On Chain Statistics and Entanglement of Flexible Linear Polymer Melts

A starting point to understand chain entanglement is to thoroughly examine chain statistical behavior. Focusing on the most familiar linear flexible polymers, we show based on the literature data that (a) at the same number n of backbone bonds most flexible linear polymers have comparable coil sizes and are similarly flexible in spite of widely varying chain thickness and (b) there are fewer chains to fill up a given volume if they are of larger chain thickness. Many models have been proposed to relate the onset entanglement molecular weight M e or M c to chain conformational characteristics. The specific predictions of these models frequently find agreement with various subsets of experimental data, but they have often been regarded to be incompatible with each other because they are derived from different physical considerations. In the present work, we compare the theoretical predictions against the extensively available experimental data on either M e or M c . The following conclusions emerge from the literature data: (a) chain thickness, not stiffness, correlates with M e in agreement with the packing model for over one hundred flexible linear polymers; (b) several other models appear to provide correlations of lesser quality for M c, to which the packing model does not apply well. However, the uniqueness of the physics controlling M c cannot be demonstrated since the percolation model, the binary contact model and the orientational correlation model all anticipate some trends in crude agreement with the limited literature data on M c .