The Onsager theory for the isotropic-anisotropic phase separation in a solution of rodlike particles is extended to the case of mixtures of such particles with different lengths. The concentration, composition, order parameters, and orientation dependent thermodynamic quantities of the coexisting phases are calculated for the case of a mixture of rods of two different lengths for different length ratios. It is found that there is a significantly higher mole fraction of the longer rods in the anisotropic phase than in the isotropic phase. The order parameter of the longer rods is higher than in the one component case, whereas the order parameter of the shorter rods first increases and then decreases as the mole fraction of the longer rods is increased. All these features are accentuated as the length ratio of the two kinds of rods increases.
A methodology for estimating the entanglement density in the amorphous phase of semicrystalline polyolefins was developed. The method is based on the analysis of the density of physical network junctions in the amorphous phase by 1 H NMR T 2 relaxation experiments. The density of the entanglement network was estimated for melt-and high-pressure-crystallized highdensity polyethylenes (HDPEs) at temperatures close to and gradually approaching melting. Its value is lower for high-pressure-crystallized HDPE than for the same melt-crystallized polymer. The network of entanglements is characterized by the fraction of entangled network chains, the weight-average molecular weight of the network chains between apparent chain entanglements, M e , and the volume average density of apparent chain entanglements. The entanglement network was studied in a series of low-and high-molecular-weight HDPEs and bimodal HDPE samples with different molecular weight characteristics and densities controlled by different contents of the 1-butene comonomer. It turns out that the molecular weight characteristics of the HDPEs influence the entanglement network. The fraction of network chains and the average density of apparent chain entanglements decrease with decreasing molecular weight M n due to the "dilution" effect caused by disentangled chain-end segments increasing the M e . The current methodology is of interest for studying the effect of crystallization conditions, molecular structures, and short-chain branches on phase composition, melting behavior, and chain entanglements in the amorphous phase of polyolefins. The method allows estimation of the fraction of network chains, which potentially can form tie-chain segments during deformation. The effect of short-chain branches and molecular weight characteristics on the creep response of polyolefins is discussed.
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