Question $1(50$ pt$)$

Apply the group contribution method of Hoftyzer$-$Van Krevelen to determine the most suitable plasticizer for poly methyl methacrylate $($PMMA$)$ binder.

$($a$)$ Compute the solubility parameters

$($b$)$ The interaction radius $($R$0)$ for PMMA is $10.$ Based on this and your answer from part $($a$),$ identify which of the following plasticizers is most suitable for use with PMMA $($solubility parameters are given in units of $($:$(MJ{m}^{-3}{)}^{\frac{1}{2}}\}$ :

$\backslash$table$[[$Plasticizers$,{}_d,{}_p,{}_h$