Polyethylene molecular dynamics

Abstract. This paper presents results from quantum molecular dynamics Simula tions applied to catalytic reactions, focusing on ethylene polymerization by metallocene catalysts. The entire reaction path could be monitored, showing the full molecular dynamics of the reaction. Detailed information on, e.g., the importance of the so-called agostic interaction could be obtained. Also presented are results of static simulations of the Car-Parrinello type, applied to orthorhombic crystalline polyethylene. These simulations for the first time led to a first principles value for the ultimate Young s modulus of a synthetic polymer with demonstrated basis set convergence, taking into account the full three-dimensional structure of the crystal. 

Fig. 7 gives an example of such a comparison between a number of different polymer simulations and an experiment. The data contain a variety of Monte Carlo simulations employing different models, molecular dynamics simulations, as well as experimental results for polyethylene. Within the error bars this universal analysis of the diffusion constant is independent of the chemical species, be they simple computer models or real chemical materials. Thus, on this level, the simplified models are the most suitable models for investigating polymer materials. (For polymers with side branches or more complicated monomers, the situation is not that clear cut.) It also shows that the so-called entanglement length or entanglement molecular mass Mg is the universal scaling variable which allows one to compare different polymeric melts in order to interpret their viscoelastic behavior. 

Dielectric relaxation measurements of polyethylene grafted with acrylic acid(AA), 2-hydroxyethyl methacrylate (HEMA) and their binary mixture were carried out in a trial to explore the molecular dynamics of the grafted samples [125]. Such measurements provide information about their molecular packing and interaction. It was possible to predict that the binary mixture used yields a random copolymer PE—g—P(AA/HEMA), which is greatly enriched with HEMA. This method of characterization is very interesting and is going to be developed in different polymer/monomer systems. 

Such doubts are removed by a comparison of results for polyethylene (PE), (Fig. 5.2) obtained at such high temperatures (namely T = 509 K), that it is already possible to carry out molecular dynamics simulations for melts of (sufficiently short but chemically realistic ) chains that reach thermal equilibrium [165,168]. 

Dynamics in Bulk Polyethylene A Molecular Dynamics Simulation Study. 

Recent advances in molecular dynamics simulations enabled Levine et al. (20) to take modeling one step further, to the molecular level. They succeeded in simulating from first principles the structure formation of 100 carbon atom polyethylene during uniaxial extension, under a variety of conditions. Figure 14.9 shows the dynamics of extensional deformation below the melting point, beautifully indicating the dynamic development of orientation and order. 

Fig. 14.9 Snapshots of a system of twenty 100 carbon atom long polyethylene chains deformed at 300 K. The initial slab at the top rapidly deforms with the applied stress in the x dimension of the slab, roughly doubling in the first 500 ps to / — 2.64 (second image from the top) then the rate of deformation is slower and doubles again in 1500ps to X — 5.15 (third image from the top). Beyond this point the cell deforms even more slowly to reach a final deformation of X = 6.28 (bottom image). In absolute values, the initial cell of dimensions 1.88 x 5.32 x 5.32 nm deforms to 11.8 x 2.23 x 1.96nm. [Reprinted by permission from M. C. Levine, N. Waheed, and G. C. Rutledge, Molecular Dynamics Simulation of Orientation and Crystallization of Polyethylene during Uniaxial Extension, Polymer, 44, 1771-1779, (2003).]...

M. C. Levine, N. Waheed, and G. C. Rutledge, Molecular Dynamics Simulation of Orientation and Crystallization of Polyethylene during Uniaxial Extension, Polymer, 44, 1771-1779 (2003). 

Let consider regularities of molecular dynamics of micellar phase of complexes polyacid-SAS on the example of PMAA complexes with dodecylsubstituted polyethylene glycol (DD-PEG, formula is presented below) [22, 23], Analogous regularities were observed under investigation of PAA complexes with DD-PEG [24],... 

Molecular dynamics are time-consuming because the nonbonded interactions scale as n where n is the number of atoms. To save time, one may implement the united atom approach, substituting some atomistic detail with an imaginary entity that represents the essential features of what has been substituted. For example, it is common to substitute methylene groups with an imaginary spherical atom with mass 14. Therefore a polyethylene chain would look like a chain of spherical atoms, appropriately rescaled, terminated by similar entities with mass = 15 for the methyl groups. 

An interesting application of the molecular dynamics technique on single chains is found in the work of Mattice et al. One paper by these authors is cited here because it is relevant to both RIS and DRIS studies and deals with the isomerization kinetics of alkane chains. The authors have computed the trajectories for linear polyethylene chains of sizes C,o to Cioo- The simulation was fully atomistic, with bond lengths, bond angles, and rotational states all being variable. Analysis of the results shows that for very short times, correlations between rotational isomeric transitions at bonds i and i 2 exist, which is something a Brownian dynamics simulation had shown earlier. 

Zhang, et al, Interfacial Characteristics of Carbon Nanotube-Polyethylene Composites Using Molecular Dynamics Simulations, ISRN Materials Science, Article ID 145042,2011. 

Saitta AM, Klein ML (1999) Polyethylene under tensile load strain energy storage and breaking of linear and knotted alkanes probed by first-principles molecular dynamics calculations. J Chem Phys 111 9434-9440... 

Uddin, N. M., Capaldi, F. M., Farouk, B. (2011). Molecular dynamics simulations of the interactions and dispersion of carbon nanotubes in polyethylene oxide/water systems. Polymer. 52(2), 288-296. 

Density and solubility parameter as a function of chain length for (a) polyethylene oxide (PEO) and (b) polyvinyl chloride (PVC). (From Luo, Z. L., and Jiang, J. W. 2010. Molecular dynamics and dissipative particle dynamics simulations for the miscibility of poly(ethylene oxide)/ poly(vinyl chloride) blends. Polymer 51 291-299.)... 

Specific volumes versus temperature using molecular dynamics simulation for blend system PHB/polyethylene (PE) (1 2 blends in terms of repeated units). 

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