Environ. Sci. Technol. 2000, 34, 1240-1245
Photolytic Transformation of Organic Pollutants on Soil SurfacessAn Experimental Approach MARIANNE E. BALMER, KAI-UWE GOSS,* AND R E N EÄ P . S C H W A R Z E N B A C H Swiss Federal Institute of Environmental Science and Technology (EAWAG), CH-8600 Du ¨ bendorf, Switzerland
Photolysis on soil surfaces is an important degradation pathway for many agrochemicals. Although the investigation of photochemical pesticide transformation on soil surfaces is required by registration authorities, knowledge of the relevant processes is limited. The quantification of photolysis on soil surfaces is of higher complexity than it is in solutions. In experiments, carried out on soil layers, the observed overall degradation rate is not only determined by photolysis itself but is also a function of the layer thickness and in many cases of transport processes. In this article we describe a theoretical framework to understand combined effects of these different processes, and we present an experimental setup that allows a separate quantification of actual photolysis and diffusive transport processes. For the two compounds p-nitroanisole and trifluralin we performed experiments on kaolinite layers of variable thickness and evaluated the results using a mathematical model. Thus, we were able to determine the actual photolysis rate constants which are independent of layer thickness and transport kinetics. The proposed theoretical and experimental concept contributes to the development of a standardized laboratory method.
Introduction Photolysis on soil surfaces is an important degradation pathway for a variety of organic compounds including agrochemicals or chemicals introduced to soils by sewage sludge applications (1-3). From the results of numerous studies it can be concluded that both direct and indirect photolytic transformation reactions of a given chemical may be quite different on soils compared to homogeneous or heterogeneous aqueous systems (e.g. refs 4-10). Despite this fact, and although the evaluation of photodegradation on soil is required for numerous chemicals by registration authorities (11), systematic investigations of this process are still lacking. One major reason for the very limited investigations are the large difficulties encountered when designing experiments that allow to evaluate and quantify the various factors that determine photochemical degradation on soils. Presently the most common experimental approach to study photodegradation of organic compounds on soils is to expose a series of thin, spiked soil layers (thickness typically between 0.25 and 2 mm) to a light source (12, 13). The overall disappearance rate coefficient of the compound, which is generally reported as photodegradation rate coefficient, is * Corresponding author phone: +41-1-823-5468; fax: +41-1-8235471; e-mail:
[email protected]. 1240
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then determined by measuring the total loss of compound from the soil layers as a function of time. However, these reported rates are of rather limited value, because they always depend on the layer thickness of the soil and in most cases also on transport kinetics which should in fact be treated separately. Because light penetration into soils is very limited (i.e. 0.1 to maximal 0.5 mm as reported by refs 6 and 14) and wavelength-dependent, the fraction of total compound actually exposed to light depends on the type of soil, on the thickness of the soil layer, and on the light absorption spectrum of the compound. Thus, the rate of transport (i.e., retarded diffusion) of the compound from dark to irradiated zones within the soil layer will heavily influence the observed overall elimination rate. Since transport depends on the gas/ solid partitioning behavior of the compound, and since sorption is strongly influenced by temperature and humidity (15, 16), these parameters also need to be controlled in experiments. For future studies, experimental approaches are needed that allow to determine the actual photolysis rate constants, that are independent of layer thickness and transport velocity of a compound. In this paper, we present a novel theoretical and experimental approach for systematic investigations of photolytic transformations of organic compounds on soil surfaces. This approach builds, in principle, on the classical method to expose homogeneously contaminated thin soil layers to light. However, in contrast to the traditional approach, several series of layers of different thicknesses are exposed concurrently. The combined set of experimental data thus obtained is analyzed by a mathematical model that takes into account the actual photolysis rate of the compound and the depth of light penetration as well as the transport of the compound within the layer. As is demonstrated using kaolinite as a model soil and two compounds with different light absorption and gas/solid adsorption characteristics as probe molecules, this approach allows the separation of transport and photolysis kinetics and thus the determination of the actual photolysis rate constants of organic compounds on solid surfaces. In addition, with the rather simple experimental device developed in this study, a better control of important parameters such as temperature, humidity, and loss by volatilization can be achieved as compared to traditional experimental setups. Hence, the work presented in this paper should contribute to the development of a routine test system for assessing the photodegradation of organic chemicals on soils. Real soils are, of course, a much more complex system than the pure kaolinite layers used here. Organic matter would affect the sorption of the test compound and may, like iron or manganese species, act as a sensitizer or quencher of photochemical reactions. Such effects, however, were beyond the scope of the present paper which focuses on the effect of layer thickness and transport on the observed degradation rate in the case of direct photolysis.
Model for Describing Direct Photolysis of Organic Chemicals in Homogeneously Contaminated Porous Layers Figure 1 depicts schematically the model assumptions made for evaluating direct photolysis rate data determined in porous thin layers. As already mentioned above, the two major processes considered are direct photolysis and diffusion of the compound from the darker to the more irradiated zones. At a given depth z, the rate of direct photolysis is assumed to obey a first-order rate law 10.1021/es990910k CCC: $19.00
2000 American Chemical Society Published on Web 03/01/2000
Rf ) 1 +
Fbulk‚Kads porosity
(6)
Combining eqs 3 and 4, the temporal change in total mass, Mtot, of the compound in the whole soil layer, which is measured in the experiment, can be expressed by
FIGURE 1. Scheme of the theoretical concept describing photolysis of organic compounds in porous solid layers. k0p denotes the actual photolysis rate at the surface of the layer, z0.5 is the depth, where the light is attenuated by half, Deff is the effective diffusion coefficient, and ztot the total layer thickness.
dC(z) ) -kp(z)‚C(z) dt
(1)
where C(z) is the concentration of the compound expressed as mass of compound per mass solid phase, and kp(z) is the first-order photolysis rate constant at the depth z (time-1). In analogy to direct photolysis in aqueous solution, k0p may be rationalized by
k0p ) 2.303‚
∫[I (λ)‚(λ)‚Φ(λ)] d(λ) λ 0
(2)
where I0(λ) is the light intensity at the surface, and (λ) and Φ(λ) are the molar decadic absorption coefficient and the quantum yield of photolysis of the compound as a function of the wavelength, λ, respectively. Note, that both (λ) and Φ(λ) of a compound adsorbed on a surface may be quite different from the corresponding values determined in aqueous solution. Therefore, prediction of k0p is presently not possible. To relate kp(z) to k0p, the first-order photolysis rate constant at the surface of the soil layer, it is assumed that the light intensity decreases exponentially with depth and that light is only attenuated by the solid (i.e. inner-filter effect is negligible). The attenuation of light at a given wavelength can then be described by a characteristic depth, z0.5(λ), over which the light intensity decreases to half. In the usual experimental setup, the degradation rate is not measured as a function of wavelength but as an integral entity for the whole spectrum. Hence, the determined values for k0p and z0.5 are weighted average values for the whole range of wavelengths where light is absorbed by the compound. Thus, kp(z) can be approximated by
kp(z) ) k0p‚e-z/(1.443z0.5)
(3)
i.e., so that kp(z) ) 0.5 × k0p at z ) z0.5. Diffusion of the compound within the soil layer can be described by Fick’s law using an effective diffusion coefficient Deff :
∂C(z) ∂2C(z) ) Deff‚ ∂t ∂z2
(4)
Deff can be approximated according to ref 17:
Deff )
Dair‚tortuosity Rf
(5)
Deff is determined by the molecular diffusivity of the compound in air, Dair, the tortuosity of the pores, and the retardation factor, Rf, that can be calculated from the soil/air partition constant, Kads (volume/mass), of the compound, the bulk density of the porous solid, Fbulk (mass/volume), and the porosity of the layer (18).
dMtot ) A‚Fbulk dt
∫
[
z)ztot
z)0
]
∂2C(z) 0 -z/(1.443z0.5) -k p‚e ‚C(z) dz ∂z2 (7)
Deff‚
where A is the area of the layer. In eq 7 there are three critical parameters, i.e., k0p, z0.5, and Deff, that determine the experimental degradation curve. k0p and z0.5 are the parameters that describe the kinetics of photolysis and which shall be derived from the experimental data. For the design and evaluation of the experiments it is useful to distinguish three different types of degradation curves that can occur depending on the relative velocity of transport and photolysis kinetics. Case (1). Diffusion from the dark to the irradiated zone of the layer is fast relative to photolysis. In this case no vertical concentration gradient will be established within the layer (Figure 2a), i.e., ∂2C(z)/∂z2 ≈ 0 in eq 7 and the change in total mass will follow a first-order rate law
dMtot ) -kobs‚Mtot dt
(8)
where kobs represents a mean photolysis rate coefficient kpmean over the whole layer with the thickness ztot.
kobs ) kmean ) p
1 ztot
∫
z)ztot
z)0
(k0p‚e-z/(1.443z0.5))dz
(9)
After integration of eq 9 and assuming that all light is absorbed within the layer [i.e. ztot . z0.5] one can express kpmean as
1.443z0.5 ztot
kmean ≈ k0p‚ p
(10)
Hence, in this first case the observed degradation rate coefficient kobs ) kpmean is inversely proportional to the layer thickness ztot. If both, k0p and z0.5 are unknown, they cannot be determined individually from these degradation curves, since the term k0p‚z0.5 in eq 10 for a specific compound is the same for any layer thickness. In this case an independent determination of the light penetration depth would be desirable. Case (2) is the transition between case (1) and case (3) and is discussed below. Case (3) represents the other extreme, where diffusion is very slow as compared to photolysis. In this case, the depletion curve of the compound shows two distinct regions (Figure 2c). The first part represents photolysis in the irradiated zone, while the second part is dominated by slow diffusion from the dark to the irradiated zone. This results in a significant discontinuity in the loss curve i.e., a breakpoint. Hence in case (3) only the initial part of the complete curve reflects the actual photolytic transformation. In this case, one single experiment is sufficient to derive k0p, Deff, and z0.5 by fitting the experimental data with eq 7: k0p can be extracted from the slope of the first part and Deff can be obtained from the slope of the second part of the curve. The break-point in the curve allows one to obtain z0.5, since its location indicates the relative mass (e.g. 0.2 in Figure 2c), which is accessible to the light without diffusive transport needed. Assuming a homogeneous contamination of the layer, this relative mass corresponds to the part of the total layer, where light penetrates i.e., about 4 z0.5, which correVOL. 34, NO. 7, 2000 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 2. Schematic depth profiles at various times of irradiation (top) and related temporal mass loss (bottom) of a compound photolyzed on a solid layer. Depicted for cases (1)-(3) as described in the text. sponds to the depth where light is attenuated by 95%. Case (3) type degradation curves have been reported in the literature (14, 19) but have not been interpreted quantitatively. Discussion of Case (2). Case (2) is the general case where the whole curve is influenced by both photodegradation and diffusion kinetics. This is the most critical case, because, as illustrated by Figure 2b, the degradation curve exhibits apparent first-order kinetics and may, therefore, be misinterpreted as a case (1) situation. Theoretical case (2) type curves deviate slightly from an ideal first-order behavior. Yet, this deviation is too small to be detected experimentally. However, case (2) can be distinguished from case (1) in that the observed degradation rate will not be inversely proportional to ztot. If experiments are done with several layer thicknesses, the unknown parameters, k0p and z0.5, can be determined by simultaneous fitting of all experiments with eq 7. Note, that there is a continuous transition between case (2) and (3).
FIGURE 3. Top view (a) and cross section (b) of the setup of the kaolinite layers sandwiched between glass plates: 2 mm thick Pyrex glass plates (1), 1 cm broad Teflon gasket, 0.25-2 mm thick (2), fold-back clips (3), red film on the bottom plate (4), and the kaolinite layer (5).
Experimental Section Materials. All chemicals were reagent grade and used as received. p-Nitroanisole (PNA) and trifluralin were purchased from Fluka and Riedl de Hae¨n, respectively (for structures of PNA and trifluralin see Figures 4 and 5). Kaolinite [Al2Si2O5(OH)4] was available as China Clay Supreme from English Clays Lovering Pochin & Co. Ltd. (St. Austell/Cornwall, U.K.) and was a well-crystallized weathering product from granitic bedrocks with a specific surface area of 12 m2 g-1 (BET) (20, 21). Kaolinite suspensions were prepared in Nanopure water (Q-H2O Barnstead). Preparation of the Kaolinite Layers. Figure 3 depicts the experimental setup. A thin (for thickness see Table 1) Teflon frame, 10 mm broad, was attached as gasket on the border of a clean 100 mm × 100 mm Pyrex glass plate (2 mm thick, light cutoff at 290 nm). A kaolinite slurry (for concentrations of the suspensions see Table 1), treated in an ultrasonic bath during 2 min, was distributed homogeneously on the glass plate and air-dried to form a layer of a defined and reproducible thickness (Table 1) and an area of 80 mm × 80 mm. The probe compound (PNA or trifluralin) was dissolved in hexane and was dispersed evenly on the air-dry kaolinite layer, using a Hamilton syringe. [Note that, the application of the chemical before preparation of the aqueous suspension yielded a very poor recovery on the final dry layers, since water competes with the compound for the kaolinite surface, resulting in evaporation of the compound during the drying 1242
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FIGURE 4. Experimental data (0) of PNA degradation on irradiated kaolinite layers of various thickness. First-order fits (- - -) were made separately for each experiment, resulting in the respective apparent first-order rate coefficients (Table 2). The simultaneous fit (s) implementing the proposed theoretical concept describes all the experiments with one set of parameters. (For Figure 4b the first-order fit and the model fit are congruent.) process.] The layer was then covered by a second Pyrex glass plate, and both glass plates were pressed together by foldback clips placed along the border of the plates. Thus, the volume of the gas phase between these glass plates was minimized to restrain loss of the compound by volatilization, to keep humidity constant, and to enable the exchange of
FIGURE 5. Experimental data (0) of trifluralin degradation on irradiated kaolinite layers of various thickness. First-order fits (- - -) made separately for each experiment (respective apparent first-order rate coefficients see Table 2). The simultaneous fit (s) describes all the experiments with one set of parameters.
TABLE 1. Experiments Carried Out on Kaolinite Layers: Concentration of Suspensions and Resulting Layer Thicknesses thickness concn of aq air dry of the kaolinite weight of calcd layer Teflon suspensiona kaolinite on thickness gasketd [g mL-1] platesb [g] ztot c [mm] [mm]
probe compde
0.050
0.13 ( 0.003
0.01
0.25
PNA
0.075
0.26 ( 0.01
0.02
0.50
PNA
0.100
0.53 ( 0.01
0.045
1.0
0.120
1.11 ( 0.01
0.09
2.0
0.200 0.240 0.300
2.12 ( 0.07 4.28 ( 0.07 5.18 ( 0.34
0.17 0.35 0.45
2.0 2.0 2.0
trifluralin PNA trifluralin PNA trifluralin trifluralin trifluralin PNA
initial concns [mg g-1] 0.23/ 0.124 0.25/ 0.122 0.24 0.25 0.24 0.074 0.24 0.24 0.23 0.145
a Used to prepare the layers on glass plates. b Determined by weighing the kaolinite scraped off the plates after irradiation given with its standard deviation. c The thickness of the kaolinite layers was calculated by dividing the mass of applied kaolinite by the bulk density Fbulk of kaolinite (1.8 g cm-3) and by the area of the layer (64 cm2). d Defining the distance between the glass plates. e Only one substance, either PNA or trifluralin, was applied for each experiment.
heat between the mineral layer, the glass plate and the surroundings. To avoid irradiation through the bottom plate by scattered light, a red film, absorbing light < 580 nm, was placed at the bottom of the plate. For more experimental details see ref 22. Irradiation of Samples. Samples were irradiated in a XENOTEST 250 (Heare¨us), equipped with a Xenon long arc lamp (type NXe 2700) and filters for the elimination of wavelength in the IR range and below 280 nm. The lamp output was about 1.3 kW, which corresponds to a light intensity of 0.6 kW m-2 (integrated over the wavelength range
of 300-800 nm) as determined by ferrioxalate actinometry according to refs 23 and 24. The relative humidity in the climate chamber was fixed at 50% in order to minimize the humidity gradient between the gas phase in the sealed plates and their surroundings. The temperature within the climate chamber was 28 ( 2 °C. The temperature on the surface of the glass plates was measured to be 33 ( 1 °C and was constant during the experiments. Determination of PNA and Trifluralin Losses. For each data point one plate was withdrawn from the climate chamber. The layer was quantitatively scraped off, weighed, and mixed. From this sample, four replicates of 25-60 mg were extracted in amber glass vials with 1.5 mL of acetonitrile in the case of PNA and with 1.5 mL of methanol in the case of trifluralin. The samples were shaken for at least 4 h at 125 U min-1 and 25 °C. After centrifugation, 0.65 mL of the PNA extract or 0.85 mL of the trifluralin extract were added to 0.35 mL or 0.15 mL of H2O Nanopure in amber HPLC vials, respectively. The analysis of PNA and trifluralin was performed on a HPLC system (Hewlett-Packard 1090 Series II/L liquid chromatograph) equipped with a data acquisition system, diode array detector, auto sampler, and a column LiChrosphere 100 RP-18 (5 µm) from Merck, 125 × 4 mm plus precolumn (10 mm). For the measurement of both substances, isocratic elution at a flow of 1 mL min-1 was used. The eluent was 35% H2O and 65% methanol for PNA and 15% H2O and 85% methanol for trifluralin. PNA peaks were quantified at 307 nm and trifluralin peaks at 275 and 380 nm. Control Experiments. Dark control experiments were carried out employing the same procedures as for regular experiments, but the plates were covered on both sides with a red film. To check whether the substance was homogeneously distributed within the vertical dimension of the layer, in each experiment a series of one or several plates was irradiated upside-down. The applied PNA concentration was varied to ensure that no concentration effects occur. Choice of the Probe Molecules. The two compounds PNA and trifluralin were chosen because of their different light absorption properties. Both substances are degraded by direct photolysis. PNA has its maximal specific rate of light absorption (under sunlight in aqueous or methanolic solution) at λm ) 314 nm, a photolysis quantum yield in solution of Φ313 ≈ 3 × 10-4, and log 314 ) 4.04 (25), while λm of trifluralin is in the range of 400-430 nm, log 400-430 ) 3.5. The photolysis quantum yield of trifluralin in aqueous solution is reported to be Φ366 ≈ 2 × 10-3 (26). The effective diffusion coefficients Deff of the two compounds were calculated from eq 5 and 6 for 35 °C with an estimated porosity and tortuosity of 0.3 and 0.5, respectively, and a bulk density of the kaolinite, Fbulk ) 1.8 g cm-3. Dair was estimated to be 0.077 cm2 s-1 for PNA and 0.050 cm2 s-1 for trifluralin, according to ref 27. The solid/air partition constants were calculated to be Kads(PNA) ) 8.0 × 106 cm3 g-1 and Kads(trifluralin) ) 2.0 × 107 cm3 g-1 for 30% relative humidity at 35 °C, what corresponds to the absolute water content of 50% relative humidity at 27 °C in the climate chamber. This calculation was based on experimental data for other compounds on kaolinite (28) and extrapolated to PNA and trifluralin using a model described in ref 29. The resulting effective diffusion coefficients were Deff(PNA) ) 8.0 × 10-10 cm2 s-1 and Deff(trifluralin) ) 3.3 × 10-10 cm2 s-1.
Results and Discussion Quality of Experimental Data. The experimental degradation data of PNA and trifluralin on irradiated kaolinite layers of various thicknesses are shown in Figures 4 and 5, respectively. For both PNA and trifluralin, the results were reproducible. Since each data point in the degradation experiments was obtained from an extra plate, the smoothness of the curves VOL. 34, NO. 7, 2000 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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indicates the high reproducibility of the whole experimental procedure. In addition, duplicate measurements of single data points and the repetition of whole degradation curves (data not shown) showed good agreement. The values obtained from plates irradiated upside-down were within the experimental error, indicating that all layerssindependent of their thicknessswere spiked homogeneously over their depth. In general, reproducibility was best for thin layers. Different initial PNA concentrations did not affect the degradation rate. Furthermore, not more than 10% of the test compound was lost in any of the dark control experiments within the experimental time range. Evaluation of the Data by First-Order Fits. In a first step, all degradation curves were evaluated according to a simple first-order degradation law (dashed lines in Figures 4 and 5). This is not really appropriate for curves of type (2) or (3) but enables one to assign the experimental data to the different cases in a simple way. As can be seen from Figures 4 and 5 all cases (1)-(3) described above are represented in our experimental data. Case (1) is observed for the PNA photolysis experiments with ztot ) 0.02 and ztot ) 0.045 mm (Figure 4b+c): the apparent first-order rate coefficient is inversely proportional to ztot (decreasing from 0.18 h-1 to 0.086 h-1) indicating that there is no influence of transport kinetics. In the thicker layers, which can be related to case (2), the apparent first-order degradation rate coefficient decreases more than proportionally to ztot. This points to a significant influence of transport kinetics on the apparent rate coefficient. Note that this influence is not obvious from the single curves (Figure 4d+e) which may still be properly fitted by a first-order degradation curve. Only the comparison of experiments with different layer thicknesses ztot indicates that transport kinetics affects the apparent first-order rate coefficient. Apparently most of the trifluralin degradation curves (ztot ) 0.045, 0.09, and 0.17 mm) belong to case (2), i.e., they are not distinguishable from first-order degradation curves but comparison of the apparent first-order degradation coefficients points to slow transport kinetics (Figures 5b-d). In the case of the thickest layer (ztot ) 0.35 mm), the trifluralin degradation curve cannot nicely be described by a first-order fit and, hence, can be assigned to case (3) (Figure 5e). For the thinnest layers [ztot ) 0.01 mm for PNA and ztot ) 0.02 mm for trifluralin (Figures 4a and 5a)] an additional effect is observed that has not yet been discussed: the apparent degradation rate coefficients from these experiments are smaller than one would expect from comparison with the degradation rate coefficient of the next thicker layers assuming a case (1) behavior. This finding can be explained with the depth of light penetration being greater than the thickness of the kaolinite layer. Thus, only part of the incoming light is absorbed and used for photolysis, while the rest penetrates through the layer. Evaluation of the Data by Simultaneous Fits. While the evaluation of the degradation curves according to a simple first-order rate law yields a good qualitative picture, it does not allow the quantitative determination of the characteristic photodegradation parameters. Instead, eq 7 which explicitly distinguishes the effects of diffusion and photolysis kinetics must be used to quantify the actual photolysis rate constant, k0p, and the light penetration depth z0.5. The idea of eq 7 is that all degradation curves of one compound on layers of different thicknesses can be described with the same set of the parameters k0p, z0.5, and Deff used as fitting parameters. However, there are some limitations due to the specific sensitivity of eq 7 for each parameter: In case (3)-curves all three parameters k0p, z0.5, and Deff can easily be determined by fitting the curves (see above). For case (1)-curves, by contrast, eq 7 is almost insensitive to Deff, and furthermore k0p and z0.5 are completely intercorrelated and cannot be 1244
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TABLE 2. Apparent First-Order Rate Coefficients and Calculated Mean Photolysis Rate Coefficients, kpmean layer apparent calcdb type of curve thickness first-order kpmean according to cases contaminant [mm] rate coeffa [h-1] [h-1] described in the text PNA
trifluralin
0.01 0.02 0.045 0.09 0.45 0.02 0.045 0.09 0.17 0.35
0.23 0.18 0.086 0.027 0.0033 1.0 0.65 0.19 0.071 (0.0093)c
0.33 0.20 0.089 0.044 0.0089 1.1 0.70 0.41 0.22 0.11
(1)d (1) (1) (2) (2) (1)d (1)d (2) (2) (3)
a Apparent first-order rate coefficient obtained from fitting each curve separately, i.e., photolytic and transportation processes are included. b Calculated from eqs 9 or 10 (if z 0 tot > 4 z0.5) with k p and z0.5 obtained from a simultaneous fit of all curves with eq 7. c In fact, the curve shows no first-order behavior, hence yielding a bad first-order fit. d In this experiments the layer thickness ztot was smaller than the light penetration depth, i.e., not all the light was absorbed.
determined separately. In the intermediate case (2), there is a rather high intercorrelation of all three parameters and their determination by fitting may include considerable uncertainties. Most of our experimental data belong to case (1) or (2), and, hence, to improve the accuracy of the fitted values of k0p and z0.5, the effective diffusion coefficient Deff was not used as a fitting parameter but was estimated by an independent method (as described in the Experimental Section). Fitting the experimental data to eq 7 resulted in the following values for the fitting parameters (( standard deviation): k0p(PNA) ) 0.69 ( 0.19 h-1 and k0p(trifluralin) ) 1.6 ( 0.13 h-1 for the actual photolysis rate constants and z0.5(PNA) ) 0.0040 ( 0.0026 mm and z0.5(trifluralin) ) 0.016 ( 0.0099 mm for depth of photolysis. Since PNA is closer to case (1) i.e., k0p and z0.5 exhibit a stronger intercorrelation, the standard deviations of the fitting parameters are higher for PNA than for trifluralin. The simultaneous fitting was performed with the simulation and data analysis program AQUASIM (30, 31). [The deviation of the fit from the experimental data in the case of trifluralin on a 0.17 mmlayer might be due to some outliers in the experimental data.] The obtained z0.5 concur with the conclusion made above, namely that within the thinnest layers not all the irradiated light is absorbed: for both PNA and trifluralin (Figure 4a and 5a) the value of 4 × z0.5, the depth where 95% of the relevant light is absorbed, is bigger than the respective ztot. The finding that z0.5 for trifluralin is higher than for PNA can be explained by the expected decrease of light penetration with decreasing wavelength, since the maximal specific rate of light absorption of trifluralin is at a markedly higher wavelength λm than that of PNA. Thus, the wavelength range, which is most relevant for the photolysis of trifluralin, is less attenuated than that most efficient for PNA photolysis. The break point in the case (3)-curve of trifluralin on the 0.35 mm-layer (Figure 5e) is located at a relative trifluralin mass of approximately 0.8. This indicates that 20% of the initial trifluralin mass was degraded without transport being required, and, hence, the light penetration depth is about one-fifth of the total layer depth ztot. This is in good agreement with the depth of 95%light attenuation, 4 × z0.5(trifluralin) ) 0.064 mm, which corresponds to 18% of the total layer depth ztot ) 0.35 mm. In accordance with the relative photolysis rate constants of PNA and trifluralin in aqueous solution, k0p of trifluralin is higher than that of PNA. Inserting the fitted values of k0p and z0.5 into eq 9, we can calculate the mean photolysis rate coefficient, kpmean (see Table 2), which is an indicator for the photolysis that would occur if diffusion kinetics were fast enough not to affect the overall degradation rate coefficient.
In case (1) kpmean is identical with the apparent first-order degradation rate coefficient. In cases (2) and (3) the discrepancy between the two coefficients is a direct measure for the importance of transport kinetics i.e., the magnitude of the diffusion term in eq 7. Furthermore, the differences between the two rate coefficients illustrate the errors that occur if the apparent first-order rate coefficients are interpreted as pure photolysis rate coefficients. The deviation of the apparent first-order rate coefficient from kpmean is much more distinct for trifluralin than it is for PNA, which can be rationalized by its lower rate of diffusion as compared to the photolysis rate. [Note, that the considerable deviation between the apparent first-order rate coefficient and kpmean for PNA degradation on the 0.01 mm-layer, which is a case (1)-curve, can be explained by the high sensitivity of this thin layer toward the relatively high uncertainty of z0.5, because not all incoming light is absorbed in this experiment. In all other cases the rather high standard errors in k0p and z0.5 cancel when they are combined to calculate kpmean.] The experimental and theoretical approach described here allows the separation of photolysis kinetics and transport kinetics in experiments with irradiated porous layers. However, it proved to be difficult to separate the contribution of k0p and z0.5 to kpmean. For this purpose an independent determination of z0.5 would be desirable.
Acknowledgments We thank Silvio Canonica, Stephan J. Hug, Franz Gu ¨ nter Kari, Thomas Ravens, Torsten C. Schmidt, and Barbara Sulzberger for helpful and critical discussion and Peter Reichert for his help with modeling and fitting the data.
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Received for review August 6, 1999. Revised manuscript received December 29, 1999. Accepted December 29, 1999. ES990910K
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