1. Batch 1 of nearly monodisperse flexible polymer A has a molecular weight of 25 kg/mol, a statistical segment length of 0.7 nm and a monomer molecular weight of 125 g/mol. Batch 2 of the same, nearly monodisperse polymer has a molecular weight of 400 kg/mol. Polymer A has a density p of 900 kg/m. a.) Compute the radius of gyration of a chain of batch 1 of polymer A in the melt. b.) A single chain of batch 2 of molten polymer A is stretched. The Helmholtz free energy A(r) = U(r) - TS(r) where r is the distance between the ends of the chain. The force f(r) on the ends of the chain is given by: f(r) = au or T,V -T Dor T,V Which of the terms, U/or or S/or, is more significant in the expression for f(r) above? Why? c.) Outline the steps needed to obtain Helmhotz free energy (A(r)) from a microscopic model of the chain deformation using the Gaussian approximation. d.) A(r) depends on r as A(r) = Hr 2 where the coefficient H is constant at constant T for a given polymer chain. i.) ii.) What is the ratio of H at 150C to that at 30C assuming that polymer A is molten at both temperatures? What is the ratio of H for batch 2 of polymer A to H for batch 1 of polymer A at 30C.