By Javier Ramos, Juan F. Vega and Javier Martínez-Salazar
Research activity in the field of macromolecular science requires the use of a variety of techniques. This is due to the intrinsic characteristics of polymeric materials, which reveal interesting physical phenomena in the length scale from sub-nanometer up to microns or, alternatively, in the time scale from picoseconds to years. Covering these wide length and time scales demands the use of powerful experimental techniques, with the combination of complementary computational tools in order to effectively resolve the processes of interest. At this respect major advances in computational power, such as the use of GPU processors, and methodologies can nowadays help to face classical problems, and to establish a shared knowledge between theorists and experimentalists.
The polyethylene phase transitions
The glass transition and the crystallization processes in polymers still remain under debate. Among all synthetic polymeric materials, polyethylene (PE) represents a model system in polymer physics. The advantage of this polymer is the simplicity of its chemical structure, and the extensive set of experimental data available to validate the simulations. The objective of this contribution is to examine fundamental physical processes in a model of entangled polyethylene (C192) using two different force fields, the so-called PYS and TraPPe-UA. We mainly focus our attention on the ability of each model to simulate complex phenomena as glass transition and especially crystallization process.
Computational modeling as a tool to understand polymer physics
Most of the minimizations and molecular dynamics (MD) simulations were performed with GROMACS 4.6.x package installed in Metrocubo Graphical Processor Units (GPU) workstations bought to Acellera. The glass transition and crystallization processes of polymer chains can be studied by cooling an amorphous system at a constant cooling rate. If the cooling is sufficiently slow, early stages of nucleation and crystallization can be studied. On the contrary, at high cooling rates a glass state is produced. Non-isothermal simulations using several cooling rates from an amorphous system in the range of 2,000 (tsim.~0.1 ns) and 0.05 K ns-1 (tsim.~4-5 μs) were performed.
The glass transition temperature (Tg) and the crystallization process
The equilibrated PE system was cooled down at different finite cooling rates, G = 1 to 2,000 K×ns-1 (high enough to prevent polymer crystallization). From these simulations one can calculate the apparent Tg versus cooling rate (Figure 1). Thus, estimate values of Tg0 of 187.0 K and 214.1 K for TraPPe-UA and PYS FFs, respectively are obtained. Experimentally, it has been usual to obtain the Tg by extrapolation to an amorphous PE free of constraints provoked by the presence of crystals, i.e. that obtained by Gordon-Taylor equation. The use of this equation gives rise to a value of Tg0 = 185-195 K. which is very close to that obtained from the TraPPE-UA system.
MD simulations at low cooling rates (G = 0.05 to 1 K·ns-1) allow one to study the crystallization process (Figure 2). A sudden drop of the specific volume and a single peak of the specific heat clearly indicate a phase transition at a crystallization temperature, Tc, during cooling. A clear segregation process (semicrystalline state) has been observed at the early stages of crystallization. Thus, one can observe two different layers, one ordered, and the other one amorphous. The final structure clearly recalls the model experimentally proposed by Ungar and coworkers for quenched long-alkanes of similar molecular length.
Towards a better understanding of the phase transitions in polymers by using large molecular dynamics simulations
We have performed simulations to capture the complex behavior of glass transition and crystallization processes at different cooling rates. This requires large simulation boxes (at the nanometer scale) and long time simulations (at the microsecond scale) well-suited to be performed in GPU processors. We can draw the following general conclusions:
- The apparent glass transition and its dependence with the cooling rate are well described by TraPPe-UA force field. In fact the extrapolated value at experimental conditions is close to that obtained for totally amorphous PE without crystalline constraints (Gordon-Taylor equation)
- For the first time the TraPPe-UA force field is employed to simulate the homogeneous early stages of the crystallization process of an entangled n-alkane. Basic experimental facts are correctly described by the simulations, primarily (i) the initial fold length expected for these high supercoolings, and (ii) the segregation of the systems in alternating ordered and disordered layers.
Reference and further reading:
- Javier Ramos, Juan F Vega, Javier Martínez-Salazar, “Molecular Dynamics Simulations for the Description of Experimental Molecular Conformation, Melt Dynamics, and Phase Transitions in Polyethylene”, 2015, Macromolecules, 48(14), 5016-5027.
- Sara Sanmartín, Javier Ramos, Juan Francisco Vega, Javier Martínez-Salazar, “Strong influence of branching on the early stage of nucleation and crystal formation of fast cooled ultralong n-alkanes as revealed by computer simulation”, 2014, European Polymer Journal, 50, 190-199
- Binder, K.; Baschnagel, J.; Paul, W. “Glass transition of polymer melts: test of theoretical concepts by computer simulation”, 2003, Progress in Polymer Science, 28(1), 115-172
- Goran Ungar and Xiang-bing Zeng, “Learning Polymer Crystallization with the Aid of Linear, Branched and Cyclic Model Compounds”, 2001, Chem. Reviews, 4157–4188