Proton Binding to Humic Acids: Electrostatic and Intrinsic Interactions

Journal of Colloid and Interface Science 217, 37– 48 (1999) Article ID jcis.1999.6317, available online at http://www.idealibrary.com on

Proton Binding to Humic Acids: Electrostatic and Intrinsic Interactions Marcelo J. Avena,* ,1 Luuk K. Koopal,* and Willem H. van Riemsdijk† *Laboratory for Physical Chemistry and Colloid Science and †Department of Environmental Science, Section of Soil Science and Plant Nutrition, Wageningen Agricultural University, P.O. Box 8038, 6700 EC Wageningen, The Netherlands Received August 31, 1998; accepted May 19, 1999

bicides and pesticides (1). The charge development is also important for the interaction of HA and FA with the surface of minerals and for their colloidal stability. The latter information is of relevance for the interpretation of the mobility of humics and for the bioavailability of ions and organic molecules bound to the humics. Humics are rather heterogeneous materials and about every HA or FA has its own properties. However, the physical chemical properties of humic substances like their charging behavior and their ability to bind ions seem to be less diverse. Model descriptions of ion binding have been used to predict field situations (2) and can be applied in chemical speciation (3) and chemical transport programs. These descriptions should be sufficiently realistic to allow predictions in a wide range of solution conditions with a reasonable degree of confidence. Examples of these descriptions can be found in the literature (4 –7). In some of these models the overall affinity for ions is separated in an intrinsic and an electrostatic part. The intrinsic part accounts for the specific (noncoulombic) ion binding properties of humics (heterogeneous site binding). The electrostatic part accounts for the long range coulombic interactions. The latter are mostly approximated by a simple model that neglects heterogeneity. The emphasis of the present article will be on the electrostatic part of such models. For the discussion of the site binding part we refer to Kinniburgh et al. (8). The acid– base properties of HA and FA are controlled by a variety of functional groups, whose affinity for protons is given by the above mentioned intrinsic and electrostatic interactions. The overall proton affinity is usually derived from proton binding curves, which can be obtained from acid– base titration measurements. Unfortunately, the electrostatic potential that governs the electrostatic interactions cannot be measured directly. Therefore, the intrinsic and electrostatic affinities can only be assessed from a series of proton binding curves with the help of an electrostatic model that accounts for the drop in the potentials between the binding sites and the bulk solution. Each model implies a series of assumptions. The most general assumption is that the electrostatic potentials at the binding sites can be represented by just one averaged smeared-out potential that neglects the effects of the chemical and structural

The proton adsorption behavior of eight humic acids (HA) and a fulvic acid (FA) was studied as a function of pH and KNO 3 concentration. The emphasis is on the comparison of the different humics with respect to their ion binding properties and on the comparison of two different models to describe the electrostatic interactions: the Donnan model and the impermeable sphere (IS) model. Viscosimetric data were used to estimate the hydrodynamic volumes and radii of the HA molecules. These data were incorporated in the electrostatic models and calculations could be carried out without any adjustable parameter. The Donnan model in combination with hydrodynamic volumes obtained by viscometry cannot adequately describe the electrostatic effects related to changes of the electrolyte concentration. This model leads to good prediction of the HA behavior if unrealistically large volumes are used for fulvics and unrealistically large volume-salt concentration dependencies are used for humics. The IS model can successfully reproduce experimental proton adsorption data with physically realistic radii. The good performance of the IS model and the poor performance of the Donnan model is directly related to the fact that the hydrodynamic volumes of the molecules are too small to allow for charge compensation within the molecular limits. The combination of viscometry with the IS model leads to a consistent description of the electrostatic in humics and to a consistent way of positioning the master curves. Therefore, the electrostatic potentials and the intrinsic affinity distributions of the different samples can be compared on an equal basis. The similarities in the intrinsic affinity distributions give faith for the possibility to develop a generic model to describe the ion binding to humics. © 1999 Academic Press

Key Words: humic acid; fulvic acid; proton binding; proton adsorption; viscometry; modeling electrostatic interactions; intrinsic affinity distributions.

INTRODUCTION

The study of proton binding by humic and fulvic acids (HA and FA, respectively) is relevant for the understanding of their charging behavior and their ability to bind cations like metal ions and charged small organic molecules such as some her1 To whom correspondence should be addressed. On leave of absence from INFIQC, Departamento de Fisicoquimica, Facultad de Ciencias Quı´micas, Universidad Nacional de Co´rdoba, Co´rdoba, Argentina.

37

0021-9797/99 $30.00 Copyright © 1999 by Academic Press All rights of reproduction in any form reserved.

38

AVENA, KOOPAL, AND VAN RIEMSDIJK

heterogeneity. With such a model, the proton concentration in the bulk solution, [H 1], can be converted to the proton concentration in the solution adjacent to the binding sites, [H s1]. If the model is adequate, the proton binding vs pH curves obtained at different electrolyte concentrations will merge in a single proton binding curve if the data are plotted as proton binding vs pH s. This curve is called the master curve, and it reflects the intrinsic affinity distribution of HA or FA for protons (9, 10). This master curve procedure has been used extensively in past years and has proved to be a very useful approach to understand the reactivity of HA and FA (6, 7, 9). Several simplifications have been used to describe the electrostatics in humics. The representation of HA and FA molecules as rigid spheres (4 – 6, 11) or rigid cylinders (6, 11, 12) is commonly found in the literature. The rigid sphere model represents compact humics, whereas the cylinder model applies to worm-like humics. In these models it is assumed that the charge is located at the surface and that all the counter- and co-ions that neutralize the charge are located in the diffuse layer outside the particle. The electric potential at the surface is derived by solving the Poisson–Boltzmann equation for these geometries, using the surface charge density as input parameter and the average radii of the spheres or the cylinders as adjustable parameters. De Wit et al. (6) and Milne et al. (11) applied this procedure to obtain a master curve. Bartschat et al. (4) successfully applied a model in which the humic molecules were represented by two size classes of impenetrable spheres to describe proton and copper binding to a HA. The description of humic molecules as impermeable particles is, however, not necessarily a good approach. An alternative and rather different representation of a HA molecule was proposed by Marinsky et al. (13) and followed by Bennedetti et al. (7) and Kinniburgh et al. (14) who describe the humics as a permeable Donnan gel. This approach considers that the humic molecule in solution has an open gel-like structure that behaves as an electrically neutral entity permeable to electrolyte ions. In the model it is assumed that all the charges of the HA molecules are neutralized by counter- and co-ions within the hydrated volume of the molecules and that the potential is constant inside and zero outside this volume. Bennedetti et al. (7) and Kinniburgh et al. (14) have applied this approach to several HA and FA samples. The electrical potential in the gel phase has been calculated by using the charge density as input parameter and the Donnan volume as an adjustable parameter to obtain a master curve. A somewhat intermediate approach has been proposed by Tipping et al. (5). These authors considered a HA molecule as a charged rigid sphere with its charge neutralized in a diffuse layer cut off at the Debye length (k 21). The electrical potential is not calculated directly, instead an electrostatic interaction factor w is empirically related to the ionic strength. The amount of the various ions that neutralizes the charge of the molecules is calculated with Donnan-type expressions.

A general problem that accrues when an electrostatic model is used without further knowledge about the dimensions of the particles is the impossibility of finding a unique solution to the electrostatics and hence to the position of the master curve. De Wit et al. (6), for example, noted that different sets of surface areas and radii resulted in equally well-merging master curves by applying the rigid sphere and the rigid cylinder models. They introduced an extra condition by relating the surface area and the radius of the particles through the density of the HA molecules in order to obtain radii within reasonable realistic values. Similarly, Bennedetti et al. (2) reported that different sets of Donnan volumes would lead to different well-merging master curves. They suggested that the volumes should preferably be measured independently in order to avoid this problem. Viscosimetric measurements are now available for a series of humic and fulvic acids (15) and they can be used to estimate the specific volumes and molecular radii of the humics. These measured volumes and radii can be incorporated in the electrostatic models and master curve calculations can be carried out without any adjustable parameter. Hence, by introduction of the measured size of the particles the separation of the electrostatic and intrinsic interactions becomes operational. The capability of the electrostatic models to describe the data can now be evaluated by analyzing to which extent the proton binding vs pH s curves obtained at different electrolyte concentrations merge into one master curve (i.e., when a good master curve is obtained the model is adequate). The first aim of this article is to compare in this way the impermeable sphere model and the Donnan model. The second aim is to compare the behavior of a series of different HA samples on an equal basis and to judge to which extent the different humics have similar electrostatic and intrinsic properties. THEORY

Size of the Humics Viscometry offers a way to obtain the specific volumes, hydrodynamic volumes, and radii of HA molecules in aqueous solutions (15). For spherical particles, the intrinsic viscosity, [h], is related to the specific volume of the HA, V HA , by @ h # 5 2.5V HA ,

[1]

where both [h] and V HA are expressed in volume/mass units. When also the molecular mass, M, is known, the molecular hydrodynamic volume, V h , and the hydrodynamic radius of the molecule, a, can be calculated, V HA 5

NA NA 4 Vh 5 p a 3, M M 3

[2]

39

PROTON BINDING TO HUMIC ACIDS

where N A is Avogadro’s number. The specific volume in an aqueous solution can also be expressed as the sum of the specific partial volume of the HA in the considered solution, v solid , and the specific hydration volume, V hydr , which is the volume of water incorporated in the solvated particle per gram of dry HA: V HA 5 v solid 1 V hydr .

[3]

The values of v solid are close to the inverse of the density of the dry material and range between 0.5 and 0.7 g/mL according to recent experimental and computed values (16). General Electrostatic Model and Two Simplifications HA and FA molecules are supposed to be internally structured gel-like particles that carry a certain charge through ionization of the functional groups. The distribution of co- and counterions that compensates this charge should obey the Poisson–Boltzmann equation and thus the potential should drop monotonously from the bulk of the HA molecule to the bulk of the solution. For instance, by assuming that the particles are spherical and of the same size, the Poisson–Boltzmann equation can be written as

S

D

1 d d c ~r! r ~r! r2 52 , r 2 dr dr « 0«

[4]

where r(r) is the diffuse space charge density at the distance r from the center of the particle, « 0 the permittivity of vacuum, « the relative dielectric constant, and c(r) the potential distribution defined with respect to the potential in the bulk solution. r(r) is given by the unequal distribution of positively and negatively charged electrolyte ions in the solution and within the gel volume. Electroneutrality requires that the total diffuse charge equals the total particle charge. Equation [4] cannot be solved analytically and numerical solutions or approximations are needed. An approximate analytical solution based on the Debye–Hu¨ckel approximation has been given by Tanford (17). Oshima and Kondo (18) have reported an analytical expression for a permeable gel with planar geometry. A further discussion of several limiting cases of the Poisson–Boltzmann equation and their applicability to humics has been given by Bartschat et al. (4). In practice, where the structure, shape, size distribution, and other characteristics of the HA molecules are not precisely known, it is preferable to use even simpler models than Eq. [4] or its approximations to represent the charge and potential distribution in humics. Two simplified models, the impenetrable sphere (IS) and the Donnan model, have been discussed in the Introduction. Although these models are strong simplifications of reality, they have the advantage that the electrostatic interactions are still explicitly taken into account and that this is done with only one parameter, the electrostatic potential near

FIG. 1. Schematic representation of the impermeable sphere and the Donnan models. A permeable sphere where the negative charges are neutralized by electrolyte ions inside and outside the gel and the potential drop is governed by the Poisson–Boltzmann equation is represented at the top of the figure. (a) Impermeable sphere, (b) Donnan.

the sites. Schematically, the general model and the two simplified models are shown in Fig. 1. The top drawing represents a spherical permeable gel carrying negative charges that are neutralized by counterions and coions inside and outside the gel, together with the potential decay according to Eq. [4]. Underneath this picture, the IS and Donnan approximation are schematically represented. Provided the average size of the particles is known, both simplified models can be tested for a given humic by applying the master curve procedure. Impermeable Sphere In the impermeable sphere model the charges of the functional groups are all located at the surface of the humic molecule and these charges are neutralized in the solution by the supporting electrolyte ions (Fig. 1a). Since the Poisson–Boltzmann equation cannot be solved analytically for spherical symmetry, numerical solutions would be needed to obtain exact results. However, the approximate analytical expression Eq. [5], that applies to a symmetrical background electrolyte gives sufficiently accurate results for the present purpose (19, 20),

s IS 5

F S

D

S

z salt F c IS z salt F c IS 2Fc salt z salt 4 2 sinh 1 tanh k 2 RT ka 4RT

DG

,

[5] where s IS is the surface charge density, c IS is the potential at the surface of the particle, c salt is the electrolyte concentration

40

AVENA, KOOPAL, AND VAN RIEMSDIJK

in the bulk solution, z salt is the charge number (without sign) of the symmetrical electrolyte, F is the Faraday constant, and k 21 is the Debye length. For a symmetrical electrolyte,

k2 5

2F 2 c salt z 2salt . RT« 0 «

[6]

For nonsymmetrical and mixed electrolytes expressions similar to Eqs. [5] and [6] have been derived (21). The surface charge density s IS is related to the charge of the backbone of the HA molecule, Q, expressed in equivalent/ mass units by the following equation:

s IS 5

where r D is expressed in charge/volume units. The negative sign in Eq. [10] derives from the fact that r D is the net charge in the Donnan phase that neutralizes the backbone charge Q. By combining Eqs. [8 –10] an equation can be obtained that relates the charge density to the Donnan potential:

FQM . 4 p a 2N A

rD 5 F

Donnan Model

j

D

j j

[11a]

j

For a symmetrical electrolyte Eq. [11a] becomes

S

r D 5 22Fc saltz salt sinh

[7]

By using Eqs. [5] and [7] it is possible to calculate the surface potential if Q and a are known for a given salt concentration. Q can be measured by potentiometric titrations and a can be estimated from viscosity measurements using Eqs. [1] and [2].

O z c FexpS 2zRTFc D 2 1G .

D

z salt F c D . RT

[11b]

By using Eqs. [10] and [11] it is possible to calculate the potential in the Donnan phase if Q and V D are known. V D follows from viscometry assuming that it is equal to V HA . MATERIALS AND METHODS

HA and FA

In this model the backbone charge of the HA molecules is distributed homogeneously over the hydrodynamic volume of the particle and this charge is fully neutralized by co- and counterions located inside the hydrodynamic volume (Fig. 1b). In this case the Donnan volume equals the specific volume of the HA if v solid is neglected (this approximation does not produce important changes in the results). The electrostatic potential is constant and uniform within the domain of the gel phase and it drops to zero at the boundary between the molecule and the solution. Under these assumptions the electroneutrality condition requires that Q/V D 1

O z ~c j

Dj

2 c j ! 5 0,

[8]

j

where V D is the Donnan volume expressed in volume/mass units, z j is the charge number of ion j, c j is its concentration in the bulk solution, and c Dj is the concentration of ion j in the Donnan volume. c Dj and c j are related by a Boltzmann factor that includes the potential c D within the gel phase:

S

c Dj 5 c j exp

D

2z j F c D . RT

[9]

The measurable magnitude Q is related to the charge density in the Donnan phase, r D , by

rD 5 2

FQ , VD

[10]

Eight different humic acids and one fulvic acid are studied. The elementary composition, origins of the samples, and viscosimetric properties have been reported previously (15). Higashiyama L (HLHA), Kinshozan P (KPHA), Kinshozan F (KFHA), Kinshozan OH (KOHHA), and Shitara Black (SBHA) were obtained from Y.-H. Yang (22). The physical and chemical properties of these samples have been reported by Kuwatsuka et al. (23) and by Tsutsuky and Kuwatsuka (24). Purified Peat humic acid (PPHA) is a well-studied sample (11, 14) prepared from a commercial Irish horticultural peat and it was obtained from D.K. Kinniburgh. The weight average molecular mass of PPHA has been obtained by equilibrium UV scanning ultracentrifugation and equals 23,000 (11). Purified Aldrich humic acid (PAHA) is obtained from Aldrich humic acid (Aldrich Chemie; code:H1,675-2) (15). The weight average molecular mass obtained by size exclusion chromatography using proteins as standards is 20,000 (25). This value is somewhat higher than that obtained with fieldflow fractionation (14,500) as reported by Beckett and Hart (26). Forest soil humic acid (FSHA) was obtained from E.J.M. Temminghoff, who studied proton and copper binding (27). It was extracted from forest floor material, taken from the Tongbergen forest (Oisterwijk, The Netherlands). Laurentian fulvic acid (LFA) was obtained from C.H. Langford (28). It derives from a sample of a podsol collected in the Laurentian Forest Preserve of Laval University, Quebec, Canada. Physicochemical characterization of the sample has been

PROTON BINDING TO HUMIC ACIDS

TABLE 1 Elementary Composition, Intrinsic Viscosity, Degree of Hydration, and Molecular Weight of HA Elementary composition (%) Sample

C

H

O

[h] a mL/g

PPHA HLHA FSHA KPHA KFHA PAHA KOHHA SBHA LFA

52.1 59.1 52.9 57.3 57.1 55.8 55.2 58.7 45.1

5.1 5.7 5.4 3.8 4.5 4.6 5.4 3.4 4.1

39.9 32.0 39.3 36.3 34.6 38.9 36.0 34.5 49.7

25 8 7.5 4 5 3.5 8 4 5

V hydr /V HA

M

0.94 0.82 0.80 0.63 0.71 0.58 0.82 0.63 0.71

23000 b 25000 22000 7000 d 10000 20000 c 25000 7000 d 10000

pH 7, c salt 5 0.1 M. From Ref. (11). c From Ref. (25). d Minimum values (see text). a b

reported by Wang et al. (28). The informed size distribution obtained by ultrafiltration allows the estimation of a weight average molecular weight of around 10,000. The molecular masses, M of the other samples are estimated from viscosimetric measurements in 0.1 M KNO 3 solutions using the Mark–Houwink equation with coefficients a 5 0.5 and K 5 0.05 g/mL suggested by Clapp et al. (29). These coefficients most likely apply to well-hydrated humics. For strongly hydrophilic humics a will probably be larger than 0.5 and for hydrophobic humics a will tend to be smaller than 0.5. Table 1 shows the intrinsic viscosity values at 0.1 M electrolyte concentration and pH 7 together with the degree of hydration calculated as V hydr /V HA , assuming a value of 1.7 g/mL for 1/n solid (see eq. [3]). According to Table 1 HLHA, FSHA, KOHHA, KFHA, and LFA have a degree of hydration ranging between 0.71 and 0.82 and for these humics the coefficients K and a proposed by Clapp et al. (29) are appropriate. For KPHA and SBHA that are only weakly hydrated the estimated M values are minimum values that should be considered with some reservation. The Mark–Houwink equation with the present coefficients overestimates the molecular mass of PPHA (strongly hydrated) and underestimates the molecular weights of PAHA (weakly hydrated). Potentiometric Titrations and pH-Stat Experiments The acid-base potentiometric titrations were performed at 22°C using a fully automated titration system (30). The pH was monitored with two pH electrodes (Ingold U272-S7) and a single calomel reference electrode (Ingold 363-S7) connected to the reaction vessel via an electrolyte bridge filled with 1 M

41

KNO 3. After each titrant addition, the rate of drift of the electrodes was measured over a 1 min interval following an initial delay of 1 min to allow adequate mixing of the titrant. The readings were accepted when the rate of drift was less than 0.1 mV min 21. A maximum reading time of 10 min (which was seldom reached) was set for two successive additions of titrant. Titrations were started with samples dispersed in 0.001 M KNO 3 solutions and 0.1 M HNO 3 and 0.1 M KOH standard solutions were used as titrants. The typical titrated volume was 35 mL. HA concentrations ranged between 1 and 1.5 g/L. Prior to the titrations, the solutions were stirred at pH about 10.3 for several hours. After that, they were titrated until pH ;3.5 and bubbled with nitrogen for at least 2 h in order to remove carbon dioxide. Then, several successive base (up to pH 10.3) and acid (down back to pH 3.3) titrations were performed. Subsequently, salt was added to increase the electrolyte concentration and after 30 min of equilibration a new titration cycle was started. In general, the first titration cycle often showed some hysteresis and in most of the cases subsequent cycles were reproducible and hardly showed significant hysteresis. The calibration of the potentiometric cell was done by both buffer calibration (pH 4, 6, 8, and 10) and by blank acid-base titrations at different ionic strength. Proper working of the cell was checked by comparing the experimental blank titration curves with calculated ones using activity coefficients derived from the improved Davies equation (31). To know the extent of H 1 binding, Q, to the HA or FA molecules the volume of acid or base required to decrease or increase the pH of an equivalent volume of the blank electrolyte solution was calculated and substracted from each data point. Since titrant addition changes the ionic strength, this magnitude was calculated explicitly for every data point, taking into account both background electrolyte ions and free H 1 and OH 2. In pH-stat titrations, the solution was maintained at a constant pH whereas its ionic strength was varied by adding a 2 M KNO 3 solution of the same pH as the titrated solution. The volume of base required to bring the sample back to the prescribed pH after each addition of electrolyte was recorded and used to measure the change of proton binding of the samples at different ionic strength. pH-stat experiments were performed at pH 5 up to an ionic strength '0.4 M. Before every experiment, a titration from pH 10.3 to 3.3 and then back to pH 5 was performed in order to avoid the hysteresis in the titration behavior. Acid-base potentiometric titrations together with pH-stat experiments allow the location of the relative position of the Q vs pH curves at different ionic strengths. However, in order to convert the data from their relative value to an absolute value, the Q value in some point must be known. To obtain this value, a HA sample initially in its protonated form and free of acid or base was dissolved in a KOH solution at a given KNO 3

42

AVENA, KOOPAL, AND VAN RIEMSDIJK

concentration. For these conditions the electroneutrality of the solution reads c OH 2 1 c NO 23 1 QC HA 5 c K 1 1 c H 1

[12]

where C HA is the HA or FA concentration in g L 21. Since the concentrations of K 1 and NO 32 are known from the amounts of electrolyte added and base used and the concentration of H 1 and OH 2 from a pH measurement and the activity coefficients, the value of Q at the measured pH can be calculated. The amounts of base and humics used were selected so that the final pH of the solution was between 5 and 9. In this case, proton and hydroxyl concentrations could be neglected, which simplifies the calculations. Once Q is calculated at the measured pH value with this procedure, the absolute location of the Q(pH) curves at that electrolyte concentration can be obtained just by shifting the curve to its correct position. All the other curves at different electrolyte concentration were relocated relative to the first one making use of the pH-stat results. Master Curve Calculation The Q(pH) curves at different electrolyte concentrations can be analyzed by the master curve approach by converting Q(pH) to Q(pH s) curves. If the potential at the binding sites is known, pH s comes directly from pH s 5 pH 2

Fcs , 2.303RT

[13]

where c s stands for the smeared-out potential of the charged sites (functional groups). For the IS model and the Donnan model c s equals c IS and c D , respectively. The potential was calculated for every Q, pH, and electrolyte concentration value using the different models with V D or a data estimated from viscometry. RESULTS AND DISCUSSION

Size of the Humics The [h] vs pH data presented previously (15) for all the HA samples studied are shown in Fig. 2 together with straight lines based on b @ h # 5 @ h # 0 1 kc salt ~pH 2 2!,

[14]

b where [h] 0 is the intrinsic viscosity at pH 2, kc salt is the slope of the [h] vs pH curve at a given salt concentration and k and b are constants. Within experimental error the intrinsic viscosity of HA increases linearly by increasing the pH at a constant ionic strength and it decreases logarithmically by increasing the supporting electrolyte concentration. At pH around 2,

where by definition HA molecules aggregate and precipitate, the charge of the HA molecule is very low or even absent and changes in the electrolyte concentration should not affect the hydrodynamic volume of the molecules or the intrinsic viscosity. Therefore, this pH value is used as the convergence point in Eq. [14]. The parameters [h] 0, k, and b are shown in Table 2. In the special cases of PPHA and KFHA the equations do not predict the abnormally high values of the intrinsic viscosity at very low pH and high electrolyte concentration. These high values are due to aggregation of the HA molecules (15) and they should be neglected. In further calculations, Eqs. [1] and [14] are used to estimate V HA . The values of V HA are used to approximate V D in Eq. [10]. They range from 0.4 to 17 mL/g for the different samples and conditions (see also Fig. 2, keeping in mind that V HA 5 [ h ]/ 2.5). The particles radii to be used in the IS model are calculated from the same volumes by substitution of V HA and M in Eq. [2]. They range from 1.1 to 5.4 nm for the different samples and conditions. Proton Binding Although all the acid-base potentiometric titrations were started at 0.001 M KNO 3, the addition of titrants modified considerably the final ionic strength of the solutions. In fact, every titration cycle from pH 3.3 to 10.3 and then back to pH 3.3 increased the electrolyte concentration by about 0.002 M. Therefore, the reproducible titration curves at low ionic strengths are recorded at salt concentrations somewhat higher than 0.001 M. Typical titration results are shown in Fig. 3, where the charging behavior of PAHA in 0.005, 0.016, and 0.1 M KNO 3 solutions is represented by symbols. As it has been reported before (7, 11), the curves at different electrolyte concentrations run almost parallel and they shift toward lower pH values by increasing the concentration. The other samples behaved similarly (see Fig. 4). The variations in Q in the pH range from 3.3 to 10.3 are between 2.6 and 4.6 mmol/g. The pH-stat results were also similar for all the samples. The proton binding increased 0.45 6 0.15 mmol/g by changing the electrolyte concentration from about 0.003 M to about 0.4 M at pH 5. Comparison of the IS and Donnan Models Figure 3 also shows the Q(pH s) results calculated with the IS and the Donnan models. Although only data for PAHA are shown, similar results were found for the other samples. The Donnan model leads to very poor results. The calculated Q(pH s) data at different electrolyte concentrations do not merge at all; they are even more separated among them than the experimental Q(pH) data. Therefore, the Donnan model in combination with measured values of V HA cannot adequately describe the electrostatic effects related to changes of the electrolyte concentration. The IS model results in reasonably well-merging curves.

PROTON BINDING TO HUMIC ACIDS

43

FIG. 2. Intrinsic viscosity at different pH and electrolyte concentration of the samples studied. (F) c salt 5 0.001 M; (D) c salt 5 0.01 M; () c salt 5 0.1 M. Lines represent predictions of Eq. [14] using the parameters of Table 2.

The adequate performance of this model also can be seen in Fig. 4, where the data and calculated IS–master curves for all the other samples are presented.

The conclusion of the comparison of the two models is that the IS model is a more realistic approximation than the Donnan model. The good performance of the IS model and the poor

44

AVENA, KOOPAL, AND VAN RIEMSDIJK

TABLE 2 Parameters a for the Fit of Viscosity Data with Eq. [14] Sample PPHA HLHA FSHA KPHA KFHA PAHA KOHHA SBHA LFA

[h] 0/mLg 25.61 6.78 5.78 2.80 0.91 3.80 6.92 4.18 5.23

21

Surface Potentials (IS Model) and Intrinsic Affinities 21

2b

k/mLg

0.58 0.34 0.31 0.37 0.17 0.40 0.30 0.30 0.41

0.037 0.170 0.170 0.093 0.560 0.020 0.100 0.020 0.022

a b The errors in the estimation of [h] 0 and the slope of lines in Fig. 2 (kc salt ) are 1.5 mLg 21 and 0.25 mLg 21, respectively, for PPHA and 0.9 mLg 21 and 0.15 mLg 21, respectively, for the other humics.

performance of the Donnan model indicates that most of the charge of the HA and FA molecules is neutralized in a diffuse region outside the molecule. The hydrodynamic volumes of the HA or FA molecule are too small to allow for charge compensation within their molecular limits. De Wit et al. (6) have already shown that a rigid sphere model could lead to good master curves for humics. The optimized radii obtained in their study ranged from 0.7 to 4.4 nm depending on the HA. These values are in agreement with the radii deduced from viscometry for the present samples. Although good master curves have been obtained with the Donnan model by Benedetti et al. (2), the optimized volumes that lead to those master curves are in conflict with the volumes obtained by viscometry. The V D values fitted to the Donnan model overestimate the effects of the electrolyte concentration on the hydrodynamic volume of the humics. For a given sample V D values fitted by Benedetti et al. (2) change for the fulvic acids by a factor of 20 when the electrolyte concentration varies from 0.1 to 0.001 M and by a factor of 6.2 for the humics. The data from Fig. 2 indicate that in general, experimental V HA (5[ h ]/ 2.5) values increase at maximum by a factor of 3 under the same conditions. The conclusion is that the Donnan model only leads to merging of Q(pH s) curves if unrealistically large volumes are used for fulvics and too large volume-salt concentration dependencies are used for humics. In some other calculations we checked these options by using for V D the volume of a sphere with radius a 1 k 21 . In this case the merging of the curves was indeed satisfactory. The main disadvantage of using a 1 k 21 as the molecular radius is that the backbone charge of the humic molecules is smeared-out over a volume that extends far beyond the physical limits of the molecule. For all humics tested in this paper the particle size is, at intermediate and low electrolyte concentrations, indeed much smaller than k 21. This means that that can be about a factor of 10 to 300 times larger than V HA . Therefore, this type of simplified Donnan model is not considered any further.

According to Eq. [13] the potential varies by about 60 mV for every pH unit that the master curve is shifted with respect to the Q(pH) curve. Comparison of the master curves obtained with the IS model and their shift with respect to the Q(pH) curves allows us to compare the intrinsic behavior and the electrical potential of the different HA and FA samples on an equal basis. Figure 5 shows the electrical potential as a function of pH and at two electrolyte concentrations for the nine samples studied. The shape of the curves is similar for all the samples and the behavior is highly non-Nernstian. The potential varies 15–20 mV per pH unit at pH lower than about 5 and 4 – 6 mV per pH unit at pH higher than about 6. The increase in the negative potential by decreasing the ionic strength from 0.1 to 0.004 M is between 20 and 40 mV depending on the pH and the HA considered. Humic acids formed by relatively small molecules such as PAHA have a relatively large potential. Humic acids formed by large molecules such as PPHA have a small potential. For example, the difference in potential between PAHA and PPHA is 30 – 40 mV depending on the pH and the electrolyte concentration. The electrical potentials in Fig. 5 are in fair agreement with previous estimates by de Wit et al. (32) for a series of 11 humic acid samples. They are also in agreement with experimentally assessed potentials. Values of zeta potentials for different humics (33, 34) and for HA coated particles (35–37) are in the range 210 to 250 mV depending on the pH and electrolyte concentration. These values are somewhat less negative than those of Fig. 5, but it should be realized that in general zeta potentials are expected to be less negative than surface potentials. By adsorbing organic acid probes on PAHA chemically bound to silica Yang and Koopal (35) derived potentials of the HA phase between 250 and 270 mV at 0.01 M electrolyte and a pH between 8 and 10. These potentials are comparable to those in Fig. 5 in general, although somewhat less negative than those for

FIG. 3. Experimental Q(pH) data and predicted Q(pH s) data according to the IS and Donnan models for PAHA. c salt : (F), solid line) 0.005 M; (h, dashed line) 0.016 M; (}, dotted line) 0.1 M.

PROTON BINDING TO HUMIC ACIDS

45

FIG. 4. Experimental Q(pH) and predicted Q(pH s) data for all the samples studied according to the IS model. The electrolyte concentration is indicated in the figure.

PAHA. Again, one might expect that probe material also underestimates the potential as with zeta potential measurements. Besides comparing the electrostatic potentials of the different humics it is also useful to compare their intrinsic properties. The first derivative of the master curve is a good approximation of the intrinsic affinity distribution (38). The calculated intrinsic affinities are shown in Fig. 6. All the distributions fall within a fairly narrow band width, suggesting that physically speaking the functional groups of the studied humics are sim-

ilar. The maxima of the distributions occurs for the humic acids in the range 3.5 to 4.5 (“carboxylic type”) and 7.5 to 8.5 (“phenolic type”). LFA has more phenolic-type groups and they are more acidic than the corresponding groups in HA. However, only one fulvic acid sample is included and it cannot be taken as general property of fulvics. In general, the differences in the distribution functions are mainly given by differences in the amount of sites within a class of pH values but not in the proton affinity range. This result compares well with the findings of Benedetti et al. (2) who observed that results

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FIG. 5. Calculated potentials at two electrolyte concentrations for the samples studied.

obtained in the laboratory for a specific HA could be used to predict the behavior in three practical situations, provided the number of carboxylic and phenolic groups was used as an adjustable parameter. CONCLUDING REMARKS

The present analysis shows that the simple impermeable sphere model is more appropriate than the simple Donnan model to unravel the intrinsic and electrostatic interactions that lead to ion binding to humics. This result is directly related to the fact that, in general, the hydrodynamic radius of the humic acid molecules is considerably smaller than the Debye length.

Previous results as obtained by De Wit et al. (6) using a similar impermeable sphere model based on a fitted particle radius compare fairly well with the present results. Therefore, when no information is available on the size of the particle, the procedure as described by De Wit et al. (6) can be used to calculate the master curve (and to obtain an estimate of the particle radius). Application of a simple Donnan model will only give results that are comparable to those obtained with the impermeable sphere model if the Donnan volumes used are larger than the specific volumes of the hydrated humics. Roughly speaking, the Donnan volume of a molecule should extend over the hydrated volume of the molecule plus the diffuse layer volume

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47

FIG. 6. Intrinsic affinity distribution function for the HA and FA studied.

(determined by k 21). The analysis of some humics presented by Benedetti et al. (7) and Kinniburgh et al. (14) is based on a Donnan model with such large volumes. Therefore, the separation of the overall affinity in an intrinsic and an electrostatic part in these studies is not largely different from the present results based on the IS model. For all the samples studied the charging behavior is similar: the charge of the humics increases gradually with increasing pH at all ionic strength values. After application of the IS model master curves and intrinsic affinity distributions are even more similar. This gives faith for the possibility of developing a generic model to describe the ion binding to humics. Such a model could be based on the IS model in combination with, for instance, the NICA model (8, 39) with average parameter values derived from the present results and adjustable capacities (total amount of carboxylic and phenolic groups). Predictions of such a model would probably be accurate within about 60.5 pH (or pM) units. For more accurate predictions the particle radius should be introduced as an adjustable parameter. ACKNOWLEDGMENTS M.J.A. thanks the Laboratory for Physical Chemistry & Colloid Science and the Department of Environmental Science, Section Soil Science and Plant Nutrition (WAU) for the first year postdoctoral fellowship and CONICET for the second one.

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