Theoretical studies of mechanisms of epoxy curing systems

The epoxy resin market is faced with an ever increasing demand for a "designer" range of properties for the epoxy end-use products. Therefore, it is necessary to obtain a complete mechanism and accurate kinetic model that has predictive capabilities. This dissertation addresses the issue in two sections. The first section is an analysis of systematic theoretical studies on the mechanisms of four main curing reactions, epoxy-amine, epoxy-phenol, epoxy-acid and epoxy-anhydride, at the molecular-level using B3LYP density functional theory. The strength of these mechanistic models is their ability to extrapolate to different reactions that use a particular epoxy resin, a particular curing agent and/or a particular catalyst. The examination of all possible reaction pathways for each curing system can allow us to predict the most preferable pathway in the system and can enable the development of a more accurate kinetic model for the system. In addition, it provides insight into the role of tertiary amines in catalyzing the curing reaction. The second section involves the development of a new kinetic model for the epoxy-amine curing system guided by quantum chemistry calculations. This accurate kinetic model for an epoxy-amine curing system has the potential to be applied to other curing systems, solving successfully an industrial issue by quantum chemistry calculation.

THEORETICAL STUDIES OF MECHANISMS OF EPOXY CURING SYSTEMS by My-Phuong Pham A dissertation submitted to the faculty of The University of Utah in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Chemistry The University of Utah May 2011 Copyright © My-Phuong Pham 2011 All Rights Reserved The Universi t y o f Utah Graduate School STATEMENT OF DISSERTATION APPROVAL The dissertation of My-Phuong Pham has been approved by the following supervisory committee members: Thanh N. Truong , Chair 07/20/2009 Date Approved Feng Liu , Member 07/20/2009 Date Approved Richard D. Ernst , Member 07/20/2009 Date Approved Jack P. Simons , Member 07/20/2009 Date Approved Valeria Molinero , Member 07/20/2009 Date Approved and by Henry S. White , Chair of the Department of Chemistry and by Charles A. Wight, Dean of The Graduate School. ABSTRACT The epoxy resin market is faced with an ever increasing demand for a "designer" range of properties for the epoxy end-use products. Therefore, it is necessary to obtain a complete mechanism and accurate kinetic model that has predictive capabilities. This dissertation addresses the issue in two sections. The first section is an analysis of systematic theoretical studies on the mechanisms of four main curing reactions, epoxy-amine, epoxy-phenol, epoxy-acid and epoxy-anhydride, at the molecular-level using B3LYP density functional theory. The strength of these mechanistic models is their ability to extrapolate to different reactions that use a particular epoxy resin, a particular curing agent and/or a particular catalyst. The examination of all possible reaction pathways for each curing system can allow us to predict the most preferable pathway in the system and can enable the development of a more accurate kinetic model for the system. In addition, it provides insight into the role of tertiary amines in catalyzing the curing reaction. The second section involves the development of a new kinetic model for the epoxy-amine curing system guided by quantum chemistry calculations. This accurate kinetic model for an epoxy-amine curing system has the potential to be applied to other curing systems, solving successfully an industrial issue by quantum chemistry calculation. TABLE OF CONTENTS ABSTRACT ....................................................................................................................... iii ACKNOWLEDGMENTS ................................................................................................. vi Chapter 1. INTRODUCTION .................................................................................................................... 1 1.1 General introduction ........................................................................................................ 1 1.2 Overview on the mechanism and kinetic models of epoxy curing reactions .................. 2 1.3 Research objectives ......................................................................................................... 6 2. SUBSTITUENT EFFECTS ON THE REACTIVITY OF EPOXY-AMINE CURING REACTION .............................................................................................................................. 8 2.1 Introduction ..................................................................................................................... 8 2.2 Computational details .................................................................................................... 10 2.3 Results ........................................................................................................................... 13 2.4 Discussion ..................................................................................................................... 20 2.5 Conclusions ................................................................................................................... 22 3. MECHANISMS OF THE EPOXY-PHENOL CURING REACTIONS ................................ 23 3.1 Introduction ................................................................................................................... 23 3.2 Computational details .................................................................................................... 27 3.3 Results ........................................................................................................................... 29 3.4 Discussion ..................................................................................................................... 38 3.5 Conclusions ................................................................................................................... 44 4. MECHANISMS OF THE EPOXY-CARBOXYLIC ACID CURING REACTIONS .......... 46 4.1 Introduction ................................................................................................................... 46 4.2 Computational details .................................................................................................... 51 4.3 Results ........................................................................................................................... 52 4.4 Discussion ..................................................................................................................... 60 4.5 Conclusions ................................................................................................................... 65 5. MECHANISMS OF THE EPOXY-ANHYDRIDE CURING REACTIONS ....................... 67 5.1 Introduction ................................................................................................................... 67 5.2 Computational details .................................................................................................... 75 5.3 Results ........................................................................................................................... 76 v 5.4 Discussion and validation .............................................................................................. 83 5.5 Conclusions ................................................................................................................... 86 6. FIRST-PRINCIPLES BASED KINETIC MODEL FOR THE EPOXY-AMINE CURING REACTION ............................................................................................................................ 88 6.1 Introduction ................................................................................................................... 88 6.2 Pham-Truong (PT) kinetic model development ............................................................ 90 6.3 Validation ...................................................................................................................... 97 6.4 Conclusion ................................................................................................................... 120 REFERENCES ..........................................................................................................121 . ACKNOWLEDGMENTS My five-year journey in the United States, especially at University of Utah, was a huge learning process I could not have done alone. It was supported by the help of many people whom I would like to deeply acknowledge. First, I would especially like to express my appreciation and gratitude to my graduate advisor Prof. Thanh N. Truong for all of his help and guidance. I have learned much from his patience, his knowledge, and his experience combined with his excellent teaching skills as well as his easy-going nature. I would like to express my sincere appreciation to my committee members, Prof. Jack S. Simons, Prof. Scott L. Anderson, Prof. Richard D. Ernst, Prof. Feng Liu and Prof. Valeria Molinero for their involvement and encouragement. I also appreciate the help I have received from many faculty and staff in the chemistry department and from the Center for High Performance Computing, who invested so much time in providing excellent teaching and assistance. The Vietnamese Ministry of Education and Training (MOET) is acknowledged for their graduate fellowship support. I would like to thank the Dow Chemical Company for the partial financial support. Many thanks to all of my past and present colleagues in my group who, by their friendship and professional help, have made my graduate study an enjoyable and worthwhile experience. I want to particularly thank Dr. Quang Nguyen, for our friendship, encouragement and support ever since we were in undergraduate school, Dr. Nguyen Pham for her contribution to Chapter 5, Dr. Hongzhi Zhang for letting me take part in some vii projects of Department of Chemical Engineering and Thomas Cook for delicately helping me to improve my English skills. Special gratitude goes to the Utah groups of Vietnamese international students and the Richardson family who made me feel the warmth of a big family. Most of all I would like to thank my family members. Without them none of this could have happened. I especially wish to thank my parents who devoted their lives to raising my sisters and me. I am immensely grateful to my husband, Binh T. Nguyen, for his encouragement and unending support in everything I do. Thanks also to my cute son, Minh T. Nguyen, for his inspiration. CHAPTER 1 INTRODUCTION 1.1 General introduction Epoxy-based polymer materials have diverse applications such as metal can coatings, automotive primers, printed circuit boards, semiconductor encapsulants, adhesives, aerospace composite materials, and even as building materials for rotor blades of wind turbines.1-3 These amorphous materials have a set of unique properties that are not commonly found in other plastic materials, such as excellent mechanical strength, outstanding chemical, moisture and corrosion resistance, good thermal, adhesive, and electrical properties; dimensional stability (i.e., low shrinkage upon curing) and a lack of volatile emissions.1, 4-6 Most industrial applications of epoxy resins are in thermosetting, a process in which an epoxy resin reacts with a curing cross-link agent known as a hardener. The largest class of hardeners (50%) utilizes primary and secondary amines. The second largest class of hardeners involves carboxylic acids and anhydrides, which make up about 36% of the class. The remaining segment of the class is phenols and related substances (cf. Figure 1.1).7 In order to achieve the desired properties, careful selection of an epoxy resin, the proper curing agent, and the right epoxy/agent curing proportions in a formulation process must be made. Sometimes additional agents such as catalysts, accelerators, fillers, solvents, diluents, plasticizers, and tougheners are required to 2 Figure 1.1. Total curing agent volume used in U.S. market (2001 data). facilitate the curing process or to improve the final properties of the products. The epoxy resin market is faced with an ever increasing demand for a "designer" range of properties of epoxy resin end-products. For example, as electronic equipment gets smaller, there is higher demand on the thermo-stability and electro-conductivity of the coating materials, a greater economic pressure for efficiency, and a larger focus on the environmental impact requirements. Meanwhile, the known formulation process, in both mechanism and kinetic models, is not fully understood and lacks predictive and functional-design capabilities. 1.2 Overview on the mechanism and kinetic models of epoxy curing reactions 1.2.1 Mechanism of epoxy-amine curing Due to their extensive use, much work has been done on amines. The general curing reaction occurs via a nucleophilic attack of the amine nitrogen on the terminal carbon of the epoxy function. The mechanism has been accepted to be a SN2-type II and thus the reaction rate obeys second-order kinetics (Scheme 2.1).7, 8 In this mechanism, a primary amine (PA) can react twice with two epoxy group Amines (primary, secondary) Phenol, others Carboxylic acid, anhydride 50% 36% P 3 Scheme 2.1. General mechanism for epoxy-amine curing. The first step is assumed to be the rate determining step and the proton transfer is fast compared to the nucleophilic attack. while a secondary amine (SA) can react only once.9 The reaction was known to be catalyzed by hydroxyl groups10, 11 or by catalytic impurities.12 Mijovic and coworkers suggested a possible concerted mechanism which involves three types of acyclic hydrogen bond complexes with reactant amine molecules, i.e., epoxy-amine, epoxy-hydroxyl and amine-hydroxyl, but considered only epoxy-amine complexes for epoxy-amine kinetics.13 Meanwhile, only the epoxy-hydroxyl complexes were used in the recent Riccardi's,14 Blanco's15 and Mounif's16 models. In other curing systems such as the curing of epoxy by phenol and the curing of epoxy by acid, the hydrogen bond complex of either epoxy-acid or epoxy-phenol is not considered. Thus, mechanisms of different kinds of epoxy curing reactions are similarly incomplete. Models of possible hydrogen bond complexes with amines have been used,13 refined or slightly altered or extended to the present time, especially Horie's model9 for epoxy-amine curing reactions. Other approaches were also employed to evaluate the reaction mechanism, particularly using kinetic modeling combined with experimental measurements.15-18 In such cases, a kinetic model was used involving a set of elementary reactions whose rate parameters were determined by fitting with experimental data from rate equation thermometric measurements conducted with the aid of differential scanning calorimetry (DSC).19, 20 Elucidation of the epoxy-amine reaction mechanism using this approach has a number of limitations. The approach cannot provide any information at the molecular-level 4 on the mechanism of individual elementary reactions. For example, it cannot address the possibility of cyclic transition states involving an epoxy and two amine molecules, described in a review by Rozenberg.21 Cyclic and acyclic transition states of the same stoichiometry cannot be distinguished by thermometric measurements although their reaction pathways for this specific reaction differ considerably; the amine addition via a cyclic transition state is believed to be a concerted one-step process, whereas the acyclic pathway is a step-wise process that occurs via an intermediate. It is a well-accepted fact that the cyclic hydrogen bond complex often stabilizes the transition state and thus it is considered to be a more favorable pathway22-24 This speculation was proven in recent studies to be incorrect; i.e., the cyclic TS pathway is energetically less favorable compared to the acyclic TS pathway by quantum calculation.8 1.2.2 Mechanism of epoxy-carboxylic acid/anhydride curing Despite being the second most important class of curing agents, not much is known in molecular detail about the mechanism of reactions using carboxylic acids and anhydrides. Steinmann found from C13-NMR and HPLC data that reaction between epoxy and a carboxylic acid not only yields the usual main products of α-hydroxy-ester and β-hydroxy-ester but also gives an abnormal β-hydroxy-ester.25 This indicates the mechanism for reaction with carboxylic acids is more complex than currently known. Reactions between epoxy and anhydrides often require a tertiary amine (R3N) Lewis base as the catalyst. Previous studies mutually agreed the mechanism is an anionic one. However, Fischer suggested R3N opens anhydride first to form a zwitterion which can then undergo reaction with the epoxy.26 Okaya, Takana and Yuki, on the other hand, suggested R3N creates a zwitterion with epoxy first before reacting with the anhydride.27 Two 5 additional mechanisms were also proposed based on initiation by tertiary amine with the participation of (1) a preexisting proton donor and (2) a proton donor formed during the reaction.7 All of these suggestions indicate only that the reaction mechanism is not fully understood. 1.2.3 Mechanism of epoxy-phenol curing Similarly, the role of tertiary amines as catalysts for curing by phenols is not understood clearly. Shechter and Wynstra proposed a mechanism in which the epoxy is opened by a tertiary amine catalyst first to form a zwitterion which then reacts with phenols.28 Sorokin et al. declared that a tertiary amine creates a complex with phenols and then this complex cures the epoxy.29 1.2.4 Kinetic model of epoxy-amine curing Since the mechanisms for epoxy curing reactions are not fully understood, current kinetic models used to approximate mechanisms are empirical or semiempirical and rely on experimental thermometric measurements of the overall process. Such models cannot specifically guarantee the completeness of the mechanism and can hide the non-completeness of the mechanism because rate constants were used as adjustable parameters. For instance, a recent study by Blanco et al.15 proposed a mechanistic model that involved the uncatalyzed reaction between epoxy and amine and the catalyzed reaction by a hydroxyl group, but did not consider the self-promoted reaction by other amines. The authors justified the accuracy of the model based on its ability to fit data from differential scanning calorimetry experiments for a given set of reaction conditions. Such an approach is far from being predictive because it cannot be extended to other reaction conditions. Furthermore, since rate parameters are being used as fitting parameters, there is no guarantee that these 6 parameters are physical. For example, in Blanco et al.'s kinetic model, the activation energy for the complex formation step between epoxy and an alcohol group is 58.2 kJ/mol.15 This is significantly higher than the well-accepted physical range for this step of 1-5 kJ/mol confirmed by the first-principles quantum chemistry calculation. 1.3 Research objectives Compared with traditional theory and experimentation, computational molecular science can be accepted as the ‘third' pillar of scientific research, providing reliable information on the mechanism, thermodynamic and kinetic parameters needed for meso- and macro-scaled modeling of the chemical process.30 Quantum chemistry calculations performed recently successfully proved that in the overall mechanism of epoxy-amine curing reactions, the acyclic transition states are more preferred energetically than cyclic transition states, which is completely opposite with previous speculation for such SN2 type II processes like curing reactions. Thus, first-principles quantum chemistry calculations can be applied to achieve a fundamental understanding of the mechanisms of curing reactions as well as the catalytic and accelerative role of Lewis bases and acids. These results are continually used to develop and validate the mechanistic model for the epoxy cured by different curing agents. The purpose of this research is to create mechanisms and kinetic models that have predictive and functional-design capabilities for epoxy curing reactions. These mechanisms and kinetic models can answer what the mechanical properties of the resulting polymer will be by using a particular curing agent, a particular epoxy resin, or by changing the reaction conditions. Curing reactions classified by four main curing agents (amines, phenols and carboxylic acids and anhydrides) were examined. Three steps are required to develop a kinetic model for a given curing reaction: (1) perform first-principles quantum chemistry 7 calculations to explore all possible reaction pathways to construct the mechanistic model; (2) calculate thermodynamic properties and rate constants for each reaction pathway using conventional statistical mechanics methods to provide necessary parameters for the mechanism model; and finally (3) carry out kinetic simulations and directly compare the results to DSC experimental data. The results are divided into two parts. The first part, involving step 1 for all four classes of curing reactions, is presented in Chapters 2, 3, 4 and 5, and concerns the understanding of mechanisms at the molecular level and catalytic roles of tertiary amines in the curing reactions. In Chapter 2, the substituent effects on the reactivity of primary/secondary amine curing agents are examined. Chapter 3 presents the catalytic role of tertiary amines based on the study of epoxy-phenol mechanisms. Chapters 4 and 5 show the overall mechanism of the second class of curing agents, carboxylic acids and anhydrides. The second part presents steps 2 and 3 specifically for epoxy-amine curing reactions (Chapter 6). CHAPTER 2 SUBSTITUENT EFFECTS ON THE REACTIVITY OF EPOXY-AMINE CURING REACTION 2.1 Introduction Amine compounds are among the earliest and most broadly used epoxy curing agents.7 Primary amines and secondary amines are highly reactive with epoxies. Depending on the substituents, these amines are generally divided into three main groups: aliphatic, cycloaliphatic and aromatic amines. Among these groups, aromatic amines typically produce cured resins having the highest chemical and thermal resistance properties; however, they require long cure cycles at high temperature (~150 0C). Cycloaliphatic amines produce products having thermal resistance and toughness superior to those from aliphatic amines but they are more expensive than aliphatic amines.7 Due to its importance of substituent effects on the reactivity, the epoxy-amine curing process has been the subject of many studies 8, 9, 13, 31-36; however, several issues are still not fully understood.7, 8, 36 It is well accepted that epoxy curing by an amine follows the SN2 type II mechanism as shown in the Scheme 2.1. In this mechanism, the hydrogen atom of the amine group does not react directly with an epoxy group but rather the nucleophilic nitrogen atom attacks a carbon atom of the epoxy ring, and then the hydrogen atom from the amine eventually transfers to the epoxy oxygen atom to form OH. Therefore, a primary amine (PA) can react twice with two epoxy groups 9 Scheme 2.1. The general mechanism of an epoxy- amine curing reaction.8 (r.d.s. stands for rate determining step). while a secondary amine (SA) can react only once. A tertiary amine, which has no active hydrogens, thus does not react with the epoxy group. However, it generally acts as a catalyst to accelerate other curing reactions by stabilizing the transition state.7 From their stoichiometric numbers, if the reactivity in a curing process by PA and SA are the same then the ratio of the reaction rates of the SA to the PA processes is 0.5.31 The mechanism suggests that the reactivity of this reaction depends on the nucleophilicity of the amine. A secondary amine, having higher basicity, is usually more nucleophilic than a primary amine.37 Therefore, a secondary amine would react faster than a primary amine. This is in contradiction to the observed slower rate of the SA processes.31, 33, 36 Previous studies suggested that steric effects are the major factor contributing to the deviation of the reaction rate ratio (SA/PA) in most systems from 0.5.31, 36 In addition, Mijovic and co-workers35 found that the reactivity ratio of PA/epoxy and SA/epoxy reactions depends on the amine structure, but is independent of the temperature. Although the ratio is generally reported to be temperature independent,9, 32, 33, 38 some authors found that the reactivity ratio increases with the curing temperature.39, 40 Since the initial stage of polymerization is in a liquid phase, wherein fluid increases in viscosity prior to gellation and hardening,41 condensed phase effects may be of importance. Our previous study found that condensed phase effects lower the activation energy of the curing reaction and became more profound with an increase in solvent polarity.8 Furthermore, the study suggested that condensed phase 10 effects may be the key factors for slower rates of reaction with secondary amines; however, systematic examinations of more sterically varied structures of SA reactions or different types of amines were not done. The objective of this study is to provide insight into the origin of the substituent effects on the relative SA/PA ratio by systematically investigating the effects of the amine structures on the reactivity of their reactions with an epoxy in both gas and condensed phases using Density Functional Theory (DFT). 2.2 Computational details 2.2.1 Physical models Since the commercial epoxies and amine curing agents are typically large and have complicated structures, it is necessary to choose physical models that can represent key functionalities of these species but are small enough to be computationally feasible. The methyl glycidyl ether (E) was chosen to be a model for bisphenol A diglycidyl ether (BADGE)7 and ring hydrogenated bisphenol A diglycidyl ether (H12-BADGE). Table 2.1 shows these commercial epoxies and their corresponding computational models. Commercial amine curing agents can be classified as aliphatic, cycloaliphatic, or aromatic. For example, the common commercial polyamine curing agents diethylenetriamine (DETA) and triethylenetetramine (TETA) are aliphatic, bis(4- aminocyclohexyl)methane (PACM) and isophorone diamine (IPDA) are cycloaliphatic, and 4,4'-diamino-diphenylmethane (DDM) and 4,4'-diamino-diphenyl sulfone (4,4'- DDS) are aromatic as shown in Table 2.2 along with their physical models.7 These model amines also consist of both primary and secondary amines. In particular, methylamine (MA) and dimethylamine (DMA) were used for aliphatic amines, 11 Table 2.1. Some common commercial epoxy structures and overview on model complexes. Common commercial epoxies Model epoxy Formula Abbreviation Formula Abbreviation O O O O O O O O BADGE H12-BADGE E Table 2.2 Some structures of commercial amines. Amines Commercial amines Formula Abbreviation Aliphatic NH2CH2CH2NHCH2CH2NH2 NH2CH2CH2NHCH2CH2NHCH2 CH2NH2 DETA TETA Cycloaliphatic H3C H3C NH2 H3C NH2 PACM IPDA Aromatic DDM 12 cyclohexylamine (CHA) and cyclohexylmethylamine (CHMA) for cycloaliphatic amines, and aniline (AA) and methylaniline (MAA) for primary and secondary aromatic amines, respectively (see Table 2.3). Propan-2-ol was used to model an alcohol (-OH) group of an external alcohol accelerator or a product hydroxyl group. 2.2.2 Computational models All electronic structure calculations were carried out using the Gaussian 03 program package.42 A hybrid nonlocal density functional theory B3LYP level of theory43 with the 6- 31G(d, p) basis set was used for locating all stationary points, namely reactants, transition states, intermediates, and products. Stationary points were characterized by normal mode analyses. To confirm the transition state for each reaction pathway, the minimum energy paths (MEPs) from the transition state to both the reactants and products were calculated using the Gonzalez-Schlegel steepest descent path method44, 45 in the mass weight Cartesian coordinates with the step size of 0.01 (amu)1/2 Bohr. To calculate the condensed effects, Table 2.3 Overview on model complexes of amine curing agents Amines Model amines Primary Amines (PA) Secondary Amines (SA) Formula Abbreviation Formula Abbreviation Aliphatic H2N CH3 MA NH H3C CH3 DMA Cycloaliphati c NH2 CHA HN CH3 CHMA Aromatic NH2 AA HN CH3 MAA 13 single-point energy calculations at the optimized structures of all stationary points were done using the polarizable continuum model (PCM)46 with a dielectric constant equal to 5 to represent the polarity of the polymer matrix. Note that the dielectric constant is about 4 for biopolymers and 3 for the final thermoset. 2.3 Results In the discussion below, we first present substituent effects on different aspects of the epoxy-amine curing reaction then discuss comparisons between the present results and experimental observations to serve as a validation of the calculated data. 2.3.1 Substituent effects on reaction pathways In our previous study,8 amine curing reaction can found to proceed by three different reaction pathways, namely: 1) an isolated pathway, wherein the epoxy reacts with the curing amine molecule alone; 2) a self-promoted pathway wherein the reaction involves two amine molecules, one acting as a curing agent and the other stabilizing the transition state; and 3) an alcohol-accelerated pathway wherein an alcohol group stabilizes the transition state. These pathways are shown in Figure 2.1. Subscripts i, s, and a designate isolated, self-promoted and alcohol-accelerated pathways, respectively. Geometries of the transition states (TS), classical barrier heights ( V ), zero-point energy corrected barriers G a V (vibrationally adiabatic ground-state barrier heights) which are activation energies at 0 K of each pathway for three different classes of amines are given in Tables 2.4-6. As the reaction proceeds from the reactant to product, the C1-O1 bond of the epoxy ring is broken and the new C1-N1 bond is formed (see Figure 2.1). The bond lengths of these two "active" bonds at the TS provide information on how close the TS to the reactant 14 (a) (b) (c) Figure 2.1. Structures of the acyclic transition states for (a) the isolated (TSi), (b) self-promoted (TSs) by an addition amine and (c) alcohol-accelerated pathways (TSa) of the methylamine curing reaction. Table 2.4 Imaginary Frequencies ( ), Selected Optimized Geometrical Parameters of the Transition States along the Acyclic TS Routes, Classical Barrier Heights ( gas V , sol V ), and Zero-point Energy Corrected Barriers ( G a gas V _ ) of the Isolated pathway (i) of Epoxy and Methylamine (MA), Dimethylamine (DMA), Cyclohexylamine (CHA), Cyclohexylmethylamine (CHMA), Aniline (AA) and Methylaniline (MAA) Reactions respectively. Parameters MAi DMAi CHAi CHMAi AAi MAAi ν≠ (i.cm-1) 374.9 376.1 367.5 362.4 330.2 342.5 d(N1-C1) (Å) 1.858 1.884 1.868 1.882 1.778 1.801 d(H1-O2) (Å) 1.931 1.953 1.932 1.946 1.848 1.876 d(C1-O1) (Å) 2.054 2.037 2.065 2.061 2.129 2.114 d(C2-O1) (Å) 1.347 1.349 1.344 1.345 1.337 1.338 d(C1-C2) (Å) 1.495 1.493 1.501 1.501 1.512 1.513 (O1-C2-C1) (deg) 92.4 91.4 92.9 92.7 96.5 95.6 (C2-C1-N1) (deg) 113.8 114.5 115.3 115.9 113.8 115.4 gas V (kJ/mol) 101.70 97.25 107.07 105.35 121.89 119.87 G a gas V _ (kJ/mol) 109.60 101.77 111.66 109.98 126.62 124.30 sol V (kJ/mol) 70.12 72.54 75.76 78.87 90.81 96.09 15 Table 2.5 Imaginary Frequencies ( ), Selected Optimized Geometrical Parameters of the Transition States along the Acyclic TS Routes, Classical Barrier Heights ( gas V , sol V ), and Zero-point Energy Corrected Barriers ( G a gas V _ ) of the Self-promoted pathway (s) of Epoxy and Methylamine (MA), Dimethylamine (DMA), Cyclohexylamine (CHA), Cyclohexylmethylamine (CHMA), Aniline (AA) and Methylaniline (MAA) Reactions respectively. Parameters MAs DMAs CHAs CHMAs AAs MAAs ≠ (i.cm-1) 388.8 384.8 381.5 373.7 370.0 377.2 d(N1-C1) (Å) 1.951 1.980 1.969 1.997 1.914 1.941 d(H1-O2) (Å) 1.973 2.006 1.994 2.008 1.919 1.957 d(H2-O1) (Å) 1.955 1.957 1.964 1.974 1.848 1.838 d(C1-O1) (Å) 1.994 1.973 1.999 1.990 2.043 2.025 d(C2-O1) (Å) 1.367 1.370 1.366 1.367 1.366 1.369 d(C1-C2) (Å) 1.482 1.480 1.484 1.483 2.043 1.487 (O1-C2-C1) (deg) 88.7 87.6 89.0 88.4 91.3 90.3 (C2-C1-N1) (deg) 111.6 112.2 112.8 113.3 112.8 113.7 gas V (kJ/mol) 76.10 72.84 81.55 79.35 84.72 83.69 G a gas V _ (kJ/mol) 85.10 78.90 87.42 84.96 91.82 89.88 sol V (kJ/mol) 61.63 64.00 66.50 71.99 73.93 78.83 Table 2.6. Imaginary Frequencies ( ), Selected Optimized Geometrical Parameters of the Transition States along the Acyclic TS Routes, Classical Barrier Heights ( gas V , sol V ), and Zero-point Energy Corrected Barriers ( G a gas V _ ) of the Propan-2-ol-accelerated pathway (a) of Epoxy and Methylamine (MA), Dimethylamine (DMA), Cyclohexylamine (CHA), Cyclohexylmethylamine (CHMA), Aniline (AA) and Methylaniline (MAA) Reactions respectively. Parameters MAa DMAa CHAa CHMAa AAa MAAa ≠ (i.cm-1) 394.5 397.5 392.6 389.1 374.0 380.5 d(N1-C1) (Å) 2.002 2.025 2.011 2.032 1.930 1.948 d(H1-O2) (Å) 1.994 2.011 1.993 2.007 1.909 1.937 d(H2-O1) (Å) 1.712 1.712 1.710 1.714 1.688 1.686 d(C1-O1) (Å) 1.951 1.934 1.963 1.955 2.026 2.016 d(C2-O1) (Å) 1.380 1.382 1.378 1.379 1.373 1.375 d(C1-C2) (Å) 1.476 1.475 1.479 1.479 1.488 1.486 (O1-C2-C1) (deg) 86.1 85.2 86.7 86.3 90.1 89.4 (C2-C1-N1) (deg) 110.7 111.1 111.5 112.3 112.2 113.2 gas V (kJ/mol) 61.60 58.32 66.73 65.28 78.09 77.36 G a gas V _ (kJ/mol) 70.50 64.28 73.58 71.60 85.31 84.22 sol V (kJ/mol) 50.83 53.87 55.37 58.91 68.75 74.74 16 (entrance) channel or to the product (exit) channel. For instance, the shortening of the C1- O1 and the lengthening of the C1-N1 bond indicate that the TS has moved closer to the reactant channel. For all amines considered in this study, the transition state of the alcohol-accelerated pathway TSa is closest to the reactant (entrance) channel, while the isolated pathway TSi is the farthest (i.e., closest to the product channel). For example, for reaction with aniline, the breakening C1-O1 bond decreases from 2.129, 2.043, to 2.026 Å while the forming C1-N1 bond increases from 1.778, 1.914, to 1.930 Å in the isolated, self-promoted, and alcohol-accelerated pathways, respectively. Corresponding with the increase in the reactant-like characteristics from TSi, TSs to TSa, the classical barrier height decreases from the isolated, self-promoted to alcohol-accelerated pathway. For example, for reaction with aniline the classical barrier is 121.89 kJ/mol for the isolated pathway, 84.72 kJ/mol for self-promoted and 78.09 kJ/mol for the propan-2-ol-accelerated pathway. This trend is consistent with the Hammond postulate, which states that more reactant-like characteristics of the transition state structure would lead to a smaller classical barrier. Such trend is observed for all types of amines and is consistent with those in the Ehlers et al. study.8 For epoxies that have an ether group such as those considered here, the transition state structure can be stabilized by two hydrogen bonds. One is between hydrogen amine H1 and the ether oxygen O2. The other is between the epoxide oxygen O1 with the hydrogen (i.e., H2) either of an amine as in the self-promoted TSs, or of an alcohol as in the alcohol-accelerated TSa transition states. The second hydrogen bond H2-O1 is the determining factor in differentiating the relative importance of each pathway since the first hydrogen bond exists in all pathways. The H2-O1 hydrogen bond is stronger in TSa as compared to 17 TSs as indicated by its shorter bond distances. In particular, for reaction with aniline the H2- O1 hydrogen bond distance is 1.848 Å in AAs and 1.688 Å in AAa corresponding to the classical barrier heights of 84.72 and 78.09 kJ/mol, respectively. 2.3.2 Substituent effects on the reactivity of curing agents Since the alcohol-accelerated pathway is the lowest energy pathway, it should have the largest dependence on the substituent effects. For this reason, the discussion on the substituent effects here is based only on the results for the alcohol-accelerated pathway. Potential energy information of this pathway for reactions with different classes of amines is given in Table 2.5. When compared to aliphatic amines, transition state structures for curing by cycloaliphatic amines have both active C1-O1 and N1-O1 bonds longer. This leads to an increase in the classical energy barriers by about 6 kJ/mol. Since aliphatic and cycloaliphatic amines exhibit similar electronic donating properties, the higher barriers in the latter are due mostly to larger steric effects. Since both aromatic and cycloaliphatic amines considered here are similar in size and thus are expected to have similar steric effects, comparisons of the transition state properties of these two amines would yield the relative importance of the electronic effects. Curing by aromatic amines leads to more product-like TS geometries when compared to those from cycloaliphatic amines. This is indicated by the elongation of the breaking C1-O1 bond and the shortening of the forming N1-O1 bond by more than 0.05 Å. In consistent with the Hammond postulate, this leads to higher barrier by about 12 kJ/mol. This can be explained by the decrease in the nucleophilicity of the amine group due to the electron withdrawing property of the phenyl substituent in aromatic amines. Furthermore, in comparison to the steric effects above, electronic effects are noticeably larger. The electronic effects suggest 18 the higher pKb amines (the weaker bases) will have lower nucleophilicities and thus would generate higher barriers. For comparison, the pKb values are 3.36 for MA, 3.27 for DMA, 3.3 for CHA 3.3, 3.1 for CHMA, 9.4 for AA and 9.16 for MAA.37 The significantly larger pKb values for aromatic amines are consistent with their larger barrier heights compared to those of aliphatic amines. This is also consistent with the experimental observation that curing of aliphatic amines can be done at room temperature while the others require higher temperatures.7 Note that pKb's for the aliphatic and cycloaliphatic amines considered here are similar, so in such case steric effects are dominant in the observed differences in the barrier heights between cycloaliphatic and aliphatic amines.47 When a methyl group replaces a hydrogen atom in the primary amines considered here, the corresponding TS geometries of all pathways for all reactions are shifted toward the reactant channel, i.e., they become more reactant-like. In particular, in alcohol-accelerated pathways, there are decreases in the C1-O1 bond lengths by 0.01-0.02 Å and increases in the C1-N1 bond lengths by 0.01-0.02 Å in all cases. This leads to lower classical barrier heights for curing by SA compared to those of PA by less than 5 kJ/mol in the three classes of amines (Table 2.5). Larger effects are observed for aliphatic amines as compared to those for aromatic amines. For example, methyl substitution lowers the barrier by 3.28 kJ/mol in the alcohol-accelerated pathways for aliphatic amines, 1.45 kJ/mol in cycloaliphatic amines, and 0.73 kJ/mol in aromatic amines. Similar to the discussion of the electronic effects above, the nucleophilicities of the amines can be used to explain the lowering of barrier heights for SA compared to PA processes. For all three classes of amines, the pKb's of SA's are smaller than those of PA's, namely, DMA (3.27) as compared to MA (3.36), CHMA (3.1) to CMA 19 (3.3) and MAA (9.16) to AA (9.4). The results suggest that SA cures faster than PA since it has a lower activation barrier. This, however, contradicts experimental observations.31, 33, 36 2.3.3 Condensed phase effects In this study, condensed phase effects due to a polymer matrix in the curing process are modeled by the PCM dielectric continuum model with a dielectric constant of 5. Figure 2.2 plots barrier heights for reactions with all three classes of amines in both the gas and condensed phases. Solvent effects lower the barrier heights in all pathways and all reactions considered here. On the average, they decrease the barriers by 28 kJ/mol in isolated pathways (Table 2.3), 10 kJ/mol in self-promoted pathways (Table 2.4) and 7 kJ/mol in alcohol-accelerated pathways (Table 2.5). Since the alcohol-accelerated pathway is dominant, solvent effects along this pathway would be most crucial to the overall dynamics of the reaction. On average, the decreases of the energy barriers are approximately equal in all reactions of three classes of amine curing agents, i.e., 15.66 kJ/mol for aliphatic amines, 16.32 kJ/mol for cycloaliphatic amines and 13.74 kJ/mol for aromatic amines. Consequently, the relative reactivity of these amine classes remain the same, i.e., aliphatic ≥ cycloaliphatic > aromatic. Unlike the results in the gas phase, in condensed phases the barrier heights of reactions with SA's are higher than those of corresponding PA's. On average, for reactions considered here in all three pathways, solvent effects lower the barrier by 18 kJ/mol for PA and 12 kJ/mol for SA processes. Specifically for the dominant alcohol-accelerated pathways, solvent effects on the average lower the barrier by 10 kJ/mol for PA and 4 kJ/mol for SA reactions. The much larger solvent effects for PAs lead to the barriers for reactions 20 Figure 2.2. Classical barrier heights (kJ∙mol-1) in both gas (dash lines) and condensed phases (solid lines) of the Isolated (■), Self-promoted (▲) and Alcohol-catalyzed (♦) pathways of Epoxy and Methylamine (MA), Dimethylamine (DMA), Cyclohexylamine (CHA), Cyclohexylmethylamine (CHMA), Aniline (AA) and Methylaniline (MAA) reactions respectively from left to right, primary amine (PA) and secondary amine (SA), or aliphatic (ali), cycloaliphatic (cyc), and aromatic (aro) amines. * Propan-2-ol is used as an alcohol accelerator. with a SA being larger than those of a PA and thus yield dramatic changes in the relative rates of SA and PA processes as indicated by the ratio of the SA/PA rate constants, from being larger than 0.5 to being smaller than 0.5. For example, the classical barrier heights of AAa and MAAa in the condensed phase are 68.75 kJ/mol and 74.74 kJ/mol as compared to 78.09 and 77.36 kJ/mol in the gas phase, respectively (Table 2.6). 2.4 Discussion The competing reactions of epoxies with secondary amine (k2) and primary amine groups (k1) were examined by different experimental methods and the ratio of the rate constants, k2/k1, were usually smaller than 0.5. In the Johncock et al. HPLC study,48 40 50 60 70 80 90 100 110 120 130 Classical barrier heights (kJ/mol) (MA) (DMA) (CHA) (CHMA) (AA) (MAA) (PA) (SA) (PA) (SA) (PA) (SA) (ali) (ali) (cyc) (cyc) (aro) (aro) 21 reactions of 3-trifluoromethylaniline with epichlorohydrin, and aniline with phenyl glycidyl ether and with some N-alkyl-N-glycidylanilines, the observed ratios were in the range of 0.14 to 0.24. Wang and Gillham39 determined the ratio k2/k1 to be in the range of 0.16-0.33 for the trimethylene glycol di-p-aminobenzoate/diglycidyl ether of the bisphenol A system using FTIR spectroscopy. In the Liu et al. study,31 these ratios were within 0.17-0.5 for epoxy and aromatic diamine resin systems. As discussed above, solvent effects are the key factor to cause these ratios to be less than 0.5, and thus are responsible for bringing theory into agreement with experimental observations. The order of the calculated classical barrier values of three classes of amines (aliphatic < cycloaliphatic < aromatic amines) also agrees well with experimental data. Kamon et al.47 used differential scanning calorimetry (DSC) to study the curing reaction of BADGE epoxy resin with diethylenetriamine (DETA, an aliphatic amine), para-amino cyclohexyl methane (PACM, a cycloaliphatic amine) and 4,4'-diamino-diphenylmethane (DDM, an aromatic amine). These amines are commercial curing agents as shown in Table 2.2. The observed activation energies for curing are 67.36, 66.53 and 74.40 kJ/mol for DETA, PACM and DDM, respectively. These can be compared with the zero point energy corrected barriers in the condensed phase: 59.73, 62.22 and 75.97 kJ/mol for the model amines (methylamine, cyclomethylhexylamine, and aniline). Zero point energy corrections were approximated by the gas phase values in this case. In addition, our results for reactions of epoxy resin with aliphatic amines have similar activation energies (59.73 - 65.23 kJ/mol) with those in the range of 54.39 - 58.57 kJ/mol used in the Horie et al. kinetic model.9 22 2.5 Conclusions In this study, substituent effects of epoxy curing reactions with three different classes of amine, namely aliphatic, cycloaliphatic, and aromatic amines were examined using quantum chemistry density functional theory. Both gas and condensed phase results reflect reactivities as expected for SN2 type II process, and correlating with the amine nucleophilicity as indicated by its pKb, and specifically following the order: aliphatic ≥ cycloaliphatic > aromatic. Comparing the curing reactivities of aliphatic and cycloaliphatic amines that have similar pKb values but different sizes and shapes provides an estimate on the importance of the steric effects in increasing the curing activation energy by about 5 kJ∙mol-1 on the average. Similarly, an increase in pKb of a curing agent leads to an increase in the activation energy when comparing reactivities of cycloaliphatic and aromatic amines that have similar sizes and shapes. In particular, changing from aliphatic to aromatic amines yields an increase of the activation energy by about 13 kJ/mol. Substituent effects are modelled by the relative rate of curing reaction with primary and secondary amines. However, solvent effects lower the activation energy in all three classes of amines by about 15 kJ∙mol-1 from the gas phase. Differences in steric and electronic effects lead to lower activation energies for curing with secondary amines comparing to primary amines. Solvent effects lower the activation energy by 10 kJ/mol for PA and 4 kJ/mol for SA along the dominant alcohol-accelerated pathway. This difference is responsible for the larger activation energy for the reactions of a SA as compared to that of a PA, and for bringing theory into agreement with experimental observation. CHAPTER 3 MECHANISMS OF THE EPOXY-PHENOL CURING REACTIONS 3.1 Introduction The majority of industrial applications of epoxy resins involve thermosettings, in which epoxy resins react with crosslinking agents known as hardeners. The two most popular hardening classes are comprised of primary/secondary amines (50%) and carboxylic acid/anhydrides (36%). Phenols and other substances constitute the remaining classes.7 Thermosetting with amines exhibits toxicity and deterioration of electrical properties at high temperature and humidity, while carboxylic acids or anhydrides require high-energy consumptions resulting from prolonged curings at high temperature.49 Meanwhile, thermosetting by phenols leads to excellent insulating characteristics, good adhesive properties, outstanding chemical resistance, retention of properties under severe operating conditions, low moisture adsorption, and no reaction by-products.1, 6 Thus, it has been used increasingly in the electronic industry as encapsulating and packing materials.5, 6, 49 Epoxy-phenol curing reactions can be carried out at moderate temperatures (150- 2000C) in the presence of catalysts such as quaternary ammonium salts, tertiary amines, and/or metal alkoxides.7, 28, 29, 50, 51 Among these catalysts, tertiary amines are often used.7, 52- 58 Using epoxy (denoted as E), phenol (denoted as PhOH), and tertiary amine catalyst (denoted as NR3), three possible hydrogen bonding complexes, namely epoxy-phenol, phenol-tertiary amine and phenol-phenol can be formed. Possible outcomes of epoxy-phenol 24 curing reactions, which are either uncatalyzed or catalyzed, are illustrated in Table 3.1. The former involves two pathways, an isolated pathway ( i R ) wherein the epoxy reacts with phenol alone, and a self-promoted pathway ( p R ) in which an additional phenol molecule forms a hydrogen bonding complex with the epoxy moiety to stabilize the transition state (TS). For catalyzed reactions, a tertiary amine can participate in two different actions. First, it can open the epoxy ring to create a zwitterion and then the epoxy zwitterion can react with a phenol curing agent similar to the uncatalyzed reactions, whether via the isolated or self-promoted pathways. The role of the NR3 catalyst can thus be used to name these reactions, distinguishing them from uncatalyzed reactions. They are described as the isolated ring opening by tertiary amine catalyzed pathway ( c i,ro R ) and the self-promoted ring opening by tertiary amine catalyzed pathway ( c p,ro R ) in Table 3.1. Second, a tertiary amine can form a hydrogen-bonding complex with a phenol curing agent first, which then reacts with the epoxy ring in a similar pathway as for the uncatalyzed reactions. The reactions are named as an isolated hydrogen bonding catalyzed pathway ( c i,hb R ) and a self-promoted hydrogen bonding catalyzed pathway ( c p,hb R ). The uncatalyzed reaction (cf. Scheme 3.1), that was not confirmed to be either isolated ( i R ) or self-promoted ( p R ), was found to be sluggish at 2000C and to proceed at a reasonable rate only at higher temperatures.5, 28, 49 In catalyzed reactions (Table 3.1), pathway ( c i,ro R ) was first suggested by Shechter and Wynstra28 in 1956 (cf. Scheme 3.2). Sorokin and Shode's experimental study proposed a pathway that occurred via a trimolecular transition state29 (Scheme 3.3) and was mostly applied to examine the effect of reactant ratio49 as well as the effects of different kinds of catalysts.5, 49, 59, 60 Such a 25 Table 3.1. Possible reactions of epoxy- phenol curing system. Uncatalyzed reaction Isolated pathway (Ri ) E + PhOH Pi i TS Self-promoted pathway ( p R ) E...HOPh + PhOH p P p TS Catalyzed reaction Isolated ring-opening by tertiary amine catalyzed pathway ( c i,ro R ) E + NR3 + PhOH c1 p,ro P c1 i,ro TS c2 p,ro TS c1 i,ro P c2 i,ro P Self-promoted ring-opening by tertiary amine catalyzed pathway ( c p,ro R ) E...HOPh + NR3 + PhOH c1 p,ro TS c1 p,ro P c2 p,ro TS c2 p,ro P c1 p,ro P Isolated hydrogen bonding catalyzed pathway ( c i,hb R ) PhOH + NR3 E + PhOH...NR3 PhOH...NR3 c i,hb TS c i,hb P Self-promoted hydrogen bonding catalyzed pathway ( c p,hb R ) E...HOPh + PhOH...NR3 PhOH + NR3 PhOH...NR3 c p,hb TS c p,hb P O + Ph OH O O H Ph OH O Ph O + Ph OH O O H Ph OH O Ph H O Ph H O Ph + PhOH (Ri) (Rp) Scheme 3.1. Uncatalyzed reactions in the epoxy-phenol curing. 26 + NR3 + PhOH + PhO O O N R R R O N R R R O N R R R OH N R R R Scheme 3.2. Shechter and Wynstra's pathways ( c i,ro R ). NR3 + + PhOH O O PhOH NR3 Scheme 3.3. Catalyzed reaction via a trimolecular TS. trimolecular transition state structure has not been confirmed as either acyclic or cyclic along the ( c p,ro R ) pathway. Along with the pathway ( c p,ro R ), the pathway ( c i,hb R ) was suggested via a cyclic transition state (Scheme 3.4). The data for one or more of the reactions in Table 3.1 were included in the kinetic modeling of the phenol curing system by fitting to experimental data using Differential Scanning Calorimetery (DSC). Although the fittings between the kinetic models and experimental data were usually reported to be reasonable,5, 59-61 such models cannot be extrapolated for other phenol curing systems nor can they prove that the mechanism is complete. To the best of our knowledge, there has not been any theoretical study on the mechanism of the epoxy-phenol curing system. From the above discussion, previously 27 R3N PhOH R3NH+ OPh- R3NH+ OPh- + R3NH+ OPh- + O O Scheme 3.4. Catalyzed pathway via a hydrogen bond complex forming ( c i,hb R ). proposed mechanisms involve competitive pathways and are not mutually exclusive as originally suggested. In addition, the roles of the tertiary amine catalysts in either opening the epoxy ring or forming a hydrogen bond complex with a phenol curing agent have not been confirmed. For instance, the pathway ( c p,hb R ), which may be the dominant pathway because the TS is stabilized by two hydrogen bonds, has not been suggested. The main objective of this study is to perform systematic theoretical studies on the mechanism of these epoxy-phenol curing reactions at the molecular-level using B3LYP density functional theory. Examination of all possible reaction pathways of an epoxy-phenol curing system at the same level of theory enables the development of a more accurate kinetic model for the system. In addition, it would also provide insight into the roles of tertiary amines in catalyzing the curing reaction. 3.2 Computational details 3.2.1 Physical models Bisphenol A diglycidyl ether (BADGE) is the basis of the liquid epoxy resin, and the phenol curing agents can be phenol-, cresol-, or bisphenol A terminated epoxy resin hardeners.7 These commercial epoxies and phenol curing agents have large and complicated structures. Therefore, it is necessary to choose physical models that can represent these 28 commercial reactants, yet are small enough to be computationally feasible. Some commercial epoxy and curing agent structures along with their models are presented in Table 3.2. Similarly, trimethylamine ((CH3)3N) is the model for catalytic tertiary amines such as triethylamine (TEA) and benzyl dimethyl amine (BDMA). 3.2.2 Computational models All electronic structure calculations were carried out using the Gaussian 03 program package.42 A hybrid nonlocal density functional theory (DFT), particularly Becke's gradient-corrected exchange-correlation density functionals B3LYP43 with the 6-31G(d, p) basis set was used to locate all stationary points. These are reactants, transition states, intermediates, and products. Normal mode analyses were done at the same level. To confirm the transition state for each reaction pathway, the minimum energy paths (MEPs) from the transition state to both the reactants and products were calculated using the Gonzalez-Schlegel steepest descent path method44, 45 in mass weight cartesian coordinates with the step size of 0.01 (amu)1/2 Bohr. Single point solvation calculations were performed on the optimized DFT geometries using a polarizable continuum model (PCM)46, 62 with a dielectric constant of 4.9 that is close to the dielectric constant of phenol (ɛ=4.6) to mimic the reactions in the solutions. It has been shown that the solvation free energies obtained from single point PCM calculations with the gas phase geometries from DFT calculations are in reasonable agreement with the values from full geometry optimizations.63, 64 All solvation calculations used the simple united atom topological model (UAO). 29 Table 3.2. Some common commercial epoxy and curing agent and tertiary amine catalyst structures and overview on the model complexes. Common commercial epoxies, phenol and catalysts Model systems Formula Abbreviation Formula Abbreviation O O O O O O O O HO OH OH OH OH CH2 CH2 n N N BADGE H12-BADGE BPA TEA BDMA O O OH N E PhOH TMA 3.3 Results The hydrogen bond precursor complex is presented first, followed by an examination of all pathways in Scheme 3.1 in both the gas and condensed phases. Geometries of the transition states (TS) and their zero-point energy corrected barriers G a ΔV are used to compare the reactivities of all pathways. Zero point energy corrected barriers in the condensed phase are approximated as reaction activation energies a E . Zero point energy corrections were approximated by the gas phase values in this case. The classical barrier in the gas phase ( V ), the zero-point energy (ZPE), and the zero-point corrected enthalpy of reaction ( H ) are also presented in Table 3.3. 30 Table 3.3. Energetic values (kJ/mol) of possible reactions in Table 1. (* is symbol for the enthalpy of reaction ΔH) Pathways V ZPE G a V sol V Ea C1 -64 9 -54 -51 -41 C2 -54 8 -46 -37 -30 C3 -60 8 -52 -48 -40 i R i TS 148 -5 143 161 156 p R p TS 98 3 101 92 95 p P 88* 4* 92* 77* 82* c i,ro R c1 i,ro TS 115 7 122 108 115 c p,ro R c1 p,ro TS 62 5 67 51 57 c1 p,ro P -13* 16* 2* -8* 7* c2 p,ro TS 13 -1 12 52 51 c2 p,ro P -135* 2* -133* -84* -82* c i,hb R c i,hb TS 171 2 173 131 133 c p,hb R c p,hb TS 108 -7 101 102 95 c p,hb P 19* 17* 36* 5* 22* 3.3.1 Hydrogen bonding precursor complexes Complexes 1-3 (cf. Figure 3.1) show possible reactant complexes between the phenol groups, the amine functional groups and the epoxy oxygen. Table 3.4 illustrates that the order of strong hydrogen bond interaction is C1 < C2 < C3 and the OH…N hydrogen bond of C3 is strongest because nitrogen is a better hydrogen acceptor (Lewis base) than oxygen. Therefore, the complexes C2 and C3 can participate in the curing reactions together with epoxy, phenol and tertiary amine. 3.3.2 Uncatalyzed reactions Uncatalyzed reactions include isolated ( i R ) and self-promoted ( p R ) pathways. Each pathway is examined for both cyclic and acyclic TS routes. As the reaction proceeds from 31 O H O H O H N R R O H O R R C1 HB_(PhOH)2 C2 HB_PhOH-E C3 HB_(PhOH)-NR3 Figure 3.1. Hydrogen bond complexes Table 3.4. Bond distance and the binding energy of hydrogen complexes C1 HB_(PhOH)2 C2 HB_PhOH-E C3 HB_PhOH-NR3 d(OH-O) (Å) 1.903 1.837 d(OH-N) (Å) 1.818 bind E (kJ/mol) -54 -46 -52 the reactant to product, the C2-O1 bond of the epoxy ring is broken and a new C2-O2 bond is formed. The transition states are presented in Figures 3.2 and 3.3 and Table 3.5. Note that all hydrogen atoms not involved in the reactions are deleted in all figures for clarity and the dashed lines illustrate the forming and breaking of bonds. In the isolated pathway ( i R ), the epoxy-phenol curing in the cyclic TS route is preferred because of its lower energy barrier as compared to the acyclic TS route. In the self-promoted pathway ( p R ), the acyclic TS route is preferred due to the advantage of its lowered energy barrier compared with the cyclic TS route. Comparing p TS to i TS , the hydrogen bond of the phenol-epoxy complex accounts for a lowering of the energy barrier by 42 kJ/mol, and p TS can be considered as a reference for the following catalyzed reactions. 3.3.3 Catalyzed reactions The tertiary amine catalyst can assume different roles: 1) Opening the epoxy ring to form a zwitterion first, after which the zwitterion attaches to a phenol and 2) Forming a hydrogen bond complex with a phenol curing agent that stabilizes the TS. 32 O2 H1 C1 C2 O3 O1 C1 C2 O3 O1 O2 H1 Figure 3.2. The cyclic (left) and acyclic (right) TS in isolated pathway ( i TS ). H1 O3 C1 C2 O4 O1 O2 H2 H1 O3 C1 C2 O4 O1 O2 H2 Figure 3.3. The cyclic (left) and acyclic (right) TS in the self-promoted pathway ( p TS ). Table 3.5. Parameter of the TS geometries in uncatalyzed reactions. (* is denoted for selected transition state) Parameters i TS p TS Route cyc acyc cyc Acyc ≠ (i.cm-1) 636 531 486 224 d(H1-O1) (Å) 1.375 1.323 1.492 d(O1-C2) (Å) 2.104 2.272 2.168 2.204 d(O1-C1) (Å) 1.398 1.319 1.392 1.361 d(C1-C2) (Å) 1.471 1.540 1.470 1.515 d(C2-O2) (Å) 2.274 1.587 2.263 1.677 d(O2-H2) (Å) 1.173 1.011 1.038 (O1-C1-C2) (deg) 94.38 104.93 98.48 99.96 (C1-C2-O2) (deg) 100.53 110.79 84.89 110.34 G a V (kJ/mol) 143* 169 141* 101 33 3.3.3.1 Ring opening by tertiary amine catalyzed pathway Pathways ( c i,ro R ) and ( c p,ro R ) in Table 3.1 are considered here. Since these pathways are different from each other by a hydrogen bond complex of an epoxy and a phenol molecule, they are an isolated ring opening by tertiary amine catalyzed pathway ( c i,ro R ) and a self-promoted ring opening by tertiary amine pathway ( c p,ro R ). Since each pathway proceeds via two steps, the numbers 1 and 2 were added to the transition states' names. The first steps of pathways ( c i,ro R ) and ( c p,ro R ) are examined and compared in both front-side and backside attachments. The transition state geometries and their parameters for the isolated ring opening by the tertiary amine pathway ( c1 i,ro TS ) are illustrated in Figure 3.4 and Table 3.6. Those of the self-promoted ring opening by tertiary amine pathway ( c1 p,ro TS ) are in Figure 3.5 and Table 3.6. In either c1 i,ro TS or c1 p,ro TS , the backside attachment is preferred vs. the front-side attachment because of a lower energy barrier and consequently, the backside energy barrier is chosen to compare to step one of each pathway. Comparing c1 i,ro TS to c1 p,ro TS (see Table 3.6), the hydrogen bond between the phenol promoter and the epoxy lowers the energy O1 C1 C2 O N O1 C1 C2 O N Figure 3.4. Front-side (left) and backside (right) attachments in the c1 i,ro TS . 34 Table 3.6. Parameter of TS geometries in the ring opening by tertiary amine catalyzed pathways. * The reference point is the product of the first step in the pathway ( c p,ro R ). Parameters c1 i,ro TS c1 p,ro TS c2 p,ro TS Route front Back front back ≠ (i.cm-1) 362 266 369 382 442 d(H1-O1) (Å) 1.599 1.607 0.983 d(O1-C2) (Å) 2.079 2.109 2.041 1.934 2.437 d(C2-N) (Å) 2.190 1.778 2.260 2.028 2.057 d(O1-C1) (Å) 1.383 1.338 1.400 1.386 1.406 d(C1-C2) (Å) 1.470 1.529 1.467 1.483 1.518 d(C2-O2) (Å) 2.104 d(H2-O2) (Å) 1.521 d(H2-O3) (Å) 1.025 d(O3-H1) (Å) 1.817 (O1-C1-C2) (deg) 93.48 94.47 90.73 84.70 112.84 (C1-C2-N) (deg) 119.53 123.96 122.85 118.55 102.52 (O1-C1-C2-N) (deg) 179 96 (O1-C1-C2-N) (deg) -82 G a V (kJ/mol) 188 122 150 67 12* O1 C1 C2 O N O1 C1 C2 O N O H1 O H1 Figure 3.5. Front-side (left) and backside (right) attachments in the c1 p,ro TS . 35 barrier by 55 kJ/mol, leading us to pursue further study of the second step of the self-promoted ring-opening by a tertiary amine pathway. Step 1 of the self-promoted ring-opening by the tertiary amine catalyzed pathway is followed by the formation of a six-centered cyclic transition state structure, in which a synchronized transfer of an electron pair takes place as shown in Figure 3.6 ( c2 p,ro TS ). A strong hydrogen bond O1-H1 can be formed by a hydrogen atom transfer either from a phenol promoter or from a phenol curing agent to the epoxide oxygen. The required energy for such a hydrogen transfer can be ignored relative to the zwitterion's creation in step 1, ( c1 p,ro TS ). This hydrogen transfer might happen before the attachment of the phenol curing agent into an epoxy which is indicated by an imaginary frequency of -442 cm-1. In the zwitterion formation ( c1 p,ro TS ), the nitrogen atom of the tertiary amine is in the plane of the epoxy ring ( (O1-C1-C2-N) = 1790) but in the six-centered cyclic formation ( c2 p,ro TS ), it is at a right angle to the epoxide plane ( (O1-C1-C2-N) = 960) (see Table 3.6). Phenol attaches to the epoxy ring on the opposite side of the tertiary amine at the epoxide atom C2 ( (O1-C1-C2-O3) = -820) and this attachment requires less energy than the first step (12 kJ/mol compared to 67 kJ/mol). This leads to a conclusion that after the epoxy ring O1 C1 C2 O N H1 O3 H2 O2 Figure 3.6. The transition state geometry ( c2 p,ro TS ) of step 2 in the pathway c p,ro R . 36 is opened by a tertiary amine, the phenol does not attach to the epoxy via either a cis- or trans-ring but on the opposite side with the tertiary amine in the epoxide plane. 3.3.3.2 Hydrogen bonded catalyzed pathways The role of the tertiary amine in this case is to form a hydrogen bond complex with a phenol curing agent. This step is followed by the attachment of this complex to the epoxy ring of either the alone epoxy in c i,hb R or to the epoxy-phenol complex in c p,hb R . Since the reaction rate of the second step is too slow compared with that of the first step, the second step is considered to be the rate-determining step. The transition state geometries and their parameters are presented in Figure 3.7 and Table 3.7. Note that due to the lower energy barrier of the acyclic TS route and the backside attachment in the previous pathways, only the acyclic TS is examined for this study. The bond lengths of two "active" bonds, the breaking O1-C2 bond and the forming C2-O2 bond, at the TS, provide information on how close the TS is to the reactant (entrance) channel or to the product (exit) channel. Comparing the two TS's of hydrogen bonding catalyzed pathways, the shortening of the O1-C2 and the lengthening of the C2-O2 bond distances indicate that the c p,hb TS is moved closer to the reactant channel than c i,hb TS . The decrease of 62 kJ/mol in the energy barrier when c p,hb TS is compared to c i,hb TS is consistent with the Hammond postulate, which states that more reactant-like characteristics of the transition state structure would lead to a smaller energy barrier. It confirms the role of the stabilization of a hydrogen bond complex between a phenol promoter and an epoxy reactant as seen in previous pathways. 37 C1 C2 O O1 O2 H2 N H1O C1 C2 O O1 O2 H2 N c i,hb TS c p,hb TS Figure 3.7. Transition state geometries of hydrogen bond catalyzed pathways. Table 3.7. Parameter of TS geometries in hydrogen bonding catalyzed pathways ( c i,hb R and c p,hb R ). Parameter c i,hb TS c p,hb TS ≠ (i.cm-1) 244 651 d(H1-O1) (Å) 1.545 d(O1-C2) (Å) 2.115 1.992 d(C2-O2) (Å) 1.695 1.846 d(O2-H2) (Å) 1.481 1.210 d(H2-N) (Å) 1.104 1.277 d(O1-C1) (Å) 1.340 1.388 d(C1-C2) (Å) 1.515 1.488 (O1-C1-C2) (deg) 95.39 87.60 (C1-C2-O2) (deg) 122.28 120.82 G a V (kJ/mol) 173 101 38 3.4 Discussion Both energetic values in the gas and the condensed phases of the pathways are presented in Table 3.3. The potential energy diagram of this reaction in the gas phase is presented in Figure 3.8. It will be assumed that the reference point is a point in which the epoxy, phenol and tertiary amine are separated infinitely. Since phenol cures epoxy by heat, both energy barriers and heat consumption are examined for the comparison on the reactivity of each reaction pathway. Energy barriers are first examined and they follow the following order: c i,hb TS (173 kJ/mol) > i TS (143 kJ/mol) > c1 i,ro TS (122 kJ/mol) > p TS = c p,hb TS (101 kJ/mol) > c1 p,ro TS (67 kJ/mol). This trend is divided into two groups: 1) A group that contains the stabilization of the hydrogen bonding between a phenol promoter and epoxy ( c i,hb TS , i TS , c1 i,ro TS ) and 2) A group that does not contain that stabilization ( p TS , c p,hb TS , c1 p,ro TS ). The first group obtains a higher energy barrier than the second by 56 kJ/mol on average. A comparison of energy barriers between two corresponding pathways whose transition states are different in the hydrogen bonding complex of epoxy and a phenol promoter yields similar results. The transition states containing such hydrogen bonding always render a lower energy barrier than the others. For instance, a lowering of 42 kJ/mol of the energy barrier is obtained when p TS is compared to i TS , 55 kJ/mol for a comparison of c1 p,ro TS and c1 i,ro TS , and 62 kJ/mol for c p,hb TS and c i,hb TS (see Table 3.7). This leads to the speculation that phenol always plays a dual role as a curing agent and as an accelerator by forming a hydrogen bond complex with epoxy to stabilize the transition state. A similar comparison is applied for two corresponding pathways that differ by a tertiary amine Figure 3.8. Potential energy for epoxy-phenol curing in the gas phase. ( 143) (55) (46) ( 122) C2 (-46) (21) (-44) (-32) (-177) C3 (-52) (121) (-98) ((-62) -200 -150 -100 -50 0 50 100 150 Relative energy (kJ/mol) Reaction coordinate TSi TSs TSiroc TSsroc TSihbc TSshbc 3) 40 molecule. As a tertiary amine participates in the reaction as an epoxide opener, its catalytic property is indicated by the decrease in energy barriers, e.g., i TS > c1 i,ro TS (group 1) and p TS > c1 p,ro TS (group 2). However, as a tertiary amine forms a hydrogen bonded complex with the phenol curing agent, the opposite result is achieved. In the first group, c i,hb TS yields a higher energy barrier than i TS by 30 kJ/mol and in the second group, c p,hb TS and p TS have the same energy barriers. Meanwhile, the hydrogen bond formation between a phenol curing agent and the NR3 catalyst is supposed to strengthen the nucleophilicity of the phenol curing agent, leading to a decrease in the energy barrier. In some pathways, the hydrogen bonding complex C2 and/or C3 participates and releases heat in the curing process. This leads to the order of energy consumption as follows: i R (143 kJ/mol) > c i,ro R (122 kJ/mol) > c i,hb R (121 kJ/mol) > p R (55 kJ/mol) > c p,ro R (21 kJ/mol) > c p,hb R (3 kJ/mol). This trend of energy consumption agrees well with the trend of the energy barriers: Pathways in which transition states are stabilized by hydrogen bonding of the epoxy and phenol promoter yield lower energy consumptions than the others by over 102 kJ/mol on average. c p,hb R is the most dominant process in curing epoxy-phenol because it has the smallest heat consumption. Heat consumption of i R , c i,ro R and c i,hb R is over forty times higher than the smallest heat consumption. Therefore, those pathways might not exist in the curing between epoxy and phenol. It also means that epoxy-phenol curing is always promoted by phenol curing agents. This is supported by Batog and coworkers' review65 that most experimental epoxy-phenol curing reactions occur completely if the ratio of epoxy: phenol functions (E:PhOH) is larger than 1. 41 Hydroxyl products can accelerate curing by hydrogen bonding with epoxy as a phenol curing agents. Due to the steric effects, those products might not combine with epoxy by hydrogen bonding or they require very high-energy consumption to react with epoxy. Thus, this process can be ignored in the epoxy-phenol curing reactions. There exist three pathways in the epoxy-phenol curing reaction. They are 1) Self promoted, 2) Ring-opening by tertiary amine catalyzed pathway and 3) Hydrogen bonding catalyzed pathway presented in both gas and condensed phases in Scheme 3.5 and Figure 3.9. The reactivity comparison is opposite with the order of heat consumption. That is self-promoted < ring-opening by tertiary amine < hydrogen bonding catalyzed pathway in both phases. The hydrogen bonded complexes and transition states are not effectively solvated because the net charge is more distributed in the molecule complex (see Table 3.7). Although energy barriers for each pathway decrease, the potential energy is shifted up in solution. This indicates reasonably that the reaction is favored in the gas phase relative to the condensed phase, or that it requires more heat consumption in the condensed phase. The products are less stable in the condensed phase than in the gas phase; however, the reaction remains endothermic. Among all reactants, transition states and products, c2 p,ro TS is most solvated, resulting in the increase of the energy barrier in the condensed phase by E + PhOH PhOH...E + PhOH + NR3 IM + PhOH...NR3 + PhOH Pp c p,ro P c p,hb P Scheme 3.5. General mechanism of epoxy-phenol curing reaction. . Figure 3.9. Potential energy for epoxy- phenol curing reaction both in the gas phase (solid lines) and in the condensed phase (dashed lines). Energetic values are in the condensed phase. (65) (52) C2 (-30) (27) (-23) (28) (-105) C3 (-70) (25) (-48) -200 -160 -120 -80 -40 0 40 80 Relative energy (kJ/mol) Reaction coordinate II_sol TSs IV_sol TSsroc VI_sol TSshbc ( ( 43 29 kJ/mol compared to that in the gas phase (Table 3.7 and Figure 3.9). This demonstrates the weak distribution of the net charge and the synchronized transfer of an electron pair in the six-membered ring (see Figure 3.6). The tertiary amine participates in two catalytic roles: 1) It leads to the easy attachment of phenol on the epoxy when during zwitterion formation, resulting in a lower energy barrier by 33 kJ/mol and 2) It forms a hydrogen bonded complex with a phenol curing agent without a lower energy barrier but with a lower heat of consumption by 52 kJ/mol. When the reaction is catalyzed by a tertiary amine that forms a zwitterion with the epoxy, its barrier energy is lowered compared to the uncatalyzed reaction, resulting in an increase in the curing rate. That means the tertiary amine's first role as a ring opener is dominant to its second role as a strengthener for a curing agent when the curing rate is considered. However, the opposite result is obtained when the heat of consumption as well as the stabilization are considered. This is achieved by the smallest energy consumption and the most stabilization of the hydrogen bonding catalyzed reaction. Although tertiary amines were known to be good catalysts for epoxy-phenol curing, resulting in their common usage in industry,7 the experimental activation energies of a tertiary amine catalyzed epoxy-phenol curing might not be found. Therefore, they can be approximated by epoxy-phenol curing with other catalysts such as trialkyl and/or triaryl nucleophiles of group Va elements and miscellaneous catalysts, e.g., tetramethylammonium hydroxide.51 In addition, tertiary amines can react with the curing agents to form salt catalysts. The activation energies of the biphenyl epoxy and phenol novolac resin system using triphenylphosphine (TPP) as a catalyst5 are 60-70 kJ/mol and the corresponding value for the diglycidyl ether of bisphenol A (DGEBA) and phenol novolac catalyzed by N- 44 benzylpyrazinium hexafluoroantimonate (BPH) is 75 kJ/mol.49 In our study, the curing of diglycidyl ether and phenol with a trimethylamine catalyst has an activation energy of 95 kJ/mol. Thus, all these activation energies are within an order of magnitude, which validates the reliability of our mechanistic model of the epoxy-phenol curing reactions. 3.5 Conclusions In this study, possible pathways in the epoxy-phenol curing reaction were examined using the quantum chemistry density functional theory. Both gas phase and condensed phase results suggest that phenol has dual roles as hardener and as self-promoter. In the second role, phenol combines with epoxies by a hydrogen bond that stabilizes the transition states, leading to a lower energy barrier by 56 kJ/mol and to decrease heat consumption by 102 kJ/mol on average. Tertiary amines assume two catalytic roles. The first role is to lower the energy barrier of the reaction by opening the epoxy ring to form a zwitterion before a phenol attaches to an epoxy in 33 kJ/mol. The second is to stabilize the transition state by hydrogen bonding with a phenol curing agent as well as to strengthen the nucleophilicity of the phenol curing agent, which does not lead to the decrease in the energy barrier but yields a smaller heat of consumption. Due to the smallest heat of consumption as well as the most stabilization in the self-promoted hydrogen bonding catalyzed reaction, tertiary amines are supposed to be promoters of phenol curing by forming a hydrogen bond complex. As epoxy-amine curing,8 epoxy-phenol curing belongs to the SN2-type II process, and the acyclic TS pathway is preferred relative to the cyclic TS pathway. The mechanism of this curing is presented in Scheme 3.5 and follows an order: self promoted < ring opening by tertiary amine < hydrogen bonding catalyzed. Without the catalyst, phenol cures epoxy 45 slowly because of a high energy barrier of about 101 kJ/mol. With the assistance of a catalyst, the energy barrier and heat consumption decrease, leading to a faster curing that agrees well with experimental observation. The resulting mechanism of epoxy-phenol curing performs predictive and functional-design capabilities. Its reactants, transition states, and products can be used as model for other systems by changing substituents on the epoxy, phenols, and even catalysts. CHAPTER 4 MECHANISMS OF THE EPOXY-CARBOXYLIC ACID CURING REACTIONS 4.1 Introduction Carboxylic acids comprise in the second most popular hardening class for curing epoxy resins. They have been used increasingly in powder coatings, accounting for the highest tonnage of epoxy curing agents in the U.S. industry. This is due to their relatively low price, widespread availability as raw materials, and good flexibility and weatherability.7 The process of this crosslinking can be described as in Scheme 4.1: the first product is a β-hydroxypropyl ester, which reacts with a second mole of carboxylic acid to yield a diester. The hydroxyl ester can also undergo polymerization by reaction of its secondary hydroxyl group with an epoxy group.7, 66 RCOOH + O RCOO OH RCOOH RCOO OH + RCOO OOCR + H2O RCOO OH + O RCOO O OH Scheme 4.1. Process of the crosslinking of epoxy- carboxylic acid. 47 This process is significant only when the temperature is around 2000C or is aided by catalysts such as tertiary amines between 800C to 1200C in a lower energy consumption reaction.66 All possible reactions for the crosslinking of epoxy-acid units can be illustrated in Scheme 4.2 which is divided into three groups: 1) a group of hydrogen bond formations, 2) a group of uncatalyzed reactions (Scheme 4.2a) and 3) a group of catalyzed reactions (Scheme 4.2b). In the first group, three hydrogen complexes, acid-acid, acid-epoxy and acid-tertiary amine can exist and both acid-epoxy and acid-tertiary amine complexes can participate synchronously in the curing. In the second group, several authors28, 66-68 suggested that epoxy and acid could react without a catalyst (isolated pathway i R ). Rokaszewski69 suggested that curing happens automatically, initiated by hydrogen donation by an acid or a hydroxyl product as presented in the self-promoted pathway p R . In Scheme 4.2b, the catalyzed reactions are currently known to proceed through only two pathways. The first is c i,ro R , as suggested by Shechter and Wynstra,28, 66 In this pathway, a tertiary amine catalyst and an epoxy were proposed to participate in the formation of a zwitterion and then this zwitterion reacted with an acid to form a product, similar to the isolated pathway. Thus, this pathway is distinguished from the isolated pathway by adding the role of the tertiary amine into its name, i.e., the isolated ring-opening of tertiary amine catalyzed pathway. In the second, c i,hb R , proposed by Sorokin and Gershanova,66, 70 the amine catalyst was assumed to form a complex with an acid, and then the complex reacts with an epoxy to form a product. Similar to the reaction in the Shechter and Wynstra's study, the reaction is named as the isolated hydrogen bonding catalyzed pathway. 48 RCOOH + O RCOO OH O O H C O R 2 RCOOH + O RCOO OH O O H C O R Ri: Isolated pathway HCOOR + RCOOH Rp: Self-promoted pathway (a) : Isolated ring opening of tertiary amine catalyzed pathway : Self-promoted ring opening of tertiary amine catalyzed pathway H2C CH O + NR'3 R'3N CH2 HC O-R' 3N CH2 HC O- + R C OH O RCOO OH + NR'3 H2C CH O + NR'3 R'3N CH2 CH O- + R C OH O RCOO OH + NR'3 + RCOOH RCOOH RCOOH R'3N CH2 CH RCOOH O-c p,ro R c i,ro R (1) Epoxy ring opening (2) Curing (1) Epoxy ring opening (2) Curing Scheme 4.2. Possible reactions in the epoxy- carboxylic acid curing system. (a) Uncatalyzed reactions in the epoxy- carboxylic acid curing system. (b) Catalyzed reactions in the epoxy- carboxylic acid curing system. 49 H2C CH O : Isolated hydrogen bonding catalyzed pathway + R O O H N R' R R' RCOO OH + NR'3 : Self-promoted hydrogen bonding catalyzed pathway H2C CH O + R O O H N R' R' R' RCOO OH + NR'3 + RCOOH HOOCR R C OH O + NR'3 R O O H N R' R' R' R C OH O + NR'3 R O O H N R' R' R' c i,hb R c p,hb R (1) Hydrogen bonding (2) Curing (1) Hydrogen bonding (2) Curing (b) Scheme 4.2 - continued. 50 To the best of our knowledge, the currently accepted mechanism for the tertiary amine catalyzed epoxy-acid curing reaction does not mention to at least two pathways. The first is c p,ro R , a reaction of an epoxy-acid complex and a tertiary amine to form a zwitterions. This zwitterion reacts with an acid in a similar fashion as in the isolated ring opening of tertiary amine catalyzed pathway. This is called the self-promoted ring opening of tertiary amine catalyzed pathway. The second is c p,hb R , a reaction of epoxy-acid complex and acid-tertiary amine complex and it can be named as a self-promoted hydrogen bonding catalyzed pathway. These reactions might be dominant pathways because they achieve stabilization of the transition state (TS) by hydrogen bonds between the epoxy and acid, leading to a lower energy consumption or an acceleration to products as proved in the epoxy-amine and epoxy-phenol curing. In addition, a suggested frontal approach in i R 71 and c i,hb R 68, 70 would lead to a high energy barrier compared to the well-known backside approach of the typical SN2 reaction as mentioned in the epoxy-amine8 or epoxy-phenol curing systems. In the review of Madec and Maréchal66 in 1985, there were over 295 cited studies on uncatalyzed, base-catalyzed, and miscellaneous-catalyzed epoxy-carboxy esterifications and polyesterifications having an emphasis on the kinetics and mechanisms of polyesterification. One or more of the reactions in Scheme 4.2 were included in kinetic modelings of the acid curing systems by fitting to experimental data using Differential Scanning Calorimetery (DSC) that could not distinguish between the production of α and β esters. Note that only one α and β esters of such reactions is needed to be included in the mechanism model. Although the fittings between the kinetic models and the experimental data were usually reported to be reasonable, such models cannot be extrapolated for other acid curing systems nor prove that the mechanism is complete. For instance, results of the curing reactions of 51 acetic acid with some epoxies catalyzed by different tertiary amines66, 72-76 cannot be extended for use in other reactions having either different epoxies or different tertiary amine catalysts. The main objective of this study is to perform a systematically theoretical study on the mechanism of these epoxy-acid curing reactions at the molecular-level using B3LYP density functional theory. Examination of all possible reaction pathways of an epoxy-acid curing system at the same level of theory enables the development of a more accurate kinetic model for the system. 4.2 Computational details 4.2.1 Physical models In industry, large molecules are utilized that are unfeasible for computation. In this study, smaller representative molecules are used. Methyl glycidyl ether was chosen to be a model for commercial epoxies, acetic acid was chosen for carboxylic acids, and trimethylamine was chosen for tertiary amine catalysts. 4.2.2 Computational models All electronic structure calculations were carried out using the Gaussian 03 program package.42 A hybrid nonlocal density functional theory B3LYP level of theory43 with the 6- 31G(d, p) basis set was used for locating all stationary points, namely reactants, transition states, intermediates, and products. Stationary points were characterized by normal mode analyses. To confirm the transition state for each reaction pathway, the minimum energy path (MEP) from the transition state to both the reactants and products was calculated using the Gonzales-Schlegel steepest descent path method44, 45 in mass weight Cartesian 52 coordinates with the step size of 0.01 (amu)1/2 Bohr. Single point solvation calculations were performed with Gaussian 0977 on the optimized DFT geometries using a polarizable continuum model (PCM)46, 62 with the acetic acid solvent (ɛ = 6.25) to mimic the reactions in solutions. It has been shown that the solvation free energies obtained from single point PCM calculations on the gas phase geometries from DFT calculations are in reasonable agreement with the values from full geometry optimization.63, 64 All solvation calculations used the UFF (Universal Force Field) radii model, which places a sphere around each solute atom, with the radii scaled by a factor of 1.1 parameters. 4.3 Results All possible reactions in Scheme 4.2 were studied respectively in the gas and the condensed phases. Hydrogen bond complex formations are examined first and followed by the examination of uncatalyzed and catalyzed reactions in the epoxy-acid curing reactions. Then, the comparison of those reactions and the validation with experimental values are performed. Geometries of the transition states (TS) and their zero-point energy corrected barriers G Va are used for the comparison of reactivity. Activation energies a E that are approximated by the barriers in the condensed phase, corrected by the zero point energy calculated in the gas phase, are used to compare with experimental values. The classical barrier in the gas phase ( V ), the zero-point energy (ZPE), and the enthalpy of reaction ( H ) at 0 K are presented in Table 4.1. 53 Table 4.1. Energetic values (kJ/mol) for all possible pathways in Scheme 4.2 of the epoxy-acid curing reaction at 0 K. (Enthalpy of reaction is reported for products) Pathways Compounds V ZPE G a V sol V Ea C1 -42 5 -37 -33 -29 C2 -47 6 -41 -37 -32 C3 -58 6 -52 -53 -47 i R i TS 135 -10 125 139 130 p R p TS 119 -5 114 117 112 p P 71 11 82 63 74 c i,ro R c1 i,ro TS 115 6 122 76 83 c p,ro R c1 p,ro TS 55 3 58 45 48 c1 p,ro P -22 19 -4 -53 -35 c2 p,ro TS 71 -7 64 86 79 c2 p,ro P -76 -3 -79 -39 -43 c i,hb R c i,hb TS 162 4 166 123 127 c p,hb R c p,hb TS 90 0 90 79 79 c p,hb P 25 12 37 -40 -29 4.3.1 Hydrogen bonding precursor complexes Complexes C1-C3 (cf. Figure 4.1) show possible reactant complexes between the acid groups, the amine catalyst functional groups and the epoxy oxygen. Note that all hydrogen atoms not involved in the reactions are deleted in all figures for clarity and the dashed lines illustrate the forming and breaking of bonds. Table 4.2 demonstrates that the order of strong hydrogen bond interaction is C1 < C2 < C3 which is consistent with the decrease of the binding energies. The OH…N hydrogen bond of C3 is strongest because nitrogen is a better hydrogen acceptor (Lewis base) than oxygen. So the complexes C2 and C3 can participate in the curing reactions together with epoxy, acid and tertiary amine. 54 O H O H O O H N O O H O C1 HB_(COOH)2 C2 HB_COOH-E C3 HB_(COOH)-NR3 O O O Figure 4.1. Hydrogen bond complexes Table 4.2. Bond distance and the binding energy of hydrogen complexes. (Binding energy bind E is calculated in the gas phase). Parameters C1 C2 C3 d(OH-O) (Å) 1.86, 1.92 1.76 d(OH-N) (Å) 1.69 bind E (kJ.mol-1) -37 -41 -52 4.3.2 Uncatalyzed reactions (Scheme 4.2a) Transition states of i R (Figure 4.2) and p R (Figure 4.3) are examined in both acyclic and cyclic routes. In the process from reactant to product via the acyclic TS, the C2- O1 bond of the epoxy ring is broken and the new C2-O2 bond is formed whereas in the process via the cyclic TS, C2-O2 bond is broken and H1-O1 is formed. These bond lengths, barrier energies, and other parameters of the transition state structures are represented in Table 4.3. In i R , the cyclic TS is characterized by a lower energy barrier than the acyclic TS by 73 kJ/mol, and thus is considered as the TS for this pathway. This agrees well with Klebanov et al.'s suggestion71 that the TS of epoxy-acid curing reaction would have a six-member ring structure where the OH group of acid forms a hydrogen bond with the oxygen atom of the epoxy and the C=O group attacks the methylene group of the epoxy from the front side. 55 C1 C2 O O1 H O2 R O C1 C2 O O1 H1 O2 O3 R Figure 4.2. Acyclic (left) and cyclic (right) transition states of i R . C1 C2 O3 O1 H1 COOR C1 C2 O3 O1 O2 H2 O R H1 COOR H2 O2 O R Figure 4.3. Acyclic (left) and cyclic (right) transition states of p R . Table 4.3. Parameters of transition state geometries of i R and p R . Parameters i TS p TS Route Acyc Cyc Acyc Cyc ≠ (i.cm-1) 445 830 508 514 d(H1-O1) (Å) 1.210 1.143 1.036 d(H1-O2) (Å) 1.191 d(O1- C2) (Å) 2.206 2.026 2.071 2.016 d(C2-O3) (Å) 2.277 d(C2-O2) (Å) 1.665 1.866 3.342 d(O1- C1) (Å) 1.327 1.411 1.397 1.434 d(C1-C2) (Å) 1.521 1.462 1.490 1.461 d(H2-O2) (Å) 1.018 0.999 (O1-C1-C2) (deg) 101.31 89.7 91.6 88.31 (C1-C2-O3/O2) (deg) 109.91 119.2 107.2 130.33 G a V (kJ/mol) 198 125 114 165 56 In p R , the acyclic TS dominates the cyclic six-member ring TS in the lower energy barrier, conflicting with the speculation that suggested a cis-opening of the epoxy ring 66-68 but agreeing well with the suggestion of a trans-opening TS.66, 78, 79 In addition, it agrees with the recent result in the epoxy-amine curing reaction that stated the acyclic TS is preferred vs the cyclic TS because of the former's smaller energy barrier.8 Due to the hydrogen donation by the acid to an epoxy ring, the energy barrier of p R is lower than that of i R by 11 kJ/mol (see Table 4.3). In addition, the sufficient amount of acid as well as the easy binding of an epoxy and an acid account for the existence of the self-promoted pathway, and thus the isolated pathway may serve as a reference for the self promoted pathway as it does not take part in the curing reaction. 4.3.3 Catalyzed reactions (Scheme 4.2b) 4.3.3.1 Ring opening of tertiary amine catalyzed pathways Pathways c i,ro R and c p,ro R in Scheme 4.2b are considered here. Since each pathway proceeds via two steps, the numbers 1 and 2 were added to both transition states and products' names. The transition states of step 1 in each pathway ( c1 i,ro TS and c1 p,ro TS ) are examined, represented in Figures 4.4 and 4.5 respectively. Step 2 is then examined only for the dominant pathway in the comparison of energy barriers of reactions in step 1. In either c1 i,ro TS or c1 p,ro TS , the backside attachment is preferred as compared to the front-side attachment because of the lower energy barrier and consequently, its energy barrier is chosen as a reference to compare which TS is dominant in the first step of each pathway. Comparing c1 i,ro TS to c1 p,ro TS (see Table 4.4), the hydrogen bond between an acid 57 O1 C1 C2 O N O1 C1 C2 O N Figure 4.4. Back-side (left) and front-side (right) c1 i,ro TS . O1 C1 C2 O N H1 O O1 C1 C2 O N H1 O O O Figure 4.5. Back-side (left) and front-side (right) c1 p,ro TS . Table 4.4. Parameters of c1 i,ro TS and c1 p,ro TS . Parameters c1 i,ro TS c1 p,ro TS Side attachment front back* back* front ≠ (i.cm-1) 362 266 397 389 d(N-C2) (Å) 2.190 1.778 2.061 2.265 d(C2-O1) (Å) 2.079 2.109 1.908 2.021 d(H1-O1) (Å) 1.479 1.533 d(C1-O1) (Å) 1.383 1.338 1.393 1.398 d(C1-C2) (Å) 1.470 1.529 1.479 1.467 (O1-C1-C2) (deg) 93.48 94.5 83.2 89.72 (C1-C2-N) (deg) 119.53 124.0 117.34 123.88 (C2-N-O1) (deg) 47.36 45.01 G a V (kJ/mol) 188 122 58 156 (* is noted for the represented TS) 58 promoter and an epoxy lowers the energy barriers by 64 kJ/mol, leading to further study of the second step of the c p,ro R pathway. In the second step of c p,ro R , the formation of a six-centered cyclic transition state structure ( c2 p,ro TS ), in which a synchronized transfer of an electron pair takes place is shown in Figure 4.6. The attachment of an acid curing agent to the epoxy is indicated by an imaginary frequency of -422 cm-1 for the vibration of the C2-O2 bond. A strong hydrogen bond O1-H1 in c2 p,ro TS can be formed by a hydrogen atom transfer either from the acid promoter or from the acid curing agent to the epoxide oxygen. The required energy for such a hydrogen transfer can be ignored relative to the zwitterion's formation in step 1 ( c1 p,ro TS ). This hydrogen transfer might happen before the attack of the acid into the methylene carbon on the epoxy ring. 4.3.3.2 Hydrogen bonding catalyzed pathways Two last pathways ( c i,hb R and c p,hb R ) in Scheme 4.2b are examined, in which the tertiary amine creates a hydrogen bond complex with an acid curing agent. It might lead to the strengthening of the nucleophilic attachment into the epoxy ring. Although they are two step reactions, the hydrogen bonding step is fast compared to the curing step. So, the transition state in the curing step is focused in this study. Due to the significantly lower energy barriers of the acyclic transition states compared with the cyclic transition states in the p R and of the backside TS compared with the front-side TS of the first step in the c i,ro R and c p,ro R , only the acyclic route is considered for this study. The parameters of those TSs are presented in Figure 4.7 and Table 4.5. The 59 O1 C1 C2 O N H1 O O O1 C1 C2 O N H1 O3 O H2 O2 O O O H Figure 4.6. Process via the second step of the c p,ro R . C2 C1 O1 O2 H2 N O C2 C1 O1 H1 O O2 H2 N O OCCH3 O O Figure 4.7. Transition state geometries of c i,ro R and c p,ro R respectively from left to right. Table 4.5. Parameters of the c i,hb TS and c p,hb TS . Parameters c i,hb TS c p,hb TS ≠ (i.cm-1) 330.4 436.2 d(O2-C2) (Å) 1.714 1.920 d(C2-O1) (Å) 2.111 1.934 d(H1-O1) (Å) 1.395 d(C1-O1) (Å) 1.336 1.398 d(C1-C2) (Å) 1.512 1.474 d(O2-H2) (Å) 1.598 1.505 d(H2-N) (Å) 1.074 1.094 (O1-C1-C2) (deg) 95.5 84.6 (C1-C2-H2) (deg) 118.2 114.4 G a V (kJ/mol) 166 90 60 hydrogen bonding of the epoxy and the acid promoter O1-H1 in this case accounts for the lower energy barrier by 76 kJ/mol. 4.4 Discussion Table 4.1 presents all energetic parameters in both the gas phase and the condensed phase. Values in the condensed phase are used for the following discussion. Energy barriers are first examined and they follow the order: c i,hb TS (166 kJ/mol) > i TS (125 kJ/mol) > c1 i,ro TS (122 kJ/mol) > p TS (114 kJ/mol) > c p,hb TS (90 kJ/mol) > c1 p,ro TS (58 kJ/mol). Note that for a two step reaction, the energy barrier of the rate-determining step accounts for the comparison with that of the other one step reactions. This trend is divided into two groups: 1) a group that does not contain the stabilization of a hydrogen bond between an acid promoter and epoxy ( c i,hb TS , i TS , c1 i,ro TS ) and 2) A group that contains this stabilization ( p TS , c p,hb TS , c1 p,ro TS ). The first group obtains an energy barrier higher than the second by 50 kJ/mol on average. The comparison of energy barriers between two corresponding pathways whose transition states differ by a hydrogen bond between an epoxy and an acid promoter yields a similar result. The transition states containing this hydrogen bond always render a lower energy barrier than the others. For instance, a lowering of the energy barrier by 11 kJ/mol is obtained when p TS is compared to i TS , 64 kJ/mol when c1 p,ro TS is compared to c1 i,ro TS , and 76 kJ/mol when c i,hb TS is compared to c p,hb TS (Table 4.1). This leads to speculation that the acid always plays a dual role as a curing agent and as an accelerator by forming a hydrogen bond complex with epoxy to stabilize the transition state. 61 A similar comparison is applied for two corresponding pathways that differ by a tertiary amine molecule. As the tertiary amine participates in the curing as a ring opener, its catalytic property is indicated by the decrease in energy barriers, e.g. i TS > c1 i,ro TS (in group 1) and p TS > c1 p,ro TS (in group 2). However, as the tertiary amine forms a hydrogen bonded complex with an acid curing agent, the result is opposite in the first group, i.e., c i,hb TS obtains a higher energy barrier than i TS by 41 kJ/mol. Meanwhile, hydrogen bond formation between an acid curing agent and a NR3 catalyst is supposed to strengthen the nucleophilicity of the acid curing agent, resulting in a decrease in the energy barrier. Since a carboxylic acid cures the epoxy by heat, both the energy barriers and heat consumption are compared. The potential energy of epoxy-acid in the gas phase is plotted in Figure 4.8. Assume that the reference point is a point at which the epoxy, the acid and the tertiary amine are separated infinitely. In some pathways, the hydrogen bonding complex C2 and/or C3 participates in the curing process and releases heat. This leads to the order of energy consumption as follows: i R (125 kJ/mol) > c i,ro R (122 kJ/mol) > c i,hb R (114 kJ/mol) > p R (73 kJ/mol) > c p,ro R (17 kJ/mol) > c p,hb R (-3 kJ/mol). This trend of energy consumption agrees well with the trend of energy barriers: pathways in which the transition states are stabilized by a hydrogen bond of the epoxy and an acid promoter result in ower energy consumptions than the others by over 91 kJ/mol on average. c p,hb R is the most dominant curing epoxy-acid because it has the smallest heat consumption. Heat consumption of the i R , c i,ro R , and c i,hb R pathways is over one hundred Figure 4.8. Potential energy for epoxy-acid curing in the gas phase. ( 125) C3 (-52) ( 144) C2 (-41) ( 73) ( 41) ( 17) (-45) (19) -93 (-124) (-3) (-56) ( 122) -150 -100 -50 0 50 100 150 Relative energy (kJ/mol) Reaction coordinate E+ COOH (COOH_NR3) +E (E_COOH)+ COOH (E_COOH)+ NR3 (E_COOH)+ (COOH_NR3) E+NR3 ( 63 times higher than the smallest heat consumption of the c p,hb R pathway. Therefore, these pathways might not participate in the curing between the epoxy and the acid and the epoxy-acid curing is likely always promoted by acid curing agents. Hydroxyl products can accelerate the curing by formation of a hydrogen bond with the epoxy in the same way acid curing agents can. Due to steric effects, those products might not combine with an epoxy by a hydrogen bond or they may require a very high energy consumption to react with an epoxy. Thus, these processes can be ignored in the epoxy-acid curing reactions or be supposed to be more difficult than the curing by acid. There exist three pathways in the epoxy-acid curing reaction that are: p R , c p,ro R and c p,hb R . This curing is mimicked in acetic acid solution by calculating the single point energy of the optimized system in the gas phase. The potential energies of these pathways in both the gas and the condensed phases are presented in Figure 4.9. The hydrogen bonded complexes and the transition states are solvated similarly. The transition states are less solvated than the products in each pathway (see Table 4.1), and the potential energy seems litle changed in the acetic acid solution but it might be more changed in other solutions. In the most dominant pathway, c p,hb R , the product is more stable in solution than in the gas phase, although the reaction is still predicted to be endothermic. The comparison is opposite to the order of heat consumption, that is self-promoted < ring opening of tertiary amine < hydrogen bonding catalyzed pathway in both phases. A tertiary amine can participate in two catalytic roles: 1) It attacks epoxy to form a zwitterion and then this zwitterion reacts with an acid, resulting in a lower energy barrier as well as heat consumption by 56 kJ/mol and 2) it forms a hydrogen bonded complex with the acid curing agent to lower the energy barrier by 24 kJ/mol and heat consumption by 76 Figure 4.9. Potential energy for epoxy- acid curing reaction both in the gas phase (solid lines) and in the condensed phase (dashed lines). Energetic values are in the condensed phase. C2 (-32) ( 80) (42) (16) (-67) ( 12) (-110) C3 (-79) (0) (-108) -150 -100 -50 0 50 100 150 Relative energy (kJ/mol) Reaction coordinate p Series6 p,ro Series8 p,hb Series10 65 kJ/mol, compared with the corresponding values in the uncatalyzed pathway ( p R ). Due to the commercial epoxies having greater steric effects compared with carboxylic acids that could lead to the more difficult attachment of a tertiary amine to the epoxy than to an acid to form a hydrogen bonding complex. In addition, the potential energies in Figures 4.8 and 4.9 demonstrate that the second role leads its pathway having the smallest energy consumption. This confirms that in the epoxy-acid curing, the tertiary amine catalysts' main function is to form a hydrogen bond with the acid curing agent, rather than opening the epoxy ring. Although there are no experimental data for the same model to compare with our results, some still can be used as validation. Batog et al.65 reported that curing reactions of 3- cyclohexene-1-carboxylic acid, 2-oxiranylmethyl ester (C10H14O3) and peracetic acid (PAA, CH3CO3H) required activation energies of 47.76 kJ/mol whereas the activation energies of the curing between oxirane, 2-[(3-cyclohexen-1-ylmethoxy)methyl] (C10H16O2) and PAA is 65.01 kJ/mol. The authors also cited the average activation energy for aliphatic-cycloaliphatic epoxy compounds (ACECs) and PAA as being about 50-72 kJ/mol. Rafizadeh80 reported that the activation energy for the curing between DGEBA and methacrylic acid with triphenylphosphine is 80 kJ/mol at 95-1000C. The activation energy for the curing of methyl glycidyl ether and acetic acid catalyzed by trimethylamine in our calculation is 79 kJ/mol. So our calculated value is comparable with other reports within an order of magnitude and consequently can be a reference point for the estimation of other epoxy-acid curing systems. 4.5 Conclusions In this study, possible pathways in the epoxy-acid curing reaction were examined using the quantum chemistry density functional theory. Both gas and condensed phase 66 results suggest that the acid has dual roles as hardener and as self-promoter. In the second role, the acid combines with the epoxy by a hydrogen bond that stabilizes the transition states, leading to a lower barrier energy by 50 kJ/mol and to a decrease of heat consumption by 91 kJ/mol on average. Tertiary amines assume two catalytic roles. The first role is to lower the energy barrier of the reaction by 56 kJ/mol by opening the epoxy ring to form a zwitterion before an acid attaches to an epoxy. The second is to stabilize the transition state by hydrogen bonding with an acid curing agent as well as to strengthen the nucleophilicity of the acid curing agent, leading to decreases in the energy barrier by 24 kJ/mol and the heat of consumption by 76 kJ/mol. Due to its having the smallest heat of consumption as well as the greatest stabilization in c p,hb R , a tertiary amine is supposed to be a promoter of acid curing by forming a hydrogen bond complex. As with the epoxy-amine curing,8 epoxy-acid curing belongs to the SN2-type II process, and the acyclic TS pathway is preferred as compared to the cyclic TS pathway. The mechanism of this curing follows the order: self-promoted < ring opening of tertiary amine catalyzed < hydrogen bonding catalyzed. Without the catalyst, an acid cures epoxy slowly because of a high energy barrier of about 114 kJ/mol. With the assistance of a catalyst, the barrier energy and heat consumption decrease, leading to a faster curing that agrees well with experimental observation. The resulting mechanism of the epoxy-acid curing performs predictive and functional-design capabilities. Its reactants, transition states, and products can be applied to the development of other systems by changing substituents on the epoxy, carboxylic acids, and even catalysts. CHAPTER 5 MECHANISMS OF THE EPOXY-ANHYDRIDE CURING REACTIONS 5.1 Introduction Anhydrides are among the first epoxy curing agents to have been used. Epoxy-anhydride systems exhibit low viscosity, long pot life, low exothermic heats of reaction, and little shrinkage when cured at elevated temperatures. Due to their unique low exothermic heats of reaction, these systems can be used in large scale applications.7 Epoxy-anhydride curing involves two steps, initiation and propagation. In the initiation step, an anhydride attaches to an epoxy ring to form an internal salt. In the propagation step, this internal salt attacks another anhydride to create another internal salt that contains an anionic carboxylate group. This anionic carboxylate group might react with an epoxy. This curing, shown in Scheme 5.1, is considered as an uncatalyzed reaction without hydroxyl groups in the backbone of epoxy resins (Ru ) but has not been mentioned as established mechanism. A well accepted mechanism for the uncatalyzed reactions involves the attachment of hydroxyl groups in the epoxy resins to the anhydride molecules to form an ester linkage and a carboxyl group. The latter then reacts with the epoxy ring to yield a diester and a new secondary hydroxyl group, thus perpetuating the mechanism (Scheme 5.2).7, 81-83 However, such a mechanism cannot apply to a system without an available hydroxyl group in the + CH CH2 O + C O C O O CH CH2 O + R OOC H2 CH C O R C O OOC H2 CH C O R C O OOC H2 CH C COO R C O R C C O C O O R O O OOC H2 CH C COO R C O R C O O OOC H2 CH C COO R C O C R O O CH O CH2 Initiation step: Propagation step: Scheme 5.1. Uncatalyzed reaction without hydroxyl groups (Ru ). C O C O O OH C O C O O OH C O C O O OH H2C CH O C O C O O O OH Half ester Diester + + R R R R Initiation step Propagation step Scheme 5.2. Uncatalyzed reaction with a hydroxyl group attacking an anhydride ( u A,OH R ). 70 epoxy backbone and it is only the mechanism for the uncatalyzed reaction having a hydroxyl group in the epoxy backbone that attacks an anhydride ( u A,OH R ). This means that the uncatalyzed reaction with an attachment of a hydroxyl group in the epoxy backbone to another epoxy ring ( u E,OH R ) has not been examined. In this reaction, the hydroxyl groups attack the epoxy ring to form a hydrogen bonded complex that then reacts with an anhydride similar to the initiation step in Ru (cf. Scheme 5.3). Up to the present time, at least two reactions, Ru and u E,OH R , that might be in the uncatalyzed reaction class are not known.Since uncatalyzed reactions of epoxy resins and anhydrides proceed slowly even at 2000C, the anhydride curing system is often catalyzed by a strong base such as a tertiary amine.7, 81 Similar to uncatalyzed reactions, the tertiary amine catalyzed reactions are divided into classes with or without hydroxyl groups in the epoxy backbone. Only the catalyzed reactions without hydrogen groups have been mentioned for the anhydride curing systems. These reactions differ in that the tertiary amine catalyst attaches either to the epoxy or to the anhydride moieties in the initiation step. In c E R , which was suggested by Okaya and Takana,27 the tertiary amine attacks the epoxide to form a zwitterion which then reacts with an anhydride molecule to form a new zwitterion with an anionic carboxylate group. The carboxylate group then reacts with the epoxide to propagate the reaction (see Scheme 5.4). In c A, R , Fischer26, 84 proposed that the tertiary amine attacks the anhydride molecule first to form a different type of zwitterion that has a carboxylate group. The carboxylate group then attacks the epoxy ring to form a diester and an oxygen anion which can propagate similar to the uncatalyzed mechanism (see Scheme 5.5). 71 OH + O CH CH2 O H O CH2 CH O H O CH CH2 + C O C O O R O H O C H2 HC O C C O O R Initiation step Scheme 5.3. Uncatalyzed reaction with a hydroxyl group attacking an epoxy ( u E,OH R ). H2C CH O + NR3 R3N CH2 HC O-R3N CH2 HC O- + C R O C O O C R C O-O O O C H CH2 NR3 Initiation step Scheme 5.4. Okaya & Takana's mechanism for a catalyzed reaction in which a tertiary amine attacks the epoxy ( c E, R ). 72 + NR3 C R O C O O C R C O-O O NR3 C R C O-O O NR3 H2C CH O + C R C O O O NR3 H2 C C H O-Initiation step Propagation step Scheme 5.5. Fischer's mechanism for a catalyzed reaction in which a tertiary amine attacks the anhydride ( c A R ). Additionally, Sorokin70, 85 suggested a catalytic mechanism wherein a tertiary amine catalyzes the reaction of a secondary alcohol with the anhydride to form a carboxylic acid, which then follows the same mechanism for acid curing (Scheme 5.6). Note that this secondary alcohol is a co-catalyst with the tertiary amine. For the tertiary amine catalyzed reactions with a hydroxyl group on the epoxy chain, these cases can be considered as reactions of two catalysts (tertiary amines and hydroxyl groups) and two moieties, epoxy and anhydride. As the initiation of the curing reactions starts from the attack of a tertiary amine (TA) on the epoxy and the anhydride moieties, we have c TA-E,OH R and c TA-A,OH R respectively in Schemes 5.7 and 5.8. Note that the hydrogen bonded complex of the epoxy-hydroxyl group is assumed to exist in this case. Similarly, in the initiation step of c OH-E,OH R and c OH-A,OH R , the hydroxyl group attacks the epoxy ring and 73 + R'OH C R O C O O C R C OR' O O OH H2C CH O + C R C O O O OR' H2 C HC OH C R C OR' O O OH NR3 NR3 Initiation step Propagation step Scheme 5.6. Sorokin's mechanism of catalyzed epoxy-anhydride curing ( c OH-A,OH R ). H2C CH O + NR3 R3N CH2 HC O-R3N CH2 HC O- + C R O C O O C R C O-O O O C H CH2 NR3 H O H O H O Initiation step Propagation step Scheme 5.7. Catalyzed reaction in which a tertiary amine attacks an epoxy with hydroxyl groups in the system ( c TA-E,OH R ). 74 + NR3 C R O C O O C R C O-O O NR3 C R C O-O O NR3 H2C CH O + C R C O O O NR3 H2 C C H O-H O H O Initiation step Propagation step Scheme 5.8. Catalyzed in which a tertiary amine attacks an anhydride with hydroxyl groups in the system ( c TA-A,OH R ). the anhydride respectively. The former is presented in Scheme 5.9 and the latter is in Scheme 5.6. Epoxy-anhydride curing reactions face the same difficulties as curings by amines, phenols or acids in that they remain incomplete mechanisms. As these incomplete mechanisms are applied to the kinetic model, they might lead to physically meaningless values. In addition, the currently known mechanisms for a particular epoxy-anhydride curing process cannot be used to extrapolate other curings, making it difficult to improve or design products. Thus, it is necessary to develop a systematic mechanism for the epoxy-anhydride system. The objective of this study is to have a molecular-modeling mechanism that performs a predictive function for the anhydride curing systems. All possible pathways of these curing systems were examined in both gas and condensed phase during Density Functional 75 OH + O CH CH2 O H O CH2 CH O H O CH CH2 + C O C O O R O H O C H2 HC O C C O O R NR3 Initiation step Scheme 5.9. Catalyzed reaction in which a hydroxyl group attacks an epoxy with hydroxyl groups in the system ( c OH-E,OH R ). Theory (DFT), and energetic information is used to evaluate competing mechanisms. 5.2 Computational details 5.2.1 Physical models Commercial epoxies and anhydride curing agents are large and complicated structures. Therefore, it is necessary to choose physical models that can fairly represent these commercial reactants but are small enough to be computationally feasible. Methyl glycidyl ether was chosen to be a model for commercial epoxies. Succinic acid anhydride (SAA) was chosen as an anhydride model, and trimethylamine was chosen for the catalysts. Additionally, 2-propanol represents either a secondary alcohol in the epoxy backbone or an alcohol catalyst. 76 5.2.2 Computational models Electronic structure calculations were carried out using the Gaussian 03 program package.42 A hybrid nonlocal density functional theory B3LYP level of theory43 with the 6- 31G(d, p) basis set was used for locating all stationary points, namely reactants, transition states, intermediates, and products. Stationary points were characterized by normal mode analyses. To confirm the transition state for each reaction pathway, the minimum energy paths (MEPs) from the transition state to both the reactants and products were calculated using the Gonzalez-Schlegel steepest descent path method44, 45 in mass weight Cartesian coordinates with the step size of 0.01 (amu)1/2 Bohr. Single point solvation calculations were performed with Gaussian 0977 on the optimized DFT geometries using a polarizable continuum model (PCM)46, 62 with an acetic acid solvent (ɛ = 6.25) to mimic the reactions in solutions. It has been shown that solvation free energies obtained from single point PCM calculations with gas phase geometries from DFT calculations are in reasonable agreement with the values from full geometry optimizations.63, 64 All solvation calculations used the UFF (Universal Force Field) radii model, which places a sphere around each solute atom, with the radii scaled by a factor of 1.1 parameters. 5.3 Results All possible reactions of the epoxy-anhydride curing as mentioned above were examined in both the gas and condensed phases. Because of the limited ability of Gaussian to mimic the anhydride solution, acetic acid was chosen as the solution for the epoxy-anhydride curing reactions. Single point energy calculations at the optimized structures of all stationary points were done using the polarizable continuum model (PCM). The 77 activation energies, approximated to be equal to the corrected energy barriers in the condensed phase, are used to compare with experimental data. Both these activation energies and the zero-point energy corrected barriers G Va in the gas phase are presented in Table 5.1. The model system is divided into four main classes, which are: 1) an uncatalyzed reaction without a hydroxyl group in the system, 2) an uncatalyzed reaction with hydroxyl groups 3) a catalyzed reaction without a hydroxyl group and 4) a catalyzed reaction with hydroxyl groups. Note that in our model, hydroxyl groups represent both hydroxyl groups in the epoxy backbone and the alcohol catalyst. In each class, the reaction whose initiation step requires the lowest barrier energy is considered to be the representative reaction for the class. Table 5.1. Energetic values (kJ/mol) of possible reactions in the anhydride curing systems. (* is noted for propagation steps) Reaction G a V Ea Location 1) Uncatalyzed reaction without a hydroxyl group Ru E + A → [TS]≠ → I u 291 261 Fig 5.1- T 5.2 2) Uncatalyzed reaction with a hydroxyl group u RE,OH E...HOR + A → [TS]≠ → u IE,OH > 240 u RA,OH A + ROH → [TS]≠ → u IE,OH (RCOOH) 130 130 Fig 5.2- T 5.1 * RCOOH + E → [TS]≠ → Diester 114 112 3) Catalyzed reaction without a hydroxyl group c RE E + NR3 → [TS]≠ → u IE,OH 122 * u IE,OH + A → [TS]≠ → u PE,OH No TS c RA A + NR3 + E→ [TS]≠ → c IA 269 262 Fig 5.3- T 5.2 4) Catalyzed reaction with a hydroxyl group c RTA-E,OH E…HOR + NR3 → [TS]≠ → c IA 64 * c A I + A → [TS]≠ → cA P No TS c RTA-A,OH (A + NR3) + E…HOR → [TS]≠ → c ITA-A,OH 216 178 Fig 5.4- T 5.2 c ROH-E,OH E…HOR + A 􀯇􀯋􀰯 􁈱􀛛􁈮 [TS]≠ → c IOH-E,OH 216 178 Fig 5.4- T 5.2 c ROH-A,OH A + ROH 􀯇􀯋􀰯 􁈱􀛛􁈮[TS]≠ → c IOH-A,OH 111 115 Fig 5.5- T 5.1 * c IOH-A,OH + E 􀯇􀯋􀰯 􁈱􀛛􁈮 [TS]≠ → Diester 90 79 78 5.3.1 Uncatalyzed reactions without a hydroxyl group ( Ru ) The transition state for the initiation step (TSu ) is depicted in Figure 5.1. Its parameters and the energy barrier of 291 kJ/mol are shown in Table 5.2. 5.3.2 Uncatalyzed reaction with a hydroxyl group ( u A,OH R and u E,OH R ) Note that the mechanism of the epoxy-anhydride curing in this case can include Ru . In u A,OH R , Scheme 5.2, 2-propanol (ROH), which represents the secondary alcohol in the C1 C2 O1 O2 C3 O3 O4 O Figure 5.1 Transition state of the initiation step in the Ru . Table 5.2. Parameters of the TSu in Figure 5.1, c A TS in Figure 5.3, and c TA-A,OH TS / c OH-E,OH TS in Figure 5.4. Parameters TSu c A TS c TA-A,OH TS ≠ (i cm-1) 376 396 384 d(H1-O1) (Å) 1.636 d(O1-C1) (Å) 1.330 1.381 1.383 d(C1-C2) (Å) 1.511 1.470 1.490 d(O1-C2) (Å) 2.210 2.136 2.022 d(C2-O2) (Å) 1.625 2.157 1.826 d(O2-C3) (Å) 1.356 1.307 1.316 d(O2-C4) (Å) 1.924 2.193 1.217 d(C4-N) (Å) 1.617 1.641 (O1-C1-C2) (deg) 101.91 97.02 89.39 (C1-C2-O2) (deg) 111.76 43.31 117.60 (C3-O2-C4-O4) (deg) -133 92.39 123.78 G a V (kJ/mol) 291 269 216 Ea (kJ/mol) 261 262 178 79 epoxy backbone, attacks SAA to form a half ester. In the transition state of the initiation step, the breaking C2-O1 bond in SAA is lengthened to 2.084 Å, the forming bond of hydrogen H1 of the hydroxyl group and the ether oxygen O1 of SAA is shortened to 1.451 Å, and the forming C2-O2 bond in the ester group is 1.712 Å (Figure 5.2- Table 5.3). The formation of a half ester is revealed by the imaginary vibration of -484 cm-1, and its energy barrier is 130 kJ/mol. This half ester possesses a carboxyl group that exhibits an attachment to an epoxy to form a diester. This step is the same as that for the uncatalyzed reaction in the epoxy-acid curing. That is, it was examined as the self-promoted catalyzed pathway of acid curing systems and its energy barrier is 114 kJ/mol in the model study. In the attachment of a hydroxyl group to an epoxy of u E,OH R , Scheme 5.3, the binding energy of the hydrogen bonding complex is -27 kJ/mol and the length of the hydrogen bond formed between the hydrogen of the hydroxyl group and the epoxy oxygen is 1.94 Å. The transition state of the reaction between this hydrogen bonded complex and an anhydride ( u E,OH TS ) is not converted in the DFT calculation. O1 C2 C1 O O3 O2 H1 Figure 5.2. The transition state of the initiation step in u A,OH R . 80 Table 5.3. Parameters of transition state geometries in the initiation step of u A,OH R and c OH-A,OH R . Parameters u A,OH TS c OH-A,OH TS Catalyst - NR3 ≠ (i cm-1) 484 455 d(O1-C2) (Å) 2.084 2.158 d(H1-O1) (Å) 1.451 1.531 d(H1-O2) (Å) 1.053 1.045 d(O2-C2) (Å) 1.712 1.613 d(H1-N) (Å) 2.609 (C1-O1-C2-O3) (deg) -50.85 -46.03 G a V (kJ/mol) 130 111 Ea (kJ/mol) 130 115 In the epoxy-phenol and epoxy-carboxylic acid curing reactions, the hydrogen bond between the acidic hydrogen and the epoxy oxygen atoms accounts for an average decrease of the energy barriers by 56 and 51 kJ/mol, respectively. Compared to phenol and acid curing agents, hydroxyl groups in the epoxy backbone might be more sterically able to reach the epoxy and form a hydrogen bonded complex. Thus, the hydrogen bond between a hydroxyl group on the epoxy backbone and an epoxy, which is the difference of the transition state in Ru and u E,OH R , might decrease the energy barrier by less than these values. Consequently, the energy barrier of the u E,OH TS might be larger than 240 kJ/mol, compared to a 291 kJ/mol energy barrier of TSu . Comparing u A,OH R and u E,OH R in the initiation step, u A,OH R is preferred because of its lower energy barrier, and thus it dominates the uncatalyzed reactions with a hydrogen group in the system. 81 5.3.3 Catalyzed reactions 5.3.3.1 Catalyzed reactions without a hydroxyl group in the system ( c E R and c A R ) In the initiation step of c E R , Scheme 5.4, the tertiary amine attacks the epoxy to form a zwitterion that was calculated in both the epoxy-phenol and the epoxy-acid curing systems as encountering an energy barrier of 122 kJ/mol in the gas phase. The intermediate zwitterion is unstable in the gas phase but stable in the condensed phase. For instance, in acetic acid solution the energy barrier is 76 kJ/mol and the enthalpy of reaction is 64 kJ/mol at 0 K. The transition state in the propagation step is not found by DFT calculation in the gas phase, however, it might exist in the condensed phase. In the initiation step of c A R , Scheme 5.5, the tertiary amine attacks the anhydride to form an internal salt. In the propagation step, the carboxylate anion reacts with the epoxy group, generating an alkoxide. The alkoxide then further reacts with another anhydride, propagating the cycle by generating another carboxylate which reacts with another epoxy group. The end product is the formation of polyester-type linkages.7 In our calculation, the transition states performing the initiation and propagation steps do not occur separately as shown in Scheme 5.5 but simultaneously. The energy barrier of this reaction is 269 kJ/mol (see Figure 5.3 and Table 5.2). In the curing process, which is catalyzed by a tertiary amine and does not contain a hydroxyl group in the epoxy backbone, the energy barrier of c E R is smaller than that of c A R by 147 kJ/mol. Thus, c E R dominates the curing and, consequently, its energy barrier of 122 kJ/mol should be chosen to be the energy barrier for this curing class. However, since the 82 C1 C2 O1 O2 C4 C3 O4 O3 O R3N Figure 5.3. The transition state of the c A R . product of the initiation step in c E R is unstable and the fact that the transition state of the propagation step could not be found in our calculations, c E R cannot be chosen to be a representative reaction. Thus, the curing prefers to happen via c A R instead of c E R . That means if there is no hydroxyl group in the epoxy backbone, the attachment of the tertiary amine catalyst on the anhydride, as well as attack of this anhydride to the epoxy ring, happen at the same time, and the energy barrier is 269 kJ/mol. 5.3.3.2 Catalyzed reactions with a hydroxyl group in the epoxy backbone Note that the epoxy-alcohol complex is assumed to exist in this case. The initiation step for c TA-E,OH R is the reaction of an epoxy-alcohol complex and a tertiary amine to form an intermediate zwitterion. This zwitterion is unstable in the gas phase but stable in the condensed phase, similar to the zwitterions in c E R . The energy barriers are 62 kJ/mol and 51 kJ/mol, respectively, in the gas and condensed phases. However, the transition state of the propagation step is not found in the DFT calculation. In c TA-A,OH R , the initiation and propagation steps occur simultaneously in our result 83 and require an energy barrier of 216 kJ/mol (see Figure 5.4 and Table 5.2). In c OH-E,OH R , the attachment of an alcohol on the epoxy forms a hydrogen bonded complex and the reaction of the hydrogen bonded complex with an anhydride occurs simultaneously as same as in the c TA-A,OH R , illustrated in Figure 5.4 and Table 5.2. In c OH-A,OH R , the initiation step is a reaction of 2-propanol and SAA that is catalyzed by trimethylamine and requires an energy barrier of 111 kJ/mol. Its transition state is depicted in Figure 5.5 and Table 5.3. The product of this reaction, a half ester, possesses a carboxylic acid group that then cures an epoxy to form a diester in the propagation step. This step is the same as the tertiary amine catalyzed epoxy-acid curing reaction that requires an energy barrier of 79 kJ/mol. In the system involving the hydroxyl group either in the epoxy backbone or from the co-catalyst with a tertiary amine, the c OH-E,OH R is most favorable among c TA-E,OH R , c TA-A,OH R , c OH-E,OH R and c OH-A,OH R because it involves the smallest energy barrier in the initiation step. However, the product of its initiation step is unstable and the transition state of the propagation step has not been found. The c OH-A,OH R process dominates the curing instead of c OH-E,OH R , resulting in the energy barrier of 111 kJ/mol in the gas phase. 5.4 Discussion and validation Table 5.1 summarizes all energetic values of the possible reactions in the anhydride curing systems in both gas and condensed phases. In the uncatalyzed reaction, when the epoxy resins do not have any hydroxyl group in the backbone, the curing of epoxy and anhydride requires 291 kJ/mol ( Ru ) in the gas phase. In case the epoxy resins contain 84 C1 C2 O1 O2 C3 C4 O4 O3 O NR3 H1O Figure 5.4. The transition state of c TA-A,OH R . O1 C2 C1 O O3 O2 N H1 Figure 5.5. The transition state of the c OH-A,OH R . hydroxyl groups, the initiation step of the curing reaction preferably happens via the attack of these hydroxyl groups to open the anhydride ring at the energy barrier of 130 kJ/mol ( u A,OH R ). However, the curing might still be slow because of the difficulty of arranging the hydroxyl group in the epoxy backbone to attach to the anhydride to form a half ester. In the reaction catalyzed by a tertiary amine, when the epoxy resins do not have any hydroxyl group in the backbone, the curing between the epoxy and anhydride is accelerated by the attachment of a tertiary amine catalyst to the anhydride that happens simultaneously with the curing. The energy barrier of this curing is 269 kJ/mol ( c A R ). In case the epoxy resins contain hydroxyl groups or the system is added to an alcohol co-catalyst with tertiary 85 amine, the anhydride is first attacked by the hydroxyl group and the energy barrier lowers to 111 kJ/mol and ( c OH-A,OH R ). The priority curing of the epoxy-anhydride systems follows the order: Ru < c A R < u A,OH R < c OH-A,OH R , which is opposite of their energy barriers in both gas and condensed phases. This indicates that the hydroxyl group might be more crucial than the tertiary amine catalyst for accelerating the curing of the epoxy by anhydride. With or without a tertiary amine catalyst, the energy barrier of the system containing hydroxyl groups in the epoxy backbone decreases the energy barrier of the system without hydroxyl groups by more than half. Meanwhile, the tertiary amine catalytic role decreases the energy barrier by 25 kJ/mol on average (comparing Ru to c A R and comparing u A,OH R to c OH-A,OH R ). As hydroxyl groups originate only from the epoxy backbone, even though the energy barrier is decreased by half, the curing might still consume more energy in bringing about a rearranggament the hydroxyl groups to reach and attack the anhydride. Therefore, the epoxy-anhydride curing might need alcohol which is a co-catalyst of the tertiary amine. In some previous studies, an alcohol together with or without added acid was used as a co-catalyst with a tertiary amine.81, 86-88 In Peyser and Bascom's study of diglycidyl ether bisphenol A (DGEBA) and hexahydrophthalic anhydride (HHPA) catalyzed by N,N‘- dimethylbenzylamine (BDMA), acid and alcohol,86 the activation energy of this curing is 104.60 kJ/mol. The kinetics of the curing reaction for a system of o-cresol formaldehyde epoxy resin/succinic anhydride (SA) and BDMA as a catalyst was investigated wit