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

Abstract

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).

United-Atom Molecular Dynamics Study of the Mechanical and Thermomechanical Properties of an Industrial Epoxy

“…For heating, we obtained values in the range of 42–56 × 10 −5 /°C for the rubbery state, and 54–63 × 10 −5 /°C during cooling. In both methods, the values coincide with previous molecular simulation studies for a similar system [ 31 ], which tends to be consistently higher than experimental results reported in the literature, around 5–9 × 10 −5 /°C for the glassy state and 16–30 × 10 −5 /°C for the rubbery state [ 34 ].…”

“…Although the glass transition is not a discrete thermodynamic transition, but rather occurs over a range of temperatures, it is common to report one point within that range where the slope of volume versus temperature changes. The transition is continuous for the small samples studied in molecular simulation [ 31 ], as can be seen in Figure 8 a. T g was, therefore, extracted from the crossing of initial slopes of the volume-temperature curves during both heating and cooling (at an effective rate of 25 K/ns). As with E , the range of data chosen for the calculation of T g can significantly affect its value.…”

“…Interestingly, Afzal et al [ 33 ] found that the discrepancy between measured and calculated T g is consistent within a simulation protocol, and hence could be accounted for with proper calibration. Alternatively, the difference between experimental and computational rates could potentially be bridged using time-temperature superposition [ 24 , 31 ].…”

Molecular Simulations of Thermomechanical Properties of Epoxy-Amine Resins

“…16 Regarding the epoxy systems investigated by molecular simulations, the most extensive research effort was found in resins resulting from the cross-linking between the diglycidyl ether of bisphenol F (DGEBF) and diethyl toluenediamine (DETDA), 9,11,12,17,18 triethylenetetramine (TETA) 10,19−21 or diethylenetriamine (DETA), 22 especially in the fields of modern aeronautics. The cross-linking of the diglycidyl ether of bisphenol A (DGEBA) resin was also widely studied with different hardeners, such as isophorone diamine (IPDA), 23−25 trimethylene glycol di-p-aminobenzoate (TMAB), 26 diethyltoluenediamine (DETDA), 4,27−29 triethylenetetramine (TETA), 27 ethylenediamine (EDA), 7 diaminodiphenyl sulfone (DDS), 30 methylenedianiline (MDA), 31 poly(oxopropylene) diamines (POP), 16,32,33 4,4′-methylenebis(cyclohexylamine) (MCA), 33 diethylenetriamine (DETA), 13,34−36 Through this, an evaluation of the performance and the reliability of general atomistic force fields and the capacity of simulation methods to reproduce the thermomechanical properties of these resins is carried out. Indeed, predicting the physical, mechanical, and thermodynamic properties of resins by using full atomistic models remains challenging because of the complexity of the interactions involved and the algorithm needed to post-treat the data.…”

“…One of the first steps to reproduce thermosetting polymers in molecular simulations is to be able to cross-link the monomers, making it possible to characterize the polymeric material. Two approaches are typically used for the cross-linking of the monomers: a “back-mapping” procedure − and a “reactive” one. − The former is based on the cross-linking of coarse-grained monomers and then the all-atom model is later back-mapped in lieu of the coarse grains, while the latter already considers an all-atom model and the cross-linking is done between the experimental reactive pairs. These cross-linking methods can also be single or multiple steps but exhibit the same topology overall …”