Onset of Entanglements Revisited. Topological Analysis

In a series of two papers, we study the onset of entanglements and the transition from Rouse-type to reptation dynamics, in the context of dissipative particle dynamics (DPD) simulations of a coarse-grained polymer melt. A set of monodisperse systems with increasing chain length is examined. We consider both static and dynamic aspects of the problem. Part I, this paper, deals with the continuous change of the polymer topology, from unentangled (short chains), to entangled (long chains). We show that as chain length increases the rate of increase of chain overlap increases asymptotically. It becomes constant when chains are sufficiently long, and in this regime a long chain topology is established. Next, we examine the onset by probing static length scales at the level of primitive paths (PPs). A simple scaling model based on a transformation of PPs from thin rods (short chains) to random walks (RWs) (long chains) is discussed qualitatively and quantitatively. The model predicts a crossover in the underlying topology, which leads to a Rouse to reptation transition in dynamics when PP conformations change from rods to to RWs. The entanglement molecular weight is interpreted as the crossover length of this transition. The predicted M c/M e ratio is one, which, though small, is compatible with packing length independence and the suppression of contour length fluctuations within the model. Part II, the following paper (DOI 10.1021/ma9011329), deals with dynamic aspects of the onset of entanglements, making possible a comparison between static and dynamic length scales.