7) (a) Calculate the time scale of a solvent molecule, initially located at the center of a polymer's pervaded volume, to diffuse out of the pervaded volume. Assume the solvent molecule is the same size b as a monomer. (b) Use the Zimm model to show that the time scale for the polymer to diffuse out of the same volume is a factor of N longer than the solvent diffusion time. (c) Show that the ratio of the diffusion coefficients of the polymer and the solvent is N". (d) Explain why the ratio of time scales (part b) is reciprocally related to the ratio of diffusion coefficients (part c). 8) (a) Explain the difference between entangled and unentangled melts? (b) Explain the physical significance of the correlation length, in a semidilute solution. How is it related to for a semi-dilute polymer solution. (c) Suppose that a polymer has Kuhn length of 0.7 nm. What is the value of for an unentangled melt of these polymers? (d) In what type of melt, unentangled or entangled, do you expect polymers to have longer relaxation times? Please exaplain.