answer part bThe data table below shows contact angle measurements recorded using a series of liquids on a polyethylene $($PE$)$ substrate.

$($a$)$ On graph paper, construct a Zisman plot to graphical estimate the critical surface tension $({}_c)$ of the PE substrate.

$($b$)$ The PE substrate undergoes a surface treatment, and the critical surface tension is now determined to be $18mN{m}^{-1}.$ If the contact angle made by bromonaphthalene is measured to be $66,$ estimate the solid$-$liquid interfacial tension $({}_{sl})$ of the modified substrate.

$\backslash$table$[[$Liquid$,$Surface tension $\backslash$gamma $($mNm$^(-1)),$Contact angle $(\backslash$deg $)],[$DMSO$,44\mathrm{.}1,47\mathrm{.}6],[$Ethylene glycol,$48,77\mathrm{.}2],[$Dilodomethane$,50\mathrm{.}8,44\mathrm{.}1],[$Glycerol$,63\mathrm{.}1,87\mathrm{.}2]]$

$[10$ marks$]$