(Solved): A block of polyisoprene rubber with a square cross-sectional area of \( 25 \mathrm{~mm}^{2} \) and l ...

A block of polyisoprene rubber with a square cross-sectional area of \( 25 \mathrm{~mm}^{2} \) and length of 40 cm is stretched using a tensile force of 10 N . The tensile strain on the rubber is 0.20. The sides of the block shorten the same amount because of the square crosssection. The molar density of the polyisoprene is \( 9.1 \times 10^{-5} \mathrm{~mol} / \mathrm{cm}^{3} \). a. Calculate the work per unit volume and the total work done on the rubber if the stress was applied at room temperature. b. Estimate the molecular weight between crosslinks for this sample. c. If the Young's modulus of this sample is a good estimate of the plateau shear modulus and the density of polyisoprene is \( 0.91 \mathrm{~g} / \mathrm{cm}^{3} \), what would be the entanglement molecular weight for this sample? d. Find the actual entanglement molecular weight of polyisoprene. Is the Young's modulus an over-estimate or under-estimate of the plateau shear modulus?