Question: please show work so i can understand how to do it for next time! thanks! 4. 1,4-Polyisoprene is a very important polymer industrially. Work from
4. 1,4-Polyisoprene is a very important polymer industrially. Work from L. J. Fetters et al. has studied the rheological properties for this polymer for several molecular weights, and determined that the plateau modulus is approximately Gc0.3MPa(M. Abdel-Goad et al., Macromolecules 2004, 37, 8135-8144). 1,4-Polyisoprene has a Kuhn length b=0.84nm, a Kuhn molar mass M0=120g/mol, and a mass density of =0.830g/cm3. (a) Sketch the plot of the stress relaxation modulus G(t) for this polymer (without solvent) from the glassy to viscous flow regimes. Note the positions of all of the following features approximately on your sketch (if they are present): Reptation time (rep), Rouse time (R), monomer relaxation time (0), entangled strand relaxation time (e), plateau modulus (Ge). You may assume Mn>Me. (b) Calculate the entanglement molecular weight (Me) of 1,4-Polyisoprene at 20C. (c) Repeat part (a) of this question if the molecular weight of the polymer is Mn=5300g/mol. Label the same values (if present). (d) 1,4-Polyisoprene has been vulcanized (i.e., crosslinked with sulfur) such that the number of Kuhn monomers between crosslinks is Ns40. Calculate the plateau modulus of this more rubbery material. Sketch G(t) just as in parts (a) and (c), remembering to label all values (if present)
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