M2 Reptation (De Gennes / Doi-Edwards Theory)

Topic

The fact that the polymer's molecular weight exceeds the critical molecular weight established by another model in this set confines each molecular chain within a tube formed by the neighboring molecular chains that entangle it; this tube restricts the chain to moving almost exclusively along its own contour, preventing it from laterally crossing the neighboring chains that form the tube's walls—much like how those same neighboring chains restrict their relative movement through these topological entanglements, a phenomenon described in detail by another model in this set. Consequently, if the polymer's molecular weight significantly exceeds this critical threshold, the molecular chain becomes confined within a longer and narrower tube.

Confined within this tube, the molecular chain diffuses by snaking along its own contour, sliding one end forward and gradually exploring new configurations beyond the original tube segment until it eventually leaves the original tube entirely; this process—reptation, or the snaking movement of the molecular chain along its tube's contour—is precisely what another model in this set predicts for the polymer under sustained load. The time it takes for the molecular chain to completely exit the original tube via reptation defines the chain's de Gennes reptation time. Consequently, because the chain is confined within a longer tube due to its higher molecular weight, this de Gennes reptation time is longer. Thus, this model—introduced via the concepts of the "tube" and "reptation"—explains (through the de Gennes reptation time) the strongly non-linear empirical scaling of this polymer melt's viscosity with its molecular weight; this scaling is far more pronounced than the linear scaling predicted by another model in this set for the unentangled regime below the critical molecular weight. Above this critical molecular weight, each additional molecular chain not only contributes its own length to the de Gennes reptation time but also lengthens the tube in which that chain is confined; it is this dual contribution that produces the strongly non-linear scaling. The fact that reptation serves as the underlying dynamic mechanism for both the chain slippage under sustained load (described by another model in this set) and the thermoplastic behavior (described by yet another model in this set) means that, fundamentally, both phenomena depend on the same de Gennes reptation time that characterized the model at the outset.

ID:4479