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On-the-fly Kinetic Monte Carlo Simulation of Aqueous Phase Advanced Oxidation Processes Xin Guo, Daisuke Minakata, and John Crittenden Environ. Sci. Technol., Just Accepted Manuscript • DOI: 10.1021/acs.est.5b02034 • Publication Date (Web): 01 Jul 2015 Downloaded from http://pubs.acs.org on July 13, 2015
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On-the-fly Kinetic Monte Carlo Simulation of Aqueous Phase Advanced Oxidation
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Processes
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Prepared for Environmental Science and Technology
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Xin Guo1
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Daisuke Minakata2
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John Crittenden1*
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1. School of Civil and Environmental Engineering, Georgia Institute of Technology, 828 West Peachtree Street, Atlanta, GA 30332 2. Department of Civil and Environmental Engineering, Michigan Technological University, 1400 Townsend Drive, Houghton, MI, 49931
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*Corresponding
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email: [email protected]
author phone: 404-894-5676
fax: 404-894-7896
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Abstract
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We have developed an on-the-fly kinetic Monte Carlo (KMC) model to predict the degradation
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mechanisms and fates of intermediates and byproducts that are produced during aqueous phase advanced
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oxidation processes (AOPs). The on-the-fly KMC model is comprised of a reaction pathway generator, a
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reaction rate constant estimator, a mechanistic reduction module, and a KMC solver. The novelty of this
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work is that we develop the pathway as we march forward in time rather than developing the pathway
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before we use the KMC method to solve the equations. As a result, we have fewer reactions to consider
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and we have greater computational efficiency.
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We have verified this on-the-fly KMC model for the degradation of polyacrylamide (PAM) using
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UV light and titanium dioxide (i.e., UV/TiO2). Using the on-the-fly KMC model, we were able to predict
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the time-dependent profiles of the average molecular weight for PAM. The model provided detailed and
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quantitative insights into the time evolution of the molecular weight distribution and reaction mechanism.
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We also verified our on-the-fly KMC model for the destruction of (1) acetone, (2) trichloroethylene
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(TCE), and (3) polyethylene glycol (PEG) for the ultraviolet light/hydrogen peroxide AOP. We
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demonstrated that the on-the-fly KMC model can achieve the same accuracy as the computer-based first-
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principles KMC (CF-KMC) model, which has already been validated in our earlier work. The on-the-fly
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KMC is particularly suitable for molecules with large molecular weights (e.g., polymers) because the
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degradation mechanisms for large molecules can result is 100’s of thousands to even millions of reactions.
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And the ordinary differential equations (ODEs) that describe the degradation pathways cannot be solved
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using traditional numerical methods, but the KMC can solve these equations.
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Introduction
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Advanced oxidation processes (AOPs) have been used for degrading recalcitrant contaminants
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into biodegradable organic compounds or into carbon dioxide and mineral acids in water.1 However,
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AOPs are mechanistically complex in nature, and numerous intermediates and byproducts are produced
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during the treatment processes. Developing method to predict the formation of intermediates and
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byproducts are important for engineering AOPs that are more effective because some of these
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intermediates and byproducts [e.g., monochloroacetic acid and dichloroacetic acid produced by the
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degradation of trichloroethylene (TCE)] may pose potential risks to human health.2,3 In addition, some of
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these intermediates and byproducts (e.g., volatile acids) may require longer reaction times to destroy.
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Consequently, we need to understand the detailed degradation mechanisms and fate of intermediates and
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byproducts during AOPs so that we can design AOPs that reduce toxicity.
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Various studies have investigated the degradation mechanisms of AOPs.4-10 Although these
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studies have shed light on the detailed elementary reactions and the radical pathways in AOPs, these
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studies are limited in the following aspects. First, experimental studies that determine the degradation
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mechanisms are time consuming, especially for larger molecules. In addition, these experimental studies
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would be cost prohibitive if we were to investigate the degradation pathways of all compounds that are
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used in commerce (e.g., thousands of organic chemical compounds are produced annually and they could
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end up in the environtment).11 Second, the kinetic models that were developed in these studies used
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lumped reactions for simplicity, which prevent us from obtaining a detailed insight into the degradation
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process and predicting the degradation mechanisms for newly discovered organic compounds in the
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environment. Third, these kinetic models also require numerical methods to solve the ordinary differential
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equations (ODEs), which might be too stiff to be solved for complicated reaction pathways. For example,
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the degradation mechanism of polyethylene glycol (PEG with a MW of 3600 Dalton) in the UV/H2O2
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process includes 522,057 species and 696,183 reactions, which might not be solved by most of the ODE
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solvers.12
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To overcome these limitations, Guo et al.12 have developed a computer-based first-principles
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kinetic Monte Carlo (CF-KMC) model to simulate organic compound degradation in AOPs. The CF-
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KMC model uses a computer algorithm that can predict the degradation pathways in AOPs for a given
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parent compound. These predicted degradation pathways consist of elementary reactions, in contrast to
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the lumped reactions that are used by traditional kinetic models. In addition, the CF-KMC model uses a
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KMC solver to solve the degradation mechanisms without solving ODEs. Hence, difficulties such as
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stiffness encountered in traditional ODE-based kinetic models are avoided. The CF-KMC model has
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successfully simulated the degradation of various parent compounds, including low molecular weight
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contaminants (e.g., acetone and TCE) and large contaminants (e.g., PEG). However, since the
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computational time for the CF-KMC model is proportional to the number of reactions that are included in
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the mechanism,13 the computational efficiency of the CF-KMC model for simulating large degradation
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mechanism can be improved by reducing the number of reactions using an on-the-fly mechanism
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generation.
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The on-the-fly KMC model can predict and solve the degradation mechanism simultaneously,
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rather than elucidating the full mechanism before calling the KMC solver to solve the equations. This on-
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the-fly strategy can significantly decrease the number of ODEs that are solved by the KMC solver, and,
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hence, it can increase the computational efficiency. In addition, the on-the-fly KMC model also uses a
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mechanistic reduction module that can remove unimportant reactions that do not contribute significantly
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to the overall degradation rate, which can further increase the computational efficiency.
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In this study, an on-the-fly KMC model is developed and verified by comparing model
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predictions to the degradation products of polyacrylamide (PAM) using the UV/TiO2 process. Detailed
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mechanisms for the degradation of PAM and fates of intermediates and byproducts are generated and
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time-dependent profiles of number averaged molecular weight (Mn) and molecular weight distribution
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(MWD) were predicted. The on-the-fly KMC model is validated by comparing the model predictions to
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experimental data. We also verified that the on-the-fly KMC model agrees with the model results that
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were obtained with the KMC method and a numerical solution to the ODEs for the degradation of acetone,
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TCE, and PEG in the UV/H2O2 process. These simulation results achieved the same accuracy as
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compared with the simulation results obtained by the CF-KMC method and numerical solution to the
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ODEs. The on-the-fly KMC model developed in this study represents a major step forward in predicting
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the degradation mechanisms and fates of degradation products for a wide range of organic contaminants
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with various sizes and functional groups.
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Figure 1 shows the general structure of the on-the-fly KMC model. For the first time step there is
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only one parent component. For subsequent time steps, the by-products that are formed during the given
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time step are added to the parent compound list or species pool, which is the collection of all species that
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exist at some point in time. Then, the on-the-fly KMC model iteratively runs the following four modules
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for each time step.
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The first module is a pathway generator14 that generates the elementary reactions that are
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included in the degradation pathway. For each time step, the pathway generator predicts the products
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from the existing species pool (i.e., products that can be directly produced from the existing species pool
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for the next elementary reaction step). Then, the pathway generator adds all newly generated products and
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reactions into the species pool and reaction list.
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The second module estimates the reaction rate constant for each newly predicted reaction. In this
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study, we used the Group Contribution Method (GCM)15 to estimate the second order reaction rate
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constants for hydroxyl radical reactions. For other reactions, the rate constants were either obtained from
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literature-reported values or estimated based on similar reactions reported in the literature (see SI),
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because there are a limited number of experimentally determined rate constants in literature. Quantum
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chemical calculations have been frequently and successfully employed to predict the degradation
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pathways and reaction kinetics for HO•-initiated reactions in aqueous phase but we did not use them in
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this study because they can not be used for large molecules and linear free energy relationships need to be
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developed for a wider variety of compounds and reacions. .16-19 Several robust tools based on the quantum
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chemical calculation, such as Linear Free Energy Relationships (LFERs),20-22 have also been developed to
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estimate reaction rate constants for various reactions for aqueous phase AOPs, including hydroxyl radical
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reactions, oxygen addition to carbon-centered radicals, disproportionation of peroxyl radicals, and
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unimolecular decay of peroxyl radicals. The LFERs can overcome the limitations of the GCM, such as
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availability of data for all possible functional groups, averaging of the impact of functional groups,
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additivity of rate constants, disregard of electronic intra- and inter-molecular effects, hydrogen bonding
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effects, steric effects, and solvation effects.20 However, we did not use them in this study because the
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LFERs for some reactions (e.g., oxyl radicals) could not be developed due to the little availability of the
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experimentally determined rate constants. Accordingly, LFERs will be integrated into the on-the-fly
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KMC model in the future.
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The third module is a mechanistic reduction algorithm that can eliminate unimportant reactions
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and species from the newly generated pathways and improve the computational efficiency of the on-the-
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fly KMC model. Briefly speaking, the unimportant reactions are those that do not significantly contribute
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to the overall reaction rate loss of a given species. In this study, we used the Directed Relation Graph
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(DRG) method with a criterion of 10-3 for the mechanistic reduction. This means that any reactions that
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contribute less than 0.1% to the degradation of a compound will be eliminated. The detailed description
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about DRG can be found in Lu et al.19 and Guo et al.24
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The last module is a KMC solver that can predict species concentrations at the next time step
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without generating and solving ODEs that describe the degradation pathway. At each time point, the
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KMC solver selects a given reaction to occur from the reaction list and updates the concentrations of
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species that are involved in this selected reaction. Then, the KMC solver calculates the time interval for
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the next time point. The detailed description of the KMC solver can be found in Gillespie25 and Guo et
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al.12
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The four modules described above will be executed iteratively for each time step until the desired
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simulation time is reached. Then the stored values of the concentrations at various times can be plotted.
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Results and Discussion
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Validation of the on-the-fly KMC model
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In the Supporting Information, we validated our on-the-fly KMC model by comparing simulation
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results that were obtained by the on-the-fly KMC model and the CF-KMC model for the degradation of
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acetone, TCE, PEG in a UV/H2O2 process. We demonstrated that the on-the-fly KMC model can achieve
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the same accuracy as the CF-KMC model in terms of concentration profiles of degradation products.
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Previously, we demonstrated that the CF-KMC gave identical results to the solution of the ODEs using
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numerical methods for the degradation of acetone and TCE in a UV/H2O2 process.12 Table 1 compares the
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computational efficiency of the on-the-fly KMC model with the CF-KMC model. We found that for large
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parent compounds (i.e., PEG and polyacrylamide (PAM)), the on-the-fly KMC model generally saves
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60%-70% CPU time as compared with the CF-KMC model. This is because that the on-the-fly KMC
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model solves only the degradation mechanism for each time step and does not have to solve the equations
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for the complete mechanism. Hence, the on-the-fly KMC model solves a smaller reaction pathway
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network as compared with the full reaction pathway network that is solved by the CF-KMC model.
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However, for small parent compounds (i.e., acetone and TCE), the computational efficiencies of both on-
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the-fly KMC model and CF-KMC model are about the same. This is because the number of reactions in
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the degradation mechanisms for small parent compounds is not large. As a result, the on-the-fly KMC
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model actually solves the same-sized mechanism as compared with the full mechanism solved by the CF-
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KMC model for most of the simulation time. Consequently, the on-the-fly KMC model cannot
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significantly increase the computational efficiency in this case.
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Mechanism generation for the degradation of PAM
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The degradation mechanism of PAM in the UV/TiO2 process was generated by the on-the-fly
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KMC model. The experimental conditions are described by Vijayalakshmi et al.26 The initial
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concentration and averaged molecular weight of PAM were 0.012 mM and 1.64 × 105 g/mol, respectively.
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The wavelength of UV light was predominantly 365 nm and the light intensity was 1.19 × 10-5
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Einstein/L·s. Commercial Degussa P-25 TiO2 was used as the photocatalyst and the quantum yield for
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HO• formation was reported to be 0.04.27 The reactor was a completely mixed batch reactor (CMBR).
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The elementary reactions in the degradation mechanism of PAM were generated by the pathway
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generator as shown in Table SI 1 of the Supporting Information. These elementary reactions cover most
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of reaction types that have been discovered to occur during aqueous phase AOPs, including: (1) hydroxyl
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radical H-atom abstraction that produces carbon-centered radicals, (2) oxygen addition to carbon-centered
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radicals, (3) beta(β) scission of oxyl radicals, and (4) hydrolysis of aldehydes. The pathway also includes
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some overall reactions, such as bimolecular decays of peroxyl radical, because experimental studies have
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not elucidated the elementary reactions. In addition, the current version of the pathway generator does not
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include the electron-transfer reactions between hydroxyl radicals and amide groups. As a result, this
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reaction was manually added into the pathway generator. The current version of the pathway generator
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also does not include the cross-disproportionation of peroxyl radicals since the reaction rates of these
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reactions are much slower than competing reactions (e.g. self-disproportionation of peroxyl radicals).28 In
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addition, we did not consider the adsorption of PAM on TiO2 particles since it was not observed by the
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experiments conducted by Vijayalakshmi et al.26
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The reaction rate constants were obtained primarily by two methods: 1) estimation based on the
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literature reported experimental values and 2) calculations from the GCM. The GCM can estimate
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hydroxyl radical reaction rate constants with an uncertainty within 0.5-2 times of the experimental values.
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The reaction rate constants that could not be obtained by the above two methods were estimated based on
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similar reactions that have been experimentally observed. Table SI 1 in the Supporting Information
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contains the values of all the reaction rate constants and how they were obtained or estimated. We
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investigated the impact of the uncertainty of reaction rate constants on the on-the-fly KMC model
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simulations. Accordingly, we conducted a sensitivity analysis and found that reaction rate constants with
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large uncertainties did not have significant impact on the accuracy of the on-the-fly KMC model
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simulations. The detailed description about the sensitivity analysis process can be found in the Supporting
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Information.
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The pathway was reduced by the DRG method with a criterion of 0.1%, which means the DRG
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method removed reactions that had rates smaller than 0.1% of overall consumption rate of a species of
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interest for each time step. The reactions removed were mainly H-atom abstractions by carbon-centered
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radicals from a C-H bond. The reduced mechanism was solved using the KMC solver with an initial
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population of 108. Details of DRG method is discussed in the Supporting Information. The process of
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determining initial population for the KMC solver can be found in authors’ previous articles.12,24
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Predicted Reaction Pathways of PAM Degradation
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Initial stage of the degradation of PAM
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Figure 2 shows the predicted degradation pathway of PAM in the UV/TiO2 process. As the first
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step, the backbone of PAM molecule has two positions that can be attacked by hydroxyl radicals via H-
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atom abstraction reaction: 1) the hydrogen atom on the α-carbon (i.e. H-abstraction A in Figure 2) and 2)
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the hydrogen atom on the β-carbon (i.e. H-abstraction B in Figure 2). The ratio of the contributions of
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these two pathways is 1:3 as estimated by the GCM. These two pathways produce two different carbon-
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centered radicals, which have radical sites located at α-carbon and β-carbon, respectively. In addition, the
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H-atom abstraction of hydrogen atom from the –CO-NH2 group with hydroxyl radical is negligible as
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reported by Karpel Vel Leitner et al.29
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Degradation of α-carbon centered radical
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The α-carbon centered radical that is generated by the H-atom abstraction of PAM (i.e., H-
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abstraction A in Figure 2) produces oxyl radical, ─ CH2─C(CONH2)(O•)─CH2─CH(CONH2)─, through
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the oxygen addition followed by the bimolecular decay of peroxyl radicals. This oxyl radical undergoes
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the β-scission reaction and generates two sub-chains ending with a O=C(CONH2)─ group and carbon-
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centered radical group, namely,, O=C(CONH2)─CH2─CH(CONH2)─ and ─CH(CONH2)─CH2•. On one
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hand, O=C(CONH2)─CH2─CH(CONH2)─ is attacked by hydroxyl radicals and is further degraded into
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low molecular weight products (LMWPs). On the other hand, ─CH(CONH2)─CH2• rapidly reacts with
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O2 to form a end-peroxyl radical, ─CH(CONH2)─CH2OO•.
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The end-peroxyl radical, ─CH(CONH2)─CH2OO•, is consumed through three bimolecular decay
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channels (i.e., bimolecular decays that are shown as A, B, and C in Figure 2). First,
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─CH(CONH2)─CH2OO• goes through the Russell reaction30 (i.e., bimolecular decay C in Figure 2) to
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produce end-hydroxyl group, which is further degraded to end-aldehyde group via the reaction with HO•.
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Second, ─CH(CONH2)─CH2OO• also directly produces end-aldehyde group (i.e., bimolecular decay B
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in Figure 2), which is hydrolyzed later to form a carboxylic acid group at the end of the molecule. The
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end-carboxylic acid group undergoes random attack by HO• again, which finally leads to the formation of
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various LMWPs. Third, ─CH(CONH2)─CH2OO• produces end-oxyl radical, ─CH(CONH2)─CH2O• (i.e.,
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bimolecular decay A in Figure 2). The contributions of these three bimolecular decay channels are same.
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The end-oxyl radical, ─CH(CONH2)─CH2O•, decays through unimolecular fragmentation by
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C─C bond scission to form formaldehyde and end-carbon-centered radical, ─CH2─•CH(CONH2), which
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is further degraded to end-peroxyl radical, ─CH2─CH(CONH2)OO•. ─CH2─CH(CONH2)OO• is
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consumed by three bimolecular decay channels (i.e., bimolecular decay D, E, and F in Figure 2) to
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produce end-hydroxyl group (─CH2─CH(CONH2)(OH)), end-acyl group (─CH2─CO─ (CONH2)), and
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end-oxyl radical group (─CH2─CH(CONH2)(O•)). On one hand, ─CH2─CH(CONH2)(OH) and
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─CH2─CO─ (CONH2) are attacked by hydroxyl radicals and finally degraded to LMWPs. On the other
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hand, ─CH2─CH(CONH2)(O•) undergoes β-scission to generate OHCCONH2 and ─CH(CONH2) ─CH2•.
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The degradation pathway of ─CH(CONH2) ─CH2• has been described above.
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Degradation of β-carbon centered radical
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The β-carbon centered radical, ─CH2─CH(CONH2)─•CH─CH(CONH2)─, that is formed by H-
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atom abstraction of PAM (i.e., H-abstraction B in Figure 2) reacts with oxygen to produce peroxyl radical,
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─CH2─CH(CONH2)─CH(OO•)─CH(CONH2)─. This peroxyl radical undergoes three degradation
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channels, which forms three products:
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(1) inner-hydroxyl group, ─CH2─CH(CONH2)─CH(OH)─CH(CONH2)─,
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(2) inner-ketone group, ─CH2─CH(CONH2)─C(=O)─CH(CONH2)─, and
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(3) inner-oxyl radical, ─CH2─CH(CONH2)─CH(O•)─CH(CONH2)─.
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The inner-hydroxyl group is further degraded to inner-ketone group, which is attacked by hydroxyl
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radicals again to finally form various LMWPs. The inner-oxyl radical undergoes β-scission to produce
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─CH2─•CH(CONH2) and OHC─CH(CONH2)─, whose degradation pathways have already been
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described above.
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Simulation Results of PAM Degradation
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Figure 3 compares the calculated profile of number averaged molecular weight (M n) with
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experimental data reported by Vijayalakshmi et al.25 The simulation results are consistent with the
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experimental data. The results showed that Mn decreases from 1.64 × 105 g/mol to 5 × 104 g/mol after 200
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minutes, which indicates the long chain PAM molecules are degraded into short chain oligomers during
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the UV/TiO2 degradation process.
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To investigate into the degradation process and associated mechanisms, we simulated the time
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evolution of the molecular weight distribution (MWD) of the PAM degradation as shown in Figure 4. The
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results from the simulation indicate a uniform and large molecular weight at the beginning (i.e., t = 0). As
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the degradation proceeds, the peak of the MWD shifts from large molecular weight to small molecular
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weight, which is consistent with the trend that is indicated by the experimental Mn profile.
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Figure 5 shows the time evolution of the total number of reactions that are included. At the initial
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stage (i.e., first 25 min), the number of reactions increases rapidly. Most of the reactions that are
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generated at this stage are H-atom abstraction reactions occurred on the backbone of PAM. At the second
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stage (i.e., 25 min to 100 min), the growth rate of the number of reactions slows down and the number of
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reactions finally converges to around 106. During this stage, the generated reactions are majorly consisted
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of oxygen addition reaction, bimolecular decay reaction, β scission reaction and so forth. At the final
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stage (i.e., 100 min to 200 min), the cumulative number of reactions evaluated keep constant around 106,
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which indicates the degradation pathway is nearly complete.
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The major low molecular weight products (LMWPs) predicted by the on-the-fly KMC model
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included formic acid and oxamic acid. The on-the-fly KMC model also predicted minor LMWPs
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including formaldehyde and glyoxylamid. We also calculated the concentration profiles of major low
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molecular weight products (i.e., formic acid and oxamic acid) and these profiles are shown in the
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Supporting Information.
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Environmental implications
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For simulating AOPs in natural waters, the on-the-fly KMC model is able to predict the impact
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of pH and alkalinity on the degradation process. The detailed information about how we implement the
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impact of pH and alkalinity can be found in authors’ previous article.31 In addition, the current version of
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the on-the-fly KMC simulates the impact of natural organic matter (NOM) on AOPs by accounting for
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NOM quenching of hydroxyl radical and UV light absorption. However, the reactions between NOM and
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radical species are complex32 and more NOM reactions may be included in the future if knowledge of the
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structural and chemical characteristics of NOM become available.
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The current version of the pathway generator in the on-the-fly KMC model can predict
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degradation mechanisms for a wide range of organic contaminants based on the known reaction rules
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discovered from the past experimental observations. These reaction rules include hydrogen-atom
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abstraction reaction from a C-H bond or O-H bond, HO• addition reaction to a C=C bond of an aliphatic
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compound, oxygen addition reaction to organic radicals, bimolecular decay of peroxyl radical reaction,
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HO2• elimination reaction, β scission reaction, 1,2-H shift reaction, hydrolysis reaction and so forth.
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However, the pathway generator still does not include some reaction rules that are specific to certain
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functional groups (e.g. S-, N-, or P-atom-containing groups, amide group, and benzene ring). In the future,
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the on-the-fly KMC model could predict the degradation mechanisms of more organic compounds by
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adding more reaction rules into the pathway generator, once these reaction rules have been experimentally
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determined.
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Acknowledgement
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This work was supported by National Science Foundation Award 0854416. The authors also
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appreciate support from the Brook Byers Institute for Sustainable Systems, Hightower Chair and Georgia
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Research Alliance at Georgia Institute of Technology, and the startup funds from the Michigan
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Technological University.
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Supporting Information
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The supporting information provides tables listing all reactions and corresponding rate constants
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included in the generated degradation mechanism of PAM. The detailed description of the sensitivity
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analysis results, mass balance analysis, and validation of the on-the-fly KMC model are also included.
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This material is available free of charge via the Internet at http://pubs.acs.org.
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TOC art
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Table Captions
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Table 1. Comparison of CPU times for the on-the-fly KMC model and the CF-KMC model. The
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processor used is 64-bit 2.4 GHz Intel® Core™ 2 Duo CPU
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Table 1. Parent Compound Acetone TCE PEG PAM
CPU Time for onthe-fly KMC model 18 sec 13 sec 12 min 20 min
CPU Time for CFKMC model 17 sec 13 sec 30 min 65 min
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Figure Captions
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Figure 1. Overall structure of the on-the-fly KMC model.
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Figure 2. Generated degradation mechanism of PAM in the UV/TiO2 process.
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Figure 3. Comparison of the on-the-fly KMC model calculations to experimental data for the number
318
averaged molecular weight.
319 320
Figure 4. Calculated time evolution of molecular weight distribution for the degradation of PAM during
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the UV/TiO2 process. The bars are the calculated mass fractions for polymers with various molecular
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weights.
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Figure 5. Time evolution of the cumulative number of reactions evaluated for the degradation of PAM
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during the UV/TiO2 process.
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Input of parent compound(s) or Species Pool at time t
Reaction pathway generator
Reaction rate constant estimator
Mechanistic reduction module
KMC solver If t < simulation time If t =simulation time
Plot concentration versus time profiles for all species 326 327
Figure 1
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Figure 2
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1.8 Experiment
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Mass fraction
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Mass fraction
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100 Time (min)
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Literature Cited 1. Glaze, W. H.; Kang, J. W.; Chapin, D. H. The chemistry of water treatment processes involving ozone, hydrogen peroxide and UV radiation. Ozone: Sci. Eng. 1987, 9, 335–352. 2. Rosenfeldt, E.J.; Linden, K.G. Degradation of endocrine disrupting chemicals bisphenol
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A, ethinyl estradiol, and estradiol during UV photolysis and advanced oxidation
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acetone in dilute aqueous solution sensitized by the UV photolysis of hydrogen peroxide.
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6. Stefan, M.I.; Bolton, J.R. Reinvestigation of the acetone degradation mechanism in dilute
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aqueous solution by the UV/H2O2 process. Environ. Sci. Technol. 1999, 33, 870-873.
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7. Stefan, M.I.; Bolton, J.R. Mechanism of the degradation of 1,4-dioxane in dilute aqueous
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solution using the UV/Hydrogen peroxide process. Environ. Sci. Technol. 1998, 32,
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8. 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.
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9. Cooper, W.J.; Cramer, C.J.; Martin, N.H.; Mezyk, S.P.; O’Shea, K.E.; von Sonntag, C.
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Free radical mechanisms for the treatment of methyl tert-butyl ether (MTBE) via
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10. Santos, L.C.; Poli, A.L.; Cavalheiro, C.C.S.; Neumann, M.G. The UV/H2O2 –
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photodegradation of poly(ethyleneglycol) and model compounds. J. Braz. Chem. Soc.
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11. Richardson, S. D. Water Analysis: Emerging contaminants and current issues. Anal. Chem. 2009, 81, 4645–4677. 12. Guo, X.; Minakata, D.; Crittenden, J. Computer-based first-principles kinetic Monte Carlo
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simulation of polyethylene glycol degradation in aqueous phase UV/H2O2 advanced
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oxidation processes. Environ. Sci. Technol. 2014, 48, 10813-10820.
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13. Yang, J; Hlavacek, W.S. The efficiency of reactant site sampling in network-free simulation of rule-based models for biochemical systems. Phys. Biol. 2011, 8, 055009. 14. Li, K.; Crittenden, J. Computerized pathway elucidation for hydroxyl radical-induced
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chain reaction mechanisms in aqueous phase advanced oxidation processes. Environ. Sci.
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Technol. 2009, 43, 2831-2837.
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15. Minakata, D.; Li, K.; Westerhoff, P.; Crittenden, J. Development of a group contribution
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method to predict aqueous phase hydroxyl radical (HO•) reaction rate constants. Environ.
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16. Fang, H.; Gao, Y.; Li, G.; An, J.; Wong, P.; Fu, H.; Yao, S.; Nie, X.; An, T. Advanced oxidation kinetics and mechanism of preservative propylparaben degradation in aqueous
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suspension of TiO2 and risk assessment of its degradation products. Environ. Sci. Technol.,
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initiated transformation of triclosan in aquatic environments. Water Res., 2014, 49, 360-
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18. An, T.; Gao, Y.; Li, G.; Kamat, P.; Peller, J.; Joyce, M. Kinetics and mechanism of •OH
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theoretical studies. Environ. Sci. Technol. 2014, 48, 641-648.
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19. Leopoldini, M.; Chiodo, S.; Russo, N.; Toscano, M. Detailed investigation of the OH
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radical quenching by natural antioxidant caffeic acid studied by quantum mechanical
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models. J. Chem. Theory and Comput. 2011,
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20. Minakata, D.; Crittenden, J. Linear free energy relationships between aqueous phase
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hydroxyl radical reaction rate constants and free energy of activation. Environ. Sci.
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Technol. 2011, 45, 3479-3486.
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21. Minakata, D.; Song, W.; Crittenden, J. Reactivity of aqueous phase hydroxyl radical with
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halogenated carboxylate anions: experimental and theoretical studies. Environ. Sci.
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Technol. 2011, 45, 6057-6065.
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22. Minakata, D.; Mezyk, S.P.; Jones, J.W.; Daws, B.R.; Crittenden, J.C. Development of
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linear free energy relationships for aqueous phase radical-involved chemical reactions.
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23. Lu, T.; Law, C.K. A directed relation graph method for mechanism reduction. Proc. Combust. Inst. 2005, 30, 1333-1341.
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24. Guo, X.; Minakata, D.; Niu, J.; Crittenden, J. Computer-based first-principles kinetic
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modeling of degradation pathways and byproduct fates in aqueous-phase advanced
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oxidation processes. Environ. Sci. Technol. 2014, 48, 5718-5725.
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25. Gillespie, D.T. Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem. 1977, 81, 2340-2361. 26. Vijayalakshmi, S.P.; Madras, G. Photocatalytic degradation of poly(ethylene oxide) and polyacrylamide. J. Appl. Polym. Sci. 2006, 100, 3997-4003. 27. Sun, L.; Bolton, J.R. Determination of the quantum yield for the photochemical generation
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of hydroxyl radicals in TiO2 suspensions. J. Phys. Chem. 1996, 100, 4127-4134.
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28. Von Sonntag, C.; Schuchmann, H-P. The elucidation of peroxyl radical reactions in
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aqueous solution with the help of radiation-chemical methods. Angew. Chem. Int. Ed. Engl.
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1991, 30, 1229-1253.
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radicals in relation to the oxidation degree of the α-carbon. Environ. Sci. Technol. 2002,
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36, 3083-3089.
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30. Russell, G.A. Deuterium-isotope effects in the autoxidation of aralkyl hydrocarbons –
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mechanism of the interaction of peroxy radicals. J. Am. Chem. Soc. 1957, 79, 3871-3877.
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31. Crittenden, J. C.; Hu, S.; Hand, D. W.; Green, S. A kinetic model for H2O2/UV process in
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a completely mixed batch reactor. Water Res. 1999, 33, 2315-2328.
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32. Westerhoff, P.; Aiken, G.; Amy, G.; Debroux, J. Relationships between the structure of
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Wat. Res. 1999, 33, 2265-2276.
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Article
On-the-fly Kinetic Monte Carlo Simulation of Aqueous Phase Advanced Oxidation Processes Xin Guo, Daisuke Minakata, and John Crittenden Environ. Sci. Technol., Just Accepted Manuscript • DOI: 10.1021/acs.est.5b02034 • Publication Date (Web): 01 Jul 2015 Downloaded from http://pubs.acs.org on July 13, 2015
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On-the-fly Kinetic Monte Carlo Simulation of Aqueous Phase Advanced Oxidation
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Processes
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Prepared for Environmental Science and Technology
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Xin Guo1
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Daisuke Minakata2
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John Crittenden1*
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1. School of Civil and Environmental Engineering, Georgia Institute of Technology, 828 West Peachtree Street, Atlanta, GA 30332 2. Department of Civil and Environmental Engineering, Michigan Technological University, 1400 Townsend Drive, Houghton, MI, 49931
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*Corresponding
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email: [email protected]
author phone: 404-894-5676
fax: 404-894-7896
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Abstract
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We have developed an on-the-fly kinetic Monte Carlo (KMC) model to predict the degradation
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mechanisms and fates of intermediates and byproducts that are produced during aqueous phase advanced
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oxidation processes (AOPs). The on-the-fly KMC model is comprised of a reaction pathway generator, a
25
reaction rate constant estimator, a mechanistic reduction module, and a KMC solver. The novelty of this
26
work is that we develop the pathway as we march forward in time rather than developing the pathway
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before we use the KMC method to solve the equations. As a result, we have fewer reactions to consider
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and we have greater computational efficiency.
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We have verified this on-the-fly KMC model for the degradation of polyacrylamide (PAM) using
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UV light and titanium dioxide (i.e., UV/TiO2). Using the on-the-fly KMC model, we were able to predict
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the time-dependent profiles of the average molecular weight for PAM. The model provided detailed and
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quantitative insights into the time evolution of the molecular weight distribution and reaction mechanism.
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We also verified our on-the-fly KMC model for the destruction of (1) acetone, (2) trichloroethylene
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(TCE), and (3) polyethylene glycol (PEG) for the ultraviolet light/hydrogen peroxide AOP. We
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demonstrated that the on-the-fly KMC model can achieve the same accuracy as the computer-based first-
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principles KMC (CF-KMC) model, which has already been validated in our earlier work. The on-the-fly
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KMC is particularly suitable for molecules with large molecular weights (e.g., polymers) because the
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degradation mechanisms for large molecules can result is 100’s of thousands to even millions of reactions.
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And the ordinary differential equations (ODEs) that describe the degradation pathways cannot be solved
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using traditional numerical methods, but the KMC can solve these equations.
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Introduction
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Advanced oxidation processes (AOPs) have been used for degrading recalcitrant contaminants
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into biodegradable organic compounds or into carbon dioxide and mineral acids in water.1 However,
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AOPs are mechanistically complex in nature, and numerous intermediates and byproducts are produced
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during the treatment processes. Developing method to predict the formation of intermediates and
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byproducts are important for engineering AOPs that are more effective because some of these
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intermediates and byproducts [e.g., monochloroacetic acid and dichloroacetic acid produced by the
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degradation of trichloroethylene (TCE)] may pose potential risks to human health.2,3 In addition, some of
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these intermediates and byproducts (e.g., volatile acids) may require longer reaction times to destroy.
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Consequently, we need to understand the detailed degradation mechanisms and fate of intermediates and
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byproducts during AOPs so that we can design AOPs that reduce toxicity.
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Various studies have investigated the degradation mechanisms of AOPs.4-10 Although these
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studies have shed light on the detailed elementary reactions and the radical pathways in AOPs, these
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studies are limited in the following aspects. First, experimental studies that determine the degradation
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mechanisms are time consuming, especially for larger molecules. In addition, these experimental studies
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would be cost prohibitive if we were to investigate the degradation pathways of all compounds that are
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used in commerce (e.g., thousands of organic chemical compounds are produced annually and they could
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end up in the environtment).11 Second, the kinetic models that were developed in these studies used
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lumped reactions for simplicity, which prevent us from obtaining a detailed insight into the degradation
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process and predicting the degradation mechanisms for newly discovered organic compounds in the
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environment. Third, these kinetic models also require numerical methods to solve the ordinary differential
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equations (ODEs), which might be too stiff to be solved for complicated reaction pathways. For example,
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the degradation mechanism of polyethylene glycol (PEG with a MW of 3600 Dalton) in the UV/H2O2
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process includes 522,057 species and 696,183 reactions, which might not be solved by most of the ODE
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solvers.12
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To overcome these limitations, Guo et al.12 have developed a computer-based first-principles
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kinetic Monte Carlo (CF-KMC) model to simulate organic compound degradation in AOPs. The CF-
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KMC model uses a computer algorithm that can predict the degradation pathways in AOPs for a given
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parent compound. These predicted degradation pathways consist of elementary reactions, in contrast to
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the lumped reactions that are used by traditional kinetic models. In addition, the CF-KMC model uses a
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KMC solver to solve the degradation mechanisms without solving ODEs. Hence, difficulties such as
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stiffness encountered in traditional ODE-based kinetic models are avoided. The CF-KMC model has
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successfully simulated the degradation of various parent compounds, including low molecular weight
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contaminants (e.g., acetone and TCE) and large contaminants (e.g., PEG). However, since the
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computational time for the CF-KMC model is proportional to the number of reactions that are included in
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the mechanism,13 the computational efficiency of the CF-KMC model for simulating large degradation
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mechanism can be improved by reducing the number of reactions using an on-the-fly mechanism
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generation.
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The on-the-fly KMC model can predict and solve the degradation mechanism simultaneously,
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rather than elucidating the full mechanism before calling the KMC solver to solve the equations. This on-
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the-fly strategy can significantly decrease the number of ODEs that are solved by the KMC solver, and,
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hence, it can increase the computational efficiency. In addition, the on-the-fly KMC model also uses a
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mechanistic reduction module that can remove unimportant reactions that do not contribute significantly
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to the overall degradation rate, which can further increase the computational efficiency.
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In this study, an on-the-fly KMC model is developed and verified by comparing model
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predictions to the degradation products of polyacrylamide (PAM) using the UV/TiO2 process. Detailed
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mechanisms for the degradation of PAM and fates of intermediates and byproducts are generated and
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time-dependent profiles of number averaged molecular weight (Mn) and molecular weight distribution
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(MWD) were predicted. The on-the-fly KMC model is validated by comparing the model predictions to
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experimental data. We also verified that the on-the-fly KMC model agrees with the model results that
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were obtained with the KMC method and a numerical solution to the ODEs for the degradation of acetone,
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TCE, and PEG in the UV/H2O2 process. These simulation results achieved the same accuracy as
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compared with the simulation results obtained by the CF-KMC method and numerical solution to the
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ODEs. The on-the-fly KMC model developed in this study represents a major step forward in predicting
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the degradation mechanisms and fates of degradation products for a wide range of organic contaminants
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with various sizes and functional groups.
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Figure 1 shows the general structure of the on-the-fly KMC model. For the first time step there is
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only one parent component. For subsequent time steps, the by-products that are formed during the given
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time step are added to the parent compound list or species pool, which is the collection of all species that
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exist at some point in time. Then, the on-the-fly KMC model iteratively runs the following four modules
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for each time step.
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The first module is a pathway generator14 that generates the elementary reactions that are
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included in the degradation pathway. For each time step, the pathway generator predicts the products
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from the existing species pool (i.e., products that can be directly produced from the existing species pool
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for the next elementary reaction step). Then, the pathway generator adds all newly generated products and
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reactions into the species pool and reaction list.
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The second module estimates the reaction rate constant for each newly predicted reaction. In this
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study, we used the Group Contribution Method (GCM)15 to estimate the second order reaction rate
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constants for hydroxyl radical reactions. For other reactions, the rate constants were either obtained from
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literature-reported values or estimated based on similar reactions reported in the literature (see SI),
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because there are a limited number of experimentally determined rate constants in literature. Quantum
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chemical calculations have been frequently and successfully employed to predict the degradation
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pathways and reaction kinetics for HO•-initiated reactions in aqueous phase but we did not use them in
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this study because they can not be used for large molecules and linear free energy relationships need to be
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developed for a wider variety of compounds and reacions. .16-19 Several robust tools based on the quantum
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chemical calculation, such as Linear Free Energy Relationships (LFERs),20-22 have also been developed to
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estimate reaction rate constants for various reactions for aqueous phase AOPs, including hydroxyl radical
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reactions, oxygen addition to carbon-centered radicals, disproportionation of peroxyl radicals, and
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unimolecular decay of peroxyl radicals. The LFERs can overcome the limitations of the GCM, such as
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availability of data for all possible functional groups, averaging of the impact of functional groups,
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additivity of rate constants, disregard of electronic intra- and inter-molecular effects, hydrogen bonding
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effects, steric effects, and solvation effects.20 However, we did not use them in this study because the
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LFERs for some reactions (e.g., oxyl radicals) could not be developed due to the little availability of the
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experimentally determined rate constants. Accordingly, LFERs will be integrated into the on-the-fly
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KMC model in the future.
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The third module is a mechanistic reduction algorithm that can eliminate unimportant reactions
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and species from the newly generated pathways and improve the computational efficiency of the on-the-
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fly KMC model. Briefly speaking, the unimportant reactions are those that do not significantly contribute
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to the overall reaction rate loss of a given species. In this study, we used the Directed Relation Graph
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(DRG) method with a criterion of 10-3 for the mechanistic reduction. This means that any reactions that
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contribute less than 0.1% to the degradation of a compound will be eliminated. The detailed description
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about DRG can be found in Lu et al.19 and Guo et al.24
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The last module is a KMC solver that can predict species concentrations at the next time step
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without generating and solving ODEs that describe the degradation pathway. At each time point, the
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KMC solver selects a given reaction to occur from the reaction list and updates the concentrations of
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species that are involved in this selected reaction. Then, the KMC solver calculates the time interval for
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the next time point. The detailed description of the KMC solver can be found in Gillespie25 and Guo et
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al.12
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The four modules described above will be executed iteratively for each time step until the desired
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simulation time is reached. Then the stored values of the concentrations at various times can be plotted.
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Results and Discussion
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Validation of the on-the-fly KMC model
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In the Supporting Information, we validated our on-the-fly KMC model by comparing simulation
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results that were obtained by the on-the-fly KMC model and the CF-KMC model for the degradation of
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acetone, TCE, PEG in a UV/H2O2 process. We demonstrated that the on-the-fly KMC model can achieve
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the same accuracy as the CF-KMC model in terms of concentration profiles of degradation products.
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Previously, we demonstrated that the CF-KMC gave identical results to the solution of the ODEs using
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numerical methods for the degradation of acetone and TCE in a UV/H2O2 process.12 Table 1 compares the
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computational efficiency of the on-the-fly KMC model with the CF-KMC model. We found that for large
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parent compounds (i.e., PEG and polyacrylamide (PAM)), the on-the-fly KMC model generally saves
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60%-70% CPU time as compared with the CF-KMC model. This is because that the on-the-fly KMC
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model solves only the degradation mechanism for each time step and does not have to solve the equations
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for the complete mechanism. Hence, the on-the-fly KMC model solves a smaller reaction pathway
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network as compared with the full reaction pathway network that is solved by the CF-KMC model.
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However, for small parent compounds (i.e., acetone and TCE), the computational efficiencies of both on-
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the-fly KMC model and CF-KMC model are about the same. This is because the number of reactions in
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the degradation mechanisms for small parent compounds is not large. As a result, the on-the-fly KMC
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model actually solves the same-sized mechanism as compared with the full mechanism solved by the CF-
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KMC model for most of the simulation time. Consequently, the on-the-fly KMC model cannot
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significantly increase the computational efficiency in this case.
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Mechanism generation for the degradation of PAM
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The degradation mechanism of PAM in the UV/TiO2 process was generated by the on-the-fly
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KMC model. The experimental conditions are described by Vijayalakshmi et al.26 The initial
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concentration and averaged molecular weight of PAM were 0.012 mM and 1.64 × 105 g/mol, respectively.
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The wavelength of UV light was predominantly 365 nm and the light intensity was 1.19 × 10-5
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Einstein/L·s. Commercial Degussa P-25 TiO2 was used as the photocatalyst and the quantum yield for
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HO• formation was reported to be 0.04.27 The reactor was a completely mixed batch reactor (CMBR).
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The elementary reactions in the degradation mechanism of PAM were generated by the pathway
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generator as shown in Table SI 1 of the Supporting Information. These elementary reactions cover most
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of reaction types that have been discovered to occur during aqueous phase AOPs, including: (1) hydroxyl
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radical H-atom abstraction that produces carbon-centered radicals, (2) oxygen addition to carbon-centered
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radicals, (3) beta(β) scission of oxyl radicals, and (4) hydrolysis of aldehydes. The pathway also includes
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some overall reactions, such as bimolecular decays of peroxyl radical, because experimental studies have
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not elucidated the elementary reactions. In addition, the current version of the pathway generator does not
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include the electron-transfer reactions between hydroxyl radicals and amide groups. As a result, this
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reaction was manually added into the pathway generator. The current version of the pathway generator
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also does not include the cross-disproportionation of peroxyl radicals since the reaction rates of these
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reactions are much slower than competing reactions (e.g. self-disproportionation of peroxyl radicals).28 In
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addition, we did not consider the adsorption of PAM on TiO2 particles since it was not observed by the
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experiments conducted by Vijayalakshmi et al.26
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The reaction rate constants were obtained primarily by two methods: 1) estimation based on the
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literature reported experimental values and 2) calculations from the GCM. The GCM can estimate
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hydroxyl radical reaction rate constants with an uncertainty within 0.5-2 times of the experimental values.
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The reaction rate constants that could not be obtained by the above two methods were estimated based on
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similar reactions that have been experimentally observed. Table SI 1 in the Supporting Information
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contains the values of all the reaction rate constants and how they were obtained or estimated. We
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investigated the impact of the uncertainty of reaction rate constants on the on-the-fly KMC model
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simulations. Accordingly, we conducted a sensitivity analysis and found that reaction rate constants with
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large uncertainties did not have significant impact on the accuracy of the on-the-fly KMC model
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simulations. The detailed description about the sensitivity analysis process can be found in the Supporting
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Information.
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The pathway was reduced by the DRG method with a criterion of 0.1%, which means the DRG
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method removed reactions that had rates smaller than 0.1% of overall consumption rate of a species of
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interest for each time step. The reactions removed were mainly H-atom abstractions by carbon-centered
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radicals from a C-H bond. The reduced mechanism was solved using the KMC solver with an initial
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population of 108. Details of DRG method is discussed in the Supporting Information. The process of
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determining initial population for the KMC solver can be found in authors’ previous articles.12,24
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Predicted Reaction Pathways of PAM Degradation
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Initial stage of the degradation of PAM
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Figure 2 shows the predicted degradation pathway of PAM in the UV/TiO2 process. As the first
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step, the backbone of PAM molecule has two positions that can be attacked by hydroxyl radicals via H-
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atom abstraction reaction: 1) the hydrogen atom on the α-carbon (i.e. H-abstraction A in Figure 2) and 2)
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the hydrogen atom on the β-carbon (i.e. H-abstraction B in Figure 2). The ratio of the contributions of
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these two pathways is 1:3 as estimated by the GCM. These two pathways produce two different carbon-
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centered radicals, which have radical sites located at α-carbon and β-carbon, respectively. In addition, the
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H-atom abstraction of hydrogen atom from the –CO-NH2 group with hydroxyl radical is negligible as
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reported by Karpel Vel Leitner et al.29
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Degradation of α-carbon centered radical
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The α-carbon centered radical that is generated by the H-atom abstraction of PAM (i.e., H-
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abstraction A in Figure 2) produces oxyl radical, ─ CH2─C(CONH2)(O•)─CH2─CH(CONH2)─, through
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the oxygen addition followed by the bimolecular decay of peroxyl radicals. This oxyl radical undergoes
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the β-scission reaction and generates two sub-chains ending with a O=C(CONH2)─ group and carbon-
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centered radical group, namely,, O=C(CONH2)─CH2─CH(CONH2)─ and ─CH(CONH2)─CH2•. On one
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hand, O=C(CONH2)─CH2─CH(CONH2)─ is attacked by hydroxyl radicals and is further degraded into
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low molecular weight products (LMWPs). On the other hand, ─CH(CONH2)─CH2• rapidly reacts with
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O2 to form a end-peroxyl radical, ─CH(CONH2)─CH2OO•.
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The end-peroxyl radical, ─CH(CONH2)─CH2OO•, is consumed through three bimolecular decay
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channels (i.e., bimolecular decays that are shown as A, B, and C in Figure 2). First,
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─CH(CONH2)─CH2OO• goes through the Russell reaction30 (i.e., bimolecular decay C in Figure 2) to
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produce end-hydroxyl group, which is further degraded to end-aldehyde group via the reaction with HO•.
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Second, ─CH(CONH2)─CH2OO• also directly produces end-aldehyde group (i.e., bimolecular decay B
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in Figure 2), which is hydrolyzed later to form a carboxylic acid group at the end of the molecule. The
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end-carboxylic acid group undergoes random attack by HO• again, which finally leads to the formation of
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various LMWPs. Third, ─CH(CONH2)─CH2OO• produces end-oxyl radical, ─CH(CONH2)─CH2O• (i.e.,
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bimolecular decay A in Figure 2). The contributions of these three bimolecular decay channels are same.
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The end-oxyl radical, ─CH(CONH2)─CH2O•, decays through unimolecular fragmentation by
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C─C bond scission to form formaldehyde and end-carbon-centered radical, ─CH2─•CH(CONH2), which
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is further degraded to end-peroxyl radical, ─CH2─CH(CONH2)OO•. ─CH2─CH(CONH2)OO• is
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consumed by three bimolecular decay channels (i.e., bimolecular decay D, E, and F in Figure 2) to
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produce end-hydroxyl group (─CH2─CH(CONH2)(OH)), end-acyl group (─CH2─CO─ (CONH2)), and
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end-oxyl radical group (─CH2─CH(CONH2)(O•)). On one hand, ─CH2─CH(CONH2)(OH) and
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─CH2─CO─ (CONH2) are attacked by hydroxyl radicals and finally degraded to LMWPs. On the other
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hand, ─CH2─CH(CONH2)(O•) undergoes β-scission to generate OHCCONH2 and ─CH(CONH2) ─CH2•.
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The degradation pathway of ─CH(CONH2) ─CH2• has been described above.
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Degradation of β-carbon centered radical
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The β-carbon centered radical, ─CH2─CH(CONH2)─•CH─CH(CONH2)─, that is formed by H-
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atom abstraction of PAM (i.e., H-abstraction B in Figure 2) reacts with oxygen to produce peroxyl radical,
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─CH2─CH(CONH2)─CH(OO•)─CH(CONH2)─. This peroxyl radical undergoes three degradation
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channels, which forms three products:
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(1) inner-hydroxyl group, ─CH2─CH(CONH2)─CH(OH)─CH(CONH2)─,
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(2) inner-ketone group, ─CH2─CH(CONH2)─C(=O)─CH(CONH2)─, and
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(3) inner-oxyl radical, ─CH2─CH(CONH2)─CH(O•)─CH(CONH2)─.
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The inner-hydroxyl group is further degraded to inner-ketone group, which is attacked by hydroxyl
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radicals again to finally form various LMWPs. The inner-oxyl radical undergoes β-scission to produce
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─CH2─•CH(CONH2) and OHC─CH(CONH2)─, whose degradation pathways have already been
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described above.
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Simulation Results of PAM Degradation
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Figure 3 compares the calculated profile of number averaged molecular weight (M n) with
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experimental data reported by Vijayalakshmi et al.25 The simulation results are consistent with the
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experimental data. The results showed that Mn decreases from 1.64 × 105 g/mol to 5 × 104 g/mol after 200
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minutes, which indicates the long chain PAM molecules are degraded into short chain oligomers during
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the UV/TiO2 degradation process.
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To investigate into the degradation process and associated mechanisms, we simulated the time
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evolution of the molecular weight distribution (MWD) of the PAM degradation as shown in Figure 4. The
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results from the simulation indicate a uniform and large molecular weight at the beginning (i.e., t = 0). As
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the degradation proceeds, the peak of the MWD shifts from large molecular weight to small molecular
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weight, which is consistent with the trend that is indicated by the experimental Mn profile.
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Figure 5 shows the time evolution of the total number of reactions that are included. At the initial
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stage (i.e., first 25 min), the number of reactions increases rapidly. Most of the reactions that are
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generated at this stage are H-atom abstraction reactions occurred on the backbone of PAM. At the second
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stage (i.e., 25 min to 100 min), the growth rate of the number of reactions slows down and the number of
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reactions finally converges to around 106. During this stage, the generated reactions are majorly consisted
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of oxygen addition reaction, bimolecular decay reaction, β scission reaction and so forth. At the final
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stage (i.e., 100 min to 200 min), the cumulative number of reactions evaluated keep constant around 106,
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which indicates the degradation pathway is nearly complete.
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The major low molecular weight products (LMWPs) predicted by the on-the-fly KMC model
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included formic acid and oxamic acid. The on-the-fly KMC model also predicted minor LMWPs
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including formaldehyde and glyoxylamid. We also calculated the concentration profiles of major low
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molecular weight products (i.e., formic acid and oxamic acid) and these profiles are shown in the
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Supporting Information.
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Environmental implications
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For simulating AOPs in natural waters, the on-the-fly KMC model is able to predict the impact
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of pH and alkalinity on the degradation process. The detailed information about how we implement the
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impact of pH and alkalinity can be found in authors’ previous article.31 In addition, the current version of
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the on-the-fly KMC simulates the impact of natural organic matter (NOM) on AOPs by accounting for
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NOM quenching of hydroxyl radical and UV light absorption. However, the reactions between NOM and
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radical species are complex32 and more NOM reactions may be included in the future if knowledge of the
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structural and chemical characteristics of NOM become available.
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The current version of the pathway generator in the on-the-fly KMC model can predict
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degradation mechanisms for a wide range of organic contaminants based on the known reaction rules
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discovered from the past experimental observations. These reaction rules include hydrogen-atom
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abstraction reaction from a C-H bond or O-H bond, HO• addition reaction to a C=C bond of an aliphatic
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compound, oxygen addition reaction to organic radicals, bimolecular decay of peroxyl radical reaction,
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HO2• elimination reaction, β scission reaction, 1,2-H shift reaction, hydrolysis reaction and so forth.
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However, the pathway generator still does not include some reaction rules that are specific to certain
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functional groups (e.g. S-, N-, or P-atom-containing groups, amide group, and benzene ring). In the future,
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the on-the-fly KMC model could predict the degradation mechanisms of more organic compounds by
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adding more reaction rules into the pathway generator, once these reaction rules have been experimentally
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determined.
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Acknowledgement
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This work was supported by National Science Foundation Award 0854416. The authors also
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appreciate support from the Brook Byers Institute for Sustainable Systems, Hightower Chair and Georgia
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Research Alliance at Georgia Institute of Technology, and the startup funds from the Michigan
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Technological University.
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Supporting Information
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The supporting information provides tables listing all reactions and corresponding rate constants
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included in the generated degradation mechanism of PAM. The detailed description of the sensitivity
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analysis results, mass balance analysis, and validation of the on-the-fly KMC model are also included.
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This material is available free of charge via the Internet at http://pubs.acs.org.
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TOC art
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Table Captions
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Table 1. Comparison of CPU times for the on-the-fly KMC model and the CF-KMC model. The
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processor used is 64-bit 2.4 GHz Intel® Core™ 2 Duo CPU
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Table 1. Parent Compound Acetone TCE PEG PAM
CPU Time for onthe-fly KMC model 18 sec 13 sec 12 min 20 min
CPU Time for CFKMC model 17 sec 13 sec 30 min 65 min
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Figure Captions
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Figure 1. Overall structure of the on-the-fly KMC model.
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Figure 2. Generated degradation mechanism of PAM in the UV/TiO2 process.
316 317
Figure 3. Comparison of the on-the-fly KMC model calculations to experimental data for the number
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averaged molecular weight.
319 320
Figure 4. Calculated time evolution of molecular weight distribution for the degradation of PAM during
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the UV/TiO2 process. The bars are the calculated mass fractions for polymers with various molecular
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weights.
323 324
Figure 5. Time evolution of the cumulative number of reactions evaluated for the degradation of PAM
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during the UV/TiO2 process.
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Input of parent compound(s) or Species Pool at time t
Reaction pathway generator
Reaction rate constant estimator
Mechanistic reduction module
KMC solver If t < simulation time If t =simulation time
Plot concentration versus time profiles for all species 326 327
Figure 1
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Figure 2
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1.8 Experiment
Averaged molecular weight (105 g/mol)
1.6
On-the-fly KMC 1.4 1.2 1 0.8 0.6 0.4 0.2 0 0
330 331
20
40
60
80 100 120 Time (min)
Figure 3
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Mass fraction
1
t=0
0.8 0.6 0.4 0.2 0 0
0.15
0.3
0.45
0.6
0.75
0.9
1.05
1.2
1.35
1.5
1.65
Molecular weight (105 g/mol)
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Mass fraction
0.4
t = 50 min
0.3 0.2 0.1 0 0
0.15
0.3
0.45
0.6
0.75
0.9
1.05
1.2
1.35
1.5
1.65
Molecular weight (105 g/mol)
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Mass fraction
0.1
t = 150 min
0.08 0.06 0.04 0.02 0 0
0.15
0.3
0.45
0.6
0.75
0.9
1.05
1.2
1.35
1.5
1.65
Molecular weight (105 g/mol)
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Mass fraction
0.05
t = 200 min
0.04 0.03 0.02 0.01 0 0
0.3
0.45
0.6
0.75
0.9
1.05
Molecular weight
335 336
0.15
1.2
(105
1.35
g/mol)
Figure 4
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1.2
Number of reactions (106)
1 0.8 0.6
0.4 0.2 0
0 337 338
50
100 Time (min)
Figure 5
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