heavy metal ion determinations in drinking water at nanomolar total concentrations. This means that they can compete with the most sophisticated techniques of instrumental analysis. With optimized ion-selective membranes based on the lead-selective ionophore 4-tert-butylcalix[4]arenetetrakis(thioacetic acid dimethylamide) as model example, a number of native and spiked drinking water samples are potentiometrically assessed for lead, and the results compared with ICPMS measurements. The goal of this work is to demonstrate that detection limits in real world samples are routinely achieved that are, with 1.5 ppb, at least 10-fold lower than the lead action limit imposed by the U.S. Environmental Protection Agency (15 ppb). In contrast to earlier reports, different conditioning and measuring protocols are followed, and membranes and inner filling solution of optimized composition are used. The sensors are shown to be useful for the speciation analysis of lead in water as well. Typical water samples are acidified to pH 4 to assess total lead rather than free, uncomplexed lead. For lead concentrations above 2 ppb, the values compare very well with ICPMS. Main interferences are found to be H+ and Cu2+, although Cu2+ only shows significant interference at levels around or above its own action limit (1.3 ppm), in which case the water sample would anyway show quality problems. An explicit, simplified flux model targeted to the practical use of these sensors explains the extent of expected interference. Sensors are shown to require a higher selectivity than predicted by models not considering ion fluxes, since in dilute samples, the counterdiffusion flux of lead from the membrane into the sample becomes potential determining. The model and experiments shown here are a foundation for future trace level applications of potentiometric polymeric membrane electrodes.

Improved detection limits and unbiased selectivity coefficients obtained by using ion-exchange resins in the inner reference solution of ion-selective polymeric membrane electrodes

By using a high concentration of an interfering ion and a low one of the primary ion in the inner reference solution of polymeric membrane ion-selective electrodes (ISEs), the lower detection limit may be improved and unbiased thermodynamic selectivity coefficients may be obtained. To this purpose, a cation-exchange resin is used here to keep the low concentration of the primary cation constant. Different compositions of the internal solution are required for obtaining optimal lower detection limits and unbiased selectivity coefficients. All ISEs studied here, i.e., for K+, Ca2+, and NH4+, based on valinomycin, ETH 5234, and nonactin/monactin, respectively, show improved lower detection limits in the range of 10(-7.6) (NH4+) to 10(-8.8) M (Ca2+). Nernstian responses and, therefore, unbiased selectivity coefficients are obtained with the K+-ISE for the discriminated ions, Na+, Mg2+, and Ca2+.

Direct potentiometric information on total ionic concentrations.

Polymeric membrane ion-selective electrodes exhibit an apparently super-Nernstian response at low sample activities if inner solutions are used that induce strong zero-current fluxes of primary ions toward the inner compartment. This is due to the limited ion fluxes in the aqueous boundary layer near the membrane. In the presence of labile complexes, the effective flux rate is increased and the emf depends on the total concentration of the ions. The concept is illustrated experimentally with calcium-selective electrodes based on the ionophore N,N-dicyclohexyl-N',N'-dioctadecyl-3-oxapentanediamide (ETH 5234) that either respond to total or free ion concentrations. Samples can be distinguished that contain varying levels of total calcium but are all buffered with EDTA to the same free calcium concentration of 5 x 10(-8) M.

Cationic or anionic sites? Selectivity optimization of ion-selective electrodes based on charged ionophores

The influence of ionic sites on the selectivities of ionophore-based ion-selective electrodes (ISEs) is described on the basis of a phase boundary potential model. The discussion presented here is significantly more general than previous ones. It is formulated for primary and interfering ions of any charges and it is valid for ISEs based on electrically charged or neutral ionophores. Furthermore, it also applies to membranes that contain more than one type of complex of the primary or interfering ion. It has been believed thus far that only ionic sites of the same charge sign as the primary ion improve the selectivities of ISEs based on charged ionophores. However, it is shown here that the charge sign of the ionic sites that give the highest potentiometric selectivities depends on the charge number of the primary and interfering ions and on the stoichiometry of their complexes with the ionophore. The validity of our model was confirmed experimentally with three ISEs based on different charged ionophores. ISEs based on lasalocid or 1-(N,N-dicyclohexylcarbamoyl)-2- (N,N-dioctadecylcarbamoyl)ethylphosphonic acid monomethyl ester (ETH 5639) as the ionophore responded selectively to Sr2+ or Mg2+, respectively, and discriminated well against other alkaline earth cations when their membranes contained anionic sites. These two electrodes are the first examples of ISEs based on charged ionophores for which maximum selectivities are obtained with membranes containing ionic sites with a charge sign opposite to that of the primary ion. On the other hand, the experimental F- selectivities of membranes based on oxo(5,10,15,20-tetraphenylporphyrinato)molybdenum-(V) improved gradually when the concentration of anionic sites was increased from 0 to 75 mol%. The selectivity-modifying influence of ionic sites for these three types of ISEs can be explained by considering the different stabilities of the 1:2 ion-ionophore complexes of the primary and of the interfering ions.

Selectivity of potentiometric ion sensors.

Selectivities of solvent polymeric membrane ion-selective electrodes (ISEs) are quantitatively related to equilibria at the interface between the sample and the electrode membrane. However, only correctly determined selectivity coefficients allow accurate predictions of ISE responses to real-world samples. Moreover, they are also required for the optimization of ionophore structures and membrane compositions. Best suited for such purposes are potentiometric selectivity coefficients as defined already in the 1960s. This paper briefly reviews the basic relationships and focuses on possible biases in the determination of selectivity coefficients. The traditional methods to determine selectivity coefficients (separate solution method, fixed interference method) are still the same as those originally proposed by IUPAC in 1976. However, several precautions are needed to obtain meaningful data. For example, errors arise when the response to a weakly interfering ion is also influenced by the primary ion leaching from the membrane. Wrong selectivity coefficients may be also obtained when the interfering agent is highly preferred and the electrode shows counterion interference. Recent advances show how such pitfalls can be avoided. A detailed recipe to determine correct potentiometric selectivity coefficients unaffected by such biases is presented.

Polymeric membrane electrodes for monohydrogen phosphate and sulfate.

A zwitterionic bis(guanidinium) ionophore bearing an anionic closo-borane cluster (1) and a dihydrochloride analogue (2) are investigated in polymeric membrane ion-selective electrodes (ISEs). Both compounds have been previously shown to complex and selectively extract oxoanions. By systematic variation of the kind and concentration of the ion-exchanger sites in the membrane, the optimal performance with the so far best sulfate selectivity is found for ISE membranes based on the dihydrochloride, whereas those with the zwitterion analogue are shown to possess a reasonably good selectivity for monohydrogen phosphate.

General description of the simultaneous response of potentiometric ionophore-based sensors to ions of different charge.

The response of ion-selective membrane electrodes is usually still described with the semiempirical Nicolskii-Eisenman equation although it cannot correctly reproduce experimental data if ions of different charges are involved. The recently published self-consistent model that was derived for two ions of any charges is now extended to any number of ions of any charge. One single explicit equation is here given for the first time for any number of monovalent, divalent, and trivalent ions. Deviations relative to the Nicolskii-Eisenman equation are shown to be especially high at low interferences and bias calibrations if done in a mixed solution of a target sample as well as multivariate calibrations with sensor arrays.

Influence of lipophilic inert electrolytes on the selectivity of polymer membrane electrodes.

Lipophilic inert electrolytes, i.e., salts without ion-exchange properties, may influence the selectivity of ionophore-based liquid membrane electrodes by affecting the activity coefficients in the organic phase. It is expected by a theoretical model that the addition of a lipophilic salt renders the ion-selective electrode more selective for divalent over monovalent ions. These predictions are confirmed with Ca(2+)-responsive membranes containing the ionophores ETH 2120, ETH 1001, and ETH 129. The effect is especially pronounced with nonpolar membrane phases containing a low concentration of charged species, where up to 2 orders of magnitude selectivity improvement is observed.

Selective optical sensing of silver ions in drinking water.

A new thiocarbamate derivative is used in polymeric sensing films together with a lipophilic chromoionophore for determining Ag+ at submicromolar levels. The membrane composition has been optimized with a view to measuring concentrations of Ag+ added as a bacteriostatic agent to drinking water. The results compare well with those obtained by ICPMS.

Selectivity of polymer membrane-based ion-selective electrodes: self-consistent model describing the potentiometric response in mixed ion solutions of different charge.

Despite its well-documented limitations, the semiempirical Nicolsky-Eisenman equation is used throughout the existing analytical literature to describe the selectivity of modern polymer membrane-based ion-selective electrodes (ISEs). In this paper, a new quantitative description for the response/selectivity function based on ion-extraction equilibria at the sample/membrane interface is presented. The proposed selectivity formalism clearly illustrates the range of validity for the conventional Nicolsky-Eisenman formalism. Extended equations are derived describing the electrode response in an exact manner, particularly with respect to analyte and interfering ions of different charge. The expression obtained corresponds to the matched potential method proposed previously by Christian and co-workers on the basis of solely empirical observations. Selectivity coefficients required for a given analytical problem with a predefined maximum error can now be predicted more accurately. Such predictions with respect to analyte and interfering ions of varying charges differ by 1-2 orders of magnitude in comparison to the selectivity values required on the basis of the extended Nicolsky-Eisenman formalism.

Nitrite-selective microelectrodes.

The development of nitrite-selective liquid membrane microelectrodes based on a synthetic charged ionophore is described. The addition of potassium tetrakis(4-chlorophenyl)borate and poly(vinyl chloride) to the membrane phase is essential to lower the ohmic resistance and to prolong the lifetime of the microelectrodes. The detection limits for sodium nitrite solutions without and with an ion background of 0.1M chloride are 10(-5.1) and 10(-4.2)M, respectively. The comparison with macroelectrodes shows that the miniaturization reduces, to some extent, the selectivity and the slopes of the EMF response functions.