Proton–metal exchange processes in synthetic and natural polyelectrolyte solution systems

Proton�/metal exchange processes in synthetic and naturalpolyelectrolyte solution systems

Julio C. Benegas a, Rodolfo D. Porasso a, Marc A.G.T. van den Hoop b,*a Department of Physics �/ IMASL, National University of San Luis, 5700 San Luis, Argentina

b National Institute of Public Health and the Environment, P.O. Box 1, 3720 BA Bilthoven, The Netherlands

Received 11 November 2002; accepted 12 June 2003

Abstract

Proton�/metal exchange processes that take place in polyelectrolyte solutions have been studied using previously

reported potentiometric titration data for polyacrylic acid (PAA) and humic acid (HA) systems obtained at different

degrees of polymer deprotonation, for various metals and at different added metal concentrations. It is shown that the

extent of the exchange process, quantified by the parameter nexch, strongly depends on the way it has been determined,

i.e. at constant polyelectrolyte characteristics or at constant pH, being significantly larger under constant pH

conditions. In addition, it is found that the exchange process depends upon polyelectrolyte structural charge density, the

degree of ionization, the type of metal and the total metal concentration in solution. For the experiments reported here,

in general the larger exchange coefficients are found for PAA at the lowest reported degree of ionization (a�/0.2) and

low pH values, while the lower values correspond to HA at the highest studied degree of ionization (a�/0.6) and high

pH values. The ability of the heavy metal ions to induce H� release increase following the order Ca:/Cd:/NiB/Pb5/

Cu. The present analysis shows that counterion condensation theory of linear polyelectrolytes appropriately describes

the experimental data, provided chemical bonding interactions are not too strong to disrupt the general polyelectrolytic

behavior.

# 2003 Elsevier B.V. All rights reserved.

Keywords: Proton�/metal exchange processes; Natural polyelectrolyte solution; Polyelectrolyte characteristics

1. Introduction

Knowledge of the interaction processes of

(heavy and proton) metal ions with macromole-

cular ligands is of importance for the understand-

ing of their physicochemical behavior in

environmental and biological systems. In natural

aquatic systems the speciation of metals, i.e. their

distribution over different physicochemical forms,

is highly dependent on the charge characteristics of

the complexing macromolecules. In general,

macromolecules of natural origin consist of var-

ious different functional groups, like carboxylic

and phenolic ones [1�/4], which can be charged due

to dissociation. Ionization characteristics of these

* Corresponding author. Tel.: �/31-30-274-4013; fax: �/31-

30-274-4411.

E-mail address: [email protected] (M.A.G.T. van

den Hoop).

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macromolecules have been studied quite exten-sively and are mainly controlled by the free

protons in the system.

For weak polyacids, like polyacrylic acid (PAA)

and humic acids (HAs), these charge character-

istics can be controlled or adjusted by acid/base

titrations of the polyacids in solution. Although

the experimental approach is rather simple, the

modeling and interpretation of the data can berather involved, especially for the case of hetero-

geneous polyelectrolytes. In this case, the analysis

of the concentration and distribution of ionizable

polymeric sites, as well as the concentration of all

species of small ions in solution and the interaction

processes between all charged species with the

functional group(s) of the polyelectrolyte should

be taken into account. Metal ion interactions withthe complexing ligands should therefore have to

compete with and/or modify the proton binding by

the (different) functional groups.

In the literature, two different experimental

approaches are found to study H�/Me2� ex-

change processes in polyelectrolyte systems: ana-

lysis at constant degree of ionization a or at

constant pH [5�/7]. In both cases, the startingpoint is the reference solution containing a par-

tially ionized polyelectrolyte with no (heavy) metal

added. Titrations at constant a are obtained by

just adding, in successive steps, a solution contain-

ing the metal ion. The amount of released H� is

given in these experiments by the change in pH. In

the experiments at constant pH, after adding the

solution containing the metal ion, hydroxidetitrant is added to return the solution to the

original pH. In this case, the amount of released

H� is given by the amount of hydroxide added.

Tipping et al. [6] observed a decrease in the

experimentally obtained H�/Cu2� molar ex-

change ratio of Sable HA with increasing pH

values at constant ionic strength from 1.38 down

to 1.12 in the pH range 4�/5. Kinniburgh et al. [7]have analyzed metal purified peat HA titration

curves at constant pH for Ca, Cd, Pb, Cu and Al,

and found that proton�/metal molar exchange

ratios varied strongly with the metal, the pH of

the solution and the free metal ion concentration.

Different models have been presented in the

literature to deal with these processes [2,7�/13]. In

the present case, the interactions and their con-sequences in polyelectrolytic solutions are ana-

lyzed within the framework of a recent extension

of counterion condensation (CC) theory [8,9] of

linear polyelectrolytes that includes, besides purely

polyelectrolytic interactions [12], chemical binding

of counterions to the polyelectrolyte [13]. In terms

of polyelectrolyte/counterion association of inter-

est here, polyelectrolytic interactions lead to delo-calized trapping of counterions in the immediate

vicinity of the polymer (CC), while the latter

results in chemical association to specific polymer

binding sites. The model has been shown to be able

to predict very well the outcome of various

experiments under different solution conditions,

for a number a heavy metal/polyelectrolyte sys-

tems, including metals like Cd, Cu, Zn, Pb and Niin solution with monoprotic polyelectrolytes like

PAA and polymethacrylic acid and multifunc-

tional polyelectrolytes like HA [14�/17].

In the present paper, experimentally obtained

potentiometric titration data of the high charged

synthetic polyelectrolyte PAA and the low charged

natural polyelectrolyte HA is analyzed with re-

spect to the H�/Me2� molar exchange process. Anumber of different experimental data are ana-

lyzed including different polyelectrolytic charge

densities and different metals at various concen-

trations using the theoretical determination of

both the changes in pKa due to ionization of the

polyelectrolyte involved and the resulting metal

speciation in solution. In the modeling section, the

theoretical procedure for determining the proton/(heavy) metal exchange that occurs upon binding

of the metal ions to a partially ionized polyelec-

trolyte will be described in some detail. In addi-

tion, it will be shown that appropriate description

of the applied procedure for obtaining the H�/

Me2� molar exchange coefficient is of great

importance for the interpretation of the data.

2. Modeling

In the literature, the interactions between the

different counterion species and the polyelectrolyte

in solution have been considered from various

theoretical frameworks, including CC theory of

J.C. Benegas et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 224 (2003) 107�/117108

linear polyelectrolytes [8,9], solution of the

Poissson�/Boltzmann equation [10,11] and differ-

ent types of parametric models that include some

of relevant interactions [2,7]. These models have

varying degrees of convenience and shortcomings

when dealing with the different experimental

approaches used in these very complex polyelec-

trolytic systems (see e.g. [18]). Our group has been

involved in developing extensions of the CC

theory, with the aim of including important

aspects of polyelectrolytes in natural systems

such as counterion competition [12], chemical

binding [13,14] and heterogeneity of functional

groups [15]. This extended model presents the

following convenient characteristics:

i) polyelectrolytic interactions, which include the

interactions between all ionic species and theeffect of the solvent, are taken into account

from first principles;

ii) different thermodynamic states for the small

ions (free in solution, restrained to a ‘con-

densation’ volume in the immediate neighbor-

hood of the polyelectrolyte and chemically

bound to particular binding sites) that are

crucial for counterion speciation are built intoor are a direct consequence of the model;

iii) entropic effects are explicitly included;

iv) the possibility of dealing with linear polyelec-

trolytes of two or more functional groups is

considered in the model;

v) the minimization of the total (excess) free

energy of the solution system determines,

among other properties, the population dis-tribution of small ions in the different thermo-

dynamic states, i.e. their speciation;

vi) the proper derivation of the total (excess) free

energy of the system allows for the straightfor-

ward determination of the functional form of

the thermodynamic variable of interest.

Within this general framework, the present

paper deals with the central problem of counterion

exchange processes, which are driven by the inter-

play of all relevant interactions. When a salt

containing a (heavy) metal is added to a solution

containing a weak polyelectrolyte, some of the

resulting metal ions are usually bound to binding

sites on the polyelectrolyte. Consequently, protonsare released from the polymer resulting in a H�/

Me2� ion exchange process that may strongly

modify the polyelectrolytic characteristics of the

solution. In the present modeling, it is assumed

that the binding sites are the ionizable groups on

the polymer. Competition with H� ions for these

binding sites and/or the shift in the pK0 upon

heavy metal binding is expected to drive the H�/Me2� exchange process of the polyelectrolyte

neighboring undissociated functional groups.

What is determined, both experimentally and

theoretically, is the change in pH that occurs

when the divalent metal salt is added to the

reference solution. Theoretically, pH is obtained

from the theoretically calculated pKa value by the

equation,

pH�pKa� log

�1 � a

a

�(1)

where pKa is calculated according to Eq. (A8) or

Eq. (A10) and Eq. (A9), respectively, in Appendix

A, and a is the degree of ionization of thepolyelectrolyte.

3. Data analysis

In the present paper, we focus on the following

experimental conditions: (i) the characteristic

properties of the polyelectrolyte itself are kept

constant by applying the experimental procedure

at constant degree of ionization of the polyacid,and (ii) the solution composition is kept constant

with respect to one of the counterions under

investigation (protons). Under the latter condi-

tions, changes of the properties of the studied

polyelectrolyte may be induced, affecting as well

the distribution of monovalent and divalent coun-

terions over free and bound states. To illustrate the

different approaches, in Fig. 1 (calculated) poten-tiometric titration curves are plotted for a weak

heterogeneous polyacid in the absence (upper solid

line) and in the presence (lower dotted line) of a

given concentration of divalent metal ions. These

potentiometric titration curves show the typical

monotonic increase over almost the whole range of

J.C. Benegas et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 224 (2003) 107�/117 109

ionization. The vertical arrows (a being constant)

represent processes in which the metal concentra-

tion has been increased resulting in a decrease inpH due to the release of protons but keeping the

degree of ionization of the polyelectrolyte con-

stant. Experimentally and theoretically, the proton

release, D[H�], is calculated from the change in

measured and calculated pH, respectively. The

horizontal arrows in Fig. 1 represent typical metal

titration experiments at constant pH. Under these

conditions, the experimental and theoretical re-lease of protons are obtained from D[H�]�/DaCp.

In both cases, the change in bound metal, DC2bound,

is obtained by calculating the concentration of

chemically bound divalent metal ions:

Cbound2 �saCp (2)

where s is the fraction of divalent metal ions

bound per polymeric ionizable group [13] and Cp is

the concentration of the polyelectrolyte functional

groups (thus including both dissociated and not

dissociated groups) at the reference and final

solution states. The H�/Me2� molar exchangecoefficient for chemical binding is defined as

follows:

nexch�D[H�]=DCbound2 (3)

4. Results and discussion

4.1. PAA at constant a

In Fig. 2, the protons released by partiallyneutralized PAA (Cp�/2.50 mmol l�1) are plotted

vs the added amount of Cd(NO)2, for three

different degrees of ionization of the polymer

(a�/0.2, 0.4 and 0.6). Experimental data (points)

were taken from the literature [5], whereas the lines

refer to our model calculations, obtained using the

model calculated change in pKa upon ionization,

at the reported solution conditions, with a PAAcharge density j�/2.85 [19] and a from the

original experimental data derived pK0 value of

4.72 [5]. The binding of Cd to PAA has been

reproduced using an intrinsic free energy of

binding, DGb�/�/12RT , where we have assumed

a binding behavior of Cd to PAA similar to the

reported binding affinity of Zn to PAA [14].

The analyzed exchange process corresponds tothe vertical arrow of Fig. 1 and can be imagined as

the release of protons observed during the stepwise

addition of the cadmium salt at constant degree of

ionization. This process appears to be strongly

dependent on the degree of ionization of the

polyelectrolyte, being very strong at a�/0.2 and

more than one order of magnitude smaller for a�/

0.6, at a metal concentration C2�/0.2 mmol l�1.From Fig. 2, it can be seen that theoretically

Fig. 1. Schematic representation of a typical potentiometric

titration curve of a heterogeneous polyacid, in the absence (*/)

and the presence (- - -) of divalent metal ions. Vertical solid

arrows represent processes at constant a and horizontal dotted

arrows represent processes at constant pH. Theoretical calcula-

tions are performed with Cp�/2.50�/10�3 mol l�1, j�/ 0.8,

C2�/0.5�/10�3 mol l�1, DGb�/�/12RT and four different

functional groups with pK0 values being: 3.7, 5.4, 6.4 and 9.0.

Fig. 2. Experimentally obtained (symbols) and theoretically

calculated (lines) values of D[H�] vs [Cd2�] for the Cd/PAA

system at different a values: 0.2 (j), 0.4 (m) and 0.6 (').

[PAA]�/2.50�/10�3 mol l�1 and j�/2.85. Theoretical calcu-

lations are performed with DGb�/�/12RT ; lines refer to a

values: 0.2 (*/), 0.4 (�/ �/ �/) and 0.6 (- - -).


calculated values agree fairly well with the experi-mental data, at least for the solution conditions

shown in Fig. 2. The release of protons can be

attribute to two different physicochemical pro-

cesses: (i) competition between cadmium and

proton ions for the same binding sites on the

polyelectrolytic chain and (ii) the decrease of the

intrinsic deprotonation constant of undissociated

groups (pK0), due to binding of metal ions atneighboring polymeric sites [20,21]. As shown

before [14], large changes (i.e. decrease) in pKa

values are observed at low values of a when

strongly binding heavy metals are added to the

polyelectrolyte solution. These changes, which are

proportional to the metal concentration, are

probably due to significant changes in the intrinsic

pK0 of unionized polymeric groups due to metalbinding to neighboring groups. These very com-

plex interactions are not yet included in the present

modeling and, therefore, the present model under-

estimates the protons released by PAA above

metal concentrations of, approximately aCp/2,

i.e. in those cases where there are more metal

ions than binding sites available in solution.

Nevertheless, the agreement between the reportedexperimental data and our theoretical calculations

is very satisfying if the binding strength and/or

metal concentrations are not so large to strongly

distort the titration curves at low ionization

values, i.e. in the experimental region where

induced changes in pK0 are not too important

(see reference [14] for a more complete discussion).

With the above data the exchange coefficient,nexch, defined in Eq. (3), has been calculated and is

represented in Fig. 3. It can be seen that the H�/

Cd2� exchange process is much more effective at

low degree of ionization (solid line) than at higher

degrees of ionization (dotted lines), where the

concentration of available binding sites (the io-

nized functional groups) are much more abundant

and there is less need of further deprotonation forallowing binding of the Cd2� ions. This result

gives further support to the proposed model of

chemical binding of heavy metal ions to a poly-

electrolyte, since a main assumption is that diva-

lent ions are chemically bound to the (charged)

sites provided by the ionization of the functional

groups of the weak polyelectrolyte.

4.2. PAA at constant pH

For various metal/PAA systems theoretical H�/

Me2� exchange coefficients at constant pH were

calculated from previously published potentio-

metric titration data [14] and are plotted vs pH

in Fig. 4. In all cases, the calculated data refer to a

change in a metal concentration from 0 to 0.25

mmol l�1 with [PAA]�/2.50 mmol l�1. The

horizontal dotted arrow lines in Fig. 1 represent

this process. The proton release is calculated

simply as the product of the change in a , Da ,

between the reference and final states, times the

concentration of polymeric ionizable groups Cp.

The change in the fraction of bound metal ions,

Fig. 3. Theoretically calculated values of the H�/Cd2� molar

exchange coefficient nexch vs [Cd2�] for the Cd/PAA system at

constant a for the same conditions as in Fig. 2.

Fig. 4. Theoretically calculated values of the H�/Me2� molar

exchange coefficient nexch vs pH values for different Me2�/PAA

systems. [PAA]�/2.50�/10�3 mol l�1 and j�/2.85. Model

calculations are performed using DGb�/�/9RT for Mg (x);

DGb�/�/9.5RT for Ca (2); DGb�/�/12RT for Zn (I) and

DGb�/�/15RT for Cu (k) [14].


DC2bound, is calculated as described in Section 2.

This calculation depends on how well the theore-

tically determined potentiometric titration repro-

duce the experimental results at the chosen pH.

Deviations between theoretical and experimental

data have been found to be larger at lower pH

values most probably due to higher uncertainties

in the theoretical calculations at low pH values due

to changes in the intrinsic deprotonation constantpK0, as discussed above. For this reason, the data

points at pH 5.5 must have an important systema-

tic error and, therefore, the lower values at pH 5.5

may not be realistic. Taking this into account, it is

seen from Fig. 4 that, for the various metal/PAA

systems, the molar H�/Me2� exchange coefficient

decreases with increasing pH. In addition ex-

change coefficients appear to be larger for thecases of Cu and Zn than for Ca and Mg. A

remarkable result is that the exchange coefficients

at constant pH are much larger that the ones

obtained at constant a for the Cd/PAA system.

4.3. HA systems at constant a

In order to investigate the effect of the chargedensity of the polyelectrolyte, previously reported

potentiometric titration data of the natural poly-

mer HA [17], has been analyzed with respect to the

proton�/metal exchange process. Fig. 5 shows the

experimental and calculated release of protons for

different total added metal concentrations forthree different values of a , for the Cd/Fluka HA

system in water solution. The theoretical lines have

been calculated by taking into account four

different functional groups, each with a character-

istic fractional abundance and intrinsic pK0 value,

as described in reference [15]. As before, an

intrinsic free energy of metal binding DGb�/�/

12RT [16,17] and a structural charge density ofj�/0.8 [15] are taken for the present experimental

conditions. A HA concentration of 2.50 mmol l�1

has been used in all cases reported here. The data

show qualitatively the same pattern observed for

the highly charged polyelectrolyte PAA, i.e. a

decrease of released protons with increasing degree

of ionization of the polyelectrolyte. For the Cd/

Fluka HA system, the absolute values of DH� are,nevertheless, smaller than in the case of Cd/PAA

described in Fig. 2.

We note that large negative changes in pKa at

initial values of ionization (the effect of the shift in

pK0) are much smaller for the HA system than in

the PAA titrations. Therefore, for HA solutions,

the model calculations can obtain proton release

data for all three added metal concentrations, evenat the lowest polymer ionization (a�/0.2). In

general, the theoretical calculations agree qualita-

tively very well with experimentally obtained data,

although our model predicts somewhat smaller

values for the release of protons at a�/0.2.

Although quite speculative, this difference might

be also the consequence of different shifts in pK0

upon metal binding for the two polymers studied.The shift in pK0 in polymeric systems, in particular

proteins and polypeptides, has been shown to

depend on the local polymeric environment [21].

In the systems studied here it should depend,

among others, on the repulsive electrostatic inter-

actions between the bound metal and the protons

of the neighboring (still) protonated functional

groups [20]. The change in pK0 should thereforedepend on the spatial separation of the ionizing

groups. Since the mean separation between func-

tional groups is about 2.5 A for PAA and about 9

A for HA, the former polyelectrolyte should show

a much stronger proton release due to the shift in

pK0. Note that for these particular polyelectrolytes

the electrostatic interaction at the second neigh-

Fig. 5. Experimentally obtained (symbols) and theoretically

calculated (lines) values of D[H�] vs [Cd2�] values for the Cd/

Fluka HA system for different a values: 0.2 (j), 0.4 (m) and

0.6 ('). [HA]�/2.50�/10�3 mol l�1 and j�/0.8 [15]. Theore-

tical calculations are performed with DGb�/�/12RT [17]; lines

refer to a values: 0.2 (*/), 0.4 (�/ �/ �/) and 0.6 (- - -).


boring PAA site is stronger than at the firstneighbor in HA.

In Table 1, both experimentally obtained [17]

and theoretically calculated proton release data as

well as theoretically calculated H�/Me2� molar

exchange coefficients are summarized for different

metal/Fluka HA systems at different degrees of

ionization, different metal concentrations but for

the same polymer concentration of Fig. 5. Calcu-lations have been made using the intrinsic pK0 of

the different functional groups and intrinsic free

energies of binding, DGb, as reported in Ref. [17].

The following pattern is observed:

i) Higher levels of released protons are found for

all metal/Fluka HA systems at the lowest

degree of ionization;

ii) The release of protons appears to increase in

the order Ca:/Cd:/NiB/Pb5/Cu;

iii) The H�/Me2� exchange coefficients cover awide range of values. Very small values are

found for highly ionized HA (high a ), while

more significant values are obtained for the

HA at low degree of ionization (a�/0.2).

Exchange coefficients increase with the con-

centration of added heavy metal for a�/0.2

and 0.4, while for a�/0.6 the exchange coeffi-

cients appear to be more or less constant overthe covered metal range. The highest values of

nexch(�/1.5) are obtained for Cu and Pb ions

at a�/0.2 and a metal concentration of 0.75

mmol l�1. Note that in all these cases, there is

not complete charge compensation, i.e. the

(effective) net polyelectrolyte charge is lower

after adding metal ion to the solution.

iv) Theoretically calculated data are in goodagreement with the experimentally obtained

ones, in particular for the lower binding

strength and lower concentrations of heavy

metal ions, i.e. in the region where the shift in

pK0 upon metal ion binding is less important.

4.4. HA at constant pH

For various metal/HA systems theoretical H�/

Me2� exchange coefficients at constant pH were

calculated by considering points of equal pH from

previously published potentiometric titration data

[17] and are plotted vs the total metal concentra-tion at pH 4 and 6 in Fig. 6 and Fig. 7,

respectively. The horizontal dotted arrow lines in

Fig. 1 represent this process. For the case of pH 4

there is a tendency for the exchange coefficient to

increase with the concentration of the added metal

ion. In the concentration range of our experi-

ments, the exchange process is stronger for Cu and

Pb than for Cd, Ni and Ca. In general under theseconditions, the calculated exchange coefficients

appear to be larger than the ones obtained at

constant a , similar to our observations for the

different metal/PAA systems. At pH 6, exchange

coefficients appear to be smaller than at pH 4 and

there is a tendency for the exchange coefficient to

decrease with the concentration of the added metal

ion. Kinniburgh et al. [7] found a similar patternfor various metal/PPHA systems in this metal

concentration range at both pH 6 and 8 in 0.1

mol l�1 KNO3.

In general, it can be seen that the exchange

process is stronger at low pH values, i.e. in the

titration region where there are more metal ions in

solution than binding sites available, therefore the

competition of H� and Me2� ions for these sitesis stronger. This result is completely in line with

the analysis at constant degree of ionization.

5. Conclusions

The H�/Me2� exchange process that occurs

when a simple salt containing heavy metal ions is

added to a polyelectrolyte solution has beenmodeled and described successfully with the ex-

tensions of the CC theory of linear polyelectrolytes

previously proposed by our group. Two important

polymers have been considered: a high charge

density, monoprotic synthetic polyelectrolyte

(PAA) and an environmentally important low

charge density, multifunctional polyelectrolyte

(HA). In both cases, it is shown that the exchangeprocess is much stronger at low ionization degrees

of the polyelectrolyte (in the Me2� ion concentra-

tion region studied here). It is furthermore found

that ion exchange coefficients increase for higher

concentrations of the Me2� added. This result can

be interpreted as a manifestation of the H�/Me2�


Table 1

Experimentally obtained and theoretically calculated values of D[H�] for Me2�/Fluka HA systems for different values of a at three

metal ion concentrations

Metal a [Me2�] (mmol l�1) D[H�] (mmol l�1) nexch

Experimental Theoretical Theoretical

Ca 0.2 0.25 0.0149/0.001 0.019 0.145DGb�/�/9RT 0.50 0.0369/0.004 0.029 0.159

0.75 0.0719/0.007 0.058 0.285

0.4 0.25 (8.089/0.81)�/10�4 1.28�/10�3 0.0060.50 (8.459/0.84)�/10�4 1.88�/10�3 0.0060.75 (3.189/0.32)�/10�3 3.96�/10�3 0.011

0.6 0.25 (1.159/0.12)�/10�5 4.35�/10�5 1.8�/10�4

0.50 (1.909/0.19)�/10�5 9.10�/10�5 2.2�/10�4

0.75 (6.079/0.61)�/10�5 1.27�/10�4 2.4�/10�4

Cd 0.2 0.25 0.0439/0.004 0.027 0.126DGb�/�/12RT 0.50 0.0889/0.009 0.066 0.268

0.75 0.1189/0.012 0.097 0.395

0.4 0.25 (9.999/0.10)�/10�4 1.18�/10�3 0.0050.50 (2.409/0.24)�/10�3 4.08�/10�3 0.0060.75 (3.719/0.37)�/10�3 5.10�/10�3 0.011

0.6 0.25 (1.719/0.17)�/10�5 4.35�/10�5 1.8�/10�4

0.50 (5.489/0.55)�/10�5 1.19�/10�4 2.4�/10�4

0.75 (1.249/0.12)�/10�4 1.44�/10�4 2.1�/10�4

Ni 0.2 0.25 0.0399/0.004 0.033 0.147DGb�/�/13RT 0.50 0.0639/0.006 0.052 0.212

0.75 0.0919/0.009 0.074 0.300

0.4 0.25 (1.389/0.14)�/10�3 1.52�/10�3 0.0070.50 (1.409/0.14)�/10�3 2.65�/10�3 0.0060.75 (2.639/0.26)�/10�3 4.09�/10�3 0.008

0.6 0.25 (4.299/0.43)�/10�5 4.62�/10�5 2.4�/10�4

0.50 (4.029/0.40)�/10�5 1.12�/10�4 2.3�/10�4

0.75 (7.629/0.76)�/10�5 1.41�/10�4 1.9�/10�4

Cu 0.2 0.25 0.0779/0.008 0.054 0.222DGb�/�/15RT 0.50 0.2469/0.025 0.180 0.733

0.75 0.4629/0.046 0.374 1.525

0.4 0.25 (1.049/0.10)�/10�3 1.54�/10�3 0.0060.50 (4.039/0.40)�/10�3 7.96�/10�3 0.0160.75 (8.689/0.87)�/10�3 1.55�/10�2 0.032

0.6 0.25 (4.499/0.45)�/10�5 4.64�/10�5 1.9�/10�4

0.50 (1.049/0.10)�/10�4 1.28�/10�4 2.6�/10�4

0.75 (1.919/0.19)�/10�4 1.55�/10�4 2.1�/10�4

Pb 0.2 0.25 0.0659/0.007 0.066 0.272DGb�/�/15RT 0.50 0.1789/0.018 0.137 0.561

0.75 0.7029/0.070 0.449 1.830

0.4 0.25 (7.739/0.77)�/10�4 1.54�/10�3 0.0060.50 (1.389/0.14)�/10�3 3.34�/10�3 0.0070.75 (7.009/0.70)�/10�3 1.93�/10�2 0.040

0.6 0.25 (2.529/0.25)�/10�5 4.64�/10�5 1.9�/10�4

0.50 (3.419/0.34)�/10�5 1.17�/10�4 2.3�/10�4

0.75 (1.049/0.10)�/10�4 1.56�/10�4 2.1�/10�4

The theoretically calculated H�/Me2� exchange coefficient, nexch, for each case is also included. In all cases [HA]�/2.50�/10�3 mol

l�1 and j�/0.8 [15].


competition for the binding sites on the polymer.

At high degrees of ionization, the binding sites (the

ionized groups) are in excess over the metal ions,

and therefore there is little need of further ioniza-

tion in order to chemically bind a Me2� ion.

On the other hand, the H�/Me2� exchange

process seems to be more effective in high charge

density polyelectrolytes (PAA) than in low charge

density polyelectrolytes (HA). This result can be

interpreted as a result of changes in the pK0 of

(still) non-ionized functional groups when Me2�

binding occurs at a neighboring group. If this is

the case, the effect should be stronger for higher

charge density polyelectrolytes, where the neigh-boring groups are closer, and therefore the elec-

trostatic interactions responsible for lowering the

pK0 should be stronger. Within this general

behavior the present results reaffirm that the

ability of the heavy metal ions to induce H�

release increase following the order Ca:/Cd:/

NiB/Pb5/Cu, which is in line with previously

observed metal ion binding strengths reported byour and other groups in the literature.

Acknowledgements

MvdH is grateful to the Universidad Nacional

de San Luis for partially funding his visit to this

university. RDP is grateful to RIVM for financing

his stay at this Institute where some of theexperiments were carried out before. JCB is a

member of the Carrera de Investigador (CON-

ICET).

Appendix A

The starting point of CC theory [8,9] is to model

the polyelectrolyte as a uniform linear array ofcharges. The fundamental assumption is that the

total polyelectrolyte charge can be smoothly

spread over the polymer.

It is convenient to define a (mean) structural

charge density, jstr, given by:

jstr�lB

bstr

(A1)

Where lB�/e2/(okBT ) is the Bjerrum length, bstr is

the average distance between consecutive charges

projected onto the polymer axis, e the elementary

charge, o the bulk dielectric constant, kB the

Boltzmann’s constant and T the temperature.

If the polyelectrolyte charge density is higherthan the critical value, jcrit, a fraction r of

counterions is condensed onto the polyelectrolyte

chain (per polymeric charged group). Paoletti et al.

[12] have shown that the thermodynamic proper-

ties of the solution are readily obtained by assum-

ing that the total condensed fraction can be written


exchange coefficient nexch vs C2 for different Me2�/Fluka HA

systems at pH 4. [HA]�/2.50�/10�3 mol l�1 and j�/0.8 [15].

Model calculations are performed using DGb�/�/9RT for Ca

(*/); DGb�/�/12RT for Cd (- - -); DGb�/�/13RT for Ni (*/ - -

*/); DGb�/�/15RT for Cu (�/ �/ �/) and DGb�/�/15RT for Pb

(*/ - */) [17].


exchange coefficient nexch vs C2 for different Me2�/Fluka HA

systems at pH 6. Model calculation parameters and symbols as

in Fig. 6.


in the following form:

r�ri�rj �r(xi�xj) (xi�xj �1) (A2)

where ri and rj stand for the fractions of con-

densed counterions of valence zi and zj , respec-

tively. According to this model, in the

condensation regime, both species of counterions

are found in the condensation volume.

Chemical binding of counterions of valence zj tothe polyelectrolyte is considered by reducing the

average charge density effectively by an amount

equivalent to a fraction s per polymeric charge

[13]:

js�jstr(1�zjs) (A3)

where s�/ [Me]b/Cp, and [Me]b is the concentra-

tion of bound metal ions. The effective chargedensity thus becomes the central characteristic of

the polyelectrolytic solution.

Following the procedure described in Refs.

[12,13], one can write analytical expressions for

the polyelectrolytic (Gpol), entropic (Gentr) and

binding (Gb) contributions to the total (excess)

free energy of the system:

Gtot�Gpol�Gentr�Gb�Gion�Gb (A4)

The contribution of each counterion species to

the total condensed fraction (xi and xj), is

calculated [12] by minimizing the total reduced

free energy of the system:

@gtot

@r�0 (A5)

@gtot

@xi

�0 (A6)

where gtot�/Gtot/RT and R is the gas constant. In

the framework of CC theory, the limiting behavior

at infinite dilution of Eq. (A5) determines the

value of the total fraction of condensed counter-

ions, r , which, for the particular case of a mixtureof monovalent and divalent counterions, it is given

by:

r�1

2 � x

�1�

1

jstr(2 � x)(1 � 2s)

�(A7)

where we have set xi �/x1�/x and xj �/x2�/1�/x .

Notice that Eq. (A7) properly reproduces the

functional form of the condensed fraction givenin Ref. [12] for the case in which no bonding

occurs (s�/0).

For the present study the thermodynamic func-

tion of interest is the apparent dissociation con-

stant, pKa, given in general by:

pKa�pK0�DpKa (A8)

where pK0 is the intrinsic pKa, characteristic of the

(isolated) ionizing group making up the polymer,and DpKa is the change in pKa due to the

ionization of the polyelectrolyte. Once the excess

free energy function, Gion, is known, we can

readily calculate:

DpKa�1

np2:303RT

@Gion

@a

�G(a; j; Cp; C1; C2; T ; o; s0) (A9)

where np is the number of polymeric charge units,

C1 and C2 stand for the analytical concentrations

of monovalent and divalent counterions, respec-

tively, and s0 is the maximum (mean) fraction of

chemically bounded counterions per polymericcharge unit, i.e. the mean stoichiometry of the

binding process.

For a heterogeneous weak polyelectrolyte like

HA, constituted by N functional groups of frac-

tional abundance (Xi ) and intrinsic pK , (pK0i ), the

overall intrinsic pK0 is a function of the degree of

ionization. Porasso et al. [14] have shown that:

pK0(a)�pK0i � log

�bi

(1 � bi)

(1 � a)

a

�(A10)

where bi stands for the ionization degree of the ith

functional group.

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Documents

Proton–metal exchange processes in synthetic and natural polyelectrolyte solution systems