J. Phys. Chem. C 2010, 114, 20055–20061
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Quantitative Prediction of Atrazine Sorption in a Manitoba Soil Using Conventional Chemical Kinetics Instead of Empirical Parameters Donald S. Gamble,*,† G. R. Barrie Webster,‡ and Marc Lamoureux† Department of Chemistry, Saint Mary’s UniVersity, Halifax, NoVa Scotia B3H 3C3, Canada and Formerly the Department of Soil Science, UniVersity of Manitoba, Winnipeg, Manitoba, Canada ReceiVed: July 10, 2010; ReVised Manuscript ReceiVed: October 14, 2010
How to predict the persistence and leaching of organic chemicals in soils is a long-standing environmental issue. The injection of soil slurries into an HPLC together with separate solution-phase analysis permits the resolution of total sorption into intraparticle-diffused and labile-sorbed fractions. Sorption site stoichiometry was revealed, and two-step sorption was confirmed. This permitted conventional chemical kinetics including Laidler’s integral rate law for second-order kinetics to be adapted to the natural mixture of irregular sorption sites. Quantitative predictions were successfully tested, and the effects of site saturation on the kinetics were demonstrated. Other authors have independently published evidence related to sorption site stoichiometry, by using scanning tunnelling and fluorescence microscopy for sorption onto idealized crystals. This presents opportunities for research advances in two directions. HPLC and microscopy methods could be used together for sorption mechanisms in both environmental and pure crystal systems. Introduction The quantitative prediction of pesticide persistence and movement in soils and aquatic systems has historically encountered some well-known difficulties. A natural soil is the ultimate example of a complex mixture of physically and chemically irregular materials. However, Friend et al. recently found that even chemically pure Al2O3 crystals can have as many as three types of sorption sites for a hydrophobic organic chemical.1 Monolayer assemblies of organic chemicals at solution-graphite interfaces have been known since the 1988 report of Foster and Frommer.2 They showed that scanning tunnelling electron microscopy could produce images of organic chemical molecules sorbed onto structurally regular graphite surfaces. The patterns of the structures were strongly influenced by the crystal lattice of the graphite. Among the publications that followed is the important new report by Ziener et al.3 that a number of monolayer structures can coexist but are dependent on the solution-phase concentration. The energy differences between the monolayer structures were small, with no measurable discontinuities. Of particular interest was a hexagonal structure that went through a maximum as solution concentration increased. Using fluorescence microscopy and silica surfaces, Schwartz et al. found that during the steady-state kinetics of surfactant sorption, each surfactant molecule displaced a water molecule.4 The labile sorption capacity θC was not reported. However, for an inherently second-order process to be approximately steady state, either of two experimental conditions would have had to be fulfilled. The first is θC(W/V) . solution concentration with the solution concentration approximately constant. The reverse is the other possibility. Either way, this is important evidence for the disruption of the structured water layer by the sorption of an organic chemical. The fast processes * To whom correspondence should be addressed. E-mail: dgamble@ ns.sympatico.ca. † Saint Mary’s University. ‡ University of Manitoba.
that the online HPLC microextraction method does not see have not yet been investigated for whole natural soils. These discoveries of discrete monolayer structures on idealized crystalline substrates have implications for the sorption of organic chemicals from solution onto soil particles. The first implication is that the diverse irregular surfaces of a soil sample can cause sorbed organic molecules to form irregular but discrete monolayer structures. Assuming that limited numbers of such structures can form on the available amounts of solution-solid interfaces, labile sorption capacities should exist. More than two dozen examples have been found with the online HPLC microextraction method.5 This has presented the opportunity of using the numbers of empty and filled sorption sites for the application of conventional chemical kinetics to the ultimate examples of irregular sorption substrates, natural soils. The experimental rate coefficients for the divers mixtures of sites are weighted averages. These weighted average rate coefficients are decreasing functions of reaction time. They are energetically closely spaced and cover a wide energy range.6 The numbers of mol/g of sites have in the past usually been unknown. If equilibria exist, law of mass action calculations produce weighted average equilibrium functions.5 When equilibria do not exist, kinetics calculations yield weighed average rate coefficients.7-9 The statistical weight for the weighted average rate coefficients is the reaction time.7-9 Although weighted average rate coefficients should be considered for predictions in natural systems, they cannot be directly related to either chemical potentials or partition functions. The extractions of differential functions for molecular level interpretations have been reported for first-order kinetics, but that is outside the scope of this work.7-9 The sorption of an organic chemical onto the surfaces of an immersed soil is known to be governed by second-order kinetics.10-12 This is frequently followed by intraparticle diffusion from surfaces sites into particle interiors.13 Although diffusion theory would be expected to apply, a number of authors have reported that experimentally the sorption into particle interiors shows first-order kinetics behavior.14-16 How-
10.1021/jp1063929 2010 American Chemical Society Published on Web 11/04/2010
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ever, there are three reasons why conventional second-order chemical kinetics have usually not been used for labile sorption. First, total sorption was not being experimentally resolved into recoverable and unrecoverable fractions. The other side of that is that the recoverable total was not being resolved into dissolved and labile sorbed fractions. This caused the next two problems. About 20 years ago, resolving total sorption into recoverable and unrecoverable fractions led to the discovery that labile sorption capacities can exist for sorption onto immersed soils.17,19 Selim and co-workers independently stated in 1994 that the measurement of total sites was needed if it could be done.10 To emphasize this point, Selim et al. subsequently substituted an indirect estimate for a direct experimental measurement. Their example was metolachlor in a clay soil.12 The molecular mass of metolachlor translates their estimate as θC ≈ 1.4 × 10-6 mol/ g. This is consistent with two Ontario examples having θC measurements for metolachlor of 0.0237 × 10-6 and 1.4 × 10-6 mol/g.19 Using unrelated experimental methods and conditions, Friendly et al. recently confirmed the existence of labile sorption capacities.1 They also cite reports of similar results.20-22 However, this type of information is still not widely used. When the numbers of empty and filled sorption sites are not determined in this way, second-order kinetics cannot be used for sorption onto surface sites. A third problem is that the first-order kinetics of intraparticle diffusion cannot be properly described when the number of filled surface sites is not known. The important reviews by Sitea et al.23 and Yeh et al.24 reported the results of sorption studies in which conventional chemical kinetics were not used. Having examined about 700 publications, they independently concluded that the empirical parameters being used were inadequate or even incorrect. The technical descriptions based on them could not be expected to give reliable predictions. However, these empirical parameters are still universally used for pesticide-soil regulatory procedures. In another comprehensive 1998 review,11 Sparks stated that future research needs include “...models that accurately describe both chemical kinetics and transport processes in multiple site, heterogeneous systems; more extensive studies on effects of residence time or aging on contaminant retentionrelease; and mechanistic studies that employ both kinetic and in situ microscopic and spectroscopic techniques (...aqueous suspensions can be examined)”. The parts of those requirements reported here include the use of aqueous slurries with which to investigate the chemical kinetics and mechanisms of sorption and the effects of aging in a multiple site heterogeneous system. A limited amount of electron microscopy is included. This work has two related objectives. It confirms the previous reports that conventional chemical kinetics can be used to predict the sorption of organic chemicals by immersed soils.5,19 In the previous example the labile sorption sites were unsaturated. In the present example, the more difficult case of saturated sorption sites was tested. As a supporting objective, the anticipated flaws in simple distribution coefficients have been experimentally demonstrated. They are a typical reason why conventional chemical kinetics should be adapted to sorption by immersed soils. Theory Previous authors, for example, Ma,10 have stated that pesticide sorption from solution onto immersed soils is a second-order kinetics process. This has recently been confirmed experimentally.5,19 Since the original 1966 report by Hamaker,13 several authors have confirmed the existence of intraparticle diffusion from surface sites into particle interiors. An HPLC method that
Gamble et al. TABLE 1: Osborne Clay Soila I. sorption properties EGME m2/g
atrazine sorption
mol/g
θC (mol/g) -4
1.00 × 10 whole soil 223.0 8.257 × 10 organic 214.9 7.957 × 10-4 matter removed
-7
σ 0.5 × 10-8
II. bulk properties % sand
% silt
% clay
% OM
initial pH
final pH
1
32
67
4
7.97
6.90
III. X-ray fluorescence analysisb,c %
unheated
heat treated
ppm
unheated
heat treated
SiO2 TiO2 Al2O3 Fe2O3 MnO MgO CaO Na2O K2 O P 2 O5 LOId sum
53.47 0.62 13.7 6.06 0.09 3.31 3.1 0.39 2.33 0.25
56.35 0.63 13.99 6.21 0.09 3.34 3.1 0.64 2.35 0.23 25.07 86.93
V Cr Co Ni Cu Zn Ga Rb Sr Y Zr Nb Ba La Pb Th U Ce Nd Cs
163.3 133.8 17.2 48.3 37.9 132.5 19.2 120.2 207.6 23.3 153 13.4 527.6 37.7 21.2 15.4 9.3 82.4 32.2 7.1
168.6 132.6 17.3 49.5 36.5 139.7 20.9 122.9 217.2 21 162.9 12.7 545.8 39.1 24.2 13.5 9.6 89.5 32.3 3.9
83.32
a
Nov 12, 2009. Two samples received on Nov 3, 2009. User: Mark Lamoreux Regional Geochemical Centre, Saint Mary’s University SuperQ quantitative analysis of pressed powders using a Phillips PW2400 spectrometer. b Total: the total values do not include trace elements. c Major element analyses based on pressed powder techniques. d LOI ) loss on ignition: might be the sum of organic materials and water.
resolves total sorption into recoverable and unrecoverable fractions has revealed labile sorption capacities.17,18 Confirmation of that by Friendly et al. is noted above.1 Using these facts, it was previously proposed that empty and filled labile sorption sites can be regarded as reactants and products for conventional chemical kinetics calculations.5,19 That is, reaction mechanisms can be described in the same way that they would with simple monomeric reagents. The general description in this case is eq 1.
θa0(W/V) + M1 a θa1(W/V) f θd1(W/V)
(1)
θa0 and M1 are empty sorption sites and solution-phase pesticide. θa1 is filled sorption sites, and θd1 is the amount that has diffused into particle interiors. It is often referred to as a bound residue because simple extractions do not recover it. W/V is the g/L of soil to solution. As previously reported, Laidler’s second-order integral rate law eq 2 is used here.24 Retaining Laidler’s notation, a and b are the initial concentrations of empty sorption sites and solution-phase pesticide. x is the filled sorption sites, θa1(W/V).
Quantitative Prediction of Atrazine Sorption
J. Phys. Chem. C, Vol. 114, No. 47, 2010 20057 TABLE 2: Spreadsheet Locations of Formulas column
formula or action
O P R Y V AB to AE
Z1 ) ab[(exp(a - b)(V/W)kF1t) - 1] Z2 ) a[(exp(a - b)(V/W)kF1t) - b] M1 ) MT - Z1/Z2 θd1(W/V) ) [ML - (W/V)θd1]{1 - exp[-kd1(tb - ta)]} θa1(W/V) ) (Z1/Z2) iterative calculations
TABLE 3: Model 4a Parameters use yellow cells for predictions W (g) 21.199952 V (L) 1.000000 θC1 (mol/g) 1.000697 × 10-7 MT ) b (mol/L) 1.2509 × 10-6 K1 (L/mol) 2.185473 × 106 W/V (g/L) 2.119995 × 101
Figure 1. Osborne clay soil. Electron micrograph.
Laidler equation parameters a (mol/L) 2.121474 b (mol/L) 1.250857 ab (mol/L)2 2.653661 a - b (mol/L) 8.706162 b2 (mol/L) 1.067430 ab2 (mol/L)2 2.264524 a - b2 (mol/L) 1.054044
Figure 2. Labile sorption of atrazine in Osborne clay soil suspensions: 25 °C, relative standard deviations ) 5%. (b) Calibration experiment for Model 4a. Initial concentration, 12 509 × 10-6 M; 21.2000 g/L of soil. (×)Test experiment. Initial concentration, 9.6954 × 10-6 M; 21.1954 g/L of soil.
1 b(a - x) ln ) kt a - b a(b - x)
(2)
The desorption is a first-order process, given by eq 3
M1 ) θa1(W/V){1 - exp[kB1(tb - ta)]}
θd1(W/V) ) θa1(W/V){1 - exp[-kd1(tb - ta)]}
(4)
Labile sorption capacities θC can range over 2 or 3 orders of magnitude for different combinations of soil and pesticide.19 High solution concentrations with small sorption capacities can cause saturation of the labile sorption sites, that is, M1 > θC and θa1 ) θC. This reduces the general scheme to a special
10-6 10-6 10-12 10-7 10-6 10-12 10-6
case having two effects. The sorption goes to completion instead of attaining equilibrium, with one of the reactants, θa0, having been used up. Equation 1 reduces to eq 5, with no observable desorption.
θa0(W/V) + M1 f θa1(W/V) f θd1(W/V)
(5)
The kinetics of intraparticle diffusion also reduce to pseudozero-order kinetics, resulting in a linear dependence of θd1 on reaction time. kd1θa1 dt becomes kd1θC dt ) k0 dt. The resulting eq 6 gives a straight line. k0 is the pseudo-zeroorder rate coefficient.
(dθa1 /dt) ) k0
(3)
As previously reported, more than a dozen authors have described bound residue formation by intrapaticle diffusion with first-order kinetics.19 Attempts to show that it should be described by diffusion theory instead have not been successful. There is a possible explanation. For a physically sorbed molecule to diffuse, it must jump from one sorption site to another one. The breaking of the physical interaction is the analogue of the breaking of the stronger covalent bond in a chemical reaction. The net movement of the sorbed molecules would be controlled by the direction of the concentration gradient. The energy of activation should then be the desorption energy. Equation 4 for bound residue formation uses the experimental values of labile sorption, θa1(W/V).
× × × × × × ×
(6)
In contrast to the other rate coefficients, k0 is a constant because it represents the constant total of the labile sorption sites, instead of representing a time scan over the mixture. Experimental Section Osborne clay soil was collected from the top 15 cm of a site just southwest of Oak Bluff, Manitoba. Table 1 lists the whole soil analysis. An electron micrograph is shown in Figure 1. The dry sorption capacity for ethylene glycol monoethyl ether was measured by the vapor deposition method (EGME). The experimental method using online HPLC microextraction has been previously reported.17 A 0.5 g amount of soil was slurried in 25 mL of aqueous atrazine solution at 25.0 °C. Two parallel series of analyses were made. In one, solution-phase atrazine was measured as a function of time. Slurry aliquots were collected in disposable syringes. After removal of the solids by 0.45 µm filters, the solution concentrations were measured by injection of the solutions into the HPLC. In the other series, total recoverable atrazine was measured as a function of time. Aliquots of unfiltered slurry were injected directly into the HPLC, which measured the total atrazine that was recoverable from the solution and from the solids. The micrometer extraction
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TABLE 4: Calibration Experiment (µmol/L) and Test Experiment (µmol/L) no.
t (days)
solution M1
sorbed θa1(W/V)
residue θd1 (W/V)
t (days)
solution M1
sorbed θa1(W/V)
residue θd1(W/V)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64
0.000 0.130 0.180 0.250 0.500 1.000 1.100 1.200 1.250 2.000 2.125 2.200 2.250 3.000 3.050 3.100 3.150 3.200 3.250 3.900 4.000 4.150 4.200 4.250 7.000 7.125 7.200 7.250 8.000 8.050 8.150 8.200 8.250 9.000 9.250 10.000 10.100 10.200 10.250 11.000 11.050 11.150 14.000 14.050 14.125 14.200 15.000 15.050 15.125 15.200 15.250 16.000 16.050 16.150 16.250 16.800 17.000 17.050 17.100 17.200 18.000 18.050 18.125 18.200
1.2509 1.0674 1.0539 1.0235 1.0224 1.0202 1.0176 1.0150 1.0137 0.9943 0.9911 0.9891 0.9879 0.9684 0.9672 0.9659 0.9646 0.9633 0.9620 0.9452 0.9426 0.9364 0.9374 0.9361 0.8650 0.8617 0.8598 0.8585 0.8391 0.8378 0.8352 0.8339 0.8326 0.8132 0.8068 0.7874 0.7848 0.7822 0.7809 0.7615 0.7602 0.7576 0.6839 0.6826 0.6807 0.6787 0.6580 0.6567 0.6548 0.6528 0.6515 0.6321 0.6309 0.6283 0.6257 0.6115 0.6063 0.6050 0.6037 0.6011 0.5804 0.5791 0.5772 0.5752
0.0000 0.1822 0.1952 0.2250 0.2237 0.2211 0.2228 0.2244 0.2252 0.2374 0.2395 0.2407 0.2415 0.2538 0.2546 0.2554 0.2562 0.2570 0.2578 0.2684 0.2701 0.2748 0.2733 0.2742 0.3190 0.3211 0.3223 0.3231 0.3353 0.3362 0.3378 0.3386 0.3394 0.3517 0.3557 0.3680 0.3696 0.3712 0.3721 0.3843 0.3851 0.3867 0.4332 0.4341 0.4353 0.4365 0.4496 0.4504 0.4516 0.4528 0.4536 0.4662 0.4667 0.4683 0.4700 0.4789 0.4822 0.4830 0.4838 0.4855 0.4985 0.4993 0.5006 0.5018
0.0000 0.0012 0.0017 0.0024 0.0048 0.0095 0.0105 0.0115 0.0119 0.0191 0.0203 0.0210 0.0215 0.0287 0.0291 0.0296 0.0301 0.0306 0.0310 0.0372 0.0382 0.0396 0.0401 0.0406 0.0669 0.0681 0.0688 0.0692 0.0764 0.0769 0.0778 0.0783 0.0788 0.0860 0.0884 0.0955 0.0965 0.0974 0.0979 0.1051 0.1055 0.1065 0.1337 0.1342 0.1349 0.1356 0.1433 0.1438 0.1445 0.1452 0.1457 0.1525 0.1533 0.1543 0.1552 0.1605 0.1624 0.1629 0.1633 0.1643 0.1719 0.1724 0.1731 0.1738
0.000 1.011 1.054 1.088 1.135 1.194 3.217 3.982 4.018 4.055 6.993 7.015 7.066 7.097 7.128 7.162 7.212 7.242 8.009 8.060 8.106 8.138 8.174 8.209 9.044 9.113 9.149 9.184 9.223 10.017 10.160 14.091 14.122 14.153 14.185 14.221 14.995 15.024 15.053 15.131 15.159 15.188 15.215 15.243 15.989 16.017 16.045 16.136 16.165 16.193 16.224 16.991 17.019 17.047 17.135 17.163 17.191 17.220 17.947 17.975 18.003 18.031 18.058 18.086
9.6954 7.4962 7.4929 7.4903 7.4866 7.4821 7.3261 7.2671 7.2642 7.2614 7.0348 7.0331 7.0292 7.0268 7.0244 7.0218 7.0179 7.0156 6.9564 6.9525 6.9490 6.9465 6.9437 6.9410 6.8766 6.8713 6.8685 6.8658 6.8628 6.8015 6.7905 6.4873 6.4849 6.4825 6.4801 6.4773 6.4175 6.4153 6.4131 6.4071 6.4049 6.4027 6.4006 6.3985 6.3409 6.3388 6.3366 6.3295 6.3274 6.3251 6.3228 6.2636 6.2615 6.2593 6.2525 6.2503 6.2482 6.2460 6.1899 6.1877 6.1856 6.1834 6.1813 6.1792
0.0000 2.1189 2.1188 2.1187 2.1186 2.1185 2.1140 2.1123 2.1123 2.1122 2.1057 2.1056 2.1055 2.1055 2.1054 2.1053 2.1052 2.1051 2.1034 2.1033 2.1032 2.1032 2.1031 2.1030 2.1012 2.1010 2.1009 2.1008 2.1008 2.0990 2.0987 2.0900 2.0899 2.0898 2.0898 2.0897 2.0880 2.0879 2.0879 2.0877 2.0876 2.0876 2.0875 2.0874 2.0858 2.0857 2.0857 2.0855 2.0854 2.0853 2.0853 2.0836 2.0835 2.0835 2.0833 2.0832 2.0831 2.0831 2.0815 2.0814 2.0813 2.0813 2.0812 2.0812
0.0000 0.0802 0.0836 0.0863 0.0901 0.0947 0.2552 0.3159 0.3188 0.3217 0.5548 0.5566 0.5606 0.5631 0.5656 0.5683 0.5722 0.5746 0.6355 0.6395 0.6431 0.6457 0.6486 0.6513 0.7176 0.7231 0.7259 0.7287 0.7318 0.7948 0.8062 1.1181 1.1205 1.1230 1.1255 1.1284 1.1898 1.1921 1.1944 1.2006 1.2028 1.2051 1.2073 1.2095 1.2686 1.2709 1.2731 1.2803 1.2826 1.2849 1.2873 1.3482 1.3504 1.3526 1.3596 1.3618 1.3640 1.3663 1.4240 1.4262 1.4284 1.4306 1.4328 1.4350
occurred at filters on line. After the chromatographic peaks had been recorded, the solids were removed from the online filters. Analysis curves were prepared by least-squares fits of the measurements. Numbers of data points correspond to the numbers of measurements. This method resolved total sorption
into labile sorbed and bound residue fractions. Determination of the total number of labile sorption sites consequently became possible. This is the labile sorption capacity θC (mol/g). It was determined by saturation of the sites, as indicated by the horizontal line in Figure 2. The initial concentration for site
Quantitative Prediction of Atrazine Sorption
J. Phys. Chem. C, Vol. 114, No. 47, 2010 20059
Figure 3. Atrazine in a suspension of Osborne clay soil: the experiment for Model 4a: 21.200 g/L of soil. Initial solution, 1.2509 × 10-6 M, 25 °C. Relative standard deviations ) 5%.
saturation was 9.70 × 10-6 M, which was almost 8 times greater than that for the calibration experiment. The labile sorption capacity, θC ) 1.00 × 10-7 mol/g, is about 4 times smaller than the 3.97 × 10-7 mol/g that was reported for atrazine with the Plainfield Sandy Soil from southwest Ontario.19 The numbers of filled and empty sorption sites were calculate using θC. Extra decimal places have been carried to avoid round off and truncation errors during computing. The correct numbers of significant figures should be used for final reporting of model predictions. Two independent experiments were conducted. One was a model calibration experiment with an initial atrazine concentration of 1.25 × 10-6 M. It was used for calculating the kinetics rate coefficients of the model. A test experiment was run with an initial atrazine concentration of 9.70 × 10-6 M. It was used for checking model predictions. Experimental Development of the Kinetics Model. Model 4a is a revision of the previously described model 1 for atrazine sorption in the Plainfield sandy soil from southwestern Ontario.19 It was set up in a Quattro Pro X4 spreadsheet using Laidler’s equation for second-order chemical kinetics for labile sorption and first-order kinetics for bound residue formation. Table 2 gives the spreadsheet locations of the kinetics formulas. Table S1 has the spreadsheet entries as Supporting Information. The kinetic rate coefficients are kF1 for labile sorption and kd for intraparticle diffusion. Table 3 has the experimental parameters in columns G-I. Data from the calibration experiment for columns A-E are listed in Table 4. Test data for the prediction spreadsheet are also listed in Table 4. It is important to note that the labile sorption capacity θC was entered into the spreadsheet, so that filled and empty labile sorption sites θa1 and θa0 could be calculated from measurements. Empty sorption sites θa0 and the solution-phase atrazine were then used as the reactants just as reagents usually are for the a and b terms in Laidler’s second-order kinetics, eq 2.25 Likewise, θa1 for filled sorption sites was the reactant for the first-order kinetics description of bound residue formation. Experimental data for the physical states of atrazine in Figure 3 were entered into spreadsheet columns C-E. The kinetic rate coefficients kF1 and kd were determined by matching physical state curves for the model to the experimental values in columns C-E. Each rate coefficient value required 10-20 iterations. Trial values were entered into the spreadsheet formulas to initiate the calculations of the kinetic rate coefficients kF1 and kd. Each series of rate coefficients was calculated separately. For each data point of a kinetics curve, the refinement of a rate coefficient continued until the calculated concentration matched the experimental value in Table 4. It was matched to a number of decimal places that was well beyond the number of significant
Figure 4. Kinetic rate coefficients for the calibration experiment 4a. Initial concentration, 1.2509 × 10-6 M.
figures. This ensured that calculation errors were not added to the measurement errors, especially during subsequent predictions. Iterative calculations were needed because the three physical states are interdependent, as seen in eq 1. To avoid a “circular reference error” spreadsheet problem, this was done by copying from formulas in the AD and AE columns of Table S2 (Supporting Information) into numerical values in columns AB and AC. The calculated values of kF1 and kd in Table S3 (Supporting Information) and Figure 4 were taken from the spreadsheet columns M and Z. A graph of the model then looked exactly like the experiment in Figure 3. Experimental Tests Of Model Predictions. After calibration with the 1.25 × 10-6 M experiment, the model was used for predicting kinetics curves for the three physical states. The curves were predicted for an initial concentration of 9.70 × 10-6 M, which is about 8 times higher than the calibration concentration. The experimental test is shown in Figure 5. A calibration that filled only about 9-23% of the sorption sites gave a reasonable prediction of a case having 100% of the sites filled. Site saturation was a much more demanding test than subsaturation cases. The site saturation was overpredicted by about 8-10%, likely because of the accumulation of measurement and data processing errors. The bound residue curve began to fail after about 15 days. In the previously reported example with an Ontario soil, the bound residue prediction had the largest error.19 The percent distributions among physical states seen in Figure 6 have the right qualitative trends. The distribution among physical phases shifted to the solution as the initial concentration increased. The sorption and bound residue errors accumulated in the solution concentration. Critique and Experimental Tests of Distribution Coefficients KD. Simple distribution coefficients are not consistent with basic chemistry. If equilibrium exists, it is properly described only by some form of the law of mass action, which accounts for all of the reactants and products. Without this correct description, quantitative predictions cannot be assumed to be reliable. For pesticide sorption from solution onto
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Figure 5. Experimental test of model 4a. Model calibrated with initial concentration of 1.2509 × 10-6 M. Prediction tested for an initial concentration of 9.6954 × 10-6 M. Predictions: (s) test, (b) solution concentrations, (9) labile sorption, (2) bound residues. Relative standard deviations )5%.
Figure 7. Experimental distribution coefficients.
Figure 6. Distributions among physical states at 14 days: effect of the initial solution concentration. Predictions: (b) remaining in solution, (9) labile sorbed fraction, (2) bound residue. Experiments in red. Relative standard deviations ) 5%.
immersed surfaces, the distribution coefficient KD is incorrect for two reasons. First, it accounts for only one of the two reactants instead of both of them. Empty sorption sites are the missing reactant. Second, it does not correctly identify the product which is the set of filled sorption sites. Ambiguous sorption data are used instead, without a clear distinction being made between labile sorption and total sorption. If the labile sorption sites have become saturated, another problem with distribution coefficients emerges. Sorption then becomes insensitive to solution concentration, which makes it useless for predicting them. However, under field conditions equilibria cannot be assumed. Dynamic conditions are instead frequent and perhaps even usual. For those cases only kinetics descriptions are correct. The anticipated flaws in KD are found in the experimental graphs of Figure 7. Regardless of whether they are plotted against reaction time, initial concentrations, or time-dependent concentrations, the KD from the calibration experiment could not be used to predict the test experiment. These difficulties would not be solved by embellishments, such as conversion to KC or KOM parameters. Conclusions The previously reported feasibility of adapting conventional chemical kinetics to the quantitative prediction of sorption by
a mixture of substrate sorption site types has been confirmed. Experimentally determined sorption site stoichiometry made it possible to do this with Laidler’s integral rate law for secondorder kinetics. Saturation of the sorption sites changed the apparent kinetics of the two-step mechanism. A natural soil was the mixture of sorption site types. An HPLC method determined its sorption site stoichiometry. Friend et al.,1 Foster and Frommer,2 and Ziener et al.3 have shown that even for idealized systems of sorption onto well-defined crystal faces, numbers of sorption site types can exist because of self-assembly. Schwartz et al.4 reported sorbate displacement by a water molecule. The information and experimental methods now available have implications for both environmental chemistry and the surface chemistry of well-characterized crystal faces. These reports1-4 of work with idealized substrates provide important insights into the diversity of sorption site types in natural soils. The variety of chemical materials and irregular physical forms in a natural soil could result in a large number of irregular types of self-assembly at solution solid interfaces. Macroscopic measurements would then yield weighted average numerical values. These would be decreasing functions of reaction time. The sorption kinetics and mechanism for pure crystal faces can be anticipated. If labile sorption capacities are found for hydrophobic molecules at solution-solid interfaces, secondorder kinetics could be used for labile sorption. Also, if they are at equilibrium, crystals above 0 K have defects that could make intraparticle diffusion from surface sites possible. The result would be two-step sorption kinetics with weighted average rate coefficients. Used together, the concepts and methods of the two areas of research would be important for environmental chemistry, chromatography column packing, and catalyst supports. Acknowledgment. Mr. Walter Fraser, Agriculture and Agrifood Canada, Winnipeg, has made this work possible by generously providing the sample of Osborne clay soil. We thank Dr. Donald Flaten, Department of Soil Science, University of
Quantitative Prediction of Atrazine Sorption Soil Science, for his advice and help with soil sample collection. Stanley Cameron of Dalhousie University and Xiang Yang of Saint Mary’s University have helped to make the research authoritative by providing the X-ray diffraction and electron microscopy for the soil sample. Supporting Information Available: Spreadsheet locations of formulas and spreadsheet entries for iterative calculations and kinetic rate coefficients. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Quiller, R. G.; Benz, L.; Haubrich, J.; Colling, M. E.; Friend, C. M. J. Phys. Chem. C 2009, 113, 2063. (2) Foster, J. S.; Frommer, J. E. Nature 1988, 333, 542. (3) Meier, C.; Roos, M.; Ku¨nzel, D.; Breitruck, A.; Hoster, H.; Landfester, K.; Groβ, A.; Behm, R. J.; Ziener, U. J. Phys. Chem. C 2010, 114, 1268. (4) Andrei, Honciuc; Alexander, L. Howard; Daniel, K. Schwartz. I. Phys. Chem. C 2009, 113, 2078. (5) Gamble, D. S. EnViron. Sci. Technol. 2009, 43 (6), 1930. (6) Gamble, D. S. Interactions Between Natural Organic Polymers and Metals in Soil and Freshwater Systems: Equilibria. In The Importance of Chemical ‘Speciation’ in EnVironmental Processes; Bernhard, M., Brinckman, F. E., Sadler, P. J., Eds.; Dahlem Konferenzen, Springer-Verlag: Berlin, Heidelberg, 1986, 217-236. (7) Shuman, M. S.; Colins, B. J.; Fitzgerald, P. J.; Olson, D. L. Distribution of stability constants and dissociation rate constants among binding sites on estuarine copper-organic complexes: rotated disk electrode studies and an affinity spectrum analysis of ion-selective electrode and potentiometric data. In Aquatic and Terrestrial Humic Materials; Christman, R. F., Gjessing, E. T., Eds.; Ann Arbor Science: Ann Arbor MI, 1983, Chapter 17, p 4816.
J. Phys. Chem. C, Vol. 114, No. 47, 2010 20061 (8) Langford, C. H.; Gutzman, D. W. Anal. Chim. Acta 1992, 256, 183. (9) Gutzman, D. W.; Langford, C. H. EnViron. Sci. Technol. 1993, 27 (7), 1388. (10) Ma, L.; Selim, H. M. Water Resour. Res. 1994a, 30 (2), 447. (11) Sparks, D. L. Kinetics of Soil Chemical Phenomena: Future Directions. In Future Prospects for Soil Chemistry; SSSA Special Publication no. 55; Soil Science Society of America: Madison, WI, 1998; Chapter 4. (12) Selim, H. M.; Ma, L.; Zhu, H. Soil Sci Soc. Am. J. 1999, 63, 768. (13) Hamaker, J. W.; Goring, C. A. L.; Youngson, C. R. Degradation of atrazine and related S-triazines. Organic pesticides in the enVironment; American Chemical Society: Washington, DC, 1966; p 23. (14) Karickhoff, S. W. Sorption kinetics of hydrophobic pollutants in natural sediments. In Contaminants and sediments; Baker, R. A., Ed.; Ann Arbor Science: Ann Arbor, MI, 1980; Vol. 2, pp 193-205. (15) Brusseau, M. L.; Rao, P. S. CRC Crit. ReV. EnViron. Control. 1989, 19, 33. (16) Ball, W. P.; Roberts, P. V. EnViron. Sci. Technol. 1991, 25 (7), 1223. (17) Gamble, D. S.; Khan, S. U. J. Agric. Food Chem. 1990, 38, 297. (18) Gamble, D. S.; Ismaily, L. A. Can. J. Chem. 1992, 70, 1590. (19) Gamble, D. EnViron. Sci. Technol. 2008, 42, 1537. (20) Henderson, M. A. Langmuir 2005, 21, 3443. (21) Henderson, M. A.; Epling, W. S.; Perkins, C. L.; Peden, C. H. F.; Diebold, U. J. Phys. Chem. B 1999, 103, 5328. (22) Suzuki, S.; Yamaguchi, Y.; Onishi, H.; Sasaki, T.; Fukui, K. I.; Iwasawa, Y. J. Chem. Soc., Faraday Trans. 1998, 94, 161. (23) Sitea, A. D. J. Phys. Chem. Ref. Data. 2001, 30 (1), 187. (24) Yeh, S.; Linders, J. B. H. J.; Kloskowski, R.; Tanaka, K.; Rubin, B.; Katayama, A.; Ko¨rdel, W.; Gerstl, Z.; Lane, M.; Unsworth, J. B. Pesticide soil sorption parameters: theory, measurement, uses, limitations and reliability. IUPAC Project, No 640/43/97. Soc. Chem. Ind. 2002, 58 (5), 419. (25) Laidler, K. J. Chemical Kinetics, 1st ed.; McGraw-Hill Book Co., Inc.: New York; 1950, Equation 32, p 10.
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