What controls the Young's modulus in the rubbery regime of an amorphous polymer?

Sliding between short segments of polymer chains

Stretching of molecular bonds

Melting of secondary bands, and an increase in free volume

Second derivative of the energy-separation curve, E∝d2Udϵ2

Changes in entropy associated with changes in molecular configuration, E=−TΩd2Sdϵ2=3nvkbT

Changes in entropy associated with changes in molecular configuration, E=−TÙd2Sdϵ2=3nvkbT

no

In the rubbery regime of an amorphous polymer, Young's modulus is mainly influenced by the sliding between short segments of polymer chains. This is because in this regime, the polymer chains are able to move and slide past each other, allowing for deformation without significant stretching or breaking of the molecular bonds.

While stretching of molecular bonds does play a role in determining Young's modulus, it is more prominent in the glassy regime of the polymer where the chains are rigid and unable to slide. In the rubbery regime, the molecular bonds are not significantly stretched, and the main deformation mechanism is the sliding motion.

The melting of secondary bands and an increase in free volume can also affect the Young's modulus of an amorphous polymer in the rubbery regime. The presence of secondary bonds, such as Van der Waals forces or hydrogen bonds, can contribute to the stiffness of the polymer. When these secondary bonds are melted, it leads to a decrease in the stiffness and an increase in free volume, resulting in a lower Young's modulus.

The other two explanations you provided (the second derivative of the energy-separation curve and changes in entropy associated with changes in molecular configuration) are not specifically related to the rubbery regime of an amorphous polymer and may have more general applicability in other contexts.