E6 Base Mechanical Properties

Topic

The elastic modulus of this polymer changes by several orders of magnitude across three distinct regimes, depending on the polymer's temperature: the glassy regime, where the polymer behaves as a rigid solid with a high elastic modulus; the rubbery regime, where the modulus drops abruptly to a much lower value but remains stable across a plateau; and the melt regime, where the polymer flows and the elastic modulus loses the meaning it held in the previous two regimes. As the polymer's temperature rises and crosses the boundaries between these regimes, the elastic modulus drops correspondingly at each of these order-of-magnitude transitions.

Within the rubbery regime, the polymer's topological entanglement density—the same density established by another model in this set for molecular weights above the critical threshold—determines the rubbery plateau modulus according to network theory: the more topological entanglements per molecular chain supported by this transient network, the greater the network's resistance to deformation and, consequently, the higher the rubbery plateau modulus. Conversely, a lower topological entanglement density—associated with a molecular weight closer to the critical value—results in a lower rubbery plateau modulus. Thus, this model—characterized by the elastic modulus and the rubbery plateau modulus introduced at the outset—also describes two specific cases of this same fundamental mechanical behavior: when the polymer exists as a block copolymer (comprising two distinct types of molecular segments alternating within a single molecular chain), its elastic modulus follows a rule of mixtures conceptually analogous to that used by another model—designed for fiber-reinforced composites—to combine the moduli of its various components; furthermore, within this rubbery regime, the relationship between the applied stress and the resulting elongation follows, to a first approximation, a Neo-Hookean stress-elongation relationship—the same relationship described in greater detail by another model in this set, based on the entropic elasticity of the entangled molecular chains. The fact that this rubbery plateau modulus—determined here by the density of topological entanglements—is identical to the modulus appearing in that Neo-Hookean stress-elongation relationship implies that, fundamentally, both models describe the same elastic behavior of this rubbery regime from two complementary perspectives.

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