Determination of the free metal ion concentration using AGNES implemented with environmentally-friendly bismuth film electrodes

Ex-situ plated Bi film electrodes (Bi-FE) have been employed, for the first time, to measure the free concentration of Pb(II) in aqueous solutions using AGNES (Absence of Gradients and Nernstian Equilibrium Stripping) with Stripping Chronopotentiometry (SCP) quantification. The amount of deposited Pbo, below a certain threshold, follows a Nernstian relationship with the applied potential. This threshold can be interpreted as the frontier of transition from surface deposition to solid (bulk) formation of Pbo. AGNES with Bi-FE yielded a very good detection limit (3σ) for Pb(II) of 6.0×10-9 M with an applied gain of 398 and a deposition time of 400 s. The ability of the Bi film electrode to perform speciation measurements was demonstrated for Pb(II)–PSS and Pb(II)–IDA systems. The measured values with the Bi-FE were in good agreement with the values obtained using the Hg film electrode and/or the values reported in the literature.


INTRODUCTION
The knowledge of the free ion concentration is fundamental to predict the bio-uptake of trace metals in natural aquatic systems 1;2

. A limited number of analytical techniques
including Donnan Membrane Tecnique (DMT) 3;4 , Complexing Gel Integrated MicroElectrode 5 (CGIME), Permeation Liquid Membrane (PLM) 6;7 or Potentiometry with Ion Selective Electrodes (ISE) 8 can be employed for the determination of the free metal ion concentrations in natural systems. However, ISE generally suffers from lack of sensitivity and the interference from other metal ions, and the commercial Pb-ISE requires total Pb(II) above micromolar 9 .
In the last decade, Absence of Gradients and Nernstian Equilibrium Stripping (AGNES) has been specifically designed 10 and developed to determine the free metal ion concentration in aquatic systems [11][12][13][14] , overcoming some of the limitations of the former methods. This electroanalytical method consists of two conceptual stages: the deposition and stripping stages. Along the first stage, the metal ion in solution M 2+ is reduced to M 0 , until a situation of Nernstian equilibrium with absence of gradients in the concentration profiles is attained. The aim of the second stage 10 , quantification of the accumulated Mº, can be achieved via different strategies leading to different variants 15 . In this work, Stripping Chronopotentiometry (SCP), which allows the discrimination of interferences and avoids blank measurements, is selected as the second stage of AGNES. A constant oxidizing stripping current is applied until full depletion 16 .
While these small-volume Hg electrodes offer an attractive performance in the stripping analysis of trace metal ions, alternative electrode materials, with a similar performance, are urgently needed for addressing growing concerns regarding the toxicity, volatility and disposal of this element. Bismuth is one of the materials that shows attractive electrochemical features and Bi film electrodes (Bi-FE) have been extensively used in the stripping analysis of trace metals [23][24][25][26] . Recently, the bismuth film electrode was successfully used for speciation analysis of trace metals by stripping chronopotentiometry (SCP) 27;28 . With the growing demand for on-site analysis, the use of non-toxic Bi-FE can represent a step ahead in going from laboratory to field studies.
The aim of the present work is to describe the implementation of AGNES with Bi-FE electrodes. To achieve this goal, the specific characteristics of ex-situ Bi-FE and the required experimental conditions of AGNES technique in the determination of the free concentration of lead(II) will be explored. The metal speciation capability of AGNES-SCP will be tested with polystyrene sulfonate (PSS) (labile system) and iminodiacetate (IDA) (non-labile system). The results will be compared with the data obtained using Hg film electrodes and with the existing theory for quantitative interpretation of SSCP curves.

Reagents
The chemicals used in the present work were of analytical reagent grade and used asreceived, unless stated otherwise. All solutions were prepared with ultra-pure water (18.3 MΩ cm, Milli-Q systems, Millipore-waters). Nitric acid 65% (suprapur) and the standard stock solutions of mercury nitrate (1001±2 mg L −1 ) and lead nitrate (999±2 mg L −1 ) were purchased from Merck. Pb(II) solutions were prepared from dilution of the certified standard. Sodium nitrate electrolyte solution (0.01M) and MES (2-(N-morpholino) World Precision Instruments, DRIREF-5 (electrolyte leakage < 8 x 10 -4 µL/h). A Denver Instrument (model 15) and a Radiometer analytical combination pH electrode, calibrated with Titrisol buffers (Merck), were used to measure pH.

Preparation of the glassy carbon substrate
Prior to deposition of the Bi films, the GC electrode was conditioned following a previously reported polishing/cleaning procedure 31 . In brief, the electrode was polished with alumina slurry (grain size 0.3 µm, Metrohm) and sonicated in pure water for 60 s, to obtain a renewed surface. Then, an electrochemical pre-treatment was carried out using 50 cyclic voltammetric scans between -0.800 and +0.800 V at 0.1 V s -1 , in NH4CH3COO (1M)/HCl(0.5 M) solution. The area of the glassy carbon electrode (geometrical value of 3.14 mm 2 ) was measured by chronoamperometry in 1.124×10 -3 M ferricyanide/1.0 M KCl solution (purged with N2 for 300 s). Before the chronoamperometric measurements, the solution was stirred for 30 s (2000 rpm) followed by a resting period of 120 s. The chronoamperometric parameters used were: E= 0.500 V and t= 3s. The electrochemically active area of the GC electrode was calculated from the slope of I vs t -1/2 Cottrell equation (diffusion coefficient of ferricyanide D = 7.63 × 10 −10 m 2 s −1 ) and the value obtained was 3.334±0.062 mm 2 (two polishing experiments, each with four replicate determinations).
When not in use, the bare GC electrode was stored dry in a clean atmosphere.

Preparation of the Bismuth film electrode
The ex-situ Bi film was prepared adopting the procedure described by Kong et al. 32 , by electrodeposition at -0.300 V for 120s at a rotation speed of 1000 rpm and using a solution containing both 8×10 -4 M of Bi 3+ and 8×10 -4 M of Sn 2+ prepared in KCl (1M) and HCl (0.13 M) media (pH ca. 0.74). According to those authors, Sn(II) ions in the electrolyte block the migration of Bi(III) ions during the deposition, whilst Sn(II) ions cannot be deposited at the applied potential (-0.3V, which was more negative than EBi(III)/Bi, but more positive than ESn(II)/Sn). As a result, the bismuth film obtained showed a compact crystal layer, a high coverage ratio and tightly and homogeneously distributed Bi deposits on the GC surface. The charge associated with the deposited Bi

AGNES measurements: optimization studies
Measurements were carried out in 20 mL of 0.01 and 0.1M NaNO3 solutions containing Pb(II) concentrations close to 10 -7 M at room temperature (21-23 ºC). All solutions were purged for 15 min with N2 at the beginning of every experiment and for 20 s (with mechanical stirring of the rotating disk electrode, RDE) after each measurement. The free metal ion concentration was determined with the variant AGNES-SCP 16 . In stage 1, at a fixed deposition potential E1, mass transfer was enhanced by rotation of the RDE at 1000 rpm. In stage 2, a stripping oxidising current Is of 0.5μA was applied until the potential reached -0.300 V.
Prior to each AGNES-SCP experiment, the peak potential (Epeak,DPV) value of lead(II) in the solution used in the experiments was determined by differential pulse voltammetry (DPV). The deposition step lasted 30 s at -0.200 V, while the solution was stirred, followed by a resting period of 5 s. The stripping step was initiated at -0.320 V and ended at -0.70 V; the DPV parameters used were: amplitude 0.025 mV and step potential 0.002 V.

Theoretical framework for the application of AGNES with solid electrodes
A key requirement for AGNES is the attainment of Nernstian equilibrium by the end of the first stage (i.e. after a sufficiently long deposition time t1). For a deposition potential E1, equilibrium means: where E 0 is the standard electrode potential, R the gas constant, T the temperatue, n the number of exchanged electrons, F the Faraday constant and curly brackets indicate activity of the enclosed species (M n+ for the analyte; M 0 for its reduced couple).
In mercury electrodes (the only ones reported up now for AGNES since its introduction in 2004), an amalgamating element (Zn, Cd, Pb) is accumulated until equilibrium. Nernst law prescribes the eventual relationship between the activities of the free metal ion in solution and of the reduced metal in the amalgam (see eqn. (1)). So, by changing the deposition potential, one changes the ratio between activities (which, for analytical purposes, is converted into a ratio of concentrations called pre-concentration factor or gain, Y) 10 .
If one uses a solid electrode and Mº deposits on it as a bulk solid phase, its activity is always unity, regardless how much metal has been deposited. So, one would switch from no deposition at all, for more positive potentials, to unlimited deposition (never reaching of equilibrium) for more negative potentials 33 , which could be labelled "runaway deposition". Thus, bulk solid deposition, the normal process on solid electrodes, seems not compatible with AGNES.
However, the possibility of a varying activity of Mº with solid electrodes is known in electrochemisty: the activity is related to the coverage of adsorbed atoms on the solid surface (e.g. below the complete formation of a monolayer): For this kind of system, assuming 0 M 1 γ = , Nernst law is often re-casted as 34 : So, we define the gain as where cº is the standard state concentration of 1 mol L -1 (a subscript θ could be added to Y as a reminder of the coverage implication, but for the sake of simplicity in this work this subscript is spared).
The aim of the second stage is quantification of the amount of Mº once equilibrium is attained. In the variant that uses stripping chronopotentiometry (SCP) in the second stage, the time for complete depletion (transition time, τ) can be determined from the evolution of the recorded potential in response to the imposed stripping current Is 21 . The faradaic charge (Q) can be rigorously computed 16 as: where Iox is the current due to other oxidants. Depending on the Is value applied, the contribution from the current due to the presence of other oxidants (IOx) can be negligible when compared with the stripping current (Is >>IOx) and the charge Q (rigorously computed with eqn. (6)) can be simplified to: Under the experimental conditions used to perform AGNES measurements at Bi film electrodes, i.e., for the IS values of 0.5 and 1 μA, the charge Q was determined using eqn.
(7) (for further details see section S1 of the supporting information).
On the other hand, with Faraday law, this charge can be computed from the number of adsorbed moles that are converted from Mº to M n+ in the stripping stage, so: where A is the active area for adsorption.
By gathering the terms inside the brackets, the direct proportionality between the analytical signal and the free concentration of analyte is evidenced: where ηθ is a proportionality factor characteristic of the number of exchanged electrons and an extensive property of the solid electrode (parallel to the previously used ηQ which was characteristic of the volume of mercury electrodes) 15;35 . The product Yηθ can be experimentally found from a calibration.
The gain can be controlled through the applied potential (E1), whose value could be computed using a rigorous expression in terms of Eº (just by re-arrangement of eqn. (4)).
In practice, the experimental determination of an accurate value of E 0 might be involved, so, in this work, we just use the potential peak of a Differential Pulse Voltammogram as a reference potential for the computation of the gain. Fortunately, the offset (between the exact gain and its surrogate) that might appear in the calibration completely cancels out with the offset in the measurement, so that a perfect knowledge of the gain is not essential for analytical purposes (i.e. AGNES quantification essentially relies in a calibrated proportionality between Q and free concentration, see eqn. (9)). Thus, here, we operationally report the gains with the expression: This means that the strength of the adsorption is controlled by the applied potential (E1).

Implementation of AGNES-SCP with Bi film electrode
The following preliminary studies were performed: i) the effect of the deposition potential E1 and the deposition time t1 required to reach AGNES conditions and ii) the stability of the electrode along several consecutive AGNES measurements.

Trajectories Q vs t1 at different E1
In this section it is demonstrated that Nernstian equilibrium is effectively reached for certain deposition potentials E1 for sufficiently long deposition times t1. Figure 1 shows   35 . This kind of limitations can be overcome by using lower gains.

Stability of Bi film electrodes
The stability and repeatability of Bi film electrode prepared following Kong et al. 32 was assessed by performing several consecutive AGNES measurements ( Figure 2). There was a slight increase in the response charge (ca. 14%) along the 40 consecutive measurements, the same tendency already reported previously by Rocha et al. 27 , when using the ex-situ plated Bi film electrode to measure Pb(II) by SCP. Nevertheless the overall relative standard deviation was just 7.5% (2σ), showing that this electrode can be used along a considerable set of measurements, with no relevant change in the active surface area. presents the calibration data: slope and correlation coefficient and the limit of detection (LOD). The measured charge increases linearly with the free concentration of Pb(II), however the interval of linearity is highly dependent on the deposition potential E1, i.e.

Calibrations of Pb(II) with Bi film electrodes
on the gain Y applied. For some deposition potential E1, there is a deviation from the linearity resulting from "runaway deposition" whose detailed analysis will be provided in according to eqn. (9) and (10)) of AGNES signals. This Nernstian behaviour is also confirmed by the linearity of the plots Q vs. Y (see Fig S3 in the supporting information).

A theoretical interpretation of the results
According to Herzog and Arrigan 36  Results in this work can be tentatively interpreted assuming a key role to adsorption of Pbº modulated by the applied deposition potential: (11) The conditional equilibrium constant K cond , which depends on the applied potential, Pb which is just a Langmuirian isotherm. This reverts to the linear (Henry) isotherm for sufficiently low coverages: Comparison with equation (5), allows numerically identifying Y with K cond .  Region B: There is adsorptive deposition under the Henry regime, so linearity holds (dark grey background). This is confirmed once more by the value of (6.11±0.48)×10 3 C M -1 obtained for the average ηθ (in agreement with the value mentioned in section 4.2). We can work with AGNES as usual (i.e. exploiting eqn. (9)). But, if we overcome the coverage threshold (corresponding to entering into region A), then multi-layer deposition starts to occur (runaway deposition) and equilibrium is no longer attained.
Region C: For very low gains (pale grey zone), the deposition potential is less negative and it is not able to trigger bulk deposition, so the linear regime extends beyond the threshold (Q<0.6 µC in this experiment) because of UPD. AGNES can be applied as usual, although some bending (e.g. following Langmuir isotherm) is expected (but, so far, not seen) when saturation of the electrode surface was approached. the window of linearity varies from the LOD of 6 nM to that value. When lower gains are applied, the upper limit of linearity increases, but because higher detection limits are attained, the lower limit of linearity also increases. For example for Y= 185 the workable concentration range will be between 11 and 600 nM. For very low gains, such as Y=51, bulk deposition was not observed (in the probed concentration range) and in this case, just the lower limit of linearity is affected, corresponding to the LOD of 34 nM.

Speciation results
The knowledge of the free metal concentration in equilibrium in a system containing complex species leads to the computation of the stability constant via:  Table 2). The Hg film electrode (thickness of 28 nm) was prepared following the procedure described by Rocha el al. 30

Pb(II)-IDA system
The experiments with Pb(II) in the presence of IDA were conducted at pH 6 and in 0.1 M NaNO3 media. The deposition potentials E1 and the time t1 needed to attain AGNES conditions were optimized (see section S4 of the supporting information). The measurements were performed using two different deposition potentials E1: -0.520 V for t1 of 210 and 240s and -0.525 V for t1 of 240s and 300 s. Table 3 shows the values of the stability constant K' and free concentration of lead(II) obtained by AGNES-SCP at Bi film electrodes.