Lattice energies of small organic molecules using density functional theory

Fiber-reinforced polymer composite materials have become increasingly important in aircraft applications because of their advantages in weight reduction and energy saving. For example, the Boeing Company has raised the use of composite materials in new aircrafts up to 50% of structural weight. Thermosetting polymers are the matrices of choice for such composites due to their high stiffness, strength, creep resistance and thermal resistance when compared with thermoplastic polymers. These desirable properties stem from the three-dimensional (3D) crosslinked structures of these polymers. Many thermosetting polymers are formed by mixing a resin (epoxy, vinyl ester, or polyester) and a curing agent. An irreversible chemical reaction cures the two components into a solid polymer with a 3D network of covalent bonds.
 
The mechanical and physical properties of thermosetting polymers depend on their chemistry, composition, and curing conditions.  The curing procedure  may be done through heat or irradiation.
 
Prior to curing thermosetting materials are usually liquids, however for some applications also solids are used, for example the molding compound used in semiconductors and integrated circuits. A  thermosettting material cannot be melted and re-shaped after the curing procedure.
 
The three dimensional network of bonds (cross-linking) makes thermosetting materials  stronger than thermoplastic materials.  They are also better suited to high-temperature applications up to the decomposition temperature.
 
Examples of crosslinked polymers include: Polyester fibreglass, polyurethanes used as coatings, adhesives,  vulcanized rubber, epoxy resins and many more.
 
In the present case study we examine the cross-linking process of the thermosetting polymer epoxy EPON-862 and the curing agent DETDA (Fig. 1) and calculate some properties of this system.
 

c9-f1-activated-detda-epon-monomers
Figure 1: Activated DETDA and EPON monomers 

The simulation cell consists of 32 DETDA and 64 EPON molecules. We have started the cross-linking procedure from three different conformations (A,B,C) of the same system. For each conformation we have chosen two initial options. First we have used the Dreiding forcefield with no additional charges and second we have applied artificial charges of +/-4e on the crosslink centers.
 
The conformations were obtained from the MAPS Amorphous Builder at 450K and 0.80 g/ml followed by 1000 steps of optimization (Fig 2). The multistep relaxation algorithm described in reference [1] was followed. Successive 50 ps NPT runs were perfrormed followed by 5 relaxation steps that are used to relax the newly formed bonds to the forcefield value.  This procedure is available as an automated PYTHON script in Scienomics' MAPS platform
 

c9-f2-molecular-systems-initial-final
Figure 2: Initial conformation containing 32 DETDA and 64 EPON molecules. 

In Figure 3a the % conversion as a function of simulation time is presented. As can be seen, the curing follows a near exponential behavior. In Figure 3b the literature results from Li and Strachan[1] are displayed for comparison, a very similar conversion rate is found in their study.
 
c9-f3a-conversion-as-a-function-of-time

c9-f3b-conversion-from-strachan
Figure 3a: Conversion (%) as a function of time Figure 3b: Conversion versus time from a literature study[1] for comparison
During conversion the free volume in the system usually reduces, hence the specific volume decreases also and the density increases accordingly. This process is called shrinking, and is also resembled by our simulations. Figure 4 displays the shrinking process by showing the specific volume as a function of conversion.

c9-f4-specific-volume-versus-conversion-rate
Figure 4: Specific volume as a function of conversion (%)

As a second property we have calculated the mechanical properties of the cross linked system, namely the Young modulus. To assess the impact of cross linking on the mechanical properties, we have also constructed a hypothetical ideal linear system, consisting of 24 EPON and DETDA monomers each. So two systems were studied:
a) A linear DETDA-EPON polymer consisting of 48 monomers.
b) An 80 % cross-linked DETDA-EPON resin obtained from the aforementioned methodology.

The tensile experiments were performed at an imposed stress rate of 1atm/ps. The stress – strain curves and the Young modulus results for both systems are presented in Figures 5 and 6.
 

c9-f5-stress-strain-of-linear-detda-epon-polymer
Figure 5: Stress-strain curve of linear DETDA-EPON polymer. The fitting of the graph gives a Young modulus of 1.44 Gpa.

c9-f6-stress-strain-of-crosslinked-detda-epon-resin
Figure 6: Stress-strain curve of linear DETDA-EPON crosslinked resin. The fitting of the graph gives a Young modulus of 3.63 Gpa which is in agreement to ref [1] and close to the experimental value of 2.76 [2].

As can be seen from the results, cross-linking has a dramatic effect on the mechanical properties of the DETDA-EPON system, the Young modulus more than doubles. Simulated moduli are usually found to be higher than experimentally determined ones, the possible reasons of higher tensile moduli of simulated structures being the fact that models are free of defects while various kinds of defects are usually present in real macroscopic samples that tend to reduce the measured values of the elastic moduli of the material. However, considering the above, satisfactory agreement with experimental results were found.
 
Summary:

A method for building 3-D cross- linked atomistic systems has been devised and tested on the DETDA-EPON epoxy system. The method has been compared to literature studies and been used to predict mechanical properties of the thermoset. Comparison with experimental results has been found satisfactory. Finally the method has been automated into a PYTHON script available within Scienomics' MAPS platform.
 
References:

  1. Strachan, A. and Li, C. Polymer 51, (2010), 6058-6070
  2. Tack JL. Thermodynamic and mechanical properties of EPON 862 with curing agent DETDA by molecular simulation. Master’s thesis, Texas A&M University, 2006