abstract: It has long been known that the variation of density and stiffness between different species signifies changes in the degree of entanglement of long-chain flexible polymer melts. An overlooked point is that, as chain length N increases, the contour length density (or mass density), and the stiffness of the system (or characteristic ratio), increase, until they reach chain length-independent values (large N asymptotic regime). Here we examine how the variation of these quantities, as chain length increases, is related with the onset of entanglements, and the associated changes in the underlying system topology. Our analysis is based on the reduction of Dissipative Particle Dynamics trajectories of a coarse-grained polymer melt to Primitive Paths (PPs). The latter are generated by using the CReTA algorithm, which constructs PPs by reducing chain conformations to the corresponding shortest paths. We will show that, as N increases, the density and stiffness exhibit an Ndependence which leads to larger chain overlap in the short, than in the long chain regime. For large N, chain overlap falls gradually to the scaling law expected of long-chain systems. At the level of PPs, the increasing overlap leads to a crossover in the system topology which can be described as a gradual transformation of PP conformations from thin rods (short chains), to random walks (long chains), A simple scaling model predicts that this transformation leads to a Rouse to reptation transition in dynamics and rheology. The entanglement molecular weight (MW), Me is interpreted as the crossover length of this transition. The predicted critical to entanglement MW ratio, Mc Me is one, which, though small, is compatible with packing length independence and the suppression of contour length fluctuations within the model. The comparison between a dynamical and a static topological analysis reveals a slowing down of Rouse modes, which is maximum at the length scale where the underlying system of PPs appears as a network of topological constraints.
References : Macromolecules 42, 7474, (2009) ;ibid. 42, 7485, (2009) Mariel