Estimation of linear, ring, and star polyethylene viscosity through proper orthogonal decomposition and Voronoi tessellation analysis of molecular dynamics data

Abstract

AbstractWe carried out molecular dynamics (MD) simulations on polyethylene (PE) with linear, ring, and four‐arm symmetrical star structures at various molecular weights (420 − 5700 g ⋅ mol−1) and temperatures (410−450 K). We then analyzed the MD data using the technique of proper orthogonal decomposition (POD) to obtain the time correlation functions of different eigenmodes, thereby calculating the viscosity of the aforementioned macromolecules. The time correlation functions show that the ring and star PEs relax much faster than their linear counterpart. Free volume size distributions and the mean fractional free volume of the equilibrated PE melts were determined by Voronoi tessellation (VT). The mean fractional free volume and the corresponding effective pressure were then used to calculate viscosity using a polymer free volume theory recently developed in our lab. The POD and VT approaches yielded similar viscosity values. Furthermore, they both successfully predicted the crossover in the molecular weight dependence of viscosity. It is interesting to note that the difference in the free volume parameters (ϕ+ − F) of various structures always fall within the range of 0.02−0.06. Here, F and ϕ+ signify the probability of a bead having enough free volume for the activation of diffusive motion or momentum transfer and the minimum required fraction of such beads, respectively. The temperature dependence of viscosity as obtained from the POD and VT approaches gave comparable apparent activation energy () values of 5.8−6.4 and 5.4−6.4 kcal ⋅ mol−1, respectively, for the three structures.