Rubbery Plateau and Entanglements

The area above the glass transition temperature (Tg) and below the melt is known as the rubbery plateau. The appearance of a rubbery plateau is the result of entanglements or crosslinks. Both the width of this region as well as the properties in this region depend on the molecular weight between entanglements (Me) or crosslinks. Only polymers that are sufficiently long can form stable, flow restricting entanglements. A good analogy is a bowl of spaghetti. When the individual strands of spaghetti are short, they can be easily separated, whereas long strands are very diffcult to separate from one the other due to the entanglements (knots). The rubbery plateau modulus, Gp, is inversely proportional to the molecular weight between the entanglements, Me:

Gp ≅ ρ R T / Me

where Gp is the shear storage modulus of the plateau region at a specific temperature T, ρ is the polymer density, and R is the gas constant.

The rubbery plateau is also related to the degree of crystallinity in a material, that is, the temperature behavior of the modulus of a semicrystalline polymer is qualitativley similar to that of a high molecular weight amorphous polymer, only the modulus is typically higher in the secondary plateau due to the reinforcement effect of the crystalline domains dispersed in the amorphous rubbery phase above the Tg but below the melting point (Tm).

Modulus vs. Temperature

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  • Summary

    Rubbery Plateau

    The appearance of a rubbery plateau is the result of entanglements or crosslinks.

  • Amorphous Polymers

  • Only polymers that are sufficiently long can form stable, flow restricting entanglements.

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