No abstract

Large numbers of conformations of unperturbed polypropylene chains are generated in Monte Carlo experiments, based on a rotational isomeric state scheme, and the average instantaneous shape in the system of principal axes of gyration is evaluated. Several new shape measures are introduced to characterize the shape anisotropy, asphericity, and acylindricity. Significant differences are found between shortand medium-length chains of different tacticity, while for long chains all shape measures converge to a common limit. The detailed three-dimensional segment density distributions are examined, and they are found to be bimodal along the longest principal axis of gyration. The loci of highest segment density are always two clearly separated domains, not containing the center of gyration, and they lie on the major principal axis separated by ca. 1.3(s2)o1/2-2.0(s2)01/2. The core of the segment distribution of an unperturbed chain is therefore dumbbell-like in shape.

We introduce an algorithm for the reduction of a computer generated atomistic polymer sample to an entanglement network of primitive paths. These networks are structural representations of the topology underlying a polymer melt. By examining network ensembles of polyethylene and cis-1,4-polybutadiene melts, we provide topological measures and statistical properties of primitive paths. We present the radial distribution function of entanglements and the distribution of the number of monomers between entanglements. A renewal point process that generates entanglement events along the monomer sequence of a chain is found to describe the statistics of detected topological constraints. We discuss chain thickness effects on topological measures and provide a method for detecting persistent chain contacts in melt configurations. A suitable scaling of acquired data leads to a unifying microscopic topological description of the melts studied.

The recently introduced end-bridging (EB) Monte Carlo move is revisited, and a thorough analysis of its geometric formulation and numerical implementation is given. Detailed results are presented from applying the move, along with concerted rotation, in atomistic simulations of polyethylene (PE) melt systems with mean molecular lengths ranging from C78 up to C500, flat molecular weight distributions, and polydispersity indices I ranging from 1.02 to 1.12. To avoid finite system-size effects, most simulations are executed in a superbox containing up to 5000 mers and special neighbor list strategies are implemented. For all chain lengths considered, excellent equilibration is observed of the thermodynamic and conformational properties of the melt at all length scales, from the level of the bond length to the level of the chain end-to-end vector. In sharp contrast, if no end bridging is allowed among the Monte Carlo moves, no equilibration is achieved, even for the C78 system. The polydispersity index I is found to have no effect on the equilibrium properties of the melt. To quantify the efficiency of the EB Monte Carlo move, the CPU time t 0 required for the chain center of mass to travel a distance equal to the root-mean-square end-to-end distance is estimated by simple analytical arguments. It is found that t 0 should scale as n/(X̄Δ2.5), where n is the total number of mers in the system, X̄ is the average chain length, and Δ ≃ [3(I − 1)]1/2 is the reduced width of the chain-length distribution function. This means that, if the size of the model system and the shape of the chain-length distribution are kept constant, systems of larger average molecular weight equilibrate faster, a remarkable attribute of the EB Monte Carlo method. The simulation results obey the estimated scaling of t 0 with X̄, n, and Δ remarkably well in the range of chain lengths and polydispersities for which the premises of the analysis are not violated (mean chain lengths greater than C156 and polydispersity indices above about 1.07). Results for volumetric behavior, structure, and chain conformation at temperature T = 450 K and pressure P ranging from 1 to 800 atm are presented, using three different PE united atom models proposed in the recent literature. All three models are shown to overestimate the density by ca. 4% and also overestimate the stiffness of chains. The Yoon et al. model is in best agreement with experimental characteristic ratios. Simulation predictions for the structure factor and for the chain-length dependence of the density are in excellent agreement with experiment.