450

Many trace metals, such as copper (Cu), iron (Fe), cobalt(Co), nickel (Ni), and zinc (Zn), are essential micronutrients tomarine phytoplankton and, as such, may control primary pro-ductivity in large regions of the open ocean. Consequently,these elements have a major influence on the global carboncycle and climate (Morel and Hudson 1985). Primary produc-tivity in uncontaminated systems can be limited by insuffi-

cient trace metals (Martin and Fitzwater 1988), but at theother end of the scale, in heavily contaminated systems, tracemetals can exhibit toxic effects (Moffett et al. 1997). Similarcomments apply to the role of trace metals’ effects on biota infreshwater systems such as lakes and rivers (Worms et al.2006). In all cases, the availability of trace metals to biota isdependent on metal speciation, the chemical form in whichmetals are present (Sunda and Guillard 1976).

The inorganic complexes that metals form in naturalwaters are well known, and their distribution can easily be cal-culated for marine, freshwater, and estuarine systems. It is wellestablished that complexes of trace metals with naturalorganic ligands play a major role in determining trace metalbioavailability (Lewis and Sunda 1978; Batley et al. 2004), withup to 99.9% of bioactive trace metals, such as Fe or Cu, beingbound to organic ligands in the ocean (Gledhill and van denBerg 1994; Rue and Bruland 1995; Moffett and Dupont 2007).Although the presence of organic ligands and their impor-tance to metal speciation is acknowledged, the compositionand source of these ligands remains largely unknown. Theyrange from specific compounds, such as siderophores pro-duced by bacteria to enhance their iron acquisition (Wilhelm

New approach to analysis of voltammetric ligand titration dataimproves understanding of metal speciation in natural watersMona Wells1, Kristen N. Buck2, and Sylvia G. Sander1,3*

1Department of Chemistry, University of Otago, PO Box 56, Dunedin, New Zealand2Bermuda Institute of Ocean Sciences, 17 Biological Station, Ferry Reach, St. George’s, Bermuda GE 013NIWA/University of Otago Research Centre for Oceanography

AbstractIn this study, previously published multiple analytical window datasets of competitive ligand exchange–adsorp-

tive cathodic stripping voltammetry titrations for dissolved copper with salicylaldoxime as the competing ligand werereanalyzed. A new numerical method was applied, the Sander-Wells (S-W) method, which is able to simultaneouslyanalyze multiple analytical window titrations as a unified dataset and calculate parameters for one to three ligandclasses in the samples. The two datasets used were from separate sampling events at Dumbarton Bridge, San FranciscoBay. The aim of this study was to see if discrete ligand classes can be resolved from these data, and how these com-pare with results obtained by applying commonly used manual calculations of individual analytical window titra-tions separately: Scatchard and van den Berg/Ružić linearizations, and the Gerringa non-linear regression. The unit-ed multiple analytical window dataset could only be analyzed simultaneously by the S-W method, and two or threediscrete ligand classes were resolved for each sample. Applying the four different data analysis methods independ-ently to each of the five analytical windows resulted in solutions spanning a continuum of conditional stability con-stants and ligand concentrations. It was shown that the sensitivity S, as well as data structure and iterative optimiza-tion, are the major reasons for different results. This study demonstrates the utility of simultaneous analysis of mul-tiple analytical window titration curves to better determine the distribution of trace metal species in aqueous systemsand the advantages of adopting such a ‘unified data set’ approach over fitting individual titration curves.

*Corresponding author: E-mail: sylvia.sander@otago.ac.nz;Phone: ++64 3 479 7844

AcknowledgmentsThis work was supported by Research Grants from the University of

Otago and the Ministry of Business, Innovation and Employment, NewZealand via a subcontract with the National Institute of Water andAtmospheric Research. K. Buck was supported at the Bermuda Instituteof Ocean Sciences (BIOS) by a CALFED Bay-Delta Science Fellowship,project R/SF-32, through the California Sea Grant program; this manu-script is BIOS contribution number 2015. We thank the two anonymousreviewers for their very insightful and constructive comments, whichgreatly improved the paper; and Birthe Kortner for her critical reading ofthe manuscript at its final stage.

DOI 10.4319/lom.2013.11.450

Limnol. Oceanogr.: Methods 11, 2013, 450–465© 2013, by the American Society of Limnology and Oceanography, Inc.

LIMNOLOGYand

OCEANOGRAPHY: METHODS

et al. 1996, 1998; Mawji et al. 2008; Homann et al. 2009;Velasquez et al. 2011; Vraspir and Butler 2009), over phy-tochelatins produced by organisms upon toxic metal exposure(Ahner et al. 1995; Ahner and Morel 1995; Dupont et al. 2004;Kawakami et al. 2006a, 2006b), to bioremineralization prod-ucts like humic substances (Xue and Sigg 1999; Laglera andvan den Berg 2009) and exopolymeric substances (EPS, Hassleret al. 2011).

Speciation is determined by the binding capacity of a lig-and for a specific metal of interest. Binding capacity, in turn,is governed by the total ligand concentration, and the condi-tional stability constants of the metal-ligand complexes,which are commonly indirectly measured by means of a com-plexometric metal-ligand titration followed by electrochemi-cal detection (for an example of a ligand titration, see Figs. 1Aand E) (Town and Filella 2000; van den Berg 1985). Twovoltammetric stripping methods are most frequently used:competitive ligand exchange–adsorptive cathodic strippingvoltammetry (CLE-AdCSV) and anodic stripping voltammetry(ASV) (Bruland et al. 2000; Bruland and Rue 2001). Pseudopo-larography and Reverse Titration (RT) CLE-AdCSV had beenintroduced in the past but recently received new attention forcases where the CLE-AdCSV and ASV methods are limited(Gibbon-Walsh et al. 2012; Hawkes et al. 2013). However,much controversy has been sparked in the past by the wayparameters reflecting binding capacity are calculated, includ-

ing how many ligands or classes of ligands can or should bereported (Hudson et al. 2003; Sander et al. 2011; Ibisanmi etal. 2011).

Early works of van den Berg introduced a linearized form ofa Langmuir isotherm that plots an approximated free metalconcentration [Mf] against the ratio [Mf]/[ML], where [ML] isan estimate of the metal-natural organic ligand complex, and[Mf] is estimated using an experimental voltammetric sensi-tivity S. This plot is commonly known as the van denBerg/Ružić plot (Ružić 1982; van den Berg 1982). When oneligand is present, a straight line is observed (see Fig. 1B); linearregression of this plot yields the total ligand concentration,[LT], as the reciprocal of the slope and the conditional stabilityconstant of the metal complex, , as the slope divided bythe intercept. Another linear representation of the data are theScatchard plot, in which [ML] is plotted against [ML]/[Mf] (seeFig. 1C), and the parameters [LT] and correspond to thex-intercept and slope, respectively, from linear regression(Scatchard 1949; Ružić 1982).

A nonlinear form of the Langmuir isotherm is commonlyknown as the Gerringa plot, shown in Fig. 1D (Gerringa et al.1995), in which [Mf] is plotted against [ML] such that [LT] and

may be determined from non-linear curve fitting. Ger-ringa et al. (1995) performed a comparison between the vanden Berg/Ružić and the Gerringa method with a specificemphasis on understanding the error structure. They con-

K cond

ML

K cond

ML

K cond

ML

Wells et al. Voltammetric copper-ligand titration analysis

451

Fig. 1. Diagram showing representative simulated experimental data of ligand titration curves for analysis of one (panel A) and two (panel E) discreteclasses of natural organic ligands present. Remaining panels illustrate common approaches to data analysis for one (B-D) and two (F-H) ligands using thevan den Berg/Ružić linearization (B and F), Scatchard linearization (C and G), and the Gerringa non-linear method (D and H) and first approximation ofparameters from these transformations (Scatchard 1949; Ružić 1982; van den Berg 1982; Gerringa et al. 1995). Red curves in Panel A and D representtitration data in the absence of a ligand with S being the slope of this linear relationship.

cluded that for the error structure found for voltammetriccomplexometric titrations, wherein outliers are to be expecteddue to the presence of surface-active organic matter, theirnonlinear method would be preferred.

Analysis of experimental data by the foregoing three meth-ods becomes difficult when two or more ligands are present insolution, particularly if the conditional stability constants ofthe ligands are not well resolved (Ibisanmi et al. 2011; Sanderet al. 2011). The van den Berg/Ružić and Scatchard plots can beanalyzed using two linear regressions, with the slopes andintercepts of both regressions again providing the total ligandconcentrations and conditional stability constants, [LiT] and

, respectively. The subscript i denote the number of dis-crete ligands (one or two). By convention values of areranked by i, with i = 1 denoting the strongest binding class (seeFigs. 1F and G). However, the weaker ligand L2 is biased by thepresence of the stronger L1 and an iterative approach is used tocompensate for this bias (Laglera and van den Berg 2003).Ibisanmi et al. (2011) introduced a way to distinguish betweenthe L1 and the sum of ligands for the nonlinear Gerringamethod (see Fig. 1H). Parameters fitted for two or even moreligands from one and the same CLE-AdCSV titration can differconsiderably for any of these commonly applied methods.Thus, for one sample with a specific composition of metals,organic ligands, and inorganic constituents, different answersmay be found depending on how the titration is interpreted,and it is debatable which result is describing the sample moreaccurately, and how results can be compared when differentinterpretation methods are used throughout the research com-munity. Interpretation of the data are a key component of theanalysis, yet remains poorly understood. Another potentialsource of error is the sensitivity S, which is needed to derive theintermediate quantity [Mf], from which [LiT] and aredetermined (Hudson et al. 2003).

In the past 10 years, there have been several attempts toaddress these problems. Hudson et al. (2003) introduced a newapproach that employs an analytical solution to achievesimultaneous estimation of [LiT] and for i discrete ligandclasses and the sensitivity S, using nonlinear regression (theirtreatment and simultaneous solution of parameters with a sin-gle S has previously been referred to as “unified,” Sander et al.2011). In enabling simultaneous analysis of all data in onestep, the Hudson et al. (2003) approach greatly reduced prop-agation of error and provided increased accuracy by using thefull data structure. Hudson et al. (2003) demonstrated thispoint via simultaneous analysis of data from replicate titra-tions conducted at multiple analytical windows, an approachthat had not been previously demonstrated.

Since the Hudson et al. (2003) approach was analytical, itwas limited in practice to the determination of two discreteligand classes, as an analytical solution to describe more eitherdoes not exist or is not commonly known. Recently, a newnumerical implementation has been developed for Cu specia-tion analysis that enables simultaneous analysis of multi-win-

dow data and has the demonstrated capability to determine[LiT] and for up to i = 5 ligand classes while simultane-ously calculating Cu speciation (Sander et al. 2011). Theapproach, here referred to as the Sander-Wells (S-W) method,was originally validated using simulated data with realisticnoise (i.e., comparable to actual voltammetric measurements),as well as limited experimental data. The S-W method wasdemonstrated to be more accurate and precise than othermanual approaches in common use by systematically com-paring results for simulated data produced to evaluate the uni-fied multiple analytical window approach. A comparison ofthe S-W method with the other unified multiple analyticalwindow approach described in Hudson et al (2003) resulted invery similar parameters of, LiT, and S (Hudson et al. 2003;Sander et al. 2011).

In the present study, we take the next step of applying theS-W method to titration data from real samples. We chose pre-viously published titrations of two samples from DumbartonBridge, San Francisco Bay, California, USA (Buck and Bruland2005) that had been analyzed for copper speciation by CLE-AdCSV using five analytical windows windows, non-simulta-neously. Here we demonstrate simultaneous solutions toparameter estimation for the multiple analytical windowdataset using the S-W method for the maximum number ofligand classes detectable; we also compare results of the S-Wmethod to those calculated in the original paper (using theScatchard approach, Buck and Bruland 2005), and by the com-monly applied van den Berg/Ružić and Gerringa methods, allthree of which analyze one analytical titration window at atime.

Materials and proceduresThe theory behind the equilibrium of a metal with one or

more organic ligand classes in a natural aqueous system, aswell as the different analytical methods of van den Berg/Ružić,Scatchard, Gerringa and Sander-Wells, have been describedpreviously (Scatchard 1949; Ružić 1982; van den Berg 1982;Gerringa et al. 2005). However, as the nomenclature is some-what inconsistent in the literature, the theory and data analy-sis methods are summarized here in brief, providing a coher-ent resumé of the basics needed to interpret and applymetal-ligand titrations. A glossary of terms and abbreviationsused here is provided in Appendix A (Table A1).Conditional equilibrium of one metal with one organic lig-and in solution

The complexation of a metal, M, with an organic ligand, L,in a natural aqueous system can be described with the follow-ing expressions:

(1a)

and

(1b)

K cond

iML

+ ← →⎯⎯ ′M Y MKf IN

IN

Lii

1

∑

K cond

iML

K cond

iML

K cond

iML

K cond

iML

+ ′← →⎯⎯M L MLKf

MLcond

Wells et al. Voltammetric copper-ligand titration analysis

452

where YIN represents an aggregate of major inorganic ligands(such as Cl–, OH–, and CO3

2–) that form complexes with thefree metal ion Mf, and M′ represents the aggregate of inorganiccomplexes formed. The term L′ represents the natural organicligand not complexed with the metal, and is referred to as anaggregate species since its actual nature is indeterminate.Thus, the speciation of a metal in a sample containing onenatural organic ligand can be described as

[MT] = [M′] + [ML] + [Mf] (2)

where square brackets denote concentration, and the subscriptT denotes total dissolved.

For the complex ML, the conditional stability constant is

(3)

where

[L′] = [LT] – [ML] (4)

The superscript “cond” stands for conditional and indicatesthat the constant is valid for the natural aqueous matrix (e.g.,sea-, fresh-, or estuarine water) in which the metal is present.

A side reaction coefficient, αML, can be defined as

(5a)

or alternatively as

(5b)

and combining Eqs. 3, 4, and 5a and rearranging yields

(6)

Conditional equilibrium in the presence of more than oneorganic ligand

For a system with more than one discrete natural organicligand class (i.e., L1, L2, …Li), where L1 denotes the stronger lig-and class measured and L2, L3, etc. the progressively weaker lig-and classes, the above expressions (Eqs. 1–6) need to beadjusted. Specifically, Eq. 2 becomes

[MT] = [M′] + [ML1] + [ML2] +. [MLi] + [Mf] (7)

Competitive exchange with an added known ligandComplexometric metal-ligand titrations for environmental

samples were first used by van den Berg (van den Berg 1982)and Ružić (1982). They are based on the assumption that nat-ural organic ligands form 1:1 complexes with metals. Thequantification of the complexes of L1 – Li with M requires the

presence of an analytically accessible species. For natural sam-ples with relatively low metal concentrations, voltammetryhas mainly been used (van den Berg 1985; Bruland 1989,1992; Bruland et al. 2000). For Zn, Cd, Pb, and Cu anodicstripping voltammetry can be used directly to quantifyorganic complexation (Xue and Sigg 2002). However CLE-AdCSV is now most frequently employed in complexometricligand titrations.

CLE-AdCSV requires the addition of a well characterizedcompetitive added ligand (AL) that forms an adsorbable andelectroactive complex of the stoichiometry 1:x with the metalunder investigation at the surface of a mercury drop electrode.The equilibrium expression

(8)

describes metal complexation with AL to form thecomplex(es) M(AL)x. For a natural sample with organic lig-ands, L1, L2, …Li amended with AL, Eq. 7 becomes

[MT] = [M′] + ∑i([MLi]) + [M(AL)x] + [Mf] (9)

The side reaction coefficient αM(AL)x can be calculated fromthe AL not bound to M (i.e., [ALf]) and the known stabilityconstants of AL per

(10)

where is the stability constant of the 1:1 complex of ALwith M conditional for the sample matrix, and is therespective conditional stability constant of the 1:x complex.This then provides a compact way to relate Mf to the elec-troactive species M(AL)x via

(11)

For this work, values for K and β in Eq. 10 using salicylal-doxime (SA) are calculated according to relationships derivedby Campos and van den Berg (1994) with log = 10.12 –0.37 log(salinity) and log = 15.78 – 0.53 log(salinity).Relating experimental observables to theory

A combined side reaction coefficient is often referred to forCLE-AdCSV titrations:

α′ = α′inorg + αM(AL)x + 1 (12)

where α′inorg is the side reaction coefficient for formation of theaggregate complexes M′,

(13)

and the constant 1 reflects contributions from [Mf]. The valueof α′ determines the so-called analytical window of a titration.For CLE-AdCSV, the analytical window is defined by the

s ruuuu ( )+β

x xM AL M ALfALx

K[AL ] +[AL ] +...+[AL ]x

x

M(AL) f MAL

cond

f M(AL)

cond

f

M(AL)

cond

x2

2α β β= ⋅ ⋅ ⋅

KMALcond

βM(AL)�cond

x

M(AL) Mx M(AL) fx

α⎡⎣ ⎤⎦ = ⋅⎡⎣ ⎤⎦

K1

cond

2

condβ

'M '

Minorg

f

α =

K = [ML]

[M ][L']

cond

fML

= [ML]

[M ]ML

f

α

K= [L']ML ML

condα

K

K=

[L ]

(1+ [M ])ML

ML

cond

T

ML

cond

f

α

Wells et al. Voltammetric copper-ligand titration analysis

453

amount of AL. In other words, as more competing ligand isadded, AL progressively outcompetes natural ligands for themetal (the weakest binding ligand being outcompeted firstand the strongest last as [AL] increases). A rule of thumb existsthat states that logαMLi should be within ± 1 of log αM(AL)x inorder for the parameters associated with αMLi (i.e., and[LiT]) to be determinable for a given amount of AL, definingthe term analytical window (van den Berg et al. 1990, Xue andSigg 2002). Because generally the total concentration of metal,[MT], is small compared with [YIN] and [ALT] added for a titra-tion, YIN and AL remain largely uncomplexed. This entails thatthe combined side reaction coefficient α′ stays nearly constant(van den Berg et al. 1990), which, in turn, means that the ana-lytical window applied to a given sample needs to be adjusteddepending on, and in anticipation of, the total natural ligandconcentration and its conditional stability constant with themetal. However, it should be noted that for analytical win-dows with a low [ALT] this assumption, i.e., [ALT] ~ [ALf], nolonger holds.

The electroactive species in an AdCSV scan, [M(AL)x] is pro-portional to the measured peak current, IP, according to

IP = f(S) [M(AL)x] (14)

where f(S) is a function of the sensitivity, S, of the mea-surement.

Substituting 11 into 14 yields

(15)

Conventionally, S is obtained by linear regression of IP ver-sus [MT] at the highest metal additions (‘simple’ internal cali-bration = SSIC). At these concentrations, the sample matrix,including the presence or absence of surface active substances,or weak organic ligands that are not fully titrated within oneanalytical window, have little or an invariant effect on thevoltammetric signal. Hudson et al. (2003) discussed differentways of deriving other complimentary forms of S, such as onefor a UV digested sample (SUV), or at very high AL (SOV).Whichever form of S is applied for a specific analytical win-dow titration, it can be used to obtain an estimate of [Mf], andthereby [MLi], the quantities that are needed for manually esti-mating the complexing parameters and [LiT] via estab-lished methods such as the van den Berg/Ružić or Scatchardlinearization and the non-linear Gerringa method (see Fig. 1).Methods of data analysis

For only one organic ligand present, the van den Berg/Ružićlinearization (Ružić 1982; van den Berg 1982) is described by

(16)

Assuming that [ALf] ≈ [ALT] and that at high values of added

metal ∑(MLi) << [M(AL)x] + [M′] + [Mf], it follows that [MT] ~ α′⋅ [Mf], which enables estimation of [Mf] from experimentaldata, through Eq. 15.

Then [ML] is obtained as [MT] – α′ ⋅ [Mf]. By plotting [Mf]versus [Mf]/[ML] it follows that [LT] is the reciprocal of theslope of the linear regression of the plot and 1/ is the x-intercept of this plot (see also Fig. 1B).

The method known as the Scatchard linearization (Ružić1982; Scatchard 1949) uses the same quantities ([Mf] and [ML])estimated as described for the van den Berg/Ružić lineariza-tion, and employs the following form of the equilibrium equa-tion:

(17)

By plotting [ML] against [ML]/[Mf], the negative slope ofthis plot yields and the x-axis intercept is [LT] (see Fig.1C).

The non-linear Gerringa equation (Gerringa et al. 1995) canbe derived from substituting Eq. 4 into Eq. 3 and rearrangingto obtain

(18)

Plotting [ML] versus [Mf], and [LT] can be obtained bynon-linear fitting of the data (see Fig. 1D).

While Eqs. 16–18 assume the presence of only one ligandin a sample, the commonly used models for CLE-AdCSV dataanalysis (e.g., van den Berg/ Ružić and Scatchard lineariza-tions, Gerringa non-linear fit) described above can theoreti-cally also be applied to two ligand systems (see Fig. 1E-H),although the quality of the resulting parameters is question-able (Ibisanmi et al. 2011; Sander et al. 2011). The under-standing that the stability constants of the stronger andweaker ligand need to be separated by two orders of magni-tude to be successfully resolved stands in conflict with therule-of-thumb that complexes can only be determined accu-rately if their respective side reaction coefficients are withinone order of magnitude of the α′ employed (van den Berg etal. 1990; Xue and Sigg 2002). Thus, if both rules are indeedvalid, it is almost impossible to accurately determine twounknown ligands in a system by performing only one titrationat a given competitive added ligand concentration. Conse-quently, Campos and van den Berg (1994) and Moffett (1995)started to perform titrations at different [ALT] to address thisissue. Later Hudson et al. (2003) introduced the practice ofperforming multiple titrations at different analytical windowsand simultaneously estimating and [LiT] for i = 1 and i =2 discrete natural ligands, as well as a unified sensitivity for allanalytical windows (SUNI). SUNI is based on RAL = S

UV([ALT])/ ,where is the sensitivity in the UV digested sample at thehighest [ALT], and the term RAL is a factor that explicitlyreflects the window-dependent variation in sensitivity. Hud-

K cond

ML

K[ML]

[M ][ML] K [L ]

f

ML

cond

ML

cond

T= − +

K cond

ML

K

K[ML]

[M ][L ]

1 [M ]

ML

cond

f T

ML

cond

f

=+

K cond

ML

K cond

iML

SUV0

SUV0

K cond

iML

I f S MP M AL f

x

α( )= ⎡⎣ ⎤⎦( )

K cond

iML

K

[M ]

[ML]

[M ]

[L ]

1

[L ]

M AL xf f

T

( )

T ML

cond

α= +

+

Wells et al. Voltammetric copper-ligand titration analysis

454

son et al. (2003) demonstrated that substantial reduction inparameter error could be achieved via use of this approach.

Another method by Sander and Wells (S-W) (Sander et al.2011) is designed for analysis of multi analytical window datawith the unified S (SUNI) introduced by Hudson et al. (2003).The approach is numerical and also calculates speciation,based on Morel Tablature (Morel and Hering 1993). Thisapproach relates the concentration of all species in the systemto mass balances via

AT c = t (19)

where AT is the transpose of a matrix that expresses speciesreaction stoichiometry in terms of principal components(Morel Tableau; Morel and Hering 1993), c is a vector of allspecies concentrations (i.e., [ALf], [Mf], [L′], [MLi], [M(AL)x],[M′]), and t is a vector of sums of total component concentra-tions (i.e., [ALT], [MT], [LiT]). The vector c is given by

c = 10K+Ax (20)

where K is a constant vector whose elements are , ,and α′inorg.

The Sander-Wells approach is automated in a MATLABapplication (MathWorks) that is primarily comprised of a two-stage optimization sequence. This approach entails first sup-plying known inputs (IP, [MT], [ALT], , and α′inorg) and aninitial guess for the parameters to be determined ( , [LiT],and SUNI). Next, x, the vector of all component concentrationsin the system, is optimized (i.e., Eq. 20 is substituted into Eq.19 and the x that best resolves the resulting equation isobtained. Using x, c is calculated to obtain species concentra-tions (Eq. 20), and species concentrations in c are used in asecond optimization step, which finds new optimized valuesof , [LiT], and S

UNI associated with c. The two optimizationsteps are iteratively repeated until one of three program ter-mination conditions occurs: 1) a user specified root-meansquared error (RMSE) function (EF, see Eq. 22) betweenobserved and calculated IP is attained, 2) parameters becomeinvariant to > 4 significant figures, or 3) a user-specified max-imum iteration number is reached.

The numerical optimization techniques used are discussedin Sander et al. (2011); a notable feature is that the programemploys a genetic algorithm to transform the initial guess val-ues into a new, optimized, but randomized initial guess thatwill be different for repeated runs of the same data. Thus, evenfor the same user-specified initial guess input the final resultwill not necessarily be identical. Ward et al. (2010) havedemonstrated the power of this approach for parameter opti-mization of underdetermined environmental models (Ward etal. 2010). As reported in our initial work (Sander et al. 2011),commonly used manual fitting methods (such as theScatchard, van den Berg/ Ružić, and Gerringa method) willproduce the same result on repeated calculations if the same

initial guess values are used (i.e., parameters are stable). How-ever, in underdetermined cases, the results may be nonethe-less incorrect (Sander et al. 2011). For the S-W method, as aresult of the genetic algorithm, the stability of results fromreplicate calculations are a useful means to assess the ade-quacy of the experimental data for obtaining useful results.Unstable results, i.e., results for which the values of the param-eters , LiT, and S

UNI differ greatly on replicate calculation,are an indication that the data structure is unsuitable forparameter determination, and hence that the accuracy of cal-culated parameters should be viewed with skepticism (Sanderet al. 2011).Back calculating curves using fitted parameters as a qual-ity assurance mechanism

Determination of and LiT using any of the above fourmethods of data analysis requires approximations. For thevan den Berg/Ružić, Scatchard, and Gerringa methods theapproximations are mentioned above, and the S-W method,being numerical, is inherently an approximation. For anygiven set of values for and LiT, however, the speciationin an aqueous system can be calculated exactly, withoutapproximation. This also enables calculation of the exactexperimental observables that correspond to a givenand LiT – i.e., the exact speciation corresponding to estimatedparameters is used to determine the exact current response,IP

calc, expected from the estimated parameters. The relativepercent difference (RPD, decimal) between predicted andexperimental data are then

(21)

Values of RPD are used to calculate an error function (asused in Sander et al. 2011) according to

(22)

where nm is the number of titration data points (m), and np isthe number of parameters (p). The denominator (nm – np), oth-erwise known as the degrees of freedom (df), normalizes thetotal error to the df, as is typically seen in many statisticalexpressions, including standard deviation. As the df accountsfor both the number of experimental data points (more beingstatistically robust) and the number of parameters (more lead-ing to increasing underdetermination or increasing solutioncollinearity), this ensures a metric wherein a one-ligand modelcan be compared to any multiple-ligand model with the sameEF, and thus can be used as an objective tool to determine thenumber of ligand classes present. In a two ligand class systema two ligand solution has the lowest EF compared to a one orthree ligand solution.

K cond

iML

K cond

iML

K cond

iML

K cond

iML

I I

I IRPD

2

P

calc

P

P

calc

P

( )( )

=−

+

RPD

n nEF i

m

m

m p

1

2∑=

−=

K cond

iML

K cond

xM(AL)

K cond

xM(AL)

K cond

iML

K cond

iML

Wells et al. Voltammetric copper-ligand titration analysis

455

The quantity IPcalc needed to determine the EF is obtained

according to

IPcalc = SUV ⋅ RAL ⋅ α′ ⋅ [Mf]

calc (23)

where [Mf]calc is the free metal concentration calculated from

the fitted/estimated parameters and LiT. For this work, weuse values of RAL as per Sander et al. (2011) and originallydescribed by Hudson et al. (2003). For the simultaneous analy-sis of all data using the S-W method, SUV and RAL is used as theinitial guess and then optimized SUNI as one of the parameters,as described in Hudson et al. (2003) and Sander et al. (2011).

For the Scatchard, van den Berg/ Ružić, and Gerringa meth-ods applied to one- or two- ligand models for single analyticalwindow titration curves we used two different approaches forS. 1) The sensitivity was used as described in Buck and Bruland(2005), wherein SUV was determined in the UV digested sam-ples at pH 8 and subsequently adjusted by RAL as appropriateto each window. 2) The S-W optimized was used for a bet-ter comparison with the results from the S-W method.Data sources used for method comparison

Buck and Bruland (2005) published a study on organic Cuspeciation in San Francisco Bay, California, USA, for whichthey performed CLE-AdCSV multiple analytical window titra-tions. Here, we use the raw CLE-AdCSV titration data recordedfor the Dumbarton Bridge sampling site sampled in Januaryand March 2003 (Buck and Bruland 2005), as these were theonly samples for which multiple analytical window ligandtitrations were performed in the presence of five different SAconcentrations, our desired level of data structure for testing(Sander et al. 2011). Details of the sample location, sample col-lection and CLE-AdCSV method used are described in Buckand Bruland (2005). Briefly, samples were collected, filtered(0.45 μm), and processed under trace metal clean conditions.Samples were stored in the dark at ~ 4°C until analyzed,within 6 d of collection. Total dissolved Cu concentrationswere determined by standard addition after UV digestion (2hours) at ambient pH and subsequent addition of 25 μM SA(final concentration). Recently, Cu-spike recovery experimentsand analysis of dissolved Cu concentrations in SAFe samplesconfirmed the suitability of the UV digestion at ambient pHfor total dissolved Cu analyses (K. Buck unpubl. data). For theligand titrations, dissolved Cu was added to up to nine vialsand a maximum added Cu of 350 nM before analysis atapproximately 1, 2.5, 10, 50, and 100 μM SA (Buck and Bru-land 2005). In some of those original titrations, a combinationof nonlinearity in peak heights above ~ 800 nA and limita-tions in sample volume resulted in only 4-8 usable data pointsin the titrations instead of the 11 intended (Buck and Bruland2005, Fig. 2). That shortage of titration points in some casesrestricted interpretation of those data both in the originalpublication and in this comparison of previously published,commonly employed and newly developed interpretationapproaches outlined here.

Assessment

Analysis of one to three ligand classes using multiple ana-lytical windows

The complete dataset for each Dumbarton Bridge sample(January and March) consists of five titration curves generatedby distinct analytical windows (see Fig. 2 and Table 1). Thedata have not previously been interpreted as a whole, withsimultaneous solution for a single set of parameters that bestdescribe the data structure reflected in titrations using all fiveanalytical windows together. Buck and Bruland (2005)reported up to 2 ligand classes per analytical window using theScatchard and van den Berg/Ružićmethods from each windowseparately, as is conventionally done (Campos and van denBerg 1994; Moffett et al. 1997; Bruland et al. 2000). The resultsfrom that analysis could be interpreted as 8 different ligandclasses per interpretation technique per sample, with a con-tinuum of conditional stability constants ranging fromlog of 14.5 and 14.6 to log of 10.6 and 10.5 for Jan-uary and March, respectively (see Buck and Bruland 2005,Table 4 therein). Buck and Bruland (2005) did not interpretthe data in this way, but instead chose a single analytical win-dow from which to report final results. However, this high-lights the incomplete nature of conventional interpretationtechniques for multiple analytical window datasets, as well asthe potential inadequacy of single analytical windowapproaches alone.

Table 1 and Fig. 2 show the results of applying the S-Wmethod to the Buck and Bruland (2005) dataset. When analyz-ing the complete multiple analytical window dataset for onlyone ligand class, both the visual comparison of IP with IP

calc andthe EFs are not satisfactory, indicating that a one-ligand modelis inadequate for this data set (Fig. 2A and D). When analyzingfor two ligand classes, the EFs are lower, and for both samples(e.g., January and March), the parameters and arewell-resolved (i.e., greater than two orders of magnitude differ-ence in value). Solving for three ligand classes the S-W methodagain returns three well-resolved ligand classes and similar EFsas the two-ligand model. For January, the EF associated withthe three-ligand results is slightly higher than that for two lig-ands. Close visual inspection of this experimental data showsthat the curves are less smooth/more erratic than those forMarch, and the EF associated with the three-ligand model forMarch is, to three decimal places, actually just lower than thatfor the two-ligand model. Because the EF is normalized to thenumber of parameters, (see Eq. 22) errors can be compared forone, two, and three ligand solutions. Thus, for March, the EFsuggests that a three-ligand model may be more appropriate todescribe the system.

Interestingly, for both January and March, the parametersand [L1T] are the same, within uncertainty, for the three-

ligand model as those obtained for the two-ligand case. Com-paring the three- and two-ligand models, the maximum dif-ference in and [L1T] values between the three-ligand and

K cond

iML

SRAL

calc KML

cond

2

KML

cond

1

KML

cond

2

KML

cond

1

KML

cond

1

KML

cond

1

Wells et al. Voltammetric copper-ligand titration analysis

456

two-ligand class models are 1% and 8%, respectively. ForMarch, a third very weak ligand class, [L3T], can be identifiedbased on the EF, whereas for January, the presence of this lig-and is only putatively suspected (given the data limitations for

the three-ligand analysis) based on comparison with theMarch results. The values for January and March differby only 6%, suggesting that [L3T] might be a very specific lig-and class. For [L3T], values are much higher in March than in

KML

cond

3

Wells et al. Voltammetric copper-ligand titration analysis

457

Fig. 2. Multi-window titration curves for January (A-C) and March (D-F) Dumbarton Bridge samples (circles) and the titration curves calculated usingcomplexation parameters obtained from data analysis using the S-W method for one (A and D), two (B and E), and three (C and F) ligand classes(squares). Resulting parameters and EF values are given in the legend. Gray shades distinguish different analytical windows, from window 1 ([SAT] ~ 100μM) being black to window 5 ([SAT] ~ 1 μM) being white. The dashed lines connect the calculated data points for each window.

Table 1. Results from analyzing all data for multi-window Cu titrations* of Dumbarton Bridge samples from January and March 2003,for one, two, or three ligand classes using the S-W method.*

log [L1T]† log [L2T]

† log [L3T]† EF‡ pCu§ SUNI||

January 20031 ligand 12.6 74 — — — — 0.46 12.68 5.22 ligands 14.6 43 11.8 81 — — 0.35 14.07 6.03 ligands 14.6 43 11.7 79 8.8 167 0.37 14.06 5.9

March 20031 ligand 13.1 66 — — — — 0.29 13.26 5.12 ligands 14.7 27 12.2 78 — — 0.19 13.69 6.33 ligands 14.7 27 12.2 72 8.3 882 0.19 13.62 6.2

*Values of [SAT] (μM) for January are 99.5, 49.8, 9.7, 2.4, and 0.94 for windows 1-5, respectively, and for March are 101.4, 50.7, 10, 2.5, and 0.97 forwindows 1-5, respectively.†All [LiT] are given in nM.‡np for is 3, 5, or 7 for one, two, or three ligands, respectively (see expression 22).§pCu = –log[Cu2+] calculated from ambient [CuT] in samples, i.e., 33.7 nM and 27.0 nM for January and March, respectively.||SUNI is the optimized sensitivity unified for all windows.

KCuLcond

1KCuL

cond

2KCuL

cond

3

January, which may relate to the occurrence in March of alarge phytoplankton bloom (Buck and Bruland 2005). Such alarge phytoplankton bloom may have resulted in additionalorganic ligands from the degradation of dead biota and/orsmall organic bio-molecules such as dissolved amino acids andoxalic acid (Sillen and Martell 1971).

The reference sensitivity SUV used for the analysis of thisunified multi detection window dataset is based on that in theUV digested sample at [SAT] = 25 μM. SUV = 6.9 and 7.8 nA/nMfor January and March, respectively. However, the unified,optimized SUNI found by the S-W method are 5.2 and 5.1nA/nM for the one-ligand model, 6.0 and 6.3 nA/nM for thetwo-ligand model, and 5.9 and 6.3 nA/nM for the three-ligandmodel for January and March, respectively. Interestingly SSIC

for the highest window was 5.1 and 5.6 nA/nM for Januaryand March, respectively, which is between the SUV and the SSIC

for this titration data set.Analysis of five individual analytical windows for one lig-and class using different methods

In the past, ligand titration data have often been fitted foronly the strongest detectable ligand class, especially if the freemetal concentration rather than the ligand concentration wasthe focus of the study (e.g., Moffett and Brand 1996, Tian etal. 2006). If individual titrations are evaluated, the data struc-

ture of titration data points (i.e., typically 8-10) is often pro-hibitive to solving for more than one ligand, as over-parame-terization makes the results statistically unsound. To avoidthis problem, the number of data points per titration must beat least double the number of parameters fitted, i.e., 6 for oneligand fits (i.e., three parameters: [L1], , and S), or for twoligands (five parameters: [L1], , [L2], , and S), it needsto be 10 data points. However, ideally the number of datapoints should be more than 10 of one titration. It should benoted here that S is also a parameter irrespective of the fittingmethod used.

In this comparison, we have applied all four methods toeach detection window titration using a one-ligand model, asit is often done by researchers working in this field. The datawere fitted, where technically possible, for only one ligandclass per analytical window, although data structure of somewindows suggested more than one ligand classes present (e.g.,window 3). Table 2 shows parameters for one ligand per win-dow and associated error function (EF) values resulting fromdata analysis of five individual analytical windows using SRAL

as the basis for all methods. However, for the S-W method,this SRAL only reflects the sensitivity at the start of the iterativeoptimization process. The final results, are based on the opti-mized sensitivity .

KML

cond

1

KML

cond

2

KML

cond

1

SRAL

calc

Wells et al. Voltammetric copper-ligand titration analysis

458

Table 2. Results of analyzing individual multi-window Cu titrations of Dumbarton Bridge samples from January and March 2003, forone ligand class per window using Scatchard (SCAT), van den Berg/Ružić (vdB), Gerringa (GERR), and Sander-Wells (S-W) methods. Thenumber of data points considered for each window can inferred from Fig. 2.

Window* January [CuT] = 33.7 nM, SUV = 6.9 nA/nM† March [CuT] = 27.0 nM, SUV = 7.8 nA/nM†

SCAT vdB GERR S-W ( )‡ SCAT vdB GERR S-W ( )‡

log 1 (high) 14.5 14.5 14.4 16.4 (5.5) 14.2 14.2 14.1 15.3 (5.9)2 14.3 14.1 14.2 15.6 (5.2) — —§ —§ —||

3 13.3 12.9 13.2 13.8 (4.5) 13.2 13.5 13.5 14.6 (4.2)4 12.3 12.2 12.2 12.4 (3.8) 12.4 12.4 12.4 12.8 (4.0)

5 (low) 12.0 12.0 12.0 12.1 (3.3) 11.7 11.8 11.8 11.9 (3.7)LT(nM) 1 (high) 63 62 64 15 84 84 94 13

2 54 71 65 24 —‡ —‡ —‡ —§

3 111 126 111 60 110 86 86 294 123 142 138 94 127 133 111 78

5 (low) 143 145 143 130 144 143 143 120EF|| 1 (high) 0.14 0.14 0.15 0.088 0.15 0.11 0.13 0.102

2 0.31 0.35 0.22 0.013 —‡ —‡ —‡ —§

3 0.34 0.48 0.34 0.074 0.57 0.55 0.28 0.0734 0.11 0.16 0.13 0.069 0.31 0.6 0.31 0.050

5 (low) 0.12 0.13 0.12 0.072 0.093 0.11 0.11 0.103*Values of [SAT] (μM) for January are 99.5, 49.8, 9.7, 2.4, and 0.94 for windows 1-5, respectively, and for March are 101.4, 50.7, 10, 2.5, and 0.97 forwindows 1-5, respectively.†SUV, the sensitivity obtained from UV digested sample, is the basis of sensitivities (SRAL) used for each window at different SA concentration. SRAL is SUV ×RAL, with RAL being 1.00, 0.99, 0.92, 0.74, and 0.52 (as calculated from Hudson et al. [2003]) for window 1-5 (high to low). For S-W the SRAL is used asinitial guess, but then gets optimized and becomes .‡Too little data, cannot be calculated.§Zero or negative degrees of freedom, EF used by S-W application (for solution convergence criterion) cannot be calculated.||np in the error function (in expression 22) EF is 3 for 1 ligands.

SRAL

calcSRAL

calc

KCuLcond

SRAL

calc

Results from S-W method are in closest agreement withexperimental data, with a maximum EF of 0.10 (average 0.07).The nonlinear Gerringa method had an average error of EF =0.23, whereas the two linearization methods, van denBerg/Ružić and Scatchard, had higher EF values of 0.27 and0.24, respectively. For the two highest analytical windows([SA] ~ 50 and 100 μM), the S-W method distinguished astronger ligand class at a concentration smaller than the dis-solved copper concentration, a known limitation of othermethods for obtaining parameters from metal ligand titrations(Bruland et al. 2000).

Conditional stability constants and ligand concentrationsobtained from the lowest analytical window (~ 1 μM SA) werecomparable for all four methods. For the higher analyticalwindows (i.e., window 1 and 2 for January and windows 1 and3 for March), the S-W method returned, in general, parametersthat correspond to a stronger ligand class present at lower con-centration compared to the other three fitting methods(Scatchard, van den Berg/Ružić, and Gerringa; Table 2). TheJanuary titration data for the highest analytical window (~ 100μM SA) returned higher ligand concentrations of 53 nM, 62nM, and 64 nM from the Scatchard, van den Berg/Ružić, andGerringa methods, respectively, whereas the S-W methodreturned a [LT] of 15 nM (Table 2). For March, the trend is sim-ilar. It should be noted that the limited number of data pointsin window 2 (~ 2.5 μM SA) makes parameter determination forthis curve meaningless as the df is negative, meaning that thedataset is over-parameterized.

Whereas it is difficult to say which result is correct whenlooking at natural samples with unknown composition, a firstapproximation of [LT] from the intercept of a linear regressionof the highest data points (see Fig. 2) would suggest a lowerrather than higher [LT]. A reason why the S-W method mayreturn lower EF’s is the fact that it treats S as a parameter thatis optimized during the interactive procedure, while using SRAL

as the initial guess only. Values for the optimized are givenin Table 2. The other 3 methods use a fixed SRAL where SUV wasdetermined from the UV digested sample and RAL was calcu-lated using the hyperbolic function as given in Hudson et al.(2003), and values for RAL used here are given in Table 2. Thereare other objective ways of choosing S, e.g., by simple internalcalibration (SSIC) or an overload titration (SOV) and argumentscan be found for the use of each of them and have been dis-cussed in detail in Hudson et al. (2003). To avoid the bias ofusing different sensitivities, we recalculated the data usingfor all methods and results are given in Appendix A (Table A2).As expected, results for [LT] and log are more comparablebetween different methods and the average EFs of the Gerringamethod is with 0.092 very comparable to that obtained withthe S-W method (i.e., 0.072), whereas the linear methods vanden Berg/ Ružić and Scatchard perform slightly weaker with anaverage EF of 0.15 and 0.23, respectively. The very good agree-ment of experimental data with back calculated data using thefitted/optimized parameters (i.e., ) indicates that the use of

SRAL based on SUV might not be representing the data correctly.

However, although results by other methods are more compa-rable, it can be noted that the S-W method still returns the low-est EFs, and this difference is likely because this method is par-ticularly robust to non-ideal data structure (Sander et al. 2011),an iterative optimization procedure.

For all four methods, the variable parameter results fromthe analysis of individual analytical windows for one ligandclass in each window might suggest the presence of a multi-tude of ligand classes with a continuum of conditional stabil-ity constants in each sample. Depending on which methodwas applied, log ranged from 16.4 and 15.3 (bothSander-Wells) for the highest window, to as low as 12.0 ± 0.1and 11.8 ± 0.1 for all 4 methods at the lowest window, in Jan-uary and March, respectively. Moffett and Brand (1996) ana-lyzed cell cultures by applying multiple analytical windowsand asked the question whether the multiple ligands theyobserved were real or whether there may be a systematic arti-fact associated with the derivation of that could accountfor the continuum of ligands binding stabilities observed. Formost applications of copper ligand titrations found in the lit-erature, one analytical window would typically have beenchosen, and many would have been analyzed for only one lig-and class. This raises the questions: “How well do single ana-lytical window titrations fitted for one ligand class representthe actual speciation of a metal in the sample? And what doesthis mean for estimating the Cu bioavailability in these envi-ronments?”

For example, for each analytical window, a different ligandconcentration is resolved each with a different stability con-stant—Does that mean that there are five different ligandclasses present when we have five analytical windows (seeTable 2). Unlikely, and this result had been recognized in thepast as an analytical effect, or artifact of the method (Moffettand Brand 1996; Bruland et al. 2000; Sander et al. 2011). Thus,the parameters obtained are a function of the chosen analyti-cal window rather than an unambiguous result. As has beenshown in two separate intercalibration exercises for Cu speci-ation in seawater (Bruland et al. 2000; Buck et al. 2012) com-parison of Cu organic complexation parameters is restricted tostudies employing the same analytical conditions (i.e., sameαM(AL)x) for titrations. However, for the assessment of Cu-bioavailability, toxicity thresholds and water quality criteria, ithas been shown that ligands especially at both ends of thecomplexing strength scale (i.e., very strong ligands and weakerligands present in high concentrations) are important todescribe a natural aqueous system accurately (Moffett et al.1997; Buck and Bruland 2005; Ndungu 2012, Sander et al.unpubl. data).Analysis of one analytical window for two ligand classesusing different methods

Analysis of one titration curve for two ligand classes is com-monly used for both Cu and Fe ligand titrations. Buck andBruland (2005) have already discussed the results of fitting

K cond

iML

K cond

iML

SRAL

calc

SRAL

calc

KML

cond

1

SRAL

calc

Wells et al. Voltammetric copper-ligand titration analysis

459

individual titration curves for two ligand classes measured atdifferent analytical windows. Table 3 shows the parameters fortwo ligand classes obtained from analysis of the window 3 (~10 μM SA) titration curve for January and March DumbartonBridge samples using the four different approaches. Resultsfrom Scatchard, van den Berg/Ružić, and Gerringa methodsare in reasonable agreement with respect to the inter-methodsimilarity of values obtained for and (see Table 3).Parameters obtained with the S-W method are quite differentfrom those returned from the other methods and returnalmost an order of magnitude lowest EFs. For both samples,the Scatchard, van den Berg/Ružić, and Gerringa methodsreturn results with a considerably higher EF (Table 3), indicat-ing less agreement between titration points back calculatedfrom results and the experimental data. While the SRAL wasused (i.e., SRAL = 6.3 and 7.2 nA/nM for January and March,respectively) for the Scatchard, van den Berg/Ružić and Ger-ringa methods, SRAL was only used as the starting conditionand then optimized in the S-W method, resulting in anof 4.5 and 4.2 nA/nM for January and March, respectively.These optimized are in better agreement with the actualslope of the titration (i.e., SSIC). Therefore the data were againrecalculated using the Scatchard, van den Berg/Ružić, and Ger-ringa methods for a two-ligand class model using the S-Woptimized . Results are given in Appendix A (Table A3).While for the January dataset, the EF improved for theScatchard method, the van den Berg/Ružić method got worse.It should be noted that the titration curves only had 7 or 8datapoints. This data structure, in combination with the lower

made it impossible to obtain results using the non-linearGerringa method, and in general, leaves them prone to prob-lems associated with the under-determination (i.e., over-para-meterization) of the system. To fit for 5 parameters (two ligandclasses), the number of data points should be at least 10. Inter-estingly, parameter solutions from the three commonly usedmethods yield [L1T] ≤ [L2T], as occurs in the majority of casesreported in the past for Cu speciation studies. The Sander-Wells results, on the other hand, produce a considerablyhigher and [L1T] > [L2T] for this window. In Sander et al.(2011), we simulated different combinations (permutations)of two ligand class systems covering a broad range of realisticcombinations from low to high concentrations of L1 and L2

and strong-to-weak complexes of ML1 and ML2. In that study,we demonstrated the difficulty in analysis of results in caseswhere [L1T] > [L2T], and how the common finding of [L1T] <[L2T] for samples with unknown ligand concentrations may, insome cases, be a result of artifacts in data analysis when usingstandard fitting approaches, which are unable to cope withthe resulting data structure (Sander et al. 2011).Consequences of a continuum of ligands versus a discretenumber of ligands for the speciation and toxicity of tracemetals in an aquatic system

The toxicity of Cu has been shown to be dependent on thefree, hydrated, metal ion [Mf], referred to as [Cu2+] for Cu

(Sunda and Guillard 1976). In the past (e.g., Moffett et al.1997; Buck and Bruland 2005; Ndungu 2012), [Cu2+] has beenextrapolated from plots of [Cu2+] against [CuT*]. [CuT*] is thecopper bound to all natural organic ligands and inorganic lig-ands in the titration sample equilibrated with AL (in our caseSA) according to Eq. 23, which is simply Eq. 9 written specifi-cally for Cu-SA:

[CuT*] = ∑i([CuLi]) + [Cu′] = [CuT] – [Cu(SA)x] (23)

The advantage of this plot is that it provides informationon both ambient [Cu2+] and how [Cu2+] varies with increasing[CuT], such as from anthropogenic input. Since the relation-ship between [Cu2+] and [CuT] depends on the ambient speci-ation and will, therefore, vary between sample locations, thisplot serves as a tool to visualize site-specific variability in Cuspeciation. The disadvantage of this plot is that it is unable toprovide information at extremely elevated [CuT], as it is lim-ited to the range of the titration data employed. Hence, themaximum level of Cu that can be inferred in this way of plot-ting [Cu2+] against [CuT*] is the ambient concentration of nat-ural ligands strong enough to compete with SA. For the Dum-barton Bridge datasets, plots of log [Cu2+] as a function of[CuT*] are shown in Fig. 3A-B and 3C-D for January and

KML

cond

1

KML

cond

2

SRAL

calc

SRAL

calc

SRAL

calc

SRAL

calc

KML

cond

1

Wells et al. Voltammetric copper-ligand titration analysis

460

Table 3. Results of analyzing window 3, [SAT] = ~ 10 μM* usingdifferent methods for Dumbarton Bridge samples from Januaryand March 2003.

SCAT† vdB GERR S-W

January 2003‡

log 13.9 14.6 14.2 14.5L1T (nM) 48 47 52 38log 12.1 11.7 11.5 12.9L2T (nM) 130 327 397 32EF§ 0.34 0.49 0.30 0.05pCu 13.67 14.24 13.98 13.88

March 2003‡

log 14.3 15.3 14.6 14.7L1T (nM) 29 30 30 28log 12.6 7.5 7.6 12.7L2T (nM) 78 2290 1910 4EF 0.38 0.85 0.77 0.09pCu 13.78 14.35 13.64 13.47

*The exact value of [SAT] (μM) for January is 9.72, and for March, it is10.01.†Values for the Scatchard method are those from Buck and Bruland (2005,Table 2).‡Number of data points considered were 7 in January and 8 in March. SUVwas inferred from UV digested sample and multiplied by RAL (i.e., 0.92),resulting in SRAL = 6.3 nA/nM for January and 7.2 nA/nM for March. For S-W, this SRAL is used in the initial guess and is then optimized as one of theparameters. The final for S-W was 4.5 nA/nM for January and 4.2nA/nM for March.§np in the error function EF (in expression 22) is 5 for two ligands.

KCuLcond

1

KCuLcond

2

KCuLcond

1

KCuLcond

2

SRAL

calc

March, respectively. Buck and Bruland (2005) had discussedthat data with respect to site-specific and national limits, aswell as potentially toxic levels of [Cu2+] for local diatomspecies. They concluded that only at the highest [CuT*], and insome cases even higher, the [Cu2+] would approach the possi-ble toxicity threshold for ambient diatom populations of log[Cu2+] = –11. However, we posit that Buck and Bruland (2005)actually underestimated future [Cu2+] predictions based specif-ically in the low analytical windows (Buck and Bruland 2005,Table 4 therein).

For the ambient [CuT] levels of 33.7 and 27 nM in Januaryand March, respectively, the log [Cu2+] calculated using param-eters obtained by the S-W method is –14.07 and –13.69 (seeTable 1 and Fig. 3) and comparable with those inferred fromthe highest analytical window fit of L1T by Buck and Bruland

(2005, Table 3 therein) and the [CuT*] versus log [Cu2+] (Fig.3A, C). From these plots, it is clear that there is good agree-ment between the original work of Buck and Bruland (2005)and the S-W interpretation applied to the same data here inthe highest analytical windows, which also best describe theambient Cu speciation dominated by the strongest ligands.Thus, both studies are in agreement for ambient [Cu2+] forthese samples. This is in line with the conclusions of Brulandet al. (2000) in terms of the analytical window effect and con-sistency in Cu2+ results despite speciation parameter differ-ences. The primary difference between these approaches inthe [Cu*] versus log [Cu2+] plots is in the characterization ofweaker ligands, which are most important for buffering [Cu2+]against increasing [CuT]. The Buck and Bruland (2005) plots,as well as speciation parameters results, appear to underesti-

Wells et al. Voltammetric copper-ligand titration analysis

461

Fig. 3. Log[Cu2+] as a function of [CuT*] in samples of Dumbarton Bridge January (A and B) and March (C and D). The short and long dashed lines cor-respond to the National CCC of 48.8 nM and the Site-Specific Objective (SSO) of 108.6 nM, respectively. The ambient total dissolved copper concen-trations at each site are represented by a solid line. The horizontal dash-dot line presents a possible toxicity threshold for ambient diatom populations(all limits are adopted from Buck and Bruland 2005). (A and C) Speciation inferred directly from titration data for each analytical window using RAL cor-rected S after UV digestion of sample (�, as described in Buck and Bruland (2005), Table 4); and Cu speciation calculated with parameters of two lig-ands obtained with S-W method for the unified multi analytical window dataset (1 μM SA: �; 2.4 μM SA: �; 9.7 μM SA: 1; 50 μM SA: �; and 100 μMSA: �). (B and D) Comparison of speciation calculated with parameters of one ligand (�), two ligands (�), and three ligands (�) obtained with S-Wmethod for the unified multi analytical window dataset.

mate the [Cu2+] at higher [Cu] compared to the S-W interpre-tation. This has particular relevance toward predictingchanges in Cu toxicity in the Cu contaminated San FranciscoBay estuary, and it should be noted that the S-W approachprovides more favorable agreement between CLE-AdCSVresults and site-specific Cu toxicity assays (long dash line inFig. 3 plots) conducted in this environment, giving furthercredence to this newly developed approach of interpretingmultiple analytical window data simultaneously.

Comparing plots of log [Cu2+] versus [CuT*] calculated usingparameters obtained by the S-W method assuming the pres-ence of one ligand class, look very different to those assumingthe presence of two or three natural ligands (Fig. 3B and D).While the one ligand solutions can be considered incorrect asindicated by a much higher EF, the two and three ligand solu-tions produce an almost indistinguishable log [Cu2+] versus[CuT*] plot. Notably, the [Cu2+] threshold for ambient diatompopulation is exceeded considerably for [CuT*] > ~ 110 nM,which approximately coincides with the site-specific waterquality objective for Cu in San Francisco Bay.

DiscussionThe application of the S-W method to real environmental

sample titrations and the comparison with some of the com-monly used manual data analysis methods highlights severalimportant issues. Since the S-W method uses the entire data setof multiple analytical window titrations, it addresses the prob-lem of under-determination of parameters for the case of twoor more ligand fits from a single-window titration. This willalso result in more statistically sound parameter estimations.The unified sensitivity SUNI used by the S-W method is based onSUV, but is then optimized during the iterative process to fit allanalytical windows best, while still taking the dependence of Swith the [ALT] into account. This allows for a more uniformand robust characterization of the complete ligand pool andeliminates the problem of individual analytical window titra-tions falling outside the analytical detection window.

The introduction of an error function (EF) that comparesthe experimental titration data with a simulated titrationusing fitted ligand parameters, and normalization for thenumber of parameters, enables the comparison of results fromunified multiple analytical window titrations, different num-ber of ligands and different evaluation methods. The twodatasets analyzed with the S-W method returned the lowest EFassuming the presence of two distinct organic ligand classesfor January and three for March.

Analyzing the individual analytical window titrations forone or two ligands by the S-W method and commonly usedmanual fitting methods (Scatchard and van den Berg/Ružićlinearizations, and Gerringa non-linear method), a multitudeof ligand classes was determined. Although the issue of arti-facts associated with the derivation of parameters using indi-vidual analytical windows has been raised before (van denBerg et al. 1990; Moffett and Brand 1996), the idea of a con-

tinuum of Cu-binding ligand classes has also been suggested(Bruland et al. 2000). Results from simulated multiple analyt-ical window datasets (Sander et al. 2011 and Sander et al.unpubl. data) suggested that even in the presence of two well-resolved ligands most commonly used manual evaluationmethods will find a multitude of ligands with different param-eters. This suggests that in a natural system, the thus farobserved ‘continuum of ligand classes’ might actually be anartifact of data analysis rather than a correct representation ofthe Cu-binding organic ligand distribution. More work isneeded to verify this question.

Comparing methods with each other has proven non-straightforward, since we applied the commonly used man-ual fitting methods (Scatchard and van den Berg/Ružić lin-earizations, and Gerringa non-linear method) with the S-Wmethod, which uses an iterative optimization routine toreturn the lowest EF result. To do this, the S-W method backcalculates titration data using the obtained parameters tooptimize the parameters to the experimental titration data.The way we applied the commonly used manual fittingmethods was not iterative, but instead, was performed asmany people working in this field do, with a simple linearor non-linear transformation to determine the parametersof [LiT] and . In the comparison, we first used the sen-sitivity, SRAL, as the basis for all calculations. However, forthe S-W method, SRAL is optimized ( ) as one of theparameters, and this optimization does not occur in themanual methods. Whereas [LiT] and generally are inreasonable agreement between the manual fitting methods(Scatchard and van den Berg/Ružić linearizations, and Ger-ringa non-linear method), the S-W method produced signif-icantly different results. The quality assurance measures ofEF within the manual fitting methods (Scatchard and vanden Berg/Ružić linearizations, and Gerringa non-linearmethod) were comparable, while the S-W method returneda much lower average EF.

A second comparison where we used the optimizedfrom the S-W method in all manual methods resulted in EFsbeing in the same order of magnitude for all four methods andthe parameters [LiT] and also being more similar betweenmethods. However, the S-W method still returned the lowestaverage EF, which can probably be assigned to the iterativeoptimization of all parameters in this method.

The impact of using different S on the EF is large, and itshould be recalled that SUV is an independently determinedparameter. Errors in any method of determination of S willpropagate (Hudson et al. 2003). Whereas only optimizesthe S to fit the single window data best, it might under- or over-estimate S when surface active substances are present or thetitration curve has not proceeded far enough to obtain the trueS for the titration. For the multi detection window approach,however, the unified S (SUNI) rationalizes discrepancies in theassigned S for each window (i.e., unified), but acknowledgesthat there is a single underlying SUV for all windows.

SRAL

calc

K cond

iML

SRAL

calc

K cond

iML

SRAL

calc

K cond

iML

Wells et al. Voltammetric copper-ligand titration analysis

462

Plans to release a first version of the S-W method programto interested parties for testing and providing feedback are inplace for late 2013. Progress can be followed on the SCORWG 139 webpage (http://neon.otago.ac.nz/research/scor/index.html). In the meantime, we encourage others to pur-sue the possibility of unified multiple analytical windowdataset treatments using other methods, such as the com-monly used linear and non-linear methods, by optimizingthe difference between experimental titration data and cal-culated titration data using the estimated parameters. Param-eters describing the system accurately should result in calcu-lated titration curves very similar to experimental data.Iterative optimizations of parameters can be applied to anyevaluation method. Using a genetic algorithm to randomizethe initial guess value can be used to return feedbackthrough the stability of the result.

Comments and recommendationsAnalyzing two sets of multiple analytical window ligand

titration datasets individually with common data interpreta-tion methods (i.e., Scatchard, van den Berg/Ružić, and Ger-ringa) confirmed known problems of Cu complexation inmarine samples, including the observation of conditional sta-bility constants varying with the analytical window applied.The apparent presence of a multitude of ligands with a con-tinuum of stability constants may be an artifact of the over-parameterization of analytical linear and non-linear fittingmethods.

The S-W method provides new opportunities to betterdefine Cu complexation in natural water systems. The resultsfrom analyzing the full multiple analytical window datasetstogether gives strong evidence for the presence of two to threediscrete ligand classes in the San Francisco Bay samples ana-lyzed. The possibility of using multiple analytical window titra-tions as a unified dataset, and being able to fully characterizethe Cu-binding ligand capacity from the strongest to the weak-est ligands, is particularly relevant toward predicting changesin the bioactive form of Cu ([Cu2+]) as a function of the totalCu concentration. We suggest, therefore, that multiple analyt-ical window titrations and simultaneous analysis of all win-dows should be routinely implemented as a more realistic rep-resentation of metal binding ligands in natural systems.

ReferencesAhner, B. A., S. Kong, and F. M. M. Morel. 1995. Phytochelatin

production in marine algae. 1. An interspecies comparison.Limnol. Oceanogr. 40:649-657 [doi:10.4319/lo.1995.40.4.0649].

———, and F. M. M. Morel. 1995. Phytochelatin production inmarine algae. 2. Induction by various metals. Limnol.Oceanogr. 40:658-665 [doi:10.4319/lo.1995.40.4.0658].

Batley, G. E., S. C. Apte, and J. L. Stauber. 2004. Speciation andbioavailability of trace metals in water: Progress since 1982.Aust. J. Chem. 57:903-919 [doi:10.1071/CH04095].

Bruland, K. W. 1989. Complexation of zinc by natural organicligands in the central north Pacific. Limnol. Oceanogr.32:269-285 [doi:10.4319/lo.1989.34.2.0269].

———. 1992. Complexation of cadmium by natural organicligands in the central north Pacific. Limnol. Oceanogr.37:1008-1017 [doi:10.4319/lo.1992.37.5.1008].

———, E. L. Rue, J. R. Donat, S. A. Skrabal, and J. W. Moffett.2000. Intercomparison of voltammetric techniques todetermine the chemical speciation of dissolved copper in acoastal seawater sample. Anal. Chim. Acta 405:99-113[doi:10.1016/S0003-2670(99)00675-3].

———, and E. L. Rue. 2001. Analytical methods for the deter-mination of concentrations and speciation of iron, p. 255-290. In D. R. Turner and K. A. Hunter [eds.], The Biogeo-chemistry of Iron in Seawater. IUPAC Series on Analyticaland Physical Chemistry of Environmental Systems. JohnWiley and Sons.

Buck, K. N., and K. W. Bruland. 2005. Copper speciation inSan Francisco Bay: A novel approach using multiple analyt-ical windows. Mar. Chem. 96:185-198 [doi:10.1016/j.marchem.2005.01.001].

———, J. Moffett, K. A. Barbeau, R. M. Bundy, Y. Kondo, andJ. Wu. 2012. The organic complexation of iron and copper:an intercomparison of competitive ligand exchange-adsorptive cathodic stripping voltammetry (CLE-ACSV)techniques. Limnol. Oceanogr. Methods 10:496-515.

Campos, M.L.A.M., and C. M. G. van den Berg. 1994. Deter-mination of copper complexation in sea water by cathodicstripping voltammetry and ligand competition with salicy-ladehydeoxime. Anal. Chim. Acta 284:481-496 [doi:10.1016/0003-2670(94)85055-0].

Dupont, C. L., R. K. Nelson, S. Bashir, J. W. Moffett, and B. A.Ahner. 2004. Novel copper-binding and nitrogen-rich thi-ols produced and exuded by Emiliania huxleyi. Limnol.Oceanogr. 49:1754-1762 [doi:10.4319/lo.2004.49.5.1754].

Gerringa, L. J. A., P. M. J. Herman, and T. C. W. Poortvliet.1995. Comparison of the linear van den Berg/Ružić trans-formation and a non-linear fit of the Langmuir isothermapplied to Cu speciation data in the estuarine environ-ment. Mar. Chem. 48:131-142 [doi:10.1016/0304-4203(94)00041-B].

Gibbon-Walsh, K., P. Salaün, and C. M. G. van den Berg. 2012.Pseudopolarography of copper complexes in seawater usinga vibrating gold microwire electrode. J. Phys. Chem.116:6609-6620 [doi:10.1021/jp3019155].

Gledhill, M., and C. M. G. Van Den Berg. 1994. Determinationof complexation of iron(III) with natural organic complex-ing ligands in seawater using cathodic stripping voltamme-try. Mar. Chem. 47:41-54 [doi:10.1016/0304-4203(94)90012-4].

Hassler, C. S., V. Schoemann, C. M. Nichols, E. C. V. Butler,and P. W. Boyd. 2011. Saccharides enhance iron bioavail-ability to Southern Ocean phytoplankton. PNAS 108:1076-1081 [doi:10.1073/pnas.1010963108].

Wells et al. Voltammetric copper-ligand titration analysis

463

Hawkes, J. A., M. Gledhill, D. P. Connelly, and E. P. Achterberg.2013. Characterisation of iron binding ligands in seawaterby reverse titration. Anal. Chim. Acta [doi:10.1016/j.aca.2012.12.048].

Homann, V. V., K. J. Edwards, E. A. Webb, and A. Butler. 2009.Siderophores of Marinobacter aquaeolei: petrobactin and itssulfonated derivatives. Biometals 22:565-571 [doi:10.1007/s10534-009-9237-0].

Hudson, R. J. M., E. L. Rue, and K. W. Bruland. 2003. Model-ing complexometric titrations of natural water samples.Environ. Sci. Tech. 37:1553-1562 [doi:10.1021/es025751a].

Ibisanmi, E. B., S. G. Sander, P. W. Boyd, A. R. Bowie, and K. A.Hunter. 2011. Vertical distributions of iron-(III) complexingligands in the southern ocean. Deep-Sea Res. II[doi:10.1016/j.dsr2.2011.05.028].

Kawakami, S. K., M. Gledhill, and E. P. Achterberg. 2006a. Pro-duction of phytochelatins and glutathione by marine phy-toplankton in response to metal stress. J. Phycol. 42:975-989 [doi:10.1111/j.1529-8817.2006.00265.x].

———, ———, and ———. 2006b. Effects of metal combina-tions on the production of phytochelatins and glutathioneby the marine diatom Phaeodactylum tricornutum. Biometals19:51-60 [doi:10.1007/s10534-005-5115-6].

Laglera, L. M., and C. M. G. van den Berg. 2003. Copper com-plexation by thiol compounds in estuarine waters. Mar.Chem. 82:71-89 [doi:10.1016/S0304-4203(03)00053-7].

———, and ———. 2009. Evidence for geochemical control ofiron by humic substances in seawater. Limnol. Oceanogr.54:610-619 [doi:10.4319/lo.2009.54.2.0610].

Lewis, J. A. M., and W. G. Sunda. 1978. Effect of complexationby natural organic ligands on the toxicity of copper to aunicellular alga, Monochrysis lutheri. Limnol. Oceanogr.23:870-876 [doi:10.4319/lo.1978.23.5.0870].

Martin, J. H., and S. E. Fitzwater. 1988. Iron deficiency limitsphytoplankton growth in the north-east Pacific subarctic.Nature 331:341-343 [doi:10.1038/331341a0].

Mawji, E., and others. 2008. Hydroxamate siderophores:occurrence and importance in the Atlantic Ocean. Environ.Sci. Technol. 42:8675-8680 [doi:10.1021/es801884r].

Moffett, J. W. 1995. Temporal and spatial variability of coppercomplexation by strong chelators in the Sargasso Sea. Deep-Sea Res. I 42:1273-1295 [doi:10.1016/0967-0637(95)00060-J].

———, and L. Brand. 1996. Production of strong, extracellularCu chelators by marine cyanobacteria in response to Custress. Limnol. Oceanogr. 41:388-395 [doi:10.4319/lo.1996.41.3.0388].

———, L. E. Brand, P. L. Croot, and K. A. Barbeau. 1997. Cuspeciation and cyanobacterial distribution in harbors sub-ject to anthropogenic Cu inputs. Limnol. Oceanogr.42:789-799 [doi:10.4319/lo.1997.42.5.0789].

———, and C. Dupont. 2007. Cu complexation by organic lig-ands in the sub-arctic NW Pacific and Bering Sea. Deep-SeaRes. I 54:586-595 [doi:10.1016/j.dsr.2006.12.013].

Morel, F. M. M., and R. J. M. Hudson. 1985. The geobiologicalcycle of trace elements in aquatic systems: Redfield revis-ited, p. 251-281. In W. Stumm [Ed.], Chemical processes inlakes. Wiley.

———, and J. G. Hering. 1993. Principles and applications ofaquatic chemistry. John Wiley & Son.

Ndungu, K. 2012. Model predictions of copper speciation incoastal water compared to measurements by analyticalvoltammetry. Environ. Sci. Technol. 46:7644-7652 [doi:10.1021/es301017x].

Rue, E. L., and K. W. Bruland. 1995. Complexation of iron(III)by natural organic ligands in the Central North Pacific asdetermined by a new competitive ligand equilibration/adsorptive cathodic stripping voltammetric method. Mar.Chem. 50:117-138 [doi:10.1016/0304-4203(95)00031-L].

Ružić, I. 1982. Theoretical aspects of the direct titration of nat-ural waters and its information yield for trace metal specia-tion. Anal. Chim. Acta 140:99-113 [doi:10.1016/S0003-2670(01)95456-X].

Sander, S. G., K. A. Hunter, H. Harms, and M. Wells. 2011. Anumerical approach to speciation and estimation of param-eters used in modeling trace metal bioavailability. Environ.Sci. Technol. 45:6388-6395 [doi:10.1021/es200113v].

Scatchard, G. 1949. The attractions of proteins for small mol-ecules and ions. Ann. N.Y. Acad. Sci. 51:660-672 [doi:10.1111/j.1749-6632.1949.tb27297.x].

Sillen, L. G., and A. E. Martell. 1971. Stability constants.Chemical Society.

Sunda, W. G., and R. L. Guillard. 1976. The relationshipbetween cupric ion activity and the toxicity of copper tophytoplankton. J. Mar. Res. 34:511-529.

Tian, F., R. D. Frew, S. Sander, K. A. Hunter, and M. J. Ellwood.2006. Organic iron(III) speciation in surface transects acrossa frontal zone: the Chatham Rise. N. Z. J. Mar. Freshw. Res.57:533-544 [doi:10.1071/MF05209].

Town, R. M., and M. Filella. 2000. A comprehensive systematiccompilation of complexation parameters reported for tracemetals in natural waters. Aquat. Sci. 62:252-295 [doi:10.1007/PL00001335].

van den Berg, C. M. G. 1982. Determination of copper com-plexation with natural organic ligands in seawater by equi-libration with MnO2. Part 1: Theory; Part 2: Experimentalprocedures and application to surface seawater. Mar. Chem.11:307-342 [doi:10.1016/0304-4203(82)90028-7].

———. 1985. Determination of the zinc complexing capacityin seawater by cathodic stripping voltammetry of zinc-APDC complex ions. Mar. Chem. 15:1-18 [doi:10.1016/0304-4203(84)90035-5].

———, M. Nimmo, P. Daly, and D. R. Turner. 1990. Effects ofthe detection window on the determination of organic cop-per speciation in estuarine waters. Anal. Chim. Acta232:149-159 [doi:10.1016/S0003-2670(00)81231-3].

Velasquez, I., B. L. Nunn, E. Ibisanmi, R. B. Goodlett, K. A.Hunter, and S. G. Sander. 2011. Detection of hydroxamate

Wells et al. Voltammetric copper-ligand titration analysis

464

Wells et al. Voltammetric copper-ligand titration analysis

465

siderophores in coastal and sub-Antarctic waters off theSouth Eastern Coast of New Zealand. Mar. Chem. 126:97-107 [doi:10.1016/j.marchem.2011.04.003].

Vraspir, J., and A. Butler. 2009. Chemistry of marine ligandsand siderophores. Ann. Rev. Mar. Sci. 1:43-63 [doi:10.1146/annurev.marine.010908.163712].

Ward, B. A., M. A. M. Friedrichs, T. R. Anderson, and A.Oschlies. 2010. Parameter optimisation techniques and theproblem of underdetermination in marine biogeochemicalmodels. J. Mar. Syst. 81:34-43 [doi:10.1016/j.jmarsys.2009.12.005].

Wilhelm, S. W., D. P. Maxwell, and C. G. Trick. 1996. Growth,iron requirements, and siderophore production in iron-lim-ited Synechococcus PCC 7002. Limnol. Oceanogr. 41:89-97[doi:10.4319/lo.1996.41.1.0089].

———, K. MacAuley, and C. G. Trick. 1998. Evidence for theimportance of catechol-type siderophores in the iron-lim-ited growth of a cyanobacterium. Limnol. Oceanogr.43:992-997 [doi:10.4319/lo.1998.43.5.0992].

Worms, I., D. F. Simon, C. S. Hassler, and K. J. Wilkinson.2006. Bioavailability of trace metals to aquatic microorgan-isms: importance of chemical, biological and physicalprocesses on biouptake. Biochimie 88:1721-1731 [doi:10.1016/j.biochi.2006.09.008].

Xue, H., and L. Sigg. 1999. Comparison of the complexationof Cu and Cd by humic or fulvic acids and by ligandsobserved in lake waters. Aquat. Geochem. 5:313-335[doi:10.1023/A:1009679819002].

———, and L. Sigg. 2002. A review of competitive ligand-exchange/voltammetry methods for speciation of tracemetals in freshwater, p. 336-370. In T. F. Rozan and M.Taillefert [eds.], Environmental electrochemistry: Analysesof trace element biogeochemistry. Oxford Univ. Press[doi:10.1021/bk-2002-0811.ch018].

Submitted 9 September 2012Revised 10 July 2013

Accepted 20 August 2013

New approach to analysis of voltammetric ligand titration dataimproves understanding of metal speciation in natural watersMona Wells1, Kristen N. Buck2, and Sylvia G. Sander1*

1Department of Chemistry, University of Otago, PO Box 56, Dunedin, New Zealand2Bermuda Institute of Ocean Sciences, 17 Biological Station, Ferry Reach, St. George’s, Bermuda GE 01

Limnol. Oceanogr.: Methods 11, 2013© 2013, by the American Society of Limnology and Oceanography, Inc.

Appendix A:

Table A1: Glossary of terms and abbreviations used (in order of use)

Term Definition Units

[LiT], Total concentration if ith ligand, i = 1,2,… n M

conditional stability constant of the metal complex with the ith ligand M-1

S Voltammetric sensitivity nA/nM

[MLi] Metal-natural organic ligand complex concentration M

[Mf] Free metal concentration M

[YIN] Aggregate of major inorganic ligands (such as Cl-, OH- and CO32-) M

α�inorg Side reaction coefficient for formation of the aggregate complexes M�

[M�] Aggregate of inorganic complexes with the metal M

[L�] Natural organic ligand concentration not complexed with the metal M

[MT] Total metal concentration M

αML Side reaction coefficient of the ML

[ALT] Total added ligand concentration M

M(AL)x Metal complexes with AL M

αM(AL)x Side reaction coefficient of the M(AL)x

[ALf] Free added ligand concentration M

Conditional stability constant of the 1:1 metal complex with AL M-1

Conditional stability constant of the 1:x metal complex with AL M-x

IP Peak current nA

SREF Reference sensitivity nA/nM

S0REF Reference sensitivity of the titration done at highest [ALT] nA/nM

SSIC Sensitivity determined by simple’ internal calibration nA/nM

SOV Sensitivity in UV digested sample nA/nM

SUNI Sensitivity unified and optimized for all [ALT] (by S-W method) nA/nM

RAL Factor that explicitly reflects the window-dependent variation in sensitivity

SRAL Sensitivity for each single titration done at a specific each [ALT]; based on SREF multiplied by RAL nA/nM

SRAL optimized by S-W method (for one specific window)

AT Transpose of a matrix that expresses species reaction stoichiometry in terms of principal components

c Vector of all species concentrations (i.e. [ALf], [Mf], [L�], [MLi], [M(AL)x], [M�])

t Vector of sums of total component concentrations (i.e. [ALT], [MT], [LiT]).

K Constant vector whose elements are , and α�inorgx Vector of all component concentrations in the system

RMS Root mean squared

EF Error function

RPD Relative percent difference %

nm Is the number of titration data points (m)

np The number of parameters (p)SA Salicyl aldoxime

Kcond

iML

KMALcond

βM(AL)�cond

x

SRAL

calc

Kcond

iML

Kcond

xM(AL)

Wells et al. Voltammetric copper-ligand titration analysis

2

Table A2. Results of analyzing individual multi-window Cu titrations of Dumbarton Bridge samples from January and March, 2003,with fixed for one ligand class per window using Scatchard (SCAT), van den Berg/Ružić (vdB), Gerringa (GERR) and Sander-Wells(S-W) methods. The number of datapoints considered for each window can inferred from Figure 2.

Window* January [CuT] = 33.7 nM March [CuT] = 27.0 nM† SCAT vdB GERR S-W ‡ † SCAT vdB GERR S-W

log 1 (high) 5.5 — — 15.4 16.4 5.9 14.2 16.2 15.3 15.32 5.2 15.3 15.5 15.4 15.6 — — — —||

3 4.5 13.8 14.5 13.8 13.8 4.2 13.3 14.3 14.9 14.64 3.8 12.4 12.5 12.4 12.4 4.0 12.6 — 12.8 12.8

5 (low) 3.3 12.0 12.1 12.1 12.1 3.7 11.8 11.9 11.8 11.9LT(nM) 1 (high) — 14 19 15 36 15 19 13

2 26 25 25 24 — — — —||

3 59 57 58 60 11 26 28 294 96 94 95 94 81 72 78 78

5 (low) 136 132 134 130 132 130 131 120EF|| 1 (high) — — 0.078 0.088 0.20 0.26 0.090 0.102

2 0.025 0.027 0.016 0.013 — — — —||

3 0.064 0.66 0.078 0.074 0.92 0.36 0.14 0.0734 0.083 0.18 0.078 0.069 0.15 — 0.090 0.050

5 (low) 0.26 0.23 0.19 0.072 0.080 0.14 0.070 0.103* Values of [SAT] (μM) for January are 99.5, 49.8, 9.7, 2.4, and 0.94 for windows 1–5, respectively, and for March are 101.4, 50.7, 10, 2.5, and 0.97 forwindows 1–5, respectively.† For all methods obtained from the S-W method optimization was used.‡ too little data, cannot be calculated.

SRAL

calcSRAL

calc

KCuLcond

SRAL

calc

SRAL

calc

Table A3. Results of analyzing window 3, [SAT] = ~10 μM* using two-ligand class model for different methods at fixed † asobtained from S-W optimization. Dumbarton Bridge samples from January and March, 2003

SCAT vdB GERR S-W

January 2003‡

log 13.8 13.0 —¶ 14.5L1T (nM) 59 61 — 38log 12.0 12.0 — 12.9L2T (nM) 123 55 — 32EF|| 0.14 0.97 — 0.05p[Cu2+]# 13.67 12.9 — 13.66March 2003‡

log — 13.1 — 14.7L1T (nM) — 29 — 28log — 12.0 — 12.7L2T (nM) — 26 — 4EF|| — 0.87 — 0.09p[Cu2+] # — 12.03 — 13.47* the exact value of [SAT] (μM) for January is 9.72 and for March it is 10.01.† for January for [SAT] = ~10 μM was 4.5 nA/nM for January and 4.2 nA/nM for March.‡ number of datapoints considered were 7 in January and 8 in March.§ for S-W was 4.5 nA/nM for January and 4.2 nA/nM for March.|| np in the error function EF (in expression 22) is 5 for two ligands.¶ data could only be fitted using a two-ligand model, i.e. not enough data points.# αinorg in January was 12 (pH7.77, salinity = 21.7) and March 71 (pH8.55, salinity = 22. 8)

SRAL

calc

SRAL

calc

SRAL

calc

KCuLcond

1

KCuLcond

2

KCuLcond

1

KCuLcond

2