Voltammetric Mechanism of Multiion Detection with Thin Ionophore-Based Polymeric Membrane

Abstract

The capability to detect multianalyte ions in their mixed solution is an important advantage of voltammetry with an ionophore-based polymeric membrane against the potentiometric and optical counterparts. This advanced capability is highly attractive for the analysis of physiological ions at millimolar concentrations in biological and biomedical samples. Herein, we report on the comprehensive response mechanisms based on the voltammetric exchange and transfer of millimolar multiions at a thin polymeric membrane, where an ionophore is exhaustively depleted upon the transfer of the most favorable primary ion, IzI. With a new volt-ammetric ion-exchange mechanism, the primary ion is exchanged with the secondary favorable ion, JzJ, at more extreme potentials to transfer a net charge of |zJ|/nJ – |zI|/nI for each ionophore molecule, which forms 1:nI and 1:nJ complexes with the respective ions. Alternatively, an ion-transfer mechanism utilizes the second ionophore that independently transfers the secondary ion without ion exchange. Experimentally, a membrane is doped with a Na+- or Li+-selective ionophore to detect not only the primary ion, but also the secondary alkaline earth ion based on the ion-exchange mechanism, where both ions form 1:1 complexes with the ionophores to transfer a net charge of +1. Interestingly, the resultant peak potentials of the secondary divalent ion vary with its sample activity to yield an apparently super-Nernstian slope as predicted theoretically. By contrast, the voltammetric exchange of calcium ion (nI = 3) with lithium ion (nJ = 1) by a Ca2+-selective ionophore is thermodynamically unfavorable, thereby requiring a Li+-selective ionophore for the ion-transfer mechanism.

Voltammetric Ion Selectivity of Thin Ionophore-Based Polymeric Membranes: Kinetic Effect of Ion Hydrophilicity

“…We assume that an excess amount of an analyte or interfering ion is present in its separate aqueous solution so that the ion-transfer reaction can be treated as a first-order reaction, i.e., $$n_{\mathrm{X}}\mathrm{normalL}false(\mathrm{normalm}false)\underset{k_{\mathrm{b},\mathrm{X}}}{\overset{k_{\mathrm{f},\mathrm{X}}}{\rightleftharpoons }}{\mathrm{L}}_{n_{\mathrm{normalX}}}{\mathrm{X}}^{z_{\mathrm{normalX}}}false(\mathrm{normalm}false)$$where an ion, ${\mathrm{X}}^{z_{\mathrm{normalX}}}false(={\mathrm{I}}^{z_{\mathrm{normalI}}}{\mathrm{or J}}^{z_{\mathrm{normalj}}}false)$, forms 1: n X (= n I or n J , respectively) complexes with an ionophore, L. This model considers the kinetics of facilitated ion transfer within a wide range from reversible cases to irreversible cases, whereas only reversible cases were considered in previous models. 11,12 The rate constants for forward and reverse reactions, k f,X and k b,X , respectively, are given by the Butler-Volmer type model 8 to yield $$k_{\mathrm{f,X}}=\frac{k_{\mathrm{normalX}}^0}{L_{\mathrm{normalT}}^{n_{\mathrm{normalX}}-1}}\exp \left[\frac{-{\alpha }_{\mathrm{normalX}}{z}_{\mathrm{normalX}}F\left({\mathrm{normal\Delta }}_{\mathrm{normalw}}^{\mathrm{normalm}}\varphi -{\mathrm{normal\Delta }}_{\mathrm{normalw}}^{\mathrm{normalm}}{\varphi }_{\mathrm{normalLX}}^{0^{\prime }}\right)}{RT}\right]$$ $$k_{\mathrm{b,X}}=k_{\mathrm{X}}^0\exp \left[\frac{(1-{\alpha }_{\mathrm{normalX}})z_{\mathrm{normalX}}F\left({\mathrm{normal\Delta }}_{\mathrm{normalw}}^{\mathrm{normalm}}\varphi -{\mathrm{normal\Delta }}_{\mathrm{normalw}}^{\mathrm{normalm}}{\varphi }_{\mathrm{normalLX}}^{0^{\prime }}\right)}{RT}\right]$$where $k_{\mathrm{X}}^0$ is the standard ion-transfer rate constant, α X is transfer coefficient (≈ 0.5 as determined experimentally 8 ), L T is the total concentration of the ionophore, ${\mathrm{\Delta }}_{\mathrm{w}}^{\mathrm{m}}\varphi$ is the phase boundary potential across the membrane/water interface, and...…”

“…Noticeably, $k_{\mathrm{X}}^0$ is conditional and is dependent on the aqueous concentration of the target ion, ${false[{\mathrm{X}}^{z_{\mathrm{normalX}}}false]}_{\mathrm{w}}$, and the total concentration of the ionophore as given by (see Supporting Information) $$k_{\mathrm{X}}^0=k^0{L}_{\mathrm{T}}^{false(1-\alpha false)false(n_{\mathrm{X}}-1false)}{false[{\mathrm{X}}^{z_{\mathrm{normalX}}}false]}_{\mathrm{w}}^{false(1-\alpha false)}$$where k 0 is the concentration-independent standard rate constant. In addition, the formal potential is conditional as given by 12 $${\mathrm{\Delta }}_{\mathrm{w}}^{\mathrm{m}}{\varphi }_{\mathrm{LX}}^{0^{\prime }}={\mathrm{\Delta }}_{\mathrm{w}}^{\mathrm{m}}{\varphi }_{\mathrm{X}}^{0^{\prime }}+\frac{RT}{z_{\mathrm{X}}F}\ln {\beta }_{{\mathrm{normaln}}_{\mathrm{normalX}}}{L}_{\mathrm{T}}^{n_{\mathrm{X}}-1}{false[{\mathrm{X}}^{z_{\mathrm{normalX}}}false]}_{\mathrm{w}}$$where ${\mathrm{\Delta }}_{\mathrm{w}}^{\mathrm{m}}{\varphi }_{\mathrm{X}}^{0^{\prime }}$ is the formal potential of simple ion transfer that represents ion hydrophilicity, 14 and ${\beta }_{n_{\mathrm{normalX}}}$ is an overall formation constant for the 1: n X ion–ionophore complex in the membrane.…”

“…In thin-layer CV, the bulk concentration of any species is maintained near the interface without mass-transport effects, because the membrane is thin enough to uniformly deplete an ionophore and its complexes, 8–12 and because the aqueous phase contains an excess amount of an analyte or interfering ion. 11,12 Accordingly, the uniform membranous concentrations of an ionophore in its free and complexed forms, [L] and $false[{\mathrm{L}}_{n_{\mathrm{normalX}}}{\mathrm{X}}^{z_{\mathrm{normalX}}}false]$, respectively, as well as free ion, ${false[{\mathrm{X}}^{z_{\mathrm{normalX}}}false]}_{\mathrm{m}}$, are used to define the overall formation constant, i.e., $${\beta }_{n_{\mathrm{normalX}}}=\frac{false[{\mathrm{L}}_{n_{\mathrm{normalX}}}{\mathrm{X}}^{z_{\mathrm{normalX}}}false]}{{false[\mathrm{normalL}false]}^{n_{\mathrm{normalX}}}{false[{\mathrm{X}}^{z_{\mathrm{normalX}}}false]}_{\mathrm{m}}}$$Similarly, the mass balance of the ionophore in the thin membrane is given by using the uniform membranous concentrations as $${\mathrm{L}}_{\mathrm{T}}=false[\mathrm{normalL}false]+n_{\mathrm{X}}false[{\mathrm{L}}_{n_{\mathrm{normalX}}}{\mathrm{I}}^{z_{\mathrm{normalX}}}false]$$The membrane composition depends on the phase boundary potential across the membrane/water interface, which is externally controlled to drive the interfacial transfer of a target ion.…”

“…11,12 Accordingly, the uniform membranous concentrations of an ionophore in its free and complexed forms, [L] and $false[{\mathrm{L}}_{n_{\mathrm{normalX}}}{\mathrm{X}}^{z_{\mathrm{normalX}}}false]$, respectively, as well as free ion, ${false[{\mathrm{X}}^{z_{\mathrm{normalX}}}false]}_{\mathrm{m}}$, are used to define the overall formation constant, i.e., $${\beta }_{n_{\mathrm{normalX}}}=\frac{false[{\mathrm{L}}_{n_{\mathrm{normalX}}}{\mathrm{X}}^{z_{\mathrm{normalX}}}false]}{{false[\mathrm{normalL}false]}^{n_{\mathrm{normalX}}}{false[{\mathrm{X}}^{z_{\mathrm{normalX}}}false]}_{\mathrm{m}}}$$Similarly, the mass balance of the ionophore in the thin membrane is given by using the uniform membranous concentrations as $${\mathrm{L}}_{\mathrm{T}}=false[\mathrm{normalL}false]+n_{\mathrm{X}}false[{\mathrm{L}}_{n_{\mathrm{normalX}}}{\mathrm{I}}^{z_{\mathrm{normalX}}}false]$$The membrane composition depends on the phase boundary potential across the membrane/water interface, which is externally controlled to drive the interfacial transfer of a target ion. The resultant current response, i , is given by $$\frac{i}{z_{\mathrm{X}}FA}=k_{\mathrm{normalf},\mathrm{normalX}}{false[\mathrm{normalL}false]}^{n_{\mathrm{normalX}}}-k_{\mathrm{normalb},\mathrm{normalX}}false[{\mathrm{L}}_{n_{\mathrm{normalX}}}{\mathrm{X}}^{z_{\mathrm{normalX}}}false]$$where A is the area of the membrane phase.…”

“…8 Advantageously, cyclic voltammetry (CV) enabled us to quantitatively and separately assess the thermodynamics and kinetics of ionophore-facilitated ion transfer across the membrane/sample interface, where mass transport can be simulated 8–10 or neglected. 11,12 Specifically, we obtained kinetically limited CVs of silver, potassium, calcium, and lead ions with the corresponding ionophores to determine standard rate constants of 9.0 × 10 −3 –9.7 × 10 −4 .cm/s. 8 Importantly, these rate constants support the electrochemical mechanism 13 based on ion–ionophore complexation at the membrane/sample interface, which excludes the alternative electrochemical–chemical mechanism based on simple ion transfer 14 followed by ion–ionophore complexation in the bulk membrane.…”