LIGAND SIZE POLYDISPERSITY EFFECT ON SSCP SIGNAL INTERPRETATION

Electrochimica Acta 166 (2015) 395–402

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Electrochimica Acta journal homepage: www.elsevier.com/locate/electacta

LIGAND SIZE POLYDISPERSITY EFFECT ON SSCP SIGNAL INTERPRETATION Luciana S. Rocha a, * , Wander G. Botero b , Nuno G. Alves c , José A. Moreira c, Ana M. Rosa da Costa c , José Paulo Pinheiro a a b c

IBB/CBME, DQF/FCT, University of Algarve, 8005-139 Faro, Portugal Federal University of Alagoas (UFAL), Arapiraca-AL, Brazil CIQA, DQF/FCT, University of Algarve, 8005-139 Faro, Portugal

A R T I C L E I N F O

A B S T R A C T

Article history: Received 23 September 2014 Received in revised form 5 March 2015 Accepted 6 March 2015 Available online 10 March 2015

The present study aims to establish unambiguously the conditions required for the validity of the average

Keywords: SSCP Size polydispersity Cadmium Lead Diffusion coefficients

diffusion (D) approximation in fully labile systems with significant ligand size polydispersity. The average diffusion coefficient is a key parameter in mass transfer that affects signal interpretation in dynamic electroanalytical techniques. To achieve this goal, the binding of Cd(II) and Pb(II) to binary and ternary mixtures containing chemically homogenous (PSS)n-COOH polymers (ligand excess conditions were required) of different sizes (4, 10 and 30 KDa) was evaluated. It was experimentally evidenced that the average diffusion coefficient (D), can indeed be computed as the weighted average of several metal-polymer complexes of diverse sizes. ã 2015 Elsevier Ltd. All rights reserved.

1. INTRODUCTION Trace metal speciation in environmental systems is an involved problem composed of many parameters varying in space and time. The most relevant fraction regarding metal bioavailability, the free hydrated cation, is a small portion of the total dissolved metal, since the metal ions form stable complexes with a variety of dissolved inorganic and organic ligands, adsorbs onto colloids and suspended matter and interacts with the living organisms. Furthermore the natural ligands, especially the natural organic matter and the microorganisms, present a polyfunctional, polyelectrolytic and polydisperse character and, thus, have a broad range of free energies of complex formation, association/ dissociation rate constants and molecular dimensions.Therefore understanding the physico-chemical processes controlling trace metal speciation is essential for predicting the metal ion transport, bioavailability and ecotoxicity in environmental systems [1]. A fundamental aspect that arises from the system not being in chemical equilibrium is that a correct interpretation of the fate and environmental impact of metal complexes, must consider the importance of the reactivity and fluxes of the metal compounds and the relative time scales of these processes [2].

* Corresponding author. Tel. : +351 289 800 900. E-mail address: [email protected] (L.S. Rocha). http://dx.doi.org/10.1016/j.electacta.2015.03.035 0013-4686/ ã 2015 Elsevier Ltd. All rights reserved.

The last decade saw a great evolution in the understanding of the chemodynamics of trace metal ions [3–5] stimulated by the development of new electroanalytical stripping techniques, like Scanned Stripping Chronopotentiometry (SSCP). SSCP is capable of a very low detection limit (<10 nM), does not suffer from organic matter adsorption interferences [6], is capable of obtaining directly kinetic parameters [6–8] and information on the chemical heterogeneity of the sample can be obtained from the signal slope [9,10]. Especially interesting is the coupling of SSCP with AGNES (Absence of Gradients and Nernstian Equilibrium Stripping) [11]. The latter yields directly the free metal concentration in solution at very low concentrations [12], using the same experimental set-up as SSCP. Therefore the consecutive use of AGNES and SSCP in the same sample delivers the free metal ion concentration, the labile metal fraction, and information on both the heterogeneity and dynamic behavior of the metal complexes) [11]. It is thus timely to take dynamic trace metal speciation and bioavailability to the field to fully realize the potential of the new techniques and theoretical models in environmental studies. Nonetheless dynamic studies of mixtures of metals in presence of various ligand types are still scarce and as a result, the interpretation of the experimental signals is still difficult, if not impossible in real environmental systems. One of the major obstacles coming from the laboratory to the field is that the knowledge of size polydispersity effect on the dynamic

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techniques signal is insufficient, since most studies refered have been performed in the laboratory with single ligands or with purified humic matter [13]. For electrochemical techniques understanding the mass transport from the bulk to the electrode surface is fundamental in the interpretation of the signal. For the case where the complex species are larger than the free metal ion the general approach, originally proposed by Cleven and Van Leeuwen in the study of metal interaction with humic acids [14,15], is to consider a weighted average of the diffusion of free and complexed metal named average diffusion coefficient, D. Later it was demonstrated that this aproach can be used in quasi-labile systems to compute the labile fraction using the Koutecky–Koryta approximation [16]. In mixtures containing heterogeneous ligands the computation of the average diffusion coefficient becomes more involved since the ratio of complexed metal to free metal increases in the diffusion layer with proximity to the electrode surface. The diffusing species are then decelerated because the diffusion coefficient of the macromolecular complex is lower than that of the metal ion, and so the total amount of reduced metal is decreased compared with that obtained in a homogeneous system with the same bulk speciation [17]. For fully labile cases [18] presented an approximated expression to the voltammetric limiting current of metal ion in presence of an heterogeneous macromolecular ligand, based on a polynomial expansion of the limiting current in terms of the fraction of the bound metal concentration in the bulk solution. Later [19] used that expression to study the complexation of Cd, Pb, and Cu by fulvic acids showing that voltammetric techniques can be applied to the studies of heterogeneous complex systems. These expressions do not take into account the size polydispersity of the ligands, even in cases where that is the reality in solution. For example for the humic matter the usual approach is to take a single value of DML, although it is well established that in reality there is a relatively broad size distribution in solution [20]. Since the key question to progress from the laboratory to the field is to assess if sample fractionation will be necessary to correctly interpret the sensor data, the first step is to establish unambiguously the validity of the average diffusion coefficient approximation. To achieve this goal in this work we will investigate the binding of Cd(II) and Pb(II) in binary and ternary mixtures of chemically homogenous polymers of different sizes. Due to the small choice of chemically homogeneous polymers we chose to synthesize polystyrene sulfonate (PSS) with three different molecular weights (4, 10 and 30 KDa). The behavior of highly charged polyelectrolytes in solution is involved, thus to keep the analysis as simples as possible it was decided to work in an intermediate ionic strenght of 10 mM in sodium nitrate medium at pH 4.0, which is low enough to dispense a buffer in electrochemical solutions but high enough to guarantee a significant degree of deprotonation of the polyelectrolyte (pKa = 1) [21]. 2. MATERIALS and METHODS 2.1. Reagents The chemicals used in the present work were of analytical reagent grade and used as-received, unless stated otherwise. All solutions were prepared with ultra-pure water (18.3 MV cm, MilliQ systems, Millipore-waters). The nitric acid 65% (suprapur) and the standard stock solutions of mercury nitrate (1001
2 mg L1), cadmium nitrate (999
2 mg L1) and lead nitrate (999
2 mg L1) were purchased from Merck. Cd(II) and Pb(II) solutions were

prepared from dilution of the certified standard. Sodium nitrate electrolyte solution (0.01 M) and MES (2-(N-morpholino)ethanesulfonic acid) buffer (0.2 M) were prepared from the solids (Merck, suprapur and Merck >99%, respectively). Solutions prepared from nitric acid (Merck, suprapur) and sodium hydroxide (0.1 M standard, Merck) were used to adjust the pH. Potassium thiocyanide, hydrochloric acid, potassium chloride were all p.a. from Merck and were used to prepare the solution for the re-dissolution of the mercury film. Potassium ferricyanide (Merck p.a.) was used to prepare a standard solution (1.029  103 M) in 1.0 M potassium chloride for determination of the carbon electrode area. Solutions of ammonium acetate (NH4CH3COO (1.0 M)/ CH3COOH (1.0 M)) (Merck) were prepared monthly and used without further purification. Sodium styrenesulfonate, S-(Thiobenzoyl)-thioglycolic acid, 4,40 -Azobis(4-cyanovaleric acid) and toluene were purchase from Sigma-Aldrich and methanol from Panreac, and they were used in the synthesis of poly(styrenesulfonate) of different sizes (4000, 10000 and 30000 Da). KBr for FTIR analysis was Sigma FTIR-grade. 2.2. Synthesis of monodisperse charged (PSS)n–COOH polymers with different sizes Samples of poly(styrenesulfonate) with 4, 10, and 30 kDa were obtained by reversible addition-fragmentation chain transfer (RAFT) polymerization of sodium styrenesulfonate in a water/ ethanol solution, using S-(Thiobenzoyl)-thioglycolic acid as chain transfer agent (CTA) and 4,40 -Azobis(4-cyanovaleric acid) as radical initiator [22]. Sodium styrenesulfonate was dried under vacuum, at 40  C, for 24 h. S-(Thiobenzoyl)-thioglycolic acid was recrystallized from toluene and dried, at 60  C, under vacuum, for 24 h. 4, 40 -Azobis(4-cyanovaleric acid) was recrystallized from methanol and dried under vacuum at room temperature, for 24 h. For the polymerization reactions and dialysis, distilled water was used. The latter procedure was carried in dialysis tubing (Sigma) with pore size of 2000 Da. In order to obtain the three desired polymer sizes, 4, 10, and 30 kDa monomers, the following CTA ratios were used: 20, 50, and 150, respectively. The radical initiator was 1 mol% of the monomer. Sodium styrenesulfonate (4 g) was dissolved under stirring conditions in 17 mL of water in a previously degased Schlenk flask, and a solution of the CTA and the radical initiator in 7 mL of ethanol was added. After three freeze-pump-thaw cycles, the Shlenk was filled with nitrogen, topped with a bubbler, and incubated in an oil bath at 70  C, under stirring, for 24 h (10 and 30 KDa) or 72 h (4 KDa). After cooling down to room temperature, the flask content was poured into a mixture of methanol/acetone (1:1, v/v). A light-pink solid was obtained by precipitation. After centrifugation for 30 minutes, at 10000 rpm, the supernatant was discarded and the solid was re-dissolved in water and the precipitation process repeated twice. The polymer was further purified by dialysis against distilled water for 24 h, with the water being replaced every 12 h. Water was removed by lyophilization affording 82%, 93% and 96% of conversion for 4 kDa, 10 kDa and 30 kDa polymers, respectively. 2.3. Characterization of monodisperse charged (PSS)n–COOH polymers The (PSS)n–COOH polymers of 4, 10 and 30 KDa were characterized by Fourier transform infrared (FT-IR) and 1H NMR spectra (for further information see section S1 of the supporting material). The infrared absorption spectra were recorded in a Bruker Tensor 27 spectrophotometer and using KBr pellets and the spectral range varied from 4000–400 cm1. The following bands

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were identified: 3065 [n (C—Har)], 2923 [nas (>CH2)], 2850 [ns (>CH2) + n (>CH—)], 1618, 1495 [n (C¼Car)], 1451 [d (>CH2)], 1186 [n (S¼O)] cm1. Regarding the 1H NMR (D2O), the spectra was acquired in a 500 MHz Varian Inova 500 spectrophotometer and the peaks identified were: 1H NMR (D2O) d 0.896–2.302 (broad signal, —CH2— and —CHPh—), 6.111–7.151 (broad signal, m-CHar), 7.255–7.797 (broad signal, o-CHar). 2.4. Electrochemical apparatus An Ecochemie Autolab PGSTAT10 potentiostat (controlled by GPES 4.9 software from EcoChemie, the Netherlands) was used in conjunction with a Methrohm 663 VA stand (Methrohm, Switzerland). A three electrode configuration was used comprising a Hg thin film plated onto a rotating glassy carbon (GC) disk (2 mm diameter, Metrohm) as the working electrode, a GC rod counter electrode, an Ag/AgCl reference electrode from World Precision Instruments DRIREF-5 (electrolyte leakage <8  104 mL/hr). A Denver Instrument (model 15) and a Radiometer analytical combination pH electrode, calibrated with Titrisol buffers (Merck) where used to measure pH. 2.5. Preparation of the glassy carbon substrate Prior to deposition of the Hg films, the GC electrode was conditioned following a previously reported polishing/cleaning procedure [23]. In brief, the electrode was polished with alumina slurry (grain size 0.3 mm, Metrohm) and sonicated in pure water for 60 s, to obtain a renewed surface. Then, an electrochemical pre-treatment was carried out using a 50 cyclic voltammetric scan between 0.8 and +0.8 V at 0.1 V s1, in NH4CH3COO (1 M)/HCl (0.5 M) solution. The geometrical area of the GC electrode is 3.14 mm2. The surface area of the glassy carbon electrode was measured by chronoamperometry in 1.124  103 M ferricyanide/ 1.0 M KCl solution (purged for 300 s). Before the chronoamperometric measurements, the solution was stirred for 30 s (2000 rpm) and followed by a resting period of 120 s. The chronoamperometric parameters used were: E = 0.5 V and t = 3 s and the measured response was the current I as a function of time t. The electrochemically active area of the glassy carbon electrode was calculated from the slope of I vs t1/2 Cottrell equation (diffusion coefficient of ferricyanide D = 7.63  1010 m2 s1). The electrochemically active area obtained was 3.334
0.062 mm2 (two polishing experiments, each with four replicate determinations). When not in use, the bare GC electrode was stored dry in a clean atmosphere. 2.6. Preparation of the Hg electrode The thin Hg film was prepared ex-situ in 0.12 mM Hg(II) nitrate in nitric acid 0.73 mM (pH 1.9) by electrodeposition at 1.3 V for 700 s at a rotation rate of 1000 rpm. The charge associated with the deposited Hg (QHg) was calculated by electronic integration of the linear sweep stripping peak of Hg, for v = 0.005 V s1. The electrolyte solution was ammonium thiocyanate 5 mM (pH 3.4). The stripping step began at 0.15 V and ended at +0.4 V [24].

2.7. SSCP and AGNES-SCP measurements Stripping chronopotentiometric measurements were carried out in 20 mL 0.01 M NaNO3 solutions containing a concentration of O(107 M) of the following individual metals: Cd(II) and Pb(II). The experimental conditions used were: deposition time (td) 45 s,

397

stripping current (Is) 2106 A, applied until the potential reached 0.30 V, rotation speed 1000 rpm. All solutions were purged for 15 min at the beginning of every experiment and for 20 s (assisted by mechanical stirring of the rotating electrode) after each SCP measurement. Measurements were made for a range of deposition potentials, from the foot to the plateau of the SSCP wave, i.e. from 0.85 to 0.60 V for Cd(II) and from 0.70 to 0.40 V for Pb(II). The free metal ion concentration was determined by AGNES-SCP according with the procedure developed by Parat et al. (2011) [25]. The measurements were performed applying a deposition potential E1 of 0.655 V (for Cd) and 0.460 V (for Pb) for a period of time t1 ranging between 180 and 210 s. The stripping step was performed by SCP using a stripping current Is of 2  106 A, applied until the potential reached 0.30 V. The rotation speed used for the RDE was 1000 rpm. All measurements were carried out at room temperature (21–23  C).

3. THEORY The theoretical basis for stripping chronopotentiometry (SCP) and its use in scanned deposition potential mode (SSCP) are well established [26]. The principles and key equations relevant for the present work are briefly recalled here. i) General equations for metal only case SSCP For a given potential, the deposition current, Id (A), originating from reduction of the metal ion of interest is given by: Id ¼

nFADM ðcM  c0M Þ

dM

where cM is the metal concentration in the bulk solution (mol m

(1) 3

),

c0M is the metal at the solution side of the electrode surface (mol m3), A is the electrode surface area, DM is the diffusion coefficient of the metal ion (m2 s1) and dM is the Nernst diffusion layer thickness (m). For the rotating disk electrode (RDE) the thickness of the diffusion layer is expressed by [27]:

dM ¼ 1:61DM 1=3 v1=2 y1=6

(2)

1

where v (rad s ) is the angular speed rotation for the RDE (v=2pvrot, where vrot is the speed of rotation) and y the kinematic viscosity (m2 s1). The general equation that describes the relation between the transition time t in the complete depletion regime and Ed is given by [26]:
  I t d td t ¼ d 1  exp  (3) Is td where Is (A) is the applied stripping current, td (s) is the chosen deposition time, and t d (s) is the characteristic time constant for the deposition process, which for a Hg drop or film electrode is defined by:

td ¼

V Hg d ADM u

(4)

where u is the free metal surface concentration ratio for a given deposition potential Ed ðu ¼ c0M =c0M0 ¼ expðnFðEd  E0 Þ=RTÞÞ and

VHg (m3) is the volume of the mercury electrode. The limiting value of the deposition current, Id (A), obtained at potentials that are sufficiently negative so that the concentration of metal ion at the electrode surface approaches zero (c0M ! 0) and the limiting transition time (t *) becomes:

t  ¼ Id td =Is

(5)

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ii) General equation for metal ions in the presence of single ligands Let us consider the case of an electroactive metal ion (M) that forms a labile 1:1 complex (ML) with a ligand (L):

Ka M+L

ML (6)

Kd

nē M0

where ka and kd are the association and dissociation rate constants, respectively. The system is dynamic at bulk level if the rates for the volume reactions are fast on the experimental time scale, t: 0

kd t; ka t >> 1

(7)

0

where ka ¼ ka cL;t . For labile complexes, the rates of dissociation/ association are sufficiently high relative to the experimental timescale, in order to maintain full equilibrium between complexed and free metal [26]. Under conditions of sufficiently excess 0 of ligand (as typically used in stripping experiments) ka is 0

approximately constant and we can define K 0 ¼ k0a ¼ KcL;t , where k

K represents the stability constant of ML and

cL;t

d

represents the

total ligand concentration in the bulk solution (mol m3). Thus we can write:

u¼

c

0

M;t =c M0 1 þ K0

(8)

(9)

1=3

v1=2 y1=6

(10)

Thus, the former Eqs. (1) and (4) can be re-written according to: nFADcM;t

d VHgd

ADð1 þ K 0 Þu

(11)

(12)

The equation for the SSCP wave for a fully labile complex ML, t , is given from Eq. (3), though substituting Id by Id;MþL :

t¼


  Id;Mþ Ltd td 1  exp  IS td

(13)

The coefficient in Eq. (3), Id t d =Is , is a factor that does not affect the position of the wave on the Ed axis [26]. Therefore, an explicit expression for the shift of the half-wave potential due to the formation of a complex, DEd,1/2 (equivalent to the DeFord–Hume expression) can be obtained considering only the exponential term. In the case of a kinetic current, the shape of the SSCP wave

(15)

tM

Considering the stepwise formation of labile complexes between the metal M with a mixture of i ligands in a set of parallel reactions and in excess of ligand: K a;i

and the corresponding diffusion layer thickness, d (m), is modified accordingly for the given hydrodynamic conditions [27]:

d ¼ 1:61D

 1 DM  D K0

Where the average diffusion coefficient D can be calculated from:
 3=2 t D ¼ DM MþL (16) 

0

DM cM þ DML cML cM;t

td ¼

DML ¼ D 

(17)

K d;i

coefficient, D (m2 s1), can be computed from the limiting transition times obtained in the presence (t MþL ) and absence (t M ) of ligand [14]. If the diffusion coefficient of the metal complex species, DML (m2 s1), is lower than that of the free metal ion (DM), i.e. DML < DM (the general case), the deposition current and t d, are modified since DM is replaced by [26]:

Id;MþL ¼

iii) General equation for metal ions in the presence of a mixture of ligands The diffusion coefficient of the complex ML, DML, resulting from the interaction between the metal M and a single ligand L, can be obtained from the stability constant (K'), computed using Eq. (12) and the mass balance for the metal:

M þ Li @ MLi

where cM,t is the total metal concentration (mol m3). For a given total metal concentration, the average diffusion

D¼

remains unchanged and the same approach can be used, yielding:

  t nF DEd;12  ln MþL (14) lnð1 þ K 0 Þ ¼  RT t M

the equilibrium relationships K 0mix become: K 0mix ¼

Xj i¼1

C MLi C M

(18)

According with DeFord and Hume (1951) [28] the overall stability constant (K 0mix ) can be calculated from the individual stability constants. Considering the transport equations for M, ML1, ML2, . . . MLi:  Xj @cM;t  ¼ r2 DM C M þ D c MLi MLi i¼1 @t

(19)

and assuming that the complexes are fully labile (i.e. fulfill the corresponding equilibrium relationship at all the spatial and time conditions) and since C M 1 ¼ C M;t 1 þ K 0mix Eq. (19) can be rewritten as: " ! # Pj Xn K01 @C M;t 1 2  i¼1 i ¼r DM þ D cM;t P P i¼1 MLi @t 1 þ ji¼1 K 0i 1 þ ji¼1 K 0i 2  ¼ Dmix r cM;t

(20)

(21)

This equation indicates that a system with the free metal and all the labile complexes MLi can be reformulated in terms of only one species with concentration cM;t and diffusion coefficient Dmix , i.e.: !
 j X 1 0 Dmix ¼ K MLi DMLi DM þ (22) 1 þ K 0mix i¼1 iv) Determination of the free metal ion concentration by AGNES-SCP The free metal ion concentration was determined by the AGNES-SCP according with the procedure developed by Parat et al. (2011). This method consists of two conceptual stages: the deposition and stripping stages. Along the first stage, the metal ion in solution M2+ is reduced to M0, until a special situation of

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Nernstian equilibrium and absence of gradients in the concentration profiles is attained [12]. This equilibrium is achieved by applying a deposition potential E1 more negative than the formal potential E0 of the couple, for a sufficiently time t1. In the second stage the concentration of the reduced metal M0 inside the mercury amalgam is measured by SCP, i.e. the time for complete depletion (transition time, t ) can be determined from the evolution of the recorded potential in response to the imposed stripping current Is [25]. The faradaic charge (Q) can be rigorously computed as: Q ¼ ðIs  Iox Þt

(24)

where Is is the stripping current applied during the stripping step and and Iox is he current due to other oxidants [29]. Under the experimental conditions used in this work, Is >> Iox and as a result Eq. (24) is reduced to: Q ¼ Is t

(25)

The charge Q is used in this work as the response function for AGNES-SCP and it can be related to the free metal concentration, ½Mnþ , in the bulk of the solution, with a proportionality factor hQ [25,29]: Q ¼ hQ ½M

nþ



(26)

Considering the formation of a labile metal complex, ML, the stability constant can be calculated from the free metal ion concentration by means of Eq. (20). 4. RESULTS AND DISCUSSION 4.1. Validation methodology To establish a validation methodology for the average diffusion coefficient approximation in mixtures of ligands (Eq. (21)), two preliminary steps are required: a) determinate the Cd(II) and Pb(II) stability parameter (K0 ) with the individual polymers (4, 10, 30 KDa PSS) and confirms the additive nature of the stability constants enunciated by DeFord–Hume [29][28], b) calculate the individual diffusion coefficients DMLof the three polymers (4, 10, 30 KDa PSS). AGNES was coupled with SSCP technique, allowing the direct determination of the free metal concentration in solution. Eqs. (20) and (15) were then used to calculate respectively, the individual values of K0 and DML. Afterwards, several binary and ternary mixtures of containing Cd or Pb and PSS with 4, 10 and 30 KDa ligands were prepared and the D in each mixture was experimentally determined using Eq. (16). The experimental values were compared with the computed “theoretical” Dmix , obtained from Eq. (22) and from the individual parameters (K0 and DML), previously determined. The binding of cations by strong polyelectrolytes is generally described by Manning counterion condensation theory [30]. Nonetheless in this work the focus is not in the binding but rather in the diffusion coefficients and by working at one ionic strength (10 mM) and one pH (=4.0), the binding analysis is kept as simple as possible. In this situation variations in binding strength are obtained solely by changing the polyelectrolyte concentration therefore the operational parameter used to design the polymer mixture experiments will be K 0 ¼ KcL;t . Since the average diffusion coefficient (Eq. (22)) is a function of DMLi and K 0MLi , the experimental design used will rely on creating ternary mixtures varying both parameters. The DMLi variation comes straightforward from the mixture of polymers (4, 10 and 30 KDa) and the variation of K 0MLi (thus K0 ) is obtained by using different relative polymer concentrations. One aspect to recall is that fully labile behaviour is necessary to verify the validity of the

399

approximation. In order to do that we decided to use K0 target values of 2, 6 and 18 and verify the experimental lability criteria [8] to check that each experiment was indeed in fully labile conditions. Strictly speaking there was no need to use two different metal ions to validate Eq. (21), nevertheless from an electrochemical point of view it is always useful verify the validity of an approach with different metal ions, and in this case it brings additional support since the polymer concentrations necessary to obtain K0 values of 2, 6 and 18 are much lower for Pb(II) than for Cd(II), making the proof more robust. There are 27 possible ternary mixtures with K0 target values of 2, 6 and 18, but some are intrinsically similar, thus it is possible to obtain the same information with a total of 19 experiments, for each metal (for more information see section S2 of the supporting material.). Since in our experimental protocol it was decided to perform sequential additions of PSS polymers to obtain the experimental K0 in each step, it was also was decided to analyze the binary experiments. Although for those not all relevant combination were studied. Table 1 summarizes the combinations used to perform the experiments. 4.2. Stability parameters of metal-PSS and their additivity Fig. 1 shows the normalized SSCP curves obtained for Cd(II) and Pb(II) in the presence of 0.5  104 M of (PSS)n-COOH of 4, 10 and 30 KDa molecular sizes. Table 2 shows the experimental values obtained for the thermodynamic stability parameter K 0 ð¼ KcL;t Þ, calculated from the shift in the E1/2 of the SSCP curves and from the free metal ion concentration determined by AGNES-SCP, for both Cd(II)–(PSS)nCOOH and Pb(II)-(PSS)n-COOH systems (4, 10 and 30 KDa) systems and using different individual concentrations of 4, 10 and 30 KDa (PSS)n-COOH (the SSCP curves obtained under these experimental conditions are presented in Appendix C). For the same polymer concentration and subtracting both end groups that do not participate in the metal binding the number of —SO 3 groups is roughly 17, 47 and 144 for the 4, 10 and 30 KDa respectively. These proportions are respected within the experimental error for the K0 values increase with the concentration of PSS. The values obtained for the higher polymer concentrations show a slight tendency to be smaller than expected, especially for the 30 KDa. This might be due to the large polymer concentration involved, but should have no bearing in the later work since the higher K0 used for each polymer was 18. The experimental K 0mix values (K 0exp ) calculated from the shift on the E1/2 of the SSCP curves for Cd(II) and Pb(II) in the presence of binary and ternary mixtures of PSS polymers, were compared with the predicted values (K 0pred ), which were calculated from the sum of the individual K0 of each PSS polymer (Eq. (23)). Fig. 2 shows the Table 1 Combinations used to perform the experiments of Cd(II) and Pb(II) with ternary and binary mixtures of (PSS)n-COOH polymers with 4, 10 and 30 KDa molecular sizes. Binary Mixture BM1 BM2 BM3 BM4 (*1) BM5 BM6(*2) BM7 BM8 (*2) BM9 (*1)

4:10 2:2 4:30 2:2 4:10 2:6 4:10 2:18 10:30 2:2 10:30 2:6 4:10 6:2 4:30 6:2 4:10 6:6

Ternary Mixture

Combination 4:10:30 KDa

Ternary Mixture

Combination 4:10:30 KDa

TM1 TM2 TM3 TM4 (*1) TM5 TM6 TM7 TM8 TM9 (*2) TM10 (*2)

2:2:2 2:6:2 2:6:6 2:18:6 6:6:2 18:2:2 1:8:2 6:2:6 18:2:6 2:2:18

TM11 TM12 TM13 TM14 TM15 TM16 TM17 TM18 TM19

6:2:2 2:6:18 2:18:18 6:18:2 18:6:2 18:18:2 6:2:18 18:18:6 18:2:18

(*1) (*1)

(*2) (*2)

(*1) These experiments were performed using only Cd(II). (*2) These experiments were performed using only Pb(II).

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0.8

plot of K 0exp ¼ f ðK 0pred Þ, where a good correlation is observed between the experimental and predicted K' values for Cd(II) with a relative standard deviation of 5.4% (24 values) for Cd(II) and 4.0% (25 values) for Pb(II), indicating that K 0exp compares well with the

0.6

K 0pred determined, following the DeFord and Hume formalism [28].

τ normalized (s)

1.2

Cd

1.0

4.3. Determination of individual diffusion coefficients of complexed metals DML

0.4 0.2 0.0 -0.85

-0.80

-0.75

-0.70

-0.65

-0.60

Ed (V)

τ normalized (s)

1.2

Pb

1.0 0.8 0.6 0.4 0.2 0.0 -0.70

-0.65

-0.60

-0.55

-0.50

-0.45

-0.40

Ed (V) Fig. 1. Experimental (symbols) and fitted (full line) SSCP waves for Cd(II) in the absence (^) and presence of 0.5  104 M of (PSS)n-COOH of 4KDa (~), 10 KDa (*) and 30KDa (&). The experiments were performed in 0.01 M NaNO3, at pH 6.5 and for a concentration of Cd(II) of 3.0  107 M and 5.0  107 M of Pb(II). Other parameters: DCd = 7.19  1010 m2 s1,DPb = 8.10  1010 m2 s 1, dM = 1.40  105 m and y = 1.00  106 m2 s1. Table 2 Stability constants K0 obtained by SSCP and AGNES-SCP for Cd(II) and Pb(II)–(PSS) using different concentrations of the individual 4, 10 and 30 KDa (PSS). (PSS)

CPSS (104 M)

K0 (Cd-PSS)

K0 (Pb-PSS)

4 KDa

0.50 1.00 2.00

4.2
0.2 8.0
0.5 14
1

9.2
0.2 17
1 27
4

10 KDa

0.50 1.00 2.00

9.5
1.3 16
2 26
2

28
4 49
3 79
4

0.12 0.25 0.50 1.00

--14
0.4 25
2 43
4

23
1 44
4 75
5 ---

30 kDa

50

Cd

Pb

K' experimental

40 30 20 10 0 0

10

20

30

40

50

K' estimated Fig. 2. Experimental (K 0exp ) vs predicted (K 0pred ) values for the stability constant K0 . The experimental values were obtain from the shift on the E1/2 of the SSCP curves of Cd(II) and Pb(II) in the presence of binary and ternary mixtures and the predicted values were determined from the sum of the individual K0 of each PSS polymer.

The diffusion coefficients of the individual polymers(DML) were determined by the decrease in the limiting transition time t * of SSCP using Eq. (15). According to Buffle et al. (2007) [13], the recommended values for the diffusion coefficient of Cd(II) and Pb(II) are respectively 7.19  1010 m2 s1 and 9.45  1010 m2 s1. We found during this study, that the use of the recommended value for Pb(II) yield to divergent results, when compared to those from Cd(II). The literature reported values for the diffusion coefficient of Cd(II), DCd, determined by various techniques in nitrate media are quite similar: 7.38  1010 m2 s1 in 0.1 M NaNO3, 6.87  1010 m2 s1in 0.1 M HNO3and range between 6.90  1010 and 7.41 1010 m2 s1 in 0.1 M KNO3 media [31]. On the other hand the values reported for the diffusion coefficient of Pb(II), DPb, vary between 7.5  1010 and 9.84  1010 m2 s1 in 0.1 M KNO3 media [31]. This large range in reported values and the divergence of the Pb(II) results as compared with the Cd(II) prompted us to take a closer look at this problem. Therefore we determined using chronoamperometric methods the Pb(II) diffusion coefficient in our experimental media, obtaining a value of DPb of 8.1 1010 m2 s1 (details in section S4 of the supporting material). For a rigorous determination of the DML a set of SSCP experiments were performed for each metal using increasing polymer concentrations. In each experiment the stability parameter K0 was calculated using Eq. (14) and the average diffusion coefficient D was computed using the decrease in limiting transition time in absence and presence of complex species (Eq. (16)), after which DML was obtained from Eq. (15). The SSCP curves obtained for both metals in presence of successive additions of 4, 10 and 30 KDa PSS polymer are provided in section S2 of the supporting information. From the individual experiments for both metals and for different metal to ligand ratios, it was possible to calculate a DML of (9.2
0.6)  1011, (6.1
0.5)  1011 and (4.0
0.6)  1011 m2 s1 for the 4, 10 and 30 KDa respectively at pH 4 and ionic strenght 10 mM NaNO3. Adamczyk et al. (2009) [32] studied the solution properties of a similar PSS of 15.8 KDa and stated that the PSS structure depends strongly on the ionic strenght of the solution varying from a cylindrical rod, at very low ionic strength, to much more flexible torus shape (semi circle) at 150 mM. They reported an equivalent hydrodynamic radius varying between 3.1 to 4 nm from ionic strength varying from 5 mM to 150 mM at pH 6.5. Applying the Stokes–Einstein equation (D ¼ K B T=6phRH ) the diffusion coefficent variation ranging from 7.2  1011 m2 s1 to 5.6  1011 m2 s1 which agrees well with our measured values, since at a lower pH (4.0 vs 6.5) the PSS is likely less charged and thus should present a higher diffusion coefficient. For comparison the diffusion coefficient for a cylindrical rod can be calculated from the Stokes–Einstein equation (D ¼ K B T=f ) with a friction factor of 6pha=ðlna=b  g Þ, where KB is the Boltzman constant, T de absolute temperature, h the viscosity of the solvent, a is the length and b the base of the cylinder and g is a parameter that is 0.3 for a/b = 1 and 0.5 for large values of a/b. Using for the parameter (a) the value of chain diameter of 1.1 nm and for the parameter (b) the value of the estimated chain length per monomer of 0.21 nm (total chain length 16.3 nm divided

L.S. Rocha et al. / Electrochimica Acta 166 (2015) 395–402

by 77 monomeric units) provided by Adamczyk et al. (2009) [32] we computed a diffusion coefficient of 5.5, 3.8 and 2.1 1011 m2 s1 for the 4, 10 and 30 KDa respectively which are much smaller than the ones obtained experimentally providing support for the suggested PSS flexibility and the torus shape in these conditions. 4.4. Determination of DML diffusion coefficients in binary and ternary mixtures of PSS The average diffusion coefficients of the labile metal complexes with the binary and ternary mixtures of PSS (Dmix ) were determined from the decrease of transition time of the SSCP waves (Dexp ) according to Eq. (16) and compared with those calculated from Eq. (22), which assumes that D is the is a weighted average of the individual components (Dpred ). Fig. 3 shows that average diffusion coefficients Dexp compares well with the predicted Dpred values, presenting a relative standard deviation of 6.7% for the Cd(II) and 8.2% for Pb(II) both using 23 experiments. These results are very good, especially taking into account that it is necessary to use K0 to compute the DML of each individual PSS polymer (Eq. (15) and it’s uncertainty is already 5.4% for Cd(II) and 4.0% for Pb(II)). Based on these results we can confirm that the average diffusion coefficient D, like the stability constant K0 , is an additive property for multiple complexes (MLi) simultaneously present in solution. 4.5. Is size fractionation necessary in environmental samples? The simple answer would be yes, nevertheless the question merits a more detailed look. The main question is that the separation process itself may introduce artifacts in the analysis; hence it would be preferable not to fractionate, or at least to

401

perform a minimal fractionation. So what is the information available in a multi-metal multi-ligand system when using electrochemical stripping techniques: first AGNES will provide each free metal concentration in the bulk, thus an important information about the thermodynamic speciation, then from the potential shift in SSCP and the slope of the SSCP curve we obtain information on the chemical heterogeneity and the stability parameter, K’, thus additional information on the thermodynamic speciation for each metal. Finally the variation in limiting transition time, t *, will yield information on the transport properties (diffusion coefficients complexes) and stability parameter K0 , but might be affected by loss of lability of some metal complexes. In this work we showed that if we have the separated material it is possible to determine the diffusion coefficients (DL) using a metal ion as probe and the stability constant values (K) with different metals (for instance Pb(II), Cd(II)). It is easy to derive that with this information it would be possible to determine the polymer concentration in binary mixtures by adding known amounts of Cd(II) and Pb(II) as probes, as long as the complexes remain fully labile. If we had determined the stability constants of another metal, like Zn(II) this would allow us to determine the polymer concentrations in ternary mixtures. Then, by looking at the metal ion as a probe to investigate the ligand concentration or characteristics, is possible to obtain extra information about a particular system. This information becomes richer as the number of metals analyzed increase. Apropos environmental samples the separation of particulate and dissolved fraction with a 0.45 mm filter will likely be necessary, but further than that it is possible that a carefully thought experimental methodology using four metal ions (Pb(II), Cd(II), Zn (II) and Cu(II)) might avoid the need for further separations. Nevertheless before reaching that stage several question need to be

2.0E-10

Cd

Daverage (m2 s-1)

1.5E-10

1.0E-10

5.0E-11

0.0E+00 2.5E-10

Pb

Daverage (m2 s-1)

2.0E-10

1.5E-10

1.0E-10

5.0E-11

0.0E+00

Fig. 3. Experimental (Dexp ) vs predicted (Dpred ) values for the average diffusion coefficient D from the interaction between Cd(II) and Pb(II) and of binary and ternary mixtures of (PSS)n-COOH polymers of different molecular sizes.

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L.S. Rocha et al. / Electrochimica Acta 166 (2015) 395–402

addressed, amongst them the effect of loss of lability of the complexes and the influence that the purification processes usually performed in the NOM (IHSS procedure to extract humic matter and similar) have in the size distribution and in the metal binding parameters.

[10]

[11]

5. CONCLUSIONS [12]

In the present work the effect of ligand size polydispersity was studied and the results showed that the stability constant K0 calculated experimentally from the shift ofthe E1/2 of the SSCP curves, were in agreement (RSD < 5%) with the predicted values assuming the DeFord and Hume additivity rule. Additionally, a validation criteria was establish for the average diffusion coefficient (D) and it was confirmed the additive nature of this parameter in systems with multiple complexes MLi. This work shows that if we have the separated material it is possible to determine the diffusion coefficients (DL) using a metal ion as probe and the stability constant values (K) with Pb(II) and Cd (II). This represents an important feature regarding the use of SSCP to perform in situ speciation analysis andthe possibility to use this technique without the sample fractionation procedure that frequently introduces artefacts to the analysis.

[13]

[14]

[15]

[16]

[17]

[18]

Acknowledgments The authors thank Fundação para a Ciência e a Tecnologia (FCTANR/AAG-MAA/0065/2012) and Faculdade de Ciências e Tecnologia (Pest-OE/EQB/LA0023/2013 and PEst-OE/QUI/UI4023/ 2014) for funding support. L. S. Rocha and N. G. Alves also thank their grants (FCT project FCTANR/AAG-MAA/0065/2012). Wander G. Botero thanks the financial support from Capes (9813/13-6).

[19]

[20]

[21]

Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j. electacta.2015.03.035.

[22]

[23]

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