Molecular Modeling of Cross-Linked Polymers with Complex Cure Pathways: A Case Study of Bismaleimide Resins

Optimal Molecular Dynamics System Size for Increased Precision and Efficiency for Epoxy Materials

Molecular dynamics (MD) simulation is an important tool for predicting thermo-mechanical properties of polymer resins at the nanometer length scale, which is particularly important for efficient computationally driven design of advanced composite materials and structures. Because of the statistical nature of modeling amorphous materials on the nanometer length scale, multiple MD models (replicates) are typically built and simulated for statistical sampling of predicted properties. Larger replicates generally provide higher precision in the predictions but result in higher simulation times. Unfortunately, there is insufficient information in the literature to establish guidelines between MD model size and the resulting precision in predicted thermo-mechanical properties. The objective of this study was to determine the optimal MD model size of epoxy resin to balance efficiency and precision. The results show that an MD model size of 15,000 atoms provides for the fastest simulations without sacrificing precision in the prediction of mass density, elastic properties, strength, and thermal properties of epoxy. The results of this study are important for efficient computational process modeling and integrated computational materials engineering (ICME) for the design of next-generation composite materials for demanding applications.

Preparation and Characterization of Bismaleimide-Resin-Based Composite Materials

This study utilized bismaleimide (BMI) resin, reinforced with introduced ether bonds, as a binding matrix, in combination with silicon carbide (SiC), for the fabrication of composite materials. A thorough investigation was conducted to assess the influence of diverse processing parameters on the mechanical properties and high-temperature thermo-oxidative stability of these composites. Experimental results indicate a notable improvement in the mechanical properties of the composites upon the incorporation of ether bonds, in contrast to their unmodified counterparts. The variation in performance among composites with different ratios and molding densities is apparent. Within a certain range, an increase in resin content and molding density is correlated with improved bending strength in the composites. With a resin content of 27.5 vol% and a molding density of 2.31 g/cm3, the composite achieved a maximum flexural strength of 109.52 MPa, representing a 24% increase compared to its pre-modification state. Even after exposure to high-temperature heat treatment, the composites displayed commendable mechanical properties compared to their pre-ether bond modification counterparts, maintaining 74.5% of the strength of the untreated composites at 300 °C. The scanning electron microscopy (SEM) microstructures of composite materials correlate remarkably well with their mechanical properties.

Multiscale Process Modeling of Semicrystalline PEEK for Tailored Thermomechanical Properties

Polyether ether ketone (PEEK) is a semicrystalline thermoplastic that is used in high-performance composites for a wide range of applications. Because the crystalline phase has a higher mass density than that of the amorphous phase, the evolution of the crystalline phase during high-temperature annealing processing steps results in the formation of residual stresses and laminate deformations, which can adversely affect the composite laminate performance. Multiscale process modeling, utilizing molecular dynamics, micromechanics, and phenomenological PEEK crystal kinetic laws, is used to predict the evolution of volumetric shrinkage, elastic properties, and thermal properties, as a function of crystalline phase evolution, and thus annealing time, in the 306-328 °C temperature range. The results indicate that lower annealing temperatures in this range result in a faster evolution of thermomechanical properties and shrinkage toward the pure crystalline values. Therefore, from the perspective of composite processing, it may be more advantageous to choose the higher annealing rates in this range to slow the volumetric shrinkage and allow PEEK stress relaxation mechanisms more time to relax internal residual stresses in PEEK composite laminates and structures.

Efficient exploration of compositional space for high-performance copolymers via Bayesian optimization

The traditional approach employed in copolymer compositional design, which relies on trial-and-error, faces low-efficiency and high-cost obstacles when attempting to simultaneously improve multiple conflicting properties. For example, designing co-cured polycyanurates that exhibit both moisture and thermal resistance, along with high modulus, is a long-term challenge because of the intrinsic trade-offs between these properties. In this work, to surmount these barriers, we developed a Bayesian optimization (BO)-guided method to expedite the discovery of co-cured polycyanurates exhibiting low water uptake, coupled with higher glass transition temperature and Young's modulus. By virtue of the knowledge of molecular simulations, benchmarking studies were carried out to develop an effective BO-guided method. Propelled by the developed method, several copolymers with improved comprehensive properties were obtained experimentally in a few iterations. This work provides guidance for efficiently designing other high-performance copolymers.

Simple and convenient mapping of molecular dynamics mechanical property predictions of bisphenol-F epoxy for strain rate, temperature, and degree of cure

It is well-known that all-atom molecular dynamics (MD) predictions of mechanical properties of thermoset resins suffer from multiple accuracy issues associated with their viscoelastic nature. The nanosecond simulation times of MD simulations do not allow for the direct simulation of the molecular conformational relaxations that occur under laboratory time scales. This adversely affects the prediction of mechanical properties at realistic strain rates, intermediate degrees of cure, and elevated temperatures. While some recent studies have utilized a time-temperature superposition approach to relate MD predictions to expected laboratory observations, such an approach becomes prohibitively difficult when simulating thermosets with a combination of strain rates, intermediate degrees of cure, and temperatures. In this study, a phenomenological approach is developed to map the predictions of Young's modulus and Poisson's ratio for a DGEBF/DETDA epoxy system to the corresponding laboratory-based properties for intermediate degrees of cure and temperatures above and below the glass transition temperature. The approach uses characterization data from dynamical mechanical analysis temperature sweep experiments. The mathematical formulation and experimental characterization of the mapping is described, and the resulting mapping of computationally-predicted to experimentally-observed elastic properties for various degrees of cure and temperatures are demonstrated and validated. This mapping is particularly important to mitigate the strain-rate effect associated with MD predictions, as well as to accurately predict mechanical properties at elevated temperatures and intermediate degrees of cure to facilitate accurate and efficient composite material process modeling.

PolySMart: a general coarse-grained molecular dynamics polymerization scheme

The development of simulation methods to study the structure and dynamics of a macroscopically sized piece of polymer material is important as such methods can elucidate structure-property relationships. Several methods have been reported to construct initial structures for homo- and co-polymers; however, most of them are only useful for short linear polymers since one needs to pack and equilibrate the far-from-equilibrium initial structures, which is a tedious task for long or hyperbranched polymers and unfeasible for polymer networks. In this method article, we present PolySMart, i.e., an open-source python package, which can effectively produce fully equilibrated homo- and hetero-polymer melts and solutions with no limitation on the polymer topology and size, at a coarse-grained resolution and through a bottom-up approach. This python package is also capable of exploring the polymerization kinetics through its reactive scheme in realistic conditions so that it can model the multiple co-occurring polymerization reactions (with different reaction rates) as well as consecutive polymerizations under stoichiometric and non-stoichiometric conditions. Thus, the equilibrated polymer models are generated through correct polymerization kinetics. A benchmark and verification of the performance of the program for several realistic cases, i.e., for homo-polymers, co-polymers, and crosslinked networks, is given. We further discuss the capability of the program to contribute to the discovery and design of new polymer materials.

Automatic Multiscale Method of Building up a Cross-linked Polymer Reaction System: Bridging SMILES to the Multiscale Molecular Dynamics Simulation

An automatic method is introduced to generate the initial configuration and input file from SMILES for multiscale molecular dynamics (MD) simulation of cross-linked polymer reaction systems. Inputs are a modified version of SMILES of all the components and conditions of coarse-grained (CG) and all-atom (AA) simulations. The overall process comprises the following steps: (1) Modified SMILES inputs of all the components are converted to 3-dimensional coordinates of molecular structures. (2) Molecular structures are mapped to the coarse-grained scale, followed by a CG reaction simulation. (3) CG beads are backmapped to the atomic scale after the CG reaction. (4) An AA productive run is finally performed to analyze volume shrinkage, glass transition, and atomic detail of network structure. The method is applied to two common epoxy resin reactions, that is, the cross-linking process of DGEVA (diglycidyl ether of vanillyl alcohol) and DHAVA (dihydroxyaminopropane of vanillyl alcohol) and that of DGEBA (diglycidyl ether of bisphenol A) and DETA (diethylenetriamine). These components form network structures after the CG cross-linking reaction and are then backmapped to calculate properties in the atomic scale. The result demonstrates that the method can accurately predict volume shrinkage, glass transition, and all-atom structure of cross-linked polymers. The method bridges from SMILES to MD simulation trajectories in an automatic way, which shortens the time of building up cross-linked polymer reaction model and suitable for high-throughput computations.

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 of Thermomechanical Properties of Epoxy-Amine Resins

All-atom molecular dynamics (MD) simulations were performed with the CHARMM force field to characterize various epoxy resins, such as aliphatic and bisphenol-based resins. A multistep cross-linking algorithm was established, and key properties such as density, glass temperature, and elastic modulus were calculated. A quantitative comparison was made and was proven to be in good agreement with experimental data, with average absolute deviations between experiments and molecular simulation comprised between 2% and 12%. Additional findings on structure-property relationships were highlighted such as the effect of the cross-linking rate and oligomerization of the resin.

Curing kinetics, thermal and erosive wear characteristics of bismaleimide blends modified by polyaryletherketone

The work aimed to study the effect of thermoplastic polyaryletherketone (PAEK) on the curing kinetics, thermal stability and erosive wear performances of bismaleimide (BMI) resin blends. Toughened bismaleimide blends were fabricated using the allyl compound modified bismaleimide resin prepolymer as matrix and PAEK as a toughening agent by blending method. The modified PAEK/BMI blends were characterized and analyzed using the fourier transform infrared (FTIR), differential scanning calorimetry (DSC), thermogravimetric analysis (TGA), the swirling water jet erosive wear apparatus, scanning electron microscope (SEM) and three-dimensional surface profilometer. No obvious glass transition was observed for PAEK modified BMI blends in the temperature range of 50–350°C. In addition, the char yields ( Yc) and the heat-resistance index ( THRI) of the PAEK/BMI blends were affected by PAEK addition. The kinetic parameters, such as the activation energy and the pre-exponential factor of the PAEK/BMI blends were also higher than that of unmodified BMI blends, indicating that the incorporation of PAEK could promote the curing reaction of the epoxy resin without changing the curing mechanism. The erosive wear rate increased with the addition of PAEK especially when the mass fraction of PAEK was 10 parts per hundred of resins ( phr.). These results suggested that the thermal stability of the PAEK/BMI blends was significantly enhanced while the erosive wear resistance decreased by introducing the PAEK.

Uncovering the Mechanism of Size Effect on the Thermomechanical Properties of Highly Cross-Linked Epoxy Resins

Epoxy resins are widely used as matrix resins, especially for carbon-fiber-reinforced plastic, due to their outstanding physical and mechanical properties. To date, most research into cross-linking processes using simulation has considered only a distance-based criterion to judge the probability of reaction. In this work, a new algorithm was developed for use with the large-scale atomic/molecular massively parallel simulator (LAMMPS) simulation package to study the cross-linking process; this new approach combines both a distance-based criterion and several kinetic criteria to identify whether the reaction has occurred. Using this simulation framework, we investigated the effect of model size on predicted thermomechanical properties of three different structural systems: diglycidyl ether of bisphenol A (DGEBA)/4,4'-diaminodiphenyl sulfone (4,4'-DDS), DGEBA/diethylenetriamine (DETA), and tetraglycidyl diaminodiphenylmethane (TGDDM)/4,4'-DDS. Derived values of gel point, volume shrinkage, and cross-linked resin density were found to be insensitive to model size in these three systems. Other thermomechanical properties, i.e., glass-transition temperature, Young's modulus, and yield stress, were found to reach stable values for systems larger than ∼40 000 atoms for both DGEBA/4,4'-DDS and DGEBA/DETA. However, these same properties modeled for TGDDM/4,4'-DDS did not stabilize until the system size reached 50 000 atoms. Our results provide general guidelines for simulation system size and procedures to more accurately predict the thermomechanical properties of epoxy resins.

Computational Modeling of Hybrid Carbon Fiber/Epoxy Composites Reinforced with Functionalized and Non-Functionalized Graphene Nanoplatelets

The mechanical properties of aerospace carbon fiber/graphene nanoplatelet/epoxy hybrid composites reinforced with pristine graphene nanoplatelets (GNP), highly concentrated graphene oxide (GO), and Functionalized Graphene Oxide (FGO) are investigated in this study. By utilizing molecular dynamics data from the literature, the bulk-level mechanical properties of hybrid composites are predicted using micromechanics techniques for different graphene nanoplatelet types, nanoplatelet volume fractions, nanoplatelet aspect ratios, carbon fiber volume fractions, and laminate lay-ups (unidirectional, cross-ply, and angle-ply). For the unidirectional hybrid composites, the results indicate that the shear and transverse properties are significantly affected by the nanoplatelet type, loading and aspect ratio. For the cross-ply and angle ply hybrid laminates, the effect of the nanoplate’s parameters on the mechanical properties is minimal when using volume fractions and aspect ratios that are typically used experimentally. The results of this study can be used in the design of hybrid composites to tailor specific laminate properties by adjusting nanoplatelet parameters.

Prediction of the Interfacial Properties of High-Performance Polymers and Flattened CNT-Reinforced Composites Using Molecular Dynamics

The next generation of ultrahigh-strength composites for structural components of vehicles for manned missions to deep space will likely incorporate flattened carbon nanotubes (flCNTs). With a wide range of high-performance polymers to choose from as the matrix component, efficient and accurate computational modeling can be used to efficiently downselect compatible resins and provide critical physical insight into the flCNT/polymer interface. In this study, molecular dynamics simulation is used to predict the interaction energy, frictional sliding resistance, and mechanical binding of flCNT/polymer interfaces for epoxy, bismaleimide (BMI), and benzoxazine high-performance resins. The results indicate that BMI has a stronger interfacial interaction and transverse tension binding with flCNT interfaces, while benzoxazine demonstrates the strongest levels of interfacial friction resistance.

Effect of Sizing Agents on Surface Properties of Carbon Fibers and Interfacial Adhesion of Carbon Fiber/Bismaleimide Composites

Physicochemical, surface, and mechanical properties of three batches of T800 grade carbon fibers (CFs) treated with three kinds of sizing agents and Toray T800H CFs were characterized to study the effect of sizing agents on surface properties. Scanning electron microscopy for morphology, atomic force microscopy calculations, and results for the content of sizing agents showed that sizing agent B improved the surface roughness and CFs with high content of sizing agent always presented small surface roughness in a certain content range 1.2-1.6%. Surface energy of CFs was calculated by Young's contact angle using the test results with water and glycol, and contact angles with LY-1 and modified-AC531 were also acquired. The results proved that CFs of sizing agent group B had the highest average surface energy and the lowest average contact angles with both LY-1 and modified-AC531. From both single-filament and tensile strength test results, the average strength of CFs of sizing agent group B was found to be the lowest, which indicated that sizing agent B had an influence on tensile strength decrease of T800 grade CFs. Comparing the results of interfacial shear strength both in a natural dry state and after hygrothermal treatment, high surface energy was found to be the key element to obtain high interfacial adhesion between T800 grade CFs and bismaleimide, and high surface roughness and low contact angle also played important roles. Among sizing agents A, B, and C, A had an effect on the interfacial shear strength decrease of CFs in the natural dry state, while C had that after hygrothermal treatment.

Molecular-Level Investigation of Cycloaliphatic Epoxidised Ionic Liquids as a New Generation of Monomers for Versatile Poly(Ionic Liquids)

Recently, a new generation of polymerised ionic liquids with high thermal stability and good mechanical performances has been designed through novel and versatile cycloaliphatic epoxy-functionalised ionic liquids (CEILs). From these first promising results and unexplored chemical structures in terms of final properties of the PILs, a computational approach based on molecular dynamics simulations has been developed to generate polymer models and predict the thermo–mechanical properties (e.g., glass transition temperature and Young’s modulus) of experimentally investigated CEILs for producing multi-functional polymer materials. Here, a completely reproducible and reliable computational protocol is provided to design, test and tune poly(ionic liquids) based on epoxidised ionic liquid monomers for future multi-functional thermoset polymers.

Entropy-driven segregation in epoxy-amine systems at a copper interface

The composition of an epoxy resin at the interface with the adherend is usually different from that in the bulk due to the enrichment of a specific constituent, a characteristic called interfacial segregation. For better adhesion, it should be precisely understood how epoxy and amine molecules exist on the adherend surface and react with each other to form a three-dimensional network. In this study, the entropic factor of the segregation in a mixture of epoxy and amine at the copper interface before and after the curing reaction is discussed on the basis of a full-atomistic molecular dynamics (MD) simulation. Smaller molecules were preferentially segregated at the interface regardless of the epoxy and amine, and this segregation remained after the curing process. No segregation occurred at the interface for a combination composed of epoxy and amine molecules with a similar size. These findings make it clear that the size disparity between constituents affects the interfacial segregation via the packing and/or translational entropy. The curing reaction was slower near the interface than in the bulk, and a large amount of unreacted molecules remained there. Finally, the effect of molecular shape was also examined. Linear molecules were more likely to segregate than round-shaped ones even though they were similar in volume. We believe that these findings, which are difficult to obtain experimentally, contribute to the understanding of the interfacial adhesion phenomena on a molecular scale.

On the Nature of Epoxy Resin Post-Curing

Post-curing is intended to improve strength, elevate glass transition, and reduce residual stress and outgassing in thermosets. Also, experiments indicate post-curing temperatures lead to ether crosslinks and backbone dehydration. These results informed molecular dynamics methods to represent them and compare the resulting thermomechanical effects. Diglycidyl ether of bisphenol A (DGEBA)-diamino diphenyl sulfone (DDS) systems were examined. Independent variables were resin length, stoichiometry, and reaction type (i.e., amine addition, etherification, and dehydration). Etherification affected excess epoxide systems most. These were strengthened and became strain hardening. Systems which were both etherified and dehydrated were most consistent with results of post-curing experiments. Dehydration stiffened and strengthened systems with the longer resin molecules due to their intermediate hydroxyl groups for crosslinking. Changes in the concavity of functions fit to the specific volume versus temperature were used to detect thermal transitions. Etherification generally increased transition temperatures. Dehydration resulted in more transitions.

Curing behavior, thermal, and mechanical properties of N,N′-(4,4′-diphenylmethane)bismaleimide/2,2′-diallylbisphenol A/3-allyl-5,5-dimethylhydantoin resin system

The 3-allyl-5,5-dimethylhydantoin (ADMH) was synthesized and characterized by Fourier transform infrared spectroscopy, 1H-nuclear magnetic resonance (NMR), and 13C-NMR spectroscopy. Then, the ADMH was used to modify the N, N′-(4,4′-diphenylmethane)bismaleimide (BDM)/2,2′-diallylbisphenol A (DABPA) resin to obtain the BDM/DABPA/ADMH resin system (BDA). The curing behavior was investigated by non-isothermal differential scanning calorimetry and the activation energy ([Formula: see text]) was obtained by Kissinger and Ozawa models. The thermomechanical property was measured by dynamic mechanical analysis. Analysis of the data revealed the complexity of the curing reaction, which was firstly dominated by the Ene reaction of allyl and C=C double bond at low and medium temperatures and was further governed by the Diels–Alder reaction and the anionic imide oligomerization occurred at high temperatures. The results demonstrated that 1-BDA had the best thermal and mechanical properties exhibiting excellent modification effect of ADMH.

MARTINI-based simulation method for step-growth polymerization and its analysis by size exclusion characterization: a case study of cross-linked polyurethane

Simulation studies of step-growth polymerization, e.g., polymerization of polyurethane systems, hold great promise due to having complete control over the reaction conditions and being able to perform an in-depth analysis of network structures. In this work, we developed a (completely automated) simulation method based on a coarse-grained (CG) methodology, i.e., the MARTINI model, to study the cross-linking reaction of a diol, a tri-isocyanate molecule and one-hydroxyl functional molecule to form a polyurethane network without and with dangling chains. This method is capable of simulating the cross-linking reactions not only up to very high conversions, but also under rather complicated reaction conditions, i.e., a non-stoichiometric ratio of the reactants, solvent evaporation and multi-step addition of the reactants. We introduced a novel network analysis, similar to size-exclusion chromatography based on graph theory, to study the growth of the network during the polymerization process. By combining the reaction simulations with these analysis methods, a set of correlations between the reaction conditions, reaction mechanisms and final network structure and properties is revealed. For instance, a two-step addition of materials for the reaction, i.e., first the dangling chain to the tri-isocyanate and then the diol, leads to the highest integrated network structure. We observed that different reaction conditions lead to different glass transition temperatures (T_g) of the network due to the distinct differences in the final network structures obtained. For example, by addition of dangling chains to the network, the T_g decreases as compared to the network without dangling chains, as also is commonly observed experimentally.

Model of the DGEBA-EDA Epoxy Polymer: Experiments and Simulation Using Classical Molecular Dynamics

Polyepoxy samples are synthesized from diglycidylether of bisphenol A (DGEBA) and ethylene diamine (EDA) monomers at a stoichiometric ratio of 2 DGEBA : 1 EDA in model conditions in order to promote a high degree of polymerization and a low density of defects and to try to approach the ideal models obtained by simulation. A slow polymerization (>24 h at ambient temperature) and a postcuring achieved in an inert atmosphere lead to a conversion degree of 92±2% and a midpoint glass transition temperature of 391±1 K. In parallel, a model is created with a multistep cross-linking procedure. In this work, all-atom molecular dynamics (MD) simulations are performed with LAMMPS and the GAFF 1.8 force field. In the initial liquid mixture of reactants (600 molecules), proper mixing is demonstrated by the calculation of the partial radial distribution functions (RDF), which show a minimum intermolecular distance of 2.8 Å and similar distributions for EDA-EDA, DGEBA-DGEBA, and DGEBA-EDA molecules in the simulation boxes. Then, in alternation with MD equilibrations, cross-linking is performed on frozen configurations by creating covalent bonds between reactive pairs within a reaction radius of 3 Å. The resulting boxes show conversion rates of 90-93% and densities close to the experimental value. Finally, a cooling ramp from 700 K to 25 K is applied in order to monitor the specific volume and the coefficient of volumetric thermal expansion (CVTE) of the polymer and to derive the glass transition temperature. Experimental thermomechanical analyses (TMA) compares well with simulations for both the specific volume and the CVTE evolutions with temperature. Whereas the uncertainty remains high with the fitting procedure used, we calculate a glass transition temperature of 390±8 K which compares very well with the experimental values (391±1 K from DSC and 380 K from TMA).

Thermal Stability of Allyl-Functional Phthalonitriles-Containing Benzoxazine/Bismaleimide Copolymers and Their Improved Mechanical Properties

Copolymerization is the typical method to obtain the high-performance resin composites, due to its universality and regulation performance. It can be employed among various resin matrices with active groups to obtain the desired structures, and subsequently, the outstanding properties. In this work, the copolymerization between the allyl-functional phthalonitrile-containing benzoxazine resin (DABA-Ph) and 4,4'-bis(Maleimidodiphenyl)methane (BMI) were monitored. The interactions among the active groups including allyl moieties, maleimide, benzoxazine rings and nitrile groups were investigated. Differential scanning calorimetry (DSC) and dynamic rheological analysis (DRA) were used to study the curing behaviors and the processing properties. The possible curing processes were proposed and confirmed by Fourier transform infrared spectroscopy (FTIR). Then, glass fiber-reinforced DABA-Ph/BMI composites were designed, and their thermal-mechanical properties were studied. Results indicated that all the composites exhibited outstanding flexural strength, flexural modulus, and high glass-transition temperatures (Tg > 450 °C). The thermal stability of the composites was studied by thermogravimetry (TGA) and evaluated by the integral program decomposition temperature (IPDT). it is believed that the excellent thermal mechanical properties and outstanding Tg as well as good thermal stability would enable the reinforced copolymer-based laminates to be applied in wider fields.