2001 Progress Report: Engineering Environmentally Benign Solvent SystemsEPA Grant Number: R828169
Title: Engineering Environmentally Benign Solvent Systems
Investigators: Broadbelt, Linda J. , Khan, Shumaila , Zhang, Qizhi
Institution: Northwestern University
EPA Project Officer: Shapiro, Paul
Project Period: September 1, 2000 through August 31, 2002
Project Period Covered by this Report: September 1, 2000 through August 31, 2001
Project Amount: $223,199
RFA: Exploratory Research - Engineering, Chemistry, and Physics) (1999) RFA Text | Recipients Lists
Research Category: Engineering and Environmental Chemistry , Water , Land and Waste Management , Air
This research project will develop the capability to construct complex chemical mechanisms for broad compound classes to allow the impact of an engineered solvent system on ozone formation to be probed. Ambient ozone in urban and regional air pollution represents one of the country's most pervasive and stubborn environmental problems. Strategies for pollution prevention in the chemical industry aimed at reducing the formation of ground level ozone have focused on identification of fugitive emissions, reduction of amounts of process chemicals, and even elimination of organic solvents from product formulations. Less attention has been paid to engineering organic solvent systems with both the properties desired for a particular application and the environmental implications of the emissions in mind. A limitation to effectively implementing this pollution prevention strategy is an inability to predict the ozone formation potential of a given solvent formulation rapidly and reliably. Because the number of experiments required to probe the impact of a given solvent formulation on ozone formation is prohibitive, prediction using detailed kinetic modeling is an attractive alternative that has been shown to successfully capture experimentally observed behavior. However, uncertainties in the application of chemical mechanisms over a wide range of conditions and to higher molecular weight species, aromatic compounds, and reaction of carbonyls still remain, limiting their predictive capability.
The proposed work builds upon our capability to generate complex reaction mechanisms via the computer. This tool for automated model construction eliminates the tedious manual effort required to construct detailed kinetic models, links the reaction with computational quantum chemistry techniques and other theoretical approaches for estimating rate constants that are unavailable experimentally, and provides a solution capability.
Our computer-generated reaction models rely on the capability to represent separate molecules down to the isomeric level using bond-electron (BE) matrices and implement reaction using matrix addition operations. The diagonal element, ii, of the BE matrix gives the number of nonbonded valence electrons of atom i, and off-diagonal entries, ij, provide the connectivity and bond order of atoms i and j. Conversion of a BE matrix representation of a reactant B to a BE matrix of a product E results from the transformation B + R = E, where R is defined as a reaction matrix. The off-diagonal entries of R represent the breaking (rij = rji < 0) or formation (rij = rji > 0) of covalent bonds. The diagonal entries indicate the number of free valence electrons that the atom i loses (rii < 0) or gains (rii > 0) through a chemical reaction. Because the number of atoms actually affected in a chemical reaction is small, the reaction transformation is a simple and efficient addition of small submatrices. The product submatrix E can then be incorporated back into the overall BE matrix and adjacency structure to represent the entire product molecule(s). In addition, the reaction submatrix is independent of the chemical species undergoing the particular transformation. Therefore, to apply this approach to a new chemistry of interest (i.e., atmospheric chemistry), it is necessary to determine and specify the reaction matrices that capture the chemical transformations the species undergo.
We have focused our recent efforts on identifying the reaction families that govern atmospheric chemistry and formulating their reaction matrices. Many reactions are those that are important because of the presence of components in the atmosphere that are integrally tied to ozone formation and independent of the volatile organic compound (VOC) emitted. Many of these reactions are photochemical reactions and are important in environments with NOx present. Although over 35 reactions were identified, there are many reactions that belong to the same reaction family, and thus would be implemented by the same reaction matrix applied to different reactants. For example, reactions involving bond fission all involve the same fundamental transformation of atoms. In the same way that reactions not directly involving VOCs could be distilled into a much smaller subset of reaction families, or matrices, the specific reactions involving VOCs also may be grouped into a small set of transformations. For example, hydrogen abstraction reactions occur for many different combinations of radicals and substrates, but would be implemented using the same reaction matrix. The explicit reactions represented by the reaction families truly translate into thousands of reactions, because a multitude of different species derived from VOCs may be present in tropospheric pollution. However, these thousands of reactions are comprised of only 21 reaction types and can therefore be efficiently implemented using computer generation algorithms.
We have implemented the reaction families that have been identified for atmospheric chemistry. To implement these reaction families correctly, several important changes had to be made to the core algorithms. First, a spin state variable and encoding scheme and an overall formal charge for molecules were added. The spin state variable was an important change to make because many atmospheric species have different spin states, and it will be necessary for quantum calculations to know the correct spin state to estimate rate constants and thermodynamic properties. For example, both singlet and triplet oxygen atoms are active atmospheric species, and, therefore, it is critical to be able to differentiate between them and obtain correct properties for them. The isomorphism algorithm, which is used to tell molecules apart, was updated to append a "(spin state)" label to the unique string code used to identify molecules if the spin state is not a singlet for molecules or a doublet for radicals. Singlet oxygen atoms would therefore have the string code "O," and triplet oxygen atoms would be labeled "O(3)," effectively distinguishing them. Similarly, formal charges of the molecules are required input by the computational chemistry software that will be used. A second important change was enforcement of proper electron counts and bond orders for all molecules. Simple atmospheric molecules such as O3, NO2, and NO3 were not being read in properly. Thus, a subroutine was written that assigned the right number of electrons and bond order for each atom in a molecule. It also was necessary to assign the right type (i.e., radical or molecule) for each species. For example, NO2 is a radical because of the unpaired electron on nitrogen. Thus, each atom was inspected for an odd electron count and assigned as a radical center. If the molecule contained any radical centers, the molecule itself was assigned to be a radical. Finally, two subroutines were expanded to allow termolecular reactions to take place. Termolecular reactions are frequent in the atmosphere, and it was necessary to be able to write reactions with three reactants. Although the majority of the structure of the code could accommodate three or more reactants, two subroutines had to be edited slightly to carry out termolecular reactions.
Once all the reactions were implemented, the next task was to determine if it was necessary to have the reverse reaction pairs for all the reactions. From the reviewed literature, no reference was found that implied that the reverse reactions of many of the reaction families would be important at conditions relevant to atmospheric chemistry. In theory, all reactions in the mechanism generation algorithms should be considered reversible so that thermodynamic consistency is rigorously maintained. However, the thermodynamic equilibrium may be so far in the forward direction that it is never achieved, and the reverse reaction is not important. The majority of the reactions that are implemented currently contain the reverse reaction pair, but 10 of them had to be investigated. To gauge the importance of the reverse reactions, reverse rates were estimated for representative reactions in each of the 10 families. Because all of the forward rate constants are known, the reverse rate constants are calculated from the equilibrium constant and its relationship to Grxn shown in equations 1 and 2.
where kr is the reverse rate constant, kf is the forward rate constant, Kp is the pressure-based equilibrium constant, R is the ideal gas constant, and i is the summation of the stoichiometric coefficients of the reactants and products. The majority of the thermodynamic data were not available in the literature, so quantum calculations were carried out on all the molecules. Both Hartree-Fock (HF) and density functional theory (DFT) calculations using a 6-31G** basis set were conducted to calculate absolute Gibbs free energies. To test how close these calculated values were to the experimental values, reactions with known values of reaction free energies were compared. The difference between the experimental and calculated values was calculated, and DFT proved to be better than HF, as expected from literature reports of the accuracy of the methods. Because most of the reactions showed the expected agreement of ? 5 kcal/mol, these calculations were deemed reasonable.
With the values of kr in hand, it was necessary to have estimates of the ambient concentrations of the particular compounds in the atmosphere to estimate the rates of the reactions. Oxygen and hydrogen concentrations were estimated based on the composition of air to be 20.99 percent and 0.01 percent, respectively. An additional assumption was made that the peroxy radical concentrations were equal to alkoxy radical concentrations as a zeroth order approximation. Once all of the concentrations were known, the estimate of the maximum possible reverse reaction rates and the estimate of the minimum possible forward reaction rates were used to obtain the rate ratios shown in Table 1. It also was taken into account that these ratios will have a certain degree of error; hence, a range of uncertainty for all reactions also is shown.
Table 1. Uncertainty of the ratio of forward to reverse reaction rates using density functional theory calculations.
Exclusion of some of the reactions is obvious from the large ratios, as well as inclusion of some based on the smaller ratios. Yet, there are certain reaction rates whose ratios are difficult to judge. To establish a threshold value that dictates which reverse reactions will be implemented and which will not be implemented, the ratio of the rates of other reaction pairs that currently are implemented in the program will be examined. Reactions will be excluded based on whether they are above or below this threshold. Work currently is underway to determine this threshold value.
Work to establish the connection between the mechanism generation algorithms and methods to calculate thermochemical properties and rate constants has begun. On-the-fly calculation of these quantities is a critical component of automated mechanism generation. Specification of rate constants by hand for large reaction systems is tedious, and the mechanism generation algorithms also may use properties such as rate constants to determine the direction of the generation process. The basic scheme for calculating properties of molecules and reactions is shown in Figure 1. The interfaces between the mechanism generation algorithms and the National Institute of Standards and Technology (NIST) Structures and Properties database, the quantum chemical software program, Gaussian, and a user-defined data library have been designed. These interfaces will allow for the properties of the molecules and the reactions of interest to be obtained as soon as they are generated. For the properties to be stored and used efficiently, two helper C++ classes, MoleculeProperty and ReactionProperty, were designed. With these classes, objects of MoleculeProperty can be passed to/from the previous interfaces and to a ReactionProperty object to calculate the properties for the reaction.
A related effort that is ongoing is the development of a program for converting two-dimensional representations of molecules to three-dimensional structures. Dr. Zhang is working in collaboration with another graduate student in the Broadbelt group, Ned Haubein. Currently, the two-dimensional representations are provided as input to a program that randomly places the atoms of the molecules and uses a penalty function based on known bonding and connectivity to convert the initial random configuration to a more favorable three-dimensional structure. The initial structure may then be refined by molecular mechanics or quantum mechanics to obtain a minimum energy structure. This program also will be the portal through which quantum mechanics is used to calculate thermochemical properties and rate constants. The accuracy and speed of this conversion algorithm currently are being tested.
Figure 1. Flowchart representing hierarchical methodology for specifying rate constants and species' properties.
Future work will involve creating a rate constant database. Pertinent literature already has been searched for available rate constant data. It already is apparent that rate constants will not be available for every reaction of interest, so the linear-free energy relationship approach will be used. Determination of the constants for the linear-free energy relationships for each reaction family also will be carried out, which will involve developing correlations from known rate constants for representative reactions and supplementing these with quantum chemical calculations. The sensitivity analysis literature also has been read extensively to grasp all the necessary concepts that will be used to reduce the reaction mechanism. Several subroutines will be written to get all the desired sensitivity coefficients needed for the analysis, and on-the-fly sensitivity analysis may be implemented to reduce the mechanism as it is being built.
Tasks also include implementing the designed interfaces and helper classes, testing them with chemical structures and reactions whose properties are already known, and integrating them with the mechanism generation algorithms. In the integration process, it is anticipated that some modifications to the mechanism generation program may be made. Further progress on the two-dimensional to three-dimensional conversion algorithm also will be made.