A Molecular Simulation Approach to Bond Reorganization in Epoxy Resins: From Curing to Deformation and Fracture

Bottom-to-top modeling of epoxy resins: From atomic models to mesoscale fracture mechanisms

We outline a coarse-grained model of epoxy resins (bisphenol-F-diglycidyl-ether/3,5-diethyltoluene-2,4-diamine) to describe elastic and plastic deformation, cavitation, and fracture at the μm scale. For this, molecular scale simulation data collected from quantum and molecular mechanics studies are coarsened into an effective interaction potential featuring a single type of beads that mimic 100 nm scale building blocks of the material. Our model allows bridging the time-length scale problem toward experimental tensile testing, thus effectively reproducing the deformation and fracture characteristics observed for strain rates of 10-1 to 10-5 s-1. This paves the way to analyzing viscoelastic deformation, plastic behavior, and yielding characteristics by means of "post-atomistic" simulation models that retain the molecular mechanics of the underlying epoxy resin at length scales of 0.1-10 µm.

Block Chemistry for Accurate Modeling of Epoxy Resins

Accurate molecular modeling of the physical and chemical behavior of highly cross-linked epoxy resins at the atomistic scale is important for the design of new property-optimized materials. However, a systematic approach to parametrizing and characterizing these systems in molecular dynamics is missing. We therefore present a unified scheme to derive atomic charges for amine-based epoxy resins, in agreement with the AMBER force field, based on defining reactive fragments─blocks─building the network. The approach is applicable to all stages of curing from pure liquid to gelation to fully cured glass. We utilize this approach to study DGEBA/DDS epoxy systems, incorporating dynamic topology changes into atomistic molecular dynamics simulations of the curing reaction with 127,000 atoms. We study size effects in our simulations and predict the gel point utilizing a rigorous percolation theory to recover accurately the experimental data. Furthermore, we observe excellent agreement between the estimated and the experimentally determined glass transition temperatures as a function of curing rate. Finally, we demonstrate the quality of our model by the prediction of the elastic modulus based on uniaxial tensile tests. The presented scheme paves the way for a broadly consistent approach for modeling and characterizing all amine-based epoxy resins.

Interfaces in reinforced epoxy resins: from molecular scale understanding towards mechanical properties

CONTEXT

We report on atomic level of detail analyses of polymer composite models featuring epoxy resin interfaces to silica, iron oxide, and cellulose layers. Using "reactive" molecular dynamics simulations to explore epoxy network formation, resin hardening is investigated in an unprejudiced manner. This allows the detailed characterization of salt-bridges and hydrogen bonds at the interfaces. Moreover, our sandwich-type composite systems are subjected to tensile testing along the interface normal. To elucidate the role of relaxation processes, we contrast (i) direct dissociation of the epoxy-metal oxide/cellulose contact layer, (ii) constant strain-rate molecular dynamics studies featuring (visco-)elastic deformation and bond rupture of the epoxy resin, and (iii) extrapolated relaxation dynamics mimicking quasi-static conditions. While the fracture mechanism is clearly identified as interface dissociation of the composite constituents, we still find damaging of the nearby polymer phase. The observed plastic deformation and local cavitation are rationalized from the comparably large stress required for the dissociation of salt-bridges, hydrogen bonds, and van der Waals contacts. Indeed, the delamination of the contact layers of epoxy resins with slabs of silica, magnetite, and cellulose call for a maximum stress of 33, 26, and 21 MPa, respectively, as compared to 84 MPa required for bulk epoxy yielding.

METHODS

Molecular dynamics simulations using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) code were augmented by a Monte Carlo-type procedure to probe epoxy bond formation (Macromolecules 53(22): 9698-9705). The underlying interaction models are split into conventional Generalized Amber Force Fields (GAFF) for non-reacting moieties and a recently developed reactive molecular mechanics potential enabling epoxy bond formation and cleavage (ACS Polymers Au 1(3): 165-174).

Study of the cross-linking density effect on the mechanical properties of h-BNNS reinforced epoxy nanocomposite part-1: a molecular dynamics simulation

Diglycidyl ether bisphenol A (DGEBA) is a thermosetting polymer with excellent cross-linking properties and an irreversible network structure that forms polymer chains when chemically reacting with hardeners such as amines and anhydrides. The resulting compound has exceptional thermomechanical and structural properties. The properties of the final compound are heavily influenced by cross-linking and network structure. In the present research, molecular dynamics (MD) simulations were used to investigate the mechanical properties of chemically cross-linked DGEBA and the curing agent diethyl toluene diamine (DETDA). The MD simulation was used to perform the cross-linking, and a comprehensive study on the mechanical properties of DGEBA/DETDA was conducted. To investigate the mechanical properties, the developed model was reinforced with hexagonal boron nitride nanosheet (h-BNNS) at various weight percentages (wt.%). The results showed that the density of the neat DGEBA/DETDA increases with increasing cross-linking. It is 1.13 g/cm³ at 90% cross-linking. Almost all cross-linking densities of neat DGEBA/DETDA had higher mechanical properties. At room temperature (300 K), the elastic modulus increases from 2.58 to 2.98 GPa for cross-linking densities of 80% (EP80), 85% (EP85), and 90% (EP90). The elastic modulus of EP85 and EP90 is 3% lower and 9% higher than the experimental value (2.71 GPa), respectively. In almost all cross-linking densities, the elastic modulus of the h-BNNS reinforced DGEBA/DETDA increases with the weight percentage (wt%) of the h-BNNS. Shear and bulk modulus increase when h-BNNS is added to the DGEBA/DETDA matrix.

A Molecular Dynamics Simulation for Thermal Activation Process in Covalent Bond Dissociation of a Crosslinked Thermosetting Polymer

A novel algorithm for covalent bond dissociation is developed to accurately predict fracture behavior of thermosetting polymers via molecular dynamics simulation. This algorithm is based on the Monte Carlo method that considers the difference in local strain and bond-dissociation energies to reproduce a thermally activated process in a covalent bond dissociation. This study demonstrates the effectiveness of this algorithm in predicting the stress-strain relationship of fully crosslinked thermosetting polymers under uniaxial tensile conditions. Our results indicate that the bond-dissociation energy plays an important role in reproducing the brittle fracture behavior of a thermosetting polymer by affecting the number of covalent bonds that are dissociated simultaneously.

Molecular Dynamic Simulations and Experiments Study on the Mechanical Properties of HTPE/PEG Interpenetrating Polymer Network (IPN) Binders

The mechanical properties of HTPE/PEG interpenetrating polymer network (IPN) binders were systemically studied with molecular dynamics (MDs) simulations and experiments. In this study, an algorithm was used to construct the crosslinking interpenetrating polymer network models and then the mechanical behaviors of Hydroxyl-terminated polyethylene glycol-tetrahydrofuran co-polyether/poly ethylene glycol (HTPE/PEG) IPN models were analyzed at a molecular scale. Firstly, glass transition temperatures (T_g), mean square displacement (MSD) and mechanical properties of IPN crosslinked model simulations showed that better thermomechanical parameters appeared at low temperatures, which were in good agreement with the experimental methods, including dynamic mechanical analysis and uniaxial tensile. Then bond-length distribution was performed to verify the crosslinked structures between prepolymers and curing agents. FTIR-ATR spectra analysis of four IPN binder specimens also gave a convictive result to the special interpenetrating polymer network of polyether polyurethane binders. Cohesive energy density and friction-free volume explained how the micro-structures of IPN crosslinked models and the force of inter-molecule chains affected the mechanical behaviors of the HTPE/PEG polyurethane matrix. Lastly, the morphology of IPN binder specimen tensile fracture indicated the mechanism at different temperatures. These studies were helpful in understanding the mechanical properties of HTPE/PEG interpenetrating polymer network binders and provide molecular insight into mechanisms of mechanical behaviors, which would guide the property improvement of HTPE propellant.

Molecular Dynamic Simulations and Experiments Study on the Mechanical Properties of HTPE Binders

The mechanical properties of HTPE binders have been systemically studied through combining the microstructure molecular simulations with macroscopic experiments. In this study, the crosslinking structures of HTPE binders were established by a computational procedure. Based on the optimized crosslinking models, the mechanical properties and the glass transition temperatures (T_g) of HTPE/N-100, HTPE/HDI, HTPE/TDI, and HTPE/IPDI binder systems were simulated; specifically, the T_g were 245.758 K, 244.573 K, 254.877 K, and 240.588 K, respectively. Then the bond-length distributions, conformation properties, cohesive energy densities, and fraction free volume were investigated to analyze how the microstructures of the crosslinking models influenced the mechanical properties of HTPE binders. Simultaneously, FTIR-ATR spectra analysis of HTPE binders proved that the special peaks, such as -NH and -NCO, could be seen in the crosslinking polyurethane structures synthesized between prepolymers and curing agents. The dynamic mechanical analysis was carried out, and it found that the T_g of HTPE/N-100, HTPE/HDI, HTPE/TDI, and HTPE/IPDI binder systems were -68.18 °C, -68.63 °C, -65.67 °C, and -68.66 °C, respectively. In addition, the uniaxial tension verified that both the ultimate stress and Young's modulus of HTPE binder systems declined with the rising temperatures, while the strains at break presented a fluctuant variation. When it was closer to glass temperatures, especially -40 °C, the mechanical properties of HTPE binders were more prominent. The morphology of the fractured surface revealed that the failure modes of HTPE binders were mainly intermolecular slipping and molecular chain breakage. In a word, the experimental results were prospectively satisfied using the simulations, which confirmed the accuracy of the crosslinking models between prepolymers and curing agents. This study could provide a scientific option for the HTPE binder systems and guide the design of polyurethanes for composite solid propellant applications.

Accurate predictions of thermoset resin glass transition temperatures from all-atom molecular dynamics simulation

To enable the design and development of the next generation of high-performance composite materials, there is a need to establish improved computational simulation protocols for accurate and efficient prediction of physical, mechanical, and thermal properties of thermoset resins. This is especially true for the prediction of glass transition temperature (T_g), as there are many discrepancies in the literature regarding simulation protocols and the use of cooling rate correction factors for predicting values using molecular dynamics (MD) simulation. The objectives of this study are to demonstrate accurate prediction the T_g with MD without the use of cooling rate correction factors and to establish the influence of simulated conformational state and heating/cooling cycles on physical, mechanical, and thermal properties predicted with MD. The experimentally-validated MD results indicate that accurate predictions of T_g, elastic modulus, strength, and coefficient of thermal expansion are highly reliant upon establishing MD models with mass densities that match experiment within 2%. The results also indicate the cooling rate correction factors, model building within different conformational states, and the choice of heating/cooling simulation runs do not provide statistically significant differences in the accurate prediction of T_g values, given the typical scatter observed in MD predictions of amorphous polymer properties.

Molecular Simulations and Network Analyses of Surface/Interface Effects in Epoxy Resins: How Bonding Adapts to Boundary Conditions

In this study, we unravel the atomic structure of a covalent resin near boundaries such as surfaces and composite constituents. For this, a molecular simulation analysis of epoxy resin hardening under various boundary conditions was performed. On the atomic level of detail, molecular dynamics simulations were employed to study crosslinking reactions and self-organization of the polymer network within nm scale slab models. The resulting structures were then coarsened into a graph theoretical description for connectivity analysis of the nodes and combined with characterization of the node-to-node vector orientation. On this basis, we show that the local bonding of epoxy resins near interfaces tends to avoid under-coordinated linker sites. For both epoxy–vacuum surface models and epoxy–silica/epoxy cellulose interfaces, we find almost fully cured polymer networks. These feature a local increase in network linking lateral to the surface/interface, rather than the dangling of unreacted epoxy groups. Consequently, interface tension is low (as compared to the work of separating bulk epoxy), and the reactivity of the resin surface appears negligible.

Multi-Scale Modelling of Plastic Deformation, Damage and Relaxation in Epoxy Resins

Epoxy resin plasticity and damage was studied from molecular dynamic simulations and interpreted by the help of constitutive modelling. For the latter, we suggested a physically motivated approach that aims at interpolating two well-defined limiting cases; namely, pulling at the vanishing strain rate and very rapid deformation; here, taken as 50% of the speed of sound of the material. In turn, to consider 0.1–10-m/s-scale deformation rates, we employed a simple relaxation model featuring exponential stress decay with a relaxation time of 1.5 ns. As benchmarks, deformation and strain reversal runs were performed by molecular dynamic simulations using two different strain rates. Our analyses show the importance of molecular rearrangements within the epoxy network loops for rationalizing the strain-rate dependence of plasticity and residual stress upon strain reversal. To this end, our constitutive model reasonably reproduced experimental data of elastic and visco-elastic epoxy deformation, along with the maximum stress experienced before fracturing. Moreover, we show the importance of introducing damage elements for mimicking the mechanical behavior of epoxy resins.

A study of the mechanical properties of the NEPE binders by molecular dynamic simulations and experiments

In this study, the crosslinking structures of nitrate ester plasticized polyether (NEPE) binders were constructed by a computational procedure. Based on the final crosslinking models, the glass transition temperatures, mechanical properties, and thermal expansion coefficients of polyethylene glycol400/multi-functional isocyanate (PEG400/N-100), polyethylene glycol400/toluene diisocyanate (PEG400/HDI), polyethylene glycol400/hexamethylene diisocyanate (PEG400/TDI) and polyethylene glycol400/isophorone diisocyanate (PEG400/IPDI) models were simulated by molecular dynamics, and could be confirmed by experiments. Then the bond-length distributions, conformation properties and cohesive energy densities were used to analyze in detail how the different cured structures influenced the mechanical and thermal properties. Furthermore, the radial distribution function, mean square radius of gyration, volume shrinkage and fraction free volume were calculated, which could directly explain the relationships between the intermolecular chains and macroscopical properties of the NEPE binders. Lastly, PEG400/N-100 and PEG400/HDI systems were chosen for the experiments. The dynamic mechanical analysis results explained that PEG400-HDI showed better flexibility and its T_g value was 45 °C lower than that of PEG400-N100. The mechanical properties illustrated that the ultimate tensile strength and Young's modulus of PEG400/N-100 were both to an extent higher than that of PEG400/HDI in the temperature range of −40 °C to 50 °C, according to the results provided by a universal tensile test machine. The experimental results were in good agreement with the simulation analysis. This work can help us to have an efficient comprehension on the crosslinking structures and micro-property relationships of the NEPE binders and act as a guidance for designing applicable polyurethanes in propellant applications.

The mechanical properties of NEPE binders were performed well with combining simulations and experiments.