Environ. Sci. Technol. 2003, 37, 482-487
Diffusion Coefficients of Humic Substances in Agarose Gel and in Water J. R. LEAD,† K. STARCHEV,‡ AND K. J. WILKINSON* CABE (Biophysical and Environmental Analytical Chemistry), University of Geneva, Sciences II, 30 Quai East Ansermet, CH-1211, Geneva 4, Switzerland
Measurements of the diffusion coefficients of five different humic substances (HS) have been performed in water and in agarose hydrogels at several pH values (in the range of 3-10) and gel concentrations (in the range of 0.7-3% w/w). Fluorescence correlation spectroscopy (FCS) and classical diffusion cells were used in parallel to probe diffusion over both microscopic and mesoscopic distance scales. In general, agreement between the techniques was reasonable, which indicated that local nonhomogenities in the gel did not play an important role. Diffusion coefficients (D) in the gel were generally in the range of 0.9-2.5 × 10-10 m2 s-1 but were generally only 10-20% lower than in solution. At low pH values, one of the studied humic substances (a peat humic acid, PPHA) formed large aggregates that could not penetrate into the gel and therefore could not be defined by a single D value. The observed decreases of D in the gel for other HS were too large to be explained by the tortuousity and obstructive effects of the gel alone. D decreased slightly with increasing gel concentration and increased slightly with pH. Because modifications of D due to pH were similar in both the gel and the free solution, it is unlikely that complexation with the gel was greatly influenced by the pH. Rather, the main effect that appeared to decrease the diffusive flux in gels was likely small increases in the hydrodynamic radii of the humic macromolecules. An anomalous diffusion model was used to describe the FCS data in the gel. The characteristic exponent determined by fitting the autocorrelation functions with this model decreased only slightly (from 0.96 to 0.90) with increasing gel concentration providing support that HS complexation with the gel fibers was not very important. The results have important implications for our understanding of the fate and behavior of the HS and their associated pollutants and for interpreting metal speciation data obtained using gelcovered analytical sensors.
Introduction Humic substances (HS) are potentially important for binding trace levels of pollutants (e.g., refs 1 and 2) with subsequent * Corresponding author e-mail:
[email protected]; phone: (41 22)702 6051; fax: (41 22)702 6069. † Present address: Division of Environmental Health and Risk Management, The University of Birmingham, Edgbaston, Birmingham, B15 2TT, U.K. ‡ Present address: Manteia SA, Zone Industrielle, CH-1267 Coinsins, Switzerland. 482
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effects on their transport (3, 4) and bioavailability (5) in aquatic systems. In systems where molecular diffusion is the predominant type of mass transport [e.g., in sediments and soil porewaters (6) and in the diffusive layer around particles and surfaces (7)], diffusion coefficients are required for a complete understanding of the system of interest. Accurate values of diffusion coefficients of HS in water and in gel are also required for the proper interpretation of chemical speciation data from several analytical techniques, notably for voltammetric microelectrodes where gels are used for anti-fouling purposes (8) and for the diffusive gradients in thin-film technique (DGT) (9, 10) where the gel layer thickness is often varied to interpret data in terms of environmental concentrations and fluxes. In both techniques, diffusive mass transport of the analyte through the gel may be rate limiting, thereby affecting speciation measurements. Several models have been proposed to interpret data obtained from the diffusion of small molecules, ions, macromolecules, and particles in gels (for reviews, see refs 11-13). If the diffusing molecules are much smaller than the average pore size of the gel, then the effective diffusion coefficient will reflect the smaller cross-sectional area available for diffusion (volume fraction of gel) and the greater distances over which the molecule must diffuse (tortuosity). For a gel that can be modeled as an assemblage of periodically spaced impenetrable spheres, the effective diffusion coefficient in the gel (Dg) will depend only on the decreased volume fraction of the gel fibers (φ) (14):
Dg 2(1 - φ) ) D (2 + φ)
(1)
where D is the diffusion coefficient in free solution and φ is the volume fraction of the gel fibers. On the other hand, where the particle size approaches the pore size, sieving and reptation models have been used to describe the diffusion of particles and molecules. In this case, an observed decrease in the value of Dg in the gel is due to a strong elastic interaction between the gel fibers and the diffusing particles or molecules such that Dg can be predicted from knowledge of the ratio of the size of the diffusing particles (Rh) and the gel fiber radius (Rf) (15, 16):
[ ( )]
Dg Rh ) exp -φ0.5 D Rf
(2)
Unfortunately, agreement between the above models and experimental data is often unsatisfactory for agarose gels (e.g., refs 17 and 18), possibly due to a fractal structure of the gel (19, 20). Therefore, anomalous diffusion models (21) have also been used to describe the diffusion of nanoparticles in agarose (12). In this case, the mean square displacement of the diffusing particles in the gel, 〈r2(t)〉, follows an anomalous power law:
〈r2(t)〉 ∝ t2/dw
(3)
where dw is the fractal dimension of a random walk in the gel (21) and t is the time of observation. In most cases, dw > 2 due to holes, bottlenecks, and dangling ends in which the particles can be temporarily trapped. It is difficult to relate this model to previous models since, for a fractal gel, the diffusion coefficient is ill-defined in that it depends on the scale of observation. In such a case, microscopic and mesoscopic measurements of diffusion coefficients should have different values. A further disadvantage of this model 10.1021/es025840n CCC: $25.00
2003 American Chemical Society Published on Web 01/07/2003
TABLE 1. Published Weight-Average Molar Masses, Charges (mequiv g-1), and C:O Ratios of Selected HS HS type
weightaverage MW
charge (mequiv g-1)d
C:O ratio
SRFA SRHA WBFA WBHA PPHA
860a 1 490a 2 400b 6 300b 23 000c
6.4 5.9 4.5 3.5 3.6
1.24 1.23 1.18 1.30 1.30
a Determined by flow field-flow fractionation (28). b Determined by ultracentrifugation (2). c Determined by ultracentrifugation (27). d Determined by potentionmetric titration (2, 27, 29).
is that it cannot distinguish between the diffusion of particles in a fractal network and the adsorption of chemically hetereogenous molecules such as the humic substances (21). Previous work (22, 23) has indicated that two of the HS (standard Suwannee River humic and fulvic acids, SRFA and SRHA) used in this study are relatively small, with hydrodynamic diameters 5% were found in the mass balance. At the end of the experiment, the diffusion cells were emptied, and the gel was verified for potential microtears by performing a second diffusion experiment with a large molar mass dye (dextran blue). Effective diffusion coefficients (Dg′) were determined from the initial fluxes (dC/dt) of the HS across a gel of thickness (x) (eq 4; 11):
Dg′ )
V x dC A ∆C dt
(4)
where V is the solution volume and A is the surface of the opening separating the two compartiments. The gel thickness was measured using optical microscopy and averaged 0.5-0.7 µm. Fluorescence Correlation Spectroscopy. The FCS method has been discussed in detail elsewhere (35, 36). In brief, laser light (excitation at 488 nm) is focused into a sample of interest using confocal optics. In this manner, a small, illuminated volume element (approximately 1.5 µm3) is created. Temporal fluctuations in the measured fluorescence intensity in the sample volume are used to derive an autocorrelation curve. In absence of any other processes that affect sample VOL. 37, NO. 3, 2003 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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fluorescence, the autocorrelation curve will be related to the translational diffusion of the fluorophore across the sample volume. Diffusion times of the HS are obtained from a best fit of the autocorrelation function (22) following calibration of the sample volume using Rhodamine-6G (R6G), which has a known diffusion coefficient of 2.8 × 10-10 m2 s-1 (37). Each data point was determined as the mean of three replicates with run times between 20 s and 10 min, depending on the experiment. The longer run times (a typical run time for R6G is 20 s) were employed to reduce noise in the autocorrelation curves, mainly because of the low quantum yield of the HS and the presence of aggregates. All FCS measurements were performed at 25 °C in an eight-welled, covered FCS cell. FCS has previously been shown to provide accurate diffusion coefficients of humic substances and their aggregates (22, 23). Because the technique measures the fluorescence intensity fluctuations of extremely small numbers of molecules, it is ideally suited for the determination of the diffusion coefficients of dilute solutions of polydisperse colloids and macromolecules. No significant variations of the fluorescence triplet fraction were observed among the different conditions (22). Finally, interlaboratory comparisons (23) have shown that FCS determinations of HS diffusion coefficients agree extremely well with diffusion coefficients measured by other nonperturbing methods such as flow field-flow fractionation and NMR. The gel was loaded with the HS by equilibrating the entire FCS sample cell for 24 h in a given HS solution (“external loading”). For the experiments using different gel concentrations, this allowed for each gel to be equilibrated with exactly the same solution under identical conditions. In a limited number of experiments, results were also acquired after mixing the HS solutions with the agarose at 60 °C, prior to the gelation step (“internal loading”). The main difference between the two techniques is that in the first, HS molecules can only penetrate into volumes that are not completely closed by fibers.
FIGURE 1. Dependence of the diffusion coefficient on the pH in the 1.5% gel (open symbols) and in free solution (solid symbols): (a) SRFA, (b) SRHA, (c) WBFA, (d) WBHA, and (e) PPHA.
TABLE 2. Diffusion Coefficients in Gel and Water Measured by FCS and Diffusion Cella
Results and Discussion pH Dependence of the Diffusion Coefficients in Gel and in Water. The structure of the agarose gel is determined by the concentration of agarose and possibly by the ionic strength (38). In this study, diffusion coefficients determined in gels that were prepared using Milli-Q water gave similar results to those prepared using a 10 mg L-1 solution of humic substances in 5 mM NaCl (i.e., internal vs external loading) suggesting that, within these limits, the ionic strength had little or no effect on the gel structure in agreement with smallangle neutron scattering results performed between 0 and 0.1 M NaCl (39). Both the internal and the external loading techniques indicated that the HS were generally small as compared to the average pore size of the gel. Diffusion coefficients for each of the five HS were measured as a function of pH in both solution and agarose gel (Figure 1, Table 2). As observed previously for the SRFA (22), in 5 mM NaCl, the values of the diffusion coefficient decreased with decreasing pH. The lower diffusion coefficients indicated a lower mobility that can most likely be explained by the formation of small aggregates (approximately 2-3 individual humic macromolecules) as the pH and therefore, the repulsive charge on the HS is lowered. Small parallel decreases were also observed in the pH curves obtained in the gels. The effect of pH is difficult to elucidate unambiguously since several processes are affected concurrently as the pH is lowered: (i) functional groups of both the HS and the gel may be protonated (increasing adsorption through a decrease in electrostatic repulsion and an increase in hydrogen or hydrophobic binding; (ii) intermolecular repulsion is de484
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HS type SRFA
pH
diff coeff in soln (FCS) × 1010 m2 s-1
2.7 ( 0.1 3.4 ( 0.1 2.2 ( 0.1 2.5 ( 0.1 2.6 ( 1.0 0.008 ( 0.001 6.9 3.0 ( 0.1
3.2 6.7 WBHA 3.1 6.8 PPHA 3.2
polydispersity ratio in soln (FCS)
diff coeff in gel (FCS) × 1010 m2 s-1
diff coeff in gel (diff cell) × 1010 m2 s-1
0.05 0.06 0.7 0.05 ndb
2.0 ( 0.1 2.5 ( 0.3 2.5 ( 0.1 2.2 ( 0.2 2.0 ( 0.1 1.0 ( 0.5 2.2 ( 0.1 1.0 ( 0.5 2.0 ( 0.1 ndb
0.1
2.4 ( 0.1
0.9 ( 0.6
a
The gel concentration in all samples was 1.5%. The standard deviations on the FCS measurements were determined from three replicate measurements. For the PPHA in solution, at pH 3.2, the autocorrelation curves were fitted with a two-component fit. In all other cases, only a single component was detected. Diffusion cell measurements were determined on duplicate measurements. The polydispersity ratio is defined as the square of the standard deviation of the distribution divided by the square of the mean of the distribution and was determined on the samples in solution. b no determination possible.
creased and can lead to aggregation (decrease in D); (iii) intramolecular repulsion is decreased leading to molecular compression (increase in D); and (iv) cation bridging reactions may be decreased by cation displacement (increase in D due to disaggregation or decreased adsorption of the HS). Nonetheless, the similarity of the decrease in D in the presence and absence of gel (Figure 1) suggested that the pH effect had the same origin in both cases. In such a case, a decrease in the diffusion coefficient as a function of the pH in the gel is most likely due to the changing nature of the HS rather than to increased interactions with the gel. Indeed,
FIGURE 3. Distribution of the diffusion times of the SRFA in free solution (circles) and in 1.5% agarose gel (squares), pH 3.2.
FIGURE 2. Distribution of the HS diffusion times at different pH values. The fractions were intensity weighted as described in ref 32. The squares are for pH 3.2, and the circles are for pH 6.7-6.9: (a) SRFA and (b) PPHA. Diffusion times of ca. 0.06 ms correspond to molecular hydrodynamic diameters of ca. 2 nm, while the larger diffusion times (10-12 ms) correspond to large aggregates with a size of ca. 300 nm (under the assumption that the aggregate is spherical and compact). we have previously shown that pH effects of the SRFA and SRHA in solution are dominated by aggregation rather than macromolecular compression (22). Cation bridging is unlikely to be important since trace metals have been extracted from these standard HS. Another important observation was that a single diffusion coefficient was sufficient to interpret the data adequately under most conditions with very good model fits (r2 > 0.99). Nonetheless, in the case of the PPHA in solution at low pH, this was not possible, presumably due to a high degree of sample aggregation and polydispersity, as has been recently observed by AFM (24) and unpublished ultrafiltration results from our laboratory. For this reason, a single diffusion coefficient cannot describe the PPHA at pH 3.2 (Figure 1e). In this case, the FCS data could only be fit by using two diffusion coefficients (Table 2), even though the relative errors remained high as compared to the other HS, presumably because of the polydisperse nature of the PPHA. Indeed, for the PPHA at pH 3.2, the larger, aggregated component that was observed at low pH values in solution was not observed in the gel, presumably because the aggregates could not penetrate into the gel pores. Distribution of the HS Diffusion Times As Measured by FCS. As seen above, the polydispersity of the HS could be hypothesized to play an important role with respect to their diffusion through the gel and in water. Therefore, HS polydispersity was examined in solution by analyzing the FCS autocorrelation curves using the method of histograms (40). For the SRFA, distributions of diffusion times through the FCS confocal volume were similar at pH 3.2 and pH 6.9, except that at low pH the curve was shifted to slightly larger diffusion times (Figure 2a). On the other hand, a very different result was observed for the peat-derived PPHA. At low pH
(3.2), a bimodal size distribution that included a significant proportion (25% by mass) of large aggregates (>300 nm) was observed (Figure 2b). Even at the higher pH values, the average sizes of the humic acids were significantly larger than those obtained for the SRFA at both pH (Table 2). On the other hand, the polydispersity of the WBHA and the SRFA were similar and significantly smaller than that of the PPHA. Note that due to the presence of two distinct component sizes, the polydispersity ratio of the PPHA could not be determined using the method of histograms. The reduction of HS diffusion in the gel could be due to (i) the adsorption of the HS by the gel; (ii) the electrostatic repulsion of the HS by the gel; (iii) the inability of a HS fraction to penetrate the gel pores due to polydispersity; or (iv) the fractal nature of the gel (i.e., decrease in D with distance). Although diffusion time distributions in the gels were not only shifted to higher values but were slightly broader than values obtained in solution (e.g., Figure 3), it is unlikely that the polydispersity of the HS increased in the gel with respect to solution since the sieving action of the gel is more likely to decrease polydispersity, as was observed for the PPHA at pH 3.2. Gel-water partition coefficients for both the IHSS HA and a more hydrophobic IHSS peat humic acid are 50% reduction in the overall charge of the SRFA and a ca. 20% reduction in the charge density of the gel have been observed at pH 3.2 as compared to pH 6.7 (29, 33, 41). Despite these large reductions in charge, only very small differences were observed between diffusion coefficients measured at the extreme pH values in the gel. Furthermore, differences due to pH were of similar magnitude to those observed in solution where no adsorption effect could be expected. The similarity of the pH decreases in gel and water and the broader distribution of diffusion coefficients in the gel was thus most likely due to an increased sieving and tortuoisity of the larger HS or by the anomalous diffusion of the HS (21) (see below). Comparison of FCS and Diffusion Cell Data. Diffusion coefficients for three different types of HS measured by the diffusion cell are also given in Table 2. In general, there is an order of magnitude agreement between the FCS and the diffusion cell techniques. Good agreement was observed between the techniques for the SRFA possibly because of its smaller size (see Table 1), slightly lower polydispersity, and weaker tendency to aggregate (23), while differences of >50% are noted for each of the two humic acids. These differences VOL. 37, NO. 3, 2003 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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must be related either to the techniques that were employed or to the nature of the HS. Two fundamental differences in the techniques could explain the differences between FCS and diffusion cell measurements. First, in the diffusion cell, the HS must cross the solution-gel interface, which is neglected in the FCS measurements. Second, the techniques operate on different size scales. The FCS technique measures diffusion coefficients locally on a submicron scale so that the value of D may depend on the local structure of the gel. In contrast, diffusion cell measurements are performed on the scale of the gel thickness, which is several hundreds of microns (mesoscopic experiments). In this case, differences due to micrometer-sized inhomogenities are assumed to be lost in the averaging process. The inhomogenity of the agarose gel is now welldocumented and may indeed lead to nonergodic behavior (42-44). Nonetheless, a 10 × 10 µm FCS scan of the gel with a 1-µm resolution between points showed no significant differences among the diffusion coefficients (data not shown). This result is probably because the HS are much smaller than the gel inhomogeneities, allowing them to explore nearly all of the available volume in the gel. If large molecules in a polydisperse mixture are prevented from penetrating the gel or if the HS are adsorbed onto the gel, overall smaller average diffusion coefficients should also be observed in the mesoscopic with respect to the microscopic measurements. Both explanations are theoretically possible for the PPHA and WBHA: their larger hydrophobicity (based on, for example, the C:O ratio in Table 1) or their slightly larger size polydispersity with respect to the other HS could explain some of the differences between the two techniques. On the other hand, as mentioned above, polydispersity differences were small, and no significant adsorption of the HS on the gel was expected, especially at pH 6.7. It would therefore appear that the most important difference between the SRFA and the humic acids is the significantly larger size of the latter HS. If this is the case, then models taking into account the sieving and elastic interactions of the HS with the gel fibers should explain a significant proportion of the differences between values made in gel and solution. This point is examined in greater detail below. Role of the Gel Concentration. An increase in gel concentration will result in an overall decrease in the average pore size, an increase in the obstructive effect, and an increased tortuosity. In the absence of aggregation, the HS molecules examined here were much smaller than the average pore size of the agarose gel (ca. 30-300 nm; 13); therefore, the geometrical effect of the gel should be adequately described by eq 1 (Figure 4). In fact, the dependence of the diffusion coefficients on the gel concentration was much too strong to be explained uniquely by eq 1. Even after taking into account the potential sieving effects of larger molecules (eq 2), it was not possible to account for the observed dependence of D on the gel concentration (Figure 4). Although eq 2 is quite sensitive to the physicochemical parameters that are employed for the gel fiber thickness (e.g., 1.9 nm, 34; 3.3-4.0 nm, 13) and the hydrodynamic radii of the HS, it was impossible to obtain the near linear dependence that observed in Figure 4. Furthermore, it is interesting to note that a similar linear decrease of a similar order of magnitude has been previously observed for the diffusion of myoglobin through various fiber volume fractions of agarose (18, 45). As discussed above, another possibility that might explain the discrepancies from the simple models and the differences between microscopic and mesoscopic measurements is that the gel is fractal. FCS autocorrelation functions were therefore also fitted by the anomalous diffusion model described in eq 3. The exponent obtained from these fits should be near 1.0 in the case of free diffusion, less than 1.0 for restricted 486
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FIGURE 4. Dependence of the diffusion coefficient of the SRFA at pH 4.6 on the gel concentration. The solid line is obtained by taking into account obstruction and tortuosity effects (eq 1), while the dashed line is obtained by also including potential sieving for a gel fibril radius of 1.9 nm and a hydrodynamic radius of 1.0 nm (eq 2).
TABLE 3. Exponent 2/dw for Diffusion of HS in Gel and Free Solutionsa gel concentration (%) HS type
0.0
0.7
1.
1.2
1.5
2.0
3.0
SRFA, pH 4.6 SRFA, pH 5.4 PPHA, pH 5.6 PPHA, pH 10.3
0.95 0.95 0.88 0.96
0.94 0.95 0.96 0.96
0.93 0.95 0.94 0.95
0.93 0.95 0.94
0.94 0.87 0.95
0.92 0.91 0.90 0.94
0.92 0.91 0.91 0.93
a For all data, the error calculated from three replicate measurements was 0.01-0.02.
diffusion, and larger than 1.0 in the case of hyperdiffusion (12). Furthermore, the exponent is expected to decrease in the case of a large polydispersity of the HS molecules. In fact, exponents determined in the gels were generally greater than 0.9, indicating that diffusion was only slightly hindered (Table 3). On the other hand, the exponent was too large to explain the observed decrease in Dg/D simply by evoking the fractal nature of the gel since in this case dw should be between 3 and 5 (12). It was clear that none of the models was completely appropriate to explain the diffusion of the HS through the agarose gel. Admittedly, the models are oversimplified in that they do not take into account physical interactions such as hydrodynamic drag or chemical interactions such as physior chemisorption. Furthermore, other factors including a cage effect in which HS molecules are trapped in gel microzones or a Donnan charge effect could also restrict the apparent diffusion coefficient in the gel, potentially explaining the overestimation of Dg/D observed in Figure 4. Measurements made by preparing the gel using HS containing solutions or by allowing a HS solution to diffuse into a preformed gel (internal vs external loading experiments) gave statistically similar diffusion coefficients. It is thus highly unlikely that the HS molecules were either temporarily or permanently trapped in the pores of the gel (cage effect). Although agarose gels are generally considered to be neutral, small quantities of pyruvic acid and sulfur groups can give the gel a slight but significant negative charge (34). Such a repulsive charge on the gel would have the effect of decreasing the effective diffusion coefficient in the gel through a decrease in the partition coefficient and may be sufficient to account for the existing discrepancy between model and experimental results (Figure 4). Finally, despite the electrostatic repulsion between the HS and the gel, a weak adsorption of the HS on the agarose is also possible at low pH. It is possible to describe
this effect quantitatively (46) if the site density, proportional to φ, and the mechanism of interaction of HS with the gel is known which is not the case here. A further quantitative distinction among the different effects contributing to the underestimation of the reduction in Dg/D is not possible. Indeed, all of the above effects (polydispersity, adsorption, Donnan charge effect, size, etc.) might contribute to some extent to the differences between the theoretical and the experimental curves observed in Figure 4. Taken together, the results indicate that, under most experimental conditions, the HS examined here had similar diffusion coefficients (and thus sizes) although the more hydrophobic HS had slightly lower diffusion coefficients. In addition, under most conditions, diffusion of the HS was only slightly hindered in gels as compared with diffusion in solution. The single exception was the very hydrophobic peat humic acid that was partially prevented from penetrating the gel because of extensive aggregation. From these results, it is clear that in-situ measurements of metal speciation in natural waters by gel-based techniques are likely to be only slightly affected by binding to molecular HS although the gel may play a physical role in excluding HS aggregates. Signals obtained from speciation techniques using the agarose protective gels are therefore likely to be most sensitive to free metals, only slightly less sensitive to metals bound to HS macromolecules, and mainly insensitive to HS aggregates.
Acknowledgments Funding for this work was provided by the Swiss National Funds (Project Nos. 2000-050629.97/1 and 2000-61648.00) and the European Union 5th Framework Biospec Project (EVK1-CT-2001-00086). We would like to thank D. Kinniburgh for providing a sample of the UKGS peat humic acid; J. D. Ritchie and E. M. Perdue for providing unpublished titration data for the SRFA and SRHA; M.-L. Tercier, N. Fatin-Rouge, and J. Buffle for helpful discussions; and N. Iten and P. Hliva for technical assistance.
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Received for review May 31, 2002. Revised manuscript received November 13, 2002. Accepted November 26, 2002. ES025840N
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