Molecular statics of polymer configurations
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I. INTRODUCTION The properties of isolated polymer molecules are certainly one of the more important contributions to the macroscopic physical properties of polymers. The mechanical properties of isolated molecules must be equally important in understanding bulk mechanical behavior. Modeling of molecules is rather complicated, however, as evidenced by the large number of models already in the literature. One of the more common is the so-called flexible model. Various authors proposing flexible models,1""7 however, as well as authors proposing freely jointed (and thus flexible) chains8"13 do not yet agree on how the flexibility of the polymer molecules should be modeled. In the present work we concentrate on developing specific, simple, and quantitatively explicit formulas for the interaction energies between atoms. Our goal is to make these as realistic as possible but at a level of complexity that is well suited for computer evaluation and at the same time can be understood by the majority of interested parties. Their simplicity should make it possible to get a grasp on the fundamental issues controlling the mechanical behavior of polymers and in the long term lead to more realistic modeling schemes that are both easy to use and to understand. The model developed in the present paper is the mathematical equivalent of constructing a molecule whose atoms obey certain premise behaviors and then examining the conformations that develop in such molecules under specific conditions. If the premise behaviors are sufficiently realistic, the resulting conformations should be equally realistic, giving us insight into the detailed molecular processes by which they are established and by which they respond to externally applied loads. 1414
J. Mater. Res. 3 (6), Nov/Dec 1988
Once we are successful at the level of single molecules, we plan to use more than one molecule to examine intermolecular phenomena as well. Our ultimate goal will be to calculate the bulk properties of a material whose atoms obey a specific set of interaction energy rules. II. MODEL The procedure employed in determining the molecular configurations is energy minimization as based on the interatomic interactions and rotational constraints of the bonds. Four energy potentials are used: covalent bond stretching, bending of covalent bond pairs, twisting of covalent single bonds with respect to other single bonds, and finally the Van der Waals interactions between nonbonded atoms. Three of the potentials are thus used to represent the covalent interactions between backbone atoms of a polymer chain, and the Van der Waals potential is used to represent interactions between atoms with no common covalent bonding. In the present treatment, we consider only single bonded carbon atom chains with tetrahedral symmetry of the bond angles in the undistorted condition. The effects of hydrogen atom pairs bonded to the backbone carbons in the simple polyethylene structure is included indirectly in both the effective Van der Waals potential and in the formulation of the twis
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