Mechanisms of Slow Sorption of Organic Chemicals to Natural Particles docx

Box 1106, New Haven, Connecticut 06504-1106 The use of equilibrium expressions for sorption to natural particles in fate and transport models is often invalid due to slow kinetics.. Sorp

Critical Review

Mechanisms of Slow Sorption of Organic

Chemicals to Natural Particles

J O S E P H J P I G N A T E L L O * A N D B A O S H A N X I N G

Department of Soil and Water, The Connecticut Agricultural Experiment Station,

P.O Box 1106, New Haven, Connecticut 06504-1106

The use of equilibrium expressions for sorption to

natural particles in fate and transport models is often

invalid due to slow kinetics This paper reviews

recent research into the causes of slow sorption and

desorption rates at the intraparticle level and how

this phenomenon relates to contaminant transport,

bio-availability, and remediation Sorption kinetics are

complex and poorly predictable at present Diffusion

limitations appear to play a major role Contending

mechanisms include diffusion through natural organic

matter matrices and diffusion through intraparticle

nanopores These mechanisms probably operate

si-multaneously, but the relative importance of each

in a given system is indeterminate Sorption shows

anomalous behaviors that are presently not well

explained by the simple diffusion models, including

concentration dependence of the slow fraction,

distributed rate constants, and kinetic hysteresis.

Research is needed to determine whether

adsorp-tion/desorption bond energies may play a role along

with molecular diffusion in slow kinetics The

pos-sible existence of high-energy adsorption sites both

within the internal matrix of organic matter and in

nanopores is discussed Sorption can be rate-limiting

to biodegradation, bioavailablity, and subsurface

transport of contaminants Characterization of

mech-anism is thus critical for fate and risk assessment.

Studies are needed to measure desorption kinetics under

digestive and respiratory conditions in receptor

organisms Conditions under which the constraint of

slow desorption may be overcome are discussed,

including the addition of biological or chemical agents,

the application of heat, and the physical alteration

of the soil.

Introduction

Sorption to natural solids is an underlying process affecting the transport, degradation, and biological activity of organic compounds in the environment Although often regarded

as instantaneous for modeling purposes, sorption may in fact require weeks to many months to reach equilibrium

It was not until the mid to late 1980s that serious study of sorption kinetics in soils and sediments began, despite early circumstantial evidence going back to the 1960s that the natural degradation of certain pesticides in the field slowed

or stopped after a while (1, 2) Sorption kinetics of

contaminants on airborne particles has just recently

received attention (3).

Fate, transport, and risk assessment models all contain terms for sorption; therefore, an understanding of the dynamics of sorption is crucial to their success Ignoring slow kinetics can lead to an underestimation of the true extent of sorption, false predictions about the mobility and bioavailability of contaminants, and perhaps the wrong choice of cleanup technology Kinetics can also be an important mechanistic tool for understanding sorption itself

In this paper, we focus on updating our knowledge of the causes of slow sorption and desorption In addition,

we discuss its significance to bioavailability and the remediation of organic pollutants Much of the research

in this area has been carried out in batch systems where particles are suspended in a well-mixed aqueous solvent Thus, we restrict discussion to phenomena occurring on

the intraparticle scale, that is, within individual soil grains

or within aggregates that are stable in water We shall exclude transport-related nonequilibrium behavior (“physi-cal nonequilibrium”), which may also play an important role in nonideal solute transport in the field and in some experimental column systems Physical nonequilibrium

is due to slow exchange of solute between mobile and less mobile water, such as may exist between particles or between zones of different hydraulic conductivities in the soil column, and occurs for sorbing and nonsorbing molecules alike It can give rise to transport behavior (plume spreading, “tailing” of the solute curve, etc.) that looks much like sorption nonequilibrium It is irrelevant

* Corresponding author telephone: (203) 7237; fax: (203) 789-7232; e-mail address: Soilwatr@yalvem.cis.yale.edu.

0013-936X/96/0930-0001$12.00/0  1995 American Chemical Society VOL 30, NO 1, 1996 / ENVIRONMENTAL SCIENCE & TECHNOLOGY 91

to bioavailability per se, except that microbial populations

and/or activity may vary within the flow regime Recent

papers discussing physical nonequilibrium are available

(4-9) We shall also exclude chemisorption involving

covalent bonds as well as “bound residue” formation, which

is defined as any organic carbon remaining after exhaustive

extraction that results from degradation of the parent

molecule It is safe to say that the mechanisms governing

sorption rates are not fully established Thus, this paper

is partly speculative

Slow Sorption and the Sorption Distribution

Coefficient

Research over the last decade or so has made it clear that

(1) the solid-phase to solution-phase distribution

coef-ficients (Kd) routinely are not measured at true equilibrium;

(2) the use of equilibrium rather than kinetic expressions

for sorption in many fate and effects models is questionable;

and (3) the kinetics of sorption are complex and poorly

predictable

In most cases, the uptake or release of organics by natural

particles is bimodal in that it occurs in fast and slow stages

The division between them is rather arbitrary, but in many

cases it occurs at a few hours to a few days Hereafter, the

term slow will be used to describe the fraction sorbed or

desorbed in the slow stage Adjectives such as resistant,

recalcitrant, rate-limiting, slowly reversible, and

nonequi-librium are also used in the literature

The magnitude of the slow fraction is not trivial, as many long-term studies testify Some recent examples appear in Table 1 During uptake, the apparent sorption distribution

coefficient (Kdapp) can increase by 30% to as much as 10-fold between short contact (1-3 d) and long contact times The values listed in Table 1 should not be construed as predictive nor necessarily representative Data are sparse, and our level of understanding is insufficient to make predictions During the slow uptake stage, experimentally observed changes in solution-phase concentration can be small over periods of many hours and are easily masked

by random analytical errors Consequently, it has been common in many routine sorption experiments to falsely conclude that the system has come to equilibrium after 1

or 2 days

Desorption likewise often reveals a major slow fraction (10-96%) following a comparatively rapid release Histori-cally contaminated (aged) samples, where contact times may have been months or years, can be enriched in the slow fraction owing to partial dissipation or degradation of more labile fractions before collection The slow fraction

of some pesticides was found to increase with contact time

in the environment (10).

When the total contaminant present must be determined

by extractionssuch as in field samples or in spiked samples where uncertain losses occurred during an experimentsthe choice of extraction conditions is important to ensure complete recovery of the analyte Extraction methods are

TABLE 1

Recent Examples of Observed Slow Sorption or Desorption in Natural Sorbentsa

Uptake contact period (d) long short approx ratio b K d app (long)/ K d app (short) slow fraction b,c ref

lindane in subsurface fine sand

(corrected for abiotic hydrolysis)

Release sparging or leaching time remaining slow fraction b ref

aPCE, tetrachloroethene; TeCB, 1,2,4,5-tetrachlorobenzene; picloram, 4-amino-3,5,6-trichloropicolinic acid; lindane,

γ-1,2,3,4,5,6-hexachlorocy-clohexane; PCB, polychlorobiphenyl congeners; EDB, 1,2-dibromoethane; TCE, trichloroethene; atrazine, 2-chloro-4-ethylamino-6-isopropylamino-1,3,5-triazine; metolachlor, 2-chloro-N-[2-ethyl-6-methylphenyl]-N-[2-methoxyethyl]acetamide; simazine, 2-chloro-4,6-bis(ethylamino)-1,3,5-triazine].

b Listed as estimates from graphs and tables in original work and may be rounded c Slow fraction ) 1 - K dapp(short)/K dapp(long) d Concentration dependent e PV, column pore (void) volumes.

commonly validated with freshly spiked soil samples.

Unfortunately, validation is seldom performed on aged

samples that are enriched in resistant fractions Hot

extraction with water-miscible solvents has been shown to

be superior for extracting resistant fractions compared to

traditional methods like solvent-shake at room temperature,

purge-and-trap, and Soxhlet techniques (11-15) It is well

known that recovery by nonmiscible solvents (e.g., hexane)

decreases with aging (16, 17) Supercritical CO2extraction

has not been fully investigated; but some reports indicate

that, even in the presence of organic solvent modifiers which

increase its solvation power, it is inferior to hot solvent for

extracting resistant fractions (18, 19) In some studies, the

slow fraction is likely to have been underestimated due to

incomplete recovery This can lead to erroneous

conclu-sions when some process of interest is being measured

against the mass of contaminant believed to be present

For example, one may deem that biodegradation is

suc-cessful when actually loss of only the labile fraction has

been evaluated

Since Kdis time-dependent on a scale well beyond that

of most laboratory sorption experiments, the true extent of

sorption is known for just a few systems Many reported

Kdvalues represent principally the fast component rather

than overall sorption (20) Free energy correlations

involv-ing Kd are thus brought into question For example,

molecular structure-Kdrelationships rest on the

assump-tion of equilibrium or at least that all compounds have

attained the same fractional equilibrium However,

sorp-tion rates can depend greatly on molecular geometry and

electronic properties This is clearly evident in regard to

diffusion through a viscous medium such as organic matter

or a pore structure (see below) Moreover, Brusseau and

co-workers (21, 22) showed that a mass transfer coefficient

determined from soil column elution was inverse

log-linearly related to the octanol-water partition coefficient

for closely related compounds and that polarity in the

molecule caused an additional decline in the mass transfer

coefficient Further research is needed to determine to

what degree nonequilibrium can influence free energy

relationships of sorption

In general, the sorption equilibrium assumption in fate

and effects models is invalid when the fate/transport process

of interest occurs over comparable or shorter time scales

than sorption Given that, one can imagine many processes

that might be more sensitive to kinetic than thermodynamic

sorption behavior; for example, uptake by an animal that

comes into brief or intermittant contact with the soil The

equilibrium assumption has been found to fail in a growing

number of cases There are numerous examples of

long-term persistence in soils of intrinsically biodegradable

compounds even when other environmental factors are

not limiting for microbial growth (2, 23-25) These are

backed by a laboratory study showing that aging of the

soil-contaminant mixture prior to the addition of microbes

reduced bioavailability (26) and by a field study showing

that aging reduced herbicidal activity (27) Also, the fact

that bioremediation of soil often levels off after an initial

rapid decline [e.g., PCBs (28) and hydrocarbons (29)] is

believed to be due mostly, if not solely, to the unavailability

of a resistant fraction

Finally, nonequilibrium sorption affects the

hydrody-namic transport of contaminants by causing asymmetrical

concentration vs time (elution) curves In relatively

homogeneous soil columns, this asymmetry is exhibited

by early breakthrough, a decrease in peak breakthrough concentration, breakthrough front tailing, and elution-front

tailing (5); whereas, nonsorbing solutes like3H2O or Cl -typically show little or no evidence of asymmetry In more heterogeneous media as exists in the field, the effect of nonequilibrium sorption on transport is less distinct

Vadose (30) and saturated zone (4) studies reveal a decrease

in velocity and aqueous-phase mass of the contaminant plume, relative to a nonsorbing tracer, with increasing travel time or distance While this is consistent with a

time-dependent increase in Kdappdue to rate-limiting sorption,

an interpretation is complicated by permeability variations

in the flow field (physical nonequilibrium) as well as

variability in Kditself within the substrata (7, 8) Both of

these can lead to tailing via plume spreading The relative importance of sorption nonequilibrium and physical non-equilibrium is likely to depend greatly on the heterogeneity

of the flow field and the type of particles that make it up

Mechanisms

Possible Rate-Limiting Steps The potential causes of slow

sorption are activation energy of sorptive bonds and mass-transfer limitations (molecular diffusion) Sorption can occur by physical adsorption on a surface or by partitioning (dissolution) into a phase such as natural organic matter (NOM) The intermolecular interactions potentially avail-able to neutral organic compoundssvan der Waals (dis-persion), dipole-dipole, dipole-induced dipole, and hy-drogen bondingsare common to both adsorption and partitioning In solution these forces are fleeting For example, the mean lifetime of the H2O‚‚‚NH3hydrogen bond

is 2× 10-12s (31) Adsorption to a flat, unhindered, and

rigid surface is ordinarily unactivated or only slightly

activated and so should be practically instantaneous (32).

Desorption, however, is generally activated The kinetic

energy of desorption (Edes*) is the sum of the

thermody-namic energy of adsorption (Q)si.e., the depth of the

potential energy wellsand the activation energy of

adsorp-tion (Ead*) (32) A physisorbed molecule where Ead* ) 0

and Q e 40 kJ mol-1will have a lifetime on the surface of e∼10-6s (32) For these reasons, most small compounds

might be expected to adsorb and desorb practically instantaneously at the microscale However, there may be

situations in which Ead* or Edes* is much greater Large or long molecules that can interact simultaneously at multiple points can be more difficult to desorb There may be steric hinderance to desorption or adsorptionsan ink bottle-shaped pore is an example Lastly, there may be a cooperative change in the sorbent induced by the sorbate

that makes Q larger, as occurs in substrate binding to

enzymes We must be open to these possibilities for pollutant molecules in highly heterogeneous systems like soil particles It is noteworthy that even small, weakly polar molecules like halogenated methanes, ethanes, and ethenes

exhibit slow sorption/desorption in soils (25, 33, 34) The

thermodynamic driving force for their sorption is hydro-phobic expulsion from water, but their main interaction with the surface is only by dispersion and weak dipolar forces

Most researchers, nevertheless, attribute slow kinetics

to some sort of diffusion limitation This is almost certainly true because sorbing molecules are subject to diffusive constraints throughout almost the entire sorption/desorp-tion time course because of the porous nature of particles Diffusion is random movement under the influence of a

concentration gradient (35) Particles are porous by virtue

of their aggregated nature and because the lattice of

individual grains in the aggregate may be fractured

Figure 1 is a conceptualization of a soil or sediment

particle aggregate showing possible diffusion processes

To reach all sorption sites, diffusing molecules must traverse

bulk liquid, the relatively stagnant liquid “film” extending

from the solid surface (film diffusion), pores within the

particle (pore diffusion), and penetrable solid phases (matrix

diffusion) Diffusion coefficients of organic molecules can

be expected to decrease along that same order, but except

for bulk aqueous diffusion, few data are available for relevant

natural particle systems The observed kinetics in any

region of the sorption vs time curve will reflect one or more

of these diffusive constraints, which may act in series or

parallel

The mixing that takes place in most experiments ensures

that bulk liquid or vapor diffusion is not rate-limiting

Likewise, film diffusion is probably not rate-limiting Film

diffusion of inorganic ions is reduced or eliminated with

vigorous mixing (36) Weber and Miller (37) and later Miller

and Pedit (38) concluded that in well-mixed batch systems

film resistance of lindane and nitrobenzene on subsurface

materials was insignificant compared to intraparticle

dif-fusion, but may have been significant for nitrobenzene in

columns (39) Film diffusion is potentially rate-limiting

for the initial fast stage of sorption; but it is not likely to be

important in the long-term phenomena we have been

considering

This leaves pore diffusion and matrix diffusion as likely

rate-limiting steps in slow processes Diffusion in pores

can occur in pore liquids or along pore wall surfaces Liquid

and surface diffusion may act concurrently and are difficult

to distinguish (40, 41) A model of hydrophobic sorption

to mineral surfaces (42) postulates that sorption occurs on

or in “vicinal” watersthe interfacial region consisting of relatively ordered sorbed water moleculessrather than on the bare surface itself If this model is correct, liquid and surface diffusion practically merge Surface diffusion is

expected to increase in relative importance: (i) in very small

pores where fluids are more ordered and viscous, and where the sorbate spends a greater percentage of time on the

surface; (ii) at high surface concentrations Surface dif-fusion was invoked for porous resins (43) and activated carbon (44, 45) because intraparticle transport appeared

to be faster than could be accounted for by liquid diffusion

A surface diffusion model was used to simulate

sorption-desorption of lindane with some success (38) However,

it has been argued that surface diffusion is insignificant on soil particles because of the discontinuity of the adsorbing

surface (33), if not the low mobility of the sorbate itself (46).

Kinetic Behavior Proposed mathematical kinetic

mod-els include first-order, multiple first-order, Langmuir-type second-order (i.e., first-order each in solute and “site”), and various diffusion rate laws The equations and their incorporation into the advection-dispersion model for

solute transport are available in several good reviews (5, 6,

40) All except the diffusion models conceptualize specific

“sites” to/from which molecules may sorb in a first-order fashion Most sorption kinetic models fit the data better

by including an instantaneous, nonkinetic fraction de-scribed by an equilibrium sorption constant None of the models are perfect, although diffusion models are more successful than first-order models when they have been

compared (20, 41) First-order kinetics are easier to apply

to transport and degradation models because they do not require knowledge about particle geometry Fit to a particular rate law does not by itself constitute proof of mechanism Nonmechanistic models have been employed

also Pedit and Miller (41), on considering the inter- and

intraparticle heterogeneity of soil, modeled the months-long uptake of diuron by a stochastic model, which treated

sorbate concentration (Kd) and first-order rate constant as continuously distributed random variables

We call attention to three features of slow sorption kinetics that, if fully explained, could lead to a deeper understanding of the causes of slow sorption First, a single rate constant often does not apply over the entire kinetic

part of the curve (20, 46-48) In the elution of field-aged

residues of atrazine and metolachlor from a soil column,

a model with a single diffusion parameter underestimated desorption at early times and overestimated desorption at

late times (20) Mass transfer coefficients obtained by

modeling elution curves depend on the contaminant

residence time in the columnsi.e., the flow rate (49) In

desorption studies, plots of the logarithm of fraction remaining vs time tend to show a progressive decrease in slope, indicating greater and greater resistance to desorption

(47) Hence, desorption in natural particles seems to be, kinetically speaking, a continuum On considering that

soil may be a continuum of compartments ordered by their

desorption rate constants, Connaughton et al (47) modeled

the increasing desorption resistance of naphthalene by assuming that the rate constant is distributed according to

a statistical Γ density function, itself having two parameters The intrinsic heterogeneity of soils on many levelsse.g., polydisperse primary and secondary particles, a wide range

FIGURE 1 Schematic of a soil particle aggregate showing the

different diffusion processes Natural “particles” are usually

aggregates of smaller grains cemented together by organic or

inorganic materials Porosity is due to spaces between grains and

fissures in individual grains.

of pore sizes, and spatial variations of mineral and organic

components on the micro-scale, etc.sis fully compatible

with continuous kinetics An underlying problem in

studying slow sorption is that we are never dealing with a

homogeneous sorption/diffusion medium

Second, the slow fraction (Ssl) is inversely dependent,

often markedly, on the initial applied concentration, Co

(14, 46, 50-52), meaning that it assumes greater importance

at lower concentration Equilibrium considerations alone

may partly explain this: when the sorption isotherm is

nonlinearsthat is, when N in the Freundlich equation (Cs

) KFCaN , where Cs and Ca are the sorbed and aqueous

concentrations), is less than unitysintraparticle retardation

will increase as the concentration inside the particle declines

(38, 46, 48) However, in some studies it appears that the

concentration dependence is steeper than expected based

on equilibrium nonlinearity In studies of TCE vapor

sorption to various porous particles at 100% relative

humidity, Farrell and Reinhard (46) showed that the slow

fraction remaining after N2 gas desorption was highly

concentration-dependent and not well simulated by

con-sidering only equilibrium nonlinearity In batch

experi-ments of a soil containing 1.26% OC (50), an empirical

nonlinear expression was used to relate “slow fraction”

(amount remaining after desorption to infinite dilution for

5 d) to initial concentration (Ssl∝Con ) The exponent n

was found to be 0.90 for PCE, 0.73 for

1,2-dibromo-3-chloropropane, and 0.49 for TCE The isotherm of TCE in

the same soil was linear (N ) 1.01) (53) While the

Freundlich parameters were not measured for the other

two compounds, experience shows (25, 53, 54) that such

compounds give linear or slightly nonlinear isotherms (N

> ∼0.9) in soils that have a substantial amount of NOM

Thus, for TCE at least, the concentration dependence of

the slow fraction is greater than the fast fraction In a study

of metolachlor and 1,3-dichlorobenzene in two soils (55),

N was greater for sorption of a fast fraction (1 d contact

time) than a slower fraction (the difference between 30 and

1 d contact times) This means that the slower fraction

becomes increasingly dominant as the total concentration

declines

Third, sorption is often kinetically hysteretic, meaning

that the slow state appears to fill faster than it empties

Further research must be done to validate this Many

examples exist of apparent “irreversible” sorption of some

fractionsor at least exceedingly long times to achieve

desorptionsfollowing relatively short contact times (1, 5,

15, 56-59) Hysteresis may be caused by experimental

artifacts or degradation (1, 5, 56) Also, to fairly assess

hysteresis from the desorptive direction requires that

samples be at true equilibrium

Kan and co-workers (15) sorbed naphthalene and

phenanthrene to a sediment (0.27% NOM) While uptake

appeared to reach equilibrium in a few days, successive

desorption stepssusually lasting 1-7 d and totalling as

long as 178 dsreleased less than 40% of chemical, even

from samples sorbed for only 1 d (Table 1) Good mass

balance was obtained upon soil extraction with CH2Cl2at

45°C Miller and Pedit (38) examined sorption of lindane

to a subsurface soil corrected for dehydrohalogenation

reactions They found that an intraparticle diffusion model,

whose parameters were obtained from uptake, could

account for most but not all of the hysteresis observed upon

sequential desorption We note that the sorbed

concen-trations declined by only 2- or 3-fold after the three-step

desorption, and the model fit seems to worsen with step Had further steps been performed to uncover more resistant fractions, it is possible that even less of the hysteresis would

have been accounted for Harmon and Roberts (48) found

the effective diffusion coefficient of PCE in aquifer sediment

to be 2-4 times smaller in the desorptive direction They cautioned that the sorptive diffusion coefficients were obtained by others using a different technique Inspection

of their data reveals that the tail end of the desorption curves tends to flatten out, indicating a substantial fraction of PCE (∼20% of initital) that is overpredicted by the model, i.e., desorbs at a much slower rate

The above three features of slow sorption suggest but

do not prove a departure from regular Fickian diffusion Fickian diffusion is symmetrical with respect to sorption and desorption, and the diffusion coefficient is concentra-tion-independent provided the sorbate does not alter the

sorbent properties (35) Further careful experiments are

needed to confirm whether sorption in soils truly deviates from Fickian diffusion If it does, one implication is that the making/breaking of bonds may play a role along with molecular diffusion in sorption/desorption rate limitations, even for classically “noninteracting” compounds like aromatic hydrocarbons and chlorinated solvents The behaviors above are in large measure a signature of sorption

to sites having a distribution of energies If interaction with an array of sites is responsible for sorption in the slow

state the following might be expected: (i) a distribution of

desorption rate constants corresponding to a distribution

of activation energies; (ii) inverse concentration

depen-dence of the slow fractionsat low applied concentration, the higher energy sites (which are more important relative

to the fast state) are populated preferentially; and (iii) kinetic

hysteresis since the activation energy of desorption is normally greater than that of sorption from/to a specific site

We may better understand the meaning of these observations in the context of the two models that have been put forth as the most likely causes of slow sorption

in natural particles: the organic matter diffusion model (OMD) and the sorption-retarded pore diffusion model (SRPD) They are shown pictorially in Figure 2 and are discussed below

Organic Matter Diffusion The OMD model postulates

diffusion through NOM solids as the rate-limiting step (5,

21) This is intuitively satisfying given the abundant

thermodynamic evidence that partitioning (dissolution) in NOM is the primary mechanism of sorption when NOM

and water are sufficiently abundant (54) NOM can exist

as surface coatings or discreet particles Supporting the OMD mechanism are the following: (1) inverse correlations

between mass transfer parameters and NOM content (20,

28, 50, 60, 61); (2) organic cosolvents increase the rate in

accord with their ability to ‘swell’ NOM (62); (3) inverse

linear free energy correlations between rate constant and

Kd or the octanol-water partition coefficient Kow(3, 21,

22); and (4) a decrease in rate for polar molecules capable

of hydrogen bonding to acceptor groups within NOM (22).

Yet these results are also consistent with SRPD if the active sorbent material in pores is taken to be NOM coatings on pore walls Moreover, OMD is at odds with the observation

of slow sorption in zero or extremely low NOM materials

(33, 46, 63).

We may ask: Are diffusion length scales and diffusion

coefficients (D) in natural particles consistent with NOM

as the diffusive medium? Desorption of resistant

field-aged pesticides (EDB, atrazine, metolachlor) in soil show

little particle size dependence down to the clay-size fraction

(20, 25), suggesting that the upper limit diffusion length

scale is on the order of the clay particles (103-102nm) If

a single effective diffusivity (Deff) applies over this radial

length, Deffwould equal∼10-17cm2/s or less Desorption

of PCBs from river sediments (28) also showed no particle

size effects and indicated diffusion length scales of ∼30

nm, corresponding to Deffof 10-20-10-21cm2/s The true

dimensions of NOM are essentially unknown, but

thick-nesses of 30-1000 nm are not unreasonable for NOM

coatings or discreet NOM particles

In regard to Deffvalues, the obvious analogy to NOM is

synthetic organic polymers The polymer-phase concept

of humics is replete in the literature Diffusion in polymers

occurs by either a place change mechanism, in which

movement is accomplished by cooperative interchange of

position of polymer segments and the penetrating molecule,

or by a defect mechanism where the penetrant may jump

between lattice defects, voids, pores, etc (64) Polymers

are said to have glassy (condensed, rigid) or rubbery (expanded, flexible) structures with respect to the order and cohesive forces of the polymer chains Likewise, humic substances are described as having condensed and

ex-panded regions (65).

Choosing a polymer to model NOM is difficult because NOM in situ is expected to be highly variable in its properties, even within the same contiguous material Furthermore, structure of and sorption to NOM can be

strongly affected by soil minerals (66, 67) Attempts have

been made to estimate the cohesive forces holding the humic polymer chains together in relation to their effects

on the diffusivity and solubility of sorbate molecules (28).

The true valuesswere it possible to determine themsare

likely to cover a wide range Reported D values in polymers

at 25-30°C for a molecule like CCl4having a diameter of 0.55 nm range over many orders of magnitude, from 10-7

cm2/s in rubbery polymers (polyethylene) to 10-17cm2/s

in glassy polymers (polyvinyl chloride) (64, 68) Diffusivity

is sensitive to the size and shape of the penetrant, much more so for glassy than rubbery polymers One might expect a molecule to experience large changes in diffusivity

as it moves between expanded and condensed regions of

NOM Accordingly, Carroll et al (28) suggest that the

bimodal desorption vs time curves of PCBs from sediments are due to desorption from these two types of phases Future work is needed on determining organic compound diffu-sivities in NOM particles and on finding appropriate polymer models

Diffusion kinetics in polymers is widely variable de-pending on polymer structure, particle size distribution, diffusant structure, diffusant concentration, temperature,

and the history of exposure (64, 69, 70) Mixtures of polymer sphere sizes can lead to bimodal diffusion curves (71, 72).

Since the diffusion rate is inversely related to the square of the radius, the proportion of fast and slow phases of the uptake or release curve depends on the size distribution Obviously, the dimensions of NOM in a given soil will be truly diverse

Relatively high diffusant concentrations can cause polymer swelling or crazing as the diffusant front advances

(69) These changes affect both the compound’s solubility

(partition coefficient) and diffusivity, which in turn dictate the shape of the kinetic curve Bimodal curves can result Pollutant concentrations in the environment may some-times be high enough (e.g., a chemical spill) to swell or soften NOM Cosolvents can do the same thing Methanol cosolvent increased the desorption rate constant of diuron

and several PAHs (62).

Usually though, we are dealing with dilute contaminant and no cosolvent Sorption under dilute conditions in rubbery polymers generally is linear and obeys Fick’s

lawsthat is, D is concentration-independent, and mass

transfer is symmetrical with respect to the forward and reverse directions and proportional to the square root of

time (64, 69, 73) Sorption in glassy polymers on the other hand is anomalous in that it is typified by nonlinear (N < 1) isotherms, concentration-dependent D, and a tendency

toward bimodal kinetics and sorption-desorption

hyster-esis (64, 68, 70, 72) This is reminiscent of sorption/diffusion

behavior of many compounds in soils

Anomalous behavior in glassy polymers has been attributed to dual-mode sorption This was first proposed

FIGURE 2 Schematic of two models for slow sorption (a) Organic

matter diffusion (OMD), illustrating diffusion through a rubbery phase

A, diffusion through a more condensed glassy phase B, and adsorption

in a “Langmuir site” C (see text) (b) Sorption-retarded pore diffusion

(SRPD) Retardation by rapid-reversible sorption to pore walls, and

“enhanced adsorption” in pores of very small diameter due to

interaction with more than one surface.

for gaseous molecules like CO2and CH4(70) and later for

small organic molecules (68, 71, 72) Dual-mode sorption

is the sum of (a) normal linear partitioning taking place in

the bulk of the polymer and (b) a hole-filling mechanism

in which the incoming molecules undergo Langmuir-like

adsorption in voids internal to the polymer matrix The

latter is the cause of isotherm nonlinearity and non-Fickian

tendencies Linear sorption can be restored by conversion

of the glassy state to the rubbery state by increasing the

temperature above the glass transition point (Tg) or by

softening with organic solvents The exact nature of the

voids is presently unknown Solid-state31P-nuclear

mag-netic resonance spectroscopy showed that mobile and

immobile sorbed forms of tri-n-butyl phosphate exist in

glassy polystyrene (74) The relative mobility of the

immobile forms appeared to span a wide range

Dual-mode sorption in NOM may rationalize

qualita-tively some behaviors of contaminants in natural

parti-clessnamely, nonlinear isotherms, competitive sorption,

and kinetic hysteresis Isotherms are often nonlinear when

a sufficiently wide solute concentration range is used (37,

39, 55, 75-77) Examples include hydrophobic compounds

in a peat soil composed almost entirely (93%) of NOM (55).

It might be expected that isotherms would linearize at high

concentrations as the adsorption sites became filled, but

this would depend on how the sites were distributed in

energy Investigators have also shown competitive sorption

between nonpolar compounds in suspensions of soils (53,

76), the mentioned peat (53), and humic-coated clay (66).

Competitive sorption clearly indicates some measure of

site specificity (53, 76).

As shown in Figure 2, we may envision NOM as a bulk

partition medium consisting of rubbery (A) and glassy (B)

regions Dispersed in the glassy regions are adsorption

sites (C) of various energies, analogous to the voids of glassy

polymers In agreement with the dual-mode model,

phenanthrene isotherms became more linear with

increas-ing temperature in soil and shale samples where NOM was

believed to be the predominant sorbent (75) This is

consistent with a transition to a more rubbery state The

nature of the adsorption sites is speculative They could

be some type of inclusion complex between the guest

pollutant molecule and host subunit(s) on the NOM

macromolecule Soil humic acid has condensed

polyaro-matic regions, even after extraction and reconstitution to

a particulate form (78, 79) It has been suggested that

polyaromatic structures provide adsorption sites (75).

Although it is far from certain at this time that the

dual-mode mechanism plays a role in slow kinetics, the

aforementioned results of ours (55), showing a decrease in

the Freundlich exponent N with time in NOM, are at least

consistent with it The existence of high-energy adsorption

sites could account for kinetic hysteresis It might be

expected that such sites would fill faster than they would

empty Thus, it is plausible that desorption becomes at

some point rate limited by release from these sites, while

sorption is principally rate limited by diffusion through

bulk NOM The nonlinear relationship between Ssland Co

discussed above is also plausibly attributed to the presence

of sites

Sorption-Retarded Pore Diffusion The SRPD model

(Figure 2) postulates the rate-limiting process to be

mo-lecular diffusion in pore water that is retarded,

chromato-graphic-like, by local sorption on pore walls (80) (Figure 2).

Walls may or may not be composed of NOM Assumptions

by most modelers are that local sorption is instantaneous, particles are uniformly porous, and sorption parameters

Kdand Deffin the pore are constant According to the SRPD model, rates are expected to be inversely dependent on the square of the particle radius, on the tortuosity of pores (bending and twisting, interconnectivity, presence of dead-end pores), on the constrictivity (steric hindrance) in the

pores, and on the Kd The inverse dependence on Kddoes not distinguish SRPD from OMD

For natural particles, observations that point to SRPD include faster rates after particle pulverization, which

reduces pore path length (25, 33, 50), and after acidification,

which was suggested to disagregate grains by dissolving the inorganic oxide cements that hold the aggregates

together (50) Correlation of rate with particle size is only

qualitative at best In one case where a rough correlation

was found (80), experiments took place over a few hours

at most In another case (33) where coarse aquifer sand

particles equilibrated PCE and TeCB generally faster than fine particles, the particles were calcite-cemented ag-gregates that had considerable internal porosity and surface

area (81) In many systems, the particle size dependence

of desorption is altogether absent (20, 25, 28, 46, 82) For example, desorption of field-aged pesticides in soil (20, 25) and PCBs in river sediments (28) was not related to the

nominal particle radius down to the clay size fraction, suggesting that the length scale of diffusion is proabably less than 100 nm The absence of size dependence might

be rationalized by assuming that most of the porosity exists

in an outer shell that is of similar thickness among size fractions Another possible reason is that sorption capacity may not be uniformly distributed within the aggregate Ball

and Roberts (33), for example, found that Kdof PCE and TeCB varied markedly among different size fractions and

a magnetically separated fraction of an aquifer material But in a study of desorption of TCE from silica with monodisperse particle sizes and narrow pore size

distribu-tions, investigators found no particle size dependence (46).

Tortuosity and constrictivity are difficult to evaluate Both are expected to vary inversely with pore size However,

in a silica pore, diameters ranging from 6 to 30 nm had

little effect on TCE desorption (46) It is possible that this

effect shows up only in pores that are smaller than 6 nm The analytical tools for measuring nanopore characteristics

in natural materials are undeveloped, and the theoretical foundations are too weak to incorporate them into the SRPD

model (33, 46, 48) Thus, research is needed on

character-izing the geometry and spatial distribution of pores The kinetic continuum discussed earlier could be rationalized

by a heterogeneous pore structure in which there is a distribution of diffusivities within the particle Thus, we may envision pores that fill and empty quickly, along with those that do so slowly

A potentially important influence on constrictivity in the pore is the viscosity of water Polar minerals have one

or more layers of water strongly sorbed on their surfaces

(83) Viscosity measurements of colloidal silica particles

in water indicate there is a monolayer more or less

immobilized on the surface (84) The water contained in

a pore of a few Angstroms in diameter may be ice-like and therefore greatly restrict solute diffusion Molecular mod-eling can potentially give insight on the structure of water

in nanopores

The long-term desorption of EDB from soil to water could not be modeled by SRPD without invoking enormous

tortuosity or constriction in pores (25) Likewise, Deff’s for

desorption of alkanes and PAHs from urban atmospheric

particles were 106times smaller than expected for sorption

retarded gaseous diffusion in pores (3) One rationale is

afforded by rejecting the SRPD assumption of instantaneous

local equilibrium in the pore For instance, a PCB required

hours to desorb from dissolved commercial humic acid

(85) From the standpoint of solutes, dissolved humic acid

macromolecules may well represent the smallest or most

penetrable humic materials existing on wall surfaces Also,

substituted benzenes required hours to desorb from

surfaces of alkyl-modified, nonporous silica gel particles

(86) Such slow stepwise desorption rates could strongly

retard transport through a pore compared to the

instan-taneous case The mathematics of diffusion in systems

containing one diffusive medium in another have been

discussed (35).

An alternative explanation for the extraordinarily small

Deffhas been offerred (46, 87) According to this enhanced

adsorption hypothesis, as the pore size decreases to roughly

the adsorbate diameter, the calculated interaction potential

increases up to 5-fold compared to the single surface case

owing to multipoint interaction of the adsorbate with pore

walls (Figure 2) Furthermore, since the pore volume is

small compared to the wall surface area, the adsorbate

spends less and less time in pore solution, ultimately being

restricted to diffusion along the surface, which may be

intrinsically slower Farrell and Reinhard (46, 87)

equili-brated TCE vapors with a column of porous silica particles

at 100% relative humidity where all micropores are expected

to be filled with water Desorption with a stream of

humidified N2proceeded in two distinct phases and was

incomplete after purging times lasting weeks The silicas

behaved similarly to natural sorbents in that (1) the diffusion

length scale was not the nominal particle radius and (2) the

slow fraction was less than linearly related to initial TCE

concentration, which was attributed to a limited sorption

capacity in high-energy micropore sites The authors

suggest that microporosity gives rise to both isotherm

nonlinearitysindicative of a distribution of site

ener-giessand slow desorption Here again, we see the

con-sequences of energetic heterogeneity in the sorbent that

was referred to earlier in a general sense and in the context

of OMD Caution is certainly called for in interpreting these

experiments Condensation of TCE in pores during the

equilibration period cannot be ruled out since vapor

concentrations were close to saturation Removal of TCE

in a condensed phase from a pore may be slower In

apparent contradiction of enhanced adsorption is the fact

that diffusion of small molecules through the micropores

(5-7 Å) of synthetic aluminosilicate zeolites is remarkably

faststhe time to reach equilibrium of small molecules like

hexane (88) and TCE (89) in micron-size particles being on

the order of 102min (D∼ 10-12cm2/s)

A form of pore diffusion that deserves more attention

is clay interlayer diffusion Hydrated metal ion-exchanged

clays (e.g., with Ca2+) do not extensively sorb hydrophobic

molecules, but neither are such compounds excluded from

hydrated interlayer spaces Na-montmorillonite in water

exhibited uptake of TCE lasting over 25 d (90) Desorption

of atrazine from some Ca2+-smectites revealed formation

of a tightly bound fraction (91) Smectites exchanged with

tetraorganoammonium cations have a much higher affinity

for hydrophobic compounds (ref 92 and references therein),

but their kinetics have not been studied Some evidence

suggests that clay interlayers are not important Mont-morillonite formed a much smaller fraction of slowly released TCE than either silica or microporous glass beads

(46) Steinberg et al (25) observed the lowest field residues

of EDB in the clay size fraction

Concluding Remarks Regarding Mechanism It is quite

likely that both OMD and SRPD mechanisms operate in the environment, often probably together in the same particle OMD may predominate in soils that are high in NOM and low in aggregation, while SRPD may predominate

in soils where the opposite conditions exist But this has not been established Slow desorption from an organic-free silica, a substance so closely related to soil minerals,

is strong evidence that the mineral fraction is important Resolving the individual contributions of OMD and SRPD

in natural materials constitutes a challenge to future investigators We have seen that both mechanisms offer the potential for high-energy adsorption sites to play a role These sites may be more rate-limiting in the desorptive direction than the sorptive direction Further research is critical in this area Evidence indicates that a decrease in the rate constant occurs with increasing molecular size and hydrophobicity However, this is consistent with all of the mechanisms discussed

Significance of Slow Sorption Mechanism to Bioavailability and Remediation

The bioavailability of chemicals in soil to microbes, plants, and animals is important from the perspective of reme-diation and risk assessment Ex situ or in situ cleanup of soil requires mass transport of contaminants through the materials, which in turn depends on sorption kinetics Microbes take up substrates far more readily from the

fluid than the sorbed states (89, 93-96) Thus, it is no

surprise that aged chemicals are resistant to degradation

compared to freshly added chemicals (25, 27, 97, 98) and

that degradation of freshly added chemicals often tails off

to leave a resistant fraction (26, 98-100) Bioavailability

has been called a major limitation to complete

bioreme-diation of contaminated soils (29, 101). The soil-contaminant-degrader system is dynamic and interde-pendent A mechanistic-based biodegradation model must

be built on the mechanism(s) governing sorption/desorp-tion, in addition to the biological mechanisms governing cell growth and substrate utilization in the matrix A number of groups are now developing

sorption-degrada-tion kinetic models (26, 102-106) Both diffusion and

two-box (equilibrium and first-order kinetic compartments) sorption concepts have been explored

The bioavailability of pollutants to wildlife and humans

is also an area of critical importance Pollutants can be taken up in pore water, by dermal contact, by particle ingestion, or by particle inhalation The dynamics of sorption are not currently incorporated into exposure and risk models for organics Availability in most cases is

assumed to be 100% (107) Recently, the following have

been demonstrated: (1) the time between spiking and

testing affects bioavailability (2, 108); (2) the kinetics of

desorption control bioaccumulation of historical

contami-nation (e.g., PAHs in benthic animals; 109); and (3)

historically contaminated soils are less toxic and/or lead to lower body burdens than equivalent amounts of spiked

soils (110, 111).

In order to model bioavailability, it is crucial that we understand sorption kinetics and the factors that influence

rates under the conditions of exposure Take particle

ingestion, for instance The intestines of warm-blooded

animals are often at higher temperature than the soil being

ingested Molecular diffusion through a viscous medium

like NOM and desorption from a surface are activated

processes and hence temperature sensitive For example,

the apparent activation enthalpy for desorption of historical

residues of EDB from soil into water was 66 kJ/mol,

corresponding to a 7-fold rate increase from 25 to 40 °C

(25) The application of heat increased the rate of

desorp-tion of PCBs from river sediment and reduced the resistant

fraction (28) Also, there is evidence that pH is important.

Acidification of a soil suspension to pH <∼2 accelerated

desorption of the slow-desorbing fraction of several

ha-logenated aliphatic hydrocarbons The amounts desorbed

in 1 h ranged from 13 to 80% of the slow fraction (50), many

times more than the control at natural pH The human

stomach can be highly acidic (pH 1.5-2) at times (112).

Soil ingested by birds is subjected to grinding in the gizzard,

which may release slow-desorbing contaminants if pore

diffusion is important Further work is needed to determine

what physiological conditions in both the digestive and

repiratory tracts may impact desorption, and further work

is needed on the design of experiments to accurately

simulate such conditions in the laboratory

Vapor and water extraction methods (pump-and-treat),

which are widely used in remediation, are limited in part

by physical nonequilibrium and sorption nonequilibrium

(113-115) These processes both cause tailing of the

contaminant plume, which increases the time invested and

the volume of sparge air or water needed to achieve cleanup

(113, 115-117) Moreover, they act to resume

contamina-tion if pumping is ceased before all the contaminant is

removed (rebound) (118-120) Ways of experimentally

separating out the contributions of physical and sorption

nonequilibrium must be sought

Experience is proving that the constraint of slow

desorption has to be overcome to achieve complete

remediation (29) We may consider the following

conceiv-able approaches to promoting desorption from the slow

state: (1) addition of biological agents capable of reaching

remote molecules; (2) application of heat; (3) addition of

chemical additives that displace the contaminant or alter

the soil structure; and (4) physical methods that alter the

soil structure

Since cells, being g0.2 µm, are too large to fit in

nanopores or within the NOM matrix, it would seem unlikely

that strains exist which can directly attack remote molecules

Guerin and Boyd (106) isolated a Pseudomonad that,

compared to another degrader, appeared to enhance the

desorption of naphthalene by providing a steep

concentra-tion gradient at the particle surface Some organisms,

especially fungi, metabolize contaminants with extracellular

enzymes Enzymes may also be added to soil to remediate

it However, enzymes are many times larger than

con-taminant molecules and probably diffuse far more slowly,

if at all, through micropores or NOM to reach resistant

molecules Moreover, sorption of enzymes may reduce

their activity (121).

As mentioned, molecular diffusion through NOM and

desorption from high-energy sites are expected to be

strongly temperature dependent Thermal desorption is

already in use in various remediation technologies for

contaminants of sufficient volatility In batch application,

the soil is heated to temperatures ranging from 200 to 500

°C in a primary chamber, and the vapors are combusted

in a secondary chamber (122-124) Steam stripping (a form

of soil vapor extraction) can remove semivolatiles from the

vadose zone (125) Bioremediation in a compost mode

where temperatures reach 60°C or more should prove advantageous The success of these methods requires a fundamental understanding of kinetics Research into sorption kinetics in regard to steam stripping has been

initiated (125).

Alteration of the soil chemistry is another approach that should be considered further based on preliminary studies

As mentioned, acidification promoted desorption (50), but

further work is needed to determine its scope and prac-ticality The use of surfactants targeted specifically to removal of slow fractions has not yet been adequately addressed in the literature To be effective, surfactants must penetrate the intraparticle matrix (nanopores or NOM) to

either (i) solubilize the contaminant by micellization or (ii)

alter the intraparticle properties of the sorbent in such a way as to promote desorption The addition of surfactants

gave mixed results in stimulating biodegradation (95, 126).

The use of organic cosolvents is a promising approach because cosolvents can increase desorption both thermo-dynamically (by enhancing solubility) and kinetically (by

softening NOM) (62) Supercritical carbon dioxide extrac-tion has been proposed for large-scale cleanup (19) It

probably would require up to 10% by weight of a polar organic cosolvent to increase its solvation power This is

an example where an understanding of sorption kinetics would prove beneficial Physical manipulation of the soil

such as grinding is known to be partially effective (25, 33,

50, 63) but would likely be impractical on a large scale.

Summary Remarks

Sorption and especially desorption in natural particles can

be exceedingly slow The rate-limiting nature of sorption has widespread implications but is poorly understood and predicted The importance of it is appreciated by con-sidering that if sorption occurs on time scales of months

or longer, true equilibrium may exist in only limited environments It is hoped that researchers who deal in fate and transport of contaminants are by now more aware

of the phenomenon itself as well as the potential for misinterpretation that can result if kinetics are ignored Slow sorption has made complete remediation difficult However, there have been legitimate questions raised by

some (2, 29, 107) about whether we even need to be

concerned about residues that desorb so slowly and are apparently largely bio-unavailable At a minimum, it is critical that we understand the factors that govern their release Sorption kinetics are extremely important in modeling the transport of contaminants in the subsurface Understanding the causes of slow sorption/desorption has been hampered by the heterogeneity of natural particles

as a sorptive and diffusive medium It is no wonder then that rate parameters seem to depend in a complex way on the soil, history of exposure, and even position along the uptake vs time curve But we can be confident that kinetics studies will lead to a deeper understanding of sorption mechanism itself Future research should focus not only

on understanding and predicting the rates of slow sorption/ desorption but also on overcoming the constraints of slow desorption for remediation purposes

We thank the U.S Department of Agriculture National

Research Initiative (Water Quality) for support and the

reviewers of the manuscript for their suggestions

Literature Cited

(1) Pignatello, J J In Reactions and Movement of Organic Chemicals

in Soil; Sawhney, B L., Brown, K., Eds.; Soil Science Society of

America: Madison, WI, 1989; Chapter 3, pp 45-97.

(2) Alexander, M In Draft Report Environmentally Acceptable

Endpoints in Soil; Gas Research Institute, Environment & Safety

Research Group 1995; Chapter 1.

(3) Rounds, S A.; Tiffany, B A.; Pankow, J F Environ Sci Technol.

1993, 27, 366-377.

(4) Roberts, P V.; Goltz, M N.; Mackay, D M Water Resour Res.

1986, 22, 2047.

(5) Brusseau, M L.; Rao, P S C Crit Rev Environ Control 1989,

19, 33.

(6) van Genuchten, M T.; Wagenet, R J Soil Sci Soc Am J 1989,

53, 1303.

(7) Goltz, M N.; Roberts, P V J Contam Hydrol 1988, 3, 37-63.

(8) Velocchi, A J Water Resour Res 1989, 25, 273-279.

(9) Gaber, H M.; Inskeep, W P.; Comfort, S D.; Wraith, J M Soil

Sci Soc Am J 1995, 59, 60-67.

(10) Pignatello, J J.; Huang, L Q J Environ Qual 1991, 20, 222.

(11) Huang, L Q.; Pignatello, J J J Assoc Off Anal Chem 1990, 73,

443.

(12) Sawhney, B L.; Pignatello, J J.; Steinberg, S M J Environ Qual.

1988, 17, 149.

(13) Pignatello, J J Environ Toxicol Chem 1990, 9, 1107.

(14) Steinberg, S Chemosphere 1992, 24, 1301-1315.

(15) Kan, A T.; Fu, G.; Tomson, M B Environ Sci Technol 1994,

28, 859-867.

(16) Karickhoff, S W In Contaminants and Sediments, Vol 2; Baker,

R A., Ed.; Ann Arbor Science: Ann Arbor, MI, 1980; pp 193-205.

(17) Eischenback, A.; Kaestner, M.; Bierl, R.; Schaefer, G.; Mahro, B.

Chemosphere 1994, 28, 683-692.

(18) Koskinen, W C.; Cheng, H H.; Jarvis, L E J.; Sorenson, B A Int.

J Environ Anal Chem 1994, 58, 379-385.

(19) Laitinen, A.; Michaux, A.; Aaltonen, O Environ Technol 1994,

15, 715-727.

(20) Pignatello, J J.; Ferrandino, F J.; Huang, L Q Environ Sci.

Technol 1993, 27, 1563-1571.

(21) Brusseau, M L.; Jessup, R E.; Rao, P S C Environ Sci Technol.

1991, 25, 134.

(22) Brusseau, M L.; Rao, P S C Environ Sci Technol 1991, 25,

1501.

(23) Pignatello, J J.; Frink, C R.; Marin, P A.; Droste, E X J Contam.

Hydrol 1990, 5, 195.

(24) Alexander, M Biodegradation and Bioremediation; Academic

Press: New York, 1994; Chapters 10 and 11.

(25) Steinberg, S M.; Pignatello, J J.; Sawhney, B L Environ Sci.

Technol 1987, 21, 1201.

(26) Hatzinger, P B.; Alexander, M Environ Sci Technol 1995, 29,

537-545.

(27) Scribner, S L.; Benzing, T R.; Sun, S.; Boyd, S J Environ Qual.

1992, 21, 115.

(28) Carroll, K M.; Harkness, M R.; Bracco, A A.; Balcarcel, R R.

Environ Sci Technol 1994, 28, 253-258.

(29) Loehr, R C.; Webster, M T In Draft Report Environmentally

Acceptable Endpoints in Soil; Gas Research Institute,

Environ-ment & Safety Research Group: 1995; Chapter 2.

(30) Jaynes, D B Soil Sci Soc Am J 1991, 55, 658-664.

(31) March, J Advanced Organic Chemistry, 3rd ed.; John Wiley &

Sons: New York, 1985; Chapter 3.

(32) Adamson, A W The Physical Chemistry of Surfaces; John Wiley

& Sons: New York, 1976.

(33) Ball, W P.; Roberts, P V Environ Sci Technol 1991, 25, 1237.

(34) Pavlostathis, S G.; Jaglal, K., J Environ Sci Technol 1991, 25,

274.

(35) Crank, J The Mathematics of Diffusion; Oxford University Press:

Oxford, United Kingdom, 1975.

(36) Sparks, D L Kinetics of Soil Chemical Processes; Academic

Press: San Diego, CA, 1989.

(37) Weber, W J.; Miller, C T Water Res 1988, 22, 457-464.

(38) Miller, C T.; Pedit, J A Environ Sci Technol 1992, 26, 1417.

(39) Miller, C T.; Weber, W J Water Res 1988, 22, 465-474.

(40) Weber, W J J.; McGinley, P M.; Katz, L E Water Res 1991, 25,

499.

(41) Pedit, J A.; Miller, C T Environ Sci Technol 1994, 28,

2094-2104.

(42) Schwarzenbach, R P.; Gschwend, P M.; Imboden, D M.

Environmental Organic Chemistry: John Wiley & Sons: New York,

1993; Chapter 11.

(43) Komiyama, H.; Smith, J M Am Inst Chem Eng J 1974, 20,

728-734.

(44) Crittenden, J C.; Weber, W J Jr J Environ Eng Div (Am Soc.

Civ Eng.) 1978, 104, 185-197.

(45) Critenden, J C.; Hand, D W.; Arora, H.; Lykins, B W J Am.

Water Works Assoc 1987, 79, 74-84.

(46) Farrell, J.; Reinhard, M Environ Sci Technol 1994, 28, 63-72.

(47) Connaughton, D F.; Stedinger, J R.; Lion, L W.; Shuler, M L.

Environ Sci Technol 1993, 27, 2397-2403.

(48) Harmon, T C.; Roberts, P V Environ Sci Technol 1994, 28,

1650-1660.

(49) Brusseau, M L J Contam Hydrol 1992, 9, 353.

(50) Pignatello, J J Environ Toxicol Chem 1990, 9, 1117 (51) Grathwohl, P.; Reinhard, M Environ Sci Technol 1993, 27,

2360-2366.

(52) Burris, D R.; Antworth, C P.; Stauffer, T B Environ Toxicol.

Chem 1991, 10, 433.

(53) Pignatello, J J In Organic substances and Sediments in Water

Vol 1; Baker, R A., Ed.; Lewis Publishers: Chelsea, MI, 1991; pp

291-307.

(54) Chiou, C T In Reactions and Movement of Organic Chemicals

in Soil; Sawhney, B L., Brown, K., Eds.; Soil Science Society of

America, Madison, WI, 1989; Chapter 1, pp 1-29.

(55) Xing, B.; Pignatello, J J ACS Environ Chem Div Proc 1995, 35

(1), 432-435.

(56) Rao, P S C.; Davidson, J M In Environmental Impact of Nonpoint

Source Pollution; Overcash, M R., Davidson, J M., Eds.; Ann

Arbor Science Publishers: Ann Arbor, MI, 1980; pp 23-67.

(57) Pignatello, J J Environ Toxicol Chem 1991, 10, 1399 (58) Di Toro, D M.; Horzempa, L M Environ Sci Technol 1982, 16,

594.

(59) Fu, G.; Kan, A T.; Tomson, M Environ Toxicol Chem 1994, 13,

1559-1567.

(60) Nkedi-Kizza, P.; Brusseau, M L.; Rao, P S C.; Hornsby, A G.

Environ Sci Technol 1989, 23, 814.

(61) Karickhoff, S W.; Morris, K R Environ Toxicol Chem 1985, 4,

469.

(62) Brusseau, M L.; Wood, A L.; Rao, P S C Environ Sci Technol.

1991, 25, 903.

(63) Ball, W P.; Roberts, P V Environ Sci Technol 1991, 25,

1223-1237.

(64) Rogers, C E In The Physics and Chemistry of the Organic Solid

State; Interscience Publishers: New York, 1965; Vol 2, pp

509-634.

(65) Hayes, M H B.; Himes, F L In Interaction of Soil Minerals with

Natural Organics and Microbes; Huang, P M., Schnitzer, M.,

Eds.; Soil Science Society of America: Madison, WI, 1986; p 103 (66) Murphy, E M.; Zachara, J M.; Smith, S C.; Phillips, J L.; Wietsma,

T W Environ Sci Technol 1994, 28, 1291-1299.

(67) Laird, D A.; Yen, P Y.; Koskinen, W C.; Steinheimer, T R.; Dowdy,

R H Environ Sci Technol 1994, 28, 1054-1061.

(68) Berens, A R Makromol Chem Macromol Symp 1989, 29,

95-108.

(69) Koenig, J L In Physical Properties of Polymers, 2nd ed.; Mark J.

E., et al., Eds.; American Chemical Society: Washington, DC, 1993; Chapter 6, pp 263-312.

(70) Vieth, W R Diffusion In and Through Polymers; Hanser Verlag:

Munich, 1991 (distributed in U.S and Canada by Oxford University Press, New York).

(71) Berens, A R Polymer 1977, 18, 697-704.

(72) Berens, A R J Membr Sci 1978, 3, 247-264.

(73) Reynolds, G W.; Hoff, J T.; Gillham, R W Environ Sci Technol.

1990, 24, 135-142.

(74) Toscano, P J.; Frisch, H L J Polym Sci 1991, 29, 1219-1221 (75) Young, T M.; Weber, W J., Jr Environ Sci Technol 1995, 29,

92-97.

(76) McGinley, P M.; Katz, L E.; Weber, W J., Jr Environ Sci Technol.

1993, 27, 1524-1531.

(77) Spurlock, F C.; Huang, K.; Van Genuchten, M Th Environ Sci.

Technol 1995, 29, 1000-1007.

(78) Chen, Z.; Pawluk, S Geoderma 1995, 65, 173-193.

(79) Schnitzer, M.; Kodama, H.; Ripmeester, J A Soil Sci Soc Am J.

1991, 55×e2 745-750.

(80) Wu, S.; Gschwend, P M Environ Sci Technol 1986, 20, 717.

(81) Ball, W P.; Buehler, C H.; Harmon, T C.; Mackay, D M.; Roberts,

P V J Contam Hydrol 1990, 5, 253-295.

(82) Novak, J M.; Moorman, T B.; Karlen, D L J Agric Food Chem.

1994, 42, 1809-1812.

(83) Drost-Hansen, W J Colloid Interface Sci 1977, 58, 251 (84) Dalton, R L.; Iler, R K J Phys Chem 1956, 60, 955