Voltammetric Characterization of Ion–Ionophore Complexation Using Thin Polymeric Membranes: Asymmetric Thin-Layer Responses

Abstract

Selective ion-ionophore complexation in a polymeric membrane is crucial to various sensing applications. In this work, we report on a novel voltammetric approach based on a thin polymeric membrane to determine the stoichiometry and overall formation constant of an ion-ionophore complex. With this approach, a ∼1.6 μm thick ionophore-doped membrane contacts an aqueous solution containing an excess amount of a target ion to facilitate voltammetric ion transfer across the membrane/water interface. Advantageously, the resultant thin-layer voltammogram shows no diffusional effect, which simplifies the theoretical modeling and quantitative analysis of the voltammogram. We predict theoretically that the complexation stoichiometry affects not only the peak current and peak potential of the thin-layer voltammogram, but also the symmetry of the peak shape with respect to the peak potential. Experimentally, a symmetric voltammogram ensures the formation of a 1:1 complex for a Na(+)-selective ionophore. By contrast, the asymmetric shape and peak current of voltammograms are used to demonstrate that a Ca(2+)-selective ionophore forms 1:3 and 1:2 complexes with calcium and magnesium ions, respectively. The complexation stoichiometry is needed to yield the formation constants that are consistent with those determined previously by potentiometry. In addition, both 1:2 and 1:1 complexes are voltammetrically observed with another Na(+)-selective ionophore, which was assumed to form only a 1:2 complex in previous potentiometric studies. The formation constants of both complexes are determined from a single voltammogram to reveal that the preceding formation of a 1:2 complex thermodynamically hampers the voltammetric observation of a 1:1 complex.

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

“…11 Specifically, the forward (or reverse) peak of a kinetically controlled CV with n I = 1 is broader at the positive (or negative) side of the peak potential. This asymmetry contrasts to the asymmetric forward (or reverse) peak of a reversible voltammogram with n I = 2 or greater, which is broader at the negative (or positive) side of the peak potential.…”

“…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...…”

“…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.…”

“…This asymmetry contrasts to the asymmetric forward (or reverse) peak of a reversible voltammogram with n I = 2 or greater, which is broader at the negative (or positive) side of the peak potential. 11 …”

“…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.…”