Loop entanglement in a constrained liquid region: simulation data, simplified models, and general measurement heuristics

Complete entanglement measurement data from a computer simulation of the random walk model of a liquid region in a semicrystalline polymer is presented for plane separations out to 54 units. These data are compared with the same measures calculated analytically in a simplified model of the simulation. A case is presented for validation of the simplified model measurements as heuristics for the more complicated calculations used in the simulation. The model simplification process is general enough to apply to any model that contains loops and ties as chains between parallel planes. The heuristics may be applied directly from knowledge of single-chain statistics. As an example application, the heuristics are calculated for a model recently introduced by Marqusee and Dill, where it is found that both physical ties and loop entanglements are more likely than in the random case. 20 ref.--AA