Calculate the full phase diagram $($composition versus temperature$)$ for $M_n=$

$1000\frac{g}{m}ol$ poly$($styrene$)($PS$)$ in n$-$hexane $($H$)$ including the binodal and spinodal curves.

Assume the PI is monodisperse, i$.$e$.$ PDI $=1.$

Suggested strategy:

Start by estimating $(T)$ using solubility parameters followed by calculating the

critical temperature $(T_c)$ and critical composition $({}_c).$ Be sure to use the solvent

molar volume to determine the degree of polymerization NPS $($number of repeat

units with the same molar volume$)$ when you make the calculations. Data: ${}_{PS}=$

$1\mathrm{.}04\frac{g}{c}{m}^3$ and ${}_H=0\mathrm{.}66\frac{g}{c}{m}^3$ and you may neglect thermal expansion.

Compute the spinodal compositions as a function of temperature for $T_{c}100C{T}_c\frac{G_m}{R}T(N_1{N}_2)\frac{G_m}{R}TT.$

Determine the binodal $(equilibrium)$ curve between $T_c$ and about $100C$ below

$T_c.$ Note, when $\frac{G_m}{R}T$ becomes asymmetric $(N_1{N}_2),$ the binodal curve $is$

most easily determined $by$ printing plots $of\frac{G_m}{R}Tvs$ volume fraction $of$

polymer $at$ various temperatures and using a double tangent construction.

Alternatively, the solutions $at$ each temperature can $be$ determined numerically

using the Gibbs free energy $of$ mixing.