$($Bonus $+5$ pts$)$ The plot below represents the spinodal curve for a polymer$-$solvent system

according to the Flory Huggins theory. Estimate $N$ for this polymer. What is the critical value

of $$ for this system? Estimate the critical temperature for this polymer$-$solvent system.

$($Bonus $+2\mathrm{.}5$ pts$)$ Assume your polymerization reaction went wrong and you obtained a

bimodal mixture of short $(N=100)$ and long $(N=5000)$ polymers. How can you utilize your

knowledge on FH theory on polymer solutions to separate$/$purify your polymer batch? Explain

briefly.

$($Bonus $+2\mathrm{.}5$ pts$)$ Flory$-$Huggins theory predicts the phase diagrams with upper$-$critical$-$

solution temperature $($UCST$)$ only. This is mainly due to the assumptions in the theory, such as

no volume change upon mixing, no composition dependence of $$ and mean$-$field$-$assumption.

In reality, many other types of phase diagrams exist. The diagrams below show some idealized

symmetric binodal curves where $$ is not composition dependent, i$.$e$.(),$ but $$ varies

differently with temperature. Match the phase diagrams, $T(),$ with corresponding $(T).$ Justify

your choices $($Note that A and E have essentially the same temperature trend$).$Flory$-$Huggins theory considers only the attractive interactions between the

molecules, therefore the interaction parameter has only the enthaplic part. Due to

volume change upon mixing, there is also entropy contribution to $\backslash$chi $.$ Experimentally it

was shown that

$=$

v where vo is the volume of the molecules $($~ $0\mathrm{.}1$

$0\mathrm{.}34$

$+$

o

$($

$$

$$

$$

$)$

$2$

$12$

kT

nm$3).$ What is the largest solubility parameter difference that allows polymer solutions

$($with polymer$$s degree of polymerization$=1000)$ to be miscible at room temperature?

$($Bonus $+5$ pts$)$ The plot below represents the spinodal curve for a polymer$-$solvent system according to the Flory Huggins theory. Estimate N for this polymer. What is the critical value of $$ for this system? Estimate the critical temperature for this polymer$-$solvent system.

$($Bonus $+2\mathrm{.}5$ pts$)$ Assume your polymerization reaction went wrong and you obtained a bimodal mixture of short $($N$=100)$ and long $($N$=5000)$ polymers. How can you utilize your knowledge on FH theory on polymer solutions to separate$/$purify your polymer batch? Explain briefly.

$($Bonus $+2\mathrm{.}5$ pts$)$ Flory$-$Huggins theory predicts the phase diagrams with upper$-$critical$-$ solution temperature $($UCST$)$ only. This is mainly due to the assumptions in the theory, such as no volume change upon mixing, no composition dependence of $\backslash$chi and mean$-$field$-$assumption. In reality, many other types of phase diagrams exist. The diagrams below show some idealized symmetric binodal curves where $\backslash$chi is not composition dependent, i$.$e$.\backslash$chi $!=\backslash$chi $(\backslash$Phi $),$ but $\backslash$chi varies differently with temperature. Match the phase diagrams, T$(\backslash$Phi $),$ with corresponding $\backslash$chi $($T$).$ Justify your choices $($Note that A and E have essentially the same temperature trend$).$

$->2->3->4->5->$