competitive equilibration techniques for determining transition metal speciation in natural waters:...

ANALYTICA CHIME4 ACTA

ELSEVIER Analytica Chimica Acta 343 (1997) 161-181

Competitive equilibration techniques for determining transition metal speciation in natural waters: Evaluation using model data

Lisa A. Miller’T’, Kenneth W. Bruland

Institute of Marine Sciences, University of California, Santa Cruz, CA 95064, USA

Received 1 July 1996; received in revised form 28 October 1996; accepted 13 November 1996

Abstract

Competitive ligand equilibration with metal titrations is one of the most important approaches currently available for determining the chemical speciation of trace metals in seawater. However, ambiguities in data interpretation still complicate the application of these methods. Here, we have used model data to explore and graphically demonstrate the effects of analytical limitations and protocols on the results obtained using competitive equilibration techniques. We have confirmed that such methods are best suited for identifying low concentrations of iigands forming strong metal complexes. Nevertheless, with care, the information obtained for weaker metal complexes and speciation in complicated ligand mixtures can give reasonable estimates of the in situ free metal ion concentration. In general, speciation results from competitive equilibration analyses cannot necessarily be extrapolated to high total metal concentrations at which complexes with unidentified weak ligands could become important.

Keywords: Metal speciation; Waters; Equilibration techniques

1. Introduction

Chemical speciation is one of the fundamental factors controlling trace metal cycling and bioavail- ability in natural waters (e.g. [ 1,2]), and the speciation of at least some dissolved transition metal cations in seawater appears to be dominated by organic ligands present at very low concentrations but forming strong metal complexes (e.g. [3-6]). Many popular methods for determining metal speciation, such as anodic stripping voltammetry, directly determine the kineti-

*Corresponding author: Fax: +47 55 23 85 84; e-mail: [email protected].

‘Present address: Institute of Marine Research, P.0. Box 1870 Nordnes, N-5024 Bergen, Norway.

tally labile (or inorganic) metal concentration in a sample (e.g. [7]), which can be prohibitively low in the presence of strong organic ligands. This has led to the development of a new class of highly sensitive speciation techniques based on competitive ligand equilibration, initiated by van den Berg and Kramer’s [g] manganese dioxide method.

In these competitive equilibration methods, the measured metal fraction is that associated with an added, well-characterized metal-binding phase or ligand which has been allowed to equilibrate with the sample. Ideally, this added metal-binding agent establishes a balanced competition for the metal with the ligands originally present. Titration of the sample (including the added competing ligands) with the

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162 L.A. Miller; K.W Bruland/Ancdytica Chimica Acta 343 (1997) 161-181

Fig. 1. Idealized titration curve (analytical signal as a function of

total metal concentration) in the presence of natural metal-binding ligands (L), at a total concentration of [b], in competition with an

analytical ligand, A. Dashed line: In the absence of natural ligands

forming complexes strong enough to compete with A, the titration line is not curved. Dotted line: After the natural ligands are fully

saturated, [MA] increases linearly with total metal ( [9]).

analyte metal (Fig. l), allows determination of the total concentrations and conditional metal-binding stability constants of the natural ligands, from which the original, unperturbed speciation can be calculated.

Over the last decade, this competitive equilibration approach has evolved into a number of powerful dissolved-phase analytical methods based on electro- chemical (adsorptive cathodic stripping voltammetry, ACSV - Cu, [7,10-181; Zn, [12,14,19,20]; Ni, [3,7]; Co, [21]; Fe, [6,22-241) and atomic absorption (competitive ligand equilibration-solvent extraction, CLE- SE [25-281) detection. Other detection systems such as chemiluminescence and inductively coupled plasma mass spectrometry may also be applicable, but as yet, have not been used to any appreciable extent.

In contrast to the dissolved-phase competition techniques, solid-phase competitions with cation exchange resins (or minerals) have been relatively under-utilized. Transition metal speciation has been determined using batch equilibration competitions

with the cation exchange chelating resin Chelex-100 [29], with manganese dioxide [8,11,30-321, and with 8-hydroxyquinoline immobilized on a vinyl polymer resin [33]. In general, solid-phase competitive equilibration methods have been limited by difficulties with clean fihration and identification of mixed ligand- surface complexes but still have potential, if these problems can be resolved. It has also been suggested that trace metal speciation can be determined using added competing metals, rather than ligands, but this approach has not yet been tested in complex natural samples [34].

Despite the successes of the technique development effort, interpretation of the results from competitive equilibration methods is often ambiguous. Here, we specifically address the following questions using model data to simulate competitive equilibration titrations:

How do the detection limit and analytical precision of the analyses constrain characterization of the natural ligands? How well can weak versus strong natural ligands be distinguished? How effectively can the few ligands calculated from competitive equilibration analyses model true speciation with more complicated ligand mixtures? How do calibration errors influence ligand char- acterizations?

Our intent has not been to provide fixed rules for the situations in which competitive equilibration methods can or cannot be used but rather to clarify the questions that must be addressed in interpreting the results. This paper extends an earlier review of ACSV methods by Apte et al. [35], reflecting the evolution of our understanding of competitive equilibration methods since that time, and including consideration of multi- ligand regimes.

2. Theory of trace metal speciation titrations

2.1. Mixed ligand classes and analytical windows

As they have been used, metal speciation titrations identify the concentrations, [Lr], and conditional metal-binding stability constants, Ki$id, for one or

L.A. Milfel: K.U! Bruland/Analytica Chimica Acta 343 (1997) 161-181 163

two discrete ligands from which the in situ equilibrium trace metal speciation is calculated. Generally, it has been acknowledged that these ligands do not necessarily represent actual, chemically distinct organic compounds, but rather less definitive ligand ‘classes’ or even just averages of incidental windows in a continuum of binding sites. Experimental evidence for such mixtures of binding sites has been found in studies specifically examining how the determined speciation varies with different analytical techniques involving different competing ligands at different concentrations [17,18,23,27,36,37].

The analytical competition strength can be defined

as

CLMA = [MAi,]/[M”+] = p~A~[A’]“, (1)

where M designates the metal cation, A is the added competing ligand, [M”+] is the concentration of the free, hydrated metal ion, ]A’] is the concentration of A not bound by the metal, and PTA: is the overall conditional formation constant of the complex MAb (the symbols used in this paper are summarized in Table 1). Hereafter, we will assume 1 : 1 metal : ligand complexation as the simplest and most intuitive case, giving

CLMA = [MA]/[M”+] = K$id[A’], (2)

where Kgid is the formation constant of the complex MA. Analogously, the strength by which the natural ligands, L, bind the metal is given by

aML = [ML]/[M”+] = C[MLi]/[M”‘]

(3)

where the subscript i indicates different natural organic ligands, [Lf] is the concentration of each ligand not complexed with the metal M, and Kg{:

is the conditional stability constant of each MLi COmpkX. The analytiCal Competition strength, aMA, lies within (generally assumed to be at the center of) an ‘analytical window’ [35] encompassing a range of natural ligand strengths, aML, which can be determined using that competition.

Van den Berg and his coworkers [36,37] have systematically studied the influence of analytical competition strength on the determined speciation. They found that the values determined for aML, the extent of binding by natural ligands, in estuarine, coastal, and

open ocean waters vary linearly with the competition strength, aMA, over up t0 ten orders Of magnitude, even when results for widely disparate samples, techniques, and metals are compared. These observed correlations between aML and aMA indicate that each analytical window could be identifying different classes of ligands in complicated mixtures of metal binding sites. In a separate study [27], three competition strengths, varying over three orders of magnitude, positively identified only two distinct copper-binding ligands in a single open ocean sample. However, even in this case, acuL varied with aC”A, evidence for two ligand classes with stability distributions about aver- age values log KFup of that were determined by the analyses. All of these studies have implied that the trace metals in marine waters are generally not bound by specific, chemically distinct ligands but rather by organic compounds with numerous types of binding sites and covering a range of binding strengths.

2.2. Linearization techniques

Total concentrations ([Lr]) and metal-binding stability constants (Kgid) for natural ligands are determined from sample titrations with the metal of interest (Fig. 1). Although it is possible to estimate [Lr] and K$id directly from the titration curve [38], more precise determinations necessitate either linearization or non-linear optimization of the data.

Two linearization methods based on a discrete ligand binding model have gained predominance in this field, that based on Scatchard’s work with small molecule binding by proteins ( [39], as described by [40]) and another derived from the Langmuir isotherm describing gas adsorption onto particles (e.g., [41], as described by [8,42]). Both these linearization methods require calculation of [M”+] and [ML] for each titration point. These quantities are obtained from the measured concentrations of total metal, [MT], and of metal in the competing analytical complex, [MA], through

[M”‘] = [MA]/oMA, (4)

[MXi] = aa[M”+], (5)

[ML]= [MT]- {[M"+]+ [M&I+ [MA]), (6)

where [MXi] is the concentration of metal bound with the major inorganic ions and ah is the inorganic side

164

Table 1

L.A. Milk< K.U! Bnrland/Analytica Chimica Acta 343 (1997) 161-181

Definitions of symbols and abbreviations

ACSV CLE-SE

[I M

[MT]

IM”+l [M”+]*

[MXil L

L1 L2

[Lrl

L’l q,q L&L:. L-3 A

[ATI

Adsorptive cathodic stripping voltammetry Competitive ligand equilibration-solvent extraction

Molar concentration of species within the brackets

Generalized metal cation

K$ , Kcond

,VXO;d’ , Kcond‘

Total molar concentration of the analyte metal Molar concentration of free hydrated metal ion

Molar concentration of free hydrated metal ion calculated from ligands determined by competition titrations

Molar concentration of metal complexed by inorganic anions

Generalized natural ligand

Strong natural ligand

Weak natural ligand

Total molar concentration of natural ligands Molar concentration of natural ligands not bound by the analyte metal

Strong natural ligands determined from competition titrations

Weak natural ligands determined from competition titrations

Total molar concentration of natural ligands determined from competition titrations

Added competing ligand

Total molar concentration of the added competing ligand

Molar concentration of the added ligand not bound by the analyte metal

Overall formation constant of metal-added ligand complex MA,,, conditional to ionic strength and side reactions of the

ligand (Eq. (1))

Formation constant of metal-added ligand complex MA, conditional to ionic strength and side reactions of the ligand

(Eq. (2)) Formation constant of metal-natural ligand complex, conditional to ionic strength and side reactions of the ligand Formation constant of metal-natural ligand complex, determined from competition titrations and conditional to ionic

strength and side reactions of the ligand

K’ Formation constant of a generalized metal-ligand complex, conditional only to ionic strength

abfA Competition strength for metal with added ligand (Eqs. (1) and (2))

QfL Extent of binding for metal by natural ligands (Eq. (3))

a&L Extent of binding for metal by natural ligands calculated from ligands determined by competition titrations

ad Inorganic side reaction coefficient of metal (Eq. (5))

SI Slope of linearization based on titration points at low metal concentrations

s2 Slope of linearization based on titration points at high metal concentrations

11 Y-intercept of linearization based on titration points at low metal concentrations

I2 Y-intercept of linearization based on titration points at high metal concentrations

SC Calibration slope from last part of the titration curve (Eq. (14))

SO Ideal calibration slope

s+ Overestimated calibration slope

S- Understimated calibration slope

reaction coefficient for M (e.g. [43]). The quantity ah is generally calculated from stability constants in the literature, while CZMA (Eqs. (1) and (2)) is determined as well as possible with constants from the literature, from experiments with model ‘natural’ ligands in artificial or UV-oxidized seawater (e.g. [19,25]), and from internal calibration, as described in Section 2.3.

The use of Scatchard plots to determine trace metal speciation has been most thoroughly described by

Mantoura and Riley [40]. In these linearizations, [ML]/[M”+] is plotted against [ML] (Fig. 2(a)),

[ML]/[M*+] = -KZ~ [ML] + K;;~ [q],

where an asterisk denotes calculated stability constants and ligand concentrations, as distinguished from the ‘true’ values. The two (or more) ligand case yields a curve rather than a line (Fig. 2(b)), but as long as two lines can be extrapolated from the extreme

LA. Millet K.M! Bruland/Analytica Chimica Acta 343 (1997) 161-181 165

(4 0%

+- i

2 I

WI

+I =K 1

:",""'[ L’,] + K;;;’ [L’,]

Ml Fig. 2. Idealized Scatchard plots of titration data. (A) One natural ligand, E@. (7). (B) Two natural ligands ( [40]). See text for explanation.

points, two ligand classes can still be determined

K cond’ = ML -s1, (8)

K cond’ = ML -&, (9)

[L;] = (Ii - K;$2/F$~)/(~;~* - K”M”fl,d’),

(10)

L,*l = I*Ifgg - [ql, (11)

where S and I are the slopes and y-intercepts, respectively, of the two extrapolated lines indicated by the subscripts 1 and 2, and the subscripts s and w respectively denote strong and weak natural ligands. It is not possible to uniquely determine more than two ligand classes from a Scatchard plot, regardless of how many ligand classes are in the sample [44].

Langmuir linearizations were originally applied to trace metal speciation in natural waters by van den Berg and Kramer [8] and Ruzic [42]. In this method, [M”+]/[ML] is plotted against [M”+],

[M”+l/[MLl = [M"+l/[Gl + V(Kch;d*[GIL (12)

(Fig. 3(a)). As in the Scatchard plots, the presence of more than one ligand in the original sample is indicated by curvature in the ‘linearization’ (Fig. 3(b)). The analytic solution of the two-ligand case [42]

breaks down if there is error in the data, and van den Berg [45] has developed a useful iterative method for calculating the ligand parameters using the two lines extrapolated from the extreme points. In van den Berg’s method, [L:] and K$f are first estimated from the line at low metal concentrations (Si and Ii) as in the single ligand case. Values for [ML,] can then be approximated from

[ML,] = Pg* [M”+] [L;] /( 1 + Kg; [M”+]) (13)

and subtracted from [ML] to give [ML,], and a new plot of [M”+]/[ML,] against [M”+] is generated, allowing estimation of [LG] and Ki$,d’. From these values, [ML,,,] is calculated, using an equation analo- gous to Eq. (13), and subtracted from [ML] to get new estimates of [ML,], leading to a new plot of EM”+]/ [ML,] against [M”+] and a better estimate of [L,] and Kcond’.The cycle is continued as many times as retkred to obtain the desired precision. As with the Scatchard plots, only two ligand classes can be determined uniquely with this technique. Also, although errors have different influences on the Langmuir and Scatchard plots, the values of [L+] and K$fd* produced are the same, since the two linearizations are algeb- raically equivalent.

Several authors have suggested that it can be useful to fit titration data directly to unlinearized discrete

166 L.A. Millet K.W. Bruland/Analytica Chimica Acta 343 (1997) 161-181

(4 (J9

CM”+1 W+l

Fig. 3. Idealized Langmuir plots of titration data. (A) One natural ligand, Eq. (12). (B) Two natural ligands. See text for explanation.

ligand models using non-linear curve fitting routines [46,47]. Although the non-linear data processing techniques generally produce individual ligands with the same characteristics as those from linearizations, an advantage of the former approach is that it more readily defines the uncertainties in [L$] and Kg:’ associated with applying discrete ligand models to titration data. However, it has been reported that if the titration data have much scatter, more than one ligand cannot be identified with a non-linear optimization [47], although this issue probably warrants further investigation.

2.3. Internal calibrations

A careful experimental calibration is usually required to account for uncertainties in thermodynamic constants used for Eqs. (4) and (5) and variations in sample matrices affecting the analytical measurements. Because rigorous and accurate external calibrations based on artificial or UV-oxidized seawater are often impractical for each sample, internal calibrations based on the limiting slope of the titration curve (Fig. 1) have been used to provide a reference against which speciation titrations can be judged (e.g. [lo]). After the natural ligands in the sample have been fully saturated by the metal, the

titration slope is given by

SC = aM4/(1+ aE*I + CXMMA). (14)

The competition strength, CZMA, is calculated from this equation, and the linearization parameters are then

[I@] = [MA]/~MA (4)

and

WI = [MT] - [MAI/Sc. (15)

2.4. Kinetics

The competitive equilibration approach assumes that the in situ speciation can be described by a thermodynamic model. Although open natural systems are not at true equilibrium, fast processes can often be described by pseudoequilibria [38,48]. For example, inorganic metal complexation in seawater is very rapid and can be accurately calculated from the steady-state concentrations of the major anions and their metal-binding stability constants, despite con- tinual fluxes of carbonate, sulfate, and chloride into and out of the oceans with slow weathering and sedimentation processes. If organic complexation of a particular metal is similarly rapid, and the ligand

LA. Milles K.U! Bndand/Analytica Chimica Acta 343 (1997) 161-181 167

concentrations are stable over periods of weeks, the organic speciation may also be at a psuedoequili- brium, represented by the values of [L+] and K$td* determined in competitive equilibration analyses. However, if the ligand concentrations are not at steady-state and vary rapidly with respect to the time- scale of organic complexation, thermodynamic parameters determined using an equilibrium analysis may not be valid. In this paper, we will focus on the ability of competitive equilibration techniques to describe marine pseudoequilibria and will pursue neither the kinetic limitations of these methods nor their possible implications for or uses in non-equilibrium systems (e.g. [24,49,50]).

3. Methods

We used the metal speciation program, TITRATOR (version 2.1, [5 11) to generate hypothetical titration data from which we calculated speciation results. Our reasons for choosing TITRATOR included the ease with which thermodynamic data for natural ligand classes can be assimilated into the program and its facility for creating and presenting titration data ana- logous to that from competitive equilibration analyses. We confirmed that TITRATOR is a valid alternative for seawater speciation calculations by comparing its output for inorganic copper complexation with calculations from other studies [52,53]. Table 2 gives the inorganic side reaction coefficients for copper in seawater, a&, as calculated by TITRATOR using the same speciation model (complexes and stability constants) as each reference. The TITRATOR values for a& agree quite well with the reported values and are constant over the full range of total metal concentrations used in this study. The small difference from the

results of Turner et al., 1981 [52] most likely results from the linearizing assumptions made in their calculations.

We constructed our model titrations on the basis of a simple, generalized, dissolved-phase ligand competition for copper in seawater with a competing ligand, A. The seawater matrix we used specified major ion interactions and inorganic copper complexation based on stability constants (K’) from the literature [54]. The calculated inorganic speciation was consistent with the complexation models of Turner et al. [52] and Byrne et al. [53], which set the free concentrations of the major ions. The competiting ligand, A, was chosen to form 1 : 1 Cu(I1) complexes of log Kpu’f = 7.6, a value giving useful competition strengths at total A concentrations between 1 and 5000 uM. In reality, existing dissolved-phase competitive equilibration methods for determining copper speciation have utilized competing analyte ligands which form CuA2 complexes [7,10-18,25-271. Therefore, in practice, lower concentrations of ligands forming complexes with lower formation constants are required to establish competitions comparable to what we have examined here. In both the adsorptive cathodic stripping voltammetric and solvent extraction techniques, the analytical signal is proportional to the total concentration of the competing complex, but in our models, we have assumed that the analytical signal is equal to [CuA], thus avoiding issues of variable phase distributions and analytical sensitivity. TITRATOR directly produced values of [Cu’+] and [CuL] as needed for the two linearization methods, and these data were used in our study of the intrinsic characteristics of the competitive equilibration techniques. However, for our investigations into the effects of errors in choosing the calibration line, we calculated [Cu2+] and [CuL] from [CUT], [CuA], and S, using Eqs. (4) and (15).

Table 2

Inorganic copper speciation, acu’, determined from TITRATOR calculations (Based on inorganic seawater speciation models from the

literature)

Reference TITRATOR values

0.5 (nh4) CUT 10 (nM) CUT 1000 (nM) CUT

Literature value

52 14.703 14.704 14.704 9.7 53 20.085 20.086 20.086 19.9

168 L.A. Miller: K.W Bruland/Analytica Chimira Acra 343 (1997) 161-181

4. Single ligand case Table 4

Competition strengths used for model titrations

We begin by reviewing how high detection limits and analytical imprecision constrain the interpretation of metal speciation data, using a simple model with one ‘natural’ copper-complexing ligand (Table 3, ligand set #I, log acUL=4.2), characteristic of those typically observed in open ocean waters (e.g. [4,26]). Each competition strength in Table 4

(1.6Llog acUA<5.3) was used to generate a hypothetical metal titration out to 20 nM as shown in Fig. 4. In the case of the weakest competition (squares in Fig. 4), the natural ligand strongly dominates over the analytical ligand aCuA<<acuL), and [CuA] does not increase appreciably until L is fully saturated. The open circles in Fig. 4 show the case where the competition strength is too great and the added ligand completely dominates over the natural ligand (aCuA~>aou~). In this situation, the titration plot is a straight line which intersects the origin, giving no indication that there are any natural organic ligands in the sample.

log acuA 1.6 3.2 4.8 5.3

[&I @M) 1 40 1600 5000

20

15

f

2 10

:

5

0

As lmg as there is no error in the data, linearization of any of the four titrations shown in Fig. 4 will produce straight lines with the same intercepts and

Table 3

Natural copper-binding ligand sets used to generate model titration

data (log acuL at 0.5 nM Cur)

Fig. 4. Model titrations of single-ligand #l ([Lr]=2 nM,

logKFup = 13.0). Lines represent linear regressions of the last points in each curve. (-¤-) Weak competition, logacUA=1.6,

limiting slope=0.509; (-v-) Medium competition, log acUA=3.2,

limiting slope=0.975; (..a..) Strong competition, log acUA=4.8,

limiting slope=0.978; (-a-) Very strong competition,

log acUA=5.3, limiting slope=0.973.

1.

2.

3.

4.

5.

LI

L2

LI

L2

L3

Ll

L2

L3

LI L2

L3

L4

L5

L6

L7

L8 L9

LIO

&I (nM) log Kg; log acuL

2 13.0 42

2 13.0 42

10 10.1 2.1

2 13.0 4.2

4 11.7 32

10 10.0 2.0

2 12.0 2.8

4 11.7 3.2

2 11.4 20

0.5 15.0 5.4

2 14.0 5.3

5 13.0 4.7

10 12.0 4.0

20 11.0 33

50 10.0 2.7

100 9.0 2.0

500 8.0 1.7

1000 7.0 1.0

10000 6.0 10

slopes (compare the linearizations in Figs. 5 and 6). What this means is that, in theory, any single metat- binding ligand can be identified accurately using the competitive equilibration approach. However, because of detection limit and precision constraints, it is generally not possible to determine ligands with acUL more than an order of magnitude either above or below ac”A, the strength of the competition (that is, outside the analytical window).

When the natural ligand dominates over the competing ligand (aCuA NI,-~~), the detection limit pre-

vents accurate analysis of the early titration points, which establish the stability constant. The conse- quences of losing confidence in those first few titration points are seen in Fig. 5, which shows line-

5 10 15 20

[C-u,]. nM

LA. Miller: K.W Bruland/Analytica Chimica Acta 343 (1997) 161-181 169

\ I- i

\ t-

1

-

-I

0 12 3

I I

I ,T,

i 2 3

[CuL], nM

/ 0 2 4

0.004 I 0.16 T

1000

500

0

0.002 - 0.12

z fz

0.000 c 0.08 7

‘;;

I=

0.04

-

4licw 0.00 0 50 100 150 200 250

[c”*+]. PM

Fig. 5. Linearizations of data from the weak competition in Fig. 4. log ac,4=1.6. Error bars determined from 3% or 0.07 nM error in [CuA].

Calculated values: [y]=2.00 nM, log Ps* = 13.0. (A) Scatchard plot. slope=-1.00x 10 13, intercept=2.OOx 104. Inset: contraction of y-axis

showing magnitude of errors in early titration points. (B) Langmuir plot. slope=5.OOx lo’, intercept=5.OOx 10-s. Inset: expansion of axes focussing on early titration points.

arizations of the data represented by squares in Fig. 4 (log aCuA=1.6). Error bars were generated by propa- gating the higher of either a f3% or f0.07 nM (corresponding to a detection limit of 0.2 nM) error in [CuA] (Table 5). In both the Scatchard and Lang-

muir plots, the calculated stability constant, KFuf*

(determined from the slope in Fig. 5(a) and the y- intercept in Fig. 5(b)), is strongly dependent upon the early titration points, with their extremely large relative uncertainties. In contrast, the ligand concentration

170 L.A. Miller; K.W Bruland/Analytica Chimica Acta 343 (1997) 161-181

0 -0.0 0.5 1 .o 1.5 2.0 0 20 40 60 80 100

[CuL], nM [co*+], fM

(B) 160

120 T

2 v

” 3 a0

Y ‘p 0

40

I I I I

Fig. 6. Linearizations of data from the very strong competition in Fig. 4. log acUA=5.3. Error bars determined from 3% or 0.07 nM error in

[CuA]. Calculated values: [L+]=2.00 nM, logK,-,, w”~* - 13.0. (A) Scatchard plot. slope=-1.00x10 - t3, intercept=2,00x 104. (B) Langmuir plot. slope=5.OOx lo*, intercept=5.00x 10.‘.

is relatively well-constrained by the later titration points in both linearizations.

Conversely, if the analytical ligand dominates over the natural one (ocuA>~ocuL), the uncertainties are more serious in the later titration points. In that case, [CuL] is calculated from the difference between two large numbers (Eq. (6)), and the analytical precision limits the ability to distinguish between the presence and absence of the natural ligand. Fig. 6 shows the linearizations of the titration at 5mM A (log oCuA=5.3, open circles in Fig. 4) with the same propagation of errors as applied in Fig. 5. The general form of the uncertainties is the same, but the relative importance of the high and low titration points has shifted. In this situation, although neither the ligand concentration nor the stability constant can be determined confidently, [L+] (from the x-intercept of the Scatchard plot, Fig. 6(a), or the slope of the Langmuir plot, Fig. 6(b)) is particularly poorly defined.

In order to determine both [L+] and log Fond* (for simplicity, the subscripts, CuL, will be omitted from the stability constants for the natural ligand complexes from here on) with any confidence, the competition strength must match the extent of binding in the sample (ocuA~ocUtJ, striking a balance between the restrictions of detection limit and analytical

imprecision. Table 6 gives the estimated ranges of [L+] and log Kcond* which can be derived from linearizations of the filled-circle data (log acUA=4.8) in Fig. 4, with the same uncertainties as those applied in Figs. 5 and 6. In this case, ocUA is only 0.6 log units higher than acUL. Although both Fond* and [L+] can be determined from this titration, they are still subject to significant uncertainties. The values calculated from Langmuir linearizations are generally more sensitive to analytical uncertainties, because Fond* and [q] are inversely related to the slope and intercept of the plot. However, interpretation of Scatchard plots is often hampered by larger immediate scatter in the data, making it difficult to discern a line.

If analytical techniques and instrumentation con- tinue to advance, thus lowering detection limits and improving precision, the useful widths of analytical windows will widen, and it will become possible to

Table 5 Propagated uncertainties in linearization parameters (h() =

uncertainty in parameter 0)

h([Cu*‘]) = ~([CUA])/W.A

WuLI) = WuA])/So

~([Cu*']/[CuL]) = [CUTI~(IC~A~)/{~C,A([C~TI- PWo)* 1 A([cuL]/[cu*+]) = ac~A[cU,l~([C~Al)/[C~Al*

L.A. Millet K.W Bruland/Analytica Chimica Acta 343 (1997) 161-181 171

Table 6

Ranges of [L+] and log Kcond* determined at a competition strength matching the extent of binding by L, based on a propagated 3% or

0.07 nM error in [CuA] (log acUA=4.8. Ligand set #l: [b&2 nM, log IF”d- -13.0, log acuL=4.2. Titration to 20 nM CuT)

Plot type Langmuir Scatchard

log F”d’

Maximum Minimum

&I

13.7 13.5 12.2 12.6

Maximum 10 nM 3nM

Minimum 1 nM 1 nM

‘see’ a greater range of binding strengths with a single titration. However, it will still be important to remem- ber that there may be unidentified ligands outside the analytical windows, even if multiple titrations at different competition strengths are performed. With careful selection of the competition strengths, it may be possible to say that any ligand not identified by the analysis could not be geochemically important. For example, ligands too weak to be seen with a competition at the same strength as the inorganic side reaction coefficient of the metal, i.e. CLM&X~‘, would be unable to compete with the inorganic ligands and therefore could not bind a significant fraction of the metal. Similarly, ligands at concentrations orders of magnitude lower than the ambient metal concentration, requiring extremely strong competitions for characterization, could have no significant effect on the overall metal speciation. Nonetheless, the possible existence of ligands outside the analytical windows must always be considered.

5. Two ligands

Competitive equilibration methods have been most successful at describing metal speciation that is dominated by low concentrations of ligands forming strong metal complexes. Confident identification of the large concentrations of weak ligands that often appear to be important to metal speciation in estuaries has proven more elusive using these techniques [7,27], even when relatively weak competitions are used. The reasons for the difficulties in characterizing these weaker ligands are demonstrated by ligand set #2 in Table 3. Again,

this ligand set is modelled after two copper-binding ligands that have been identified in open ocean samples (e.g. [4,55]).

Fig. 7(a) shows a model titration of ligand set #2 with a medium competition strength (log oCuA=3.2, between the values of ocuL for the two natural ligands). The linearizations in Fig. 7(b) and (c) show unequivocally that there is more than one ligand present, but the determination of each ligand is dependent upon only a couple of critical points which are subject to relatively large errors. In addition, the concentration of the weak ligand, [L;], is underestimated. This is because that ligand is less than 50% bound by the end of the titration. When there is more than one ligand in the sample, and the weak ligand is not fully saturated, the strong one heavily weights the values of [CuL] calculated from Eq. (6). Fig. 8 shows how important this effect is and indicates the degree of ligand saturation required to accurately calculate its concentration in the presence of a stronger ligand. In this case, in order to determine the concentration of LZ to within 95%, it must be at least 60% bound by the end of the titration, requiring a total copper concentration of 200 nM. The more similar the ligands are, the less important it is to fully titrate the weak ligand, but an unsaturated weak ligand appears to be stronger and at a lower concentration (that is more like the strong ligand) than it really is.

Difficulty in saturating weak binding sites is the primary factor precluding determination of large concentrations of very weak ligands, such as humic acids, by competitive equilibration. In the presence of stronger ligands, a humic-like ligand class characterized by a metal-binding stability constant of lo8 M-’ and a concentration of 1 pM (acuL=102) could require metal titration to concentrations up to 0.1 mM or even higher. Titration over such wide ranges in metal concentration poses serious laboratory contamination threats. In addition, the linearization assumption that the competing ligand concentration is much higher than that of the metal ([A~]B[MT]) is violated when a titration at a low competition strength is carried out to high metal concentrations, and more complicated data processing methods are then required.

The weak ligand in our model, La (o+UL=102.1), can be determined with reasonable confidence using the weak competition strength (o.,-UA=10’~6) and the same values for [Cur] as in Fig. 7(a). In this case, several

172 L.A. Millet K.W Bruland/Analytica Chimica Acta 343 (1997) 161-181

(A) 120

100

80

I r

- 60 7 2

40

20

0

I I I I I I

,.,.@

.,’

,_,’

,,,’

9,“’ ,,,’

,_,’ _;’

,.I’

,.tn ..” . ..’

,/

B’, , (, /-

20 40 60 80 100 120 140

[CUT], nM

0 2 4 6 8 10 12

[CuL], nM

0 0.0 0.4 0.8 1.2 ^^

0.6 I 16

.’ - 0.4 - ,’ 14

,’ - 12

0.3

0.2

0.1

0.0

0 20 40 60 80

[Cu2’l, PM

Fig. 7. Titration of 2-ligand set #2 (Li: 2 nM, log Kyd = 13.0; Ls: 10 nM, log Kyd = 10.1). log acUA=3.2. Error bars determined from 3% or 0.07 nM error in [CuA]. Filled symbols: points used for linear regressions. Calculated values: [L;] =2.04 nM, logKyd* = 13.0,

[L;]=8.18 nM, logKyd*= 10.4. (A) Titration. B) Scatchard plot. S,=-9.68x 10’s, 1,=2.00x 104, Ss=-2.70~10’~, Is=276. Inset: expansion of y-axis focussing on later titration points. (C) Langmuir plot. S1=4.84x lo*, 11=5.00x lo-‘, &=9.79x 107, 12=3.62x 10e3. Inset: expansion

of axes focussing on early titration points.

points with relatively minor uncertainties define [L;] Fig. 5, compounded by a limited number of low metal in both linearizations. On the other hand, the early addition points. Therefore, although the weak compe- points are extremely non-linear and have very large tition provides a good determination of the weak uncertainties in relation to their slopes and intercepts. ligand, a stronger competition is still required to This is the same detection limit problem examined in identify confidently the strong ligand. Conversely, a

L.A. Miller; K.W Bndand/Analytica Chimica Acta 343 (1997) 161-181 173

0 20 40 60 80 100

Fig. 8. Calculated concentration of a weak ligand (percentage of

the true total weak ligand concentration) as a function of its percent

saturation at the end of the titration. Ligand set #2 analyzed with

medium competition strength, log acUA=3.2, and varying final

metal concentration.

strong competition (ocuA= 104s) gives very confident estimates of [L;] and Kyd*, although evidence for the presence of the weak ligand nearly disappears, and the linearizations are only slightly curved.

The most important point when dealing with two ligands is that results from a single analytical window can be misleading. In addition to the issues of detection limits and data precision discussed in Section 4, specific conditions must be met in order to determine confidently the concentrations and metal-binding stability constants of weak versus strong ligands. At the beginning of the titration, several points are required before the strong ligand is saturated if Kyd* is to be determined. Also, if the weak ligand is not saturated at the end of the titration, its concentration may be underestimated and its stability constant overestimated, making it more difficult to distinguish from the strong ligand. At the extremes, titrations at competitions weaker than the weakest ligand or stronger than the strongest ligand may only allow identification of one ligand. Even when windows of intermediate competition strength are used, and curved linearizations make it clear that more than one ligand is present, the necessity of using a few extreme titration

points to calculate [L+] and Fond* for the two ligands gives rise to large uncertainties in those values. There- fore, if one wishes to confidently characterize both disparate ligands with confidence, at least two titrations at different windows are required.

6. Three or more ligands

Despite mounting evidence that complex mixtures of binding sites are usually responsible for metal speciation in marine waters, investigators generally interpret their titration data in terms of discrete ligands, primarily because application of continuous distribution models is more complicated [56-581. Moreover, recent work has shown that it may not be possible to uniquely characterize the ligand distribution in a sample, whether discrete or continuous, from a single analytical titration unless the precision in the data is within a relative standard deviation on the order of lo-“% [59] ! Therefore, the important question is not whether a particular ligand model is rigorously accurate, but whether geochemically useful parameters such as free metal ion concentration (or activity) and total extent of organic binding, oML, can be effectively modelled by the discrete ligands generated from competitive equilibration titrations.

6.1. Multiple, distinct ligands

Ligand set #3 in Table 3 is a simple model of three very different ligands with individual values of log ocUL between 2.0 and 4.2. We constructed titrations of this ligand set using the three competition strengths at log ocUA of 1.6,3.2, and 4.8 (with titration points every 1 nM up to 20 nM and then every 6 nM up to 160 r&I, and assuming perfect accuracy and precision). All of the linearizations were curved and gave two ligands, as summarized in Table 7. The free metal concentrations, [Cu2+]*, and the total extents of binding due to the natural ligands, oEUL, in Table 7 were determined by calculating copper speciation at 0.5 nM Cur without the competing ligand, A, but with the two ligands evaluated from each titration.

As shown in Table 7, the attributes of Lf determined from all three competitions uniquely characterize L,. On the other hand, LG is influenced by both of the two weaker ligands, Lz and Ls, and as the compe-

174 L.A. Millq K.W Bruland/Analytica Chimica Acta 343 (1997) 161-181

Table 7 Titration results for a diverse set of ligands (Ligand set #3: L,: 2 nM, IogK, co”d = 13.0; L1: 4nM, logKyd = 11.7; Lx: lOnM,

log Kyd = 10.0. log olcuL = 4.25 and [Cu*+]=28.2 fM at 0.5 nM CuT. Each titration to 160 nM total copper. Tabulated values of [Cu*+]* and

logcy& were determined by calculating speciation of 0.5 nM CuT with L; and LG)

log %A El Wf) log Kyd’ [L;l OW log Kpd* [al*+]* (fM) a log a&La

1.6 2.86 12.9 13.1 10.2 28.3 4.22

3.2 2.70 12.9 11.3 10.5 28.6 4.24

4.8 2.03 12.9 4.15 12.0 29.3 4.23

a At [CuT]=0.5 nM.

tition strength increases, Ls has less influence on Lz. Ultimately, with the strongest competition (log a,&!, =4.8), Ls has no impact on the calculated ligands, and Lz provides a good characterization of LZ.

Thus, at the initial copper concentration (0.5 nM), where the speciation is dominated by Li, the total extent of binding and the free metal concentration are established quite well by any of the three competitions (Table 7). However, as the copper concentration increases, the stronger ligands are saturated and become less important, concomitant with increasing significance of the weaker ligands. Fig. 9 shows the speciation calculated from each ligand set in Table 7 as a function of the total copper concentration (in the absence of the competing ligand, A). Here, we see that as stronger competitions are used, the calculated speciation based on LK and LG deviates from the ‘true’ speciation at lower total metal concentrations. In particular, the ligands determined from the titration at log ~1c~A14.8 (dotted lines in Fig. 9) severely underestimate the extent of copper complexation at metal concentrations higher than the calculated total natural ligand concentration, [L+] (6.2 nM). It is important to note that even with strong competitions, titrations to higher metal levels determine weaker ligands better (Fig. 8), thereby improving the fit with the true speciation at higher metal concentrations. The slight deviations from true speciation at intermediate metal concentrations (2-15 nM Cur) can also be explained by the different weighting of Li, LZ, and Ls in the calculated ligands, Lz and Lk.

6.2. Mixed l&and classes as modelled by discrete ligands

Ligand set #4 in Table 3 is a simple model of three similar ligands at a total concentration of 8 nM and

with an overall, weighted mean stability constant

K gT = C(LiIKEL)I[LTI

of lo”.75 M-’ (log acUr_=3.65). The Scatchard and Langmuir plots from titrations of ligand set #4 at the competition strengths over the range 1.6<log a~“~s4.8 were nearly linear and each could be interpreted in terms of a single ligand, as shown in Table 8. The estimates of [L’] and Kcond* were 7.0 to 8.0 nM and 1O11.7o to T 1O11s M-l, respectively. The strongest competition preferentially emphasizes the strong copper-binding aspects of the ligand class, giving a high stability constant but a low ligand concentration. On the other hand, the weak competition generates the right ligand concentration but a low stability constant. The same pattern was seen in actual iron speciation samples from the Mediterranean analyzed at two different competition strengths [23]. Despite these small errors in the calculated values for [L;] and log Fond*, the speciation ([Cu*+]* and CL& at low metal concentrations is still determined accurately with all three competition strengths.

As a final test of how well the discrete ligands from competitive equilibration methods can model more complicated speciation, we designed a set of ten ligands to approximate a continuous distribution (ligand set #5 in Table 3). We conducted two sets of model titrations using the first three competition strengths in Table 4, one set out to 50 nM total copper and one to 1 pM (each with 26 evenly spaced points). Each titration with each competition strength was distinctly curved and yielded two ligand classes, as summarized in Table 9. Again, all of the calculated ligand pairs give very good estimates of the original copper speciation at a low metal concentration. How- ever, stronger competitions yield ligands at lower

L.A. Miller; KU? Bruland/Analytica Chimica Acta 343 (1997) 161-181 175

(A) 0 10 20

03 0 10 20 30

0.3

0.2 4

0.1 z 5 . 3 ?i ; E N

0.0 ,+ .

2 1

1

0 0 40 80 120 160

[Cu,], nM

Fig. 9. Fit between two-ligand models (Table 7) generated from titrations of a diverse ligand set (#3) and true speciation with increasing

copper concentration ([AT] =O). (--- ) speciation based on all three ligands in set #3; (- - -) speciation based on two ligands calculated

from weak competition, log czCuA=1.6; (- - -) speciation based on two ligands calculated from medium competition, log acUA==3.2; (...) speciation based on two ligands calculated from strong competition, log acuA=4.8. (A) Fit between calculated and true values of aCuL. (B) Fit

between calculated and true values of [Cu*+]. Insets: expansions of axes focussing on low total metal concentrations.

176 LA. Miller; K.W! Bruland/Analytica Chimica Acta 343 (1997) 161-181

Table 8 Titration results for a set of similar ligands (Ligand set ##4: Lr:2 nM, log Kyd = 12.0; Ls: 4 nM, log Kyd = 11.7; Ls: 2 IN, log yd = 11.4.

log ac,c=3.62 and [Cu2’]=0.12 pM at 0.5 nM Cur. Each titration to 80 nM Cur. Tabulated values for [Cu2+]* and log II& were determined

by calculating speciation of 0.5 nM Cur with L*)

log acuA

1.6

3.2

4.8

F-4 (nM)

8.0

7.8

7.0

log Fond*

11.70

11.73

11.81

[Cu2+]* (PM) =

0.13

0.14

0.12

log o;,r_

3.58

3.56

3.61

’ At [Cur]=O.5 nM.

Table 9 Titration results for a complex ligand mixture (Ligand set #5. log acUL=5.69 and [Cu2+]=l.0 fM at 0.5 nM Cur. Tabulated values for [Cu2+]

and log a& were determined by calculating speciation of 0.5 nM Cur with Lf and L;)

log acuA [J-:1 WI)

Titrated to 50 nM Cur

1.6 3.5

3.2 3.4 4.8 2.7

Titrated to 1 uM Cur

1.6 38

3.2 29

4.8 I1

a At [Cur]=O.5 nM.

log Kcondt s P-3 (nM) log F$“d’ [cuZ+]* (f-M) log &.

14.2 70 10.8 1.1 5.68

14.2 47 11.3 1.0 5.68 14.3 16 12.5 1.0 5.70

13.1 1000 8.1 1.1 5.67

13.2 230 9.4 1.1 5.65

13.7 47 II.1 0.98 5.71

concentrations that form metal complexes with higher stability constants. In addition, titration out to higher metal concentrations generally gives weaker ligands at higher concentrations.

Therefore, the extent to which the speciation at elevated copper concentrations can be fit with the two calculated ligands depends upon how strong a competition was used in determining them and to what metal concentrations the sample was titrated (Fig. 10). Since the divergence patterns for CL&,_ and [CL’+]* mirror each other, Fig. 10 only shows [Cu2+]*. In general, the fits hold best at lower copper concentrations, and the results from weaker windows or from titrations out to elevated metal concentrations can be applied to higher metal levels before significant deviations from true behaviour become apparent.

most important limitation arises when attempting to predict how a system will respond to elevated total metal concentrations. As has been noted before [46], extrapolation of titration results to high metal concentrations can severely underestimate complexation, particularly when strong competitions are used, leav- ing important weak ligands unidentified. If speciation results are to be applied over a wide range of metal concentrations, multiple analyses at different competition strengths will be required, in order generate enough discrete ligands to effectively model the system.

7. Internal calibrations

To summarize our findings from multiple ligand Up to this point, we have assumed that the analy- systems, speciation in samples with complex ligand tical sensitivity (in the absence of any natural organic distributions can be modelled quite well with the two- ligands) in the specific sample medium is accurately or one-ligand sets determined from competitive equi- established by an external calibration that is indepen- libration titrations, within certain constraints. The dent of the specific titration analysis. In actual ana-

L.A. Millq K.W. Bndand/Analytica Chimica Acta 343 (1997) 161-181

(A) 0%

m *’

#’ #’

’ / ,,’ /

,/”

i-/

. / :, H

, -. I : : : : : ,* : ,’

: .’ : ,’

: ,’

/.4&l 0 10 20 30 40 50 0.0 0.2 0.4 0.6 0.8 1 .o

[CUJ. nM rcu,1. PM

177

30

25

20

F 15 2

; 10

5

0

Fig. 10. Fit between [CL?+]* based on two-ligand models (Table 9) and true values of [&+I based on a mixed ligand set (#5), with

increasing copper concentration ([A=]=O). ( -) speciation based on all ten ligands in set #5; (- - -) speciation based on two ligands

calculated from weak competition, log acUn=1.6; (- - -) speciation based on two ligands calculated from medium competition, log acUA=3.2;

(...) speciation based on two ligands calculated from strong competition, log acUA=4.8. Calculated values of [Cu’+] based on titrations to (A)

50 nM [Cu7] and (B) 1 pM [CuTI. Insets: expansions of axes focussing on low total metal concentrations.

lyses, uncertainties in side reactions of the added ligand and unknown effects of individual sample matrices necessitate internal calibrations based on the limiting slope of the titration curve, as described in Eq. (14).

If a weak natural ligand which can compete with the analytical ligand is not fully saturated by the end of the titration, the calibration slope will be underestimated. The effect of underestimating the calibration slope in this way is demonstrated by a titration of ligand set #2 (at a competition strength of log o.cuA=3.2) to only 10 nM total copper(I1). In this case, we calculated [Cu2+] and [CuL] from Eqs. (4) and (15) using the observed titration slope at 10 nM Cur (S,=O.910), instead of using the values directly produced by the TITRATOR program, as in our earlier analysis of this ligand set with the same competition (Fig. 7). With log acuA=3.2 and in the absence of any natural ligands, the ideal titration slope is Z&=0.977. At 10 nM Cur, Li is 98% bound while L2 is only 0.6% associated with the metal, and the linearizations are not curved. Despite the low calibration slope, Li is accurately represented by the one calculated ligand

([q) = 2.0&I, log Pond* = 13.0). In fact, the limited concentration range invites a higher titration point density, making it possible to determine the strong ligand much more precisely (more data points are dedicated to its calculation) than shown in Fig. 7. As shown in Section 6, this single ligand result is ade- quate for describing the system at low metal concentrations.

Even when all the natural organic ligands have been saturated and further increases in [MA] are limited only by the analytical sensitivity, random scatter in the data can lead to uncertainties in the slope. This effect is demonstrated by a weak competition titration (log ocuA=1.6) of the same two-ligand set (#2). In theory, as long as there is a high titration point density at low copper concentrations and no error in the data, both ligands can be accurately characterized with this titration. Fig. 11 shows the titration, including error bars and a reasonable range of slopes for the calibration line. In addition to the 3% (or 0.07 nM) uncertainty in [CuA], a 1% (or 0.05 nM, at low metal additions) uncertainty in [Cur] has been included. The ideal slope in this case is S,=O.511, and in

178 L.A. Miller: K.W Bndand/Anaiytica Chimica Acra 343 (1997) 161-181

60 ,:’

60 80 100 120 140

[CUT]. nM

Fig. 11. Titration of 2-ligand set #2 (L,: 2 nM, log Kyd = 13.0;

Lz: 10 nM, log Kyd = 10.1). log acuA==1.6. Error bars determined from 3% or 0.07 nM error in [CuA] and 1% or 0.05 nM error in

[CuTI. Dashed lines represent calibration lines giving maximum

and minimum slopes based on uncertainties in titration data

(0.44~&~0.53).

Fig. 11 the observed slope, S,, could vary between 0.44 and 0.53. Using these values, we calculated [Cu*+] and [CuL] at each titration point from Eqs. (4) and (15) (instead of using the [Cu*+] and [CuL] output from TITRATOR) and generated Scatchard and Langmuir plots corresponding to the two extremes. The resulting equations and estimates for [L+] and log Pond* are presented in Table 10.

Uncertainty in the slope has little effect on the

characterization of L1. The reason for this can be understood by returning to Eq. (15). In the first titration points, which are critical to determining L1, most of the copper is bound by L1, and [CuA] (and therefore, the term containing S,) is essentially zero. As [CuA] increases, S, becomes more important, and small errors in its value will have a much greater effect on the calculation of [CuL]. In fact, if the slope is underestimated, the values of [CuL] calculated from Eq. (15) can eventually become negative. Under these conditions, it is not possible to fit a reasonable line to the later titration points in the linearizations, and L2 cannot be characterized.

In conclusion, the internal calibrations appear to be valid for determining strong ligands, and poor estima- tions of the limiting slope mainly influence the characterization of weak ligands. If the slope is overestimated, the extent of binding due to L2 is significantly underestimated (calculated [Lz] is high, but log Kyd* is low). Underestimating the limiting slope because of an undersaturated weak ligand only exaggerates an already existing inability to accurately determine that ligand. However, if all the ligands in the sample are saturated, and the slope is still underestimated because of analytical uncertainty in the later data points, the values calculated for [CuL] can become negative, thus frustrating efforts to identify the weak ligand.

If it is important to accurately determine such weak ligands, some sort of an external calibration may be needed. Analyses of relatively clean freshwater samples can probably be conducted without any calibra-

Table 10 Impact of calibration slope errors on linearization results (log a,-,~=1.6. S,=O.511. Ligand set #2: LI : 2nM, logKyd = 13.0;

Lz : lOnM, loged = 10.1)

S+=O.527 s_ =0.444

Langmuir

Scatchard

Calculated ligands

Li:

L2:

y,=4.99x lo-‘+4.88x 10s~~ y1=4.99x 10-5+4.89xlosxl y2=o.0345+3.33 x 107x2

y,=2.01 x 104-9.78x 10’2x, y,=2.OOx 104-9.80x 10’2x, y,=29.0-9.67x 108x2

[L;] = 2.1 nM logKTd* = 13.0 [L;j = 2.0&l IogKP”d’ = 13.0 [L;] = 28nM logKyd* = 9.0 -

L.A. Millel: K.U? Bruland/Analytica Chimica Acta 343 (1997) 161-181 179

tion beyond the published stability constants for the components of the system, if they are available. In most cases, open ocean samples can probably be calibrated confidently with artificial seawater titrations, since the salt matrix of seawater is very well understood and organics are generally low. However, in extremely complex samples such as those from estuaries (ironically, places where large concentrations of weak ligands appear to be most important), careful calibration is the most difficult, and even a titration of a UV-oxidized sample may be inadequate. An important point, however, is that an external calibration may not be necessary as long as one is only interested in the ligands responsible for strong complexation and no attempt is made to extrapolate the results to high metal concentrations.

8. Conclusions

In this study, we have used computer-generated model data to show how competitive equilibration techniques can be used to accurately determine trace metal complexation in natural water samples. In particular, we have identified many of the analytical limitations of these techniques, as well as some specific requirements for effective metal speciation analyses.

With perfect data (that is, with infinitely small detection limits, absolute precision, and ideal calibrations), as long as there is only one ligand present, its concentration and metal-binding stability constant can be accurately determined. When more than one ligand is present, however, several titration points before a strong ligand is saturated are required for that ligand to be fully characterized. At the other extreme, undersaturated weak ligands cannot be distinctly resolved from the stronger ones. If the sample contains more than two ligands, it is not possible to uniquely identify all of them from a single titration, but up to two ligands from each analytical window (at different competition strengths) can be calculated and used to model the actual speciation at the initial, in situ metal concentration. Extrapolation of this modelled speciation to metal levels above the total determined ligand concentration may underestimate the total extent of binding, if there are unidentified weak ligands present. In general, the results from titrations at weaker

competitions can be applied up to higher metal concentrations.

Analytical realities further limit the utility of speciation results from the competitive equilibration techniques, but most of these limitations can be bypassed by conducting titrations at different competition strengths. The detection limit sets the degree to which a strong ligand can be determined by a weak competition, and conversely, the ability to characterize a weak ligand with a strong competition is limited by the analytical precision. Therefore, natural ligands are determined most effectively when the competition strength matches the natural extent of binding (oMA approximately 0.1-10 times CY.&.

The practice of using an internal calibration to account for matrix variations and poorly understood sample chemistry is very effective for identifying strong ligands. However, caution is advised when applying an internal calibration to the determination of weak ligands, since errors in the calibration slope have a greater impact on the later titration points.

In theory, with a weak enough competition, speciation dominated by very large concentrations of very weak ligands, such as humic acids, should be acces- sible by competitive equilibration methods, but such analyses are limited by practical concerns. First, errors in the internal calibration have a profound effect on the determination of weaker ligands. In addition, as the competition strength required to determine weak ligands decreases (or,+, + at), extremely low competing ligand and high metal concentrations become necessary, and all benefits of competitive equilibration methods are lost. In such cases, use of these techniques simply complicates the analysis, thereby reducing precision and increasing the potential for contamination, and it is best to use a method that directly responds to the in situ concentration of one of the species (e.g. anodic stripping voltammetry [7]).

Based on our observations here, we have developed experimental design recommendations for situations when the analyst is not able to anticipate the speciation in a given sample. Initially, we suggest examining a window at a strength only slightly higher than the inorganic complexation for the metal (CLMA 2 ad). The titration should be carried out to a total metal concentration at least an order of magnitude higher than the original [MT], to encourage saturation of any important weak ligands that may be present. If results

180 L.A. Milk< K.W. Bruland/Analytica Chimica Acta 343 (1997) 161-181

are available in near real time, metal additions should be continued until a constant slope has been attained. In addition, the first few titration points should be close together, and at least three additions should be used to double the ambient total metal concentration. This should allow identification of strong metal-binding ligands at or near the same concentration as the metal [35]. If there is evidence for a strong ligand at a low concentration, a titration at a stronger competition strength (oMA an order of magnitude or more higher than for the first titration) is probably required to characterize it. The combination of these two analytical windows should identify any ligands that may be important to the metal speciation, although more refinement of the competition strengths may be required, depending upon the precision and accuracy desired. In particular, analyses at many competition strengths will be necessary if one wishes to accurately predict the speciation over a wide range of metal concentrations. Finally, external calibrations need only be done if a class of weak metal-binding ligands is found to be important.

As with any analytical method, the competitive ligand equilibration techniques have their limitations. However, with careful and thoughtful analysis, these methods can be extremely powerful tools for the study of trace metal speciation in seawater.

Acknowledgements

This work was supported by ONR grant N00014- 93-I-0884. We wish to thank Dr. Beatriz Baliiio for enlightning discussions about validating models and an anonymous reviewer for helping us clarify the presentation.

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I61

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PI

[91

UOI

Cl11

[I21

[I31

Cl41

[I51

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u71

Cl81

u91

PO1

Pll

P21

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competitive equilibration techniques for determining transition metal speciation in natural waters:...

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