Humic Substances Considered as a Heterogeneous Donnan Gel Phase

Environ. Sci. Technol. 1996, 30, 1805-1813

Humic Substances Considered as a Heterogeneous Donnan Gel Phase M . F . B E N E D E T T I , * ,† W . H . V A N R I E M S D I J K , * ,‡ A N D L. K. KOOPAL§ Department of Soil Science and Plant Nutrition and Department of Physical and Colloid Chemistry, Wageningen Agricultural University, Dreijenplein 10, 6703 HB Wageningen, The Netherlands

A Donnan model in combination with a site-binding model is applied to interpret proton binding to humic substances as a function of pH at different salt levels. The Donnan model accounts for the salt effect on the charging behavior; it can only be successfully applied if it is assumed that the specific volume of humic substances is strongly dependent on the ionic strength. Empirical relationships have been derived that relate the volume of the Donnan phase with the ionic strength. For fulvic acid, the Donnan approach is physically not very realistic. The approach presumably mimics the behavior of the diffuse double layer around the relatively small fulvic acid molecules. For humic acids, however, the approach is physically realistic. The Donnan approach is a relatively simple and numerically efficient technique to account for the effects of ionic strength on the charging behavior. The ionic composition of the gel phase follows directly from the technique. The insight obtained on the swelling behavior of the humic acids may be of use for interpreting binding of organic pollutants in natural systems.

Introduction Natural organic matter (NOM) plays an important role in the binding and fate of inorganic as well as organic compounds in the natural environment. NOM may control the metal ion concentrations in soils and natural waters and therefore affect the mobility of metal ions through soils and aquifers (1, 2). NOM is also one of the primary adsorbents for synthetic organic compounds in the environment (3-6). Results of these studies suggest that the binding of organic pollutants by natural organic matter depends on the chemical and structural characteristics of * Corresponding authors e-mail addresses: [email protected]. jussieu.fr; [email protected]; fax: 31-83-708-37-66. † On leave from CEREGE URA CNRS 132, BP80 13545 Aix en Provence, Cedex, France. ‡ Department of Soil Science and Plant Nutrition. § Department of Physical and Colloid Chemistry.

S0013-936X(95)00012-5 CCC: $12.00

 1996 American Chemical Society

the NOM and may depend on the aqueous chemistry of the systems. For instance, soil-water partitioning coefficients may be influenced by entrapment in structural voids of the NOM (7) or in micelle-like microdomains (8). The most studied and most reactive fractions of organic matter are the humic (HA) and fulvic (FA) acids. These substances are polydisperse mixtures of natural organic electrolytes that have different functional groups. The aqueous chemistry of the humic substances will control the polarity and the conformation of humic substances. Intramolecular interactions in humic substances and intermolecular interactions between humic substances will change their physical properties (9). Those interactions depend on pH, salt concentration, and type of ions in solution. The few studies made on the effect of such parameters on binding of organic pollutants to humic substances show that the binding may depend on pH and salt level (3, 7, 10). The binding generally decreases with decreasing pH and increasing salt concentration (3, 7). Binding studies of metal ions to humic substances are numerous (2, 11-13), and the binding is dependent on pH and salt levels. For the quantification of interactions, models are needed that account for the effects of pH and salt concentration on the behavior of humic substances. Several attempts have been made to model electrostatic interactions. Tipping and Hurley (12) used an empirical equation to relate charge and potential. Marinsky and Ephraim (14) employ a Donnan potential term. Cabaniss and Morel’s criticism of Marinsky and co-workers was that the graphical tests used by these authors are not mathematically correct and therefore not useful for distinguishing Donnan behavior from other possible electrostatic descriptions. Later, de Wit et al. (16, 17), Bartschart et al. (18), Barack and Chen (19), and Milne et al. (20) compute the electrostatic potential with the Poisson-Boltzmann equation, assuming a given geometry (e.g., spherical or cylindrical) for the shape of the fulvic acid or the humic acid particles. However, this approach is not fully satisfactory for humic acids. Using the average “electrostatic” radius of HA particles and an estimated density, de Wit et al. (17) calculated molecular weights of several humic substances. The thus estimated molecular weights for the humic acids are rather small. For instance, de Wit et al. (17) calculated a mean molecular weight of 6920 and 1840 for humic acids PRHS-A and LFHS, respectively, while the gel chromatography measured values for these same humic acids are 30 000 and 15 000 (21), respectively. In this paper, we will develop a Donnan type model that, in principle, should be able to account for the salt effect on the protonation of various humic substances. The Donnan approach, if physically realistic, also gives structural information on the behavior of humic acid particles with respect to changes in salt concentrations and pH. This information may be useful for a better interpretation of interactions of both metal ions and organic pollutants with humic substances.

Model for Proton and Salt Binding Electrostatic Interactions: The Donnan Approach. Humic substances have a three-dimensional structure (22) that

VOL. 30, NO. 6, 1996 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

9

1805

may have similar properties as a polyelectrolyte gel (14, 23-25). It is assumed that at least both carboxylic and phenolic groups are present and that the dissociation of these groups leads to a potential either at the humic particle “surface” or inside a gel phase. The charge as a function of pH can be obtained from potentiometric proton titrations of humic material (16) at a series of salt concentrations. For a simple Donnan model, it may be assumed that at each charge the overall electroneutrality of the gel phase is entirely preserved by the penetration of salt ions in the gel phase. The electroneutrality of a negative gel in the presence of a 1:1 electrolyte (AB) is given by eq 1a (26):

Q/νD ) [AD+] + [HD+] - [BD-] - [OHD-]

(1a)

where Q is the charge of the humic substance in equiv kg-1 humic, νD is the specific volume of electrolyte in the gel phase in L kg-1 humic and [AD+], [HD+], [BD-], and [OHD-] are the concentrations of A+, H+, B-, and OH- in the gel phase in equiv L-1. Under normal conditions [AD+] and [BD-] are always much larger than [HD+] and [OHD-], and eq 1a can be simplified to

Q/νD ) [AD+] - [BD-]

(1b)

The charge Q in the gel phase leads to an electrostatic Donnan potential ψD that to a reasonable approximation is independent of the position in the gel phase. Under these conditions, the concentration of each ion i in the gel phase can be related to its concentration ci in the bulk by a Boltzmann factor:

ci,D ) ci exp(-ziFψD/RT)

(3)

For monovalent salts, it follows from eq 3 that

χD- ) 1/χD+

(4)

The combination of eqs 1b, 2, and 4 gives

Q/νD ) cs(χD+ - 1/χD+)

(5)

where cs is the salt concentration. Equation 5 can also be written as

(χD+)2 + (-Q/[νDcs])χD+ - 1 ) 0

(6)

There is only one physically realistic solution to eq 6 since χD+ can only be positive. For a given salt level and a known value of Q, the only unknown parameter to solve eq 6 for χD is νD. To obtain νD, the master curve procedure (16) can be used because the present Donnan model allows the calculation of the pH in the gel phase (pHD) according to eq 2: +

pHD ) pH - log(χD )

(7)

At different salt concentrations, different Q(pH) curves are found due to a difference in electrostatic interactions. According to our Donnan model, the electrostatic interactions are measured by χD. The salt effect should thus vanish when the Q(pH) curves at the different salt levels are replotted as a function of pHD. Plotting the results at different salt concentrations as Q(pHD) therefore allows us

1806

9

Non-Ideal Competitive Adsorption Isotherm: NICA Model. In general, humic material is strongly heterogeneous, and in order to describe proton binding to the humic material, an heterogeneous site binding model is required. Assuming that the electrostatic interactions can be accounted for by the Donnan model, we may incorporate these in the site-binding model by using the concentrations in the gel phase (see eq 2). For proton binding, this is equivalent to find a model for the master curve. In general, not only protons may bind specifically (non-Coulombic) to the humics but also other ions. To describe ion binding in general, we therefore prefer a model that takes both the heterogeneity and the competition into account. Good results have been achieved with the recently developed NICA model (13, 29). In this model, the chemical heterogeneity distribution is not necessarily of identical shape for the different absorbing ions. Apart from a general heterogeneity part that is the same for all ions, the NICA model takes ion-specific heterogeneity or non-ideality into account. The basic NICA equation is

(2)

where ψD is the Donnan potential in volts, zi is the ionic charge of i, F is Faraday’s constant (C mol-1), R is the gas constant (J mol-1 K-1), and T is the temperature (K). To simplify the notation, χi,D is introduced:

χi,D ) exp(-ziFψD/RT)

to check our Donnan model. When all curves merge into one master curve (16, 17), the Donnan model provides an appropriate way to account for the effect of salt level on the charge of the humic acid. Moreover, the master curve is “free” of electrostatic interactions, and it can be further analyzed to obtain the distribution of intrinsic proton affinity constant (27, 28). The intrinsic affinity distribution reflects the chemistry of the dissociating groups of the humic.

ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 30, NO. 6, 1996

Qi,t ) Qmax

{

(K ˜ ici,D)ni

∑

∑(K˜ c

ni p i i,D) }

i

∑

(K ˜ ici,D)ni 1 + {

(8) (K ˜ ici,D)ni}p

i

i

where Qi,t is the total amount of component i bound to the humic substance, Qmax is the total site density. K ˜ i is a median affinity constant, and ci,D is the concentration of i in the Donnan phase. The value of p (0 < p e 1) accounts for the intrinsic chemical heterogeneity of the sorbent, which is the same for all components i. The parameter ni accounts for the ion specific heterogeneity or non-ideality that is not accounted for by intrinsic heterogeneity and/or the electrostatic model (n * 1 non-ideal, n ) 1 ideal). Experimental evidence shows that there are two major types of sites in the affinity distributions for the binding of protons and/or metal ions to humic substances (carboxylic type groups and phenolic type groups) (17, 30, 31). The NICA model is extended to reflect this by introducing a bimodal intrinsic affinity distribution that transforms eq 8 to

Qi,t ) Qmax,1

{

(K ˜ i,1ci,D)ni

∑

∑(K˜

ni p i,1ci,D) }

i

+

∑

(K ˜ i,1ci,D)ni 1 + {

i

(K ˜ i,1ci,D)ni}p

i

{

(K ˜ i,2ci,D)ni

i

i,2ci,D)

ni p i,2ci,D) }

i

Qmax,2

∑(K˜

∑(K˜

ni

∑(K˜

1+{

(9) i,2ci,D)

}

ni p

i

where the subscripts 1 and 2 relate to the first and second peak of the affinity distribution. If the proton is the only cation that specifically binds to the humic, the extended

TABLE 1

Origin and Characteristic of the Humic Substances Studied name

ref

purified peat humic acid (PPHA) humic substance (PRHS-A) humic acid (HA) Suwannee River fulvic acid (SRFA) FA no. 3 (FA3) Lake Drummond fulvic acid (LDFA)

presentation kg-1(pH)

20

∆equiv

21

equiv kg-1(pH)

23 25

R(pH) R(pH)

17 18

equiv kg of C-1(pH) equiv kg of C-1(pH)

Mw 23 000 30 000 829 1500-2500

NICA (eq 9) simplifies to eq 10:

Q ) Qmax,1

{K ˜ 1[H]D}m1

{K ˜ 2[H]D}m2 + Q max,2 1 + {K ˜ 1[H]D}m1 1 + {K ˜ 2[H]D}m2 (10)

where m (m ) nHp) is a heterogeneity parameter that reflects the combined effect of the intrinsic heterogeneity (p) and the ion specific-heterogeneity (nH). Equation 10 is equivalent to the bimodal Langmuir-Freundlich isotherm (20, 29). In combination with the Donnan model, it can be used to describe proton binding to humic materials.

Data Compilation In a recent publication, de Wit et al. (17) compiled for 11 different humic substances data sets of Q(pH) measured at different salt levels. Owing to the similar behavior of the different fulvic and humic acids during protonation, only four data sets are chosen from de Wit et al. (HA, PRHS-A, SRFA, FA3) to be studied in the present approach. The data sets were selected to obtain a wide pH range and salt level range. Additionally, two recently published data sets for Lake Drummond fulvic acid (LDFA) (18) and a purified peat humic acid (PPHA) (20) are also analyzed. Those data sets were chosen because of the wider range of pH covered by the experimental data compared to previously published data sets and because of the high quality of the experimental data. The characteristics of the different humic substances are given in Table 1. In the following, the data sets are analyzed as Q (equiv kg-1) vs pH curves. The Q(pH) curves are taken as published, except for the PPHA data set. In the latter to calculate Q, the initial charge Q° was estimated from the original titration data given by Milne and coworkers (20), Q° ) 0.77.

Results Master Curves. The calculation of the specific gel volumes would be simple and straight-forward if the position of the master curve would be known a priori. It is not possible to solve this problem in a unique and rigorous way without making simplifying assumptions since both a pH change and a salt change may affect the gel volume. We have chosen to present the approach used and then to discuss the results and alternative approaches later. Preliminary calculations show that it is not possible to account for the salt effects with a Donnan approach if it is assumed that the specific gel volume is the same for all the salt levels. This indicates that swelling and shrinking are essential features of humic substances if the Donnan model

is physically realistic. Therefore, it is assumed that νD is constant for a given ionic strength, independent of pH. Using this simplifying assumption, different sets of volumes may be used to obtain a master curve for a given humic. Hence, it is not possible to obtain a unique master curve. The problem would be fully determined if the gel volumes had been determined independently. Estimations of specific gel volumes can be derived from techniques such as viscometry and small angle X-ray scattering (SAXS). The results obtained for νD will be compared later in the Discussion section with gel volumes of other humics to test the physical relevance of the obtained volumes. One humic acid (PPHA) and one fulvic acid (FA3) have been selected to obtain Donnan volumes as a function of ionic strength, because the data of PPHA and FA3 cover a relatively wide pH range. For other humic and fulvic acids, the master curve was constructed by using the same data sets at a particular ionic strength. For salt levels not covered by the reference data sets, a volume was chosen so that the curve coincides with the master curve. In general, the volumes estimated from viscometry data range from 1.56 to 4.2 L kg-1 for fulvic acids and from 1.9 to 4.6 L kg-1 for humic acids for the 0.1 and 0.01 M salt concentration, respectively, assuming a spherical shape (32). Those estimated values were used as starting values during the iterative process of the construction of the master curves for all humic substances. In this way a well-defined master curve can be obtained for the selected humic and fulvic acid. Master curves for the other humic substances were created under the assumption that the relation between gel volume and ionic strength is independent of the type of humic or fulvic acid. In other words, it is assumed that the specific gel volumes of all humic acids are the same at a given ionic strength. Both the Q(pH) and Q(pHD) curves for the humic acids are shown in Figure 1. It follows that good master curves are obtained for all humic acids. The range of salt levels covered is from 0.001 to 2 M. Figure 2 shows the results for the fulvic acids; it follows that two of the three fulvic acids have reasonable master curves. For LDFA, the shifted curves do not merge very well into a single curve. Donnan Potential. Figure 3 shows the calculated Donnan potential as a function of pH for PPHA and FA3. It can be concluded that ψD is nonlinear, non-Nerstian, and strongly dependent on the salt level. At increasing ionic strength, the screening of the charge becomes more efficient, which results in smaller electrostatic interactions and smaller ψD values. The fulvic acids experience smaller salt effects, which result in lower potentials. Aqueous Volume of the Gel Phase (νD). The specific gel volumes obtained are given in Table 2 and plotted as a function of the ionic strength in Figure 4. Different relationships between salt level and Donnan volume are obtained for humic and fulvic acids, reflecting the difference in salt effect on the charging and swelling behavior for both types of humic substances. The relatively high volumes for the fulvic acids are the consequence of a high charge (equiv kg-1) in combination with a low salt effect. Radius of Humic Particles. In general, the size of humic substances has been investigated with various techniques (see ref 33 for a review). Hydrodynamic radii or radii of gyration of the humic particles are sometimes given instead of volumes. The volume estimated with the Donnan approach can, in principle, be used to calculate radii of humic particles if their molecular weights are known. The


9

1807

FIGURE 1. Experimental Q(pH) curves and Q(pHD) curves for the Donnan model for data sets corresponding to humic acids: (×) 0.001 M; (9) 0.01 M; (() 0.02 M; (O) 0.1 M; (0) 0.2 M; (-) 0.33 M; (larger solid box) 2 M. Similar salt levels for different humic acids are represented by the same symbol. The symbols pointed to by the MC (master curve) caption represent the data points after the Donnan correction and show the degree to which the Donnan correction removes the ionic strength effect.

FIGURE 2. Experimental Q(pH) curves and Q(pHD) curves for the Donnan model for the data sets corresponding to fulvic acids: (×) 0.001 M; (9) 0.01 M; (O) 0.1 M; (+) 1 M. Similar salt levels for different fulvic acids are represented by the same symbol. The symbols pointed to by the MC (master curve) caption represent the data point after the Donnan correction and show the degree to which the Donnan correction removes the ionic strength effect. TABLE 2

Water Content in the Gel Phase (νD in L kg-1) Estimated with Master Curve Approach for Different Humic and Fulvic Acids (See Text for Details)a νD for all humic acids

I (M)

FIGURE 3. Donnan potential for a fulvic acid (FA3) and a humic acid (PPHA) as a function of pH and ionic strength: (9) 0.01 M; (O) 0.1 M; (-) 0.33 M; (+) 1 M.

total volume of a humic particle is given by

2 1 0.33 0.2 0.1 0.02 0.01 0.001 0.001

(L

kg-1)

radii (nm) PPHA

PRHS-A

0.15

1.9

2.1

0.5 0.7 0.8 1.1 1.8 5

2.1

2.3

2.3 2.5 2.8 3.7

2.5 2.7 3.0 3.9

νD for all fulvic acids νD (L

kg-1)

radii (nm) SRFA

FA3

1

0.8

1

2.5

1

1.2

1.5

2 2.9

10 30* 80**

2.9

a

(11)

* and ** correspond to SRFA and LDFA, respectively. Radii of selected humic and fulvic acids particles calculated from the aqueous volume of the humic substance using eq 19. Mw used for the calculation are from Table 1. Densities: for humic acids FHs ) 1.66 kg L-1 and for fulvic acids FHs ) 2.17 kg L-1

where Vw (L) is the aqueous volume of the humic particle and VHS (L) is the volume of the humic material without water. The specific volume calculated with the Donnan approach νD (L kg-1) is defined as

bulk density of the humic substance (kg L-1) is given by

Vp ) Vw + VHS

νD ) Vw/mHS

(12)

where mHS is the mass of the humic particle (kg). The dry

1808

9


FHS ) mHS/VHS

(13)

By combining eqs 12 and 13, we obtain

FHSνD ) Vw/VHS

(14)

TABLE 3

Assessed Intrinsic Parameters Describing Q(pHD)a name

log K˜ H

m

Qmax (equiv kg-1)

PPHA carboxylic PPHA phenolic HA PRHS-A FA3 carboxylic FA3 phenolic SRFA LDFA

2.99 8.62 3.35 3.19 2.52 9.5 2.56 2.70

0.46 0.32 0.47 0.4 0.39 0.39 0.44 0.38

2.76 3.33 3.61 3.78 5.65 2.17 5.53 5.12

a

Data obtained by coupling the NICA model and the Donnan model.

obtained. As a measure of the goodness of fit, two parameters are used, the correlation coefficient r2: jk

∑(x - xˆ )

2

i

FIGURE 4. Relationship between the estimated aqueous volume of the humic substances and the ionic strength. HA, humic acid; FA, fulvic acid; I, ionic strength. Line 1 corresponds to the empirical law: vD ) 0.24I-0.43 derived for humic acids; line 2 corresponds to empirical law: vD ) 0.46I-0.67 derived for fulvic acids.

Equation 14 can be combined with eq 11 to give

Vp ) Vw[1 + 1/(FHSνD)]

r2 ) 1 -

(15)

The combination of eqs 12, 15, and 16 gives

Vp ) mHS(1 + FHSνD)/FHS

(17)

The mass of a particle of humic substance is given by

mHS ) Mw/Na

(18)

where Mw is an average molecular weight and Na is Avogadro’s number (mol-1). If as a first approximation, we assume that the humic gel is sphere-like, the combination of eq 17, eq 18, and the volume of a sphere gives

x

r)3

3Mw (1 + FHSνD) 4FHSNaπ

(19)

where r is the radius of the humic particle. The radii were calculated for the humic substances with known values of Mw (Table 1). Dry bulk density ranges from 1.4 to 2 kg L-1 (34, 35). The calculations were made with median values of 1.66 and 2.17 kg L-1 for HA and FA, respectively, and the radii are given in Table 2. The results show that the Donnan radius of the humic acid particles almost doubles going from 2 M to 0.001 M. The radius of the fulvic acids is smaller than that of the humic acids due to the lower molecular weight of the fulvic acids. Description of Q(pHD) and Q(pH) curves. Master Curve Description. Table 3 gives the parameters for the description of the Q(pHD) curves. For samples PPHA and FA3 titrated over a large pH range, the bimodal distribution is used resulting in six parameters. For the other data sets, eq 10 is reduced to a single distribution and only three parameters are required to describe the master curve. For all data sets, a very good description of the Q(pHD) master curve is

2

i

i)1

and the RMSE:

(16)

njk

∑(x - xˆ)

( ) jk

∑

The total specific volume of the particle of humic substance (νtm) is given by

νtm ) Vp/mHS ) (Vp/Vw)(Vw/mHS)

i

i)1

RMSE )

0.5

(xi - xˆi)2

i)1

jk - l

where xi is the measured value for data point i, xˆi is its fitted value, jk is the number of data points; l is the number of parameters; xˆ is the average value of measured data points. The values of r2 are in the range of 0.973-0.999, and RMSE ranges from 0.06 to 0.2. The log K ˜ H values of the first peak range from 2.52 to 3.19 and can be assigned to carboxylic moieties (13, 36). For PPHA and FA3, the observed log K ˜ H values for the second peak are 7.95 and 9.5, respectively, and they can be assigned to more weakly acid groups such as phenol, alcohol, and enol (13, 36). The parameter m reflects the apparent heterogeneity of the humic substance (29). The values of m are in all cases smaller than one, indicating that the humic substances are chemically heterogeneous. Fulvic acids have more reactive sites per mass of substance (Qmax1,FA > Qmax1,HA) than humic acids. The distribution among the two types of sites (carboxylic versus phenolic) agrees with literature data (2, 34). Carboxylic sites are the most abundant in fulvic acids while for the humic acids the proportion of both types of sites is similar (2, 34). The PPHA has slightly more phenolic type of sites than carboxylic type of sites. Binding Isotherms. The Donnan model and the NICA model can be combined to describe experimental Q(pH) curves. Results are illustrated in Figure 5 for two examples, one a humic acid (PRHS-A) the other a fulvic acid (FA3). The curves for both sets give an excellent description of the experimental data sets. Similar results (not given here) are obtained for the other humic substances.

Discussion The good merging of the curves corresponding to different salt levels into one master curve for the various data sets analyzed supports the Donnan approach. However, a critical assumption is made to obtain these master curves.


9

1809

FIGURE 5. Calculated Q(pH) curves for a fulvic acid and a humic acid based on the combination of the NICA model and the Donnan approach compared to the experimental Q(pH) data: (×) 0.001 M; (9) 0.01 M; (O) 0.1 M; (+) 1 M.

The volume of the Donnan phase has been assumed to change with salt level and not with charge. In the following we will discuss this assumption and a few alternative approaches and test the physical reality of the results obtained by comparing the results with independent information on size, shape, and volume. Effect of Salt versus Effect of pH. In the simplified Donnan approach, several hypotheses can be made for the changes of the volume of the aqueous gel phase with salt concentrations and pH. The simplest assumption is that the volume is independent of charge and salt level (37). This kind of approach cannot be applied to humic substances since the master curve cannot be constructed in this case. Moreover, this assumption is not realistic since numerous studies show that the humic substances can shrink and swell (9) as a function of salt. A Donnan approach for humic substances was previously used by Marinsky and co-workers (14, 23, 38, 39). Marinsky et al. assumed the volume to be independent of the salt concentration but dependent on particle charge. This approach is claimed to be successful for a synthetic gel and fulvic acids (14). However, a discrepancy was observed between data and model when applied to humic acids (26). An incorrect assessment of the gel phase volume could be the major factor responsible for the discrepancy (26). Experimental evidence (32, 40) shows that the intrinsic viscosity of humic substances is more sensitive to changes in salt level than to changes in pH. This result was shown for both humic and fulvic acids. Similarly, Reuter (41) used a combination of viscometry and gel permeation chromatography to demonstrate that the size of dissolved humic substances is reduced with increased salt content of the water. More recently, Plette et al. (42) showed, with a similar Donnan approach for bacterial cell walls, that the volume is primarily affected by the salt level. All these findings support the assumption that the Donnan volume of humic substances is more sensitive to changes in salt than in pH. It is nevertheless of course possible to construct a master curve assuming that the volume is affected by both salt level and particle charge. One relatively attractive option that we have explored in this respect (not shown here) is based on the observation that the charging curves at different salt levels are often quite similar in shape. This might suggest that the potential is primarily dependent on salt level and hardly on the pH. This situation arises when it is assumed that the molar concentration of charged sites in the gel phase (Q/νD) is constant at a given salt level. It follows from eq 6 that this leads to a potential that is independent of the pH at a given ionic strength. This

1810

9


situation leads to a shape of the charging curve that is independent of the salt level. One can always construct a master curve with this assumption if the shapes of the different charging curves are indeed highly similar. The potential at a given salt level and thus the shift factor (eq 7) depend on the assumed molar concentration for a particular salt level. In this case, one can construct the master curve with additional assumptions and test the physical reality by comparing the results with independent measurements on gel volume and size of the humic molecules. This approach does not lead to satisfactory results when it is used for the description of metal ion binding to humic acids. We previously stated that within a certain range, different sets of volumes may be used to obtain a master curve. For instance, for humic acids a different combination of volumes assuming that νD ) 2.5 L kg-1 at I ) 0.01 M will result in a shift of the master curve of 0.2 on the pH axis toward the uncorrected data points in a Q(pH/pHD) graph. This small uncertainty in the position of the master curve is comparable to the difference in position that results from assuming either a cylindrical or a spherical double layer model for humic acids (17). This uncertainty will hardly affect the values of the intrinsic parameters that are derived from the master curve. Volumes of the Fulvic Acids. For FA, the merging of the different curves into one master curve is not perfect, especially for samples LDFA and SRFA (Figure 2). Such a result could imply that a Donnan approach is not realistic for the FA. Cabaniss and Morel (15) previously suggested that the Donnan approach used by Marinsky and coworkers (14, 24, 25) is not the appropriate model for FA. The lack of merging for the FA could be due to a wrong estimation of the volume from the first data set (FA3). An alternative approach to obtain the master curve is to assume as a first approximation that the curve at the highest salt level is free of electrostatic interactions (i.e., 1 M ) master curve). This assumption is derived from the observation that the electrostatic potential is the lowest at the highest salt level (16-19). The highest salt level is 1 M for the data set FA3. The volumes obtained for 0.1 and 0.01 M salts for FA3 are then 20 and 40 L kg-1, if the 1 M curve is assumed to be the master curve. The quality of the master curve did not improve under this assumption. Moreover, as we will see later, these volumes are not in accord with independent estimates. Ghosh and Schnitzer (32) report for FA intrinsic viscosities equal to 5.4 L kg-1 and 12 L kg-1 for I ) 0.1 M and I ) 0.01 M, respectively. Visser (43) reports smaller values of 0.7-2.3 L kg-1 for aquatic FA in a 0.1 M NaCl also measured by viscometry. The intrinsic viscosity for nearly spherical particles can be written as (44)

[η] ) ζ(ν2 + ν1δ1)

(20)

where ζ is a shape factor equal to 2.5 for a sphere and >2.5 for asymmetric particles. ν2 and ν1 (in L kg-1) are the partial specific volume of the solute (i.e., humic substance) and the solvent (i.e., water + salt), respectively, and are equivalent to the reciprocal of the density (i.e., ν2 ) 1/F2, ν1 ) 1/F1), and δ1 is the degree of hydration (i.e., effective solvation) (in kg kg-1) and νD ) ν1δ1. Therefore, assuming a constant shape factor for a sphere-like fulvic acid particle and regardless of the absolute levels, the changes in νD with salt level should be proportional to the changes in [η]

according to

∆[η] ) ζ∆νD

(21)

From literature data (32), ∆[η] ) 6.9 L kg-1 for fulvic acids for salt concentrations ranging from 0.01 to 0.1 M. However, eq 21 results in ∆[η] ) 50 L kg-1 for the same salt level (using ζ ) 2.5 and δ1 ) 1 kg kg-1) when calculated from the changes in Donnan volumes (∆νD ) 20 and 40 L kg-1). Also, the large variation in volume that follows from the Donnan approach (from 0.5 to 80 L kg-1) is not in agreement with the generally proposed structure of FA. Langford et al. (45) depicted the FA as a relatively small molecule (800) with a limited number of side chains. This structural model implies that the FA molecule can only swell and shrink to a limited extent. The volumes estimated with the Donnan approach may therefore have a different meaning than the one implied by the Donnan theory. The Donnan model can be seen to mimic the salt effect as it results from essentially a diffuse double layer (46). Volumes of the Humic Acids. For humic acids, it is also possible to use the curve at the highest salt concentration as an approximation of the master curve. The highest salt concentration for the humic acids is the 2 M experiment (HA in Figure 1). If this curve is the master curve, then the estimated volumes are equal to 10 and 6.5 L kg-1 for the 0.2 and 0.02 M salt concentration, respectively. This result is physically not realistic since the highest salt level has the highest volume. This leads to the conclusion that the 2 M curve is not a good approximation of the master curve. For the highest salt concentration, the aqueous volume can be seen as the amount of water associated with the counterions permeating into the humic acid gel to compensate the charge. The molar volume of hydrated sodium ion is 0.135 L mol-1 Na+ in combination with an average charge density of 1.8 equiv kg-1 leads to an estimated minimum water content of 0.23 L kg-1. This volume is close to the volume used for the 2 M salt concentration (0.15 L kg-1). The obtained volumes can also be compared with results from viscometric measurements. A complicating factor in such a comparison is the unknown shape factor ζ in eq 20. Assuming that the obtained volumes are physically realistic, one can calculate the shape factor from viscometric data published in the literature. Ghosh and Schnitzer (32) report intrinsic viscosities for a humic acid equal to 7.32, 14.08, and 20 L kg-1 for 0.1, 0.01, and 0.001 M, respectively. The Donnan volumes combined with the data of Ghosh and Schnitzer (32) with ν2 ) 0.6 L kg-1 (35) for humic acid and assuming δ1 ) 1 kg kg-1 lead to shape factors of 5.2, 5.9, and 3.6 for 0.1, 0.01, and 0.001 M, respectively. The results suggest that the humic particles are oblong particles. The more spherical shape at the low salt may be an artifact. If the salt level of the titration experiment would have been 0.002 instead of 0.001, a value of 3.4 L g-1 follows from the linear regression line of Figure 3, resulting in a shape factor of 5. The shape factor values may vary with a different combination of Donnan volumes. However, VD values have a limited uncertainty range, for instance, at 0.01 M salt level it is estimated to range from 1.8 to 2.5 L kg-1. The resulting uncertainty in the shape factors is small, ζ ) 5.3 ( 0.7, and points toward one type of geometry for the humic acid particles. The results therefore in our opinion indicate that the shape is probably not strongly dependent on the

salt level and the Donnan volumes are in agreement with the viscometric data. The calculated radii can also be compared to radii that are obtained by light scattering techniques. The radius of gyration that is obtained with these techniques should be multiplied with a factor between 0.66 and 0.855 to obtain the hydrodynamic radius (44). Wershaw (47) reports radii ranging from 2.4 to 9 nm. Thurman et al. (48) for humic acids give radii ranging from 0.5 to 2.2 nm. The radii calculated with the Donnan approach (Table 2) fall within the range that follows from the reported measurements. For instance, Cameron et al. (49) report a hydrodynamic radius equal to 2.8 nm in a 0.07 M salt for a humic acid with a Mw similar to that of PPHA. According to the regression line in Figure 4, this humic would have a radius of 2.4 nm. This value is within the error range of the radius reported by Cameron et al. (49) and the uncertainty associated with the regression line. Structural Implications. Based on viscosity measurements, Ghosh and Schnitzer (32) proposed that the humic molecules are flexible linear colloids that can assume a random coiled conformation with changes in humic material concentration, pH, and salt level. However, to have an agreement between the hydration volume derived from the protonation experiments and the viscosity measurements, it is necessary to assume that the shape of the humic acids is approximately independent of the salt level. The attractiveness of the swelling gel model with an approximately constant shape over the random coil model is that it is in accord with both viscosity measurements and protonation data. This gel model for humic acids may also be in agreement with a likely structure of humic acids. The humic acids are formed by polymerization of different smaller molecules (33, 34). This polymerization will probably not occur along one axis only. Thus, a sheet-like structure will be formed as observed by electron microscopy (22). Due to cross-linking and intramolecular interactions, a gel phase seems more likely than a fully flexible linear polyelectrolyte. Inside this 3D structure, charge will be distributed and ions will permeate from the outer solution. In some areas of the humic acid molecule where cross-linking may be important, hydrophobic areas may exist that can strongly interact with organic pollutants. In a recent study on the binding of polycyclic aromatic hydrocarbon (PAH) by dissolved humic material, Schaultman and Morgan (7) showed that the binding of PAH decreased with increasing salt for humic acids while the effect of salt on the binding to fulvic acids was much smaller. Moreover, they show that the partition coefficient of the PAH was 2-3 times smaller for fulvic acids as compared to humic acids. These results support the Donnan model proposed for humic acids and the conclusion that fulvic acids have a different physical structure. In the Donnan model, the decrease in volume with increasing salt will induce a decrease in the size of the voids in humic acids into which organic compounds may penetrate. A pseudomicellar structure for humic acids (47) could also explain the changes in volume predicted by the Donnan approach. However, according to Schlautman and Morgan (7), a pseudomicellar structure implies that partition coefficients for hydrophobic organic compounds increase with salt concentrations; this behavior is in conflict with their measurements. The relatively small size, the lack of voids, and the relatively high charge density of the fulvic acid structure can explain the relatively small binding


9

1811

of organic pollutants in these molecules. Also the small salt effect on binding of hydrophobic chemicals is based on the structural concept for fulvic acids presented here. Heterogeneous Binding Models. There is overwhelming evidence that the proton and metal ion binding to humic substances over a wide range of conditions can only be described if one takes chemical heterogeneity into account (2, 11-13, 16, 17, 31). The results of the heterogeneity analysis are dependent on whether or not electrostatic interactions are accounted for separately in the model approach. The division of the total affinity into an electrostatic part and an “intrinsic” part can only be done once a particular electrostatic model has been chosen to account for the electrostatic effects. The results obtained for the intrinsic heterogeneity depend to some extent on the choice of one of the various options that exist to account for the electrostatic effects. This shows that the separation of the electrostatics and chemistry is not entirely unique. The use of an explicit electrostatic model has the advantage that one can discriminate between ions specifically bound to reactive groups and diffusely bound ions to compensate the negative charge of the humic substances. This may be especially important if one is interested in the binding behavior of macro ions in natural systems (Na, K, Ca). Another reason to combine an intrinsic heterogeneous binding model with an electrostatic model is the possibility for interpretation of changes of ionic strength on metal ion binding. The intrinsic average affinity constant of the first peak is for the various humic acids relatively constant (≈3.25 ( 0.05). The same applies for fulvic acids that have a lower average affinity constant than the humic acids (≈2.65 ( 0.05). The heterogeneity parameter m is also quite similar for all fulvic acids (≈0.41 ( 0.03). The value of m for the humic acids are also similar (≈0.44 ( 0.04). These results suggest that differences in gel volume and intrinsic binding properties between different humic acids are not very large. The same applies to different fulvic acids. This finding is of importance if one wants to apply model results obtained from laboratory studies to field situations.

Conclusion The good merging of the curves corresponding to different salt levels into one master curve for various data sets analyzed supports the Donnan approach developed here. For fulvic acid the Donnan model is physically not very realistic because the changes in Donnan volumes as a function of salt are too large probably. The Donnan volume is mimicking the salt effect as it results from essentially a diffuse double layer. However, the Donnan model can be used as an empirical model to describe the salt effect on the charging behavior. The advantage of the use of a Donnan approach is its mathematical simplicity once the relationship between volume and ionic strength has been established. For humic acids, the Donnan approach seems physically realistic. Good master curves are obtained, and the Donnan volumes are not in conflict with independent viscometric data. The results suggest that the humic particles are oblong particles and that the specific volumes of the humic acids are more dependent on the ionic strength than on pH. The results suggest that differences in gel volume and intrinsic binding properties between different humic acids are not very large. The same applies to different fulvic acids. This finding is of importance if one wants to apply model results

1812

9


obtained from laboratory studies to field situations. The insight obtained on the swelling behavior of the humic acids may also be of use for interpreting binding of organic pollutants in natural systems.

Acknowledgments This work was partly funded by the European Union STEPCT90-0031 and the DGSRD of the European Union, via Program Environment, Contract EV5V-CT94-0536.

Literature Cited (1) Sposito, G. CRC Crit. Rew. Environ. Control 1986, 16, 193-229. (2) Buffle, J. Complexation reactions in aquatic systems; Ellis Horwood Limited: Chichester, 1988; p 692. (3) Carter, C. W.; Suffet, I. H. Environ. Sci. Technol. 1982, 16, 735740. (4) Gauthier, T. D.; Seitz, W. R.; Grant, C. L. Environ. Sci. Technol. 1987, 21, 243-248. (5) Gauthier, T. D.; Shane, E. C.; Guerin, W. F.; Seitz, W. R.; Grant, C. L. Environ. Sci. Technol. 1986, 20, 1162-1166. (6) Senesi, N. In Migration and fate of pollutants in soils and subsoils; Petruzzelli, D., Helfferich, F. G., Eds.; Springer-Verlag: Berlin, 1993; pp 47-74. (7) Schlautman, M. A.; Morgan, J. J. Environ. Sci. Technol. 1993, 27, 961-969. (8) Engebretson, R. R.; von Wandruszka, R. Environ. Sci. Technol. 1994, 28, 1934-1941. (9) Hayes, M. H. B.; MacCarthy, P.; Malcolm, R. L.; Swift, R. S. Humic Substances II: In search of structure; Hayes, M. H. B., MacCarthy, P., Malcolm, R. L., Swift, R. S., Eds.; Wiley & Sons: Chichester, 1989; p 764. (10) Traina, S. J.; Spontak, D. A.; Logan, T. J. J. Environ. Qual. 1989, 18, 221-227. (11) Cabaniss, S. E. Environ. Sci. Technol. 1992, 26, 1133-1139. (12) Tipping, E.; Hurley, M. A. Geochim. Cosmochim. Acta 1992, 56, 3627-3641. (13) Benedetti, M. F.; Milne, C. J.; Kinniburgh, D. G.; Van Riemsdijk, W. H.; Koopal, L. K. Environ. Sci. Technol. 1995, 29, 446-457. (14) Marinsky, J. A.; Ephraim, J. Environ. Sci. Technol. 1986, 20, 349354. (15) Cabaniss, S. E.; Morel, F. M. M. Environ. Sci. Technol. 1989, 23, 746-747. (16) De Wit, J. C. M.; Van Riemsdijk, W. H.; Nederlof, L. K.; Kinniburgh, D. G.; Koopal, L. K. Anal. Chim. Acta 1990, 232, 189-207. (17) De Wit, J. C. M.; van Riemsdijk, W. H.; Koopal, L. K. Environ. Sci. Technol. 1993, 27, 2005-2014. (18) Bartschat, B. M.; Cabaniss, S. E.; Morel, F. M. M. Environ. Sci. Technol. 1992, 26, 284-294. (19) Barak, P.; Chen, Y. Soil Sci. 1992, 154, 184-195. (20) Milne, C. J.; Kinniburgh, D. G.; de Wit, J. C. M.; Van Riemsdijk, W. H.; Koopal, L. K. Geochim. Cosmochim. Acta 1995, 59 (6), 1101-1112. (21) Tipping, E.; Backes, C. A.; Hurley, M. A. Water Res. 1988, 22, 597-611. (22) Chen, Y.; Schnitzer, M. In Humic Substances II: In search of structure; Hayes, M. H. B., MacCarthy, P., Malcolm, R. L., Swift, R. S., Eds.; Wiley & Sons: Chichester, 1989; pp 621-638. (23) Marinsky, J. A.; Gupta, S.; Schindler, P. J. Colloid Interface Sci. 1982, 89, 401-411. (24) Ephraim, J.; Marinsky, J. A. Environ. Sci. Technol. 1986, 20, 367376. (25) Ephraim, J.; Alegret, S.; Mathuthu, A.; Bicking, M.; Malcolm, R. L.; Marinsky, J. A. Environ. Sci. Technol. 1986, 20, 353-366. (26) Marinsky, J. A.; Wolf, A.; Bunzl, K. Talanta 1980, 27, 461-468. (27) Nederlof, M. M. Ph.D. Thesis, Wageningen Agricultural University, 1992. (28) Nederlof, M. M.; Van Riemsdijk, W. H.; Koopal, L. K. Environ. Sci. Technol. 1992, 26, 763-771. (29) Koopal, L. K.; van Riemsdijk, W. H.; de Wit, J. C. M.; Benedetti, M. F. J. Colloid Interface Sci. 1994, 166, 51-60. (30) Perdue, E. M.; Reuter, J. H.; Parrish, R. S. Geochim. Cosmochim. Acta 1984, 48, 1257-1263. (31) De Wit, J. C. M.; van Riemsdijk, W. H.; Koopal, L. K. Environ. Sci. Techol. 1993, 27, 2015-2022. (32) Ghosh, K.; Schnitzer, M. Soil Sci. 1980, 129, 266-276. (33) Hayes, M. H. B.; MacCarthy, P.; Malcolm, R. L.; Swift, R. S. In Humic Substances II: In search of structure; Hayes, M. H. B., MacCarthy, P., Malcolm, R. L., Swift, R. S., Eds.; Wiley & Sons: Chichester, 1989; pp 690-733.

(34) Stevenson, F. J. In Humic substances in soil, sediment and water; Aiken, G. R., Mcknight, D. M., Wershaw, R. L., MacCarthy, P., Eds.; Wiley & Sons: New York, 1985; pp 13-52. (35) Reid, P. M.; Wilkinson, A. E.; Tipping, E.; Jones, M. N. Geochim. Cosmochim. Acta 1990, 54, 131-138. (36) Perdue, E. M. In Humic substances in soil, sediment and water; Aiken, G. R., McKnight, D. M., Wershaw, R. L., MacCarthy, P., Eds.; Wiley & Sons: New York, 1985; pp 493-527. (37) Alegret, S.; Escalas, M.-T.; Marinsky, J. A. Talanta 1984, 31, 683687. (38) Marinsky, J. A.; Gupta, S.; Schindler, P. J. Colloid Interface Sci. 1982, 89, 421-426. (39) Marinsky, J. A. J. Phys. Chem. 1985, 89, 5294-5302. (40) Chen, Y.; Schnitzer, M. Soil Sci. Soc. Am. J. 1976, 40, 866-872. (41) Reuter, J. H. Abs. Geol. Soc. Am. Annu. Mtg. 1977, 1140. (42) Plette, A. C. C.; Van Riemsdijk, W. H.; Benedetti, M. F.; Van der Wal, A. J. Colloid Interface Sci. 1995, 173, 354-363. (43) Visser, S. A. Plant Soil 1985, 87, 209-221. (44) Tanford, C. Physical chemistry of macromolecules; Wiley & Sons: New York, 1961; p 710.

(45) Langford, C. H.; Gamble, D. S.; Underdown, A. W.; Lee, S. In Aquatic and terrestrial humic materials; Chsistman, R. F., Gjessing, E. T., Eds.; Ann Arbor Science: Ann Arbor, 1983; pp 219-237. (46) Davies, J. T.; Rideal, E. K. In Interfacial Phenomena; Academic Press: New York, 1963; Chapter 2. (47) Wershaw, R. L. In Humic Substances II: In search of structure; Hayes, M. H. B., MacCarthy, P., Malcolm, R. L., Swift, R. S., Eds.; Wiley & Sons: Chichester, 1989; pp 545-559. (48) Thurman, E. M.; Wershaw, R. L.; Malcolm, R. L.; Pinckney, D. J. Org. Geochem. 1982, 4, 27-35. (49) Cameron, R. S.; Thornton, B. K.; Swift, R. S.; Posner, A. M. J. Soil Sci. 1972, 23, 394-408.

Received for review January 10, 1995. Revised manuscript received June 7, 1995. Accepted February 1, 1996.X ES950012Y X

Abstract published in Advance ACS Abstracts, April 15, 1996.


9

1813

Humic Substances Considered as a Heterogeneous Donnan Gel Phase

Recommend Documents