Characterization of copper complexation with natural dissolved organic matter (DOM)—link to acidic...

Water Research 36 (2002) 5083–5101

Characterization of copper complexation with naturaldissolved organic matter (DOM)—link to acidic moieties of

DOM and competition by Ca and Mg

Yuefeng Lu1, Herbert E. Allen*

Department of Civil and Environmental Engineering, University of Delaware, Newark, DE 19716, USA

Received 1 March 2001; accepted 1 May 2002

Abstract

We investigated Cu complexation by three dissolved organic matters (DOMs) collected by reverse osmosis (RO).

Alkalimetric titration, pH-stat Cu and Ca titrations, pH edges of Cu–DOM complexation, and Ca/Mg–Cu exchange

experiments were investigated at I ¼ 10�2 M for DOM samples of 10mg C/L. The proton and Cu binding

characteristics indicated similarity for all three DOMs. All Cu titrations employed ion selective electrode measurement

and indicated the presence of relatively small amounts of strong Cu-binding sites. Four distinct classes of Cu binding

sites are required for FITEQL 4.0 to provide good fits to the entire curves. The estimated total Cu binding site density is

4.55mmol/g C, much less than the total acidity but very close to the phenolic site content. Cu–DOM complexation

increases approximately 10-fold per pH unit, even at relatively high pH (>8). We suggest that sites characterized as

phenolic based on alkalimetric titration, not carboxyl sites, account for the majority of Cu complexation under natural

water conditions, and Cu–DOM complexation is principally through the replacement of H+ by Cu2+ at the phenolic

binding sites. The Cu–H exchange ratio is 1:1 for the first three sites and about 1:2 for the 4th site. This 4-site model

describes well the pH dependency of Cu–DOM complexation and provides good estimates of free Cu concentrations

throughout wide total copper (CuT) and pH ranges. Comparison between Ca–DOM and Cu–DOM complexation

demonstrated that (i) Ca–DOM complexation increases much less than an order of magnitude per pH unit and

decreases at higher Ca concentration, different from that of Cu–DOM complexation; and (ii) Cu–DOM complexation

is highly non-linear, in contrast to the much reduced extent of non-linearity of Ca–DOM complexation. Ca/Mg–Cu

exchange experiments showed small competition effect, less than expected by a simple competition model, and the

competition tended to reduce with increasing Ca or Mg concentrations. The extent of the competition by Mg and Ca

are essentially comparable. Put all together, it suggests that Ca and Mg are preferably bound by carboxyl sites,

especially at relatively high concentrations, resulting in a weakened apparent competition effect. r 2002 Elsevier

Science Ltd. All rights reserved.

Keywords: Dissolved organic matter (DOM); Complexation; Copper; Ion selective electrode (ISE); Calcium; Magnesium; Competition

1. Introduction

In natural waters, complexation by natural dissolved

organic matter (DOM) can dominate the speciation of

trace metals and thus control the metal toxicity and

bioavailability (e.g., [1–5]). Humic substances that

constitute the majority of the DOM consist of a mixture

of non-identical large molecules bearing various kinds of

*Corresponding author. Tel.: +1-302-831-8449; fax: +1-

302-831-3640.

E-mail address: [email protected] (H.E. Allen).1Present address: Connecticut Agricultural Experiment Sta-

tion, Department of Soil and Water, New Haven, CT 06511,

USA.

0043-1354/02/$ - see front matter r 2002 Elsevier Science Ltd. All rights reserved.

PII: S 0 0 4 3 - 1 3 5 4 ( 0 2 ) 0 0 2 4 0 - 3

complexing functional groups that exhibit in total a wide

range of affinities for metal ions [6]. Two major types of

functional groups are usually indicated as being of the

greatest importance: carboxyl and phenolic groups, for

which the average pKa’s are estimated to be around 4.5

and 10, respectively [7]. The sites characterized as

phenolic can also include other functionalities, for

example, amines and amides.

Numerous investigations have been conducted of

complexation of metal ions by natural organic matter

and a number of model interpretations have been

developed (e.g., [8–11,6,1,12–20]). Most current models

incorporate multi-ligand representation, divided into

two categories: discrete ligand models and continuous

distribution ligand models. However, most models are

curve-fitting exercises; stability constants attained are

dependent on pH, ionic strength and the presence of

competing metal ions, etc. [21,11,22,23], thus lacking

capability of prediction. Recently, Smith and Kramer

[24] have employed fluorescence quenching to define

stability constants and site concentrations for five

domains involved in the binding of Cu to fulvic acid.

Among those models, WHAM [5] based on Humic Ion-

Binding Model V by Tipping and coworkers [14–17]

probably represents the most comprehensive model that

describes proton and metal ions binding by humic

substances. It assumes two major classes of binding sites,

carboxyl and phenolic; however, Model V simply

assumes that metal ion affinities are directly related to

the proton affinities and the possibility that different

metal ions may not have the same heterogeneity was not

considered [25]. Model VI [20] moved forward with two

main advances: (i) the ‘‘parallelism’’ between proton

binding and metal binding affinities were relaxed and (ii)

greater ranges of binding strength was taken into

account (e.g., by allowing tridentate sites).

In addition, natural waters contain a variety of ions

that may compete to a greater or a lesser extent for the

available binding sites. Although the binding affinities of

the major metal ions Ca and Mg are much weaker than

that of Cu [1,26], the effect of Ca and Mg may be an

important aspect to consider when characterizing Cu–

DOM complexation due to the abundance of Ca and

Mg ions in most natural waters. The simplest models to

describe the competition assume simple competition for

the same binding sites. However, lack of extensive

competition effects by Ca and Mg for Cu–DOM

complexation has been reported in several studies

[11,26] Hering and Morel [1]; [25,27,23]. Tipping [15]

applied Model V to fit the competition between alkaline

earth cations and trace metal with literature data, but

found that in some cases, the competition calculated by

Model V was more substantial than the observations.

This might result from the ‘‘fully coupled’’ nature of

metal ion specific binding affinities assumed in the

model.

Despite the variety of studies on Cu complexation

with DOM that have been reported, there is still a need

to conduct comprehensive sets of experiments, including

proton binding, copper binding and competition studies,

etc. for the same DOM, to obtain systematic informa-

tion on complexation characteristics of DOM, and

therefore evaluate and refine the existing models. There

exists discrepancies regarding how to relate metal–DOM

complexation behavior with acidic moieties of DOMs

and which types of functional groups play most

important roles in Cu complexation in natural waters.

The Cu binding sites are usually much less than the total

proton association sites [28], resulting in difficulties to

model Cu–DOM complexation based on proton binding

characteristics [29].

The present study systematically characterized the

acid–base, Cu complexation, Ca complexation and Ca/

Mg–Cu competition characteristics of DOMs collected

from three sources. The study is an extension of previous

studies conducted by group (e.g., [30]), and emphasized

(I) linking Cu–DOM complexation characteristics with

the acidic characteristics of DOMs, and (II) evaluating

whether DOMs from different origins are of significant

difference with respect to acidic and Cu complexation

properties. The effect of the presence of major metal

ions on Cu–DOM complexation was evaluated by

quantitatively analyzing Cu–DOM complexation, Ca–

DOM complexation and the displacement of Cu ions by

Ca/Mg all together. The Ca/Mg–Cu exchange experi-

ments were carried out by measuring the displacement of

Cu ions by the addition of Ca or Mg ions to DOM

solutions pre-equilibrated with Cu ions, which is

different from the methods employed in most studies

[11,1], in which Cu titrations at different fixed Ca or Mg

backgrounds were compared. The advantage of this

method is the obtaining of more systematic information

for modeling competition.

2. Experimental

2.1. Isolation, treatment and basic characterization of

DOM

DOMs were isolated from 0.45 mm filtered natural

waters employing a portable reverse osmosis (RO)

system (Model PROS/2S, RealSoft, Norcross, GA)

[31,32]. Three DOMs were collected from the Suwannee

River, GA, Drummond Lake in the Great Dismal

Swamp, VA, and the Newport River, NC (referred to

GA-DOM, VA-DOM and NC-DOM). Further details

of the collection and characterization are presented in

Ma et al. [30]. The concentrated DOM samples were

passed through a H+-saturated cation-exchange resin

(Dowex 50WX8, Fluka Chemical Co, Milwaukee, WI)

column to remove both trace metals and major cations.

Y. Lu, H.E. Allen / Water Research 36 (2002) 5083–51015084

To avoid losing humic acid (HA) on the resin due to the

strongly acidic condition, HA was separated in advance

by acidic precipitation (pHE1) and was later recom-

bined with the material that passed through the cation-

exchange column. Concentrations of metal ions were

determined by ICPOES (Spectro Analytical Instru-

ments, Kleve, Germany). Dissolved organic carbon

(DOC) was determined using a Tekmar-Dohrmann

DC-190 TOC analyzer (Rosemount Analytical Inc.,

Dohrmann Division, Cincinnati, OH). DOMs were also

analytically fractionated to quantify the fractions of

humic acids (HA), fulvic acids (FA) and hydrophilic

fraction (HyI) by an acidic precipitation�XAD-8 resin

sorption method [33]. Basic characterizations of the

three DOMs are shown in Table 1.

2.2. Titration

The Cu–DOM complexation reactions were investi-

gated by titration employing a cupric ion selective

electrode (Cu-ISE, Model 94-29, Orion Research,

Boston, MA) to measure free Cu2+ concentrations.

pH was determined by a PerpHect Rose Sure-Flow

combination electrode (Model 8272BN, Orion Re-

search, Boston, MA). In all titrations, the reactor was

thermostated at 2570.11C. The DOM solution was

purged with N2 (Grade 5.0) before and during the

titration period to eliminate the interference of carbo-

nate. Ca titrations followed analogous procedures and

free Ca2+ was detected by a Ca-ISE (Model 9320BN,

Orion Research, Boston, MA). The total Cu back-

ground in diluted DOM samples (usually DOC=10mg/

L) was lower than 10�8M and the Ca and Mg

backgrounds were much lower than 10�6M (see Table

1).

The Cu-ISE was calibrated with a Cu-ethylenedia-

mine (EN) buffer method [34] in the same ionic strength

electrolyte solution (NaNO3) immediately preceding

each sample titration. The Nernstian response was

maintained at [Cu2+] as low as 10�17M and multiple

calibrations showed stable slopes, 29.070.5mV/pCu.

The performance of the Cu-ISE was also tested by a Cu

titration of a 10�4M EN solution following the same

procedures as for DOM samples. The measured titration

curve was consistent with the calculated curve by

MINEQL+ throughout the total Cu range 10�7–

5� 10�5M (figure not shown), indicating the Cu-ISE

is a reliable technique for free Cu2+ measurements. No

‘‘memory effect’’ was found for the Cu-ISE working

with either EN buffer or DOM samples.

2.2.1. Alkalimetric titrations of DOM

An aliquot of 100ml of concentrated DOM sample

was acidified with HNO3 to bring the pH to around 2.5.

The acidified sample was then titrated by addition of

0.1M carbonate-free NaOH automatically in increments

of 0.010–0.050mL, until the pH increased to 11. For

most titrations about 60–70 additions were made and 2–

5min between additions were allowed for reaction. The

pH usually became stable (o0.01 pH unit/2min) in less

than 2min. It is necessary to carry out the titration

rapidly to limit the possibility of errors arising from

base-catalyzed side reactions [35,7].

2.2.2. pH-stat Cu titrations of DOM

pH-stat Cu titrations were performed at pH 6.0, 7.0

and 8.0 to encompass the typical pH range in natural

freshwaters. The DOM samples were prepared by

dilution of the concentrated DOM with DI-water and

ionic strength was adjusted to 10�2M with NaNO3.

DOC of most of the diluted samples was 10mg/L. A 50

or 100mL portion of the DOM sample was transferred

into the acid pre-cleaned cell and titrated with

5� 10�4M and 10�2M Cu(NO3)2, CuT ranging from

10�7M up to 2� 10�4M. The titrant was added every

5–30min, which resulted in stable potential readings

(o0.5mV/5min). The pH was kept constant (70.02

pH) by addition of 0.1M HNO3 and NaOH as

necessary. An alternative way to control pH is utilizing

‘‘Better’’ buffers, which are claimed not to complex

metal ions [36]. Two ‘‘Better’’ buffers, MES (for pH 5.5–

6.5) and MOPS (for pH 6.5–7.5), have been tested for

Table 1

Characterization of DOM samples after removal of metal ions by cation-exchange

DOC (mg/L) Metal ions Ionic strength (M)a Fractions of DOC (%)b

Cu2+ Ca2+ Mg2+ Na+ K+ HA FA Hydrophilic

(mg/L) (mg/L)

GA-DOM 1046716.3 10.2 6.6 0 1500 1.17 0.065 5.1 83.5 11.4

VA-DOM 775.978.2 14.4 292 170 3370 3.50 0.147 9.8 73.2 17.0

NC-DOM 905.1711.5 15.9 484 231 3680 2.12 0.16 20.4 65.3 14.3

a Ionic strength was estimated from the cation and anion concentrations.bThe fractions were estimated by an analytical fractionation method of XAD-8 sorption combined with acid precipitation [33]. The

percentages of the fractions are based on OC content.

Y. Lu, H.E. Allen / Water Research 36 (2002) 5083–5101 5085

their applicability in metal–DOM systems. The Cu

titration curves with and without the buffers overlap

each other in the entire Cu concentration range,

indicating that no observable Cu complexation by the

buffers was found.

2.2.3. pH edges of Cu–DOM complexation

pH edges of Cu binding were performed following the

same procedure as the potentiometric titrations except

that (1) a known concentration of Cu2+ was added

before the titration and (2) diluted DOM was used

(DOC=10mg/L). Both pH and free Cu2+ were

monitored. The titrations were conducted at three

constant CuT (1� 10�6, 3� 10�6, and 9� 10�6M).

2.2.4. pH-stat Ca titrations of DOM

The Ca–DOM complexation was investigated by

titration of GA-DOM with CaCl2 solution at pH 6, 7

and 8 as were the titrations employing Cu as titrant. The

ionic strength was adjusted to 10�2M by addition of

4M KCl. Practically, the Ca-ISE method has a

Nernstian response limit around 10�6M. Therefore,

the Ca titrations were conducted in the CaT range from

4� 10�6 to 1� 10�4M.

2.2.5. Ca or Mg–Cu exchange on DOM binding sites

Competition of Ca and Mg with Cu at reactive

functional groups of DOM was investigated by a Ca or

Mg–Cu exchange method, that is, examining the change

of free Cu2+ concentration resulting from incremental

addition of Ca2+ or Mg2+ to the DOM solution

(DOC=10mg/L, ionic strength=10�2M) that has been

pre-equilibrated with fixed concentration of added Cu.

After pH adjustment (6.0 or 7.0), and the addition of Cu

([Cu]T=2� 10�6 or 5� 10�6M), the DOM sample was

equilibrated for approximately 1 h and then titrated with

incremental addition of Ca2+ or Mg2+ from 10�6 to

10�3M. Free Cu2+ concentration was monitored by the

Cu-ISE and the amount of Cu displaced from DOM by

each of the cations was thus determined.

2.3. Discrete-site model fitting

Alkalimetric, Cu and Ca titration curves were fitted

with multiple discrete-site model with FITEQL 4.0,

which permits the site densities ðLT;iÞ and conditional

stability constants to be obtained simultaneously.

3. Results and discussion

3.1. Proton binding of DOM—alkalimetric titrations

Fig. 1(a) shows that the shapes of the alkalimetric

titration curves for the three DOMs are similar and the

acid neutralizing capacities (ANC) are approximately

proportional to their DOC levels, implying a similar

distribution of proton binding groups exists for the three

DOMs. It is believed that their acidity is primarily due

to the presence of carboxyl and phenolic functional

groups. Perdue [7] found that the frequency of the

carboxyl groups is approximately a Gaussian distribu-

tion with a mean pKa of about 4.5, and pKa values of

99% of the carboxyl groups fall in the range of 1–8; the

2

4

6

8

10

12

pH

0

5

10

15

20

25

30

35

2 8pH

0.0 0.5 1.0 1.5 2.0

Volume of 1N NaOH, ml

∆pH

/ ∆m

l

4 6 10 12(a) (b)

Fig. 1. Titration of 100mL aliquots of GA-DOM (1046mg DOC/L), NC-DOM (776mg DOC/L), VA-DOM (905mg DOC/L). (a)

Alkalimetric titration curves showing lines fitted by a 4-site model with constants determined using FITEQL 4.0. (b) Differential plots

of alkalimetric titrations. The endpoint of carboxyl groups was determined [37] to be pH=8.0. I ¼ 10�2M; T ¼ 251C. J GA-DOM;

& VA-DOM; } NC-DOM.


phenolic groups are similarly distributed around a mean

pKa of about 10, and the pKa values of 98% of the

phenolic carboxyl groups fall in the range of 7–13. The

transformed differential plots in Fig. 1(b) show that the

maximum DpH/DmL values, which may represent the

endpoint of carboxyl groups, occurred sharply at

pHB8.0 for all the three DOMs, in agreement with

Thurman [37] and Perdue [7]. The proton binding site

densities of carboxyl and phenolic groups were esti-

mated by the calculation of ANC (Table 2). pH 8.0 was

designated as the endpoint of carboxyl groups, and

phenolic content was estimated as twice the base

consumption by DOM between pH 8.0 and 10.0 [35,7].

Our estimation for carboxyl and phenolic contents are

about 93% and 86%, respectively, of their total contents

based on the pKa distributions described by Perdue [7].

Here, we have termed them ‘‘carboxyl’’ and ‘‘phenolic’’

groups, but they do not necessarily represent actual

entities. The operational nature of such functional group

methodology should not be confused with the represen-

tation of reality. All three DOM have similar acidic

groups content and carboxyl/phenolic ratios: the aver-

age total, carboxyl and phenolic groups are 13.5970.45,

9.5070.63 and 4.0970.19mmol/g C, respectively

(equivalent to 6.80, 4.75 and 2.05mmol/g OM, if

assuming C comprises 50% of DOM, which is usually

valid); carboxyl and phenolic groups comprise about

70% and 30% of total acidic sites, respectively.

Leenheer et al. [38] reported carboxylic site densities

between 4.15 and 6.8mmol/g of Suwannee River fulvic

acid; whereas, Smith and Kramer [39] reported

6.0mmol/g for the same fulvic acid. Our study’s

carboxyl site density of 4.75mmol/g OM falls in the

same range.

3.1.1. Proton binding site densities and pKa: discrete-site

model fits with FITEQL

Fitting with monoprotic discrete-site models by

FITEQL 4.0 indicated that at least 3 sites were required

to fit the curves well, and a 4-site model gave a better fit.

The fitted curves by the 4-site model are compared with

the measurements in Fig. 1(a). LT;i and pKa;i distribu-

tions obtained by the 4-site model are shown in Fig. 2

and demonstrate that the proton binding sites and pKa

Table 2

Estimated contents of carboxyl and phenolic groups by the ANC method

Carboxylic

(mmol/g C)

Phenolic (mmol/g C) Total acidic

groups (mmol/C)

Fraction of

carboxylic

groups

Fraction of

phenolic groups

GA-DOM 9.37 4.21 13.58 0.69 0.31

VA-DOM 10.18 3.87 14.05 0.72 0.28

NC-DOM 8.95 4.20 13.15 0.68 0.32

Avg.7SD 9.5070.63 4.0970.19 13.5970.45 0.7070.02 0.3070.02

0

1

2

3

4

5

6

7

8

0

1

2

3

4

5

6

7

8

0

1

2

3

4

5

6

7

8

0 2 8

GA-DOM

Site

Den

sity

, mol

/kg

CSi

te D

ensi

ty, m

ol/k

g C VA-DOM

Site

Den

sity

, mol

/kg

C NC-DOM

4 6 141210

pKa

pKa

pKa

0 2 84 6 141210

0 2 84 6 141210(a)

(b)

(c)

Fig. 2. pKa spectra of proton binding sites determined by

FITEQL 4.0 with a monoprotic discrete 4-site model for the

titration of (a) GA-DOM, (b) VA-DOM and (c) NC-DOM

samples shown in Fig. 1.


distributions for the three DOMs are analogous.

Average total acidic site densities obtained by 3-site

and 4-site models are 12.21 and 12.54mmol/g C,

respectively, slightly smaller than the ANC estimates.

For the 4-site model, pKa peaks are divided into 4

groups corresponding to pKa of 3.3, 4.8, 6.8 and 9.6,

compared with Smith and Kramer [39] using DISI

technique, in which the acidity constants were grouped

into four classes: strong ðpKao5Þ; intermediate strong

ð5:1opKao7:5Þ; intermediate weak ð7:6opKao9:2Þ;and weak ðpKa > 9:3Þ: According to Perdue [7] of the

pKa values for model organic ligands in NOM, the first

two classes of acidic groups (pKa 3.3 and 4.8) should be

categorized as carboxyl with total site densities of

8.17mmol/g C; the weakest acidic sites can be approxi-

mately considered as phenolic groups and are around

2.8mmol/g C, a little less than that obtained by ANC

estimation. This is primarily due to the fact that the

titration curves terminated at pH around 11, resulting in

underestimation of the weakest acidic groups.

3.2. Cu complexation by DOM

3.2.1. pH-stat Cu titration of DOM

The pH-stat Cu titration curves of DOMs at pH 6.0,

7.0 and 8.0 are shown in Fig. 3. The comparison of the

Cu binding by DOMs from different sources at pH 7.0

(Fig. 4) indicates the similarity of Cu binding affinities

among the three DOMs although minor deviations exist,

and all titration curves show the presence of relatively

small amounts of very strong Cu-binding sites evidenced

by the deviation from the prediction by WHAM Model

V. Such strong binding was accompanied by a slow

approaching to equilibrium observed at very low Cu

loading. The similarity of Cu binding we found

here provides the possibility to predict Cu–DOM

GA-DOM

[Cu2+

] = [Cu]T

VA-DOM

[Cu2+

] = [Cu]T

10−7

10−6 10

−5 10−4

10−3

[Cu]T, M

10−7

10−6 10

−5 10−4

10−3

[Cu]T, M

10−7

10−6 10

−5 10−4

10−3

[Cu]T, M

10−15

10−13

10−11

10−9

10−7

10−5

[Cu2+

], M

[Cu2+

] = [Cu]T

NC-DOM

10−15

10−13

10−11

10−9

10−7

10−5

[Cu2+

], M

10−15

10−13

10−11

10−9

10−7

10−5

[Cu2+

], M

(a) (b)

(c)

Fig. 3. Comparison of the 4-site model (Eq. (4)) predictions with the pH-stat Cu titration curves for (a) GA-DOM, (b) VA-DOM, and

(c) NC-DOM. DOC=10mg/L; I ¼ 10�2 M; T ¼ 251C. Points are experimental data and lines are model predictions. Dashed line is

[Cu2+]=[Cu]T. J pH=6; & pH=7; } pH=8.


complexation behavior and speciation for different

natural waters. On the other hand, the binding affinities

are of slight difference among three DOMs following the

sequence GA-DOMoVA-DOMoNC-DOM, which

may be explained by the differences in humic to fulvic

ratios (HA/FA) among these DOMs (GA-DOMoVA-

DOMoNC-DOM, refer to Table 1), as it is believed

that humic acid has stronger Cu binding affinity than

fulvic acid [16].

Cu bound by DOM (mol Cu/kg C) was calculated by

subtracting inorganic complexes (mainly hydroxide

complexes) from CuT and plotted vs. [Cu2+] in Fig. 5.

The Cu complexation is strongly enhanced by increasing

pH. For all three DOMs, plots of pCu vs. logCuL

(figures not shown) superimposed fairly at different pHs

except at the very low end representing the small amount

of strongest sites, implying an overall pH dependence of

approximate 1. In addition to the Cu titrations at 10mg/

L DOC, a Cu titration was also conducted at 100mg/L

DOC to examine if the Cu binding site densities are

DOM concentration dependent. The overlap of the

normalized CuL (mol Cu/kg OC) vs. [Cu2+] plots at

different DOCs (Fig. 5) indicated DOM binding site

densities are independent of DOC, which is in agreement

with Cabaniss and Shuman [11].

3.2.2. pH edges of Cu–DOM complexation

Consistent with the 1:1 pH dependence observed in

pH-stat Cu titrations, Fig. 6 shows that, for all three

CuT, logCu2+ can be roughly described by a linear

relationship with pH with a downward slope of 1 when

pH>6, where the complexation by DOM is dominant.

This observed 1:1 pH dependence does not agree with

10−7

10−6

10−5 10

−4 10−3

[Cu]T, M

[Cu2+

] = [Cu]T

10−15

10−13

10−11

10−9

10−7

10−5

[Cu2+

], M

GA-DOM

VA-DOM

NC-DOM

Fig. 4. Comparison of Cu titration curves for DOMs from

different sources at pH 7.0. Points are experimental values and

lines are predictions using WHAM Model V. DOC=10mg/L;

I ¼ 10�2 M; T ¼ 251C.

10−13

10−11 10

−910

−710

−5

[Cu2+

], M

10−3

10−2

10−1

100

101

Cu

boun

d, m

ol/k

g O

C

Fig. 5. Effect of DOM concentration on Cu complexation of

GA-DOM at pH 7.0. DOC=10mg/L; I ¼ 10�2 M; T ¼ 251C.

J DOC=10mg/L, without Better buffer; & 10mg/L, with

Better buffer; } 100mg/L, without Better buffer.

3 5 7 9

pH

4 6 8 1010−12

10−11

10−10

10−9

10−8

10−7

10−6

10−5

10−4

[Cu2+

], M

Fig. 6. Comparison of the 4-site model (Eq. (4)) predictions

with the experimental pH edge curves at different CuT for GA-

DOM. DOC=10mg/L; I ¼ 10�2 M; T ¼ 251C. Points are

experimental data and lines are model predictions. J

[Cu]T=1� 10�6M; & [Cu]T=3� 10�6M; }[Cu]T=9� 10�6M.


Cabaniss and Shuman [11], who modeled Cu–DOM

complexation as Cu binding to a mixture of zero- and

1st-order sites at lower pH and a mixture of 1st- and

2nd-order sites at higher pH. When pH is low, the lines

bend downward and free Cu2+ concentration ap-

proaches CuT, as protons tend to compete for the

DOM binding sites. For the lowest CuT of the three,

1� 10�6M, the linear relationship occurs even at pH as

low as 4. Dissociation kinetics were also examined by

instantly lowering the pH back to 4 after a forward

titration of a sample containing CuT 3� 10�6M. Free

Cu2+ increased sharply in the first few minutes, and then

the increase became much slower with time (figure not

shown). Even after 1 h, the [Cu2+] was stillo40% of the

[Cu2+] initially equilibrated at the same pH (4.0) at the

beginning of the titration. The very slow kinetics of

Cu2+ dissociation from DOM sites through H+

exchange suggests that a substantial portion of Cu2+

is complexed by very strong binding sites that have slow

dissociation kinetics. Our observation is consistent with

Rate and McLaren [40] on Cu-humic acid dissociation

kinetics that indicated substantial portions of slowly

dissociated Cu (CuS) and non-dissociated Cu (CuN)

under various conditions.

3.2.3. Multi-site model fitting of Cu–DOM complexation

by FITEQL 4.0

Our fitting indicated that four classes of Cu binding

sites are required to fit well the whole curves, especially,

to cover the lowest Cu concentration end that represents

the strong binding affinity zone. The obtained site

densities ðLT;iÞ and conditional stability constants ðKcCuLÞ

for the 4-site model are listed in Table 3. The total

ligands are categorized into distinctive classes from

larger amounts of weaker Cu binding sites to smaller

amounts of stronger sites. The conditional stability

constants for the 4th site—the strongest site obtained by

the present study are high, from 1011.5 to 1013.5 at pH 8.

This confirms Xue and Sigg’s finding [42] by ligand

exchange—DPCSV technique. Such strong Cu binding

sites have been suggested by some researchers to be

contributed by nitrogen and sulfur containing sites in

DOM [43,44,28]. Although the estimated LT’s are

slightly different from curve to curve, the site distribu-

tions demonstrated similarity for all the titrations

among all three DOMs. The total site densities estimated

by the 3-site and the 4-site models are 4.1671.17 and

4.5670.91mmol/g C, respectively. The average ratios of

Li;T=LT are 0.772:0.186:0.042 by the 3-site model and

0.742:0.198:0.060:0.020 by the 4-site model, which are

very close to each other except for the very small amount

of the strongest site that accounts for 2% of LT included

in the 4-site model. The similarity made the normal-

ization of Cu binding sites for all the DOMs possible.

The heterogeneity of DOM ligands precludes a definitive

determination of the binding properties of the ligands.

3.2.4. Discussion of pH dependence—carboxyl or

phenolic?

The complexation by DOM can be modeled by

discrete-site model, as demonstrated in Eq. (1), based

on the following assumptions: (1) the formation of Cu–

DOM complexation is only through free Cu2+, and

hydrolyzed Cu is not considered to be complexed by

DOM binding sites; (2) Cu2+ ions compete with H+ for

binding sites, and monoprotic sites are usually assumed

but polyprotic sites may apply in some cases; (3) only 1:1

binding stoichiometry (CuL) is considered.

CuL ¼XN

i¼1

CuLi ¼XN

i¼1

LT;iKCuLi½Cu2þ�

1þ KH;i½Hþ� þ KCuLi½Cu2þ�

¼XN

i¼1

LT;iKCuHLi½Cu2þ�

1=KH;i þ ½Hþ� þ KCuHLi½Cu2þ�

; ð1Þ

KH;i ¼½HLi�

½Hþ�½L�i �; KCuLi

¼½CuLi�

½Cu2þ�½L�i �

and

KCuHLi¼

½CuLi�½Hþ�

½Cu2þ�½HLi�¼

KCuLi

KH;i;

where LT;i (mol/L) is the total site density of the ith site,

CuLi (mol/L) is Cu bound by the ith DOM binding site,

N is the number of types of sites. The denominator of

the equation represents the total site densities, and the

three terms of the denominator represent deprotonated

sites (L�), protonated sites (HLi), and Cu bound sites

(CuLi), respectively.

Due to the complicated characteristics of DOM,

typically conditional stability constants are employed

to quantify metal complexation with DOM. In our

study, most of environmental variables such as ionic

strength, temperature were constant and other metal

ions have been removed, the conditional stability

constants can be considered to be mainly functions of

pH, which is assumed to be due to the competition of Cu

and protons for the binding sites. One can express the

conditional stability constants at a fixed pH as follows:

Cu2þ þ Li ¼ CuLi; KcCuLi

¼½CuLi�

½Cu2þ�½Li�; ð2Þ

where KcCuLi

is the conditional stability constant, Li is

the apparent free binding site (unoccupied by Cu2+) and

may be protonated or deprotonated (Li ¼ L�i þHLi).

Therefore, the following relationship can be derived:

KcCuLi

¼KCuLi

1þ KH;i½Hþ�¼

KCuHLi

1=KH;i þ ½Hþ�: ð3Þ

When pH > log KH; the protonated [HLi]{ deproto-

nated ½L�i �; so that Cu complexation is independent of

pH: KcCuLi

¼ KCuLi¼ KH;iKCuHLi

¼ constant; when

pHologKH; deprotonated [L�]{protonated [HLi], so

that KcCuLi

¼ KCuLi=KH;i½Hþ� ¼ KCuHLi

=½Hþ�; and in this


Table3

Conditionalstabilityconstantsandsitedensities

ofCu–DOM

complexationobtained

bythe4-sitemodelfitwithFITEQL4.0(D

OC=10mg/L;

I¼10�2M;

T¼251C)

Sample

pH

No.of

data

Upper

range(M

)log

K1

log

K2

log

K3

log

K4

L1;T

L2;T

L3;T

L4;T

WSOS/

DFa

LT

Ratioof

Li;T=L

T

CuT

Cu2+

(mmol/gC)

(mmol/gC)

12

34

GA-D

OM

7.0

18

3.9E-05

3.6E-06

5.373

6.916

8.388

10.440

4.556

1.021

0.320

0.090

0.00367

5.897

0.773

0.173

0.054

0.015

7.0

buffer

19

2.9E-05

2.85E-06

5.530

6.921

8.483

10.579

2.871

0.932

0.251

0.054

0.00078

4.054

0.708

0.223

0.062

0.013

8.0

17

2.3E-05

9.88E-08

6.865

8.330

9.609

12.049

3.432

0.598

0.253

0.069

0.00139

4.283

0.801

0.140

0.059

0.016

VA-D

OM

6.0

19

7E-05

3.23E-05

4.616

6.058

7.527

9.470

3.708

1.226

0.384

0.098

0.00464

5.318

0.697

0.231

0.072

0.018

7.0

18

3.8E-05

3.96E-06

5.487

7.039

8.687

11.507

3.682

1.055

0.312

0.084

0.00612

5.049

0.729

0.209

0.062

0.017

8.0

17

2.3E-05

1.02E-07

6.946

8.572

10.069

12.975

3.197

0.562

0.184

0.083

0.00274

3.943

0.811

0.142

0.047

0.021

NC-D

OM

6.0

18

3.5E-05

5.97E-06

5.130

6.604

8.067

9.891

3.203

1.072

0.332

0.080

0.00208

4.607

0.695

0.233

0.072

0.017

7.0

21

3.9E-05

2.18E-06

5.803

7.331

8.938

11.637

3.486

1.225

0.369

0.096

0.00974

5.080

0.686

0.241

0.073

0.019

8.0

15

2E-05

1.93E-08

7.850

9.420

11.113

13.197

2.181

0.522

0.101

0.109

0.00086

2.804

0.778

0.186

0.036

0.039

Avg.

3.368

0.913

0.278

0.085

4.559

0.742

0.198

0.060

0.020

SD

0.648

0.28

0.0916

0.016

0.913

0.049

0.040

0.013

0.008

RelativeSD

(%)

19.2

30.7

32.9

19.2

20.0

6.59

19.9

21.0

38.7

aWSOS/D

Fisanindicatorofgoodnessoffit.Usuallyvalues

between0.1and20are

commonforareasonablygoodfit[41].


case log KcCuL is linearly pH dependent with a slope of

�1. As has been discussed earlier for pH-stat titrations

and pH edge data, Cu–DOM complexation is roughly

1:1 pH dependent (log [Cu2+] vs. pH), and the binding

still increases at the highest pH measured (pH 9).

Therefore, the majority of the Cu binding sites should

still be protonated so there has to be an average log KH

greater than 9. It is well known that phenolic sites have

an average log KH around 10–10.5, whereas, carboxyl

sites have an average log KH around 3.5–4.5 [7,37]. At

the pH of most natural waters, most carboxyl groups are

dissociated. If carboxyl sites are responsible for the

majority of Cu binding, such pH dependency should not

be observed. Based on the above analysis, we suggest

that phenolic sites account for the majority of Cu

complexation throughout the pH range of interest (pH

5–9) except at very high Cu concentrations, whereas Cu

bound by carboxyl groups, which have much weaker Cu

binding affinities, is small compared with phenolic

groups. In this case, the Cu complexation is mainly

through Cu–H exchange at the phenolic sites. This

should be valid under typical natural water conditions

(low Cu concentration and not too low pH) without

losing accuracy significantly. For example, even at CuTas high as 10�5M, >99% of Cu was bound by DOM

sites at pH 7 (refer to Fig. 4). Carboxyl sites are not

expected to be so strong. In addition, the slow

dissociation kinetics described earlier is usually asso-

ciated with strong binding sites, but the dissociation

from carboxyl sites should be very fast.

The hypothesis is supported by Hansen et al. [45] that

protons released per Cu bound was close to 1 for three

lagoon samples at pH 6 and 7. Our finding is also in

good agreement with Benedetti and coworkers’ NICA

model studies [10,19,25], which indicated that (i) the

contribution of phenolic sites to Cu binding is sub-

stantial over the whole pH and Cu concentration range

except at very high Cu concentrations (pCu2+o6) and

low pH, (ii) phenolic sites still dominate at lower pH if

the free Cu concentration is low, and (iii) based on the

model fitting to data for H, Ca, Cd, Cu and Pb binding

by a peat humic acid, with the exception of Ca, the

binding constants for those metal ions are considerably

greater for the phenolic sites than for the carboxylic

sites. It was indicated by some researchers [46,26] that

metal ions are bound by simultaneous action of acidic

carboxyl groups and phenolic hydroxyl groups.

Although it is possible that trace metals may be bound

to some of the carboxyl groups having a favorable steric

location (e.g., forming a chelate by a carboxyl site

associated with an adjacent phenolic site [37]), this kind

of reaction will not be distinguished by the model

formulation described here.

It is not possible to model Cu–DOM complexation by

directly relating Cu binding sites with total proton

association sites, due to the fact that fitted Cu binding

site densities are usually much less than the H site

densities [28]. We found that the estimated LT for Cu

binding is 4.16 (the 3-site model) or 4.55mmol/g C (the

4-site model), much less than the average total acidic

sites 12.5mmol/g C but are very close to the average

phenolic-site density, 4.1mmol/g C. This fact appears

consistent with our argument that phenolic-sites account

for the majority of Cu complexation. If true, it will

considerably simplify modeling without much loss of

accuracy. Based on this hypothesis, we performed

normalized fits by assigning LT of 4.5mmol/g C

(phenolic-sites only) and the site distribution of

0.75:0.20:0.05:0.02 for the four classes of sites. Plots of

log Kci vs. pH for the three DOMs in Fig. 7 indicate that

log Kci is linearly pH dependent with slopes of close to 1

(0.83–1.25) for K1; K2 and K3; and much greater (1.26–

1.87) for K4: This verifies the 1:1 Cu–H exchange

stoichiometry for the ith site (i ¼ 1; 2 and 3); however,

the 4th site (strongest site) needs to be described by a

stoichiometry other than 1:1 for a better fit. In the

present study we chose 1:2. Cu–H exchange constants

(KCuHLi) were then calculated (Table 4), with the

somewhat arbitrary assumption that pKa of the Cu

binding site is around 10 so that deprotonated sites are

negligible ðL�i {HLi þ CuLiÞ: The KCuHLi

values at each

pH (6, 7, or 8) for the different DOMs agree well. The

minor differences existing among the DOMs might

reflect the effect of HA% of DOMs.

Therefore, a 4-site discrete model can be established in

this study to describe Cu–DOM complexation. In this,

four classes of Cu binding sites are distinguished, with

1:1 Cu–H exchange ratio for the first three sites and 1:2

for the 4th site. The model assumes that only phenolic

sites account for the majority of Cu binding, whereas

more acidic carboxyl sites do not. The model implies

that the Cu–DOM complexation is primarily through

the replacement of H+ by Cu2+ at the phenolic binding

sites. Within the pH range of interest, deprotonated sites

are negligible ð½L�i �{½HLi�Þ so that the model formula-

tion is as follows:

CuL ¼X

i

CuLi ¼XN¼3

i¼1

LT;iKCuHLi½Cu2þ�

½Hþ� þ KCuHLi½Cu2þ�

!

þLT;4KCuH2L4 ½Cu

2þ�

½Hþ�2 þ KCuH2L4 ½Cu2þ�

: ð4Þ

Figs. 3 and 6 compared the model simulations of

[Cu2+] with the experimental pH-stat titrations and the

pH edges. The Cu–H exchange constants in Table 4 were

employed. The results indicate that the model describes

well the Cu–DOM complexation behavior over wide

total Cu concentration and pH ranges for natural

waters.

Takacs et al. [28] argued that the carboxyl groups

contributed the majority of Cu complexation sites but

have not provided experimental evidence. In their data


there was no correlation of Cu binding sites (A1) with

proton binding sites TO1 (representing carboxyl sites)

for nine DOMs (refer to Fig. 3 in reference). We

compared A1 with both proton binding sites, TO1

(carboxyl sites) and TO3 (phenolic sites) for their data,

which is shown in Fig. 8. Even though some systematic

errors may exist among different DOM samples, which

often happens in titration data fitting, it is still evident in

Fig. 8 that A1 correlates much better with TO3

(phenolic sites)—the variances of A1 and TO3 follow

the same trend in most cases, in contrast, they are rather

randomly related with TO1 (carboxyl sites).

3.3. Ca–DOM complexation and comparison with Cu–

DOM complexation

The results of Ca–DOM complexation are compared

with Cu titrations in Fig. 9. The results show that

although both Ca–DOM and Cu–DOM complexation

are pH dependent, the pH dependence of Ca–DOM

complexation is much less than that of Cu–DOM

complexation (o1). The latter has a pH dependency of

approximately 1:1 and remains fairly constant through-

out the whole concentration range. In addition, the Ca–

DOM complexation curves at different pHs (Fig. 9(d))

tend to come closer with increasing CaT, indicating the

pH dependence decreases at higher Ca concentration.

Conditional stability constants ðlog KidÞ and site den-

sities ðLT;iÞ for Ca–DOM complexation obtained by N-

site (N ¼ 1; 2 and 3) models are given in Table 5.

Essentially the total binding site densities by different

methods are in good agreement. For the 3-site model

fits, the increases of log Kid with increasing pH are much

less than 1, moreover, the variation with pH is minimum

for the 1st type of sites (weakest sites), e.g., only 0.033

from pH 7 to 8, while larger for the 2nd and 3rd sites

4

5

6

7

8

9

10

5 7 8 9

pH

4

5

6

7

8

9

10

6

7

8

9

10

11

12

8

9

10

11

12

13

14

6 5 7 8 9

pH6

5 7 8 9

pH6

log

K4

log

K2

log

K1

log

K3

5 7 8 9

pH

6

(a) (b)

(d)(c)

Fig. 7. Conditional stability constants for copper complexation obtained by normalized 4-site model fit for three DOMs vs. pH. J

GA-DOM; & VA-DOM; } NC-DOM.


(stronger sites), both of which are about 0.45. This

quantitatively confirms the above observations about

the titration curves. An additional observation was that

Ca–DOM complexation reached apparent equilibrium

usually in no more than a few minutes, much faster than

Cu–DOM complexation. The latter takes usually 10–

30min, or even longer at low Cu loading and high pH,

to reach apparent equilibrium. The slow association

kinetics for Cu, as have previously discussed, is believed

to be due to binding with strong binding sites [47].

Likewise, the fast kinetics for Ca may imply interaction

with relatively weak binding sites, e.g. carboxyl-type

sites.

We have postulated that the majority of Cu com-

plexation by DOM under natural water conditions is

attributed to phenolic sites instead of more acidic

carboxyl sites. Therefore, the difference in pH depen-

dency for Ca–DOM complexation compared with that

for Cu–DOM complexation may imply that, although a

portion of Ca ions may be bound by phenolic sites at

low Ca concentration and relatively high pH, the

majority of DOM complexed Ca tends to be bound by

carboxyl sites, especially at high Ca concentrations and

low pH.

3.3.1. Non-linearity of metal–DOM interaction

Non-linearity of sorption processes arises from site-

specific interactions, and may occur because of hetero-

geneity of site energies [48]. The Freundlich model has

been extensively used to describe the non-ideal sorption

behavior of organic compounds to soil organic matter

[49,48]. The log–log plots for both Cu–DOM and

Table 4

Conditional Cu–H exchange stability constants of Cu–DOM obtained from the 4-site model. log KHLiassumed to be 10

Sample pH KCuHL1 KCuHL2 KCuHL3 KCuH2L4a

GA-DOM 7 �1.30 0.09 1.66 �3.658 �1.27 0.09 1.62 �4.44

Average �1.29 0.09 1.64 �4.05

VA-DOM 6 -1.06 0.49 1.87 �2.517 �1.32 0.28 1.87 �2.648 �1.30 0.14 1.94 �3.15

Average �1.23 0.30 1.89 �2.77

NC-DOM 6 �0.76 0.90 2.20 �2.277 �0.89 0.76 2.27 �2.308 �0.77 0.82 2.69 �2.53

Average �0.81 0.83 2.39 �2.37

aDefinition:

KCuHLi¼

½CuLi�½Hþ�

½Cu2þ�½HLi�for i¼ 1; 2; and 3;

KCuH2Li¼

½CuLi �½Hþ�2

½Cu2þ�½H2Li �for i¼ 4:

Fig. 8. Comparison of Cu binding site densities with carboxyl

and phenolic site densities for 9 DOM samples reported by

Takacs et al. [28] for samples collected from Norwegian lakes.

Sample numbers are those used in Takacs et al.’s paper.


Ca–DOM show that the complexation appears to be

able to be described by Freundlich Equation (Eq. 5) with

the exception of a deviation for Cu occurring in the

lowest concentration range (Fig. 9):

½ML� ¼KF½M2þ�n; ð5Þ

where KF is termed Freundlich coefficient, and n (slopes

of the log–log plots, usually 0onp1) may represent an

overall measure of both the relative magnitude and

diversity of site energies. The fitted n values are given in

Table 6.

It is noticeable from Fig. 9 that, for Cu–DOM

isotherms, the deviation of the fitted lines from the data

occurred due to the deviation at the low ends of Cu–

DOM curves, and thus caused the underestimation of n

values, especially at higher pHs. Therefore, we also re-

fitted the results by ignoring a few data points at the low

ends that represent the 4th site in our 4-site model. As a

result, the re-fitted lines came closer to the trends of data

and gave less variation among different pH. The results

demonstrate that: (i) Cu–DOM complexation is highly

non-linear; by contrast, the extent of non-linearity of

Ca–DOM complexation is much less; n values for Cu–

DOM range 0.39–0.32 corresponding to pH 8–6, which

are comparable with the literature [25], whereas for

Ca–DOM the n values range 1.0–0.61; (ii) n values of

Cu–DOM isotherms for three DOMs are fairly constant;

(iii) the non-linearity of both Ca–DOM and Cu–DOM

isotherms tend to increase with increasing pH; however,

the variation is small for Cu (e.g., for VA-DOM,

−14

Cu-GA-DOM

−12 −10 −8 −6 −4

log ([Cu2+], M)

−14 −12 −10 −8 −6 −4

log ([Cu2+], M)

−14 −12 −10 −8 −6 −4

log ([Cu2+], M)

1.0

0.5

0.0

−0.5

−1.0

−1.5

−2.0

−2.5

−3.0

log

(CuL

, mol

Cu

/kg

OC

)

1.0

0.5

0.0

−0.5

−1.0

−1.5

−2.0

−2.5

−3.0

log

(CuL

, mol

Cu

/kg

OC

)

1.0

0.5

0.0

−0.5

−1.0

−1.5

−2.0

−2.5

−3.0

log

(CuL

, mol

Cu

/kg

OC

)

Cu-VA-DOM

Ca-GA-DOMCu-NC-DOM

1.0

0.5

0.0

−0.5

−1.0

−1.5

−2.0

log

(CaL

, mol

Ca/

kg O

C)

(a) (b)

(c) (d)

−6.0 −5.5 −5.0 −4.5 −4.0

log ([Cu2+], M)

Fig. 9. Comparison of Cu–DOM and Ca–DOM complexation at pH 6, 7 and 8 by OC normalized binding. (a)–(c) Cu–DOM

complexation isotherms for GA-DOM, VA-DOM and NC-DOM, respectively, and (d) Ca–DOM complexation for GA-DOM.

DOC=10mg/L; I ¼ 10�2 M; T ¼ 251C. J pH=6; & pH=7; } pH=8. Solid lines are Freundlich fits. Slope n values are listed in

Table 6.


n ¼ 0:39 at pH 6 to 0.33 at pH 8) but relatively

significant for Ca (e.g. n ¼ 1:01 at pH 6 to 0.61 at pH 8).

The reasons for the non-linearity are not well under-

stood at this time. Benedetti et al. [10] and Kinniburgh

et al. [25] attributed it in their NICA model to ion-

specific non-ideality, distinguished from the intrinsic

heterogeneity contribution of DOM. We found that the

n values for Cu, Cd, Ca obtained by their study were

0.64, 0.81, 0.52 for carboxyl-type sites and 0.33, 0.48,

0.32 for phenolic-type sites, respectively, similar among

different metal ions bound to the same type of sites but

significantly different between carboxyl-type sites and

phenolic-type sites. Therefore, we suggest that the non-

linearity is linked primarily to the types of binding sites,

e.g. carboxyl sites and phenolic sites; metal ions’

complexation with carboxyl sites is less non-linear

represented by higher n value, whereas, complexation

with phenolic sites is more non-linear characterized by a

lower n value. This is consistent with our hypothesis

previously made that Cu ions are preferably bound to

phenolic sites, whereas Ca ions tend to be bound by

carboxyl sites especially at relatively high Ca concentra-

tion and low pH. This suggestion also explained the

observation that the extent of non-linearity of Ca–DOM

Table 5

Ca–DOM binding site densities and conditional stability constants

pH LT;i; mmol/g C logKdi R

i ¼ 1 2 3 1 2 3

1-site model (Langmuir)

6 6.975 3.472 0.998

7 2.728 4.161 0.998

8 2.573 4.414 0.997

2-site model (by FITEQL) WSOS/DF

6 — — No convergence —

7 8.711 5.416 3.251 4.819 0.012

8 2.908 2.505 4.139 5.602 0.025

3-site model (by FITEQL), site densities constraineda WSOS/DF

6 3.375 0.9 0.225 No convergence —

7 3.375 0.9 0.225 3.633 4.083 5.126 0.00316

8 3.375 0.9 0.225 3.666 4.534 5.577 0.00365

aWith the assumption that Ca ions occupy the same sites of DOM as Cu ions, total Ca binding site density was constrained to the

same values as obtained by the normalized 4-site model for Cu–DOM complexation, except that the 4th site was ignored as the data for

the Ca–DOM curves did not cover such low concentrations.

Table 6

Freundlich fits and comparison of the nonlinearity of Cu–DOM and Ca–DOM complexation

pH Cu–DOM complexation Ca–DOM complexation

No. of data n1a R No. of data n2

a R n R

GA-DOM 6 — — — — 1.005 0.9991

7 18 0.383 0.9996 17 0.379 0.9999 0.743 0.9986

8 17 0.370 0.9987 14 0.388 0.9997 0.609 0.9985

VA-DOM 6 19 0.387 0.9989 19 0.387 0.9989

7 18 0.326 0.9978 15 0.344 0.9996

8 17 0.293 0.9937 13 0.333 0.9978

NC-DOM 6 18 0.399 0.9974 17 0.391 0.9983

7 22 0.324 0.9992 19 0.33 0.9994

8 15 0.274 0.9930 10 0.322 0.9976

an1 is the value fitted for all the data; n2 is the value refitted with the few data points at low ends of isotherms (corresponding to the

4th site) ignored.


and Cu–DOM complexation both tend to decrease with

decreasing pH and that the variation is only subtle for

Cu but relatively significant for Ca, because our

hypothesis does not exclude the possibility that some

Cu ions can be bound to carboxyl sites (especially, low

pH, and high Cu loading relative to DOM) and that a

small portion of Ca ions can be bound to phenolic sites

especially at low Ca loading and high pH. In fact, for

both ions the binding to carboxyl sites is enhanced at

lower pH and the binding to phenolic sites is enhanced

at higher pH, so that the non-linearity is correspond-

ingly reduced with decreasing pH. The point is that at

pH as low as 6, Cu binding to phenolic sites is still

dominant so that the decrease of non-linearity for Cu–

DOM complexation is only minimal.

3.4. Ca/Mg competition with Cu for DOM binding sites

The results of Ca–Cu competition for three DOMs at

two [Cu]T, 2� 10�6 and 5� 10�6M, and two pH values,

6.0 and 7.0, are shown in Fig. 10. Small but detectable

competition was observed under all conditions. The

results demonstrate that (i) for all three DOMs, there is

a similar tendency of Cu displacement by the addition of

Ca2+ shown at both pH 6 and 7 and at both [Cu]T; (ii)

the increases of [Cu2+] when Ca concentration increased

from background levels ({10�6M) to 10�3M are all

less than one order of magnitude (Dlog [Cu2+]=0.35–

0.82); (iii) the displacement of Cu2+ by addition of Ca

for GA-DOM is somewhat less than for VA- and NC-

DOM; and (iv) the Ca effect on the Cu2+ displacement

is a little greater at lower [Cu]T than at higher [Cu]T, and

likewise it is greater at pH 7 than at pH 6. In addition,

the linear plots of [Cu2+] vs. [Ca]T (Fig. 10(d)) showed

that the displacement of Cu2+ continuously becomes

less with increasing [Ca]T, indicating the overall compe-

tition of Ca is stronger at lower [Ca]T and is weakened

with increasing [Ca]T. The effect of Mg2+ on Cu–DOM

complexation is compared with that of Ca2+ for both

VA-DOM and NC-DOM at [Cu]T=2� 10�6M and pH

7.0 (figure not shown).

The extent of competition of Ca or Mg with Cu

observed in our experiments is somewhat greater than

literature has reported ([11,26]; Hering and Morel [1];

[25,23]). Sunda and Hanson [26] found only minor

competition effects by Ca/Mg—at 1 mM [Cu]T and pH

7.7, log [Cu2+] increased by 0.12 units when [Ca2+]

increasing from 0.26 to 2.7mM, and increased by 0.2

units when [Mg2+] increased from 0.04 to 0.94mM,

which is probably due to the fact that the [Ca2+] they

started from was high. Hering and Morel [1] performed

Cu titrations of Suwannee humic acid at pH 8.2–8.3 and

found little or no effect of Ca at 10�2M. Cabaniss and

Shuman [11] performed acid–base titrations of Cu-

Suwannee fulvic acid (1 mM [Cu]T, 5mg/L FA) over a

4.4–9.0 pH range and increases in log [Cu2+] of up to 0.3

units at 1.0mM Ca or Mg and up to 0.6 units at 10mM

Ca or Mg were observed at high pH.

A simple competition model that assumes competitive

binding by H+ and other cations M2+ such as Ca2+

with Cu2+ for the same binding sites can be expressed as

in Eq. (6), and if for a fixed pH, can be simplified by

employing conditional stability constants (Eq. 7).

CuLi ¼LT;iKCuLi

½Cu2þ�

1þ KH;i½Hþ� þ KCa;i½Ca2þ� þ KCuLi

½Cu2þ�; ð6Þ

CuLi ¼LT;iK

cCuLi

½Cu2þ�

1þ KcCaLi

½Ca2þ� þ KcCuLi

½Cu2þ�: ð7Þ

We examined the simple competition model by

performing a simulation of Ca–Cu competition for

GA-DOM with MINEQL+ using the 4-site discrete site

model described earlier. The constrained binding site

densities and corresponding conditional stability con-

stants for Cu and Ca obtained separately from Cu–

DOM complexation and Ca–DOM complexation (see

Tables 3 and 5) were employed. The simulations were

conducted under the same conditions as the experi-

ments, and the results are shown in Fig. 11. Disregard-

ing the initial minor gaps between simulation and

measured [Cu2+], the MINEQL+ simulation is con-

sistent with measurements at low Ca concentrations.

However, it tremendously overestimates the displaced

Cu2+ when [Ca]T is higher than about 10�5M (roughly

the beginning of binding with the 1st type of sites). The

discrepancy of [Cu2+] is up to nearly one order of

magnitude, and this discrepancy is exacerbated at lower

total Cu concentration. Therefore, Ca and Mg do not

simply compete with Cu for the same binding sites on

DOM, especially at high Ca or Mg concentrations.

Although the lack of competition has been reported in

literature as discussed earlier, no satisfactory explana-

tion has been offered so far. McKnight and Wershaw

[23] suggested Ca ions compete with Cu for some part of

binding sites but not for other sites, but they did not

specify which part of the binding sites allowed competi-

tion. Based on the above experimental observations and

discussion, we propose that the lack of comprehensive

competition is because the majority of Ca and Mg tends

to be bound by carboxyl sites; by contrast, Cu tends to

be bound principally by phenolic sites. At a low Ca and

Mg concentrations, Ca and Mg compete weakly with Cu

for the phenolic-type binding as Ca and Mg have a

much weaker stability constant than that of Cu; when

the Ca or Mg concentration is higher, the excess Ca or

Mg tends to be bound principally by carboxylic-type

sites, resulting in a weakened apparent competition

effect on the Cu–DOM complexation since there is no

substantial competition for the carboxylic sites between

Cu and Ca or Mg.


Our findings are essentially in agreement with

Kinniburgh et al. [25] applying the NICA-Donnan

Model that reported the relative strength of binding is

in the following sequences: for carboxylic-type sites

H+cPb2+>Cu2+>Cd2+>Ca2+ and for phenolic-

type sites H+cCu2+>Pb2+cCd2+cCa2+. With the

exception of Ca, the stability constant values for the

metal ions, especially for Cu, are considerably greater

for the phenolic-type sites than for the carboxylic-type

sites. When fitting the competition between alkaline

earth cations and trace metal with Model V, Tipping [15]

also found that the larger is the assumed value of pKMHB

for Ca2+, i.e., the weaker is Ca binding at the type B

sites (phenolic sites), the less competition is predicted;

whereas, variations in pKMHA have much less effect.

This is also consistent with our findings.

10−7 10−6 10−5 10−4 10−3

[Ca]T, M10−7 10−6 10−5 10−4 10−3

[Ca]T, M

10−7 10−6 10−5 10−4 10−3

[Ca]T, M

0 100 5 10−4 1 10−3 2 10−3

[Ca]T, M

0.0

1.0 10−7

2.0 10−7

3.0 10−7

4.0 10−7

5.0 10−7

VA-DOM

[Cu2+

], M

10−10

10−9

10−8

10−7

10−6

NC-DOM

[Cu2+

], M

10−10

10−9

10−8

10−7

10−6

[Cu2+

], M

10−10

10−9

10−8

10−7

10−6

[Cu2+

], M

VA-DOMGA-DOM

(a) (b)

(c) (d)

Fig. 10. Effect of Ca concentration on Cu–DOM complexation. (a)–(c) Log–log scale plots for GA-DOM, VA-DOM, and NC-DOM,

and (d) a linear plot for VA-DOM. DOC=10mg/L; I ¼ 10�2 M; T ¼ 251C. J [Cu]T=2� 10�6M, pH=6; & [Cu]T=5� 10�6M,

pH=6, K [Cu]T=2� 10�6M, pH=7; ’ [Cu]T=5� 10�6M, pH=7.


4. Summary

In this study, the Cu complexation, acid–base, Ca/Mg

complexation and their competition with Cu character-

istics of DOMs collected from three sources were

systematically investigated by employing an ISE techni-

que. Alkalimetric and Cu titrations indicated similar

distributions of proton and Cu binding sites for all three

DOMs. The slight differences of Cu binding affinities

among three DOMs may be partly attributed to

different HA/FA ratios. All DOMs showed the presence

of small amounts of very strong Cu-binding sites. The

Cu–DOM complexation has an overall pH dependence

for log [Cu2+] of approximately 1 even at relatively high

pH (>8), whereas the pH dependence for Ca–DOM

complexation is much less than 1. Cu–DOM complexa-

tion isotherms are highly non-linear; in contrast, the

extent of non-linearity of Ca–DOM complexation is

much less. Ca/Mg compete weakly with Cu for DOM

sites, and the competition continuously becomes weaker

with increasing Ca/Mg concentrations.

Putting together all the results, we suggest that sites

characterized as phenolic based on alkalimetric titra-

tions, rather than more acidic carboxyl sites, account for

the majority of Cu–DOM complexation under natural

water conditions, and the complexation is principally

through the replacement of H+ by Cu2+ at the phenolic

binding sites; in contrast, the majority of Ca and Mg

tends to be bound by carboxyl sites, especially at high

Ca and Mg concentrations. This explains the lack of

comprehensive competition of Ca/Mg with Cu for DOM

complexation. Based on the above assumption, a 4-site

model was constructed to describe Cu–DOM complexa-

tion. The Cu–H exchange ratio is 1:1 for the first three

sites and 1:2 for the 4th site. This model describes well

the pH dependency of Cu–DOM complexation and

provides good estimates of free Cu2+ concentrations

throughout wide CuT and pH ranges. Our conclusions

are supported by (i) different characteristics with respect

to pH dependency, non-linearity, association–dissocia-

tion kinetics and binding strength demonstrated by Cu–

DOM and Ca–DOM complexation, (ii) analysis of the

correlation between model-fitted acidic sites and Cu

binding sites, and (iii) interpretation of the results of Cu

ion displacement from DOM sites by Ca or Mg.

Acknowledgements

We gratefully thank the International Copper Asso-

ciation, the US Environmental Protection Agency, and

the Water Environment Research Foundation for

support of the research. We thank Dr. James R. Kramer

of McMaster University for his thoughtful comments on

the paper.

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