TECHNICAL REPORTS

852

Th e feasibility of the ideal adsorbed solution theory (IAST) in reducing the complexity associated with predicting the sorption behaviors of 12 neutral organic compounds (NOCs) contained in complex mixtures as a fewer number (four to six) of pseudocompounds (groups of compounds) to simulated aquifer sorbents was investigated. All sorption isotherms from individual- and multiple-pseudocompound systems were fi t reasonably well (r2 ≥ 0.953) by the Freundlich sorption model over the range of aqueous concentrations evaluated (i.e., ≤200 μmol L−1). Th e presence and magnitude of mutual competition among pseudocompounds varied depending on the composition of the mixtures (i.e., concentrations and polarities of pseudocompounds) and the properties of sorbents (i.e., the fraction of organic carbon and the availability of hydrophilic specifi c sorption sites). Finally, comparisons between the IAST-based predictions with individual-pseudocompound sorption parameters and experimentally measured data revealed that the accuracy in predicting the sorption behaviors of several NOCs in terms of a fewer number of pseudocompounds decreased with increasing deviations from the assumption of equal and ideal competition in the IAST (i.e., diff erential availability of sorption sites and nonideal competitions among pseudocompounds).

Modeling Sorption of Neutral Organic Compound Mixtures to Simulated Aquifer Sorbents with Pseudocompounds

Jin Chul Joo,* Charles D. Shackelford, and Kenneth F. Reardon

Environmental contamination of the subsurface typically results in the presence of complex mixtures of compounds (e.g., gasoline, fuel hydrocarbon/chlorinated solvents, pesticides, landfi ll leachate, etc.). Unfortunately, models describing the subsurface fate and transport of neutral organic compounds (NOCs) in mixtures routinely ignore mixture eff ects, such as competitive or synergistic sorption and degrada-tion (Clement, 1997; Haws et al., 2006). However, when such mixture eff ects are signifi cant, the determination of pairwise interaction parameters among NOCs is required to accurately predict the fate and transport of the NOCs (Haws et al., 2006). Even if the entire system of diff erential equations including pairwise interaction terms describing the fate and transport of NOCs in a mixture can be solved simultaneously in space and time, such a detailed approach (i.e., one equation per NOC with interaction parameters) becomes increasingly more complicated and less computationally effi cient as the number of NOCs in the mixture increases, limiting the practical utility of this approach.

A potentially more appealing and more practical approach for describing the fate and transport of several NOCs contained within a complex mixture is the “lumping approach.” Th is approach involves grouping NOCs with similar fate and transport behaviors into a fewer number of pseudocompounds (i.e., hypothetical compound groups) and then dealing with the behaviors of the pseudocompounds instead of the behaviors of the individual NOCs (Calligaris and Tien, 1982; Simpson and Narbaitz, 1997; Joo et al., 2012). For example, Joo et al. (2012) showed that the individual sorption behaviors of 12 NOCs contained in mixtures was adequately represented by the sorption of only four to six pseudocompounds, with the number of pseudocompounds depending on the hydrophobicity of the NOC, the type of mineral surface (e.g., quartz, metal oxide, etc.), and the fraction of organic carbon (foc) for the sorbent. Th ey also found that the Freundlich sorption parameters for each individual pseudocompound were successfully represented by the aqueous-phase, mole-fraction weighted averages of the single-sorbate Freundlich sorption parameters for the respective NOCs

Abbreviations: ACE, acetone; BEST, batch equilibrium sorption test; 2-BUT, 2-butanone; 2,4-DMP, 2,4-dimethyl phenol; foc, fraction of organic carbon; HA, humic acid; 2-HEX, 2-hexanone; IAST, ideal adsorbed solution theory; NOC, neutral organic compound; p-CRE, p-cresol; PHE, phenol.

J.C. Joo, Korea Institute of Construction Technology, 2311, Daehwa-Dong, Ilsanseo-Gu, Goyang-Si, Gyeonggi-Do, 411-712, Republic of Korea; C.D. Shackelford, Dep. of Civil and Environmental Engineering, 1372 Campus Delivery, Colorado State Univ., Fort Collins, CO 80523-1372; K.F. Reardon, Dep. of Chemical and Biological Engineering, 1370 Campus Delivery, Colorado State Univ., Fort Collins, CO 80523-1370. Assigned to Associate Editor Dongqiang Zhu.

Copyright © American Society of Agronomy, Crop Science Society of America, and Soil Science Society of America. 5585 Guilford Rd., Madison, WI 53711 USA. All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher.

J. Environ. Qual. 42:852–860 (2013)doi:10.2134/jeq2013.01.0025Supplemental data fi le is available online for this article.Received 24 Jan. 2013.*Corresponding author (jcjoo@kict.re.kr).

Journal of Environmental QualityORGANIC COMPOUNDS IN THE ENVIRONMENT

TECHNICAL REPORTS

www.agronomy.org • www.crops.org • www.soils.org 853

comprising the pseudocompound (i.e., without conducting sorption tests).

Because each pseudocompound behaves as an individual compound, using pseudocompounds in multiple-component sorption models can render such models more amenable to describing the sorption behavior of complex mixtures. However, before this approach can be adopted, the ability of multiple-component sorption models using pseudocompounds to adequately represent the sorption behaviors of the individual NOCs in mixtures must be evaluated. In this regard, several empirical and thermodynamic multiple-component sorption models have been developed using only sorption isotherm parameters derived from individual components. Th ese models include a model based on the ideal adsorbed solution theory (IAST) (Radke and Prausnitz, 1972), the multiple-component Langmuir model (Do, 1998), and the Polanyi-based multiple-component model (Xia and Ball, 2000). However, the IAST has been shown to adequately predict multiple-component sorption for numerous heterogeneous sorbents and a variety of sorbates with diff erent solubilities in aqueous solutions, whereas the more mechanistically based Langmuir and Polanyi-based models have been shown to be ineff ective in describing the distribution of adsorption sites in natural heterogeneous sorbents (Calligaris and Tien, 1982; Hand et al., 1985; McGinley et al., 1993; Xing et al., 1996; Simpson and Narbaitz, 1997; Li and Werth, 2001; Wigton and Kilduff , 2004; Haws et al., 2006; Faria and Young, 2010).

Although the individual sorption behaviors of 12 NOCs contained in mixtures were found to be adequately represented by the sorption of only four to six pseudocompounds ( Joo et al., 2012), no attempt has been made to evaluate the ability to predict the sorption behaviors of individual compounds in complex mixtures on the basis of the sorption behaviors of the pseudocompounds. Th us, the purpose of this study was to evaluate the capability of the IAST using parameters from sorption isotherms of individual pseudocompounds for predicting the sorption behaviors of 12 NOCs contained in mixtures. Th e specifi c objectives of this study were to investigate the interactions among pseudocompounds in mixtures (i.e., competitive vs. synergistic eff ects) in terms of sorption to simulated aquifer sorbents with low foc (≤0.221%) and to evaluate the feasibility and the accuracy of using the IAST with pseudocompounds to predict the sorption behaviors of the individual NOCs contained in mixtures.

Materials and MethodsTh e materials and methods used in this study have been

described in detail elsewhere ( Joo et al., 2008a, 2008b, 2011, 2012) and are summarized in the Supplemental Material to facilitate availability. Briefl y, the descriptions include (i) the extraction and characterization of humic acid (HA) ( Joo et al., 2008a); (ii) the preparation procedures and characterization of model sorbents (i.e., uncoated sand, FeOOH-coated sand, Al2O3–coated sand, and HA-coated sand with diff erent foc) ( Joo et al., 2008a, 2008b); (iii) the physicochemical properties of the 12 NOCs, including six polar compounds (acetone [ACE], 2-butanone [2-BUT], 2-hexanone [2-HEX], phenol [PHE], p-cresol [p-CRE], and 2,4-dimethyl phenol [2,4-DMP]) and six nonpolar compounds (benzene,

toluene, m-xylene, chlorobenzene, 1,4-dichlorobenzene, and 1,2,4-trichlorobenzene) ( Joo et al., 2008a); (iv) the preparation procedures for the solutions of each pseudocompound and the mixtures with 12 NOCs ( Joo et al., 2011, 2012); (v) the analytical methods using gas chromatography with a fl ame ionization detector and a mass selective detector ( Joo et al., 2008a, 2011); (vi) the methodology for the batch equilibrium sorption tests (BESTs) ( Joo et al., 2008a); and (vii) the determination of the equilibration time (i.e., 48 h) for the BESTs ( Joo et al., 2008a, 2011).

Cluster analysis was adopted for the lumping analysis to assess the similarity among the 12 NOCs considered in this study with respect to their sorption behaviors. Th e lumping procedure was performed using SAS 9.1 (SAS Institute, Inc.) with various clustering algorithms and options, and the best number of clusters and cluster components were determined based on statistics criteria and thermodynamic sorption background. Th e procedure and the analysis for the lumping approach for describing the sorption of NOCs in mixtures to simulated aquifer sorbents have been described elsewhere ( Joo et al., 2012).

Modeling Sorption of Neutral Organic Compound in MixturesDetermination of Pseudocompounds

Th e pseudocompounds used in this study previously were determined based on cluster analysis and experimental sorption data ( Joo et al., 2012). Aft er the lumping schemes for grouping the 12 NOCs into pseudocompounds were obtained, the resulting pseudocompounds were determined to approximate the sorption behaviors of the 12 NOCs contained in mixtures in terms of hydrophilic mineral surfaces and HA-coated sands with diff erent foc (Table 1). Th en, each pseudocompound was prepared by dissolving the respective NOCs belonging to each pseudocompound at various concentrations (≤200 μmol L−1). Aft er conducting the BESTs with individual- and multiple-pseudocompound systems, the aqueous-phase and solid-phase molar concentrations of each pseudocompound were calculated by summing the aqueous-phase and solid-phase molar concentrations of the respective NOCs belonging to each pseudocompound at equilibrium in each batch bottle, respectively.

Ideal Adsorbed Solution TheoryTh e IAST has been successfully applied with regard to the

prediction of sorption equilibrium for mixtures of NOCs in dilute aqueous solutions to activated carbon (Calligaris and Tien, 1982; Hand et al., 1985; Wigton and Kilduff 2004) and soils and sediments (McGinley et al., 1993; Xing et al., 1996; Li and Werth, 2001; Faria and Young, 2010). Th e underlying assumptions of the IAST are that (i) sorbates in mixtures have access to the same sorption sites; (ii) the sorbed phase forms an ideal two-dimensional solution in dilute aqueous solutions, analogous to the three-dimensional Raoult’s law; and (iii) the total spreading pressure is equivalent for individual-sorbate and multiple-sorbate systems under conditions of equal activity in solution at any given temperature (Xing et al., 1996; Haws et al., 2006; Faria and Young, 2010). Despite the potential limitation associated with the assumption of ideality in the sorbed phase,

854 Journal of Environmental Quality

the IAST has been used widely because the IAST has a solid theoretical foundation and requires only individual-sorbate sorption isotherms in predicting multiple-sorbate sorption.

Ideal Adsorbed Solution Theory with Freundlich Sorption ModelTh e Freundlich sorption model was used to describe and

interpret all sorption isotherm data in this study because the Freundlich sorption model has been shown to capture the heterogeneous nature of sorption sites within simulated aquifer sorbents ( Joo et al., 2008a, 2011, 2012). Th e Freundlich isotherm model can be written as follows:

Cs = KfCn [1]where C (μmol L−1) and Cs (μmol kg−1) are the aqueous-phase and solid-phase molar concentration of the sorbate at equilibrium, respectively; Kf [(μmol kg−1)/(μmol L−1)n] is the Freundlich unit sorption capacity; and n (dimensionless) is the joint measure of the relative magnitude and diversity of energies. A useful relationship between the aqueous-phase and solid-phase molar concentration of any sorbate, i, is as follows ( Joo 2007):

1/s,

1s,

f,s,

1

; 1 to

inN j

jjii N i

jij

CnC

C i NKC n

=

=

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥= =⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

∑

∑ [2]

Th e expression given as Eq. [2] may be considered as a simplifi cation of the IAST based on the Freundlich sorption model and can be combined with the mass balance in each batch bottle used for BESTs to eliminate aqueous-phase molar concentration in the IAST-based predictions as follows ( Joo 2007):

Cs,i = (Ci,int − Ci)V/Ms [3]

where Ci,int is the initial molar concentration of sorbate i in the mixture, V is the volume of the solution, and Ms is the mass of sorbent in each batch bottle. Finally, the value of Cs,i can be

determined by solving the following expression for Fi set equal to zero:

( )s,1 s,2 s,N1/

s,

1s,s,int s,

f,s,

1

, ,

0; 1 to

i

inN j

jjii i N i

jij

F C C C

CnCMC C i NKV C n

=

=

⋅⋅⋅

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥= − − = =⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

∑

∑

[4]

Th e IAST-based predictions for Ci and Cs,i based on Eq. [3] and [4] were performed using combinations of Ms, V, and Ci,int in each batch bottle and the Freundlich sorption parameters for individual pseudocompounds (Kf,i and ni). In all cases, Ms and V were held constant, whereas the values of Ci,int were varied in each batch bottle.

Th e set of N nonlinear simultaneous equations with N unknown Cs,i values can be solved by using a Newton-Raphson algorithm (e.g., Hand et al., 1985; McGinley et al., 1993; Xing et al., 1996; Li and Werth, 2001; Faria and Young, 2010). In this study, the MATLAB soft ware (R2007a, Th e Mathworks, Inc.) using a Newton-Raphson algorithm was used for solving these nonlinear equations. Similar to the results from Xing et al. (1996) and Faria and Young (2010), sensitivity analysis for the Freundlich sorption parameters indicated that uncertainty in sorption exponent (n) was more sensitive than that in sorption capacity (Kf ).

Comparison of Sorption Results between Measured and Predicted Data

Th e agreement between the predicted data using the IAST and the experimentally measured data was evaluated in terms of the average percent error (APE) defi ned as follows:

,mes ,pred

,mes1

100%APE

p i i

iip

X X

X=

−= ∑ [5]

Table 1. Compositions of pseudocompounds representing the sorption behaviors of 12 sorbates contained in mixtures to hydrophilic mineral surfaces and to humic acid–coated sands with diff erent fractions of organic carbon.†

Sorbates

SorbentsMineral surfaces HAS‡

Uncoated sand

FeOOH-coated sand

Al2O3–coated sand

HAS 1 (foc = 0.051%)

HAS 2 (foc = 0.119%)

HAS 3 (foc = 0.221%)

1,2,4-Trichlorobenzene A§ A A A A A1,4-Dichlorobenzene A A A B B BChlorobenzene B B B B C Cm-Xylene B B B B B CToluene B B B B C DBenzene B B B B C D2,4-Dimethyl phenol C C C C D Ep-Cresol C C C C D EPhenol C C C C D E2-Hexanone C C C C D E2-Butanone D D D D E FAcetone D D D D E F

† Data from Joo et al. (2012).

‡ foc, fraction of organic carbon; HAS, humic acid–coated sands.

§ A, B, C, D, E, and F represent each pseudocompound to which neutral organic compound in mixtures are assigned.

www.agronomy.org • www.crops.org • www.soils.org 855

where Xi,mes and Xi,pred are the measured and predicted data, respectively, for either C or Cs, and p is the number of data values. Th is error function attempts to minimize the fractional error distribution between the experimentally measured sorption data and the corresponding predicted data for C and Cs over the entire range in concentrations.

Results and DiscussionSorption to Hydrophilic Mineral SurfacesIndividual Pseudocompounds

Results for the sorption of each individual pseudocompound and respective component compounds to uncoated sand are shown in Fig. 1 and Supplemental Fig. S1, and similar results obtained for FeOOH-coated and Al2O3–coated sands are provided in the Supplementary Material. For the data shown in Fig. 1 and Supplemental Fig. S1, good fi ts (r2 ≥ 0.969) of the Freundlich sorption model to the measured data were observed over the aqueous concentration ranges evaluated (i.e., C ≤ 200 μmol L−1), and each pseudocompound showed distinguishably diff erent sorption behaviors in terms of sorption capacity (Kf ) and nonlinearity (n). Th ese results indicate that each pseudocompound was comprised of component NOCs with similar sorption capacities and nonlinearity. Consequently,

the sorption behavior of 12 NOCs contained in mixtures to diff erent types of hydrophilic mineral surfaces was approximated reasonably well (r2 ≥ 0.961) by a fewer number (n = 4) of pseudocompounds.

Multiple PseudocompoundsTh e sorption isotherms for multiple-pseudocompound

systems are shown in Fig. 1 to facilitate comparison with those for individual-pseudocompound systems (see Supplementary Material for FeOOH-coated and Al2O3–coated sands). As indicated in Fig. 1a and 1b, the sorption of pseudocompounds A and B comprised of nonpolar NOCs was not aff ected by the presence of all other pseudocompounds with diff erent structural and physicochemical properties. Th ese results indicate that there were little, if any, mixture eff ects for sorption of pseudocompounds A and B to hydrophilic mineral surfaces. Also, the eff ects of changes in mixture composition on the sorption of pseudocompounds A and B to hydrophilic mineral surfaces were found to be insignifi cant ( Joo et al., 2012).

Th e nearly linear and noncompetitive sorption of pseudocompounds A and B can be attributed to the accumulation of nonpolar NOCs in the vicinal water region nearest the hydrophilic mineral surfaces, without competition for the specifi c sorption sites with other nonpolar NOCs (Xing et al., 1996; Joo et al., 2008a, 2011, 2012). Additionally, nonpolar

Fig. 1. Measured and predicted sorption isotherms for pseudocompounds to uncoated sand in individual- and/or multiple-pseudocompound systems. (a) Pseudocompound A (1,2,4-trichlorobenzene, 1,4-dichlorobenzene). (b) Pseudocompound B (chlorobenzene, m-xylene, toluene, benzene). (c) Pseudocompound C (2,4-dimethyl phenol, p-cresol, phenol, and 2-hexanone). (d) Pseudocompound D (2-butanone, acetone).

856 Journal of Environmental Quality

NOCs cannot compete with polar NOCs or water molecules for the specifi c sorption sites on these hydrophilic mineral surfaces and, therefore, sorb further from the surface due to the inability to associate via H-bonding (Xing et al., 1996; Joo et al., 2008a, 2011, 2012).

In contrast, the sorption of pseudocompounds C and D shown in Fig. 1c and 1d decreased and became more linear in the presence of the other pseudocompounds relative to the sorption of the respective individual pseudocompound. Also, the capacity (Kf ) decreased, and linearized sorption (n→1) of pseudocompounds C and D occurred in a selective manner among the hydrophilic mineral surfaces (see Supplementary Material for FeOOH-coated and Al2O3–coated sands). Th us, unlike the sorption of pseudocompounds A and B comprised of nonpolar NOCs, the sorption of pseudocompounds C and D comprised of polar NOCs was aff ected by the presence of other pseudocompounds with diff erent structural and physicochemical properties.

Th ese complex mixture eff ects for pseudocompounds C and D to hydrophilic mineral surfaces can be attributed to the mutual competition between pseudocompounds C and D for hydrophilic specifi c sorption sites. Although the direct variations of Freundlich sorption parameters (Kf and n) for pseudocompounds to hydrophilic mineral surfaces in terms of experimental conditions were not shown in this study, the suppression of the nonlinear interactions of pseudocompound C (i.e., 2,4-DMP, p-CRE, PHE, and 2-HEX) with hydrophilic specifi c sites by higher polarities of pseudocompound D (i.e., 2-BUT and ACE) has been reported in previous papers ( Joo et al., 2011, 2012). As a result, pseudocompound D suppressed the nonlinear interactions of pseudocompound C during sorption to hydrophilic sorption sites, such that the sorption capacity for pseudocompound C decreased signifi cantly. Th us, the presence and magnitude of mutual competition for the pseudocompounds comprised of polar NOCs in multiple-pseudocompound systems varied and depended on the composition of the mixtures (i.e., concentrations and polarities of pseudocompounds) and the properties of sorbents (i.e., specifi c volume of vicinal water region and availability of hydrophilic specifi c sorption sites).

Predictions Based on Ideal Adsorbed Solution TheoryPredicted sorption data based on the IAST were compared

with the corresponding experimentally measured data shown in Fig. 1 for uncoated sand (see Supplementary Material for FeOOH-coated and Al2O3–coated sands). As shown in Fig. 1, the IAST-based predictions closely simulated the sorption behaviors for pseudocompounds A, B, and C, whereas the IAST overpredicted the competition versus pseudocompound D with greater polarities (i.e., 2-BUT and ACE). Also, as indicated by the values of APE shown in Table 2, the accuracy of the IAST-based predictions with individual-pseudocompound sorption parameters to various hydrophilic mineral surfaces depended on the properties of pseudocompounds and mineral surfaces.

For the IAST-based predictions of the pseudocompounds comprised of nonpolar NOCs (i.e., A and B) shown in Fig. 1a and 1b, the sorption capacities were not suppressed by the pseudocompounds comprised of polar NOCs (i.e., C and D) because the sorption capacities of hydrophilic mineral surfaces for individual pseudocompounds C and D were lower by a factor ranging from three to eight than those for individual pseudocompounds A and B. Also, competitive sorption between pseudocompounds A and B was not expected to be signifi cant in IAST-based predictions because the sorption of individual pseudocompounds A and B was nearly linear. Th erefore, the IAST-based predictions closely simulated the observed sorption behaviors of pseudocompounds A and B, which were not aff ected by the presence of other pseudocompounds with diff erent structural and physicochemical properties in multiple-pseudocompound systems.

Conversely, the sorption capacities for the pseudocompounds comprised of polar NOCs (i.e., C and D) were signifi cantly suppressed by those for the pseudocompounds comprised of nonpolar NOCs (i.e., A and B) due to the much greater sorption capacities for pseudocompounds A and B. Also, competitive sorption between pseudocompounds C and D as predicted by the IAST was expected because the sorption behaviors of individual pseudocompounds C and D were nonlinear. Due to the assumption of equal and ideal competition in the

Table 2. Comparison between predicted and experimentally measured concentrations for sorption of pseudocompounds to hydrophilic mineral surfaces.

Sorbents Pseudocompound designationAverage percentage error†

No. of data C range Cs rangeC‡ Cs§

μmol L−1 μmol kg−1 μmol L−1 μmol kg−1

Uncoated sand A 11.4 5.91 8 7.17–90.7 1.39–20.1B 9.31 12.6 8 14.5–198 2.75–34.4C 6.39 14.6 8 15.6–197 0.42–5.72D 7.81 45.8 8 7.91–100 0.18–2.02

FeOOH-coated sand A 13.8 14.9 8 6.40–99.7 1.19–20.2B 10.5 13.3 8 13.0–189 1.56–24.4C 6.01 8.05 8 13.5–199 0.93–10.6D 14.5 38.6 8 6.79–99.0 0.29–3.68

Al2O3–coated sand A 7.65 16.5 8 6.11–94.1 1.29–16.2B 9.08 14.1 8 13.9–200 1.89–29.6C 4.92 12.6 8 15.3–201 0.99–7.57D 5.58 42.5 8 7.81–103 0.38–3.02

† Calculated based on the Eq. [5].

‡ Aqueous–phase molar concentration of pseudocompound at equilibrium (μmol L−1).

§ Solid-phase molar concentration of pseudocompound at equilibrium (μmol kg−1).

www.agronomy.org • www.crops.org • www.soils.org 857

IAST, the predicted sorption of pseudocompounds C and D was suppressed by the presence of pseudocompounds A and B, but this suppression did not occur in the experimental results. Consequently, the IAST predicted the capacity (Kf )-decreased and the linearized (n→1) sorption behaviors of pseudocompounds C and D, shown in Fig. 1c and 1d, respectively.

In contrast to the closely predicted sorption behavior of pseudocompound C, the competition between pseudocompounds A, B, and C versus pseudocompound D was overpredicted based on the diff erences between the predicted and experimentally measured sorption behaviors shown in Fig. 1d. Th is apparent overprediction in the competition for pseudocompound D can also be attributed to the assumption of equal and ideal competition in the IAST.

Although the IAST assumed that all pseudocompounds behave ideally and have equal access to the same sorption sites, the experimental data indicated that the presence and magnitude of the mutual competition between the pseudocompounds comprised of polar NOCs (i.e., C and D) varied and depended on the composition of the mixtures and the properties of sorbents in multiple-pseudocompound systems ( Joo et al., 2012). Also, the diff erentiated sorption domains and the lack of competition between pseudocompounds comprised of polar NOCs versus those comprised of nonpolar NOCs for the hydrophilic sorption sites represent a violation of these assumptions in the IAST. Furthermore, pseudocompound D was found to be more powerful competitor than pseudocompound C for hydrophilic-specifi c sorption sites in multiple-pseudocompound systems ( Joo et al., 2012). Th at is, the observed existence of unequal and nonideal competitions among pseudocompounds violates the assumption inherent in the IAST of equal and ideal competition.

Th e IAST closely predicted the sorption behavior of pseudocompound C in multiple-pseudocompound systems (Fig. 1c). Th is apparent contradiction can be attributed, in part, to the combined eff ect based on the IAST prediction of competition between pseudocompounds A, B, and D versus pseudocompound C, despite the observation from the experimental data that the sorption capacity and the sorption nonlinearity for pseudocompound C were suppressed primarily by the more competitive pseudocompound D (i.e., 2-BUT and ACE) in the real sorption process.

Sorption to Humic Acid–Mineral Complexes with Diff erent Fractions of Organic CarbonIndividual Pseudocompounds

Results for the sorption of each individual pseudocompound and respective component compounds to HAS with diff erent foc are shown in Fig. 2 and Supplemental Fig. S6 for HAS3, and similar results obtained for HAS1 and HAS2 are provided in the Supplementary Material. Th e 12 NOCs contained in mixtures can be lumped into four, fi ve, and six pseudocompounds for HAS1 (foc = 0.051%), HAS2 (foc = 0.119%), and HAS3 (foc = 0.221%), respectively (Table 1). As the foc of the HAS increased, the NOCs with higher Koc (i.e., 1,2,4-trichlorobenzene and 1,4-dichlorobenzene) were separated from the pseudocompounds comprised of nonpolar NOCs due to the greater dependency of sorption on foc with increasing Koc. Th us, in terms of the sorption

behaviors of the 12 NOCs in mixtures to the HAS, the number of pseudocompounds increased with increasing foc.

For the data shown in Fig. 2, good fi ts (r2 ≥ 0.987) of the Freundlich sorption model to the measured data were observed over the aqueous concentration ranges evaluated (i.e., C ≤ 200 μmol L−1), and each pseudocompound showed clearly diff erent sorption behavior in terms of sorption capacity (Kf ) and nonlinearity (n). Th ese results also indicate that each pseudocompound was comprised of component NOCs with similar sorption capacities and nonlinearity.

Multiple PseudocompoundsBased on comparison of the sorption behaviors between

individual and multiple pseudocompound systems shown in Fig. 2 for HAS3 (see Supplementary Material for HAS1 and HAS2), the sorption of pseudocompounds comprised of nonpolar NOCs (i.e., A, B, C, and D) was not aff ected by the presence of all other pseudocompounds (i.e., A, B, C, D, E, and F) with diff erent structural and physicochemical properties. Th us, there were little, if any, mixture eff ects for sorption of pseudocompounds A, B, C, and D to HAS with diff erent foc. Th is result is similar to that previously noted for the hydrophilic mineral surfaces and indicates that the eff ect of changes in mixture composition on the sorption of the pseudocompounds comprised of nonpolar NOCs to HAS with diff erent foc was insignifi cant ( Joo et al., 2012).

Th e absence of mixture eff ects for pseudocompounds A, B, C, and D can be attributed to the dominance of partitioning of nonpolar NOCs into loosely knit macromolecules of HA, relative to the adsorption or hole-fi lling of nonpolar NOCs onto tightly knit macromolecules of HA (Xing et al., 1996; Joo et al., 2011, 2012). Additionally, nonpolar NOCs cannot compete eff ectively with water molecules or polar NOCs for the oxygen and hydroxyl containing functional groups of the HA (Xing et al., 1996; Joo et al., 2008a, 2011, 2012). Th us, sorption of an individual pseudocompound comprised of nonpolar NOCs to the HAS was not signifi cantly altered by the presence and quantity of other pseudocompounds in multiple-pseudocompound systems.

Conversely, as shown in Fig. 2 for HAS 3 (see Supplementary Material for HAS1 and HAS2), the sorption of pseudocompounds E and F comprised of polar NOCs was aff ected by the presence of other pseudocompounds with diff erent structural and physicochemical properties. Compared with the sorption in individual-pseudocompound systems, the sorption of pseudocompounds E and F decreased and became more linear (n→1) in the presence of all other pseudocompounds. However, sorption capacity and nonlinearity were aff ected to diff erent extents not only by the changes in mixture compositions but also by the properties of HASs, indicating that the sorption of pseudocompounds E and F to HAS was more complex than that of pseudocompounds A, B, C, and D.

Th ese complex mixture eff ects for sorption of pseudocompound E and F to HAS can be attributed to mutual competition for site-specifi c hydrophilic interactions, such as H-bonding with the functional groups of HA and surface hydroxyls of mineral surfaces (Xing et al., 1996; Joo et al., 2011, 2012). Similar to sorption to hydrophilic mineral surfaces, pseudocompounds with greater polarity (i.e., 2-BUT and ACE)

858 Journal of Environmental Quality

can suppress the nonlinear interactions of pseudocompounds with lesser polarity (i.e., 2,4-DMP, p-CRE, PHE, and 2-HEX) ( Joo et al., 2011, 2012). However, with increased availability of hydrophilic interaction sites, the eff ect of mixture compositions on the sorption of pseudocompounds comprised of polar NOCs to HASs decreased with increasing foc (see Supplementary Material for HAS1 and HAS2). Th us, the suppression in the nonlinear sorption of a given pseudocompound comprised of

polar NOCs by other pseudocompounds in mixtures appears to have occurred in a complex and selective manner, depending on the composition of the mixture (i.e., concentration and polarity of the pseudocompounds comprised of polar NOCs) and the properties of the sorbents (i.e., foc values and availability of hydrophilic interaction sites). As a result, the sorption of the pseudocompounds comprised of polar NOCs contained in mixtures to the relatively low-surface-area aquifer materials with

Fig. 2. Measured and predicted sorption isotherms for pseudocompounds to humic acid–coated sand (foc = 0.221%) in individual- and/or multiple-pseudocompound systems. (a) Pseudocompound A (1,2,4-trichlorobenzene). (b) Pseudocompound B (1,4-dichlorobenzene). (c) Pseudocompound C (chlorobenzene, m-xylene). (d) Pseudocompound D (toluene, benzene). (e) Pseudocompound E (2,4-dimethyl phenol, p-cresol, phenol, 2-hexanone). (f) Pseudocompound F (2-butanone, acetone).

www.agronomy.org • www.crops.org • www.soils.org 859

low foc (≤0.221%) was subject to greater variation and, therefore, was more diffi cult to predict than that of pseudocompounds comprised of nonpolar NOCs contained in the same mixtures.

Predictions Based on Ideal Adsorbed Solution TheoryTh e comparisons between the IAST-based predictions and

the corresponding experimentally measured data are shown in Fig. 2 for HAS3 (see Supplementary Material for HAS1 and HAS2). Whereas the IAST-based predictions closely simulated the sorption behavior for pseudocompounds A, B, C, and D comprised of nonpolar NOCs, the IAST overpredicted the competition versus pseudocompounds E and F comprised of polar NOCs, especially for pseudocompound F with the greater polarities (i.e., 2-BUT and ACE). Also, as evident from Table 3, the accuracy of the IAST-based predictions using pseudocompounds in mixtures to HAS with diff erent foc depended on the properties of pseudocompounds and sorbents.

Due to the lower sorption capacities for individual pseudocompounds comprised of polar NOCs by a factor ranging from 2 to 22 relative to those for individual pseudocompounds comprised of nonpolar NOCs, there was negligible competition between pseudocompounds comprised of nonpolar NOCs and pseudocompounds comprised of polar NOCs in the IAST-based predictions. Also, competitive sorption among pseudocompounds A, B, C, and D comprised of nonpolar NOCs based on the IAST-based predictions was not signifi cant due to the linear sorption behavior for the individual pseudocompounds comprised of nonpolar NOCs. Th erefore, the IAST closely predicted the sorption behaviors of pseudocompounds comprised of nonpolar NOCs, which were not signifi cantly altered by the presence and quantity of other pseudocompounds in the multiple-pseudocompound systems.

However, the sorption capacities for pseudocompound E and F comprised of polar NOCs were suppressed by those for pseudocompounds A, B, C, and D comprised of nonpolar

NOCs due to the much greater sorption capacities for individual pseudocompounds comprised of nonpolar NOCs. Furthermore, competitive sorption between pseudocompounds E and F was expected in terms of the IAST-based predictions because the sorption of individual pseudocompounds E and F was nonlinear. Th erefore, the IAST predicted the capacity (Kf )-decreased and the linearized (n→1) sorption behaviors of pseudocompounds E and F shown in Fig. 2e and 2f, respectively.

In contrast to the closely predicted sorption behavior of pseudocompound E shown in Fig. 2e, the competition between all pseudocompounds versus pseudocompound F was overpredicted in terms of the diff erences between the IAST-based predictions and the corresponding experimentally measured data shown in Fig. 2f. Th is apparent overprediction in the competition for pseudocompound F can be attributed to the assumption of equal and ideal competition inherent in the IAST because the experimental data indicate that the presence and magnitude of the mutual competition between the pseudocompounds comprised of polar NOCs (i.e., E and F) varied. Also, the diff erentiated sorption domains and lack of competition between pseudocompounds comprised of polar NOCs versus those comprised of nonpolar NOCs for the hydrophilic sorption sites represent a violation of these assumptions in the IAST, such that the IAST overpredicted the competition versus pseudcompound F. However, the IAST closely predicted the sorption behavior of pseudocompound E in multiple-pseudocompound systems (Fig. 2e). Th is apparent contradiction can be attributed, in part, to the combined eff ect based on the IAST prediction of competition between pseudocompounds A, B, C, D, and F versus pseudocompound E despite the observation from the experimental data that the sorption capacity and the sorption nonlinearity for pseudocompound E were suppressed primarily by the more competitive pseudocompound F (i.e., 2-BUT and ACE) in the real sorption process.

Table 3. Comparison between predicted and experimentally measured concentrations for sorption of pseudocompounds to humic acid–coated sands with diff erent fractions of organic carbon.

foc PseudocompoundAverage percentage error†

No. of data C range Cs rangeC‡ Cs§

% μmol L−1 μmol kg−1 μmol L−1 μmol kg−1

0.051 A 7.63 13.5 7 3.66–37.5 4.69–34.6B 4.12 7.89 7 23.4–221 7.83–58.3C 1.70 17.9 7 22.6–195 0.51–6.43D 4.39 63.1 7 11.4–104 0.52–3.08

0.119 A 7.83 14.1 8 1.92–24.5 6.25–52.8B 10.4 15.7 8 5.98–76.0 4.03–55.3C 4.82 6.12 8 9.99–128 4.01–46.4D 8.82 14.8 8 13.2–192 1.36–15.6E 4.72 62.6 8 7.87–98.7 0.26–3.54

0.221 A 9.87 11.5 7 1.82–20.1 4.62–61.5B 9.34 16.5 7 2.42–31.3 2.01–37.5C 10.7 6.96 7 7.17–76.6 5.56–46.9D 5.93 10.3 7 9.67–87.6 2.43–24.8E 2.94 7.58 7 21.5–186 4.50–28.6F 4.58 46.0 7 10.9–100 0.75–6.84

† Calculated based on the Eq. [5].

‡ Aqueous–phase molar concentration of pseudocompound at equilibrium (μmol L−1).

§ Solid-phase molar concentration of pseudocompound at equilibrium (μmol kg−1).

860 Journal of Environmental Quality

Summary and ConclusionsTh e capability of the IAST using parameters from individual-

pseudocompound sorption isotherms to predict the sorption of NOCs in complex mixtures containing 12 NOCs with a wide range of hydrophobicities (i.e., −0.24 ≤ log Kow ≤ 4.23) and simulated aquifer sorbents was investigated. Whereas sorption of the pseudocompound comprised of nonpolar NOCs to the mineral surface and the HA-mineral complexes was not signifi cantly altered by the presence and quantity of other pseudocompounds, the suppression in the sorption of the pseudocompound comprised of polar NOCs by all other pseudocompounds occurred in a complex and selective manner, depending on the composition of mixture (i.e., concentration and polarity of the pseudocompounds comprised of polar NOCs) and the properties of sorbents (i.e., foc values and availability of hydrophilic interaction sites).

In spite of the attraction of IAST-based predictions for simplifying the complexity associated with describing the sorption behaviors of individual NOCs contained in complex mixtures, the IAST-based predictions with pseudocompounds were accurate only for the situation where the availability of sorption sites was similar among the pseudocompounds, and the sorption behaviors among the pseudocompounds closely approximated ideal competitions. Also, deviations from ideal sorption behavior for the pseudocompounds varied and depended on the composition of the mixtures (i.e., concentration and polarity of pseudocompounds) and the properties of sorbents (i.e., foc values and availability of hydrophilic interaction sites). As a result, these deviations from ideal sorption behavior were not represented well by the IAST-predicted sorption behaviors. Nonetheless, considering that the lumped approach (i.e., pseudocompounds) represents a tradeoff between accuracy and simplicity, the IAST-based prediction with pseudocompounds did off er reasonable accuracy with respect to predicting multiple-component sorption equilibrium while reducing the computational requirements. However, to further improve accuracy, modifi cations of the IAST with pseudocompounds in the form of adding terms (e.g., molecular descriptors) or empirical correlations (i.e., activity coeffi cient) to account for diff erential availability of sorption sites and nonideal competitions among pseudocompounds are recommended.

AcknowledgmentsFinancial support for this study was provided by the USEPA’s Science to Achieve Results (STAR) Program (STAR R-82935501-0) and by the Korean Ministry of Environment as Th e GAIA project (no. 2012000550005).

ReferencesCalligaris, M.B., and C. Tien. 1982. Species grouping in multicomponent

adsorption calculations. Can. J. Chem. Eng. 60(6):772–780. doi:10.1002/cjce.5450600608

Clement, T.P. 1997. RT3D-A modular computer code for simulating reactive multi-species transport in 3-dimensional groundwater aquifers. Draft report. PNNL-SA-28967. Pacifi c Northwest National Laboratory, Richland, WA.

Do, D.D. 1998. Adsorption analysis: Equilibria and kinetics. Imperial College Press, London. p. 191–248.

Faria, I.R., and T.M. Young. 2010. Modeling and predicting competitive sorption of organic compounds in soil. Environ. Toxicol. Chem. 29(12):2676–2684. doi:10.1002/etc.343

Hand, D.W., S. Loper, M. Ari, and J.C. Crittenden. 1985. Prediction of multicomponent adsorption equilibria using Ideal Adsorbed Solution Th eory. Environ. Sci. Technol. 19(11):1037–1043. doi:10.1021/es00141a002

Haws, N.W., W.P. Ball, and E.J. Bouwer. 2006. Modeling and interpreting bioavailability of organic contaminant mixtures in subsurface environments. J. Contam. Hydrol. 82(3–4):255–292. doi:10.1016/j.jconhyd.2005.10.005

Joo, J.C. (2007). Lumped approach for sorption of organic contaminant mixtures to simulated aquifer sorbents. Ph.D. diss., Colorado State University, Fort Collins, CO.

Joo, J.C., C.D. Shackelford, and K.F. Reardon. 2008a. Sorption of nonpolar neutral organic compounds to humic acid-coated sand: Contributions of organic and mineral components. Chemosphere 70(7):1290–1297. doi:10.1016/j.chemosphere.2007.07.052

Joo, J.C., C.D. Shackelford, and K.F. Reardon. 2008b. Association of humic acid with metal (hydr)oxide-coated sands at solid-water interfaces. J. Colloid Interface Sci. 317(2):424–433. doi:10.1016/j.jcis.2007.09.061

Joo, J.C., C.D. Shackelford, and K.F. Reardon. 2011. Sorption of neutral organic compounds in mixtures to mineral surfaces and humic acid-mineral complexes. J. Hazard. Toxic Radioact. Waste 15(3):188–198. doi:10.1061/(ASCE)HZ.1944-8376.0000070

Joo, J.C., C.D. Shackelford, and K.F. Reardon. 2012. Lumping analysis for sorption of neutral organic compounds in mixtures to simulated aquifer sorbents. J. Environ. Eng. 138(5):552–561. doi:10.1061/(ASCE)EE.1943-7870.0000498

Li, J., and C.J. Werth. 2001. Evaluating competitive sorption mechanisms of volatile organic compounds in soils and sediments using polymers and zeolites. Environ. Sci. Technol. 35(3):568–574. doi:10.1021/es001366e

McGinley, P.M., L.E. Katz, and W.J. Weber, Jr. 1993. A distributed reactivity model for sorption by soils and sediments: 2. Multicomponent systems and competitive eff ects. Environ. Sci. Technol. 27(8):1524–1531. doi:10.1021/es00045a006

Radke, C.J., and J.M. Prausnitz. 1972. Th ermodynamic of multi-solute adsorption from dilute liquid solutions. AIChE J. 18(4):761–768. doi:10.1002/aic.690180417

Simpson, R.K.D., and R.M. Narbaitz. 1997. An evaluation of multicomponent adsorption equilibria models. Can. J. Civ. Eng. 24(5):828–839. doi:10.1139/l97-017

Wigton, A., and J.E. Kilduff . 2004. Modeling trichloroethylene adsorption by activated carbon preloaded with natural dissolved organic matter using a modifi ed IAST approach. Environ. Sci. Technol. 38(22):5825–5833. doi:10.1021/es049676a

Xia, G.S., and W.P. Ball. 2000. Polanyi-based models for the competitive sorption of low-polarity organic contaminants on a natural sorbent. Environ. Sci. Technol. 34(7):1246–1253. doi:10.1021/es9812453

Xing, B., J.J. Pignatello, and B. Gigliotti. 1996. Competitive sorption between atrazine and other organic compounds in soils and model sorbents. Environ. Sci. Technol. 30(8):2432–2440. doi:10.1021/es950350z