Polyethylene, molecular symmetry

When we compared the viscosities of solutions of natural rubber and of guttapercha and of other elastomers and later of polyethylene vs.(poly)cis-butadiene, with such bulk properties as moduli, densities, X-ray structures, and adhesiveness, we were greatly helped in understanding these behavioral differences by the studies of Wood (6) on the temperature and stress dependent, melting and freezing,hysteresis of natural rubber, and by the work of Treloar (7) and of Flory (8) on the elasticity and crystallinity of elastomers on stretching. Molecular symmetry and stiffness among closely similar chemical structures, as they affect the enthalpy, the entropy, and phase transitions (perhaps best expressed by AHm and by Clapeyron s... 

Because of its exceptional symmetry, the polyethylene molecule fits so readily into a crystalline lattice, in spite of its lack of molar cohesion, that its tendency is to crystallize into spherulite structures on relaxation rather than revert to a disordered state. However, the degree and type of chain branching that interrupts the geometrical regularity of the polyethylene molecular structure causes a local... 

This theoretical calculation is used to idealize a macromolecule and to calculate the fundamental frequency v, which is then compared to the experimental frequency. In the calculation of molecular symmetry, periodicity of potential functions and force constants were introduced. If the results of these calculations are in agreement with those from experiment, then the assumed parameters (symmetry, potential function, and force constant) contain information about the actual macrmolecule. A detailed calculation is illustrated by the smdy of polyethylene (see Bower and Maddams, 1989). 

Spanget-Larsen, J., and N. Fink. 1990. Molecular symmetry of 2,5-dimethyl-1,6,6a. lambda.4-trithiapentalene Infrared linear dichroism in stretched polyethylene. J. Phys. Chem. 94 8423-8425. 

Due to the symmetry of 19a, which possesses a methyl group on each and every ninth carbon, the carbon NMR spectrum displays only six resonances. This conclusively demonstrates that these techniques are able to prepare polymers whose regularity can be controlled with ease. The polymers themselves are sufficiently high in molecular weight to mimic crystallization behavior of polyethylene in its substituted forms. 

Order and dense paeking are relative in the context of these systems and depend on the point of view. Usually the term order is used in eonneetion with translational symmetry in molecular structures, i.e. in a two-dimensional monolayer with a erystal strueture. Dense packing in organic layers is conneeted with the density of crystalline polyethylene. 

Another aspect of high chain symmetry is the possibility of molecular motion within the crystal lattice contributing to higher T. For example, polyethylene and polytetrafluoroethylene are both sufficiently symmetrical to be considered as smooth, stiff cylindrical rods. In the crystal, these rods tend to roll over each other and change position when thermally agitated. This motion within the crystal lattice, called premelting, effectively stabilizes the lattice. Consequently, more thermal energy is required to break down... 

A third, less obvious limitation of sampling methods is that, due to the heavy computational burden involved, simpler interatomic potential models are more prevalent in Monte Carlo and molecular dynamics simulations. For example, polarizability may be an important factor in some polymer crystals. Nevertheless, a model such as the shell model is difficult and time-consuming to implement in Monte Carlo or molecular dynamics simulations and is rarely used. United atom models are quite popular in simulations of amorphous phases due to the reduction in computational requirements for a simulation of a given size. However, united atom models must be used with caution in crystal phase simulations, as the neglect of structural detail in the model may be sufficient to alter completely the symmetry of the crystal phase itself. United atom polyethylene, for example, exhibits a hexagonal unit cell over all temperatures, rather than the experimentally observed orthorhombic unit cell [58,63] such a change of structure could be reflected in the dynamical properties as well. 

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