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1. For a particular polymer solution there are 1000 solvent molecules for each solute (polymer) macromolecule. The ratio of molar volumes of every polymer molecule to solvent molecule is 1000. The polymer-solvent interaction parameter has the form X₁ = (AAW₁)-(A'AW.). (a) As a basis for this problem, take an aliquot of this polymer solution that contains exactly 2000 reference- volume-sized units. Write the numerical values for ni, nz, v₁, v2 where n indicates number of molecules and v is volume fraction. (2 points) (b) Using the numerical values from (a), write an expression for the total free energy of mixing, AF, for the selected aliquot (2 points) (c) Write separate expressions for 4S, 4Sm and AHM. (2 points) (d) Explain the origin of the second term in Equation above. (2 points) The ratio of molecular volumes of polymer and solvent in the solution described above is suddenly changed to 500 by a process which dimerizes the solvent (connect every two original solvent molecules together into a new two-piece. solvent molecule). Assume A' in Equation is equal to zero and answer the following questions for this new solution. (e) Write the numerical values of ni, n2, V₁, V2 for this new solution, keeping the aliquot volume the same as above, i.e. 2000 reference-volume-sized units. (2 points) (f) Write an expression for 4S for this new case and compare to your answer in part (c) above. (2 points) (g) Write an expression for AHM for this new case and compare to your answer in part (c) above. (2 points) (h) Let A'=0 for both solution, i.e. the original one with monomeric solvent and the second one containing dimeric solvent molecules. Use your free energy expressions to defend the statement: "In a side-by-side comparison, the solution with the dimerized solvent will become cloudy first as temperature is lowered from a high value, Th, at which both solutions are optically clear and homogeneous. (2 points)