E3 Entanglements and Critical Molecular Weight

Topic

When the molecular weight of this polymer—the same molecular weight established by another model in this set based on the polymer's chain-length distribution—exceeds a critical molecular weight specific to the polymer, topological entanglements arise between neighboring molecular chains: any molecular chain long enough to surpass this critical molecular weight (along with its neighbors) becomes physically trapped among those neighboring chains, without any chemical cross-linking binding them together. The extent to which this molecular weight exceeds the critical molecular weight determines the number of such topological entanglements per molecular chain; consequently, a greater excess results in a higher number of entanglements.

According to network theory applied to these topological entanglements, the number of entanglements per molecular chain determines the polymer's rubbery plateau modulus: within this theoretical framework, each topological entanglement functions analogously to a chemical cross-link in a permanent network, physically restricting the relative movement of the neighboring molecular chains it entraps. Thus, a higher number of topological entanglements per molecular chain results in a correspondingly higher rubbery plateau modulus. Thus, in this model—which was introduced by considering topological entanglements and the rubbery plateau modulus—this critical molecular weight establishes the boundary between two distinct dynamic regimes for the polymer: below this critical molecular weight, and lacking sufficient topological entanglements between neighboring chains, the polymer moves according to the Rouse regime (described in greater detail by another model in this set); conversely, above this critical molecular weight, with each molecular chain trapped by topological entanglements with its neighbors, the polymer moves via reptation—a regime also anticipated by a different model in this set. Consequently, when the polymer's molecular weight exceeds this critical threshold, it leaves the entanglement-free Rouse regime and shifts to movement governed by the reptation regime.

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