An adapted version of the annealing algorithm to identify primitive paths of a melt of ring polymers is presented. This algorithm ensures that the primitive path length becomes zero for nonconcatenated rings, and that no entanglements are observed. The bond-fluctuation model was used to simulate ring-linear blends with N=150 and 300 monomers. The primitive path length and the average number of entanglements of the linear component were found to be independent of the blend composition. In contrast, the primitive path length and the average number of entanglements on a ring molecule increased approximately linearly with the fraction of linear chains, and for large N , they approached values comparable with linear chains. Threading of ring molecules by linear chains, and ring-ring interactions were observed only in the presence of linear chains. It is conjectured that for large N , these latter interactions facilitate the formation of a percolating entangled network, thereby resulting in a disproportionate retardation of the dynamical processes.

We describe the modifications that a spatially varying external load produces on a Born-Oppenheimer potential energy surface (PES) by calculating static quantities of interest. The effects of the external loads are exemplified using electronic structure calculations (at the HF/6-31G(∗∗) level) of two different molecules: ethane and hexahydro-1,3,5-trinitro-s-triazine (RDX). The calculated transition states and Hessian matrices of stationary points show that spatially varying external loads shift the stationary points and modify the curvature of the PES, thereby affecting the harmonic transition rates by altering both the energy barrier as well as the prefactor. The harmonic spectra of both molecules are blueshifted with increasing compressive "pressure." Some stationary points on the RDX-PES disappear under application of the external load, indicating the merging of an energy minimum with a saddle point.

A lattice model is used to estimate the self-diffusivity of entangled cyclic and linear polymers in blends of varying compositions. To interpret simulation results, we suggest a minimal constraint release model for the motion of a cyclic polymer infiltrated by neighboring linear chains. Both the simulation and recently reported experimental data on entangled DNA solutions support the simple model over a wide range of blend compositions, concentrations, and molecular weights.

The bivariate, or cross branching distribution of a gas-phase produced, film-grade ethylene 1-hexene copolymer with enhanced Elmendorf tear in machine direction, MD, and in transverse direction, TD, (> 400 g/mil) and high dart impact has been characterized through the analysis of fractions obtained by molecular weight and 1-hexene composition. The molecular weight fractions, obtained by a solventnon-solvent fractionation technique, are each mixtures of molecules with at least two different 1-hexene compositions, one component with a constant relatively high density ($1 mol% hexene) and a second of a lower density broadly distributed along the molecular weight fractions. The content of the low density component increases with increasing molecular weight of the fraction while the level of 1-hexene decreases. The mixed compositional character of these fractions is easily inferred by their high crystallization rates and both high melting and crystallization temperatures compared to the values of model random ethylene copolymers. The set of compositional fractions obtained by TREF display an increasing 1-hexene concentration with increasing molecular weight, and except for the highest molecular weight components (Mw > 150,000 g/mol) their melting and crystallization behavior followed the random pattern. Higher than expected melting temperatures and a constancy of the high melting temperature peak with increasing crystallization temperature, suggests that the intra-chain 1-hexene distribution of the highly branched, high molecular weight fraction deviates strongly from the random behavior. These structural features and the bimodal character of the composition distribution of this resin, that contains high molecular weight chains with both low and high 1-hexene contents, are correlated with the enhanced key film properties.

The mechanical behavior of an ensemble of athermal fibers forming a nonbonded network subjected to triaxial compression is studied using a numerical model. The response exhibits a power law dependence of stress on the dilatation strain and hysteresis upon loading and unloading. A stable hysteresis loop results after the first loading and unloading cycle. In the early stages of compaction, strain energy is associated primarily with the bending of fibers, while at higher densities, it is stored primarily in the axial deformation mode. It is shown that the exponent of the power law, and the partition of energy in the axial and bending modes depends on the ratio of the bending to axial stiffness of the fibers. Accounting for interfiber friction does not change the functional form of the stress-strain relationship or the exponent. The central feature that distinguishes the mechanics of this system from that of bonded random networks is the relative sliding at contacts and the ensuing fiber rearrangements. We show that suppressing sliding leads to a much stiffer response. The results indicate that the value of the exponent of the stress-strain power law is determined not only by fiber bending and the formation of new contacts, but also by the relative sliding and axial deformation of fibers.