Article pubs.acs.org/est
Development of Linear Free Energy Relationships for Aqueous Phase Radical-Involved Chemical Reactions Daisuke Minakata,*,† Stephen P. Mezyk,‡ Jace W. Jones,§ Brittany R. Daws,‡ and John C. Crittenden∥ †
Department of Civil and Environmental Engineering, Michigan Technological University, 1400 Townsend Drive, Houghton, Michigan 49931, United States ‡ California State University Long Beach, 1250 Bellflower Boulevard, Long Beach, California 90840, United States § Department of Pharmaceutical Sciences, University of Maryland School of Pharmacy, 20 North Pine Street Baltimore, Maryland 21201, United States ∥ Department of Civil and Environmental Engineering and the Brook Byers Institute for Sustainable Systems, Georgia Institute of Technology, 820 West Peachtree Street, Atlanta, Georgia 30332, United States S Supporting Information *
ABSTRACT: Aqueous phase advanced oxidation processes (AOPs) produce hydroxyl radicals (HO•) which can completely oxidize electron rich organic compounds. The proper design and operation of AOPs require that we predict the formation and fate of the byproducts and their associated toxicity. Accordingly, there is a need to develop a first-principles kinetic model that can predict the dominant reaction pathways that potentially produce toxic byproducts. We have published some of our efforts on predicting the elementary reaction pathways and the HO• rate constants. Here we develop linear free energy relationships (LFERs) that predict the rate constants for aqueous phase radical reactions. The LFERs relate experimentally obtained kinetic rate constants to quantum mechanically calculated aqueous phase free energies of activation. The LFERs have been applied to 101 reactions, including (1) HO• addition to 15 aromatic compounds; (2) addition of molecular oxygen to 65 carbon-centered aliphatic and cyclohexadienyl radicals; (3) disproportionation of 10 peroxyl radicals, and (4) unimolecular decay of nine peroxyl radicals. The LFERs correlations predict the rate constants within a factor of 2 from the experimental values for HO• reactions and molecular oxygen addition, and a factor of 5 for peroxyl radical reactions. The LFERs and the elementary reaction pathways will enable us to predict the formation and initial fate of the byproducts in AOPs. Furthermore, our methodology can be applied to other environmental processes in which aqueous phase radical-involved reactions occur.
1. INTRODUCTION
compounds. Therefore, a full mechanistic understanding of the formation of intermediates and byproducts is important. Three components are needed to predict the formation of intermediate radicals and stable byproducts based on experimental studies, including (1) radical and thermal reaction pathways,21 (2) absolute reaction rate constants,17 and (3) a numerical-based computer model to temporally and spatially calculate the concentration of each species.22 Although the general degradation of organic compounds in AOPs has not yet been elucidated, a number of past experimental studies and kinetic modeling efforts have revealed the initial formation of intermediate radicals and stable byproducts (Figure 1).5−7,23 In aqueous phase AOPs, carbon (C)-centered radicals are typically produced by H atom abstraction by HO• from a C−H bond or by HO• addition to an unsaturated carbon in an alkene or
Advanced oxidation processes (AOPs) produce highly reactive electrophilic hydroxyl radicals (HO•) in the aqueous phase at ambient temperature and atmospheric pressure. The HO• rapidly reacts with most electron-rich sites on organic compounds. Consequently, AOPs are attractive and promising technologies because they can destroy a wide variety of toxic organic compounds.1−3 Target compounds include (1) trace level organic compounds,4−9 (2) dissolved organic matter,10−14 (3) industrial wastewater containing polymers and/or nonbiodegradable refractory organic chemicals, and 4) RO retentate from municipal wastewater reclamation plants.15 In AOPs, radical-involved reactions induced by the HO• produce a variety of radical intermediates and stable byproducts.5−7 Some of these compounds (e.g., carboxylates and haloacetates) exhibit a much lower reactivity with HO•16,17 and could persist after AOP treatment, which could result in potential risks to human health in drinking water or reclaimed water.18−20 In addition, the byproducts may be more toxic than the parent © 2014 American Chemical Society
Received: Revised: Accepted: Published: 13925
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Figure 1. Generic form of initial elementary reaction pathways.
aromatic compound. The C-centered radicals react with tripletstate molecular oxygen (3O2) that is dissolved in water to produce peroxyl radicals. The peroxyl radicals undergo the unimolecular decay and/or the disproportionation.24 A shortlived tetroxide is expected to form by the disproportionation reactions between peroxyl radicals and stable byproducts (e.g., aldehydes, ketones, and carboxylic acids) are produced after the decay of the tetroxide.25 However, the detailed reaction mechanisms of the tetroxide are not fully understood. The peroxyl radical reaction mechanisms are the dominant pathways for the production of intermediates and byproducts.24−26 The prediction of reaction rate constants for a series of radical-involved aqueous phase reactions in AOPs has been a challenging task. A group contribution method (GCM) was developed as the first and most sophisticated comprehensive computational tool for the prediction of aqueous phase HO• reaction rate constants.17 To date GCM has been used to predict more than 500 HO• reaction rate constants within a factor of 2 from the experimental values. The limitations of GCM, such as the requirement for large data sets and the lack of quantified electron push−pull effects, solvation effects, steric effects, and the contribution of molecular diffusion, indicate that there is a need for more sophisticated computational tools to predict aqueous phase reaction rate constants. Minakata and Crittenden developed linear free energy relationships (LFERs) for aqueous phase HO• reactions to relate experimentally obtained kinetic rate constants to the quantum-mechanically calculated aqueous phase free energies of reactions.27,28 The resulting LFERs predicted the aqueous phase HO• rate constants within a factor of 5 from the experimental values. However, the reactions that occur after the reaction of HO• are critical for predicting the formation of intermediates and byproducts, and so a uniform theory is needed to completely predict reaction rate constants for these radical species. In this study, we have developed LFERs for the aqueous phase radical-involved reaction mechanisms that occur in the initial phase of AOP treatment. Once the LFERs have been established and applied uniformly for radical-involved aqueous phase reactions, they can be combined with the elementary reaction pathways to computationally predict the formation of intermediate radicals and stable byproducts.
k=
kDkchem kD + kchem
(1)
where kD and kchem are the diffusion-limited rate constant and second-order reaction rate constant for the chemical reaction, respectively. The kD value can be calculated using Smoluchowski’s equation,30 as shown in eq 2: kD = 4πDl rN0/1000
(2)
where Dl is the liquid phase diffusion coefficient for the solute and radical (cm2/s), r is the radius of the molecule (Å), and N0 is Avogadro’s number. The diffusivities of small, uncharged molecules in water can be calculated using the Hayduk-Laudie correlation,31 which is derived from the Wilke-Chang correlation.32
Dl =
13.26 × 10−5 (μω )1.14 (Vb)0.589
(3)
where μω is the viscosity of water (cP, 1 kg/m·s = 1000 cP) and Vb is the molar volume of the solute at the temperature at which a liquid boils at 1 atm of pressure (cm3/mol). The thermodynamics for diffusion-limited aqueous phase radical-involved reactions is not well established. Accordingly, we hypothesize that the generalized free energy profile of a diffusion-limited reaction can be drawn as a function of the reaction coordinate, as shown in Figure 2. The overall reaction
Figure 2. Hypothetical free energy profile for aqueous phase radicalinvolved chemical reactions.
react is an exothermic reaction (i.e., ΔGreact aq < 0, where ΔGaq is the aqueous phase free energy of reaction). In this process, the diffusion free energy that requires the formation of the initial vdW complex is exothermic. The chemical reaction is driven by the aqueous phase free energy of activation, ΔGact aq , and the free energy difference between the vdW complex and the transition state, defined as ΔGTS−complex . The kchem value may be expressed aq using an LFER,33,34 as shown in eq 4:
2. LINEAR FREE ENERGY RELATIONSHIPS Measurements of aqueous phase radical reactions indicate that these reactions are nearly diffusion-limited; the reactants encountered in the solvation cage due to diffusion create an initial van der Waals (vdW) complex. Then, the chemical reaction produces a stable radical. The observed overall reaction rate constant, k, can be expressed as in eq 1.29 13926
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varied by flowing the ambient-temperature solution through a short, temperature-controlled condenser just prior to the irradiation cell. Solution heating/cooling occurred for less than 20 s, and the actual solution temperature was measured immediately after the cell using a thermocouple placed directly in the exit flow. The temperature stability of this system was 18.0 MΩ) that was presaturated with the appropriate gas mixed to give desired oxygen concentrations (N2O and O2): high dissolved solute concentration (i.e., typically 1−2 mM) with gas concentrations calculated using the selected volume ratio and initial gas concentrations of [N2O] = 2.6 × 10−2 M and [O2] = 1.25 × 10−3 M. Peroxyl radical reaction formation rate constant measurements were performed using the LINAC pulse radiolysis facility at the Radiation Laboratory at the University of Notre Dame.37 Exact radical concentrations were determined using N2Osaturated solutions of KSCN (1.00 × 10−2 M) at λ = 475 nm (Gε = 5.2 × 10−4 m2 Gy1−)38 with an average dose of 3−5 Gy delivered per 2−3 ns pulse. The solution temperature was
SD =
1 n−1
n
∑ [(kexp, i − kcalc, i)/kexp,i]2 i=1
(10)
where kexp,i and k calc,i are the experimental and calculated reaction rate constants of compound i, respectively, and n is the number of rate constants. For each reaction mechanism, Tables provided in the SI (i.e., addition of molecular oxygen to Ccentered radicals of aliphatic compounds and cyclohexadienyl radicals for Table S1, addition of HO• to aromatic compounds for SI Table S2, unimolecular decay of peroxyl radicals for SI Table S3, and disproportionation of peroxyl radicals for SI Table S4) summarize the experimentally obtained reaction rate constants based on Arrhenius kinetic parameters and rate constants reported in the literature, calculated kD values and associated parameters for Smoluchowski’s equations, kchem 13927
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values and theoretically calculated ΔGact aq,calc values. Detailed discussions are provided in the following sections. 4.1. Hydroxyl Radical Addition to Aromatic Compounds. The aqueous phase reaction of HO• with an aromatic ring occurs mainly by addition typically at a rate that is close to the diffusion-limit. The functional group(s) and location(s) affect the reactivity of HO• both by changing the electron density distribution around the aromatic compounds and through steric effects. When functional groups contain aliphatic C−H bonds and/or nitrogen (N)-, sulfur (S)-, or phosphorus (P)-atom-containing compounds, the HO• can abstract a H atom from the C−H bond and/or interact with N, S, or P atoms.17 We calculated the contribution of reaction rate constants resulting from the aliphatic branches using the GCM17 and subtracted those from the experimentally obtained reaction rate constants reported in the literature. Accordingly, the rate constant from the chemical reaction for HO• addition to the aromatic ring, kchem is given by the expression:
this study this study
this study
0.62 0.86
3.2
10 (5, 8) 27 (24, 27)
9 (2, 8)
−1.14 27.09 G4+SMD −0.41 13.62 G4+SMD
−0.39 13.00 G4+SMD
disproportionation of peroxyl radicals O2 addition to cyclohexadienyl radicals(aromatic)
unimolecular decay of peroxyl radicals
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(11)
0.31 (calibration) 1.05 (prediction) this study
act(ortho) ΔGaq,calc ,
Minakata et al., 2011
this study Minakata and Crittenden, 2011
0.05
0.19 (calibration) 1.38 (prediction) Minakata and Crittenden, 2011
act(meta) ΔGaq,calc ,
act(para) ΔGaq,calc
where and are the theoretically calculated aqueous phase free energies of activation for HO• addition to the aromatic ring at the ortho, meta, and para positions, respectively. The contribution from the ipso position was insignificant due to the high steric effect and was not included in the LFER. Based on the experimental data set (n = 15), the calculated LFER for HO• addition to an aromatic ring is ln kchem = −0.14 ΔGact aq,calc +20.60 (Figure 3). The specific chemical compounds
Figure 3. LFER for HO• addition to aromatic compounds with a single functional group. Error bars represent the range of previously reported reaction rate constants in the literature.
used for the LFER were only those that contained a single functional group. Nitrosobenzene (NO) and methylphenyl sulfoxide (SOCH3) were excluded from our LFER fitting because their reported HO• rate constants were very close to or greater than the diffusion reaction rate (i.e., 1.13 × 1010 M−1 s−1). The SD was 0.5 (n = 15), which indicates that 0.19% of the data used for the LFER fitting were distributed more than plus/minus one standard deviation (i.e., ± σ) from the experimental values if we assume the difference follows a normal distribution. The SI summarizes how the SD value is compared to the standard deviation under the assumption of a
reference
2.4
12 (11,12) 41 (18, 38)
total no. of compounds (no. of compounds within difference of factor of 2 and 5) SD
0.5
40 (33, 39)
−0.088 19.93 G4+SMD
−0.14 20.60 M06-2X/Aug-ccpVDZ 15 (14, 15) −0.30 23.09 G3+COSMORS 12 (4, 10) −0.73 23.37 G4+SMD −0.42 21.08 G3+COSMO-RS ρ σ QM method
HO• addition to aromatic compounds HO• addition to alkenes H-abstraction from C−H (Ionized) H-abstraction from C−H (neutral)
Table 1. Overall Comparisons of Coefficients for the LFERs and the Sample Deviation
O2 addition to Ccentered radicals (aliphatic)
kchem = − ρ(ΔG act(ortho) + ΔG act(meta) + ΔG act(para) aq,calc aq,calc aq,calc ) + σ
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CH3COO•CH2 (kexp = 1.4 × 1010 M−1 s−1)45 was too inconsistent and was not included for the LFERs and subsequent predictions. The LFER for aliphatic C-centered radicals and the calculated kD values were used to predict rate constants, kcalc, for the 19 C-centered radicals that contain multiple functional groups. Figure 4b compares the experimentally obtained kexp to the predicted kcalc values. Some kexp values are from our experiments and others are from the literature, which involve more than one elementary reaction pathways. Some kexp values are the overall reaction rate constant for the parallel elementary reactions. Accordingly, the kexp values for each parallel reaction was estimated by the relative k values which were determined by the GCM.17 For example, when HO• reacts with CH3CH2OH, two C-centered radicals, •CH2CH2OH and CH3•CHOH are produced and each Ccentered radical subsequently reacts with molecular oxygen to produce •OOCH2CH2OH and CH3CH(OH)OO•. We used the ratio of the rate constants for each reaction to determine the individual rate constant from the observed overall rate constant for reactions. The GCM considers all possible elementary reactions for HO• and we estimate the rate constant by adding up the contribution of each functional group on the rate constant.17 The predicted kcalc values were calculated from the kD and kchem using eq 1. The kD was calculated from eq 2 and the kchem was obtained based on the theoretically calculated ΔGact aq,calc values and the calibrated LFER for O2 addition (i.e., ln kchem = −0.088 ΔGact aq,calc + 19.93). It was found that more than 75% of the predicted kcalc values are within a factor of 2 from the kexp values (Figure 4b). In Figure 3b, the kexp values include both the experimentally obtained values of this study [i.e., •CH2CH2OH, CH3•CHOH, •CH2(CH3)2C(OH), •CH2(CH3)2COCH3, (CH3)3CO•CH2, CH3CH2C(CH3)2O•CH2 and •CH2CH3CHOCH(CH3)2] and values from the literature. The Arrhenius Ea and A values of our experimentally obtained temperature-dependent values are approximately 4.1−4.3 kcal/mol and (1.62−2.82) × 1010 M−1 s−1, respectively. The SD of the calibrations was 0.31 (n = 19), and that of the predictions was 1.05 (n = 19), which indicates that 0% and 67.0% of the data used for the calibration and prediction were distributed more than ± σ from the experimental values, respectively. Similarly, the LFER for cyclohexadienyl radical reactions with molecular oxygen was determined to be ln kchem = −0.41ΔGact aq,calc + 13.62 (n = 9) (Figure 4a). The cyclohexadienyl radical is a product from the HO• with aromatic compounds. Three isomers (i.e., ortho-, meta-, and para-) and two resonance structures for each isomer were considered to optimize the transition state structures for the cyclohexadienyl radicals (a total of 27) and molecular oxygen. The SD was 0.86 (n = 9), which indicates 36.0% of the data was more than ± σ from the experimental values. Due to the limited availability of experimental data for cyclohexadienyl radicals, no predictions could be made. The LFER includes our experimentally obtained value [(3.3 ± 0.2) × 108 M−1 s−1] for the hydroxycyclohexadienyl radical (•C6H6−OH) produced from the HO• reaction with benzene, which is consistent with the value (i.e., 3.1 × 108 M−1 s−1) reported by Fang et al. (1995).46 Our measured Arrhenius Ea and A values are 3.3 ± 0.2 kcal/mol and (8.86 ± 0.73) × 1010 M−1 s−1, respectively. To compare the C-centered radical reactivity with other radical-centered species, the ΔGact aq,calc for HOCHC•H and a nitrogen (N)-centered radical (hydrazyl, •N2H3) were also calculated. The experimental kexp values of molecular oxygen addition were 1 × 109 M−1 s−1 for HOCHC•H47 and 3.8 ×
normal distribution. Only one of the 15 rate constants differed by more than a factor of 2 from the experimental value. 4.2. Molecular Oxygen Addition to Carbon-Centered Radicals. The LFER for the addition of molecular oxygen to aliphatic C-centered radicals was determined to follow the expression as ln kchem = −0.088 ΔGact aq,calc + 19.93 when using the SMD solvation model (n = 19) as shown in Figure 4a. Again,
Figure 4. LFERs for the addition of molecular oxygen to aliphatic Ccentered radicals (○) and cyclohexadienyl radicals (Δ), respectively, and its comparison with other radicals: •N2H3(▱) and HOCH •CH(□) (4a, top). A comparison of experimental kexp with predicted kcalc for aliphatic C-centered radicals using the LFER calibration (4b, bottom).
the specific compounds used for the LFER calibration contained only one functional group, with the exception of CF3•CHCl. The reason we used the compounds with single functional groups was to determine the impact of a single functional group on the ΔGact aq,calc. A literature-reported rate constant for •CH2CH2OH (kexp = 6.6 × 109 M−1 s−1)44 and 13929
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108 M−1 s−1 for •N2H348 at 25 °C, respectively. The corresponding kchem are 1.1 × 109 M−1 s−1 and 3.9 × 108 M−1 s−1, while the ΔGact aq,calc values are −36.0 and 12.8 kcal/mol for HOCHC•H and •N2H3, respectively (Figure 4a). While HOCHC•H exhibits similar values to other aliphatic Ccentered radicals, •N2H3 has a significantly larger ΔGact aq,calc value. Factors affecting the low reactivity of the N-centered radical include (1) conformations; (2) solvation, and (3) stability. The N-centered radical is classified as the σ-radical that has a pyramidal conformation due to localization of an unpaired electron on the sp3 orbital.49 The p-orbital of the unpaired electron joins with the surrounding π-orbitals and hence reduces its reactivity.49 The N-centered radical typically indicates a larger or similar solubility to typical hydrophilic Ccentered radicals and this may affect the equilibrium portion of O2 addition (i.e., •N2H3 + O2 →•OONH2).50 Finally, the stability of the peroxyl radicals that are formed (•OON2H3) expects to slow the subsequent peroxyl radical decays.50 However, the elementary reaction steps for the peroxyl radical bimolecular decays are not understood well. Further studies of the stability and subsequent reaction mechanisms of peroxyl radicals are ongoing. 4.3. Disproportionation of Peroxyl Radicals. There are 10 reaction rate constants reported in the literature for the disproportionation reaction of peroxyl radicals in the aqueous phase.51 Based on the optimized structures of reactants, transition states (shown in SI) and associated aqueous phase free energies of activation, we obtained the LFER kchem = −1.14 ΔGact aq,calc + 27.09 with the SMD solvation model (n = 10) (Figure 5). The overall SD was 0.62 (n = 10), which indicates
calculated ΔGact aq,calc appears to be too small. To investigate if this discrepancy results from the solvation process, we applied the other solvation method (COSMO-RS42,43) and obtained a value of 2.6 kcal/mol for ΔGact aq,calc, which is still smaller than other values. In fact, the calculated gaseous phase ΔGact gas,calc was 0.32 kcal/mol, and this value is also significantly smaller than act the ΔGgas,calc values for other peroxyl radicals. These investigations lead us conclude that two primary hydrogen atoms and an alcohol hydrogen atom might have enhanced peroxyl radical reactivity, resulting in a significantly smaller ΔGact aq,calc. The LFER calibration indicates that the position and availability of the C−H bond in peroxyl radicals significantly affects the reactivity of peroxyl radical disproportionation. The trimethylperoxyl radical, (CH3)3COO•, has a tertiary carbon with no available C−H bonds, which dramatically reduces the disproportionation reaction rate of the peroxyl radical. Khursan and Martemyanov observed a correlation between the reaction rate constant of peroxyl radical disproportionation in organic solvent and the Taft constants of the corresponding secondary and tertiary peroxyl radicals.52,53 These authors also reported that the disproportionation of primary peroxyl radicals was independent of the functional groups on the peroxyl carbons. Our LFER clearly indicates that the tertiary peroxyl radical (i.e., trimethylperoxyl radical) requires a significantly larger ΔGact aq,calc (i.e., 12.2 kcal/mol). And ΔGact aq,calc drives the overall reactivity of peroxyl radical disproportionation reactions in the aqueous phase regardless of the functional groups and availability of C− H bonds on the peroxyl carbon. We anticipate that the degradation pathways of the tetroxide created from the peroxyl radical disproportionation reactions will also affect the stability of the peroxyl radical, and the backward reaction from tetroxide to peroxyl radicals. Further investigations of the elementary reaction pathways of tetroxide degradation are ongoing. 4.4. Unimolecular Decay of Peroxyl Radicals. Twelve first-order reaction rate constants have been reported in the literature for the unimolecular decay of peroxyl radicals.51 The corresponding LFER we obtained was ln kchem = −0.39 ΔGact aq,calc + 13.00 (n = 9) (Figure 6). The SD was 3.2 (n = 9), which indicates 99.7% of the data was more than ± σ from the experimental values. The data point for the dihydroxymethyl peroxyl radical was significantly different from the LFER by greater than 40% and as its rate constant was reported as k >1.0 × 106 s−1, we did not include this value in our calculation. The optimized structures of the transition states for the trichloromethylperoxyl and (CH3)2CHOC(CH3)2OO• peroxyl radicals could not be accurately determined because of the difficulties in mathematical convergences. In contrast to the other second-order reactions, the firstorder reaction rate constants for the unimolecular decay of peroxyl radicals ranged from 10 s−1 to 106 s−1, and the associated ΔGact aq,calc ranged from 2.3 to 24.8 kcal/mol. There are five experimental values that are reported for Arrhenius kinetic parameters (i.e., Ea and A values) for the (CH3)2C(OH)OO•, (CH3)2C(OH)OO•, •OOCHOHCH2OH, •OOCH(OH)CH(OH)CH2OH, and HOCH2[CH(OH)4]OO• peroxyl radicals. The Ea values ranged from 7.89 to 14.3 kcal/mol, and A ranged from 2.0 × 108 s−1 to 6.3 × 1012 s−1. The experimentally obtained ΔGact aq,exp from eqs 7−9 were 13.4 kcal/ mol ∼15.0 kcal/mol, which is consistent with our theoretically calculated ΔGact aq,calc. 4.5. Implication for Predicting Byproduct Formation in the Aqueous Phase AOPs. Predicting the aqueous phase
Figure 5. LFER for the disproportionation reaction of peroxyl radicals.
14.7% of the data was more than ± σ from the experimental values. The hydroxymethylperoxyl radical (HOCH2OO•) exhibits a difference from the LFER by a four magnitudes of order and is excluded to determine the LFER. As the reported reaction rate constant (3.0 × 108 M−1 s−1) appears to be a reasonable value due to the presence of a primary peroxyl radical with an alcohol functional group, the theoretically 13930
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startup fund from Michigan Tech and HPC cluster “Superior”. JC and DM acknowledge financial support from the Brook Byers Institute for Sustainable Systems, Hightower Chair, and the Georgia Research Alliance at Georgia Tech. Experimental peroxyl radical measurements were performed at the Radiation Research Laboratory, which is supported by the U.S. Department of Energy.
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(1) Hoigné, J. Chemistry of aqueous ozone, and transformation of pollutants by ozonation and advanced oxidation processes. In The Handbook of Environmental Chemistry Quality and Treatment of Drinking Water; Hubrec, J., Ed.; Springer: Berlin, 1998. (2) Glaze, W. H.; Kang, J.-W.; Chapin, H. D. The chemistry of water treatment processes involving ozone, hydrogen peroxide and ultraviolet radiation. Ozone. Sci. Eng. 1987, 9, 335−352. (3) Glaze, W. H.; Kang, J.-W. Advaced oxidation processes. Test of a kinetic model for the oxidation of organic compounds with ozone and hydrogen peroxide in a semibatch reactor. Ind. Eng. Chem. Res. 1989, 28, 1580−1587. (4) Li, K.; Stefan, M. I.; Crittenden, J. C. Trichloroethene degradation by UV/H2O2 advanced oxidation process: Product study and kinetic modeling. Environ. Sci. Technol. 2007, 41, 1696− 1703. (5) Stefan, M. I.; Bolton, J. R. Mechanism of the degradation of 1, 4dioxane in dilute aqueous solution using the UV/hydrogen peroxide process. Environ. Sci. Technol. 1998, 32, 1588−1595. (6) Stefan, M. I.; Bolton, J. R. Reinvestigation of the acetone degradation mechanisms in dilute aqueous solution by the UV/H2O2 process. Environ. Sci. Technol. 1999, 33, 870−873. (7) Stefan, M. I.; Mack, J.; Bolton, J. R. Degradation pathways during the treatment of methyl tert-butyl ether by the UV/H2O2 process. Environ. Sci. Technol. 2000, 34, 650−658. (8) Kang, J.-W.; Angelalin, H.-M.; Hoffmann, M. Sonolytic destruction of methyl tert-butyl ether by ultrasonic irradiation: The role of O3, H2O2, frequency and power density. Environ. Sci. Technol. 1999, 33, 3199−3205. (9) Liang, J.; Palencia, S. L.; Yates, S. R.; Davis, K. M.; Wolfe, L. R. Oxidation of methyl tertiary-butyl ether (MTBE) by ozone and peroxone processes. J. Am. Water Works Assoc. 1998, 91 (6), 104−114. (10) Westerhoff, P.; Mezyk, S. P.; Cooper, W. J.; Minakata, D. Electron pulse radiolysis determination of hydroxyl radical rate constants with Suwannee river fulvic acid and other dissolved organic matter isolates. Environ. Sci. Technol. 2007, 41, 4610−4646. (11) Bazri, M. M.; Barbeau, B.; Mohseni, M. Impact of UV/H2O2 advanced oxidation treatment on molecular weight distribution of NOM and biostability of water. Water Res. 2012, 46, 5297−5304. (12) Lamsal, R.; Walsh, M. E.; Gagnon, G. A. Comparison of advanced oxidation processes for the removal of natural organic matter. Water Res. 2011, 45, 3263−3269. (13) Ratpukdi, T.; Siripattanakul, S.; Khan, E. Mineralization and biodegradability enhancement of natural organic matter by ozoneVUV in comparison with ozone, VUV, ozone-UV, and UV: Effects of pH and ozone dose. Water Res. 2010, 44, 3531−3543. (14) Kreller, D. I.; Turner, B. F.; Namjesnik-Dejanovic, K.; Maurice, P. A. Comparison of the effects of sonolysis and γ-radiolysis on dissolved organic matter. Environ. Sci. Technol. 2005, 39, 9732−9737. (15) Westerhoff, P.; Moon, H.; Minakata, D.; Crittenden, J. C. Oxidation of organics in retentates from reverse osmosis wastewater reuse facilities. Water Res. 2009, 43 (16), 3992−3998. (16) Buxton, V. B.; Greenstock, C. L.; Helman, W. P.; Ross, A. B. Critical review of rate constants for reactions of hydrated electrons, hydrogen atoms and hydroxyl radicals (•OH/•O−) in aqueous solution. J. Phys. Chem. Ref. Data. 1988, 17 (2), 513−795. (17) Minakata, D.; Li, K.; Westerhoff, P.; Crittenden, J. Development of a group contribution method to predict aqueous phase hydroxyl radical (HO•) reaction rate constants. Environ. Sci. Technol. 2009, 43, 6220−6227.
Figure 6. LFER for the unimolecular decay of peroxyl radical.
radical reaction rate constants is a critical component to predict the formation of the intermediate radicals and stable byproducts that are produced in the aqueous phase AOPs. The direct calculations of the aqueous phase second-order reaction rate constants within the accuracy of difference of the factor of 2 requires approximately ±0.5 kcal/mol of accuracy 54 for the ΔGact aq,calc based on the transition state theory (TST). This calculation is still not feasible using the currently available computational chemistry tools. The LFERs we developed in this study can predict the rate constants within a factor of 2−5. They can be used to predict the concentrations of intermediate radicals and stable byproducts by combining their reaction pathways and rate constants with the known reaction pathways such as HO• reactions. Careful analysis should be performed on the effects from the errors caused by the rate constant prediction to the kinetically predicted concentrations of species. Currently, the methodology used in this study is applied to identify the elementary reaction pathways for the tetroxide decays that produce major byproducts in the aqueous phase AOPs.
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ASSOCIATED CONTENT
S Supporting Information *
Additional information as noted in the text. This material is available free of charge via the Internet at http://pubs.acs.org.
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REFERENCES
AUTHOR INFORMATION
Corresponding Author
*Fax: 906-487-1830; e-mail: [email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by the National Science Foundation Awards CBET 1435926 and 1402053. Any opinions, findings, conclusions, or recommendations expressed in this publication are those of the authors and do not necessarily reflect the view of the supporting organizations. DM wishes to acknowledge the 13931
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(18) Dodd, M. C.; Kohler, H-P.E.; von Gunten, U. Oxidation of antibacterial compounds by ozone and hydroxyl radical: Elimination of biological activity during aqueous ozonation processes. Environ. Sci. Technol. 2009, 43, 2498−2504. (19) Eljarrat, E.; Barceló, D. Priority lists for persistent organic pollutants and emerging contaminants based on their relatice toxic potency in environmental samples. Trends Anal. Chem. 2003, 22 (10), 655−665. (20) Woo, Y.-T.; Lai, D.; McLain, J. L.; Manibusan, M. L.; Dellarco, V. Use of mechanism-based structure-activity relationships analysis in carcinogenic potential ranking for drinking water disinfection byproducts. Environ. Health Perspect. 2002, 110, 75−87. (21) Li, K.; Crittenden, J. C. Computerized pathway elucidation for hydroxyl radical-induced chain reaction mechanisms in aqueous phase advanced oxidation processes. Environ. Sci. Technol. 2009, 43 (8), 2831−2837. (22) Guo, X.; Minakata, D.; Junfeng, N.; Crittenden, J. C. Computerbased first-principles kinetic modeling of degradation pathways and byproduct fates in aqueous phase advanced oxidation processes. Environ. Sci. Technol. 2014, 48, 5718−5725. (23) Cooper, W.; Cramer, C. J.; Martin, N. H.; Mezyk, S. P.; O’Shea, K. E.; von Sonntag, C. Free radical mechanisms for the treatment of methyl tert-butyl ether (MTBE) via advanced oxidation/reductive processes in aqueous solutions. Chem. Rev. 2009, 109 (3), 1302−1345. (24) von Sonntag, C. Free-radical-induced DNA damage and its repair. In A Chemical Perspective; Springer-Verlag: Berlin Heidelberg Germany, 2006. (25) von Sonntag, C.; Schuchmann, H.-P. The elucidation of peroxyl radical reactions in aqueous solution with the help of radiationchemical methods. Angew. Chem., Int. Ed. Engl. 1991, 30, 1229−1253. (26) Schaefer, T.; Schindelka, J.; Hoffmann, D.; Herrmann, H. . Laboratory kinetic and mechanistic studies on the OH-initiated oxidation of acetone in aqueous solution. J. Phys. Chem. A 2012, 116, 6317−6326. (27) Minakata, D.; Crittenden, J. Linear free energy relationships between the aqueous phase hydroxyl radical (HO•) reaction rate constants and the free energy of activation. Environ. Sci. Technol. 2011, 45, 3479−3486. (28) Minakata, D.; Song, W.; Crittenden, J. Reactivity of aqueous phase hydroxyl radical with halogenated carboxylate anions: Experimental and theoretical studies. Environ. Sci. Technol. 2011, 45, 6057−6065. (29) Brezonik, P. L. Chemical Kinetics and Process Dynamics in Aqueous Systems; Lewis Publishers: Boca Raton, FL, 2002. (30) von Smoluchowski, M. Versuch eine mathematicschen Theorie der Koagulationskinetik kolloidaler Losungern. Z. Phys. Chem. 1917, 92, 129−168. (31) Hayduk, W.; Laudie, H. Prediction of diffusion coefficients for non-electrolytes in dilute aqueous solutions. AIChE J. 1974, 20 (3), 611−615. (32) Wilke, C. R.; Chang, P. C. Correlation of diffusion coefficients in dilute solutions. AIChE J. 1955, 1, 264−270. (33) Greig, I. R. The analysis of enzymic free energy relationships using kinetic and computational models. Chem. Soc. Rev. 2010, 39, 2272−2301. (34) Klähn, M.; Rosta, E.; Warshel, A. On the mechanism of hydrolysis of phosphate monoesters dianions in solutions and proteins. J. Am. Chem. Soc. 2006, 128, 15310−15323. (35) Cramer, C. J. Essential of Computational Chemistry, 2nd ed.; John Wiley & Sons. Ltd.: England, 2004; Chapter 11. (36) Pu, J.; Gao, J.; Truhlar, D. G. Multidimensional tunneling, recrossing, and the transmission coefficient for enzymatic reactions. Chem. Rev. 2006, 106, 3140−3169. (37) Whitman, K.; Lyons, S. Miller, R.; Nett, D.; Treas, P.; Zante, A.; Fessenden, R. W.; Thomas, M. D.; Wang, Y. In Proceedings of the ’95 Particle Accelerator Conference and International Conference on High Energy Accelerators, Dallas, Texas, May 15, 1995.
(38) Buxton, G. V.; Stuart, C. R. Re-evaluation of the thiocyanate dosimeter for pulse radiolysis. J. Chem. Soc., Faraday Trans. 1995, 91, 279−281. (39) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; Nakatsuji, H.; Caricato, M.; Li, X.; Hratchian, H. P.; Izmaylov, A. F.; Bloino, J.; Zheng, G.; Sonnenberg, J. L.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Montgomery, Jr., J. A.; Peralta, J. E.; Ogliaro, F.; Bearpark, M.; Heyd, J. J.; Brothers, E.; Kudin, K. N.; Staroverov, V. N.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Rega, N.; Millam, N. J.; Klene, M.; Knox, J. E.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Zakrzewski, V. G.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Dapprich, S.; Daniels, A. D.; Farkas, Ö .; Foresman, J. B.; Ortiz, J. V.; Cioslowski, J.; Fox, D. J. Gaussian 09, Revision D.1; Gaussian, Inc., Wallingford CT, 2009. (40) Curtiss, L. A.; Redfern, P. C.; Raghavachari, K. Gaussian-4 theory. J. Chem. Phys. 2007, 126, 084108. (41) Marenich, A. V.; Cramer, C. J.; Truhlar, D. G. Universal solvation model based on solute electron density and on a continuum model of the solvent defined by the bulk dielectric constant and atomic surface tensions. J. Phys. Chem. B 2009, 113, 6378−6396. (42) Klamt, A. Estimation of gas-phase hydroxyl radical rate constants of oxygenated compounds based on molecular orbital calculations. Chemosphere 1996, 32 (4), 717−726. (43) Klamt, A.; Jonas, V.; Burger, T.; Lohrenz, J. C. W. Refinement and parametrization of COSMO-RS. J. Phys. Chem. A 1998, 102, 5074−5085. (44) Cullis, C. F.; Francis, J. M.; Raef, Y.; Swallow, A. J. Studies of radiation-induced reactions of ethylene in aqueous solution. II. Reactions in the presence of oxygen as studied by pulse radiolysis and γ-irradiation techniques. Proc. R. Soc. (London) Ser. A 1967, 300, 443−454. (45) Nenadovi ć, M. T.; Mićić, O. I. Pulse radiolysis of methyl acetate in aqueous solutions. Radiat. Phys. Chem. 1978, 12, 85. (46) Fang, X.; Pan, X.; Rahmann, A.; Schuchmann, H.-P.; von Sonntag, C. Reversibility in the reaction of cyclohexadienyl radicals with oxygen in aqueous solution. Chem.Eur. J. 1995, 1 (7), 423− 429. (47) Schulte-Frohlinde, D.; Anker, R.; Bothe, E., Hydroxyl radical induced oxidation of acetylene in oxygenated aqueous solution. The formation of a highly acidic intermediate. In Oxygen and Oxy-Radicals in Chemistry and Biology; Rodgers, M. A. J., Powers, RL., Eds.; Academic Press: New York, NY, 1981; p61−7. (48) Buxton, G. V.; Stuart, C. R. Radiation chemistry of aqueous solutions of hydrazine at elevated temperatures. J. Chem. Soc., Faraday Trans. 1997, 93 (8), 1535−1538. (49) Matyjaszewski, K.; Davis, T. P. Handbook of Radical Polymerization; Wiley-Interscience. A John Wiley & Sons, Inc. Publication: Hoboken, 2002. (50) Alfassi, Z. B.; Huie, R. E.; Neta, P. The •NH2 radical in aqueous solutions. In N-Centered Radicals, Chapter 15; Alfassi, Z. B., Ed.; John Wiley & Sons Ltd., 1998. (51) Neta, P.; Huie, R. E.; Ross, A. B. Rate constants for reactions of peroxyl radicals in fluid solutions. J. Phys. Chem. Ref. Data. 1990, 19 (2), 413−515. (52) Khursan, S. L.; Martemyanov, V. S. Influence of substituents on rate constants for recombination of tertiary peroxyl radicals. React. Kinetc. Catal. Lett. 1989, 40 (2), 253−258. (53) Khursan, S. L.; Martemyanov, V. S. Influence of substituents on rate constants for recombination of tertiary peroxyl radicals. React. Kinet. Catal. Lett. 1989, 40 (2), 269−275. (54) Eyring, H.; Gershinowitz, H.; Sun, C. E. The absolute rate of homogeneous atomic reactions. J. Chem. Phys. 1935, 3, 786−796.
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Development of Linear Free Energy Relationships for Aqueous Phase Radical-Involved Chemical Reactions Daisuke Minakata,*,† Stephen P. Mezyk,‡ Jace W. Jones,§ Brittany R. Daws,‡ and John C. Crittenden∥ †
Department of Civil and Environmental Engineering, Michigan Technological University, 1400 Townsend Drive, Houghton, Michigan 49931, United States ‡ California State University Long Beach, 1250 Bellflower Boulevard, Long Beach, California 90840, United States § Department of Pharmaceutical Sciences, University of Maryland School of Pharmacy, 20 North Pine Street Baltimore, Maryland 21201, United States ∥ Department of Civil and Environmental Engineering and the Brook Byers Institute for Sustainable Systems, Georgia Institute of Technology, 820 West Peachtree Street, Atlanta, Georgia 30332, United States S Supporting Information *
ABSTRACT: Aqueous phase advanced oxidation processes (AOPs) produce hydroxyl radicals (HO•) which can completely oxidize electron rich organic compounds. The proper design and operation of AOPs require that we predict the formation and fate of the byproducts and their associated toxicity. Accordingly, there is a need to develop a first-principles kinetic model that can predict the dominant reaction pathways that potentially produce toxic byproducts. We have published some of our efforts on predicting the elementary reaction pathways and the HO• rate constants. Here we develop linear free energy relationships (LFERs) that predict the rate constants for aqueous phase radical reactions. The LFERs relate experimentally obtained kinetic rate constants to quantum mechanically calculated aqueous phase free energies of activation. The LFERs have been applied to 101 reactions, including (1) HO• addition to 15 aromatic compounds; (2) addition of molecular oxygen to 65 carbon-centered aliphatic and cyclohexadienyl radicals; (3) disproportionation of 10 peroxyl radicals, and (4) unimolecular decay of nine peroxyl radicals. The LFERs correlations predict the rate constants within a factor of 2 from the experimental values for HO• reactions and molecular oxygen addition, and a factor of 5 for peroxyl radical reactions. The LFERs and the elementary reaction pathways will enable us to predict the formation and initial fate of the byproducts in AOPs. Furthermore, our methodology can be applied to other environmental processes in which aqueous phase radical-involved reactions occur.
1. INTRODUCTION
compounds. Therefore, a full mechanistic understanding of the formation of intermediates and byproducts is important. Three components are needed to predict the formation of intermediate radicals and stable byproducts based on experimental studies, including (1) radical and thermal reaction pathways,21 (2) absolute reaction rate constants,17 and (3) a numerical-based computer model to temporally and spatially calculate the concentration of each species.22 Although the general degradation of organic compounds in AOPs has not yet been elucidated, a number of past experimental studies and kinetic modeling efforts have revealed the initial formation of intermediate radicals and stable byproducts (Figure 1).5−7,23 In aqueous phase AOPs, carbon (C)-centered radicals are typically produced by H atom abstraction by HO• from a C−H bond or by HO• addition to an unsaturated carbon in an alkene or
Advanced oxidation processes (AOPs) produce highly reactive electrophilic hydroxyl radicals (HO•) in the aqueous phase at ambient temperature and atmospheric pressure. The HO• rapidly reacts with most electron-rich sites on organic compounds. Consequently, AOPs are attractive and promising technologies because they can destroy a wide variety of toxic organic compounds.1−3 Target compounds include (1) trace level organic compounds,4−9 (2) dissolved organic matter,10−14 (3) industrial wastewater containing polymers and/or nonbiodegradable refractory organic chemicals, and 4) RO retentate from municipal wastewater reclamation plants.15 In AOPs, radical-involved reactions induced by the HO• produce a variety of radical intermediates and stable byproducts.5−7 Some of these compounds (e.g., carboxylates and haloacetates) exhibit a much lower reactivity with HO•16,17 and could persist after AOP treatment, which could result in potential risks to human health in drinking water or reclaimed water.18−20 In addition, the byproducts may be more toxic than the parent © 2014 American Chemical Society
Received: Revised: Accepted: Published: 13925
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Figure 1. Generic form of initial elementary reaction pathways.
aromatic compound. The C-centered radicals react with tripletstate molecular oxygen (3O2) that is dissolved in water to produce peroxyl radicals. The peroxyl radicals undergo the unimolecular decay and/or the disproportionation.24 A shortlived tetroxide is expected to form by the disproportionation reactions between peroxyl radicals and stable byproducts (e.g., aldehydes, ketones, and carboxylic acids) are produced after the decay of the tetroxide.25 However, the detailed reaction mechanisms of the tetroxide are not fully understood. The peroxyl radical reaction mechanisms are the dominant pathways for the production of intermediates and byproducts.24−26 The prediction of reaction rate constants for a series of radical-involved aqueous phase reactions in AOPs has been a challenging task. A group contribution method (GCM) was developed as the first and most sophisticated comprehensive computational tool for the prediction of aqueous phase HO• reaction rate constants.17 To date GCM has been used to predict more than 500 HO• reaction rate constants within a factor of 2 from the experimental values. The limitations of GCM, such as the requirement for large data sets and the lack of quantified electron push−pull effects, solvation effects, steric effects, and the contribution of molecular diffusion, indicate that there is a need for more sophisticated computational tools to predict aqueous phase reaction rate constants. Minakata and Crittenden developed linear free energy relationships (LFERs) for aqueous phase HO• reactions to relate experimentally obtained kinetic rate constants to the quantum-mechanically calculated aqueous phase free energies of reactions.27,28 The resulting LFERs predicted the aqueous phase HO• rate constants within a factor of 5 from the experimental values. However, the reactions that occur after the reaction of HO• are critical for predicting the formation of intermediates and byproducts, and so a uniform theory is needed to completely predict reaction rate constants for these radical species. In this study, we have developed LFERs for the aqueous phase radical-involved reaction mechanisms that occur in the initial phase of AOP treatment. Once the LFERs have been established and applied uniformly for radical-involved aqueous phase reactions, they can be combined with the elementary reaction pathways to computationally predict the formation of intermediate radicals and stable byproducts.
k=
kDkchem kD + kchem
(1)
where kD and kchem are the diffusion-limited rate constant and second-order reaction rate constant for the chemical reaction, respectively. The kD value can be calculated using Smoluchowski’s equation,30 as shown in eq 2: kD = 4πDl rN0/1000
(2)
where Dl is the liquid phase diffusion coefficient for the solute and radical (cm2/s), r is the radius of the molecule (Å), and N0 is Avogadro’s number. The diffusivities of small, uncharged molecules in water can be calculated using the Hayduk-Laudie correlation,31 which is derived from the Wilke-Chang correlation.32
Dl =
13.26 × 10−5 (μω )1.14 (Vb)0.589
(3)
where μω is the viscosity of water (cP, 1 kg/m·s = 1000 cP) and Vb is the molar volume of the solute at the temperature at which a liquid boils at 1 atm of pressure (cm3/mol). The thermodynamics for diffusion-limited aqueous phase radical-involved reactions is not well established. Accordingly, we hypothesize that the generalized free energy profile of a diffusion-limited reaction can be drawn as a function of the reaction coordinate, as shown in Figure 2. The overall reaction
Figure 2. Hypothetical free energy profile for aqueous phase radicalinvolved chemical reactions.
react is an exothermic reaction (i.e., ΔGreact aq < 0, where ΔGaq is the aqueous phase free energy of reaction). In this process, the diffusion free energy that requires the formation of the initial vdW complex is exothermic. The chemical reaction is driven by the aqueous phase free energy of activation, ΔGact aq , and the free energy difference between the vdW complex and the transition state, defined as ΔGTS−complex . The kchem value may be expressed aq using an LFER,33,34 as shown in eq 4:
2. LINEAR FREE ENERGY RELATIONSHIPS Measurements of aqueous phase radical reactions indicate that these reactions are nearly diffusion-limited; the reactants encountered in the solvation cage due to diffusion create an initial van der Waals (vdW) complex. Then, the chemical reaction produces a stable radical. The observed overall reaction rate constant, k, can be expressed as in eq 1.29 13926
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varied by flowing the ambient-temperature solution through a short, temperature-controlled condenser just prior to the irradiation cell. Solution heating/cooling occurred for less than 20 s, and the actual solution temperature was measured immediately after the cell using a thermocouple placed directly in the exit flow. The temperature stability of this system was 18.0 MΩ) that was presaturated with the appropriate gas mixed to give desired oxygen concentrations (N2O and O2): high dissolved solute concentration (i.e., typically 1−2 mM) with gas concentrations calculated using the selected volume ratio and initial gas concentrations of [N2O] = 2.6 × 10−2 M and [O2] = 1.25 × 10−3 M. Peroxyl radical reaction formation rate constant measurements were performed using the LINAC pulse radiolysis facility at the Radiation Laboratory at the University of Notre Dame.37 Exact radical concentrations were determined using N2Osaturated solutions of KSCN (1.00 × 10−2 M) at λ = 475 nm (Gε = 5.2 × 10−4 m2 Gy1−)38 with an average dose of 3−5 Gy delivered per 2−3 ns pulse. The solution temperature was
SD =
1 n−1
n
∑ [(kexp, i − kcalc, i)/kexp,i]2 i=1
(10)
where kexp,i and k calc,i are the experimental and calculated reaction rate constants of compound i, respectively, and n is the number of rate constants. For each reaction mechanism, Tables provided in the SI (i.e., addition of molecular oxygen to Ccentered radicals of aliphatic compounds and cyclohexadienyl radicals for Table S1, addition of HO• to aromatic compounds for SI Table S2, unimolecular decay of peroxyl radicals for SI Table S3, and disproportionation of peroxyl radicals for SI Table S4) summarize the experimentally obtained reaction rate constants based on Arrhenius kinetic parameters and rate constants reported in the literature, calculated kD values and associated parameters for Smoluchowski’s equations, kchem 13927
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values and theoretically calculated ΔGact aq,calc values. Detailed discussions are provided in the following sections. 4.1. Hydroxyl Radical Addition to Aromatic Compounds. The aqueous phase reaction of HO• with an aromatic ring occurs mainly by addition typically at a rate that is close to the diffusion-limit. The functional group(s) and location(s) affect the reactivity of HO• both by changing the electron density distribution around the aromatic compounds and through steric effects. When functional groups contain aliphatic C−H bonds and/or nitrogen (N)-, sulfur (S)-, or phosphorus (P)-atom-containing compounds, the HO• can abstract a H atom from the C−H bond and/or interact with N, S, or P atoms.17 We calculated the contribution of reaction rate constants resulting from the aliphatic branches using the GCM17 and subtracted those from the experimentally obtained reaction rate constants reported in the literature. Accordingly, the rate constant from the chemical reaction for HO• addition to the aromatic ring, kchem is given by the expression:
this study this study
this study
0.62 0.86
3.2
10 (5, 8) 27 (24, 27)
9 (2, 8)
−1.14 27.09 G4+SMD −0.41 13.62 G4+SMD
−0.39 13.00 G4+SMD
disproportionation of peroxyl radicals O2 addition to cyclohexadienyl radicals(aromatic)
unimolecular decay of peroxyl radicals
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0.31 (calibration) 1.05 (prediction) this study
act(ortho) ΔGaq,calc ,
Minakata et al., 2011
this study Minakata and Crittenden, 2011
0.05
0.19 (calibration) 1.38 (prediction) Minakata and Crittenden, 2011
act(meta) ΔGaq,calc ,
act(para) ΔGaq,calc
where and are the theoretically calculated aqueous phase free energies of activation for HO• addition to the aromatic ring at the ortho, meta, and para positions, respectively. The contribution from the ipso position was insignificant due to the high steric effect and was not included in the LFER. Based on the experimental data set (n = 15), the calculated LFER for HO• addition to an aromatic ring is ln kchem = −0.14 ΔGact aq,calc +20.60 (Figure 3). The specific chemical compounds
Figure 3. LFER for HO• addition to aromatic compounds with a single functional group. Error bars represent the range of previously reported reaction rate constants in the literature.
used for the LFER were only those that contained a single functional group. Nitrosobenzene (NO) and methylphenyl sulfoxide (SOCH3) were excluded from our LFER fitting because their reported HO• rate constants were very close to or greater than the diffusion reaction rate (i.e., 1.13 × 1010 M−1 s−1). The SD was 0.5 (n = 15), which indicates that 0.19% of the data used for the LFER fitting were distributed more than plus/minus one standard deviation (i.e., ± σ) from the experimental values if we assume the difference follows a normal distribution. The SI summarizes how the SD value is compared to the standard deviation under the assumption of a
reference
2.4
12 (11,12) 41 (18, 38)
total no. of compounds (no. of compounds within difference of factor of 2 and 5) SD
0.5
40 (33, 39)
−0.088 19.93 G4+SMD
−0.14 20.60 M06-2X/Aug-ccpVDZ 15 (14, 15) −0.30 23.09 G3+COSMORS 12 (4, 10) −0.73 23.37 G4+SMD −0.42 21.08 G3+COSMO-RS ρ σ QM method
HO• addition to aromatic compounds HO• addition to alkenes H-abstraction from C−H (Ionized) H-abstraction from C−H (neutral)
Table 1. Overall Comparisons of Coefficients for the LFERs and the Sample Deviation
O2 addition to Ccentered radicals (aliphatic)
kchem = − ρ(ΔG act(ortho) + ΔG act(meta) + ΔG act(para) aq,calc aq,calc aq,calc ) + σ
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CH3COO•CH2 (kexp = 1.4 × 1010 M−1 s−1)45 was too inconsistent and was not included for the LFERs and subsequent predictions. The LFER for aliphatic C-centered radicals and the calculated kD values were used to predict rate constants, kcalc, for the 19 C-centered radicals that contain multiple functional groups. Figure 4b compares the experimentally obtained kexp to the predicted kcalc values. Some kexp values are from our experiments and others are from the literature, which involve more than one elementary reaction pathways. Some kexp values are the overall reaction rate constant for the parallel elementary reactions. Accordingly, the kexp values for each parallel reaction was estimated by the relative k values which were determined by the GCM.17 For example, when HO• reacts with CH3CH2OH, two C-centered radicals, •CH2CH2OH and CH3•CHOH are produced and each Ccentered radical subsequently reacts with molecular oxygen to produce •OOCH2CH2OH and CH3CH(OH)OO•. We used the ratio of the rate constants for each reaction to determine the individual rate constant from the observed overall rate constant for reactions. The GCM considers all possible elementary reactions for HO• and we estimate the rate constant by adding up the contribution of each functional group on the rate constant.17 The predicted kcalc values were calculated from the kD and kchem using eq 1. The kD was calculated from eq 2 and the kchem was obtained based on the theoretically calculated ΔGact aq,calc values and the calibrated LFER for O2 addition (i.e., ln kchem = −0.088 ΔGact aq,calc + 19.93). It was found that more than 75% of the predicted kcalc values are within a factor of 2 from the kexp values (Figure 4b). In Figure 3b, the kexp values include both the experimentally obtained values of this study [i.e., •CH2CH2OH, CH3•CHOH, •CH2(CH3)2C(OH), •CH2(CH3)2COCH3, (CH3)3CO•CH2, CH3CH2C(CH3)2O•CH2 and •CH2CH3CHOCH(CH3)2] and values from the literature. The Arrhenius Ea and A values of our experimentally obtained temperature-dependent values are approximately 4.1−4.3 kcal/mol and (1.62−2.82) × 1010 M−1 s−1, respectively. The SD of the calibrations was 0.31 (n = 19), and that of the predictions was 1.05 (n = 19), which indicates that 0% and 67.0% of the data used for the calibration and prediction were distributed more than ± σ from the experimental values, respectively. Similarly, the LFER for cyclohexadienyl radical reactions with molecular oxygen was determined to be ln kchem = −0.41ΔGact aq,calc + 13.62 (n = 9) (Figure 4a). The cyclohexadienyl radical is a product from the HO• with aromatic compounds. Three isomers (i.e., ortho-, meta-, and para-) and two resonance structures for each isomer were considered to optimize the transition state structures for the cyclohexadienyl radicals (a total of 27) and molecular oxygen. The SD was 0.86 (n = 9), which indicates 36.0% of the data was more than ± σ from the experimental values. Due to the limited availability of experimental data for cyclohexadienyl radicals, no predictions could be made. The LFER includes our experimentally obtained value [(3.3 ± 0.2) × 108 M−1 s−1] for the hydroxycyclohexadienyl radical (•C6H6−OH) produced from the HO• reaction with benzene, which is consistent with the value (i.e., 3.1 × 108 M−1 s−1) reported by Fang et al. (1995).46 Our measured Arrhenius Ea and A values are 3.3 ± 0.2 kcal/mol and (8.86 ± 0.73) × 1010 M−1 s−1, respectively. To compare the C-centered radical reactivity with other radical-centered species, the ΔGact aq,calc for HOCHC•H and a nitrogen (N)-centered radical (hydrazyl, •N2H3) were also calculated. The experimental kexp values of molecular oxygen addition were 1 × 109 M−1 s−1 for HOCHC•H47 and 3.8 ×
normal distribution. Only one of the 15 rate constants differed by more than a factor of 2 from the experimental value. 4.2. Molecular Oxygen Addition to Carbon-Centered Radicals. The LFER for the addition of molecular oxygen to aliphatic C-centered radicals was determined to follow the expression as ln kchem = −0.088 ΔGact aq,calc + 19.93 when using the SMD solvation model (n = 19) as shown in Figure 4a. Again,
Figure 4. LFERs for the addition of molecular oxygen to aliphatic Ccentered radicals (○) and cyclohexadienyl radicals (Δ), respectively, and its comparison with other radicals: •N2H3(▱) and HOCH •CH(□) (4a, top). A comparison of experimental kexp with predicted kcalc for aliphatic C-centered radicals using the LFER calibration (4b, bottom).
the specific compounds used for the LFER calibration contained only one functional group, with the exception of CF3•CHCl. The reason we used the compounds with single functional groups was to determine the impact of a single functional group on the ΔGact aq,calc. A literature-reported rate constant for •CH2CH2OH (kexp = 6.6 × 109 M−1 s−1)44 and 13929
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108 M−1 s−1 for •N2H348 at 25 °C, respectively. The corresponding kchem are 1.1 × 109 M−1 s−1 and 3.9 × 108 M−1 s−1, while the ΔGact aq,calc values are −36.0 and 12.8 kcal/mol for HOCHC•H and •N2H3, respectively (Figure 4a). While HOCHC•H exhibits similar values to other aliphatic Ccentered radicals, •N2H3 has a significantly larger ΔGact aq,calc value. Factors affecting the low reactivity of the N-centered radical include (1) conformations; (2) solvation, and (3) stability. The N-centered radical is classified as the σ-radical that has a pyramidal conformation due to localization of an unpaired electron on the sp3 orbital.49 The p-orbital of the unpaired electron joins with the surrounding π-orbitals and hence reduces its reactivity.49 The N-centered radical typically indicates a larger or similar solubility to typical hydrophilic Ccentered radicals and this may affect the equilibrium portion of O2 addition (i.e., •N2H3 + O2 →•OONH2).50 Finally, the stability of the peroxyl radicals that are formed (•OON2H3) expects to slow the subsequent peroxyl radical decays.50 However, the elementary reaction steps for the peroxyl radical bimolecular decays are not understood well. Further studies of the stability and subsequent reaction mechanisms of peroxyl radicals are ongoing. 4.3. Disproportionation of Peroxyl Radicals. There are 10 reaction rate constants reported in the literature for the disproportionation reaction of peroxyl radicals in the aqueous phase.51 Based on the optimized structures of reactants, transition states (shown in SI) and associated aqueous phase free energies of activation, we obtained the LFER kchem = −1.14 ΔGact aq,calc + 27.09 with the SMD solvation model (n = 10) (Figure 5). The overall SD was 0.62 (n = 10), which indicates
calculated ΔGact aq,calc appears to be too small. To investigate if this discrepancy results from the solvation process, we applied the other solvation method (COSMO-RS42,43) and obtained a value of 2.6 kcal/mol for ΔGact aq,calc, which is still smaller than other values. In fact, the calculated gaseous phase ΔGact gas,calc was 0.32 kcal/mol, and this value is also significantly smaller than act the ΔGgas,calc values for other peroxyl radicals. These investigations lead us conclude that two primary hydrogen atoms and an alcohol hydrogen atom might have enhanced peroxyl radical reactivity, resulting in a significantly smaller ΔGact aq,calc. The LFER calibration indicates that the position and availability of the C−H bond in peroxyl radicals significantly affects the reactivity of peroxyl radical disproportionation. The trimethylperoxyl radical, (CH3)3COO•, has a tertiary carbon with no available C−H bonds, which dramatically reduces the disproportionation reaction rate of the peroxyl radical. Khursan and Martemyanov observed a correlation between the reaction rate constant of peroxyl radical disproportionation in organic solvent and the Taft constants of the corresponding secondary and tertiary peroxyl radicals.52,53 These authors also reported that the disproportionation of primary peroxyl radicals was independent of the functional groups on the peroxyl carbons. Our LFER clearly indicates that the tertiary peroxyl radical (i.e., trimethylperoxyl radical) requires a significantly larger ΔGact aq,calc (i.e., 12.2 kcal/mol). And ΔGact aq,calc drives the overall reactivity of peroxyl radical disproportionation reactions in the aqueous phase regardless of the functional groups and availability of C− H bonds on the peroxyl carbon. We anticipate that the degradation pathways of the tetroxide created from the peroxyl radical disproportionation reactions will also affect the stability of the peroxyl radical, and the backward reaction from tetroxide to peroxyl radicals. Further investigations of the elementary reaction pathways of tetroxide degradation are ongoing. 4.4. Unimolecular Decay of Peroxyl Radicals. Twelve first-order reaction rate constants have been reported in the literature for the unimolecular decay of peroxyl radicals.51 The corresponding LFER we obtained was ln kchem = −0.39 ΔGact aq,calc + 13.00 (n = 9) (Figure 6). The SD was 3.2 (n = 9), which indicates 99.7% of the data was more than ± σ from the experimental values. The data point for the dihydroxymethyl peroxyl radical was significantly different from the LFER by greater than 40% and as its rate constant was reported as k >1.0 × 106 s−1, we did not include this value in our calculation. The optimized structures of the transition states for the trichloromethylperoxyl and (CH3)2CHOC(CH3)2OO• peroxyl radicals could not be accurately determined because of the difficulties in mathematical convergences. In contrast to the other second-order reactions, the firstorder reaction rate constants for the unimolecular decay of peroxyl radicals ranged from 10 s−1 to 106 s−1, and the associated ΔGact aq,calc ranged from 2.3 to 24.8 kcal/mol. There are five experimental values that are reported for Arrhenius kinetic parameters (i.e., Ea and A values) for the (CH3)2C(OH)OO•, (CH3)2C(OH)OO•, •OOCHOHCH2OH, •OOCH(OH)CH(OH)CH2OH, and HOCH2[CH(OH)4]OO• peroxyl radicals. The Ea values ranged from 7.89 to 14.3 kcal/mol, and A ranged from 2.0 × 108 s−1 to 6.3 × 1012 s−1. The experimentally obtained ΔGact aq,exp from eqs 7−9 were 13.4 kcal/ mol ∼15.0 kcal/mol, which is consistent with our theoretically calculated ΔGact aq,calc. 4.5. Implication for Predicting Byproduct Formation in the Aqueous Phase AOPs. Predicting the aqueous phase
Figure 5. LFER for the disproportionation reaction of peroxyl radicals.
14.7% of the data was more than ± σ from the experimental values. The hydroxymethylperoxyl radical (HOCH2OO•) exhibits a difference from the LFER by a four magnitudes of order and is excluded to determine the LFER. As the reported reaction rate constant (3.0 × 108 M−1 s−1) appears to be a reasonable value due to the presence of a primary peroxyl radical with an alcohol functional group, the theoretically 13930
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startup fund from Michigan Tech and HPC cluster “Superior”. JC and DM acknowledge financial support from the Brook Byers Institute for Sustainable Systems, Hightower Chair, and the Georgia Research Alliance at Georgia Tech. Experimental peroxyl radical measurements were performed at the Radiation Research Laboratory, which is supported by the U.S. Department of Energy.
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Figure 6. LFER for the unimolecular decay of peroxyl radical.
radical reaction rate constants is a critical component to predict the formation of the intermediate radicals and stable byproducts that are produced in the aqueous phase AOPs. The direct calculations of the aqueous phase second-order reaction rate constants within the accuracy of difference of the factor of 2 requires approximately ±0.5 kcal/mol of accuracy 54 for the ΔGact aq,calc based on the transition state theory (TST). This calculation is still not feasible using the currently available computational chemistry tools. The LFERs we developed in this study can predict the rate constants within a factor of 2−5. They can be used to predict the concentrations of intermediate radicals and stable byproducts by combining their reaction pathways and rate constants with the known reaction pathways such as HO• reactions. Careful analysis should be performed on the effects from the errors caused by the rate constant prediction to the kinetically predicted concentrations of species. Currently, the methodology used in this study is applied to identify the elementary reaction pathways for the tetroxide decays that produce major byproducts in the aqueous phase AOPs.
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ASSOCIATED CONTENT
S Supporting Information *
Additional information as noted in the text. This material is available free of charge via the Internet at http://pubs.acs.org.
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REFERENCES
AUTHOR INFORMATION
Corresponding Author
*Fax: 906-487-1830; e-mail: [email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by the National Science Foundation Awards CBET 1435926 and 1402053. Any opinions, findings, conclusions, or recommendations expressed in this publication are those of the authors and do not necessarily reflect the view of the supporting organizations. DM wishes to acknowledge the 13931
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