Activation energies of phenanthrene desorption from carbonaceous materials: Column studies

Journal of Hydrology 369 (2009) 234–240

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Activation energies of phenanthrene desorption from carbonaceous materials: Column studies Guohui Wang 1, Peter Grathwohl* Center for Applied Geoscience, University Tübingen, Sigwartstrasse 10, D-72076 Tübingen, Germany

a r t i c l e Keywords: Activation energy Desorption Phenanthrene Coals Column leaching

i n f o

s u m m a r y Sorption/desorption kinetics of phenanthrene from two carbonaceous samples (lignite and high-volatile bituminous coal (HC)) at different temperatures was monitored using an on-line column method. Pulverized samples (<30 lm) were equilibrated in the column for 2 months before desorption began. The desorption rates declined initially fast, followed by an extended tailing part, which could be described very well by a single parameter spherical diffusion model accounting for non-linear sorption. Desorption was carried out at stepwise increased temperatures (20–90 °C), and the apparent activation energies were calculated based on the Arrhenius relationship for each of totally three temperature steps. The apparent activation energies were in an order of 58–66 kJ mol1 and 70–71 kJ mol1 for lignite and HC, respectively and they did not increase significantly during the leaching procedure. At the end of the experiments desorption was almost complete and only 0.2% (lignite) and 6% (HC) of the initially sorbed phenanthrene was present after the last temperature step. Fitted diffusion coefficients as well as the comparison between the apparent activation energies and sorption/desorption enthalpies obtained for the same samples from equilibrium isotherms imply that the diffusion occurred in organic matter of the lignite and in micropores of the high-volatile bituminous coal, where higher apparent activation energies are expected. Ó 2009 Elsevier B.V. All rights reserved.

Introduction Dependency of sorption/desorption rates on temperature is determined by the activation energy, which essentially describes how chemical rate constants vary with temperature. It is generally accepted that two mechanisms may limit the mass-transfer in sorption/desorption of hydrophobic organic compounds (HOCs) in natural organic matter: (1) molecular diffusion in an organic matrix (Brusseau and Rao, 1989, 1991; Brusseau et al., 1991) or (2) aqueous diffusion in intraparticle pores (Rao et al., 1980; Wu and Gschwend, 1986; Ball and Roberts, 1991b). Since diffusion is positively temperature-dependent, both mechanisms are considered to be activated processes. Diffusion in an organic matrix is postulated to be analogous to diffusion in polymers, where diffusion occurs through holes that are distributed discontinuously throughout the material (Ten Hulscher and Cornelissen, 1996). Pore diffusion depends on diffusion coefficients and sorption sites distributed along the pore walls, which retards the sol-

* Corresponding author. Tel.: +49 7071 2975429; fax: +49 7071 5059. E-mail addresses: [email protected] (G. Wang), [email protected] (P. Grathwohl). 1 Present address: Department of Geology, University at Buffalo (SUNY), 876 Natural Sciences Complex, Buffalo, NY 14260, USA. 0022-1694/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jhydrol.2009.02.018

ute transport. If sorption is temperature-dependent (i.e. decreases with increasing temperature), then this additionally affects the pore diffusion rates. Diffusion through micropores is considered as molecule jumps from one low-energy site to the next (Karger and Ruthven, 1992). Ten Hulscher and Cornelissen (1996) reviewed the diffusion of organic compounds in polymers and report average activation energies of 60 kJ mol1. Values higher than 100 kJ mol1 can be expected for glassy or highly crosslinked polymeric matrixes (Johnson and Weber, 2001). A number of studies have been carried out to investigate the desorption kinetics and related activation energies using different organic compounds in different sorbents (model substances, soils and sediments; see Table 3). Cornelissen et al. (1997) studied the slow desorption of PAHs and PCBs from laboratory-spiked and fieldcontaminated sediment samples and determined activation energies in the range of 60–70 kJ mol1. Castilia et al. (2000) determined activation energies in column experiments on desorption of trichloroethene from model substances and natural geosorbents (silica gel, soil, sediment) of 47–94 kJ mol1, which is consistent with the values found for diffusion in micropores. Chihara et al. (1978) found activation energies between 10 and 50 kJ mol1 for diffusion of hydrocarbons in zeolites and molecular sieves. Johnson and Weber (2001) investigated desorption of phenanthrene using heated and superheated water at different

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temperatures (75–150 °C) and report activation energies of about 40–80 kJ mol1. Ghosh et al. (2001) measured the activation energies of PAHs in a coal containing subfraction and clay/silt subfraction of a harbor sediment, and found that the coal containing subfraction has 3 times higher activation energies than the clay/ silt subfraction. Kleineidam et al. (2004) carried out column desorption experiments using aquifer materials which experienced more than a 1000 days long-term sorptive uptake of phenanthrene. The desorption rates were very well fit by the retarded pore diffusion model simply by forward modeling using the parameters from the long-term sorptive uptake batch experiment. No hysteresis was observed and the desorption activation energies were in the range from 45 to 59 kJ mol1. Several models have been developed to simulate slow solute leaching in column tests. The desorption rate constants are obtained by fitting models to data from desorption experiments (such as concentration, flux, remaining mass). The intraparticle diffusion model is widely used to represent desorption kinetics of contaminants in geosorbents (Wu and Gschwend, 1986; Ball and Roberts, 1991b; Grathwohl and Reinhard, 1993; Kleineidam et al., 2004). Meanwhile the two/multi-site/stage first-order models, which need simpler math and no geometry characterization of the geosorbents, are also developed to interpret the slow and very slow desorption rates (Cornelissen et al., 1997, 1998; Ten Hulscher et al., 1999). Altfelder and Streck (2006) compared these two concept models and concluded that the intraparticle model performs better than the first-order model, especially in a long-term leaching process up to months or years. The two or multi-site/stage models need more than one rate constant as fitting parameters which depend on column length and flow velocity (Young and Ball, 1995, 2000). In diffusion models (e.g. the spherical diffusion model) usually only one rate constant to simulate desorption kinetics is sufficient for a homogeneous samples (i.e. comprising one grain size class and one type of particles) whereas for heterogeneous samples (i.e. different grain sizes and different particles) again multi-rate diffusion models are needed. In this study, desorption kinetics of phenanthrene from two carbonaceous materials was investigated in flow-through column experiments with stepwise increases of the temperature, and the concentrations observed were fitted using a spherical intraparticle diffusion model. The main objectives of this study were (1) to determine the apparent diffusion coefficient for desorption, (2) to calculate the apparent desorption activation energies from stepwise temperature increases using a high resolution on-line column technique, (3) to find out if the apparent activation energy changes with increasing desorption in order to elucidate potential apparent hysteresis phenomena which should lead to increased activation energies along with the increased degree of desorption, and (4) to compare the measured apparent activation energies with existing thermodynamic data on diffusion in polymers, micropores and water in order to elucidate potential desorption mechanisms.

Materials and methods Pulverized lignite and high-volatile bituminous coal (HC) were selected for the column experiments in this study. The grain size of the particles was less than 30 lm (HC) or below 10 lm (lignite) which allows for fast sorption/desorption. Phenanthrene was used as the probe compound and was obtained as pure product (98%) from Aldrich Chemical Corp. Physicochemical properties, thermodynamic parameters (on sorption/desorption) and sample characteristics are listed in (Wang et al., 2007; Wang, 2008). Column package and pretreatment Stainless steel HPLC columns with 8 cm length and 1 cm inner diameter were used. About 0.2 g pulverized sample was scattered evenly on a clean glass wool mat, which was then rolled and packed into the column. Two metal frits were placed at both ends of the column to prevent leaching of fine particles. Then the column was filled with Millipore water from the bottom using a HPLC pump at a flow rate of 0.5 ml min1. The total filling time was recorded and the pore volume was calculated from mass of water in the column. The dead volume of all the stainless steel capillary connection tubes was considered as well (less than 0.25% of the total water-filled volume). On–line column experiments The sorption and subsequently desorption column experiments were monitored on line. The column setup is shown in Fig. 1. The packed column was connected to a HPLC system instead of the usual separation column. A fluorescence detector with emission/ extinction wavelengths of 249/345 nm was used to monitor phenanthrene concentrations and the signals were recorded using chromatography software every 5 s. This high resolution of the measurement was needed in order to follow the effluent concentrations in sufficient detail at each temperature step. Temperature control was ensured keeping the column in a water bath. Calibration of the fluorescence signal was carried out for each temperature step in order to account for any baseline shift in the signal. Baselines were quite stable as shown in Fig. 3. For each calibration 4–6 standard solutions (2–150 lg L1) were used and electrical signals (mV) were converted to concentrations (lg L1). Phenanthrene solutions were prepared using degassed Millipore water and stock solutions in methanol; they were kept in the dark and poisoned with sodium azide at a concentration level of 200 mg L1 in order to inhibit bacterial growth and thus to prevent biodegradation of the phenanthrene. For the initial breakthrough experiments, the inflow phenanthrene solution was renewed every 24 h. The inflow solution was directly connected to the HPLC pump using stainless steel capillary tubing (see Fig. 1). The phenanthrene solution was pumped through the sample column with a constant flow rate of 1.42 or 1.45 ml min1 under a controlled temperature

fluorescence detector HPLC pump

steel column in water bath Phe. solution / water

signal recorder

Fig. 1. On-line column setup for the sorption/desorption experiments.

effluent

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(25 °C for lignite and 20 °C for HC) until complete breakthrough (or up to 85% of the input concentration) was observed. The concentrations of the inflow phenanthrene solutions were around 10–12% of the solid phenanthrene aqueous solubility at 25 °C (121 lg L1 for lignite and 150 lg L1 for HC, respectively). After the sorption uptake step, the sample column was detached from the HPLC system, closed tightly with stainless steel fittings and kept at 20 °C for about 2 months. Sorption equilibrium was established for the fine particles in the column after this two-month period (Wang et al., 2007). Thereafter, desorption experiments were carried out. The equilibrated column was reinstalled in the HPLC system again, where another HPLC pump and new tubing (to avoid memory effects) was used to purge the column with clean water at a pumping rate of 2.96 ml min1. The water used for purging was again deionized, degassed, spiked with sodium azide (200 mg L1) and tested for potential phenanthrene background. After the concentrations in the effluent decreased significantly at 20 °C (about 120–250 h), the temperature was stepwise increased first to 46 °C, then to 77 °C and finally to 90 °C in case of HC sample (see Fig. 3). After the desorption experiments, the samples together with the glass wool were removed from the column, immediately transferred to an extraction cell and extracted with acetone and toluene in an accelerated solvent extraction (ASE) device in order to determine the residual phenanthrene in the sample after the column desorption procedure. In order to check the reproducibility of the procedure, the experiment with the lignite sample was repeated under slightly different temperature steps of 30, 40, 50 and 77 °C. Apparent activation energy (Ea,app) If in the tailing part of a desorption experiment, the temperature is stepwise increased a corresponding increase of the desorption rates and thus an increase of the effluent concentrations is expected. Then the apparent activation energy (Ea,app (kJ mol1)) of desorption for each individual temperature step (from T to T0 ) can be calculated according to the Arrhenius relationship in the two temperature point form (Silberberg, 2003):

   0 TT 0 C Ea;app ¼ R 0 ln C T T

ð1Þ

where C and C0 are the transient effluent aqueous concentrations (in lg L1 or fluorescence signal (mV)) before and after the temperature step, respectively (i.e., the lowest concentration in the tailing part before the temperature increase and the highest concentration just after the temperature step). R is the universal gas constant. This equation requires that the solid loading (Cs) stays constant during each temperature step. In Eq. (1), the regression of ln (C0 /C) was used to replace the classical regression using rate constants (Johnson and Weber, 2001; Kleineidam et al., 2004) because at constant flow rates the concentrations are directly proportional to the rates and concentration data were monitored directly in high resolution. The measured Ea,app represents the overall temperature effect, including both the equilibrium driving forces for desorption (i.e., thermodynamics of phase partitioning or adsorption) and the kinetics of desorption (diffusion). The determined value is expected to be the combination of the desorption enthalpy (equilibrium thermodynamics) and the temperature effects on diffusion (i.e., mobility of the solute and viscosity of the water) as described in

Ea;app

D0aq TT 0 ¼ R 0 ln Daq T T

!

 0 ! TT 0 Cw þR ln Cw T  T0

ð2Þ

where Cw denotes the equilibrium concentrations in the pore water and Daq is the aqueous diffusion coefficient. The first and the second terms on the right side of Eq. (2) represent the activation energy for aqueous diffusion of the solute in water (or the organic matrix) and the equilibrium desorption enthalpy, respectively.

Spherical intraparticle diffusion model Solute diffusion from aqueous phase into spherical particles can be described by Fick’s 2nd Law in radial coordinates:

" # @C @ 2 C 2 @C þ ¼ Da @t @r2 r @r

ð3Þ

where r is the radial distance from the center of a grain. Da denotes the apparent diffusion coefficient, which depends on the aqueous diffusion coefficient (Daq), the intraparticle porosity (e), the distribution coefficient (Freundlich KFr and 1/n for non-linear sorption); the bulk density of the particle (q) and the tortuosity factor (sf).

Da ¼

Daq e ðe þ qK Fr c1=n1 Þsf

ð4Þ

sf is estimated from the intraparticle porosity based on Archie‘s law using an empirical exponent m:

sf ¼ e1m

ð5Þ

A numerical code (SMART developed by Finkel et al., 1999) coupling Eqs. (3)–(5) to advection was used to model the column effluent concentrations using m, thus the pore diffusion coefficient, as the only fitting parameter. Longitudinal dispersion could be neglected because in such column experiments it is very small and because the model was fit to the extended tailing part of desorption curve where dispersion is no longer significant. Nonlinear sorption was considered by implementing Freundlich sorption isotherms determined for the samples at the same temperatures (Wang et al., 2007). Results and discussion Sorptive uptake Breakthrough curves of phenanthrene in the columns are shown in Fig. 2. Pumping lasted 121/92 h for lignite/HC columns, and the sorbed mass as compared to the expected uptake at equilibrium (M/Meq) was 0.79 and 0.16 for lignite and HC, respectively. The sorbed mass M at time t was calculated by integration of the breakthrough curve. The equilibrium sorptive uptake (Meq) expected at the inflow concentration was calculated based on results from previous batch equilibrium sorption experiments (see Wang et al., 2007). The total mass present in the column after sorptive uptake was 480 lg and 330 lg for lignite and HC, respectively. Desorption Fig. 3 shows the concentrations in the leachate of the lignite and HC columns. Desorption was initially fast, but followed by an extended tailing part. The temperature was increased stepwise in the extended tailing part where the release of phenanthrene is believed to be purely limited by intraparticle diffusion. The stepwise increase of temperature caused immediate concentration increases, which reflects that desorption is thermodynamically an endothermic process. The leaching curves were predicted with the model SMART. The model input parameters, fitted m values, thus the calculated apparent diffusion coefficients are compiled in Table 1. In case of lignite, the phenanthrene concentrations measured follow very well the intraparticle diffusion model (see Fig. 3). The observed apparent diffusion coefficient at 20 °C was 2.58  1015 cm2 s1, where the fitted value for m was 2.56. The predicted concentrations are slightly lower than the experimental data in the beginning of desorption probably due to some background fluorescence because initially also DOC leached from the lignite. The initial high DOC

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1.0

a

b

0.8

0.6

M /Meq

0.8

C /C0

1.0

HC

0.4

Lignite

0.6 0.4

Lignite 0.2

0.2

0.0

0.0

0

20

40

60

80

100

120

140

HC 0

20

40

60

80

100

120

140

Time [h]

Time [h]

Fig. 2. (a) Phenanthrene breakthrough curves for the lignite and HC columns; (b) relative accumulated mass in the sorbents during the breakthrough experiment.

Concentration [µg/L]

70 60

Lignite

50

m = 2.56

40 30

20°C

20

46°C

77°C

10 0

0

50

100 150 200 250 300 350 400 450 500

Time [h]

Concentration [µg/L]

20

HC m = 1.7

15

10

20°C

46°C

77°C

90°C

5

concentrations (indicated by yellow colored effluent) are probably due to generation of DOC during the 2-month equilibration of the lignite column. Yellow colored effluent water was again observed at the 77 °C step immediately after the temperature increase. The DOC release from soil and sediment is reported as a rate-limited process (Cao et al., 1999; Wehrer and Totsche, 2005). Thurman (1985) reported that the DOC content of uncolored fresh water could be still up to 2–8 mg L1. Therefore, a certain DOC related fluorescence can not be excluded for the lignite sample even if the column effluent was non-colored. For the HC sample, the intraparticle diffusion model fits the effluent concentrations again very well even in the tailing part using just a single apparent diffusion coefficient (9.41  1014 cm2 s1, the fitted value for m was 1.7). The slight initial overestimation might be due to fast desorbing domains in the coal followed by slow diffusion from micropores (Li and Werth, 2004; Cheng and Reinhard, 2006). Ahn et al. (2005) investigated the intraparticle diffusion of phenanthrene and pyrene in polymers, coke, and activated carbon, and found that the sorption kinetics in the polymer and coke samples can be described well by the intraparticle diffusion model, whereas a branched pore model combining the macro- and micropore domains has to be used to simulate the sorptive uptake in activated carbon, which is characterized by a high micropore volume. Mass balance

0 0

200

400

600

800

1000

1200

Time [h] Fig. 3. Phenanthrene concentrations during column desorption with stepwise increased temperatures for the lignite and high-volatile bituminous coal (HC) samples; solid line: intraparticle pore diffusion model (‘‘m” is the fitted empirical exponent accounting for pore geometry/tortuosity); symbols: measured concentrations.

Table 2 shows the mass balance of phenanthrene sorbed and desorbed in the column experiments based on integration of the breakthrough curves. The ‘‘residual” indicates mass recovered by the ASE extraction after the desorption experiment was finished. In case of lignite, the desorption seems to recover more mass than was sorbed during the loading of the column, which likely is due to the background fluorescence from DOC. However, the most impor-

Table 1 Sample characteristic and observed apparent diffusion coefficients (20 °C) of phenanthrene in the lignite and HC samples through intraparticle diffusion model (SMART), where m is the only fitting parameter. Sample

Daqa (cm2 s1)

Dab (cm2 s1)

logKFr; 1/n (L kg1); (–)

mc (–)

r (mm)

qd (g cm3)

ee (%)

sff (–)

Lignite 0.21 g HC 0.17 g

5.86E06 5.86E06

2.58E15 9.41E14

4.28; 0.83 4.55; 0.57

2.56 1.7

0.0007 0.01

1.29 1.32

1.02 1.50

1280 19

a

Daq was calculated using Daq = 13.26  105/(g1.14 V 0.589) (Hayduk and Laudie, 1974). Da was calculated by Eqs. (4) and (5), where the averaged pore water concentrations from the 20 °C tailing breakthrough were used (lignite: average 6.18 lg L1, range 7.32–5.04 lg L1during the 75–121 h period; HC: average 0.87 lg L1, range 1.028–0.72 lg L1 during the 150–280 h period); for the sorption and other parameters, see Wang (2008). c In m the standard deviation is extremely little probably below 1%. d Refer Wood et al. (1983). e Calculated as e = intraparticle pore volume/(mass/bulk density), where the intraparticle volume were measured by BET method (see Wang, 2008). f Calculated by Eq. (5). b

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in Table 3. For both samples the Arrhenius plots are parallel for the different temperature steps except the 77–90 °C step for HC. In addition, similar apparent activation energies were determined for the second lignite sample, which was examined at slightly different temperature steps, indicating that the experimental technique provides robust results. As an important result, no trend of increasing Ea,app with progressing desorption is observed. The apparent activation energies determined are 70–71 kJ mol1 and 58–66 kJ mol1 within the temperature range of 20–77 °C for HC and lignite, respectively. Only in the 0.21 g-lignite experiment a significant difference in the apparent activation energies was observed with increasing temperature (66 kJ mol1 at the 46–77 °C step compared to 58 kJ mol1 at the 20–46 °C step). This, again, might be due to enhanced DOC leaching at 77 °C (yellowish colored effluent). The HC sample seems to show an elevated Ea,app at the 77–90 °C step which, however, is uncertain because of the very low signals recorded (4.6 mV and 9.3 mV after the step) close to the baseline (3 mV) measured before the desorption . Table 3 also reports activation energies from literature for different materials and solutes. In general, high values for Ea have been associated with diffusion of HOCs in condensed organic matter, coals, and shale materials. In contrast, diffusion in amorphous organic matrices which occurs in soils show lower values for Ea. The apparent activation energies determined in this study are within the wide range reported in the literature. The equilibrium

Table 2 Phenanthrene mass balance in lg in the column experiments; residual: extracted after the column desorption. Samples

Lignite HC

Sorption

Residual

Desorption

On-line curve integration

GC/MS

On-line curve integration

480 330

0.8 19.4

524.3a 340b

a Based on the stable effluent concentrations after 12 pore volumes (first 15 min); the earlier signal was affected by background fluorescence attributed to DOC. b The fluorescence signal was baseline corrected (3 mV) by the signal measured before desorption was started.

tant result reported in Table 2 is the residual mass in the lignite column after desorption of just 0.8 lg, which accounts for only 0.17% of the initially sorbed phenanthrene. In case of HC, 5.9% of the sorbed phenanthrene still remained in the sorbent after more than 1000 h of leaching even at elevated temperatures. Desorption activation energies Fig. 4 shows the Arrhenius plots based on concentration increases at each temperature step. The mass desorbed during each temperature step was less than 5% of the total mass in the column, thus Cs was considered as reasonably constant for the calculation of Ea,app. The apparent activation energies determined are compiled

5.0

5.0 46ºC

3.0

77ºC

2.0 1.0

20ºC

0.0 -1.0 -2.0 0.32

46ºC

Lignite

0.34

HC

4.0

LnC [µg/L]

LnC [µg/L]

4.0

46ºC

77ºC

3.0 2.0 1.0

90ºC

0.0 -1.0

0.36

0.38

0.40

0.42

-2.0 0.32

46ºC

77ºC 0.34

0.36

0.38

20ºC 0.40

0.42

1/RT

1/RT

Fig. 4. Arrhenius plots for the determination of apparent desorption activation energies (Ea,app) from concentration increases at each temperature step for the lignite and the high-volatile bituminous coal (HC) samples.

Table 3 Activation energies (kJ mol1) at the individual temperature steps, desorption enthalpies determined in equilibrium batch experiments for the two carbonaceous samples, as well as activation energies from literature. Samples

Temperature step

20–46 °C

46–77 °C

77–90 °C

HC 0.17 g

Ea,app D Ha Ea,app D Ha Temperature step Ea,app D Ha

70 32 58 24 30–40 °C 60 24

71 36 66 28 40–50 °C 58 25

(114) 47

Compound PCBs and PAHs TCE Phenanthrene Phenanthrene EDB PAHs PAHs Phenanthrene Organic compounds

Ea 60–70 47–94 41–74 83–86 66 115–139 37–41 45–59 average 60

Temperature 20–60 °C 30–60 °C 75–150 °C 75–150 °C 40–97 °C 30–400 °C 30–400 °C 20–70 °C 25–110 °C

Lignite 0.21 g Lignite 0.20 g (repeated)

Literature reported activation energies Sample Sediments Silica gel/solids Soil Shale Soil Coal particles Silt/clay Aquifer materials Elastomeric polymers

50–77 °C 61 27

Cornelissen et al. (1997) Castilia et al. (2000) Johnson and Weber (2001) Johnson and Weber (2001) Steinberg et al. (1987) Ghosh et al. (2001) Ghosh et al. (2001) Kleineidam et al. (2004) Ten Hulscher and Cornelissen (1996)

a DH: Desorption enthalpies determined from equilibrium batch experiments (see Wang, 2008) for the respective solid loading (Cs) at each temperature step; if diffusion occurs in water then additionally 16.9 kJ mol1 are expected corresponding to the activation energy of phenanthrene diffusion in water (see Kleineidam et al., 2004).

G. Wang, P. Grathwohl / Journal of Hydrology 369 (2009) 234–240

E a [kJ/mol]

80

References

70 60 50 40 30 20 20

239

25

30

35

40

45

50

Enthalpy [kJ/mol] Fig. 5. Comparison of equilibrium enthalpies (Wang, 2008) and apparent activation energies for phenanthrene desorption from lignite (diamonds) and high-volatile bituminous coal (triangles); filled and open diamonds: duplicate lignite samples; dashed line: expected correlation if the activation energy of aqueous diffusion of phenanthrene in bulk water (16.9 kJ mol1) is added to the enthalpy.

desorption enthalpies determined at the same loading level (Wang, 2008) can be compared to the Ea,app values compiled in Table 3, and can give some hints on the diffusion process (see Fig. 5). If diffusion in the pore water controls the sorption/desorption kinetics, then differences between the activation energy of desorption and the equilibrium enthalpy of sorption/desorption should correspond to the activation energy of diffusion of phenanthrene in bulk water (16.9 kJ mol1, Kleineidam et al., 2004). The comparison shows that all plotted data are above the dashed line (i.e., equilibrium enthalpies plus 16.9 kJ mol1), which means much slower diffusion rates than expected for phenanthrene diffusion in the pore water. In case of lignite, diffusion in the organic matter matrix could explain this difference. For instance, a diffusion coefficient of 1  1010 cm2 s1 is reported for phenanthrene diffusion at 25 °C in fine polyoxymethylene particles (Ahn et al., 2005). This value is more than 4 orders of magnitude lower than phenanthrene diffusion in water (6.7  106 cm2 s1). For the HC sample, higher activation energies could be expected because of diffusion in micropores. Activation energies for diffusion are larger in micropores than in mesopores or macropores for liquids and gases (Werth and Reinhard, 1997). Conclusions This study shows that a single parameter intraparticle diffusion model fits the desorption of phenanthrene from carbonaceous materials (lignite and high-volatile bituminous coal) very well. Fitted apparent diffusion coefficients indicate that sorption in the organic matrix (lignite) and micropores (HC) may be important. The apparent activation energies of phenanthrene desorption do not increase more than expected from the increase of the sorption enthalpy at decreasing loadings (Cs), which indicates that there is no significantly slower desorption mechanism appearing which would limit desorption in the long term. Furthermore, the residual mass recoveries prove that more than 94% of the initially sorbed phenanthrene mass was released during the desorption experiments. The comparison between the determined apparent activation energies and the enthalpies from equilibrium sorption/ desorption isotherms combined with the activation energy expected for the diffusion in water implies that diffusion in the coals occurs in the organic matter matrix of the lignite and in the pore water in micropores in the high-volatile bituminous coal. Acknowledgements This research was funded by Deutsche Forschungsgemeinschaft (DFG) under Project number GR 971/16-1 and ‘‘AquaTerra”, a European Union FP6 integrated project (Project no. 505428 (GOCE)).

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