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Published online 29 October 2007
Published in Soil Sci Soc Am J 71:1813-1821 (2007)
DOI: 10.2136/sssaj2007.0082
© 2007 Soil Science Society of America
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SOIL PHYSICS

Sorption of Trichloroethylene in Humic Acid Studied by Experimental Investigations and Molecular Dynamics Simulations

Yang-hsin Shih*

Department of Soil and Environmental Sciences, Center of Nanoscience and Technology, National Chung Hsing Univ., 250, Kuo-Kuang Rd., Taichung 402, Taiwan, R.O.C

* Corresponding author (yhs{at}nchu.edu.tw).


   ABSTRACT
TOP
 NOTES
 ABSTRACT
INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Gas transport of volatile organic compounds through soils is important for understanding the fate of these organic compounds. Soil organic matter plays a key role in the transport of organic compounds in soils; however, studies have not been performed at the molecular level. A gravimetric experimental method and a computer simulation method were used to study the sorption–desorption of organic contaminants in humic substances. The average apparent diffusivities of trichloroethylene (TCE) in soil humic acid are 1.1 x 10–8 cm2/s for sorption and 3.0 x 10–9 cm2/s for desorption. The activation energies are 29.3 and 59.5 kJ/mol for sorption and desorption, respectively. The molecular simulation results of the kinetics and the activated energy of TCE sorption in humic acid are in good agreement with the experimental data. Both results indicate that the sorption rate of TCE to humic acid increases with the environmental temperature. The sorption of TCE into humic acid is mainly diffusion controlled. Molecular dynamics of chlorinated volatile organic compounds in natural humic substances does yield meaningful results, which can help with understanding the sorption mechanism of organic chemicals in soils at the molecular level.

Abbreviations: MD, molecular dynamics • TCE, trichloroethylene • VOC, volatile organic compound


   INTRODUCTION
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Sorption processes play an important role in the fate of organic contaminants in soils and contribute to the complexity of contaminant transport problems in the environment. The sorption–desorption kinetics limits the efficiency of soil and groundwater remediation as well as the bioavailability of organic contaminants (Carmichael et al., 1997; Karapanagioti et al., 2001). Slow sorption–desorption rates can be attributed to diffusion through the meso- and micropore spaces (Steinberg et al., 1987; Ball and Roberts, 1991; Grathwohl and Reinhard, 1993; Farrell and Reinhard, 1994; Pignatello and Xing, 1996; Werth et al., 2000) and diffusion in soil organic matter (Huang and Weber, 1997; Rounds et al., 1993), or a combination of these processes (Luthy et al., 1997; Shor et al., 2003; Kleineidam et al., 2004).

Knowledge of the sorption behavior of volatile organic compounds (VOCs) in soil humic substances is vital to predicting their fate and transport in soils. Shih and Wu (2005) indicated that the sorption rates of one monoaromatic compound with soil humic substances are slower than those with soil inorganic matter. Sorption to humic substances is thought to contribute to the irreversible retention of xenobiotic compounds. Schlebaum et al. (1998) suggested that the nonlabile fraction of pentachlorobenzene can be attributed to the binding of this chlorinated compound with the humic acid structure. Aochi and Farmer (1997) found that sorbed 1,2-dichloroethane in humic acid was strongly retained. Trichloroethylene (TCE) is currently an environmental contaminant of great concern because it is toxic, volatile, and carcinogenic, and widespread in contaminated soils and groundwater. Characterization of humic acid–TCE interactions with respect to sorption kinetics and thermodynamics is important to assessments of the fate of TCE in the environment.

The sorption kinetics of VOCs with different types of environmental sorbents has been examined (Ball and Roberts, 1991; Grathwohl and Reinhard, 1993; Piatt and Brusseau, 1998; Wu and Gschwend, 1986; Chang et al., 1997; Shih and Wu, 2002a,b, 2004, 2005; Kim et al., 2005). These studies focused on measuring the rates of sorption and diffusion in complex soil aggregates or soil humic substances at large length scales. Different rate models have been used to simulate contaminant uptake and release on a macroscopic scale. The mechanism controlling sorption dynamics still remains unclear due to the difficulty in observing its dynamic behavior at the microscopic level (Brusseau and Rao, 1989).

Due to the development of fundamental physical theories and their applications with numerical simulation techniques, molecular modeling techniques have been applied to environmental issues. Several studies have been performed using computer-aided molecular modeling techniques to understand environmental phenomena such as the persistence of pesticides in mammals (Vetter and Scherer, 1999), the sorption mechanisms of organic chemicals adsorbed onto clays and minerals (Kubicki et al., 1997; Teppen et al., 1998; Boyd et al., 2001; Farrell et al., 2002; Luo and Farrell, 2003), and the interactions of contaminants with natural organic matter (Kubicki and Apitz, 1999).

Molecular dynamics (MD), one of the molecular simulation methods, based on interatomic interactions, can be very useful for understanding the dynamic behavior and transport mechanism of chemicals in solids. Several studies have applied this method to obtain new insights into transport mechanisms in organo-clay (Zeng et al., 2004), polymers (Theodorou, 1996; Li et al., 1997), and membranes (Takaba et al., 1997). To our knowledge, however, there is very little research to combine experimental and molecular modeling works involved in sorption kinetics and thermodynamics study of organic contaminants in humic substances.

Therefore, in this work we studied the sorption–desorption kinetics of TCE with soil humic acid using a microbalance for rate measurements. A molecular dynamics simulation technique was intended to estimate the sorption kinetics of TCE in a humic acid matrix. By comparing the experimental and computational data, the predication capacity of MD simulation was examined. The thermodynamic properties of TCE into humic acid studied by both methods were also evaluated. The possible mechanism governing the sorption of TCE in humic acid was studied.


   MATERIALS AND METHODS
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Sorption–Desorption Experiment Followed by the Gravimetric Method
Humic acid disks were prepared by pressing a standard soil humic acid powder (Leonardite humic acid standard) obtained from the International Humic Substance Society (St. Paul, MN) under a pressure of 12.7 N/m2 for 1 min. Four disks made from the soil humic acid were 0.30, 0.31, 0.22, and 0.30 mm in thickness, and weighed 45.2, 46.3, 36.2, and 44.8 mg, respectively (Table 1 ). Their average density was 1.26 g/cm3, which is close to that of dry peat and muck (Rutherford and Chiou, 1992). The disks were oven dried (105°C) overnight and stored in a dessicator before use.


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  		Table 1. Conditions and results of the experiments to determine sorption and desorption of trichloroethylene (TCE) in four standard soil humic acid disks by the gravimetric method.

 
The apparatus and procedure used for sorption and desorption have been described elsewhere (Chang et al., 1997). Briefly, the experimental apparatus was maintained in a thermostatic room at three temperatures: 15.0 ± 0.4, 25.0 ± 0.5, and 35.0 ± 0.5°C. The disk was hung on the sample arm of a Cahn 200 electric microbalance (Thermo Fischer Scientific, Waltham, MA) and enclosed in a glass chamber. Before each experiment, the disk was purged with N2 gas at 50 mL/min to remove sorbed impurities until a constant weight was reached. The experiments were terminated when the change in weight could not be distinguished from the base noise of the microbalance, which was about 2 µg. A steady flow of N2 gas through liquid TCE in a bottle was mixed with a flow of pure N2 gas to obtain a constant vapor concentration of TCE. The TCE concentration was determined with a Hewlett-Packard 5890II gas chromatograph equipped with a flame ionization detector (Hewlett-Packard Co., Palo Alto, CA). Reported concentrations were the averages of three measurements for each experiment.

Estimating the Diffusivity
The one-dimensional mass conservation equation to describe the variation of TCE concentration in a humic acid disk with a thickness of 2l is

Formula 1[1]

Formula 2[2]
where q (mg/cm3) is the TCE concentration in the disk at a distance x from the center plane of the disk at time t, D is the apparent diffusivity of the TCE inside the disk, l is the half-thickness of the disk, Mt is the total sorbed mass of TCE in the disk at time t, and S is the surface area of one flat side of the disk.

The following are the initial and boundary conditions for the TCE sorption:

Formula 3[3]

Formula 4[4]

Formula 5[5]
where qe, the equilibrium sorbed concentration, can be estimated from the ultimate TCE mass sorbed by the humic acid, Me (qe = Me/Sl). The analytical solution for the fraction of equilibration is available (Crank and Park, 1968) and can be expressed as

Formula 6[6]
where Me is the ultimate sorbed mass and f(t) is a dimensionless expression that is zero at t = 0 and is unity when t approaches infinity.

For the desorption process, the humic acid disk, after being equilibrated with TCE, was purged with 50 mL/min of pure N2 gas. The initial and boundary conditions were

Formula 7[7]

Formula 8[8]
and Eq. [6]. The analytical solution during desorption is

Formula 9[9]

Using this diffusion model, the diffusivity can be estimated by the best fit of the experimental results using the least-squares method.

Molecular Dynamics Calculations
The basic building block structure of humic acid was produced using the Cerius2 molecular simulation software package (Accelrys Software, San Diego, CA). Cerius2 software has been used to simulate the diffusion coefficients of chemicals in polymers (Li et al., 1997; Rivin et al., 2004; Pavel and Shanks, 2003) and to study sorption and diffusion of organic contaminants in the environment (Kubicki, 2005; Shih et al., 2006). Because the periodicity of the unit cell can be imposed in this software, there are no collisions of any atoms on the walls. And one simulation cell can mimic an entire polymer macromolecule to save calculation cost. The 3D-Sketcher, open force-field (OFF), charge equilibration, polymer and amorphous polymer builder, energy minimizer, NVT MD, polymer properties, and dynamic analysis modules of Cerius2 software were used to perform the computations and calculate the density, diffusion coefficient, and activation energy and to predict the correlation between these properties.

The chemical structure of humic acid may have significant complexity. This complexity leads to a wide variation in humic acids between soils. A humic acid model cannot cover all this variation but including the most important components of humic acid can contribute to soil science. Several researchers studied the structure of humic acid and tried to build its molecular model (Chefetz et al., 2002; Zang et al., 2000); however, only limited three-dimensional molecular structures of humic acid were proposed and tested. The secondary structure of the humic acid matrix built by Temple–Northeastern–Birmingham (TNB), referred to as the TNB humic acid monomer, has been proposed previously (Davis et al., 1997; Jansen et al., 1996; Sein et al., 1999). The building block, TNB humic acid monomer C36H30N2O15, was used to build the multiple-element structural models of humic acid. The humic acid model consisting of eight monomers was built by adding one monomer after another gradually, while, at the same time, the energy minimization calculations were performed to assure its stable conformation. Five water molecules were added randomly to this model and the structure was energy minimized again. Following the equilibration, the TCE molecule was inserted into preexisting cavities within the humic acid matrix. After the energy minimization of the above structure, one humic acid model was obtained.

The motion and the applied force to atoms in MD simulations are based on Newton's second law:

Formula 10[10]
where F is the force applied to the atom, m is the mass of the atom, a is the acceleration, and r is the position vector. The MD model tracks the time evolution at the atomic level of an ensemble of particles acting under specified interatomic forces by numerically solving the equation of motion in an iterative manner. The calculation of the forces in one specific system allows prediction of the positions and velocities of all atoms at the next time step based on Eq. [10]. Subsequently, a new system configuration is obtained and the next iteration starts. The energy terms of one given system configuration and the velocities of the atoms can be calculated using intramolecular and intermolecular potential functions. The potential energy, E, for an arbitrary geometry of molecules can be characterized by the following terms:

Formula 11[11]
The first four terms represent bonded interactions: bond stretching (EB), bond angle bending (EA), torsion (ET), and inversion (EI). The last two terms represents unbonded interactions, possessing van der Waals (EvdW) and electrostatic (EE) character. The definitions of these energy terms and the values of the parameters constitute a force field. The force field descriptions obtained from the known structures are able to predict the energies of unknown structures.

The interatomic potentials for TCE and humic acid were obtained from the parameterized universal force field (UFF) (Accelrys Software, San Diego, CA). This force field has been used in the simulation of organic chemicals in polymers (Li et al., 1997) and humic substances (Shih et al., 2006). The UFF is a purely harmonic force field with a potential expression; bond stretching is described by a harmonic term. Bond angle bending is described by a three-term Fourier cosine expansion. Torsion and inversion are described by cosine-Fourier expansion terms. Van der Waals interactions are described by a Lennard–Jones potential. And electrostatic interactions are described by a Coulombic term. The total energy is expressed as a sum of these bonded and unbonded interactions. An Ewald summation method with the automatic parameter search was used for the long-range corrections of the electrostatic potential. Atomic charges were calculated using the charge equilibration (Qeq) method (Rappé and Goddard, 1991). All the calculations were performed on SGI Origin 2000/3800 workstations at the National Center for High-Performance Computing in Taiwan.

Simulations were run by using the Dynamic module of the Cerius2 molecular modeling suite with the NVT ensemble and the periodic boundary conditions. In the NVT ensemble, the number of molecules N, volume V, and temperature of the system T are kept constant. These simulations at 300, 325, and 350 K were equilibrated for 50 ps and then run for 200 ps, when data were collected for mean square displacement of the migrations. The time step of 1 femtosecond (fs) was used for the integration of the equation of motion. The temperature was maintained by coupling the system to a temperature bath using the Nosé–Hoover approach (Hoover, 1985). From the molecular dynamics trajectories of the system, we were able to calculate the diffusion coefficient via the Einstein relationship.

The calculation for diffusion coefficients is based on statistical mechanical principles (Theodorou, 1996; Haile, 1997). In short, the diffusion coefficient, D, can be computed from the proportionality constant according to Einstein's relationship:

Formula 12[12]
where ri(t) is the center of mass of the penetrant i at time t.


   RESULTS AND DISCUSSION
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
CONCLUSIONS
 REFERENCES
 
Sorption Experiments
Four sets of experimental conditions and sorption results for soil humic acid by the gravimetric method are shown in Table 1. The sorption of TCE on the humic acid disk took about 18 h to reach steady state at 15°C (Fig. 1a ). It took more time, however, for complete desorption. There was no residual TCE mass remaining in these humic acid disks after desorption (Fig. 1). A similar reversibility with humin was observed for toluene but not for n-hexane or acetone in humin (Shih and Wu, 2002b).


Figure 1
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  		Fig. 1. Experimental results (squares) and model best fit (solid lines) of trichloroethylene sorption and desorption in soil humic acid disks: (a) Disk A at 15°C, (b) Disk B and (c) Disk C at 25°C, and (d) Disk D at 35°C.

 
The retention of chlorinated compounds by humic substances has been suggested as the possible mechanism in the sequestration of hydrophobic organic chemicals by soils (Ball and Roberts, 1991; Aochi and Farmer, 1997; Huang and Weber, 1998). The resistance to desorption of TCE from contaminated soils has been presented by Pavlostathis and Jaglal (1991) and Pavlostathis and Mathavan (1992). They also found a linear relationship between the soil partition coefficient and the resistant desorption fraction of TCE. The TCE sorption–desorption process in soil humic acid seemed completely reversible in this study, however, because there was no resistant fraction for the desorption of TCE from humic acid as measured by the microbalance.

The distribution coefficient, Kd [(g/kg)/(mg/L)], between the solid phase and the gaseous phase is defined by

Formula 13[13]
where Cg is the TCE concentration (mg/L) in the gaseous phase and W is the weight of the disk (g). The observed Kd decreased with decreasing temperature in the relative pressure (P/P0) range from 0.0091 to 0.015 (Table 1).

Applying the van't Hoff equation, the relationship between the change in enthalpy ({Delta}H) and Kd can be quantified as

Formula 14[14]
where R is the ideal gas constant and T is the absolute temperature (K).

The enthalpy change of TCE sorption is –26.8 kJ/mol for soil humic acid (Fig. 2 ), indicating that the sorption process is a moderately exothermic process. This value is slightly larger than that of 23.0 kJ/mol for 1,1,1-trichloroethane vapor sorption on a silt loam soil with 1.6% organic matter (ten Hulscher et al., 1996).


Figure 2
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  		Fig. 2. Plots of (top) lognormal distribution coefficient (lnKd) vs. the inverse absolute temperature (1/T) for trichloroethylene sorption, and (bottom) lognormal sorption diffusion coefficient (lnDs) and lognormal desorption diffusion coefficient (lnDd) vs. 1/T for trichloroethylene sorption and desorption in soil humic acid at temperatures ranging from 15 to 35°C.

 
The small enthalpy change from condensed liquid TCE to sorbed TCE was found to be 8.0 kJ/mol, obtained by subtracting the TCE vapor condensation enthalpy (–34.8 kJ/mol). The sorption process is mainly a van der Waals physical sorption. There appears to be no chemical bond formed or broken during sorption or desorption. The relatively small net toluene vapor sorption enthalpies of 14.7 kJ/mol with the humic acid (Chang et al., 1997) and 6.3 kJ/mol with humin isolated from a Yangminshan soil (Shih and Wu, 2002a) were similarly obtained. These findings are consistent with the estimated small net enthalpies for the sorption of volatile organic compounds to soil humic substances (Chang et al., 1997; Shih and Wu, 2002a; Chiou et al., 1988).

Sorption Kinetics
Two-stage sorption was observed in each sorption on soil humic acid (Fig. 1). A first sorption stage with a relatively small sorption capacity was followed by a second sorption stage with a much higher capacity. The biphasic sorption kinetics of organic vapors have been observed in uptake by macromolecules, such as the sorption of toluene vapor by poly(aryl-ether–ether-ketone) (Wolf et al., 1992) and other organic vapors by polyvinyl chloride (Berens, 1989), ethylcellulose (Barrer and Barrie, 1957), and cellulose acetate (Bagley and Long, 1955). In general, anomalous diffusion begins with a relatively rapid first uptake phase, followed by a slowly increasing sorbed phase concentration to reach true equilibrium (Bagley and Long, 1955).

The observed two-stage sorption kinetics can be explained by models of diffusion in polymers (Chang et al., 1997; Shih and Wu, 2002b). The first-stage sorption is confined to only near-surface regions involving little polymer relaxation. A certain level of energy is required to overcome the intermolecular and intramolecular forces of the polymer network to form a space or free volume for the vapor penetrant (Rogers, 1985); thus, time is required for the TCE vapor to solvate the humic acid surface. Similar two-stage results have been reported for the sorption of organic compounds in polymers (Kishimoto and Matsumoto, 1964; Wolf et al., 1992) and humic substances (Chang et al., 1997; Shih and Wu, 2002b).

The second stage is mainly driven by the energy associated with the relaxation of humic acid polymer chains. A diffusion–relaxation model has been used to explain the observed anomalies in polymers (Rogers, 1985; Berens and Hopfenberg, 1978). An expansion of polymers occurs following the absorption of a sorbate until the elastic forces raise the chemical potential of the sorbate to equal its value in the bulk gas phase (Crank and Park, 1968). The stressed polymer chains will slowly relax, lowering the sorbate's chemical potential and allowing additional sorbate to be sorbed until equilibrium is reestablished (Berens and Hopfenberg, 1978; Weber et al., 2001).

The rate of TCE penetration is quantified by the diffusivity in the humic acid matrix. The endpoints of the first stage of sorption are taken to be the starting points of the true diffusion process because the second stage of TCE sorption is believed to be controlled by diffusion of TCE molecules in the humic acid matrix after the tightly bound surface structure of the disks is opened during the first stage. Figure 1 shows the time courses of sorption and desorption and the simulation of the weight changes by using a diffusion model. Diffusivity ranged from 2.0 x 10–8 to 1.0 x 10–9 cm2/s, which is lower than the diffusivity of TCE in water by a factor of 1000. The average of the two best-fitting diffusivities of TCE at 25°C is 1.1 x 10–8 cm2/sec. The regression coefficients between experimental and fitting data are higher than 0.96 shown in Fig. 1; however, the diffusion model fits better in the sorption direction than in the desorption direction and desorption diffusivities are lower than sorption ones. This asymmetrical nature of the diffusion may result from the different states of the sorbent. During sorption of TCE, the humic acid matrix is undergoing physical modification, perhaps irreversibly, as a swelling of the sorbent to facilitate uptake. The smaller desorption than sorption diffusivity, which is consistent with the "opening up" of the humic acid matrix, increases the sorption domain of TCE and thus decreases the driving force for desorption. Consequently, sorption and desorption could be occurring from different physicochemical states of the humic acid matrix.

Thermodynamics of Diffusion
Trichloroethylene sorption and desorption diffusivities increase with temperature (Table 1). An increase in temperature raises the rate of diffusion because it provides more energy to facilitate the vibration of polymer segments and helps to mobilize VOC molecules. Hence, TCE molecules can overcome the activation energy barrier more easily when they are squeezing through the macromolecular matrix.

Applying the Arrhenius equation, the effect of temperature on diffusivity can be quantified as (Crank and Park, 1968)

Formula 15[15]
where E is the activation energy of diffusion. By plotting lnD vs. 1/T (Fig. 2), the E values for sorption and desorption are found to be 29.3 and 59.5 kJ/mol, respectively. These values are the same order of magnitude as the activation energy of toluene sorption (42.3 kJ/mol) and desorption (65.8 kJ/mol) into humic acid (Chang et al., 1997), the activation energy of 84.2 kJ/mol for 1,2,3,4-tetrachlorobenzene in polystyrene (Cornelissen et al., 1998), and the diffusion activation energy of 46.5 kJ/mol for propane into rubber (Michaels and Bixler, 1961).

Molecular Dynamics Simulation
The proposed humic acid model is based on the combination of the structural unit of humic acid obtained from the experimental data and retro-biosynthetic analyses (Sein et al., 1999). The link between the amine and carboxylate of these TNB humic acid monomers generates a stable helical structure, as mentioned by Sein et al. (1999). The unit cell dimensions are 1.91 by 1.93 by 2.00 nm. The simulation cell is periodic in three dimensions. None of the atoms in these MD simulations are fixed to make cooperative motions of humic acid molecules with TCE.

The effect of the simulation time on the calculated values of the diffusion coefficient was examined and is shown in Fig. 3 . The calculated diffusion coefficient value decreases as the simulation time becomes longer, and reaches a stable lowest value around 200 ps. The short simulation time of 20 ps has been used to obtain the diffusion coefficients of chemicals in amorphous polymers (Li et al., 1997).


Figure 3
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  		Fig. 3. Effect of simulation time on the diffusivity of trichloroethylene in humic acid.

 
The influence of the density of the humic acid matrix on the diffusion coefficients of organic contaminants has been studied (Shih et al., 2006). In that study, the diffusivities of organic compounds decreased with increasing density of the humic acid matrix. The density of 1.27 g/cm3 was close to the experimental density of the humic acid disks in the experiments. The effect of water content in the humic acid matrix on the simulations of sorption kinetics of organic compounds in the humic acid model was discussed (Shih et al., 2006). Water molecules that diffuse into the humic acid matrix could affect the diffusion process of the target compound molecule. Not only could water molecules interact with the diffusants, but they could also occupy the free space inside the humic acid network. The diffusivities decreased to 10–12 cm2/s and were far from the experimental results when more than five water molecules were added in the humic acid model. Too many water molecules added into the unit cell will limit the diffusion process of the target compound due to less void for its movement. The model of humic acid with five water molecules was selected as the simulated model in this study.

During the simulation, the TCE molecule underwent diffusive movements inside the humic acid network. The mean-square displacement is an average of squared distances summed across all possible positions of the origin. The mean-square displacement of TCE in the humic acid model was plotted as a function of time in Fig. 4 . The diffusion coefficient was calculated from the slope of the mean-square displacement curve using Eq. [12].


Figure 4
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  		Fig. 4. Mean-square displacement of a penetrating trichloroethylene molecule from its origin in the humic acid model as a function of the simulation time t.

 
The averaged diffusivity of TCE in humic acid estimated by MD simulations is 8.60 x 10–9 cm2/s at 298 ± 9.5 K. The temperature was set at 298 K in a canonical (NVT) ensemble and constraint through the Nosé–Hoover thermostat. During the MD calculations, the variation of velocities of each atom along each time step causes fluctuation in the energy. Consequently, this fluctuation in energy will cause a fluctuation in temperature. Sane et al. (2002) showed a typical temperature fluctuation around 20°C in a constant-temperature ensemble during MD simulations. The temperature in these MD simulations was well controlled. Compared with the average diffusivity of sorption and desorption, 7.0 x 10–9 cm2/s at 298 K, the estimated value of this study is very close to the experimental results. The estimated diffusivity, however, is around two times smaller than the sorption experimental values and around three times higher than the desorption experimental values. The diffusion coefficients determined via MD simulation were approximately four times larger than the experimental values (MacElroy, 1996). Li et al. (1997) mentioned that the difference between the calculated and experimental diffusivities of organic chemicals in polymer systems could be more than four orders of magnitude. A comparison with the experimental results revealed a good agreement with the computed data at room temperature in this study.

The average computational diffusivities of 1.79 x 10–8 cm2/s at around 325 K and 4.55 x 10–8 cm2/s at around 350 K were calculated and are shown in Table 2 . The diffusivity of TCE increases with temperature, which is consistent with the experimental results. It can also be observed in the results of the MD simulation that a higher temperature will increase the rate of diffusion due to its giving more energy to facilitate the displacement of the polymer segments, and helping the mobility of VOC molecules.


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  		Table 2. Calculated diffusion coefficients of trichloroethylene at three different temperatures.

 
As shown in Fig. 5 and estimated by Eq. [15], the activation energy barrier of 32.7 kJ/mol is required when a TCE molecule is squeezing through the humic acid macromolecular matrix. This value is close to the sorption activation energy of TCE at 29.3 kJ/mol into the humic acid but it is lower than the desorption activation energy. In general, the activation energies obtained from MD simulations were approximately two times lower than those observed experimentally (MacElroy, 1996; Tang et al., 2004). With the current composition of the humic acid model, MD simulations were able to compute the activation energy with a fair degree of accuracy; however, to predict more complex properties such as different activation energies for sorption and desorption, further modeling refinements are needed.


Figure 5
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  		Fig. 5. Lognormal diffusion coefficient (lnD) vs. the inverse absolute temperature (1/T) for trichloroethylene sorption in the humic acid model. Temperature ranged from 300 to 350 K.

 
Based on the results of molecular simulation in this study and comparison with the experimental results, we propose that the TCE penetration rates were controlled by diffusion of TCE molecules into the humic substance matrix.

Diffusion of Organics in Soils
The diffusivities measured and predicted in this study are on the same order as the diffusivity of TCE into humic acid in the aqueous phase obtained by Piatt and Brusseau (1998). They also came close to the intra-organic-matter diffusivities of tetrachloroethene in soils, ranging from 3.6 x 10–8 to 2.2 x 10–9 cm2/s, estimated by Ball and Roberts (1991). The present TCE diffusivity is slightly larger than the values of TCE with soil grains (about 10–10 cm2/s) estimated by Grathwohl and Reinhard (1993) and those with soil and sediments (6.2 x 10–10 and 1.73 x 10–9 cm2/s, respectively) measured by Werth and Reinhard (1997). The diffusivity in humic substances are slightly low, however, compared with the diffusivity of other VOCs in polymers; for example, the diffusivities are 5.2 x 10–7 and 1.7 x 10–7 cm2/s for benzene and o-xylene, respectively, in natural rubber at 25°C (Guo et al., 1995), 2.1 x 10–7 cm2/s for propane into amorphous natural rubber at 25°C (Michaels and Bixler, 1961), and 1.8 x 10–7 cm2/s for toluene in butyl rubber at 30°C (Schneider et al., 1994). Comparing these diffusivities, the humic acid matrix seems less flexible than the rubbery polymers.

Slow TCE desorption could be attributed to diffusion through micropores in mineral solids (Farrell et al., 1999; Werth and Reinhard, 1997). The sorption of hydrophobic solutes to the micropores of inorganic matrices, however, is probably not the source of the observed slow desorption processes with soils and sediments (Huang et al., 1996). Pignatello (1990) indicated that the slow release of residual aliphatic halocarbons from soils results from a molecular diffusion from remote sites in the soil organic matter matrix. LeBoeuf and Weber (2000) proposed that the glassy regions of organic macromolecules are responsible for the slow release of sorbed organic contaminants. Weber et al. (2001), Ball and Roberts (1991), Nkedi-Kizza et al. (1989), and Bouchard et al. (1988) suggested that the intra-organic-matter diffusion through humic substances results in a slow desorption of hydrophobic solutes in soils.

The apparent diffusivities of VOC molecules into soil humic substances are in the order of about 10–9 cm2/s (Piatt and Brusseau, 1998; Chang et al., 1997; Shih and Wu, 2002a,b). The thickness of a humic substances coating of three sandy aquifers was around 10 to 100 µm (Holmen and Gschwend, 1997). Piatt and Brusseau (1998) indicated that the organic coating thickness was around 20 µm for two soils. According to these length scales in these typical soils and the diffusivity given above, the time that VOC molecules need to penetrate a soil organic matter matrix could be only a few minutes. The results indicate that the intrinsic penetration process with soil humic substances could not be responsible for the slow sorption–desorption of VOCs to and from soils.

The computer-simulated results for the sorption kinetics and thermodynamics of TCE in soil humic acid are in good agreement with the experimental data. The MD simulation method has been demonstrated to provide useful information without the risk of producing hazardous chemicals during the experiments. Our study suggests that the computer-simulation technique could be a clean research method to predict the sorption kinetics of organic chemicals in the soil environment at the molecular level.


   CONCLUSIONS
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 NOTES
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
REFERENCES
 
The diffusion process of organic chemicals into a compressed disk of soil humic substances was used to mimic the process in natural soil systems on the basis that the humic acid disk has a density similar to that of natural soil humic substances. As the density of a polymer decreases, the penetrating rate of chemicals into a macromolecule increases (Crank and Park, 1968; Li et al., 1997). A shorter sorption–desorption time is expected if the density of humic substances in the environment is less than that in this study. On the other hand, the diffusivities extrapolated from humic acid disks for natural soils should be regarded conservatively because soil humic substances are coated on mineral surfaces rather than existing as thick disks in this study. Our diffusivities, however, obtained from gravimetric experiments and computer simulations in soil humic acid, are close to the calculated diffusivities of TCE in natural humic acid in soil aggregates (Piatt and Brusseau, 1998). The integration of experimental investigations and molecular simulations offers a better understanding of the sorption kinetics of organic compounds associated with humic acid and soil organic matter and facilitates problem-solving capabilities in soil chemistry and soil remediation.


   ACKNOWLEDGMENTS
 
I thank Prof. Shian-chee Wu of the Graduate Institute of Environmental Engineering, National Taiwan University in Taiwan, Republic of China, for providing a microbalance. I gratefully acknowledge the financial support of the National Science Council of Taiwan, R.O.C. (Contracts NSC 94-2313-B-005-064 and NSC 96-2313-B-005-006).


   NOTES
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ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
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Received for publication February 25, 2007.


   REFERENCES
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 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
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