1377

Environmental Toxicology and Chemistry, Vol. 21, No. 7, pp. 1377–1383, 2002q 2002 SETAC

Printed in the USA0730-7268/02 $9.00 1 .00

MODELING SORPTION ISOTHERMS OF VOLATILE ORGANIC CHEMICAL MIXTURESIN MODEL AND NATURAL SOLIDS

JUN LI and CHARLES J. WERTH*Department of Civil and Environmental Engineering, University of Illinois at Urbana–Champaign, Urbana, Illinois 61801, USA

(Received 6 August 2001; Accepted 14 January 2002)

Abstract—Parameters from single-component isotherm models were used in multicomponent isotherm models to predict the aqueousphase sorption of trichloroethylene (TCE) in the presence of tetrachloroethylene (PCE) in four zeolites, Tenax, and three naturalsolids. The Langmuir, the Polanyi–Dubinin, and the Freundlich or the Langmuir–Freundlich isotherm models were used to simulatesingle-component sorption in zeolites. The Langmuir two-site, the Polanyi–Dubinin two-site, and the Freundlich or the Langmuir–Freundlich isotherm models were used to simulate single-component sorption in Tenax and natural solids. Two-site models havebeen used previously to model sorption in soils and sediments, and they combine an adsorption component (e.g., Langmuir) witha linear partitioning component. By using parameters from the different single-component isotherm models, the multicomponentLangmuir, the ideal adsorbed solution theory, and the Polanyi theory were each used to predict multicomponent sorption. In general,the ability to predict TCE sorption in the presence of PCE depended more on the choice of the single-component model than themulticomponent model, and better results were obtained when the Freundlich or the Langmuir–Freundlich isotherm was used forsingle-component sorption. This suggests that the more mechanistically based Langmuir and Polanyi-type models may not adequatelydescribe the distribution of adsorption sites in some model and natural solids. The Freundlich or the Langmuir–Freundlich model,although empirical, has greater flexibility in characterizing sorbent heterogeneity and results in better multicomponent modelpredictions. However, this last statement is tenuous, because more solids must be tested against various model combinations.

Keywords—Competitive sorption Chemical mixtures Isotherm models

INTRODUCTION

The fate and transport of organic contaminants in the sub-surface are controlled by various physical and chemical pro-cesses, of which sorption is one of the most important. Sorptionisotherms commonly are used to describe the equilibrium dis-tribution of organic chemicals in soils and sediments. Sorptionequilibrium can be simulated by isotherm models that directlyor indirectly provide researchers information on sorbent ca-pacity and sorption mechanisms. Because multiple organicchemicals often coexist in the environment, evaluating iso-therm models that can be applied to multicomponent solutesystems is paramount to predicting the fate and transport ofcontaminants in soils and sediments.

Natural soils and sediments comprise both mineral and or-ganic components. With respect to uptake of hydrophobic or-ganic compounds, sorption to mineral surfaces generally is notsignificant when natural organic matter is present [1], and itis often described with a linear isotherm [2,3]. Organic matteris generally accepted to have both a partitioning domain andan adsorption domain ([3] and references therein). Sorption tothe partitioning domain has been attributed to uptake in organicmatter such as humic substances that are geologically young,and often is described with a linear isotherm [3]. Sorption tothe adsorption domain has been attributed to uptake in hydro-phobic micropore spaces or voids formed in recalcitrant orcondensed organic matter [4] and in mineral aggregates [5,6].Sorption to this domain often is observed to be nonlinear[3,4,7–10]. In recent investigations, several authors also haveattributed isotherm nonlinearity to preferential adsorption tohigh surface area carbonaceous materials such as soot, graph-ite, charcoal, and kerogen [10–13].

* To whom correspondence may be addressed (werth@uiuc.edu).

Researchers have used both empirical and mechanisticallybased isotherm models to simulate sorption in soils and sed-iments. One of the most frequently used models is the em-pirically based Freundlich isotherm shown in Equation 1

Nq 5 K CF (1)

where q is the sorbed concentration, C is the aqueous con-centration, and KF and N are empirical constants related tosorbent capacity and heterogeneity, respectively. The Freun-dlich isotherm has been found to fit various natural solid–solutesystems [5,6,14–16]. For cases where isotherms are not log–log linear (i.e., the Freundlich model is inadequate), the Lang-muir–Freundlich isotherm has been used instead [17,18]

Nq (bC)5 (2)

0 NQ 1 1 (bC)

where Q0 represents the adsorption capacity of the sorbent,and b and N are empirical constants related to sorbent prop-erties. Like the Freundlich isotherm, the Langmuir–Freundlichisotherm is empirically based.

In addition to empirical models, more recent efforts havedeveloped mechanistically based models to simulate sorptionin soils and sediments. Of these, the two-site model is the mostcommon. It combines a partitioning domain and an adsorptiondomain. Sorption to the partitioning domain has been describedwith a linear isotherm and sorption to the adsorption domainhas been described with either a Langmuir isotherm or a Po-lanyi–Dubinin isotherm. The Langmuir isotherm is derived byassuming that the number of sorption sites with identical en-ergy is limited and that no interactions occur between neigh-boring sorbate molecules [19]. The Langmuir isotherm hasbeen widely applied to sorption in microporous sorbents suchas zeolites [20]. The Langmuir two-site model originally was

1378 Environ. Toxicol. Chem. 21, 2002 J. Li and C.J. Werth

applied to sorption in polymers [21], and more recently tosorption in humic substances and natural solids [4,16,22,23].The Langmuir two-site model is shown in Equation 3

0Q (bC)q 5 1 K C (3)d1 1 (bC)

where Q0 was defined in Equation 2 and in this work it rep-resents the maximum mass adsorbed per mass of sorbent, b isan empirical constant related to sorbent properties, and Kd isthe distribution coefficient for the partitioning domain.

The Polanyi–Dubinin isotherm is based on a pore-fillingmechanism, where a pure phase of adsorbate forms in pores,and the adsorption potential of pores diminish during filling[24,25]. The Polanyi–Dubinin model has been applied to ad-sorption on activated carbons [26,27]. The Polanyi–Dubinintwo-site model was recently applied to sorption on soils andsediments [28]. This two-site model is shown in Equation 4

belwq 5 w r exp 2a 1 K C (4a)0 d1 2[ ]Vm

Cse 5 RT ln (4b)lw C

where w0 is the maximum adsorbed volume per mass of sor-bent, r is the density of the liquid sorbate, a and b are empiricalconstants related to sorbent properties, elw is the available ad-sorption potential in water, Vm is the molar volume of theadsorbate, R is the gas constant, T is the temperature, and Cs

is the solubility of the solute.In multicomponent systems, the equilibrium distribution of

one sorbate can be altered by the presence and quantity ofother sorbates. Several theories have been developed to de-scribe the sorption of chemical mixtures. For sorption in mi-croporous materials such as activated carbons and zeolites, theLangmuir isotherm has been extended to account for multiplesorbates [20]. Like its single-component counterpart, the mul-ticomponent Langmuir isotherm, shown in Equation 5, is basedon the assumptions that the number of sorption sites withidentical energy is limited (regardless of the sorbate), and thatno interactions occur between neighboring sorbate molecules

q b C1 1 15 ,0Q 1 1 b C 1 b C 1 · · ·1 1 1 2 2

q b C2 2 25 (5)0Q 1 1 b C 1 b C 1 · · ·2 1 1 2 2

The parameters in Equation 5 are defined similar to those inEquation 3.

For soils and sediments, the ideal adsobed solution theory(IAST) has been widely used to predict the sorption of chem-ical mixtures [7,18,22]. The IAST assumes that the solutionis ideal, that is, that the activity coefficient of each solute is1.0 and no change in the area per molecule occurs upon mixing.The IAST also assumes that the sorbed phase is thermody-namically ideal, which necessarily follows that at equilibriumthe spreading pressures of each adsorbate in a mixture are thesame, and they are equal to the spreading pressure of themixture [20,29]. This relationship is described by Equation 6

0Ci 0RT dCi0 0 0p (C ) 5 q (C ) 5 p (6)i i E i i mix0A Ci0

where p is the spreading pressure of component i or the mix-

ture, A is the specific adsorbent surface area, is the aqueous0Ci

phase concentration in equilibrium with , and is the sorbed0 0q qi i

phase concentration from the single-sorbate isotherm. Basedupon the above principles, the IAST equations can be derivedby following Myers and Prausnitz [20,29,30]. The IAST equa-tions for a binary mixture with the Freundlich or the Lang-muir–Freundlich isotherm for single solute sorption were pre-sented previously [18].

One characteristic of the IAST is that it does not specifythe form of the single-sorbate isotherm. For activated carbons,different empirical isotherms have been used for single-solutesorption when the IAST was used to predict multisolute sorp-tion [17,31–33]. For soils and sediments, the Freundlich iso-therm is most commonly used [7,18,22].

The Polanyi theory has also been used to predict the sorp-tion of chemical mixtures in soils and sediments. As in IASTwe assume the solution is ideal. We also assume that the ad-sorbates are uniform in composition, which necessarily followsthat at equilibrium the adsorption potentials of each adsorbateare the same, and they are equal to the adsorption potential ofthe adsorbate alone with the same adsorbed volume as the totalvolume of the mixture [24]. This relationship is described byEquation 7a

C Cs s(e ) 5 RT ln 5 RT ln x (7a)lw i 1 2 1 2C* Ci i

Cix 5 (7b)i C*i

x 5 1 (7c)O i

where is the equilibrium aqueous concentration of singleC*iadsorbate i with the same adsorbed volume as the total ad-sorbed volume of the mixture. The rest of the parameters weredefined in Equation 4b. As defined in Equation 7b, the molefraction of component i in the adsorbed phase is the quotientof the equilibrium aqueous concentration divided by the C*of the same component. Equation 7c is an additional conditionto determine the individual mole fraction. Equations 7a to ccoupled with the single-sorbate isotherm (e.g., Eqn. 4) can besolved simultaneously to predict mixture sorption.

Similar to the IAST, different forms of the single-sorbateisotherm have been used when the Polanyi theory was usedto predict multicomponent sorption. Greenbank and Manes[34] first used a polynomial equation to describe single-solutesorption for activated carbons. More recently, Xia and Ball[28,35] used the Polanyi–Dubinin two-site model to describesingle-solute sorption for soils and sediments.

The three theories (or models) for predicting the sorptionof chemical mixtures are intrinsically different. The multicom-ponent Langmuir theory, an extension of the single-componentLangmuir theory, is thermodynamically consistent only whenthe volumetric adsorption capacity is the same for each com-ponent [20]. For both the IAST and Polanyi theory, the ad-sorbed phase is assumed uniform in this work, even thoughthe Polanyi theory can be extended to nonuniform adsorbates[24]. Under this assumption, the IAST obeys the Gibbs ad-sorption isotherm and is thermodynamically consistent (theexcess Gibbs energy is zero) [32]. However, the Polanyi theoryis not, as pointed out by Sircar and Myers [36]. Nevertheless,this assumption of adsorbate uniformity does not pose anysignificant deviation from experimental data [24]. With theIAST, sorption is evaluated at equivalent spreading pressure,

Modeling competitive sorption of chemical mixtures Environ. Toxicol. Chem. 21, 2002 1379

Table 1. Properties of sorbentsa

Natural solids C/H OC%Recalcitrant

OC%Micropore

volume (ml/g)

CatlinU.S. EPA-8Vandalia

8.14.70.67

3.80.190.20

3.50.140.09

0.00290.00140.0050

Model solids Si/Al

Theoreticalpore size

(A)

Measuredpore size

(A)

Microporevolume(ml/g)

TenaxUTD-1AUTD-1BMordeniteH-ZSM-5

NA75

1681865

NA7.5 3 107.5 3 106.7–7.0

5.4; 5.2–5.8

.5.57.67.55.1

4.9; 6.2

0.00640.210.210.210.37

a C/H 5 atomic carbon to hydrogen ratio; OC% 5 organic carboncontent by weight; Si/Al 5 atomic silicon to aluminum ratio; NA5 not applicable.

and with the Polanyi theory sorption is evaluated at equivalentadsorption potential. For sorbates that do not differ substan-tially from each other, a common correlation curve (sorbedvolume vs adsorption potential) can be obtained. When thiscorrelation curve is used as the single-sorbate isotherm, theIAST and the Polanyi theory are mathematically identical.Previous research has found that the IAST and the Polanyitheory yield similar modeling results for sorption of chemicalmixtures to activated carbons [34] and to natural solids [35].

In a recent paper [18], we performed single and binaryisotherm experiments on model solids such as polymers andzeolites, and on natural soils and sediments. The model solidswere used as surrogates for the different sorption environmentsin natural solids. Isotherm results indicate that pore size andpolarity of micropore spaces formed in recalcitrant or con-densed organic matter control the competitive sorption of sol-ute mixtures in soils and sediments, and that smaller morehydrophobic micropores result in stronger competition. Hence,these isotherms represent a unique data set that describes thesorption of single and binary solutes as a function of sorbentproperties.

In this work, we evaluate the ability of single-componentand multicomponent sorption models to simulate and predict,respectively, single and binary solute sorption to the sorbentspreviously measured [18]. We analyze the effect of choosingdifferent single-component sorption models on the predictivecapability of multicomponent sorption models. Our objectivesare to demonstrate which pair of single-component and mul-ticomponent models best represents our experimental data, andto evaluate competitive sorption mechanisms based on themodeling results. This is critical as accurate modeling of mul-ticomponent sorption is important to predict the fate and trans-port of contaminants in soils and sediments and to predict therisk that these chemicals pose to potential receptors.

EXPERIMENTAL BACKGROUND

Sorbates

Isotherms for two common chlorinated contaminants, tri-chloroethylene (TCE) and tetrachloroethylene (PCE), weremodeled in this study. The octanol–water partition coefficient(KOW) and the water solubility (Sw) at 308C for TCE are 339and 1,333.2 mg/L, respectively, and those for PCE are 759and 236.34 mg/L, respectively. As shown previously [18], PCEis more competitive than TCE in hydrophobic adsorption sites.

Sorbents

Isotherms were measured previously on three natural solidsand five model solids [18]. A detailed sorbent characterizationalso was given in that study [18]. Selected properties of thesorbents are presented in Table 1. The three natural solids areCatlin silt loam, U.S. Environmental Protection Agency, Re-gion 8 (U.S. EPA-8) sediment, and Vandalia till. The atomicratio of carbon to hydrogen (C/H) value is a measure of thedegree of aromaticity of the sorbent, which is related to theamount of recalcitrant or condensed organic matter [37–39].The C/H value decreases from Catlin, to U.S. EPA-8, to Van-dalia. Catlin has the highest total and recalcitrant organic car-bon content (OC%). The other two natural solids, U.S. EPA-8 and Vandalia, have about the same total OC%, with Vandaliahaving the least recalcitrant OC%. Micropores in natural solidsare characterized by a range of pore widths [18], indicatingthe heterogeneous structure of these sorbents.

The five model solids are one synthetic polymer, Tenax(2[C6H4O]x2, Alltech Associates, Deerfield, IL, USA), andfour zeolites (provided by K. Bulkas, University of Texas atDallas, Dallas, TX, USA). Tenax is a glassy polymer composedof organic macromolecules and is hydrophobic in nature. Theratio of silicon to aluminum (Si/Al ) of the zeolites indicatestheir hydrophobicity [40]. As shown in Table 1, UTD-1B ismost hydrophobic and Mordenite is least hydrophobic; thehydrophobicity of UTD-1A and H-ZSM-5 are intermediate andare similar to each other. Micropores in Tenax are characterizedby a range of widths, similar to those of natural solids [18].Micropores in zeolites are characterized by a narrow distri-bution of widths, as expected based on their uniform structure[18]. As indicated by the theoretical pore sizes in Table 1, thepore sizes of UTD-1A and UTD-1B are larger than those ofMordenite, and those of Mordenite are larger than those of H-ZSM-5.

Isotherm experiments

Single-sorbate isotherms were performed for TCE and PCE[18]. The initial loading of TCE ranged approximately from0.2 to 730 mg, and that of PCE ranged from 0.22 to 800 mg.Dual-sorbate isotherms were performed with the initial loadingof TCE similar to that in single-sorbate experiments, and withthe initial loading of PCE maintained at approximately 800mg. Isotherm methods were described in detail previously [18].

MODELING APPROACH

Table 2 summarizes the modeling approaches used. Single-component sorption in zeolites was simulated with the Lang-muir, the Polanyi–Dubinin, and the Freundlich or the Lang-muir–Freundlich (F/LF) isotherm models. Single-componentsorption in Tenax and the three natural solids was simulatedwith the Langmuir two-site, the Polanyi–Dubinin two-sitemodels, and the F/LF isotherm models. Single-sorbate iso-therm parameters were obtained by minimizing the sum of therelative least squared (SRLS) error between the model fits andthe isotherm data. When the Langmuir isotherm model wasused for zeolites, values of b1 for TCE, b2 for PCE, and Q0

were determined simultaneously for TCE and PCE by mini-mizing the SRLS errors between the model fits and the ex-perimental data. The value of Q0, when converted to units ofvolume (i.e., w0), was the same for TCE and PCE for ther-modynamic consistency [20]. When the Langmuir two-site

1380 Environ. Toxicol. Chem. 21, 2002 J. Li and C.J. Werth

Table 2. Modeling approacha

Multicomponent model MCL IAST Polanyi theory

Single component model Langmuir or Langmuir two-site Langmuir or Langmuir two-siteF/LF

Polanyi-Dubinin orPolanyi–Dubinin two-site

Langmuir or Langmuir two-siteF/LF

a MCL 5 multicomponent Langmuir; IAST 5 ideal adsorbed solution theory; F/LF 5 Freundlich or Langmuir–Freundlich isotherm model.

model was used for Tenax and the three natural solids, valuesof and b1 for TCE, K and b2 for PCE, and Q0 wereKd d1 2

determined simultaneously for TCE and PCE. Similar to ze-olites, the value of Q0 for a solid, when converted to w0, wasthe same for TCE and PCE. For the Polanyi–Dubinin or thePolanyi–Dubinin two-site model, values of a1 and b1 for TCEand a2 and b2 for PCE were determined separately for TCEand PCE. The parameters w0 and, if necessary, and ,K Kd d1 2

were obtained from the Langmuir or the Langmuir two-sitemodel. Attempts to determine w0 (along with a1, b1, a2, andb2) by the Polanyi–Dubinin or the Polanyi–Dubinin two-sitemodel were not successful, because the model failed to con-verge on a unique solution. For the F/LF isotherm model,values of N and KF or b for single solute sorption of TCE andPCE were obtained previously [18].

Multicomponent sorption, that is, the sorption of a TCE-PCE mixture, was predicted by the multicomponent Langmuirtheory, the IAST, and the Polanyi theory. When the multicom-ponent Langmuir model was used, the single-component sorp-tion was fitted by the Langmuir or the Langmuir two-site mod-el. When the IAST was used, the single-component sorptionwas fitted by the Langmuir or the Langmuir two-site model,and the F/LF isotherm. When the Polanyi theory was used,the single-component sorption was fitted by the Polanyi–Du-binin or the Polanyi–Dubinin two-site model, the Langmuir orthe Langmuir two-site model, and the F/LF isotherm. For Ten-ax and natural solids, the three multicomponent sorption mod-els were applied only to predict the adsorption component ofthe binary solute sorption. The total sorption was the sum-mation of a partitioning component obtained from or KKd d1 2

from the Langmuir two-site model and an adsorption com-ponent predicted by a multicomponent sorption model. In allcases, the goodness of the multicomponent model predictionswas evaluated based on the SRLS error.

RESULTS

Single-sorbate isotherms

Table 3 presents the fitting parameters for the single-com-ponent sorption of TCE and PCE, and the SRLS errors foreach fit. The maximum adsorbed volume, w0 obtained fromthe Langmuir or the Langmuir two-site model is listed in col-umn 2. For zeolites, w0 represents the total possible sorbedvolume, and for Tenax and natural solids w0 represents themaximum amount of TCE or PCE adsorbed. The w0 value ofMordenite is small compared to the other zeolites and is about2% of its micropore volume given in Table 1. This is probablydue to its weak hydrophobicity (smallest Si/Al ratio). The w0

values of the other zeolites and Tenax are one half to one thirdof their micropore volumes. The w0 values of natural solidsare about 0.0001 to 0.04% of their micropore volumes. Themicroporosity measured for natural solids includes microporespace not only in organic matter but also in inorganic com-ponents. Hence, only a small fraction of the total microporosity

(i.e., the nonpolar fraction) may be available for TCE and PCEin these natural solids. Also, the adsorbed volume decreasesfrom Catlin to U.S. EPA-8 to Vandalia. As expected, their C/H ratios and the recalcitrant OC% values decrease in the sameorder (Table 1). The rest of Table 3 presents the values of

and obtained from the Langmuir two-site model forK Kd d1 2

Tenax and natural solids, the fitting parameters bi (i 5 1 or 2)from the Langmuir or the Langmuir two-site model, and bi

9ai

from the Polanyi–Dubinin or the Polanyi–Dubinin two-sitemodel, and the SRLS errors of each fit. The SRLS errors rangefrom 0.0631 to 1.58.

Figure 1 presents the model fits of single-sorbate TCE iso-therms for the four zeolites from the Langmuir and the Po-lanyi–Dubinin models. All the fitted values are among thespread of the experimental data. Figure 2 presents the modelfits of single-sorbate TCE isotherms for Tenax and the threenatural solids from the Langmuir two-site model. As shownin Figure 2, sorption in Tenax is dominated by adsorption(indicated by the short-dashed lines) for almost the entire con-centration range, and partitioning (indicated by the long-dashed lines) exceeds adsorption only when approaching thehighest concentration. For the natural solids, the adsorptioncomponent dominates the total sorption at lower concentra-tions and the extent of its domination decreases from Catlinto U.S. EPA-8 to Vandalia, in accordance with the trend oftheir recalcitrant OC% (Table 1). Similar behavior has beenobserved previously [16,23]. The Polanyi–Dubinin two-sitemodel also was applied to these sorbents and very similarresults were obtained (data not shown). Model fits from theF/LF isotherm model have been presented previously [18].

Dual-sorbate isotherms

Figure 3 shows the SRLS errors for the predicted sorptionof TCE in the presence of PCE for each sorbent by using themodeling approaches listed in Table 2. All approaches giverelatively consistent SRLS errors for all eight sorbents exceptthe IAST–Langmuir two-site approach for Catlin and the Po-lanyi–F/LF approach for UTD-1B. Among all, the IAST–F/LF approach gives the best predictions (consistently smallSRLS values for all sorbents).

Figure 3 also shows that for all the sorbents, the SRLSerrors of the IAST–F/LF approach and the Polanyi–F/LF ap-proach are similar, and below those of all the other approaches(except Polanyi–F/LF for UTD-1B). For the three approachesof the same single-component isotherm model, that is, theLangmuir or the Langmuir two-site, but of different multi-component models, that is, the multicomponent Langmuir the-ory, the IAST, and the Polanyi theory, the SRLS errors arealso similar (except IAST–Langmuir two-site for Catlin).These results suggest that similar predictions are obtained forTCE sorption in the presence of PCE when the same single-component sorption model is used, regardless of the multi-component sorption model. The Polanyi theory with the Po-

Modeling competitive sorption of chemical mixtures Environ. Toxicol. Chem. 21, 2002 1381

Tab

le3.

Fit

ting

para

met

ers

and

sum

ofre

lati

vele

ast

squa

red

(SR

LS

)er

rors

for

sing

le-s

orba

teis

othe

rms

oftr

ichl

oroe

thyl

ene

(TC

E)

and

tetr

achl

orot

hyle

ne(P

CE

)a

Sor

bent

w0

(ml/

g)

Lin

ear

TC

EK

d 1(m

g/g)

/(m

g/m

l)

PC

EK

d 2(m

g/g)

/(m

g/m

l)

Lan

gmui

r

TC

E

b 1(m

g/m

l)S

RL

Sb

PC

E

b 2(m

g/m

l)S

RL

S

Pol

anyi

–Dub

inin

TC

E

a9c 1b 1

SR

LS

PC

E

a′ 2b 2

SR

LS

UT

D-1

AU

TD

-1B

Mor

deni

teH

-ZS

M-5

Ten

axC

atli

nU

.S.

EPA

-8

0.05

820.

0698

4.31

310

23

0.06

203.

533

102

3

1.19

310

26

4.13

310

28

— — — —80

2 3.98

0.18

4

— — — —1.

913

103

7.98

0.65

5

0.01

050.

0394

0.01

430.

727

1.55

5.86

7.25

0.93

50.

570

0.69

70.

511

0.30

90.

263

0.31

4

0.18

60.

549

0.21

80.

823

9.05

12.8

24.6

0.20

51.

140.

153

0.06

310.

293

0.10

30.

198

176

337

139

860

1.33

310

3

7.83

310

3

4.00

310

3

1.45

1.84

1.36

2.57

2.86

3.90

3.63

1.58

1.40

1.16

0.75

20.

418

0.24

70.

319

495

750

429

686

1.34

310

4

3.60

310

4

115

1.88

2.16

1.83

2.15

3.75

3.20

1.78

0.20

51.

280.

373

0.23

20.

250

0.08

370.

183

Van

dali

a6.

873

102

90.

140

0.67

910

80.

261

279

0.10

3D

idno

tco

nver

gebe

caus

epo

refi

llin

gco

mpo

nent

was

too

smal

l

aR

esul

tsfr

omF

reun

dlic

hor

Lan

gmui

r–F

reun

dlic

his

othe

rms

are

pres

ente

din

Li

and

Wer

th[1

8].

bS

RL

S5

S[(

esti

mat

ed2

mea

sure

d)/m

easu

red]

2 ,n

isth

enu

mbe

rof

data

poin

ts.

n i 51

ca

5a i

(RT

).

9b i

i

Fig. 1. Model fits of single-sorbate trichloroethylene isotherms forzeolites UTD-1A, UTD-1B, Mordenite, and H-ZSM-5. Experimentaldata are denoted by symbols. The solid lines are fitted results fromthe Langmuir model. The short-dashed lines are fitted results fromthe Polanyi–Dubinin model.

Fig. 2. Model fits of single-sorbate trichloroethylene isotherms forTenax and the natural solids Catlin, U.S. Environmental ProtectionAgency, Region 8 (EPA-8), and Vandalia from the Langmuir two-sitemodel. Experimental data are denoted by symbols. The solid lines arefitted results of the total sorption. The short-dashed lines are fittedresults of the Langmuir portion. The long-dashed lines are fitted resultsof the linear portion.

lanyi–Dubinin or the Polanyi–Dubinin two-site model gavethe worst predictions among all approaches.

Effect of adsorption component

Figures 4 and 5 present multicomponent model predictionsfor Tenax and Catlin, respectively, using multicomponentLangmuir with Langmuir two-site, IAST with Langmuir two-site, Polanyi with Langmuir two-site, and Polanyi with Polan-yi–Dubinin two-site models. Results from U.S. EPA-8 andVandalia are similar to those from Catlin, and are not shown.In TCE-PCE mixture experiments, PCE was kept at a constanthigh concentration throughout the concentration range of TCE.Figures 4 and 5 show that in the presence of PCE, the ad-sorption component of TCE is reduced to such an extent that,except when the IAST is used, it does not affect the totalsorption. The measured isotherms in Figures 4 and 5 showsome curvature on the log–log plots, indicating that the con-tribution of adsorption to total uptake varies with concentra-tion. Predicted isotherms in Figures 4 and 5 do not capturethis curvature, and the adsorption and partition componentsare parallel throughout the measured isotherm. Hence, pre-dicting multicomponent sorption from the two-site models

1382 Environ. Toxicol. Chem. 21, 2002 J. Li and C.J. Werth

Fig. 3. The sum of relative least squared (SRLS) errors of differentapproaches for each sorbent. MCL 5 multicomponent Langmuir;IAST 5 ideal adsorbed solution theory; F/LF 5 Freundlich or Lang-muir–Freundlich isotherm model.

Fig. 5. Model predictions for sorption of trichloroethylene in the pres-ence of tetrachloroethylene in Catlin by four approaches. Experimentaldata are denoted by symbols. The solid lines are predictions of thetotal sorption. The short-dashed lines are predictions of the adsorptionportion. The long-dashed lines represent the linear portion. The long-dashed lines often overlap with the solid lines. MCL 5 multicom-ponent Langmuir; IAST 5 ideal adsorbed solution theory.

Fig. 4. Model predictions for sorption of trichloroethylene in the pres-ence of tetrachloroethylene in Tenax by four approaches. Experimentaldata are denoted by symbols. The solid lines are predictions of thetotal sorption. The short-dashed lines are predictions of the adsorptionportion. The long-dashed lines represent the linear portion. The long-dashed lines often overlap with the solid lines. MCL 5 multicom-ponent Langmuir; IAST 5 ideal adsorbed solution theory.

yields results that are not consistent with the data or the ap-parent sorption mechanisms.

Figures 4 and 5 also show that the model predictions forthe adsorption and the partitioning components by the mul-ticomponent Langmuir with the Langmuir two-site, the Polanyitheory with the Langmuir two-site, and the Polanyi theorywith Polanyi–Dubinin two-site are similar to each other; theadsorption components are uniformly below the partitioningcomponent by about the same order of magnitude. The samebehavior was observed for U.S. EPA-8 and Vandalia (data notshown). For the three natural solids, the relative distance be-tween the adsorption and the partitioning components increas-es from Catlin (2.1 orders of magnitude), to U.S. EPA-8 (2.5),to Vandalia (3.0). The performance of the multicomponentmodels to predict TCE sorption in the presence of PCE im-proves as the magnitude of the adsorption component decreas-es from Catlin to U.S. EPA-8 to Vandalia (Fig. 3). Hence,when the fraction of the isotherm controlled by adsorptiondecreases, the predictive capability of the multicomponentmodels seems to improve. However, this result is misleadingbecause TCE partitioning is not affected by PCE, and becausemixture isotherms are increasingly controlled by partitioningas the significance of the adsorption component decreases.These results suggest that the success of predicting the sorptionof chemical mixtures depends on the significance of the ad-

sorption and partitioning components and the accuracy withwhich they are represented by single-sorbate isotherms.

DISCUSSION

The performance of the three multicomponent sorptionmodels cannot be judged without considering which single-component model is used. The variations of the SRLS errorsshown in Figure 3 suggest limitations of these models. TheLangmuir model assumes that the sorbent has identical sorp-tion sites and that the sorbate molecules are noninteracting.Both the IAST and the Polanyi theory assume that the adsor-bates have the same properties as the bulk liquid. In mixtureexperiments, the concentration of PCE was kept at a constanthigh concentration, and one order of magnitude below its sol-ubility limit. At this high PCE loading, the TCE-PCE inter-actions may be important inside micropores, especially forsorption of the less competitive TCE. By assuming an idealsolution, the multicomponent models also do not account forsorbate–sorbent interactions. Hence, the multicomponent mod-els may not adequately describe the mixture sorbate isotherms.

This work finds that the sorption of solute mixtures in allsolids tested is generally better predicted when the F/LF iso-therm model is used for single-component sorption. We pro-pose that, under their respective assumptions, neither the Lang-muir nor the Polanyi–Dubinin model may adequately describethe distribution of adsorption sites present in these solids. Forzeolites, this inadequacy is more evident (i.e., SRLS valuesare generally greater) because only adsorption controls soluteuptake. For Tenax and natural solids, the effect is less evidentbecause partitioning dominates TCE uptake when PCE is pre-sent. When a two-site model is used to separate a single-sorbateisotherm into an adsorption and a partitioning component, anyerrors in the single-sorbate partitioning component directlyaffect the predicted mixture isotherm. Use of the F/LF isothermavoids this problem, because it assumes a continuous distri-bution of sorption sites and, thus, has greater flexibility incharacterizing sorbent heterogeneity. This may explain whythe F/LF model for single-sorbate isotherms is more robustand somewhat better with respect to predicting multicompo-nent sorption. This hypothesis requires further testing, becausemore solids must be tested against various model combina-tions.

Modeling competitive sorption of chemical mixtures Environ. Toxicol. Chem. 21, 2002 1383

Acknowledgement—This research was funded by the National ScienceFoundation (grant BES-9803563). We thank William P. Ball and twoanonymous reviewers.

REFERENCES

1. McCarty PL, Reinhard M, Rittmann BE. 1981. Trace organics ingroundwater: Processes affecting their movement and fate in thesubsurface environment. Environ Sci Technol 15:40–51.

2. Huang W, Schlautman MA, Weber WJ Jr. 1996. A distributedreactivity model for sorption by soils and sediments. 5. The in-fluence of near-surface characteristics in mineral domains. En-viron Sci Technol 30:2993–3000.

3. Luthy RG, Aiken GR, Brusseau ML, Cunningham SD, GschwendPM, Pignatello JJ, Reinhard M, Traina SJ, Weber WJ Jr, WestallJC. 1997. Sequestration of hydrophobic organic contaminants bygeosorbents. Environ Sci Technol 31:3341–3347.

4. Xing B, Pignatello JJ. 1997. Dual-mode sorption of low-polaritycompounds in glassy poly (vinyl-chloride) and soil organic matter.Environ Sci Technol 31:792–799.

5. Farrell J, Reinhard M. 1994. Desorption of halogenated organicsfrom model solids, sediments, and soil under unsaturated con-ditions. 1. Isotherms. Environ Sci Technol 28:53–62.

6. Werth CJ, Reinhard M. 1997. Effects of temperature on trichlo-roethylene desorption from silica gel and natural sediments. 1.Isotherms. Environ Sci Technol 31:689–696.

7. McGinley PM, Katz LE, Weber WJ Jr. 1993. A distributed re-activity model for sorption by soils and sediments. 2. Multi-com-ponent systems and competitive effects. Environ Sci Technol 27:1524–1531.

8. McGinley PM, Katz LE, Weber WJ Jr. 1996. Competitive sorptionand displacement of hydrophobic organic contaminants in satu-rated subsurface soil systems. Water Resour Res 32:3571–3577.

9. Young TM, Weber WJ Jr. 1995. A distributed reactivity modelfor sorption by soils and sediments. 3. Effects of diagenetic pro-cesses on sorption energetics. Environ Sci Technol 29:92–97.

10. Kleineidam S, Rugner H, Ligouis B, Grathwohl P. 1999. Organicmatter facies and equilibrium sorption of phenanthrene. EnvironSci Technol 33:1637–1644.

11. Karapanagioti HK, Kleineidam S, Sabatini DA, Grathwohl P, Lig-ouis B. 2000. Impacts of heterogeneous organic matter on phen-anthrene sorption: Equilibrium and kinetic studies with aquifermaterial. Environ Sci Technol 34:406–414.

12. Chiou CT, Kile DE. 1998. Deviations from sorption linearity onsoils of polar and nonpolar organic compounds at low relativeconcentrations. Environ Sci Technol 32:338–343.

13. Chiou CT, Kile DE, Rutherford DW, Sheng G, Boyd SA. 2000.Sorption of selected organic compounds from water to a peat soiland its humic-acid and humin fractions: Potential sources of thesorption nonlinearity. Environ Sci Technol 34:1254–1258.

14. Grathwohl P. 1990. Influence of organic matter from soils andsediments from various origins on the sorption of some chlori-nated aliphatic hydrocarbons: Implications on KOC correlations.Environ Sci Technol 24:1687–1693.

15. Ball WP, Roberts PV. 1991. Long-term sorption of halogenatedorganic chemicals by aquifer material. 1. Equilibrium. EnvironSci Technol 25:1223–1237.

16. LeBoeuf EJ, Weber WJ Jr. 2000. Macromolecular characteristicsof natural organic matter. 2. Sorption and desorption behavior.Environ Sci Technol 34:3632–3640.

17. Kilduff JE, Wigton A. 1999. Sorption of TCE by humic-preloadedactivated carbon: Incorporating size-exclusion and pore blockagephenomena in a competitive adsorption model. Environ Sci Tech-nol 33:250–256.

18. Li J, Werth CJ. 2001. Evaluating competitive sorption mecha-

nisms of volatile organic compounds in soils and sediments usingpolymers and zeolites. Environ Sci Technol 35:568–574.

19. Adamson AW. 1990. Physical Chemistry of Surfaces, 5th ed. JohnWiley, New York, NY, USA.

20. Ruthven DM. 1984. Principles of Adsorption and AdsorptionProcesses. John Wiley, New York, NY, USA.

21. Vieth WR, Sladek KJ. 1965. A model for diffusion in a glassypolymer. J Colloid Sci 20:1014–1033.

22. Xing B, Pignatello JJ, Gigliotti B. 1996. Competitive sorptionbetween atrazine and other organic compounds in soils and modelsorbents. Environ Sci Technol 30:2432–2440.

23. LeBoeuf EJ, Weber WJ Jr. 1997. A distributed reactivity modelfor sorption by soils and sediments. 8. Sorbent organic domains:Discovery of a humic acid glass transition and an argument fora polymer-based model. Environ Sci Technol 31:1697–1702.

24. Manes M. 1998. Activated carbon adsorption fundamentals. InMeyers RA, ed, Wiley Encyclopedia Series in EnvironmentalScience, Vol 1—Environmental Analysis and Remediation. JohnWiley, New York, NY, USA, pp 26–68.

25. Crittenden JC, Sanongrai S, Bulloch JL, Hand DW, Rogers TN,Speth TF, Ulmer M. 1999. Correlation of aqueous-phase adsorp-tion isotherms. Environ Sci Technol 33:2926–2933.

26. Weber JW Jr, van Vliet BM. 1981. Synthetic adsorbents and ac-tivated carbons for water treatment: Overview and experimentalcomparisons. Am Water Works Assoc J 8:420–431.

27. Crittenden JC, Hand DW, Arora H, Lykins BW Jr. 1987. Designconsiderations for GAC treatment of organic chemicals. Am Wa-ter Works Assoc J 1:74–82.

28. Xia G, Ball WP. 1999. Adsorption–partitioning uptake of ninelow-polarity organic chemicals on a natural sorbent. Environ SciTechnol 33:262–269.

29. Radke CJ, Prausnitz JM. 1972. Thermodynamics of multi-soluteadsorption from dilute liquid solutions. AICHE 18:761–768.

30. Myers AL, Prausnitz JM. 1965. Thermodynamics of mixed-gasadsorption. AICHE J 11:121–127.

31. Fritz W, Schlunder EU. 1981. Competitive adsorption of twodissolved organics onto activated carbon. I. Adsorption equilibria.Chem Eng Sci 36:721–730.

32. Jossens L, Prausnitz JM, Fritz W, Schlunder EU, Myers AL. 1978.Thermodynamics of multi-solute adsorption from dilute aqueoussolutions. Chem Eng Sci 33:1097–1106.

33. Crittenden JC, Luft P, Hand DW, Oravitz JL, Loper SW, Ari M.1985. Prediction of multi-component adsorption equilibra usingideal adsorbed solution theory. Environ Sci Technol 19:1037–1043.

34. Greenbank M, Manes M. 1981. Application of the Polanyi ad-sorption potential theory to adsorption from solution on activatedcarbon. 11. Adsorption of organic liquid mixtures from watersolution. J Phys Chem 85:3050–3059.

35. Xia G, Ball WP. 2000. Polanyi-based models for the competitivesorption of low-polarity organic contaminants on a natural sor-bent. Environ Sci Technol 34:1246–1253.

36. Sircar S, Myers AL. 1973. Surface potential theory of multilayeradsorption from gas mixtures. Chem Eng Sci 28:489–499.

37. Gauthier TD, Seitz WR, Grant CL. 1987. Effects of structuraland compositional variations of dissolved humic materials onpyrene KOC values. Environ Sci Technol 21:243–248.

38. Perminova IV, Grechishcheva NY, Petrosyan VS. 1999. Rela-tionships between structure and binding affinity of humic sub-stances for polycyclic aromatic hydrocarbons: Relevance of mo-lecular descriptors. Environ Sci Technol 33:3781–3787.

39. Xing B, Chen Z. 1999. Spectroscopic evidence for condenseddomains in soil organic matter. Soil Sci 164:40–47.

40. Karger J, Ruthven DM. 1992. Diffusion in Zeolites and OtherMicroporous Solids. John Wiley, New York, NY, USA.