Question $1(50pt)$

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

$($a$)$ Compute the solubitity 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 sutable for use with PMMA $($solubility parameters are given in units of $($:$(M*m^{-3}{)}^{12}$