Environ. Sci. Technol. 2001, 35, 2727-2733
Modeling Competitive Cation Exchange of Aromatic Amines in Water-Saturated Soils J O S EÄ R . F AÄ B R E G A , † C H A D T . J A F V E R T , * , † HUI LI,‡ AND LINDA S. LEE‡ School of Civil Engineering and Department of Agronomy, Purdue University, West Lafayette, Indiana 47907
Competitive association to several components of soil through ion exchange processes influences the fate of organic cations in the environment. To examine these processes, the distributions of aniline and 1-aminonaphthalene between aqueous 5 mM CaCl2 solutions and three different Indiana soils were evaluated. Solute ratios (Sr) of aniline to 1-aminonaphthalene of 0.4-4.7 were employed, and the soil solutions ranged in pH from 2.7 to 7.5, with all measurements made 24 h after the introduction of the chemicals to the soils. Two previously proposed equilibrium modelssthe two-site (TS) and distributed parameter (DP) modelsswere modified to predict competition. These models assume instantaneous equilibrium of the following reversible processes: (i) acid dissociation of the protonated organic base (BH+ aq) in the aqueous phase; (ii) ion exchange on the soil between the protonated organic base and 2+ 2+ inorganic divalent cations (D2+ aq ) Caaq + Mgaq ); and (iii) partitioning of the nonionic species of aniline (Baq) to soil organic carbon. The TS model is a general mass action model that does not take into consideration cation exchange site heterogeneity, whereas the DP model considers association constants to these sites to be distributed in a log-normal fashion. To describe competition for cation exchange sites within the DP model, it was necessary to add a correlation coefficient (F) that relates the ion-exchange association constant (KBH) probability density distribution functions of the two compounds. The value of F is characteristic of each soil. Results indicate that competition has a greater effect at low pH values, where ion exchange is the predominant process. For all cases, these models capture the general trends in the soilwater distribution data of both amines. The DP model also captures the nonlinearity of the 1-aminonaphthalene isotherms at low pH while at the same time capturing the nearly linear isotherms of aniline as a competing organic base.
Introduction Because aromatic amines are often present in the environment as mixtures, the potential exists for there to be some competition with respect to some physical and chemical fate processes. For example, ion exchange is an environmental process in which competition for sites has the potential to * Corresponding author phone: (765) 494-2196; fax: (765) 4961107; e-mail:
[email protected]. † School of Civil Engineering. ‡ Department of Agronomy. 10.1021/es001654a CCC: $20.00 Published on Web 06/01/2001
2001 American Chemical Society
influence chemical fate in the environment (1-8). Competitive cation exchange has been studied for partially ionized nitrogen heterocyclic compounds (1, 2) and organic cations such as methylcridinium ion in the presence of competing inorganic cations (7). Adsorption of ionizable compounds to activated carbon has also been studied (8). Despite these and other publications (3-6), few if any studies have attempted to model competitive cation exchange of protonated amine cations to soils when competing adsorption of the neutral conjugate base occurs also. In a previous paper (9), we reported on and modeled the cation exchange of individual organic species with calcium and magnesium ions on soils with different solution pH values and organic carbon contents under conditions in which sorption of the nonionic species also occurs and must be considered. We showed that for the five midwestern U.S. soils examined, excellent agreement between the experimental sorption isotherms and model predictions resulted when applying the same solute dependent Koc and cationexchange constant over all of the soils. Hence, measurable soil properties from which distribution can be estimated are the soil organic carbon content, the (pH-dependent) cationexchange capacity, the solution pH, and the total concentration of inorganic divalent cations (Ca2+ plus Mg2+) in the soil. In the previous paper (9), two models were presented to describe the short-term soil-water phase distribution of aromatic amines: a discrete two-site (TS) model and a distributed parameter (DP) model. These models consider the following processes as those responsible for the speciation and sorption of aromatic amines in soils: (i) acid dissociation of the protonated base (BH+ aq) in the aqueous phase, (ii) mass transfer of the neutral species (Baq) to soil organic carbon, and (iii) cation exchange of BH+ aq with inorganic 2+ cations (Ca2+ aq and Mgaq ) on the soil. The TS model is a general mass action model that accounts for cation exchange with a single exchange coefficient, KBH, for each organic base, whereas the DP model employs a Gaussian distribution on log KBH values, with mode µ and standard deviation σ. Hence, the latter model is better able to predict the nonlinearity of sorption isotherms that result from the heterogeneity of cation-exchange sites. In soils at low pH where the organic cation is the prevalent amine species, ion exchange is the dominant phase transfer process (9, 10). In high-pH soils, mass distribution occurs mostly through the neutral species, B, and is a function of chemical hydrophobicity (9, 11-14). Between these two reversible processes, in natural soils, ion exchange generally is of greater magnitude for typical organic bases, resulting in greater loss of chemical to the soil with decreasing pH (9, 15). Our intent in this study is to invoke within these two mass action models (9) any equations and/or terms necessary to account for multicomponent cation exchange to soil. Modification of the TS model to predict mass transfer in multicomponent mixtures of bases is trivial as the addition of each additional base simply adds a pair of analogous mass action and mass balance equations to the model. Modification of the DP model is more complicated, as it is not necessary, for example, for the high-affinity exchange sites within the Gaussian distribution of exchange sites for one amine to display high affinity for all amines. For these compounds, size, hydrophobicity, and other factors may affect affinity for specific sites. In the application of the DP model, a unique set of log KBH,i values for each amine, i, is obtained by partitioning the Gaussian distribution of exchange sites into discrete groups. In practice, sites are VOL. 35, NO. 13, 2001 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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TABLE 1. Mathematical Expressions for the CTS Modela
taneous equations that are conveniently solved by the Newton-Raphson iterative method (19): 1 1
[B]T ) 1[BH+]aq +
{
1
Ka 1[BH+]aq +
+
[H ]aq
Kocfoc 1Ka 1[BH+]aq +
+
[H ]aq
m ‚ v
(
[D]T 2 1 1 K [BH+]aq m/v G [D2+]0.5 aq [D2+]0.5 aq
2 2
[B]T ) 2[BH+]aq +
{
2
Ka 2[BH+]aq +
[H ]aq
Kocfoc 2Ka 2[BH+]aq +
[H ]aq
+
+
m ‚ v
(
partitioned into 600 groups of equal number with the total number of sites set equal to the cation-exchange capacity (CEC). Competition within the 600 groups of sites can be accounted for by correlating KBH,i values of one amine with those values of the other amine. The bivariate normal density function (16) is employed to make this correlation. In this study we interpret trends in the data by invoking within the models the minimum complexity necessary to account for the phenomenological trends observed over changes in pH, soil, and organic amine concentrations. Data are presented that span the range of phenomenological complexity as interpreted by the modelssfrom conditions where primarily noncompetitive partitioning of neutral amines occurs to conditions where competitive cation exchange dominates.
Model Development Competitive Two-Site Model. The mass action and material balance equations of the TS model for the case in which multiple organic bases exist in solution are provided in Table 1. In this table, Ka refers to the acid dissociation constant of the conjugate acid (mol/L), Baq is the neutral aqueous organic base, Koc is the partition coefficient of B to soil organic carbon, foc is the fraction of organic carbon, Boc is the concentration of B associated with soil organic carbon, KG (M-0.5) is the selectivity coefficient employing the Gapon cation-exchange convention (17), BHS and D0.5S are the organic and inorganic 2+ (Ca2+ aq and Mgaq ) cations, respectively, that are attached to cation-exchange sites on the soil (S-), and all other terms are defined in the table. When two organic amines are present, the TS model contains three chemical components: 1BH+ aq, 2BH+ , and D2+, where the preceding superscripts on BH+ aq aq aq distinguish between the two amine components and where 2+ 2+ D2+ aq is the sum of the aqueous Caaq and Mgaq concentrations. Protons are not included as a component because the pH is known. In these equations, a total of 11 species exist + 2 2+ 1 2 1 1 2 2 (1BH+ aq, Baq, BHaq, Baq, BHS, Boc, BHS, Boc, Daq , D0.5S, and + Haq), where “species” are defined according to the conventions outlined by Morel and Hering (18). Combining the equations in Table 1 results in the following set of simul2728
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[S]T )
{
(1)
[D]T 2 2 2 K [BH+]aq m/v G [D2+]0.5 aq [D2+]0.5 aq
a j represents the aromatic amine (1 or 2); S (mol/kg) is the total T concentration of negatively charged cation exchange sites equal to the pH-specific cation exchange capacity (CEC); DT (mol/L) is the total mass of divalent inorganic cations per aqueous phase volume; jBT (mol/L) is the total mass of the organic base per aqueous phase volume for the organic amine j; N is the number of aromatic amines present in the system (i.e., 2); and m and v are the soil mass and aqueous phase volume, respectively.
)}
}
)}
(2)
[D]T 2 1 1 + - [D2+]0.5 aq ( KG [BH ]aq + m/v [D2+]0.5 aq 2 2 ([D]T - [D2+]aq) (3) KG 2[BH+]aq) + m/v
This system of equations is referred to as the competitive two-site (CTS) model. Competitive Distributed Parameter Model. As previously described (9), the introduction of distributed parameters requires the addition of the concentration of vacant sites (S-) as another component to help formalize the numerical solution. In practice, the number of vacant sites is made negligible by setting the association coefficient for D2+ aq to a very large value. This, in turn, forces the association coef+ 2 ficients for 1BH+ aq and BHaq to be large when they are evaluated, forcing essentially all sites to be occupied by either + j j D2+ aq or BHaq. The ratio of the association coefficients of B + 2+ Haq to Daq for vacant sites defines the cation-exchange coefficients following the Gapon convention. Following the approach taken by Griffioen (20), cation exchange is modeled as three independent association processes between the three + + 1 2 cations present in the system (i.e., D2+ aq , BHaq, and BHaq) and S . Equation 4 depicts the relationship among all mass transfer and speciation processes
where 1KBH, 2KBH, and KD are the association constants for 1BH+ , 2BH+ , and D2+, respectively. Extension of the model aq aq aq to two or more organic solutes requires correlating the log KBH,i values of the different amines for the specific soil sites or group of sites. The frequency distribution of log KBH,i values is represented as a normal probability distribution function
f(X) )
2 2 1 e[-(1/2σX )(x-µX) ] σXx2π
(5)
where f(X) is the frequency of sites at log jKBH,i () x); µ and σ represent the mode and standard deviation, respectively; j denotes the compound; and i denotes the specific site or group of sites having a specific binding coefficient. A perfect correlation (i.e., F ) 1) between the probability distribution functions of the two compounds means that a constant ratio of log 1KBH,i/log 2KBH,i occurs over all soil cationexchange sites; that is, the high-affinity sites for one amine are the high-affinity sites for the other amine. In this case, eq 5 could be employed separately for each amine and group of sites, partitioning exchange sites into discrete groups. If the ratio log 1KBH,i/log 2KBH,i is random or less than constant over discrete groups of exchange sites, the bivariate normal density function (16) can be used to describe the probability distribution function of the second amine
fY|X(y|x) )
2 1 e[-(1/2){(y-µY/X)/σY/X} ] σY/Xx2π
TABLE 2. Mathematical Expressions for the CDP Model
(6)
where fY|X (y|x) is the conditional density function of variable Y given the value of X. In our specific case, y represents aniline’s log KBH values and x represents those of 1-aminonaphthalene. The values for µY/X and σY/X are defined by
µY/X ) µY + F(σY/σX)(x - µX)
(7)
σY/X ) σYx1 - F2
(8)
and
where F is the correlation coefficient. The log KBH values for 1-aminonaphthalene are defined by the normal probability distribution (eq 5) called the marginal density function. Possible values of F range from -1 to +1. The magnitude of F measures the degree of linear correlation between log KBH,i values, paired by site, of the two amines. Thus, at F values
