Yoann Louis
email: louis@univ-tln.fr

Cédric Garnier
email: c.garnier@ism.u-bordeaux1.fr

Véronique Lenoble
email: lenoble@univ-tln.fr

Stéphane Mounier
email: mounier@univ-tln.fr

Neven Cukrov
email: ncukrov@irb.hr

Dario Omanović
email: omanovic@irb.hr

Ivanka Pižeta
email: pizeta@irb.hr

Kinetic and equilibrium studies of copper-dissolved organic matter complexation in water column of the stratified Krka River estuary (Croatia)

Keywords:

An interaction of dissolved natural organic matter (DNOM) with copper ions in the water column of the stratified Krka River estuary (Croatia) was studied. The experimental methodology was based on the differential pulse anodic stripping voltammetric (DPASV) determination of labile copper species by titrating the sample using increments of copper additions uniformly distributed on the logarithmic scale. A classical at-equilibrium approach (determination of copper complexing capacity, CuCC) and a kinetic approach (tracing of equilibrium reconstitution) of copper complexation were considered and compared. A model of discrete distribution of organic ligands forming inert copper complexes was applied. For both approaches, a home-written fitting program was used for the determination of apparent stability constants (K i equ ), total ligands concentration (L iT ) and association/dissociation rate constants

). A non-conservative behaviour of dissolved organic matter (DOC) and total copper concentration in a water column was registered. An enhanced biological activity at the freshwater-seawater interface (FSI) triggered an increase of total copper concentration and total ligand concentration in this water layer. The copper complexation in fresh water of Krka River was characterised by one type of binding ligands, while in most of the estuarine and marine samples two classes of ligands were identified. The distribution of apparent stability constants (log K 1 equ : 11.2-13.0, log K 2 equ :8.8-10.0) showed increasing trend towards higher salinities, indicating stronger copper complexation by autochthonous seawater organic matter.

Copper complexation parameters (ligand concentrations and apparent stability constants) obtained by atequilibrium model are in very good accordance with those of kinetic model. Calculated association rate constants (k 1 1 :6.1-20 × 10 3 (M s) -1 , k 2 1 : 1.3-6.3 × 10 3 (M s) -1 ) indicate that copper complexation by DNOM takes place relatively slowly. The time needed to achieve a new pseudo-equilibrium induced by an increase of copper concentration (which is common for Krka River estuary during summer period due to the nautical traffic), is estimated to be from 2 to 4 h. It is found that in such oligotrophic environment (dissolved organic carbon content under 83 µM C , i.e. 1 mg C L -1 ) an increase of the total copper concentration above 12 nM could enhance a free copper concentration exceeding the level considered as potentially toxic for microorganisms (10 pM).

Introduction

It is well known that in aquatic systems the dissolved natural organic matter (DNOM) plays a major role in metals speciation, affecting their bioavailability and toxicity towards micro-and macroorganisms [START_REF] Buffle | Complexation reaction in Aquatic Systems-analytical approach[END_REF][START_REF] Bruland | Controls of trace metals in seawater[END_REF][START_REF] Hirose | Metal-organic matter interaction: ecological roles of ligands in oceanic DOM[END_REF][START_REF] Sunda | Effects of cupric and zinc ion activities on the survival and reproduction of marine copepods[END_REF]. Interaction of metals with DNOM depends on the physicochemical conditions of the system: ionic strength, pH, competition with other major and trace cations [START_REF] Bruland | Controls of trace metals in seawater[END_REF][START_REF] Lu | Characterization of copper complexation with natural dissolved organic matter (DOM)-link to acidic moieties of DOM and competition by Ca and Mg[END_REF].

Modelling/prediction of trace metal speciation is mainly based on data obtained under conditions which are defined as stationary (assumption of equilibrium). However, dynamic feature of chemical reactions in natural systems leads to non-equilibrium conditions. Systems such as rivers, lakes, estuaries and oceans surface could be under permanent, highly fluctuating physicochemical changes, generating metal speciation far from equilibrium (Hering andMorel, 1989, 1990;[START_REF] Langford | Kinetic versus equilibrium studies for the speciation of metal complexes with ligands from soil and water[END_REF].

It has been shown that in marine environments kinetics of trace metal complexation can be considerably lowered, mainly because of competitive effect with calcium-magnesium cations. Slow dissociation rate of Ca-Mg DNOM-complexes and competition with other trace elements are key factors which control degree of trace metal complexation and kinetics of its association with DNOM [START_REF] Hering | Kinetics of trace metal complexation: role of alkalineearth metals[END_REF][START_REF] Raspor | Kinetics and mechanism of trace metal chelation in sea water, presented in part at the Vth International Symposium, Chemistry of the Mediterranean[END_REF].

Many experimental studies of DNOM-metal interactions do not take account of kinetics [START_REF] Benedetti | Metal ion binding to colloids from database to field system[END_REF] or assumes fast kinetics [START_REF] Cheng | Comparison of zinc complexation properties of dissolved natural organic matter from different surface waters[END_REF], defining the chemical system at equilibrium. As this equilibrium is a simplification, it could be reasonable to take such data with caution if they are used to predict metal speciation in natural systems using software such as e.g. FITEQL, PHREEQ, MINTEQ, MINEQL, CHESS, which assume that system is at equilibrium [START_REF] Westall | MINEQL, a computer program for the calculation of chemical equilibrium composition of aqueous systems[END_REF][START_REF] Herbelin | FITEQL 4.0: A Computer Program for Determination of Chemical Equilibrium Constants from Experimental Data[END_REF][START_REF] Van Der Lee | CHESS Tutorial and Cookbook[END_REF]Dudal and Gerard, 2004 and references therein). As a consequence, an overestimation of the metal toxicity could arise. Thus, if reactions are slow, the application of speciation models to natural water systems requires knowledge about kinetics.

There are no available analytical techniques capable to measure "true" non-equilibrium metal speciation in natural systems. A few attempts for in-situ electrochemical measurements are first step in obtaining "real-time" metal speciation in dynamic aquatic environments (Tercier-Waeber et al., 2005 and references therein). Such analyses provide information about operationally defined fraction of trace metals with respect to the applied analytical procedure. Further efforts to develop long-lasting and robust electrochemical sensors with high sensitivity and selectivity to different metal species are needed.

An alternative approach directed to explore dynamic nature of metal speciation is to study kinetics of chemical reactions induced by the addition of metal ions or other complexing ligand. In few papers, ligand exchange kinetics were applied to study the release of metal already bound to DNOM (e.g. [START_REF] Hassan | Kinetic speciation of Ni(II) in model solutions and freshwaters: competition of Al(III) and Fe(III)[END_REF][START_REF] Fasfous | Kinetics of trace metal competition in the freshwater environment: some fundamental characteristics[END_REF][START_REF] Langford | Kinetic versus equilibrium studies for the speciation of metal complexes with ligands from soil and water[END_REF]. However, an important aspect in the dynamic metal speciation studies is to predict the kinetics of metal complexation by DNOM excited by the increase of metal concentration. Few studies were performed in order to characterize the kinetics of organic ligands complexation with trace metals using simple ligands such as EDTA and/or extracted humic substances [START_REF] Ma | Effect of kinetics of complexation by humic acid on toxicity of copper to Ceriodaphnia dubia[END_REF]Hering andMorel, 1989, 1990), or natural sample but with high dissolved organic carbon (DOC) contents [START_REF] Achterberg | Species kinetics and heterogeneous reactivity of dissolved Cu in natural freshwaters[END_REF]. The outcome of such experiments contributes to the global knowledge of the trace metal behaviour in natural aquatic systems.

Due to low organic carbon content (8-83 µMC; [START_REF] Vetter | Combining reverse osmosis and electrodialysis for more complete recovery of dissolved organic matter from seawater[END_REF]) associated with trace levels of metals (rarely higher than some nM), the study of DNOM binding properties in unpolluted systems remains complex, needing convenient analytical techniques usable at very low metal and carbon concentrations. Among all the analytical techniques developed for trace metal analysis and speciation (GFAAS, ICP/MS, ISE, etc.), voltammetric and potentiometric stripping techniques and particularly the differential pulse anodic stripping voltammetry (DPASV) are suitable to apply in natural conditions, especially in a chloride media without any pre-treatments, minimizing possible DNOM structural or physico-chemical modifications [START_REF] Buffle | Voltammetric environmental trace metal analysis and speciation: from laboratory to in situ measurements[END_REF].

The aim of this study is to develop and to explore an analytical procedure and a modelling scheme in order to determine and compare copper-DNOM complexing parameters under assumption of equilibrium conditions and under kinetic regime. For this purpose samples from water column of the non-polluted highly stratified Krka River estuary having low concentrations of metal and organic mater (but with expected seasonal increase of copper concentration) were studied. Dynamics of copper complexation and corresponding speciation scheme initiated by the increased copper concentration were considered.

Experimental

Sampling site and sampling procedure

The Krka River is a medium sized non-contaminated river of 49 km of length with an average flow measured over the last 50 years varying between 40 and 60 m 3 s -1 [START_REF] Bonacci | Definition of catchment area in karst: case of the river Krčić and Krka, Croatia[END_REF]. The Krka River estuary starts below waterfalls (Skradinski buk) and ends at the mouth of the Šibenik channel. Along the estuary total length of 23.5 km, water column is permanently stratified because of a sheltered geography and a low tidal range (20-50 cm). Due to low anthropogenic activities [START_REF] Cukrov | Spatial distribution of trace metals in the Krka River, Croatia: an example of the self-purification[END_REF], Krka River and its estuary are oligotrophic (DOC content under 83 µMC), with ultratrace levels of heavy metals [START_REF] Elbaz-Poulichet | Trace metal behaviour in a highly stratified Mediterranean estuary: the Krka (Yugoslavia)[END_REF]. However, during summer the total copper concentration increases, mainly because of nautical traffic [START_REF] Omanović | Trace metal detection in Šibenik bay, Croatia: Cadmium, lead and copper with anodic stripping voltammetry and manganese via sonoelectrochemistry. A case Study[END_REF].

Numerous studies have been performed in the Krka River estuary (e.g. special issue of Marine Chemistry, 1991, volume 32). According to these studies the most dynamic layer in the water column is the freshwater-seawater interface (FSI), on which an accumulation of biologically produced organic matter and associated contaminants (e.g. trace metals) could occur [START_REF] Žutić | A film of organic matter at the fresh-water/sea-water interface of an estuary[END_REF][START_REF] Svensen | Plankton distribution and vertical flux of biogenic matter during high summer stratification in the Krka estuary (Eastern Adriatic)[END_REF]. Unfortunately, only one paper dealing with an interaction of trace metals with NOM has been published up to now [START_REF] Plavšić | Determination of the copper complexing ligands in the Krka river estuary[END_REF], where an overview of the copper complexing capacity in the Krka River estuary was presented, showing that the concentration of ligands forming inert copper complexes remained at the same level as 25 years ago.

Samples for our study were collected on the 20th of April 2007 and 1 year later on the 6th of March 2008 in the Krka River estuary (Croatia, Fig. 1). Four samples in 2007 and four in 2008 were taken on a depth profile near the scientific marine station "Martinska", Ruđer Bošković Institute (Point 2 on the map, GPS coordinates: 43°44′ 07.92 N, 15°52′39.61 E) located in front of Šibenik town. Depth profile samples were taken by scuba-diving in pre-cleaned 1 L FEP (Fluorinated Ethylene Propylene, Nalgene) bottles. The salinity of samples ranged from 5 to 38 in 2007 and from 13 to 38 in 2008. Two additional samples (denoted as "end-members" of the profiles) were taken in 2008: the first one was sampled in the Krka River (Point 1 on the map, GPS coordinates: 43°48′12.42 N, 15°58′18.48 E) and represents fresh water which inflows into the estuary and the second one was taken in the sea (Point 3 on the map, GPS coordinates: 43°42′ 44,88 N, 15°47′43,98 E) out of the estuary direct influence. Both samples were collected at 0.2 m depth in 1 L FEP bottles (Nalgene). Data points for these two end-member samples are marked in the figures by individual symbols (at depth 0 and -8.5 m). All samples were filtrated on-site through 0.45 µm pre-cleaned cellulose nitrate filter (Sartorius) and stored in pre-cleaned 500 mL FEP or PFA bottles (PerFluoroAlkoxy, Nalgene) at 4 °C in the dark until analysis (for voltammetric experiments). Samples for DOC measurements were stored in glass tubes (Shimadzu), which are combusted in an oven (Herrmann Moritz, Four MF4) at 450 °C during 4 h to remove carbon.

Chemicals and instrumentation

All the vessels used were cleaned with 10% nitric acid (Fisher Scientific, analytical grade) and rinsed with ultra-pure water (Millipore Milli-Q system). Copper solutions (10, 100 and 1000 µM) used for titration were prepared from AAS copper standard (1 g L -1 , Fluka). Acidification of samples, when needed, was performed using 65% HNO 3 (Merck, Suprapur).

Concentrations of DOC were determined using a TOC-V analyser (Shimadzu), calibrated using sodium hydrogenophtalate standard solutions, with an accuracy of 0.8 µM C .

All voltammetric measurements were carried out with voltammetric analyser PSTAT10 or PGSTAT12 (EcoChemie, Utrecht, The Netherlands) controlled by GPES 4.9 software (Eco Chemie) coupled with the three electrodes system of 663VA Stand (Metrohm, Swiss). The working electrode was a static mercury drop electrode (SMDE) (size 1, 0.25 mm 2 of area), while a platinum wire was used as a counter electrode. Potentials were given vs. Ag|AgCl (sat. KCl) reference electrode. 20 ml of a sample, supported in a PFA electrochemical cell (Metrohm), was stirred with a Teflon rotating stirrer at 3000 rpm. Dissolved oxygen was removed from the solution prior to analysis by purging with ultra-pure nitrogen for at least 15 min. To exclude evaporation of the sample, a water-saturated nitrogen blanket was maintained above the solution surface during the whole experiment. All experiments were performed at room temperature (24 ± 2 °C). pH was controlled by a pH meter (Metrohm, 713 PHM) with a combined pH-micro-electrode (Mettler, Inlab422, reference electrode: Ag|AgCl|KCl 3.0 M). Initial pH values in all analysed samples were between 7.9 and 8.1. During the titration, pH increased from 0.3 up to 0.5 unity of pH because of partial removal of carbonates from the solution (CO 2 degassing). Copper speciation is thus partly changed in the cell-solution during titration, however according to simulation using VisualMINTEQ, a change of copper portion associated with strong organic ligands at the ambient conditions in the water column is negligible. Finally, the used method (DPASV) determines conditional complexation parameters (dependent on the applied procedure), and non-ideal conditions are common for such a type of study. For the speciation calculation, a pH value of 8.5 was defined for all the samples. Three automatic burettes (Cavro XE 1000 syringe pumps, Tecan, Swiss) were used to automate copper titration.

The conditions used for DPASV measurements of electro-labile copper were already presented (see [START_REF] Louis | Speciation of trace metals in natural waters: the influence of an adsorbed layer of natural organic matter (NOM) on voltammetric behaviour of copper[END_REF]. The important point is the deposition time which is divided in two parts: (i) 297 s at a deposition potential (E dep ) of -0.5 V and (ii) 3 s at a deposition potential of -1.6 V. This strong negative potential allows the removal of surface active substances which may adsorb at the electrode surface, producing artefacts on copper stripping peak and inaccuracy on the determination of DNOM/Cu binding parameters [START_REF] Louis | Speciation of trace metals in natural waters: the influence of an adsorbed layer of natural organic matter (NOM) on voltammetric behaviour of copper[END_REF]. The other parameters used are a pulse amplitude of 25 mV, a potential step increment of 2.5 mV, a time between pulses of 0.1 s with a pulse duration of 0.05 s. The potential was scanned from -0.6 V to 0.05 V or to 0.2 V depending on the sample salinity.

Total dissolved copper concentrations (Cu T ) were determined in acidified and UV-digested sample (3 h on the Metrohm 705 UV Digester, or 12 h under 150 W Hg lamp) by a standard addition method (duplicate DPASV measurements on the unspiked sample followed by four or five additions of standard Cu solution) [START_REF] Capodaglio | Speciation of trace metals in seawater by anodic stripping voltammetry: critical analytical steps[END_REF][START_REF] Omanović | Trace metal detection in Šibenik bay, Croatia: Cadmium, lead and copper with anodic stripping voltammetry and manganese via sonoelectrochemistry. A case Study[END_REF]. Detection limit for copper under applied experimental conditions was estimated to 2 × 10 -10 M.

Experiment design and modelling

20 ml of each sample was titrated with copper, covering concentration range from 0.5 nM to about 800 nM. A titration with copper additions with consistently distributed concentrations along the logarithmic scale (Garnier et al., 2004b) was applied (similar increments in log[Cu] T ). After each copper addition, DPASV measurements were repeated each 6 min (corresponding to the minimal time Author's personal copy needed to perform an analysis) using the above described procedure. In this way 20 voltammograms per addition, representing the labile part of copper, were obtained within 2 h. These repetitive voltammograms were used in the kinetic study (Fig. 2B). After these 2 h, two additional voltammograms were recorded, which were used for the at-equilibrium analysis (Fig. 2A). For each sample, at least 12 copper additions were performed to accomplish titration.

Peak area was chosen as a characteristic signal value and further used for the calculation of labile copper concentrations according to the sensitivity obtained at the end of the titration curve (measured peak area vs. added total Cu concentrations). This linear part of the titration curve corresponds to copper concentrations at which ligands active sites responsible for copper complexation are nearly saturated. At least four end-points were used for the sensitivity calculation.

At-equilibrium approach

Classical way to characterize DNOM reactivity toward metals consists in applying a conceptual model, which could be either a discrete [START_REF] Lenoble | Combination of 13C/ 113Cd NMR, potentiometry, and voltammetry in characterizing the interactions between Cd and two models of the main components of soil organic matter[END_REF][START_REF] Sposito | Trace metals in contaminated waters[END_REF][START_REF] Tipping | Modelling the chemical speciation of trace metals in the surface waters of the Humber system[END_REF][START_REF] Town | Dispelling the myths: is the existence of L1 and L2 ligands necessary to explain metal ion speciation in natural waters?[END_REF] or a continuous [START_REF] Benedetti | Metal ion binding to colloids from database to field system[END_REF][START_REF] Dzombak | Metal-Humate interactions: 1 Discrete ligand and continuous distribution models[END_REF][START_REF] Kinniburgh | Metal ion binding by humic acid: application of the NICA-Donnan Model[END_REF] distribution of binding sites. Fitting of the obtained experimental data could be performed using linear [START_REF] Muller | Chemical speciation of copper and zinc in surface waters of the western Black Sea[END_REF][START_REF] Ružić | Theoretical aspects of the direct titration of natural waters and its information yield for trace metal speciation[END_REF][START_REF] Scatchard | The attraction of proteins for small molecules and ions[END_REF] or non-linear methods (Dudal and Gerard, 2004 and references therein;[START_REF] Huber | Computer modelling of trace metal ion speciation: practical implementation of a linear continuous function for complexation by natural organic matter[END_REF][START_REF] Lu | Characterization of copper complexation with natural dissolved organic matter (DOM)-link to acidic moieties of DOM and competition by Ca and Mg[END_REF].

According to DNOM structural heterogeneity, mono-and multidentate ligands could be expected [START_REF] Tipping | Modelling the chemical speciation of trace metals in the surface waters of the Humber system[END_REF]. However, it has been shown in a theoretical study that the corresponding binding parameters are often inaccurately determined [START_REF] Garnier | An analysis of distinguishing composite dissolved metal-ligand systems measurable by stripping voltammetry[END_REF] due to experimental and fitting uncertainties. Therefore in this study, DNOM binding properties towards copper were modelled using a discrete distribution of mono-dentate binding ligands (L i ), each defined by 2 parameters: a total site concentration (L iT ) and a conditional stability constant (K i equ ) (Garnier et al., 2004a;[START_REF] Sposito | Trace metals in contaminated waters[END_REF].

Association between copper and a mono-dentate ligand (L i ) could be described by the following equation:

Cu 2 + + L i f K equ i CuL 2 + i with K equ i = CuL 2 + i h i Cu 2 + Â Ã × L i ½ ð1Þ
where [Cu 2+ ] and [L i ] are free copper and i-th ligand concentration, respectively.

In this study, the DNOM reactivity was only described by interactions toward Cu 2+ . Indeed, the characterisation of DNOM interactions with competition cations such as H + or Ca 2+ necessitates additional experiments, after numerous and time consuming DNOM concentration/purification steps (e.g. [START_REF] Louis | Characterisation and modelling of marine dissolved organic matter interactions with major and trace cations[END_REF] which is not the object of this study. So, the mass balance for the i-th ligand is restricted to the equation:

tL iT b = tL i b + tCuL 2+ i b ð2Þ
DPASV measurement leads to the determination of the electrolabile Cu fraction ([Cu] labile ), which mostly corresponds to inorganic copper complexes, while a difference between a total (Cu T ) and a labile Cu fraction corresponds to organic complexes (∑[CuL i 2+ ]), nonlabile under the chosen voltammetric parameter conditions. The relation between free and labile copper concentrations could be expressed as:

Cu ½ 2 + = α Cu ½ labile ð3Þ
where α is the side reaction coefficient. Inorganic chemical composition of solution and pH was taken into account to calculate the inorganic speciation of copper, and so the α value for each experimental data point, using thermodynamic stability constants from MINEQL and MINTEQ databases.

For each sample, determination of the at-equilibrium complexing parameters (L iT, K i equ ) was performed by fitting a measured set of electro-labile copper concentrations, using the software PROSECE (Garnier et al., 2004b). An example of experimental data set and fitting curve is shown in Fig. 2A. Data are fitted using 1-and 2-ligands models and the one leading to a statistically better fit is chosen. A validation of data fitting procedure was elaborated in details by Garnier et al. (2004b). Although the physico-chemical structure of these one or two classes of natural ligands is unknown, their presumption is often sufficient to correctly describe the DNOMmetal properties in the natural environment [START_REF] Town | Dispelling the myths: is the existence of L1 and L2 ligands necessary to explain metal ion speciation in natural waters?[END_REF].

For each of the optimised binding parameters, a confidence interval value is calculated by PROSECE as the maximal absolute variation (in percentage) of the parameter value corresponding to a 10% increase of the fitting error (sum of the difference between measured and calculated concentrations expressed in log) [START_REF] Louis | Characterisation and modelling of marine dissolved organic matter interactions with major and trace cations[END_REF]. Author's personal copy

Kinetic approach

Interaction between copper and a mono-dentate ligand (L i ) could be described by the following pseudo-first order reaction:

Cu 2 + + L i f k 1 i k -1 i CuL 2 + i with k 1 i k -1 i = K equ i ð4Þ
where k i 1 ((Ms) -1 ) and k i -1 (s -1 ) are the association and dissociation rate constants, respectively. Association/dissociation rates for inorganic copper complexes are known to be high, and so the corresponding reactions are supposed to be at-equilibrium [START_REF] Buffle | Complexation reaction in Aquatic Systems-analytical approach[END_REF]. The rate of concentration change after addition of copper(II) ions for i organic ligands can be described by:

dCu 2 + dt = X i -k 1 i Cu 2 + h i L i ½ + k -1 i CuL 2 + i h i ð5Þ
For each sample, the α value is determined from the results of the PROSECE fitting of the at-equilibrium titration measurements. Using Eq. ( 3), the Eq. ( 5) could be rearranged, and for one organic ligand it reads:

dCu labile dt = -k 1 1 Cu labile ½ L 1 ½ T -Cu ½ T -Cu labile ½ À Á À Á + k -1 1 Cu ½ T -Cu labile ½ À Á α ð6Þ
and for two organic ligands:

dCu labile dt = 1 α α Cu labile ½ -k 1 1 L 1 ½ T -k 1 2 L 2 ½ T + Cu ½ T -Cu labile ½ À Ák 1 2 k equ 2 + αk 1 2 Cu labile ½ ! + K equ 1 α Cu labile ½ L 1 ½ T 1 + K equ 1 α Cu labile ½ ! k 1 1 -k 1 2 Cu labile ½ α + k 1 1 K equ 1 - k 1 2 K equ 2 ! ! 0 B B B B B @ 1 C C C C C A ð7Þ
For one set of kinetic binding parameters values (L iT , k i 1 and k i -1 ), calculation of Cu labile for each equilibration time is carried out by numerical integration of functions ( 6) or ( 7). This integration implies the definition of an additional parameter, Cu labile concentration at 0s of equilibration time (Fig. 2B, open triangle). This "initial" labile copper concentration could be estimated either numerically (sum of the equilibrated Cu labile concentration from the previous addition and the added Cu) or graphically (initial trend of the curve [Cu labile ] vs.

time). As this parameter could have considerable impact on the obtained results, its accurate estimation is of essential importance.

Modifying the PROSECE algorithm (Garnier et al., 2004b), a new program (available on request) devoted for the kinetic data fitting has been written. Calculation algorithms were written using a platform of the numerical calculation program Octave (freeware). The fitting code consisted in an integration subroutine (LSODE function) coupled to an optimisation loop. Experimental data (i.e. the measured Cu labile concentrations vs. equilibration time after Cu addition to a sample) were fitted using 1-or 2-ligands model, with the number of ligands determined by at-equilibrium approach. For each addition, the optimal set of binding parameters was obtained, from which the average value and a standard deviation were calculated. An example of data set and fitting curve is shown in Fig. 2B.

Results and discussions

Salinity, DOC and copper depth profiles

The salinity (Fig. 3A), the dissolved organic carbon (Fig. 3B) and the total dissolved copper concentration (Fig. 3C) profiles showed the same trend of vertical distribution between the two sampling campaigns (in 2007 and in 2008) (Table 1). All three profiles indicate a well stratified water column with three different regions: (i) an upper brackish layer, (ii) a thin Freshwater / Seawater Interface (FSI) layer (thickness less than 50 cm) at a depth of about 1.5 m where the salinity sharply increases and (iii) the bottom seawater layer.

The main difference which can be observed between 2007 and 2008 is a higher salinity of brackish surface layer in 2008 with a measured value of 13, compared to only 5 in 2007 (Fig. 3A). This difference could be explained by a lower river flow for the period of sampling in 2008 (~22 m 3 s -1 comparing to ~37 m 3 s -1 in 2007), favoured by stronger wind which caused enhanced mixing of layers. In 2007, an enhanced biological activity at the surface water layer has been visually observed, not noticeable in 2008.

It can be observed that in the freshwater sample, the measured DOC concentration (43.2 ± 0.9 µM C ) was half of the concentration found in the seawater sample (80.0 ± 1.7 µM C ). This characteristic has already been observed [START_REF] Cauwet | Carbon inputs and biogeochemical processes at the halocline in a stratified estuary: Krka River, Yugoslavia[END_REF] for this river, showing that it is a very clean system, submitted to very low anthropogenic inputs.

DOC observed variations according to salinity followed a parabolic trend (full line, inset Fig. 3B) and not the dilution line of a conservative mechanism (short dash, inset Fig. 3B). It means that in the estuarine Author's personal copy mixing zone, there was an additional source of carbon. [START_REF] Ahel | Effect of salinity gradients on the distribution of phytoplankton pigments in a stratified estuary[END_REF] have already observed in this same estuary an enhanced biological activity in the FSI layer. Knowing that the major part of the DNOM in the aquatic environment is due to degradation or exudation from living organisms [START_REF] Buffle | Complexation reaction in Aquatic Systems-analytical approach[END_REF], this exacerbated biological activity can explain the higher amount of dissolved organic carbon found in this layer.

Concerning total dissolved copper concentrations, it can be underlined that in the freshwater sample taken in the Krka River, measured concentration is very low, about 2.4 ± 0.1 nM. Comparison of this value with the one measured 20 years earlier (1.78 nM) in the same river [START_REF] Elbaz-Poulichet | Trace metal behaviour in a highly stratified Mediterranean estuary: the Krka (Yugoslavia)[END_REF] shows that the Krka River maintains very low concentrations of trace metals owing to the efficient mechanism of self-purification [START_REF] Cukrov | Spatial distribution of trace metals in the Krka River, Croatia: an example of the self-purification[END_REF] and the absence of significant anthropogenic sources. The observed variations of total Cu concentrations with salinity also followed a parabolic trend (full line, inset Fig. 3C). Such increase of metal concentration in the FSI layer has already been described for a vertical profile of this [START_REF] Elbaz-Poulichet | Trace metal behaviour in a highly stratified Mediterranean estuary: the Krka (Yugoslavia)[END_REF] and other estuaries [START_REF] Baeyens | The biogeochemical behaviour of Cd, Cu, Pb and Zn in the Scheldt estuary: results of the 1995 surveys[END_REF][START_REF] Waeles | Distribution and chemical speciation of dissolved cadmium and copper in the Loire estuary and North Biscay continental shelf, France[END_REF][START_REF] Waeles | Seasonal variations of dissolved and particulate copper species in estuarine waters[END_REF], and is attributed to a particulate/dissolved metal exchange. When riverine particular organic matter negatively charged reaches the FSI, its ionic charge becomes neutral, due to major cations adsorption, leading to particles coagulation. These cations compete with trace metals initially bound at the particle surface, leading to metal release into the dissolved phase.

Copper-dissolved organic matter complexing parameters

In Fig. 4A andB, the depth profiles of ligand concentrations and apparent stability constants calculated with at-equilibrium approach are presented, respectively. All the obtained values are gathered in Table 1.

The river end-member sample was described by only one ligand with a low concentration (16.3 ± 0.6 nM) associated with a quite high stability constant (log K equ = 10.9 ± 0.1), ascribed to the class of strong ligands (L 1 ). This high apparent stability constant is expected to decrease from the river to the sea, due to the increase of major divalent cations competition effect. So, reaching the estuarine zone, this "riverine ligand" will have a decreasing affinity toward copper to the order of magnitude of this of the weaker class of ligands (L 2 ) found in the estuarine samples. This effect was described by [START_REF] Hamilton-Taylor | Laboratory measurements and modeling of metal-humic interactions under estuarine conditions[END_REF], studying copper speciation in estuarine conditions for a humic acid.

The sea end-member sample is characterized by 2 ligands (L 1 and L 2 ), with lower concentrations (6.1 ± 0.2 and 58.0 ± 1.4 nM, respectively) and higher stability constants (12.3 ± 0.1 and 10.0 ± 0.1, respectively) compared to other samples of the estuary profile. Differences of the two end-member samples characteristics could partly be linked to different DNOM sources: terrigeneous in the river, and autochthonous in the seawater. This hypothesis could be supported by the DOC increase observed along the salinity gradient, linked to an in-situ DNOM production, probably by biota known to produce strong ligands [START_REF] Mcknight | Release of weak and strong copper-complexing agents by algae[END_REF][START_REF] Coale | Copper complexation in the Northeast Pacific[END_REF].

In case of conservative water mixing, it is expected that the ligands concentrations should also be conservative. However, the same is not expected for copper stability constants which are salinity dependent, as explained before. [START_REF] Shank | Strong copper complexation in an organic-rich estuary: the importance of allochthonous dissolved organic matter[END_REF] observed a conservative trend of ligand concentration in the organic-rich Cape Fear estuary, where terrigeneous humic substances are the principal source of DNOM due to high river flow associated to low biological activity. In the Krka River estuary, for both campaigns, non-conservative behaviour was observed for ligands concentrations (Fig. 4A, solid line). The same is valid when observing the site densities (ratios of ligand to DOC concentrations) for the 2008 results: from 31 µeq g C -1 in the river, reaching 115 µeq g C -1 at the surface of the estuary, decreasing to 88.1 ± 3.5 95.2 11.2 ± 0.1 9.3 ± 0.1 6.9 ± 0.8 80.9 ± 14.8 87.9 11.9 ± 0.8 4.0 ± 0.3 -7.8 ± 0.6 9.5 ± 0.3 3.7 ± 0.3 -5.8 ± 0.4 1.1 19 69.5 ± 0.9 7.8 ± 0.4 / 67.6 ± 2.2 67.6 / 9.7 ± 0.1 / 69.2 ± 3.1 69.2 / 10.0 ± 0.5 3.7 ± 0.5 -6.3 ± 0.9 1.2 31 80.8 ± 0.9 8.5 ± 0.5 6.3 ± 0.4 83.6 ± 3.4 89.9 11.9 ± 0.4 9.4 ± 0.1 6.2 ± 0.2 83.4 ± 7.8 89.6 11.5 ± 0.3 3.8 ± 0.3 -7.7 ± 0.3 9.7 ± 0. Decreasing ligand concentrations from the FSI to the sea water layer was already observed in the Narragansett Bay by [START_REF] Wells | The complexation of "dissolved" Cu, Zn, Cd and Pb by soluble and colloidal matter in Narragansett Bay, RI[END_REF].

L 1 L 2 ∑L K 1 equ K 2 equ L 1 L 2 ∑L K 1 equ k 1 1 k -1 1 K 2 equ
The stability constants values obtained in this study increased from the estuary surface to the bottom (Fig. 4B), implying stronger ligands in the seawater layer. It could be explained by a production of autochthonous organic matter, originating from the biological activity (Fig. 3B).

The at-equilibrium binding parameters determined for the 2008 samples were incorporated in the speciation program MINEQL to calculate copper speciation with respect to salinity and total copper concentration depth profiles. The obtained depth profile for the organic copper fraction (Fig. 4C) showed a minimum in the FSI layer in spite of the strong increase of total copper concentration and the increase (respectively decrease) of weak (respectively strong) ligand concentration. The inorganic copper fraction increased in the FSI layer, leading to free copper concentration (in inset, Fig. 4C) as high as 20 pM, two times higher than the toxicity limit for marine phytoplankton defined by [START_REF] Sunda | Effects of cupric and zinc ion activities on the survival and reproduction of marine copepods[END_REF] (dotted line in inset of Fig. 4C). The same tendency was observed for the 2007 samples (data not shown), even stronger as the calculated free copper concentration reached 77 pM in the FSI.

Calculated total ligand concentrations were in positive correlation with the measured total copper concentrations (data not shown). So, the complexing properties of the DNOM present in the estuary seemed to be in a great extent controlled by the autochthonous DNOM produced at the estuary surface, probably by biological activity [START_REF] Svensen | Plankton distribution and vertical flux of biogenic matter during high summer stratification in the Krka estuary (Eastern Adriatic)[END_REF]. Despite a higher density of binding sites, these additional ligands were not sufficient to completely buffer the increase of dissolved copper in the FSI, probably coming from particles release.

It could be reasonable to assume that at the FSI layer an exchange of the copper complexation ligands type occurs: from riverine ligands to marine ligands. It was recently showed by [START_REF] Wang | Copper speciation by competing ligand exchange method using differential pulse anodic stripping voltammetry with ethylenediaminetetraacetic acid (EDTA) as competing ligand[END_REF] that attainment of the copper complexation equilibrium with spiked EDTA in model solution of SRFA and HA took at least overnight (12 h). Accordingly, the copper complexation properties determined for the samples taken at the FSI and taking into account ligands exchange, could be considered as transitional, representing a dynamic exchange conditions in this layer.

In order to determine the complexing parameters, experimental curves obtained with kinetic approach as the one shown in Fig. 2B were fitted by discrete models as explained in Section 2.3.2. Average binding parameters (L iT and logK equ i ) obtained for each studied sample using the kinetic approach were compared to the same parameters obtained using the at-equilibrium approach. Results showed a good agreement between both techniques (Fig. 5). It could be noticed that almost all "kinetic" stability constant are higher for about 0.2 logarithm units (Fig. 5B). We suppose that this small deviation could arise from uncertainty in Cu labile (at 0 s) estimation and/or from insufficient waiting time in the at-equilibrium approach.

Although leading to similar results, these two approaches of data fitting should be considered as complementary. By fitting experimental data, the at-equilibrium approach allows averaging uncertainty due to analysis errors and as the comprised range of metal/ligand ratio is more important, it leads to a better estimation of the ligands concentration. However, this approach supposes that after each addition a new pseudo-equilibrium is reached. The kinetic approach treats all the data points after each addition, and allows determining for each class of ligands not only the stability constant K i equ but its association (k i 1 ) and dissociation (k i -1

) rate constants. Still, one should be aware that there are obstacles such as (i) uncertainty in the estimation of the labile copper concentration at 0 s of equilibration time, (ii) most of the curves (all except for the few last copper additions) are fitted under conditions of non-saturated ligands, and (iii) at the lowest total copper concentrations, when the curvature of the labile copper concentration versus the equilibration time is well defined, the measured labile copper concentrations are close to the detection limit of the DPASV method, and so quite noise affected.

Variation of association/dissociation constants and their application in the prediction of dynamics of copper complexation by DNOM

The association constants values obtained for both campaigns were systematically higher for the strong class of ligands (log k 1 1 average value of 4.1) compared to the weak class (average value of 3.5) (Table 1). Variation of the dissociation constants was bigger (log k 1 -1 and log k 2 -1 average values of -8.2 and -6.1, respectively). The range of obtained association/dissociation constants values is comparable to those from the literature, even if there are scarce and rarely concern DNOM. Author's personal copy [START_REF] Raspor | Kinetics and mechanism of trace metal chelation in sea water, presented in part at the Vth International Symposium, Chemistry of the Mediterranean[END_REF] observed a strong decrease of EDTA association rate toward different trace metals with increasing divalent cations concentrations, and pointed out the major role of calcium. The slow association rate of the ligands analysed in our study could be equally linked to a competition between copper and major divalent cations vs. the DNOM binding sites. Indeed, DNOM complexation with copper needs a preliminary dissociation of DNOM complexes with major cations, which could be slow [START_REF] Hering | Slow coordination reactions in seawater[END_REF]. [START_REF] Raspor | Kinetics and mechanism of trace metal chelation in sea water, presented in part at the Vth International Symposium, Chemistry of the Mediterranean[END_REF] have calculated k 1 values vs. Pb in different seawater samples ranging from 3.2 to 3.6. Taking into account that Cu is known to form stronger complexes with EDTA than Pb, its association constants should be slightly higher. Ligands analysed in our study showed association constants in the same range of values, even if the transposition of constants from different ligands with different trace metals is not obvious (although it is the assumption of the linear free energy relationship (LFER) [START_REF] Hirose | Chemical speciation of trace metals in seawater: a review[END_REF]). [START_REF] Hering | Slow coordination reactions in seawater[END_REF], studying salinity influence on copper complexation by a mixture of EDTA and extracted humic substances, have supposed that copper association rate with extracted NOM should not be modified, and have calculated that association rate of the model strong ligand with copper should have decreased due to highest competition effect of divalent cations. But they followed the complexation of extracted NOM using fluorescence quenching technique, which is less sensitive and selective than DPASV, and with higher copper and DOC concentrations than in our study. [START_REF] Ma | Effect of kinetics of complexation by humic acid on toxicity of copper to Ceriodaphnia dubia[END_REF] have studied the kinetic of copper association with extracted humic acid in presence of calcium. According to the equation describing the kinetic copper complexation with ligands (see Eq. ( 5)), they defined association constants as, k i ⁎ =k i 1 × L i assuming that L i corresponds to the total concentration of ligand (L iT ) and not the free one, which dramatically simplifies the fitting procedure. Applying our program and using their values obtained for the strongest ligand concentration (L iT ) and association rate (k i ⁎ ), the log of corresponding association constant could be estimated to 3.2. Despite different analytical conditions (artificial sample, higher total copper and humic acid contents, potentiometric detection), this value is of the same order as those obtained in our study.

The dissociation constants obtained for the weak ligands (log k 2 -1 average value of -6.1) were lower than the value of -5 obtained by ) of -8, showing the importance of strong complexing sites which were able to strongly complex copper and so can easily dominate metal speciation in the environment.

Author's personal copy

From these data, it can be deduced that the main difference in DNOM reactivity for strong ligands was mainly due to their very small dissociation constants. Generally, the small increase of association constants coupled with a decrease of the dissociation ones explained the higher stability constants (K i equ ) found in samples of higher salinity.

These experiments gave us important additional information on DNOM reactivity in natural system. The obtained data are essential for ecosystems that are periodically or often under dynamic conditions where new equilibration processes can significantly change metal speciation.

According to [START_REF] Cukrov | Spatial distribution of trace metals in the Krka River, Croatia: an example of the self-purification[END_REF], the Krka River has a small input of copper to the estuary along the year. However, [START_REF] Omanović | Trace metal detection in Šibenik bay, Croatia: Cadmium, lead and copper with anodic stripping voltammetry and manganese via sonoelectrochemistry. A case Study[END_REF] observed increased copper concentration in the surface layer during the summer, probably due to traffic of tourist's boats, with total copper concentrations higher than 12 nM (Fig. 6A, crosses). Our results from 2008 are given for comparison (Fig. 6A, triangles). A simplified simulated total copper concentration depth profile (Fig. 6A, dashed line) was defined in order to trace response of the copper speciation induced by its increased content. For the simulated increased copper concentration, the calculated free copper contents for each depth in the upper layer overpassed the toxicity limit of 10 pM defined by [START_REF] Sunda | Effects of cupric and zinc ion activities on the survival and reproduction of marine copepods[END_REF], contrary to our values obtained in the 2008 samples (Fig. 6B open diamonds and diamonds, respectively).

To predict the dynamics of copper complexation in the water column of the Krka River estuary, dependences of Cu labile concentrations versus equilibration time (from 0 to 500 min) were calculated for the given depth profile of total copper concentrations (data not shown). From the obtained curves, time for 50% (t 50 ) and for 99% (t 99 ) of copper complexation was determined (Fig. 6C). The fastest achievement of a new equilibrium initiated by copper additions was observed for surface and sea water samples. Half of the total metal complexation was accomplished in 25 min and the pseudo-equilibrium was reached in 2 h30 min (t 99 ). In the FSI layer, longer time was needed, with t 99 values reaching 4 h30 min. The sample at salinity 31 (depth -1.2 m) compared to the sample at salinity 19 (depth -1.1 m) showed slightly lower free copper concentrations but considerably longer equilibration times (Fig. 6B andC). The difference in free copper concentration is attributed to the presence of an additional stronger ligand (L 1 ) at the point of salinity 31 (see Fig. 4A andB), not present at the point of salinity 19. The difference in equilibration time is attributed to slower association rates (see Table 1).

Taking into account the hydrodynamic variations expected in such an estuary, these long equilibrium times are not negligible and indicate that the studied system is often not at equilibrium, particularly at the mixing interface between fresh and sea waters, where major biogeochemical processes occur.

Conclusion

Two comparative approaches were used to study copper-dissolved natural organic matter (DNOM) interaction in the water column of the stratified Krka River estuary: (i) an at-equilibrium and (ii) a kinetic approach. Both approaches are based on the measurement of labile copper complexes at increasing total copper concentration by DPASV.

Obtained results revealed non-conservative behaviour of total dissolved copper and DOC distribution along the salinity gradient. Owing to the software developed for the fitting of experimental data for both at-equilibrium and kinetic model, one or two discrete classes of natural ligands forming inert copper complexes were resolved. For the surface brackish layer, copper complexation is characterized by only one class of ligands with relatively low concentration (16.3 nM) and quite high apparent stability constant (log K 1 equ = 10.9), while for most of the other samples, two classes of binding ligands were distinguished (log K 1 equ : 11.2-13.0, log K 2 equ : 8.8-10.0). An increase of apparent stability constants with the salinity indicated stronger interaction of copper with autochthonous ligands produced in-situ as a result of biological activity. Although a kinetic approach is not common in the determination of metal complexation parameters, our results validated its applicability and reliability in the determination of apparent stability constants and ligand concentrations. In addition, the kinetic model provided a calculation of the association/dissociation rate constants, allowing evaluation of the dynamic properties of copper complexation. Relatively slow formation rates of copper complexation (k 1 1 :6.1-20 × 10 3 (M s) -1 , k 2 1 : 1.3-6.3 × 10 3 (M s) -1 ) indicate that in the water column of the Krka River estuary, an achievement of the pseudoequilibrium (99%) of copper complexation (induced by copper concentration increase) could last up to 4 h30 min.

In spite of the fact that the Krka River estuary is considered as nonpolluted, an increase of the copper concentration in surface water layers above 10 nM (as a consequence of the copper dissolution from the anti-fouling boats coatings) could take place during summer season. Taking into account very low DOC content, it is estimated that the concentration of toxic copper specie (free ion, Cu 2+ ) could surpass the toxic threshold level (10 -11 M). Considering slow kinetics of copper complexation, this toxic concentration could be even higher than its equilibrium value.

Obtained results confirmed that in water systems subjected to fast and frequent physico-chemical perturbations, metal speciation is often not at equilibrium. Thus, the dynamic properties of metal complexation should be provided in addition to the metal speciation data predicted by numerical models, which assume equilibrium conditions.

In order to better describe, understand and be able to predict the copper behaviour and cycling at the very location of the Krka River estuary, more frequent samplings at characteristic points of this stratified estuary are envisaged and other are in course.

Fig. 1 .

 1 Fig. 1. Locations of sampling sites: 1-Freshwater sample of Krka River, 2-Depth profile samples (Krka River estuary), 3-Seawater sample.

Fig. 2 .

 2 Fig. 2. Sample of salinity 13 (2008) titrated with copper in logarithmic increments. (A)-at-equilibrium obtained experimental points (□), dotted line: non-complexing line, full line: fitting curve. (B)-fitting of the kinetic experimental data (•) for the copper concentration indicated on the plot (A), dashed line: total metal, full line: fitting curve, □-data used for at-equilibrium fitting, △-estimated Cu labile value at 0 s of equilibration time.

Fig. 3 .

 3 Fig. 3. Salinity (A), DOC (B) and total dissolved copper (C) depth profiles of samples taken in 2007 (△) and in 2008 (▲); marked area represents the depth range where FSI layer occurred for both 2007 and 2008 sampling events. Insets: Same parameters in relation to salinity; Full and dashed lines represent parabolic and conservative variations of DOC (B) and total dissolved copper (C), respectively.

  determined.80 µeq g C-1 in the FSI and to 60 µeq g C -1 in the seawater layer.

Fig. 4 .

 4 Fig. 4. Ligand concentrations (A) and stability constants (B) as a function of depth for strong (◯,•) and weak (△,▲) ligands for samples taken in 2007 (◯,△) and in 2008 (•,▲). Dotted line: salinity profile for 2008; full line: sum of total ligand concentrations for 2008. (C)-Calculated inorganic (■) and organic (X) copper fractions according to depth profilefor samples from 2008. Inset: free copper concentration ( ◆ ) and the toxicity limit of 10 pM (according toSunda et al., 1987) represented by dotted line. Marked area represents the depth range where FSI layer occurred for both 2007 and 2008 sampling events.

Fasfous

  et al. (2004) for a model solution of Laurentian river fulvic acid. This difference could partly be explained by their different analytical conditions: pH 5 and a low ionic strength (6 µM).The strong ligand noticeable for the 2008 samples indicated a very slow dissociation constant (log k 1 -1

Fig. 5 .

 5 Fig. 5. Comparison of the complexing parameters (A-ligands concentrations and B-stability constant) obtained by the kinetic and the at-equilibrium approaches for samples taken in 2007 (◯,△) and 2008 (•,▲). Parameters obtained for strong (◯,•) and weak (△,▲) complexes.

Fig. 6 .

 6 Fig. 6. (A)-comparison of total copper concentration profiles for 2008 (▲) and those obtained by Omanović et al. (2006) (X). Dashed line represents projection of total copper concentration profile (see text for details). (B)-corresponding free copper concentration for 2008 (♦) and for the projected profile (◊); dotted line represents toxicity limit (see text). (C)-reaction time of organically complexed Cu (calculations according to the projected profile),-kinetics for 50% (♦), and for 99% (◊).

Table 1

 1 Results for samples collected in 2007 and 2008 vs depth: salinity, DOC, total copper concentration (Cu

	fitting using
	iT ), stability constants (K equ i ), association/dissociation constants (k 1 i ,k -1 i ) as a result of data

T ), total ligand concentration (L

Y.Louis et al. / Marine Chemistry 114 (2009) 110-119

Acknowledgements

The authors wish to thank the French research group MONALISA (convention number: n°03/1214910/T) supported by the IFREMER institute, the French Ministry of Education and Research, Provence-Alpes-Côte d'Azur regional council and the Ministry of Science, Education and Sports of the Republic of Croatia (through Grant No. 098-0982934-2720) for Y. L. Ph.D. support and funding.

Author's personal copy


Dario Omanovi
email: omanovic@irb.hr

Cédric Garnier
email: cgarnier@univ-tln.fr

Yoann Louis
email: louis@univ-tln.fr

Véronique Lenoble
email: lenoble@univ-tln.fr

Stéphane Mounier
email: mounier@univ-tln.fr

Ivanka Pižeta
email: pizeta@irb.hr

Significance of data treatment and experimental setup on the determination of copper complexing parameters by anodic stripping voltammetry

Keywords:

Different procedures of voltammetric peak intensities determination, as well as various experimental setups were systematically tested on simulated and real experimental data in order to identify critical points in the determination of copper complexation parameters (ligand concentration and conditional stability constant) by anodic stripping voltammetry (ASV). Varieties of titration data sets (Cu measured vs. Cu total ) were fitted by models encompassing discrete sites distribution of one-class and two-class of binding ligands (by PROSECE software). Examination of different procedures for peak intensities determination applied on voltammograms with known preset values revealed that tangent fit (TF) routine should be avoided, as for both simulated and experimental titration data it produced an additional class of strong ligand (actually not present). Peak intensities determination by fitting of the whole voltammogram was found to be the most appropriate, as it provided most reliable complexation parameters.

Tests performed on real seawater samples under different experimental conditions revealed that in addition to importance of proper peak intensities determination, an accumulation time (control of the sensitivity) and an equilibration time needed for complete complexation of added copper during titration (control of complexation kinetics) are the keypoints to obtain reliable results free of artefacts.

The consequence of overestimation and underestimation of complexing parameters is supported and illustrated by the example of free copper concentrations (the most bioavailable/toxic specie) calculated for all studied cases. Errors up to 80% of underestimation of free copper concentration and almost two orders of magnitude overestimation of conditional stability constant were registered for the simulated case with two ligands.

Introduction

In natural waters trace metals are associated with inorganic and organic ligands, forming complexes of various strengths [START_REF] Bruland | Treatise on Geochemistry[END_REF][START_REF] Buffle | Complexation Reactions in Aquatic Systems: An Analytical Approach[END_REF]. Inorganic side of metal complexation is well known and easily predictable, but complexation with ligands from the natural organic matter (NOM) is still not completely known and is a subject of great scientific interest and challenge [START_REF] Bruland | [END_REF][4][5].

Continuous or discrete models of complexing sites distribution accountable for metal complexation are mostly used to characterize NOM-metal interactions [START_REF] Bruland | [END_REF][5][6][7][8][9][10][11][12][13]. It is shown that discrete models of one to three classes of natural ligands are often sufficient to fit experimental data [START_REF] Bruland | [END_REF]5,13]. Among many, voltammetric techniques such as anodic stripping voltammetry (ASV) and competitive ligand exchange-adsorptive cathodic stripping voltammetry (CLE-AdCSV) are widely used because of their excellent sensitivity and selectivity in natural water samples [START_REF] Bruland | [END_REF]5,6,[8][9][10][11][12][13][14][15]. Both techniques are based on sample titration by metal of interest (usually copper), followed by the mathematical treatment of measured data to obtain one or more conditional stability constants of formed metal complexes and concentrations of corresponding ligands. For this purpose linearization method proposed by Ruži ć and vandenBerg is widely used [16,17], although non-linear fitting approaches were practiced and shown to be superior [START_REF] Bruland | [END_REF]7,18]. Distinguishing of more complex and also more probable bi-ligand and mixed metal-ligand complexes than simple 1:1 metal-ligand systems is shown to be achievable too [19]. One of the major factors obstructing the calculation of more complex metal-ligand system is the precision of measurements.

For most of complexation studies, calculated complexation parameters are restricted to be used for modelling of metal spe-ciation in a particular aquatic environment and are not considered to be applied on larger spatial scale. In dynamic environments such as estuaries, a large variety of complexing properties could be obtained, ensuring prediction of metal speciation only on limited part of a water body [8,14].

However, not only the diversity in water composition could generate large differences in complexing parameters, but the experimental setup, data treatment and calculations, systematic errors in the analytical method or interpretation of the data could result in variations of complexation properties for the same studied sample, even if the same technique is used.

Recently a discussion regarding equilibration time in CLE-AdCSV attracted attention of the scientific community, finishing finally as "unresolved issue" [15,[20][21][22]. Equilibration time during titration is a critical part for the ASV, as well. Very large differences in equilibration time are reported in the literature, ranging from only few minutes to overnight equilibration [START_REF] Bruland | [END_REF]6,8,9,[12][13][14]23,24]. Checking of signal stability during larger period of time (e.g. more than 1 h) is favoured [8,24], in order to ensure reliable determination of complexing parameters. Two hours of equilibrium time is found to be sufficient for copper to reach equilibrium higher that 95% in estuarine conditions [8].

The comparison of the complexation parameters found in the literature is a common practice in this type of studies, whether the same or different measurement technique is used. The two mostly used electrochemical techniques ASV and CLE-AdCSV operate at different "detection windows" [START_REF] Bruland | [END_REF]6,11,25]. The "detection window" of AdCSV could be adjusted by the concentration of added competing ligand. The conditional stability constants determined by this technique are generally higher than that of ASV [START_REF] Bruland | [END_REF]. However, for example, in a study of Bruland et al. [START_REF] Bruland | [END_REF], it is found that with ASV three different classes of binding ligands were distinguished and characterized, compare to the two-class obtained by CLE-CSV. Thus it is not straightforward to directly compare metal complexation parameters obtained by these two different techniques, and it should be avoided. However, a complementary study by both techniques is always advisable [START_REF] Bruland | [END_REF], regarding their "detection windows".

The aim of speciation studies is the estimation of complexing parameters which could be used to predict the concentration of different metal species in a particular aquatic environment. The most important metal specie is a free metal ion, as it is confirmed to be the most bioavailable/toxic to biological organisms [26]. Thus, it should be expected that whichever the measurement technique used, the calculated free ion concentrations should not be in a high discrepancy for the same studied sample.

For example, it is found that >99% of copper at its ambient concentration (few nM) in seawater is bound to complexing sites which correspond to stronger class of organic ligand (of lower concentration), while weaker class of ligands (of higher concentration) are considered as potential "buffering capacity" for increased copper concentration [START_REF] Bruland | [END_REF]8]. For natural waters with low dissolved organic carbon (DOC) and low copper concentration this type of binding ligands could be efficiently calculated only if the corresponding range of copper concentrations in titration curve is covered. Usually this range starts at the ambient concentration, which in turn requires sufficient sensitivity of the applied voltammetric technique (as the measurable copper concentration could be below nM level). Using inadequate measuring procedure (e.g. short accumulation time) this range could be missed, resulting in impossibility of the determination of stronger type of binding ligands.

The most noticed complication in ASV is found to be an adsorption of surface active substances (SAS) originating from NOM on the surface of the electrode [27][28][29]. Fortunately, such problems could be effectively eliminated by applying very negative "desorption potential" (e.g. -1.5 V) for a short period of time (1% of total accu-mulation time) at the end of the accumulation period [10,29,30]. Without this desorption step, a broad and relatively high peak overlapping with the oxidation peak of copper appears, which is usually assigned to copper peak by most of the authors.

Taking all of the above-mentioned points into account, an overand under-estimation of both conditional stability constants and ligand concentrations could occur, which in turn lead to incorrect metal speciation determination. To avoid this inaccuracy and to correctly predict metal speciation (as much as possible), not only the verified measurement procedures, but also the peak treatment procedures should be obeyed.

Following this idea, the purpose of this paper is to present on both model data and real samples an effect of different data treatment routines and experimental setups on the determination of copper complexing parameters. In addition, an implication on free copper concentration estimation at its ambient conditions is illustrated.

Experimental, simulation and fitting

Experimental

Sample description

Samples were collected by scuba-diving [31] (pre-cleaned 1 L FEP bottles, Nalgene) in March 2008 in the Krka River estuary (Croatia) along a depth profile near the scientific marine station "Martinska", Ruder Boškovi ć Institute (GPS coordinates: 43 • 44 07.92N, 15 • 52 39.61E). These samples have already been the object of a previous study (for more details about the sampling zone, sampling protocol and analytical techniques, see [8]). The two samples, selected to be studied in more detail concerning experimental conditions (equilibration time, deposition time, addition of Triton-X-100), correspond to depths 1.2 m (sample 1) and 3.8 m (sample 2), respectively. Salinity, total dissolved Cu and dissolved organic matter concentrations are as follows: 31, 8.47 ± 0.54 nM, 0.97 ± 0.01 mg C L -1 (sample 1) and 38, 4.84 ± 0.63 nM, 0.89 ± 0.02 mg C L -1 (sample 2).

Instrumentation

All voltammetric measurements were carried out using an Autolab potentiostat (EcoChemie, Utrecht, The Netherlands) (PGSTAT12) equipped with a Metrohm 663 VA stand (Metrohm, Herisau, Switzerland). The instrument was computer-controlled using GPES 4.9 control software. The working electrode was a static mercury drop electrode (size 1, 0.25 mm 2 ), the counter electrode was a platinum wire, and the reference electrode was Ag|AgCl (sat. NaCl). Stirring of the solution was performed by built-in Teflon stirrer rotating at 3000 rpm. All measurements were performed at room temperature (22 ± 1 • C), in a PFA cell. pH was controlled by a Metrohm pH meter (Model 713) with a glass pH electrode. Three automatic burettes (Cavro XE 1000 syringe pumps, Tecan, Swiss) were used to automate copper titration in logarithmic mode. Differential pulse anodic stripping voltammetry (DPASV) was applied as adequate sensitive and robust measuring technique because it gives high signal to noise ratio and reasonable high scan rate. The following experimental parameters were used: pulse amplitude, A = 20 mV; potential step increment, E st inc = 2 mV; time between pulses, t int = 0.1 s; pulse duration, t mod = 0.04 s.

Simulation of voltammograms

Simulated voltammograms of copper (from which peak area is used for the construction of titration curves) were obtained as follows: on smoothed voltammogram without copper signal, obtained in real seawater sample without accumulation (considered here as baseline current), simulated voltammograms of copper (using 1/cosh 2 function) with increasing peak heights were added. Intensities of copper signals were calculated according to copper concentrations not bound to hypothetical organic ligands L 1 ([L 1 ] = 3 nM, log K 1 = 10) and L 2 ([L 2 ] = 50 nM, log K 2 = 8) assuming sensitivity of 0.2 nA nM -1 [32]. Simulated copper titration starting with concentration of 2.9 nM (i.e. matching the real concentrations in Šibenik bay) up to 600 nM was performed in 15 equal increments of copper additions in logarithmic scale ( pCu). Two sets of "pure" simulated data were constructed comprising one-ligand system (L 1 ) and two-ligand system (L 1 and L 2 ). In addition, other parallel sets of voltammograms were constructed with a random noise (ranged between ±4 × 10 -11 A, estimated according to real measurements) added to the voltammetric curves in order to reproduce real measurement conditions, leading to two sets of "noised" simulated data.

Modes of peak determination

The area under the peak is used as a measure of the signal. The area is calculated by integration of baseline-subtracted voltammograms. For this purpose three different procedures for baseline approximation were tested:

(1) TF -tangent fit -the baseline in the potential range of the peak is defined as linear (the most used procedure of peak determination). ( 2) SF -spline fit -the baseline in the potential range of the peak is defined as a spline function using points preceding and following the range of peak appearance. This function is automatically performed by home-written software. (3) VF -voltammetric fit -each voltammogram is fitted in the complete potential range scanned, by combination of polynomial (I

poly baseline = a × E 3 + b × E 2 + c × E + d), exponential (I exp baseline = ˛× exp(ˇ× E + )
) and up to two 1/cosh 2 functions [START_REF] Bard | Electrochemical Methods: Fundamentals and Applications[END_REF]. All the parameters of these functions are optimized using the Solver subroutine of Excel to fit the complete voltammogram. The peak area is then determined by integration of the 1/cosh 2 functions which corresponds to copper peak. This peak determination procedure was already successively applied in previous studies [8,[START_REF] Lenoble | [END_REF]35].

For both simulated and experimental titration curves, voltammetric sensitivities (nA nM -1 ) were determined by linearization of the 3-5 last points (the range where organic ligands are already saturated by copper) [START_REF] Bruland | [END_REF]8,9]. Using corresponding sensitivities, the relationships of [Cu] measured vs. [Cu] total were constructed, and used for the further calculations and transformations. In total 30 titration data sets (12 simulated and 18 experimental) were generated for both simulated and experimental data.

Tool for fitting-PROSECE

For each data set, the concentration of complexing ligands ([L] i,T ) and corresponding conditional stability constants (K i ) were determined by fitting software named PROSECE [7]. Data are fitted assuming models comprising one-and two-class of binding ligands (L 1 and L 2 ). The confidence interval is calculated by PROSECE as the maximal absolute variation (in percentage) of the parameter value corresponding to a 10% increase of the fitting error (sum of the difference between measured and calculated concentrations expressed in log) [8,35]. For the experimental titration data sets, the inorganic copper speciation is taken into account in the model fitted by PROSECE, and accordingly, the conditional stability constant are given in respect to free Cu 2+ . It is assumed that the electrolabile copper measured by DPASV mostly corresponds to the free and inorganic copper complexes. For simulated titration data sets copper speciation is restricted to its free (Cu 2+ ) and organic (CuL 1 , CuL 2 ) fractions.

The following parameters were used in the calculations of inorganic copper speciation: pH, major inorganic cations and anions concentrations (calculated from the salinity). Stability constants used for inorganic copper speciation were those provided by MINEQL [START_REF] Westall | MINEQL: A Program for the Calculation of Chemical Equilibrium Composition of Aqueous Systems[END_REF] and MINTEQ databases.

Results and discussion

Effect of data treatment procedures (simulated titrations)

Four cases of simulated voltammetric titrations were generated defining (1) one-ligand system ([L 1 ] T = 50 nM, log K 1 = 8), (2) twoligand system ([L 1 ] T = 3 nM, log K 1 = 10, [L 2 ] T = 50 nM, log K 2 = 8), and in addition, (3) and (4) the same as ( 1) and ( 2) with the random noise added to simulated voltammograms. Each titration curve was fitted by means of discrete model of site distribution assuming (i) one-class ligand model and (ii) two-class ligand model. An analysis of variances is used as criterium for decision of acceptance of the correct model (F-test).

One-class ligand (L 1 ) simulated titrations

In Table 1 copper complexing parameters obtained by PROSECE fitting to titration data constructed by three different modes of peak intensities determination (TF, SF and VF) are presented, for both pure and noised voltammograms.

For both pure and noised data sets, the PROSECE fitting of titration curve produced an additional "false" class of ligand in the case of TF mode of peak determination, while the two other modes (SF, VF) gave accurate and expected results (only one-class of ligand). It is important to point out that PROSECE fitting of the two-ligand model to simulated one-ligand titration data produced two conditional stability constants which were not significantly different (see Table 1), which in turn suggests that fitting data to two-ligand model is not reasonable. This is clearly illustrated in Table 1 for the complexing parameters obtained by fitting of titration data obtained by SF and VF and additionally supported by the not significant (NS) difference in variances. In Fig. 1 titration data obtained for all three modes of peak determination are illustrated, where an effect of underestimation of peak intensities by TF mode is obvious. In addition, for TF mode two inflection points are clearly noticeable, indicating virtual existence of two classes of binding ligands.

The appearance of the additional "false" class of ligand in the case of TF is caused by the non-ideal approximation of voltammogram baseline, which is a drawback of this method [START_REF] Pižeta | [END_REF]. Namely, the baseline under the peak is approximated by the straight line. If the position of the peak is on the flat part of the voltammogram, this will not cause significant error in peak height (area) determination. However, if the peak position is on the rising or descending part of the voltammogram (as frequently observed for Zn and Cu in ASV measurements with Hg electrode), the peak height (area) could be extremely underestimated (>50%). Inaccuracy in peak determination is more pronounced at small peak intensities, leading to higher relative errors at lower concentrations. The effect of smaller peak intensity determination at starting part of the titration curve (at low total copper concentrations) caused the appearance of this additional "false" class of ligand in the case of TF.

Two-class ligand (L 1 and L 2 ) simulated titrations

Results of PROSECE fitting of simulated titration data constructed as two-class ligand model are presented in Table 2. Similarly to previous case, TF mode produced unsatisfactory results regarding the accuracy and the precision. As a first, PROSECE fitting with one-class ligand model resulted in underestimation of total ligand concentration (23%), while the fitting with two-class ligand model (the expected one) lead to the overestimation of the con-

Variation of experimental parameters (real samples)

According to our previous study [8], two samples were selected to examine the variation of different experimental parameters, as well as different modes of peak intensities determination, on the determination of copper complexing parameters: S1-sample 1 (salinity 31) and S2-sample 2 (salinity 38). These two samples were selected since in S1 two-class and in S2 one-class of binding ligands were identified in the previous study. Titration by copper was performed in the range from 1 nM to 335 nM of added copper.

The influence of deposition (accumulation) time and equilibration time after addition of copper into the sample were tested on sample 1. Three different analytical conditions were adjusted: (A) 5 min of equilibration time between copper additions and 60 s of deposition time, (B) the same as (A) but with 300 s of deposition time and (C) the same as (B) but with 2 h of equilibration time between copper additions. For all three cases the deposition potential of -0.5 V was used, with a short "desorption step" (3 s) at -1.5 V at the end of accumulation step [START_REF] Bruland | [END_REF]8,10,35], in order to remove adsorbed organic matter from the mercury electrode surface. The deposition potential of -0.5 V was selected according to pseudopolarograms (stripping current vs. deposition potential curves) [8,10], and corresponds to potential where reduction of only reactive/labile copper (inorganic and kinetically labile weak organic complexes) takes place, while strong inert organic complexes are electroinactive. Sixty seconds of deposition time was selected as it is deposition time often used for such kind of measurements [12,38].

In Table 3 complexing parameters obtained by PROSECE fitting are presented. Since for natural samples the number of different classes of binding ligands is not known, the reasonable approach in complexing parameters estimation is to follow guidelines obtained on model titrations. In this manner, complexing parameters obtained by using VF (voltammetric fit) of peak intensities determination were considered as accurate values. In addition, the fitting results for the other two modes of peak intensities determination were provided for comparison and further speciation analysis.

Three different experimental complexation results were obtained from the different experimental procedures. According to F-test, one-class ligand model is assigned to experimental procedures in which equilibration time after copper addition was only 5 min (cases A and B), while two classes of ligands were assigned to data set obtained using 2 h of equilibration time (case C). Taking into account total ligand concentrations assigned to all three cases, the highest value is obtained for the case C (95.6 nM), while only 17.0 nM for the case B. Ligand concentration for case A (34.9 nM) is in-between. Comparing cases A and B (60 s and 300 s accumulation time), an overestimation of the ligand concentration for the case A is a consequence of the poor sensitivity obtained with only 60 s of accumulation time. Although we used the most precise mode of peak intensities determination (VF), underestimation of very low copper signals occurred (for the first few points, the copper peak is not registered at all), which is finally recognized as complexation and resulted in higher ligand concentration. Although one-class of ligand is assigned for the case B, evidently different conditional stability constants for two-class ligand model were obtained (SF and VF), which in turn could serve as an alert for additional systematic analysis of data and/or "request" for repeated measurement.

As in natural samples initial concentration of free/labile copper complexes might be very small, it is important to adjust the measuring procedure in order to accurately determine that value. Higher sensitivity is accomplished by longer deposition time, which should be adjusted according to previously measured total concentration, which should always be known for the studied sample. Those three cases are illustrated in Fig. 2, where relationship of negative logarithms of measured vs. total copper concentrations (pCu labile vs. pCu T ) and corresponding fitting lines are plotted.

Kinetics of metal complexation with natural ligands is controlled by competitive reaction with other divalent cations in the sample [35,39,40]. Although the natural systems are in socalled "dynamic equilibrium", the prediction of metal speciation is performed according to complexation parameters determined assuming equilibrium conditions during measurement. However, in the literature authors reported wide varieties of equilibration time, ranging from only several minutes to overnight equilibration, which subsequently implied suspicion on "at equilibrium" conditions in many studies. In our previous paper, we showed that 2 h is sufficient to reach at least 95% equilibrium after each copper addition [8]. Case C corresponds to this experimental procedure. Following this approach, two-class of binding ligands were determined for the case C, and finally assigned to sample S1. Longer time needed to reach equilibrium is a consequence of slow kinetics of copper complexation which is more pronounced at the middle range of titration curve (see Fig. 2). The highest total ligand concentration (95.6 nM) is determined by this experimental approach.

The variation of experimental procedures is further extended on sample S2 (salinity 38). Again the effect of equilibration time is tested, while in addition, the influence of surface active substance (SAS, 2 mg L -1 of Triton-X-100) is inspected, based on its positive effect registered in solutions with model ligands (EDTA) [41]. For all three procedures, 300 s of accumulation time is applied. Cases D and Similarly as for sample S1, lower total ligand is determined for shorter equilibration time (27.2 nM, case D; comparing to 107.7 nM, case F), which is in line with previous elaboration regarding the kinetics of copper complexation. Addition of T-X-100 to the sample (case E) yielded about 20-30% higher total ligand concentrations comparing to case D. However, to our present knowledge, "3 s desorption step" procedure [10] is enough for reliable results, so for the sake of simplicity in a final procedure it should have the advantage over surfactant addition.

In addition to the presented experimental parameters variation, the influence of three different modes of peak intensities determination for the case F is illustrated in Fig. 3. Although the total concentration of complexing ligands estimated by the tangent fit (TF) and voltammetric fit (VF) is almost equal (108 nM), TF mode produced appearance of additional strong ligand. This anomaly is evident in Fig. 3, where almost one order of magnitude lower free/labile copper concentration is quantified by TF at actual total copper concentration in the sample S2 (4.84 ± nM).

Estimation of free copper concentration

The purpose of the complexation studies is the determination of trace metal speciation in natural aquatic systems. Obtained complexation parameters are subsequently used to predict metal speciation for studied aquatic environment using mathematical modelling software [START_REF] Westall | MINEQL: A Program for the Calculation of Chemical Equilibrium Composition of Aqueous Systems[END_REF][START_REF] Herbelin | FITEQL 4. 0: A Computer Program for Determination of Chemical Equilibrium Constants from Experimental Data[END_REF][START_REF] Tipping | [END_REF][START_REF] Van Der Lee | User's Guide Nr[END_REF][START_REF] Verweij | CHEAQS Pro, Program for Calculating CHemical Equilibria in AQuatic Systems[END_REF]. The concentration of free metal ion is the most examined parameter in toxicological studies, as well as studies regarding bioavailability. Thus, calculation of free copper was performed using complexation parameters given in Tables 1234, in order to show variations in its concentration regarding different mode of peak intensities determination and alterations of experimental setup. MINEQL [START_REF] Westall | MINEQL: A Program for the Calculation of Chemical Equilibrium Composition of Aqueous Systems[END_REF] was used for this purpose. Two levels of total copper (5 nM and 25 nM) were selected, which relate to low level of total copper in examined estuary during non-touristic seasons [8,[START_REF] Omanovi Ć | [END_REF], and increased level occurring during summer season as a result of copper leaching from large number of touristic boats coated by antifouling paint.

In Fig. 4 free copper concentration for simulated titration data sets are presented. Dashed lines represent expected values of free copper for the two simulated cases: one-class of binding ligands and two-class of binding ligands. As a result of appearance of addi- tional class of binding ligand (for one-ligand model) and estimation of higher conditional stability constants (for two-ligand model), free copper concentration calculated by parameters provided by TF mode are strongly underestimated. As expected, a lower relative error in free copper concentration is obtained at higher total copper concentration (25 nM, TF results), because active binding sites at this concentration are partly saturated. Thus, effects of inadequate peak determination are more pronounced at lower copper concentrations. Better results in free copper concentration prediction are obtained by other two modes of peak determination (SF and VF). Generally, a slightly lesser precision and accuracy were obtained for noised simulated data sets. However, free copper concentration predicted by VF mode favourably agreed with expected values.

Alterations in predicted free copper concentration for real samples are presented in Fig. 5a andb. Contrary to simulated case where exact values of free copper concentrations are known, for real samples the most-probable values were considered to be those calculated by using complexation parameters obtained by VF mode and 2-h of equilibrium time. Regarding the different experimental setup, more than one order of magnitude difference in free copper concentration could be calculated. We should highlight again here, that divergences obtained at low level of total copper are not followed at higher copper concentrations. For example for sample S2, for the two modes of peak intensities determination (D and E), very high overestimation of free copper is predicted for 25 nM of total copper due to underestimation of the total ligand concentration, while for 5 nM level, predicted free copper concentrations were around expected (case D) or underestimated (case E) due to overestimation of the conditional stability constants. To keep the consistency of the text detailed elaboration of each separate case is avoided.

Conclusions

Overestimation or underestimation of metal complexation parameters (ligand concentrations and conditional stability constants) is likely to occur if proper data treatment routines and experimental parameters were not respected. It is well demonstrated that fitting of copper titration data (both simulated and experimental) obtained by the tangent fit (TF) mode of peak intensi-ties determination (the most commonly used method) revealed an existence of additional virtual class of strong binding ligand, which actually does not exist. More sophisticated modes of peak intensities determination which take into account curvature behaviour of baseline in the potential range of copper peak appearance (denoted here as spline fit (SF) and voltammetric fit (VF)) are proposed for reliable determination of complexation parameters. The SF procedure has the advantage to be less time consuming than the VF one, but could lead to incorrect results if performed automatically on a set of voltammograms presenting baseline and/or peak shape/position variations, so need to be carefully used. As a supplementary method of signal processing, a first or second derivative could be used, as they are less dependent on voltammogram baseline shape [47]. However, in simple model systems we found that intensities obtained by derivative methods are strongly dependent on half-peak width (which variation is frequent for Cu peak). As the estimation of the signal intensities is a very important subject in voltammetric data treatment and handling, it is a concern of our interest of both theoretical and experimental verification.

In addition to correct data treatment, appropriate experimental parameters which will take into account kinetics of the copper chemistry in real water systems should be strictly followed. Having this as an imperative, accumulation time should be adopted to be sufficient for proper determination of copper electroactive concentrations at its ambient level, while in addition, adequate time for attainment of equilibrium after each copper addition during titration should be secured. An unwanted side effect of inadequate determination of complexation parameters is incorrect prediction of copper speciation, which is more pronounced at lower total copper concentrations.

The following parameters are recommended in order to obtain more reliable copper complexation parameters in estuarine/marine systems using ASV: deposition potential of -0.5 ± 0.1 V, at least 300 s of deposition time including "desorption step" at more negative potential for a short period of time (e.g. 3 s at -1.5 V), at least 2 h of equilibration time after each copper addition, and finally proper peak intensity determination which include the best available method of baseline approximation (voltammetric fit in our case). Unfortunately, this procedure is time consuming (around 20-30 h per sample), and could be partly shortened if aliquots of sample with increasing copper additions were already separately prepared and left to equilibrate overnight. However, the later procedure is more complicated for handling and measurement, with higher contamination risk.

Fig. 1 .

 1 Fig. 1. Influence of different modes of peak intensities determination (TF, SF, VF) on the titration data for simulated one-class ligand model. Solid lines represent PROSECE fit based on F-Test significant model.

  simulated two-class ligand model; P, N = pure, noised data; TF, SF, VF = tangent, spline, voltamogram fit for baseline correction; 1L, 2L = fit to one-class and two-class ligand model; s = standard deviation of fit; F-test (˛= 0.05) S = significant difference, NS = not significant difference. The best fitting is highlighted in bold.

Fig. 2 .

 2 Fig. 2. Titration data for sample S1 obtained for different experimental setup using VF as a mode of peak intensities determination. Solid lines represent PROSECE fit based on F-Test significant model.

Fig. 3 .

 3 Fig. 3. Titration data for sample S2 obtained using different modes of peak intensities determination (TF, SF, VF) for the same experimental setup (2 h of equilibration time and 300 s of accumulation time). Solid lines represent PROSECE fit based on F-Test significant model.

Fig. 4 .

 4 Fig. 4. Free copper concentrations calculated by MINEQL for simulated cases for 5 nM of total copper in the solution (filled symbols) and 25 nM (hollow symbols); circles, triangles -one-class ligand and two-class ligand model simulated titration; P, N -pure and noised data; T, S, V -tangent, spline and voltamogram fit for baseline correction; 1, 2 -PROSECE fit to one-class ligand and two-class ligand model. Dashed lines: expected free copper concentrations for both total copper concentrations and both simulated titrations.

  a TF, SF, VF = tangent, spline, voltamogram fit for baseline correction; 1L, 2L = fit to one-class and two-class ligand model; s = standard deviation of fit; F-test (˛= 0.05) S = significant difference, NS = not significant difference. The best fitting is highlighted in bold.

Fig. 5 .

 5 Fig.5. Free copper concentrations calculated by MINEQL for sample S1 (a) and sample S2 (b) for 5 nM of total copper in the solution (filled symbols) and 25 nM (hollow symbols); Experimental setup: A -eq. 5 min td. 60 s, B -eq. 5 min td. 300 s, C -eq. 2 h td. 300 s, D -eq. 5 min td. 300 s, E -TX eq. 5 min td. 300 s, F -eq. 2 h td. 300 s; T, S, V -tangent, spline and voltammogram fit for baseline correction; 1, 2 -PROSECE fit to one-class ligand and two-class ligand model. Dashed lines: expected free copper concentrations for both total copper concentrations and both samples.

Table 1

 1 Copper complexing capacity parameters as results of different procedures for simulated one-class ligand model a .

		1st ligand				2nd ligand				ligand		s	F-Test
		L1 (nM)	+/-	log KCuL1	+/-	L2 (nM)	+/-	log KCuL2	+/-	LT (nM)	+/-
	S1P-TF-1L S1P-TF-2L	46.8 3.4	3.9 0.0	8.37 10.03	0.04 0.03	50.4	0.4	8.08	0.01	46.8 53.9	3.9 0.4	0.102 0.009	S
	S1P-SF-1L S1P-SF-2L	53.3 31.8	0.7 0.7	7.97 7.98	0.00 0.02	21.6	0.7	8.01	0.03	53.3 53.4	0.7 0.9	0.014 0.011	NS
	S1P-VF-1L S1P-VF-2L	49.3 13.2	0.1 0.1	8.01 8.00	0.00 0.01	36.2	0.1	8.00	0.01	49.3 49.5	0.1 0.1	0.001 0.001	NS
	S1N-TF-1L S1N-TF-2L	46.9 4.6	3.7 0.0	8.37 9.67	0.04 0.01	49.6	0.3	8.03	0.01	46.9 54.2	3.7 0.3	0.088 0.007	S
	S1N-SF-1L S1N-SF-2L	50.2 1.8	1.2 0.2	7.99 8.88	0.02 0.11	49.7	0.8	7.93	0.02	50.2 51.5	1.2 0.8	0.032 0.032	NS
	S1N-VF-1L S1N-VF-2L	49.4 4.0	0.4 0.2	8.01 8.00	0.00 0.04	45.4	0.2	8.00	0.01	49.4 49.4	0.4 0.3	0.014 0.007	S
	Expected	50.0		8.0						50.0	0.0

a S1 = simulated one-class ligand model; P, N = pure, noised data; TF, SF, VF = tangent, spline, voltamogram fit for baseline correction; 1L, 2L = fit to one-class and two-class ligand model; s = standard deviation of fit; F-test (˛= 0.05) S = significant difference, NS = not significant difference. The best fitting is highlighted in bold.

Table 2

 2 Copper complexing capacity parameters as results of different procedures for simulated two-class ligand model a .

		1st ligand				2nd ligand				ligand		s	F-Test
		L1 (nM)	+/-	log KCuL1	+/-	L2 (nM)	+/-	log KCuL2	+/-	LT (nM)	+/-
	S2P-TF-1L S2P-TF-2L	38.4 3.9	2.8 0.0	8.75 11.54	0.00 0.02	46.9	0.6	8.28	0.01	38.4 50.7	2.8 0.6	0.388 0.037	S
	S2P-SF-1L S2P-SF-2L	50.2 3.7	3.9 0.0	8.26 9.71	0.03 0.01	56.0	0.3	7.94	0.01	50.2 59.7	3.9 0.3	0.082 0.006	S
	S2P-VF-1L S2P-VF-2L	47.0 2.9	3.2 0.0	8.24 10.00	0.04 0.01	49.5	0.1	8.00	0.01	47.0 52.4	3.2 0.1	0.098 0.001	S
	S2N-TF-1L S2N-TF-2L	38.3 6.2	6.2 0.1	8.76 10.40	0.12 0.03	49.8	1.1	8.08	0.02	38.3 56.0	6.2 1.1	0.224 0.054	S
	S2N-SF-1L S2N-SF-2L	52.1 6.2	2.3 0.3	8.20 9.00	0.01 0.06	54.9	1.0	7.89	0.02	52.1 61.1	2.3 1.1	0.050 0.029	S
	S2N-VF-1L S2N-VF-2L	47.1 2.8	3.2 0.0	8.24 10.26	0.04 0.04	49.4	0.3	8.02	0.01	47.1 52.2	3.2 0.3	0.104 0.024	S

Table 3

 3 Copper complexing capacity parameters as results of different procedures for sample 1 of salinity 31 a .

	Case		1st ligand				2nd ligand				ligand		s	F-Test
			L1 (nM)	+/-	log KCuL1	+/-	L2 (nM)	+/-	log KCuL2	+/-	LT (nM)	+/-
		Eq5m td 60 s TF-1L Eq5m td 60 s TF-2L	25.5 13.1	3.0 0.6	11.73 12.31	0.04 0.15	30.4	2.4	10.26	0.07	25.5 43.5	3.0 2.5	0.217 0.128	S
	A	Eq5m td 60 s SF-1L Eq5m td 60 s SF-2L	36.7 8.2	2.9 0.1	10.68 12.63	0.05 0.11	35.4	1.1	10.01	0.03	36.7 43.6	2.9 1.1	0.132 0.028	S
		Eq5m td 60 s VF-1L Eq5m td 60 s VF-2L	34.9 33.4	1.0 0.8	10.57 10.60	0.02 0.03	2.2	2.1	9.79	0.30	34.9 35.6	1.0 2.3	0.043 0.043	NS
		Eq5mn td 300 s TF-1L Eq5mn td 300 s TF-2L	18.4 14.0	0.6 0.2	11.00 11.23	0.02 0.02	51.2	7.9	8.81	0.08	18.4 65.2	0.6 7.9	0.041 0.024	S
	B	Eq5mn td 300 s SF-1L Eq5mn td 300 s SF-2L	18.3 16.2	0.6 0.3	10.75 10.83	0.02 0.03	68.4	14.2	8.34	0.10	18.3 84.7	0.6 14.2	0.033 0.026	NS
		Eq5mn td 300 s VF-1L Eq5mn td 300 s VF-2L	17.0 15.9	0.6 0.5	10.73 10.77	0.02 0.04	70.0	49.2	8.03	0.36	17.0 85.9	0.6 49.2	0.042 0.041	NS
		Eq2h td 300 s TF-1L Eq2h td 300 s TF-2L	26.6 11.1	3.0 0.4	10.95 11.85	0.04 0.12	65.7	3.1	9.45	0.03	26.6 76.8	3.0 3.1	0.100 0.029	S
	C	Eq2h td 300 s SF-1L Eq2h td 300 s SF-2L	35.0 7.5	3.5 0.4	10.37 12.06	0.03 0.52	83.0	4.8	9.31	0.04	35.0 90.5	3.5 4.8	0.093 0.054	S
		Eq2h td 300 s VF-1L Eq2h td 300 s VF-2L	74.2 6.7	5.9 0.4	9.84 11.91	0.03 0.39	88.8	3.6	9.40	0.03	74.2 95.6	5.9 3.6	0.085 0.039	S

a TF, SF, VF = tangent, spline, voltamogram fit for baseline correction; 1L, 2L = fit to one-class and two-class ligand model; s = standard deviation of fit; F-test (˛= 0.05) S = significant difference, NS = not significant difference. The best fitting is highlighted in bold.

Table 4

 4 Copper complexing capacity parameters as results of different procedures for sample 2 of salinity 38 a .

	Case		1st ligand				2nd ligand				ligand		s	F-Test
			L1 (nM)	+/-	log KCuL1	+/-	L2 (nM)	+/-	log KCuL2	+/-	LT (nM)	+/-
		Eq5m td 300 s TF-1L Eq5m td 300 s TF-2L	14.8 10.2	0.7 0.1	11.16 11.49	0.04 0.02	25.4	1.1	9.55	0.03	14.8 35.6	0.7 1.1	0.059 0.024	S
	D	Eq5m td 300 s SF-1L Eq5m td 300 s SF-2L	16.8 15.1	0.3 0.2	10.74 10.82	0.01 0.02	95.2	33.1	7.96	0.18	16.8 110.3	0.3 33.1	0.020 0.017	NS
		Eq5m td 300 s VF-1L Eq5m td 300 s VF-2L	20.7 9.2	0.8 0.2	10.60 11.15	0.02 0.04	18.1	1.0	9.85	0.05	20.7 27.2	0.8 1.0	0.044 0.022	S
		TX Eq5m td 300 s TF-1L TX Eq5m td 300 s TF-2L	20.7 9.9	0.9 0.1	11.17 11.84	0.03 0.02	25.1	0.5	9.99	0.02	20.7 35.0	0.9 0.5	0.069 0.017	S
	E	TX Eq5m td 300 s SF-1L TX Eq5m td 300 s SF-2L	19.3 9.5	0.8 0.1	10.94 11.54	0.02 0.03	26.0	0.9	9.75	0.02	19.3 35.6	0.8 0.9	0.050 0.015	S
		TX Eq5m td 300 s VF-1L TX Eq5m td 300 s VF-2L	19.6 11.5	0.8 0.3	11.03 11.53	0.02 0.06	26.1	1.8	9.69	0.04	19.6 37.6	0.8 1.8	0.056 0.036	NS
		Eq2h td 300 s TF-1L Eq2h td 300 s TF-2L	69.7 16.8	7.9 1.3	10.84 11.67	0.04 0.11	91.1	7.1	9.91	0.06	69.7 107.9	7.9 7.2	0.185 0.098	S
	F	Eq2h td 300 s SF-1L Eq2h td 300 s SF-2L	92.5 17.3	4.9 1.3	10.18 10.86	0.02 0.07	95.2	6.2	9.76	0.04	92.5 112.6	4.9 6.4	0.065 0.059	NS
		Eq2h td 300 s VF-1L Eq2h td 300 s VF-2L	107.7 21.6	3.3 3.3	10.02 10.01	0.01 0.12	86.1	3.3	10.02	0.04	107.7 107.7	3.3 4.6	0.041 0.041	NS

Acknowledgements

The financial support of the Ministry of Science, Education and Sports of the Republic of Croatia, under the Project "Interactions of trace metals in aquatic environment" (098-0982934-2720), is gratefully acknowledged. Financial support obtained in the framework of a PHC ECONET (18842QB) program gave the opportunity to organize joined meeting, associated to funds from the ANR MARSECO project used for the acquisition of a part of the used voltammetric equipment, as well as funds from the French Ministry of Education and Research for Y. Louis PhD support are acknowledged.