Problem $27.$ This problem involves plotting a phase diagram for mixtures of

poly$($isobutylene$)($PIB$)$ and $1,4-$poly$($butadiene$)($PB$)$ in the melt state. For simplicity

assume equal molecular weights and monodisperse polymers, $M_{\frac{?}{PI}B}=M_{PB},$ and a

common density of $=0\mathrm{.}87\frac{g}{c}{m}^3.$

Determine the molecular weight required to place the critical temperature at $100C.$

Calculate the spinodal $($stability$)$ curve and plot this on a Figure with $$Cdel$\frac{G_m}{d}el{}_i{G}_{m}25$

$C.$

Calculate the binodal $(equilibrium)$ curve and include this $in$ the phase diagram.

Hint: This problem $is$ easily completed using a numerical solution for del$\frac{G_m}{d}el{}_i$ based $on$

the symmetric form $of{G}_m.$