Molecular dynamics predictions of thermomechanical properties of an epoxy thermosetting polymer

Filled Elastomers: Mechanistic and Physics-Driven Modeling and Applications as Smart Materials

Elastomers are made of chain-like molecules to form networks that can sustain large deformation. Rubbers are thermosetting elastomers that are obtained from irreversible curing reactions. Curing reactions create permanent bonds between the molecular chains. On the other hand, thermoplastic elastomers do not need curing reactions. Incorporation of appropriated filler particles, as has been practiced for decades, can significantly enhance mechanical properties of elastomers. However, there are fundamental questions about polymer matrix composites (PMCs) that still elude complete understanding. This is because the macroscopic properties of PMCs depend not only on the overall volume fraction (ϕ) of the filler particles, but also on their spatial distribution (i.e., primary, secondary, and tertiary structure). This work aims at reviewing how the mechanical properties of PMCs are related to the microstructure of filler particles and to the interaction between filler particles and polymer matrices. Overall, soft rubbery matrices dictate the elasticity/hyperelasticity of the PMCs while the reinforcement involves polymer-particle interactions that can significantly influence the mechanical properties of the polymer matrix interface. For ϕ values higher than a threshold, percolation of the filler particles can lead to significant reinforcement. While viscoelastic behavior may be attributed to the soft rubbery component, inelastic behaviors like the Mullins and Payne effects are highly correlated to the microstructures of the polymer matrix and the filler particles, as well as that of the polymer-particle interface. Additionally, the incorporation of specific filler particles within intelligently designed polymer systems has been shown to yield a variety of functional and responsive materials, commonly termed smart materials. We review three types of smart PMCs, i.e., magnetoelastic (M-), shape-memory (SM-), and self-healing (SH-) PMCs, and discuss the constitutive models for these smart materials.

Noncovalent Interactions in Mechanical Response of Thermoset Epoxy Resin

Free volume in polymers is known to influence the mechanical response of the polymers. Noncovalent interactions such as hydrogen bonds, Coulombic electrostatic interactions, and van der Waals interactions are present within these free volume regions. The manuscript presents a comprehensive identification, characterization, and evolution of noncovalent interactions as a thermoset epoxy resin (typically used as an interfacial adhesive material) is subjected to uniaxial tension, shear, and shock loading. Even though noncovalent interactions dominate uniaxial tension and shear response (up to strain levels of 50% wherein covalent bond dissociation is not observed), both covalent and noncovalent interactions define response for shock loading. Van der Waals interactions dominate the response as the samples are subjected to strain levels of 50% in tension and shear. In contrast, hydrogen bonds influence shock response.

Tensile Stress Reduction and Strain Concentration of Epoxy Resin Caused by Heterogeneity: A Multiscale Approach Combining Molecular Dynamics Simulation and Finite Element Method

In this study, we investigated the effect of heterogeneity on the mechanical properties of epoxy resin by combining coarse-grained molecular dynamics (CG-MD) and finite element method (FEM) simulations. To evaluate the heterogeneity effect in the uniaxial elongation, heterogeneous and homogeneous FEM models of micrometer-scale cubic epoxy resin were constructed. For the heterogeneous FEM model, parameters of nanometer-scale elements were determined by CG-MD simulations, where nanometer-scale blocks have different cross-linked structures. For the homogeneous FEM model, the averaged parameters were used for all elements. The calculated stress-strain (S-S) curves of the heterogeneous model exhibit similar tensile stress values when compared to the experimental data, whereas the homogeneous model yields notably higher values. Moreover, a clear strain concentration associated with the formation of the shear band-like structure was observed in the heterogeneous model and not in the homogeneous model.

Understanding the Effect of Grain Boundaries on the Mechanical Properties of Epoxy/Graphene Composites

This work presents a molecular dynamics (MD) simulation study on the effect of grain boundaries (GBs) on the mechanical properties of epoxy/graphene composites. Ten types of GB models were constructed and comparisons were made for epoxy/graphene composites containing graphene with GBs. The results showed that the tensile and compressive behaviors, the glass transition temperature (Tg), and the configurations of epoxy/graphene composites were significantly affected by GBs. The tensile yield strength of epoxy/graphene composites could be either enhanced or weakened by GBs under a tensile load parallel to the graphene sheet. The underlying mechanisms may be attributed to multi-factor coupling, including the tensile strength of the reinforcements, the interfacial interaction energy, and the inflection degree of reinforcements. A balance exists among these effect factors, resulting in the diversity in the tensile yield strength of epoxy/graphene composites. The compressive yield strength for epoxy/graphene composites is higher than their counterpart in tension. The tensile/compressive yield strength for the same configuration presents diversity in different directions. Both an excellent interfacial interaction and the appropriate inflection degree of wrinkles for GB configurations restrict the translational and rotational movements of epoxy chains during volume expansion, which eventually improves the overall Tg. Understanding the reinforcing mechanism for graphene with GBs from the atomistic level provides new physical insights to material design for epoxy-based composites containing defective reinforcements.

Impact of the Force Field on the Calculation of Density and Surface Tension of Epoxy-Resins

The molecular simulation of interfacial systems is a matter of debate because of the choice of many input parameters that can affect significantly the performance of the force field of reproducing the surface tension and the coexisting densities. After developing a robust methodology for the calculation of the surface tension on a Lennard-Jones fluid, we apply it with different force fields to calculate the density and surface tension of pure constituents of epoxy resins. By using the model that best reproduces the experimental density and surface tension, we investigate the impact of composition in mass fraction on uncured epoxy resins and the effects of degree of cross-linking on cured resins.

Spatial Distribution of the Network Structure in Epoxy Resin via the MAXS-CT Method

We have succeeded in visualizing the spatial heterogeneity of the reaction ratio in epoxy resins by combining medium-angle X-ray scattering (MAXS) and computed tomography (CT). The reaction ratio is proportional to the degree of cross-linking between epoxy and amine in epoxy resins. The reaction ratio and its spatial inhomogeneity affect the toughness of epoxy resins. However, there has been no non-destructive method to measure the spatial inhomogeneity of the reaction ratio, although we can measure only the spatially averaged reaction ratio by Fourier-transform infrared spectroscopy (FT-IR). We found that the scattering peak reflected the cross-linking structures in the q region of MAXS and that the peak intensity is proportional to the reaction ratio. By reconstructing CT images from this peak intensity, we visualized the spatial heterogeneity of the reaction ratio. The application of this method may not be limited to epoxy resins but may extend to studying the heterogeneity of cross-linked structures in other materials.

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.

A Possibility for Quantitative Detection of Mechanically-Induced Invisible Damage by Thermal Property Measurement via Entropy Generation for a Polymer Material

Entropy generation from a mechanical and thermal perspective are quantitatively compared via molecular dynamic (MD) simulations and mechanical and thermal experiments. The entropy generation values regarding mechanical tensile loading—which causes invisible damage—of the Polyamide 6 (PA6) material are discussed in this study. The entropy values measured mechanically and thermally in the MD simulation were similar. To verify this consistency, mechanical and thermal experiments for measuring entropy generation were conducted. The experimentally obtained mechanical entropy was slightly less than that calculated by MD simulation. The thermal capacity is estimated based on the specific heat capacity measured by differential scanning calorimetry (DSC), applying the assumed extrapolation methods. The estimated entropy generation was higher than the aforementioned values. There is a possibility that the entropy-estimating method used in this study was inappropriate, resulting in overestimations. In any case, it is verified that entropy increases with mechanical loading and material invisible damage can be qualitatively detected via thermal property measurements.

Molecular Dynamics Investigation of the Thermo-Mechanical Properties of the Moisture Invaded and Cross-Linked Epoxy System

In spite of a high market share of plastic IC packaging, there are still reliability issues, especially for the effects of moisture. The mechanism between moisture and epoxy polymer is still obscure. A multi-step cross-linking approach was used to mimic the cross-linking process between the DGEBA resin and JEFFAMINE^®-D230 agent. Based on the molecular dynamics method, the thermo-mechanical properties and microstructure of epoxy polymer were analyzed. In this paper, the degree of cross-linking ranged from 0% to 85.4% and the moisture concentration ranged from 0 wt.% to 12 wt.%. The hydrogen bonds were investigated in the moisture invaded epoxy polymer. Although most of the hydrogen bonds were related to water molecules, the hydrogen bonds between the inside of epoxy polymer were reduced only a little as the concentration of moisture increased. The diffusion coefficient of the water molecules was found to increase with the increase of moisture concentration. When the moisture concentration was larger than 12 wt.% or smaller than 1.6 wt.%, the diffusion coefficient was less affected by the epoxy polymer. In addition, the free volume and the thermal conductivity of the epoxy polymer were considered. It was found that the moisture could increase the thermal conductivity from 0.24 to 0.31 W/m/K, identifying a coupling relationship between moisture and thermal properties. Finally, the mechanical properties of epoxy polymer were analyzed by uniaxial tensile simulation. The COMPASS and DREIDING force fields were used during the uniaxial tensile simulation. A better result was achieved from the DREIDING force field compared with the experiment. The degree of cross-linking was positively correlated with mechanical properties. For the system with the largest degree of cross-linking of 85.4%, the Young's modulus was 2.134 ± 0.522 GPa and the yield strength was 0.081 ± 0.01 GPa. There were both plasticizing and anti-plasticizing effects when the water molecules entered the epoxy polymer. Both the Young's moduli and yield strength varied in a large range from 1.38 to 2.344 GPa and from 0.062 to 0.128 GPa, respectively.

Effect of Terminal Groups on Thermomechanical and Dielectric Properties of Silica-Epoxy Composite Modified by Hyperbranched Polyester

To study the effect of hyperbranched polyester with different kinds of terminal groups on the thermomechanical and dielectric properties of silica-epoxy resin composite, a molecular dynamics simulation method was utilized. Pure epoxy resin and four groups of silica-epoxy resin composites were established, where the silica surface was hydrogenated, grafted with silane coupling agents, and grafted with hyperbranched polyester with terminal carboxyl and terminal hydroxyl, respectively. Then the thermal conductivity, glass transition temperature, elastic modulus, dielectric constant, free volume fraction, mean square displacement, hydrogen bonds, and binding energy of the five models were calculated. The results showed that the hyperbranched polyester significantly improved the thermomechanical and dielectric properties of the silica-epoxy composites compared with other surface treatments, and the terminal groups had an obvious effect on the enhancement effect. Among them, epoxy composite modified by the hyperbranched polyester with terminal carboxy exhibited the best thermomechanical properties and lowest dielectric constant. Our analysis of the microstructure found that the two systems grafted with hyperbranched polyester had a smaller free volume fraction (FFV) and mean square displacement (MSD), and the larger number of hydrogen bonds and greater binding energy, indicating that weaker strength of molecular segments motion and stronger interfacial bonding between silica and epoxy resin matrix were the reasons for the enhancement of the thermomechanical and dielectric properties.

Molecular Characterization of Polymer Networks

Polymer networks are complex systems consisting of molecular components. Whereas the properties of the individual components are typically well understood by most chemists, translating that chemical insight into polymer networks themselves is limited by the statistical and poorly defined nature of network structures. As a result, it is challenging, if not currently impossible, to extrapolate from the molecular behavior of components to the full range of performance and properties of the entire polymer network. Polymer networks therefore present an unrealized, important, and interdisciplinary opportunity to exert molecular-level, chemical control on material macroscopic properties. A barrier to sophisticated molecular approaches to polymer networks is that the techniques for characterizing the molecular structure of networks are often unfamiliar to many scientists. Here, we present a critical overview of the current characterization techniques available to understand the relation between the molecular properties and the resulting performance and behavior of polymer networks, in the absence of added fillers. We highlight the methods available to characterize the chemistry and molecular-level properties of individual polymer strands and junctions, the gelation process by which strands form networks, the structure of the resulting network, and the dynamics and mechanics of the final material. The purpose is not to serve as a detailed manual for conducting these measurements but rather to unify the underlying principles, point out remaining challenges, and provide a concise overview by which chemists can plan characterization strategies that suit their research objectives. Because polymer networks cannot often be sufficiently characterized with a single method, strategic combinations of multiple techniques are typically required for their molecular characterization.