Configurational Statistics of Polyethylene Chains

摘要

A mathematical procedure is described to handle the configurational statistics of a chain placed on a rigid lattice, allowing for firsthyphen;neighbor interaction between consecutive rotational states. Many statistics connected with chain bonds orientation with respect to a fixed reference frame are calculated easily. Assuming a diamond lattice, results are reported for polyethylene chains with different lengths: They include theW(r) endhyphen;tohyphen;end vector distribution, the principal meanhyphen;square radii of gyration of the polymer coils both under a fixed force applied to the chain ends and under a fixed endhyphen;tohyphen;end distance, the plots oflang;cos2PHgr;rang;and offGvsrPHgr;equals;anglebetween a chain bond and the direction of the force,fGequals;fractionofgaucherotational states). The last two results allow derivation of the average optical polarizability and of the internal energy for different chain elongations. Both the calculated characteristic ratioCinfin; and its derivative with temperature agree with the experimental data.