You have three vials containing poly$($methylmethacrylate$)$ PMMA $($characteristic ratio $C_{}=$

$8\mathrm{.}65)$ in butyl chloride at $35\mathrm{.}4C($a $-$solvent for PMMA under these conditions$).$

Sample A: $0\mathrm{.}1$ moles of pure, monodisperse $10,000\frac{g}{m}ol$ PMMA

Sample B: $0\mathrm{.}7$ moles of pure, monodisperse $90,000\frac{g}{m}ol$ PMMA

Sample C: $0\mathrm{.}1$ moles of pure, monodisperse $500,000\frac{g}{m}ol$ PMMA.

a$.)$ You measure the radius of gyration of each PMMA component in each solution. The

radius of gyration of sample $B$ is $7\mathrm{.}84nm$ What is the $R_g$ of Sample A$?$

b$.)$ What is the mean square end$-$to$-$end distance of a molecule of Sample C$?$

c$.)$ What is the statistical segment length of Sample B$?$

d$.)$ The polymer from Sample B is dried and then re$-$dissolved in toluene at $25C,$ a good

solvent for PMMA. Explain qualitatively the changes that take place in the mean square

end$-$to$-$end distance of the Sample $B$ in toluene at $25C$ relative to its mean square end$-$

to$-$end distance in butyl chloride at $36C.$

e$.)$ The solvent is removed from Sample $B$ by evaporation at $150C,$ above the glass

transition temperature of PMMA to form a polymer "melt". What value of Rg will be

found?