Journal of Mechanics Engineering and Automation 5 (2015) 655-666
doi: 10.17265/2159-5275/2015.12.002
A Molecular Dynamic Modelling of Cross-Linked Epoxy Resin Using Reactive Force Field: Thermo-Mechanical Properties
Olanrewaju Aluko1, S. Gotham2 and G. M. Odegard2
1. Department of CSEP, College of Arts and Science, University of Michigan-Flint, Flint, MI 48502, USA
2. Department of Mechanical Engineering & Engineering Mechanics, Michigan Technological University, Houghton, MI 49931, USA
Abstract: The reactive force field was used to study the molecular dynamics of cross-linked EPON 862 (diglycidyl ether of bisphenol-F) and DETDA (diethylene toluene diamine) system in order to predict its thermo-mechanical behavior under different loading conditions. The approach for building the EPON 862/DETDA structures, cross-linking, and equilibration of the systems, and the evaluation of the models are presented. The mechanical properties such as Young’s and shear moduli, Poisson ratio, and yields strength as well as thermal properties such as glass transition temperature and coefficient of thermal exp
ansion are predicted. The results are in close agreement with both experimental data and simulated results in literature.
Key words: Reactive force field, molecular dynamics, thermo-mechanical, equilibration.
1. Introduction
Materials that have specific and unusual properties are needed for a host of high-technology applications such as those found in the aerospace, underwater, bio-engineering, and transportation industries Therefore, the engineering needs for fiber-reinforced composites with polymeric matrices continues to increase as engineers seek specialized materials with superior mechanical properties that can be tailored to support the requirements of structural components.  In light of this, fiber-reinforced epoxy composite materials have received the attention of many researchers [1-15] due to their formidable combination of characteristics such as high specific modulus and strength, good compatibility between the fibers and epoxy materials and low weight. The performance of epoxy based materials can be further improved through computational molecular dynamics
reactive materials studiesCorresponding author: Olanrewaju Aluko, Ph.D., assoc. professor, research fields: mechanics of advanced materials and nanocomposites. studies under different force fields. Varshney et al. [1] utilize
d CVFF (consistent valence force field) to study cross-linking procedure and predict molecular and material properties of epoxy-based thermoset (EPON 862/DETDA). Different approaches to build highly cross-linked polymer network are discussed and a multistep relaxation procedure for relaxing the molecular topology during cross-linking was presented. They calculated several material properties such as density, glass transition temperature, thermal expansion coefficient, and volume shrinkage during curing and their results were in agreement with experimental data.
Li and Strachan [2] used molecular dynamics with a procedure to describe chemical reactions to predict the atomic structure and properties of the thermosetting polymer epoxy (EPON-862) and curing agent (DETDA). The DREIDING force field is employed with environment-dependent atomic charges obtained self consistently during the dynamics. They proposed
a computationally efficient method to describe charge
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A Molecular Dynamic Modelling of Cross-Linked Epoxy Resin Using Reactive Force Field:
Thermo-Mechanical Properties
656
evolution based on the observation that atomic charges evolve significantly only during chemical reactions and in a repeatable manner. They used two
chemistry models with different relative rates for primary and secondary amine reactions to mimic the
curing process in two extreme cases of processing conditions. Their simulations showed that differences
in chemical reaction rates of interest affect properties
for intermediate conversion degrees (~40-70%) but not for the higher conversion rates of interest in most
applications. The predicted density, coefficient of thermal expansion, glass transition temperature and
elastic constants of the resulting polymers are in agreement with experiments. Abbott et al. [3] presented a generalized structure generation methodology for amorphous polymers by a simulated
polymerization technique and 21-step molecular dynamics equilibration, which is particularly effective
for high-T g  polymers. Validation of the methodology
is provided by comparison of the simulations and experiments for a variety of structural, adsorption, and
thermal properties, all of which showed excellent
agreement with available experimental data.
Doherty et al. [4] described a methodology to build
cross-linked atomistic structures for
poly(methacrylate). They performed simulations allowing a progressive crosslinking and polymerization reaction using molecular dynamics. They also used an explicit velocity rescaling molecular dynamics al
gorithm to relax the local energetic stresses caused by bond formation. However, the obtained network structure from their analysis was not characterized for mechanical properties because that was not the focus of their study. Other computational studies [5, 6] involving crosslinking of epoxies have been performed on relatively small model systems (less than 2,200 atoms). Yarovsky and Evans [7] developed a methodology that was applied to low molecular weight water soluble epoxy resins cross-linked with different curing agents that are being considered for use as a primer coating on steel. Their simulations allowed the crosslink density and the amount of free crosslinking
sites in the coatings to be predicted. Shrinkage of the resin upon curing was reproduced by the simulation
and the barrier properties of model coatings were estimated. Their developed methodology has a
potential to significantly impact on the design and development of new coatings with improved barrier and adhesion properties.
Wu and Xu [8] performed crosslinking simulations for epoxy resin system based on DGEBA (diglycidyl
ether bisphenol A) and IPD (isophorone diamine). They used the DREIDING force field with charge equilibration to build the structure but COMPASS force field for property prediction. They found that
COMPASS provides a more accurate description of elastic properties. Their DREIDING prediction of
Young’s modulus (about 50 GPa) is not in good agreement with the result of Li et al. [2] who utilized the same force field to obtain Young’s’ modulus in the
range 3.2-3.5 GPa. Littell et al. [9] conducted experimental tests using small test specimens on epoxy resin in tension, compression, and shear over a wide range of strain rate and their results have been found to be very useful as benchmark for simulated results. Komarov et al. [10] documented a new computational method where the polymer network is polymerized at a coarse-grained level and then mapped into a fully atomistic model. Molecular dynamics are then carried out with the OPLS force field. The predicted T g  is about 20 K lower than that of experimental results; this underestimation would increase once the extremely high cooling rates of MD taken into account.  Lin et al. [11] reported a single-step polymerization method for the creation of atomistic model structures of cross-linked polymers. A simulated annealing algorithm was used to identify pairs of reacting atoms within a cutoff distance and all crosslinking bonds were created in a single step. Bandyopadhyay et al.
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