QUESTION $1$: $(35$ pts$)$:

$($a$)(6$ pts$)$ Describe an experiment from which you can estimate the Flory interaction parameter, $,$ for a given polymer and solvent?

$($b$)(12$ pts$)$ Flory$-$Huggins theory considers only the attractive interactions between the molecules, therefore, the interaction parameter has only the enthalpy part. Due to volume change upon mixing, there is also entropy contribution to $.$ Experimentally, it was shown that $=0\mathrm{.}34+\frac{v_o}{kT}({}_1-{}_2{)}^2$ where $v_o$ is the volume of the molecules $n{m}^3).$ What is the largest solubility parameter difference that allows polymer solutions $($with polymer's degree of polymerization $=1000)$ to be miscible at room temperature? Take Boltzmann constant, $k=1\mathrm{.}38{10}^{-23}\frac{J}{K}.$

$($c$)(4$ pts$)$ Based on your finding, what solvents listed in Table $7\mathrm{.}1($attached$)$ can dissolve polystyrene with degree of polymerization $1000.$

$($d$)(13$ pts$)$ With the help of a sketch, explain briefly how osmotic pressure measurement work for polymer solutions. The figure below shows the osmotic pressure data obtained for polystyrene in cyclohexane at three different temperatures. The straight lines are linear regression fits. Estimate the molecular weight of PS and the second virial coefficients at each temperature. Is this a number or a weight average molecular weight? At which temperature, the chains are swollen with respect to the ideal chain conformation.Describe an experiment from which you can estimate the Flory interaction

parameter, $\backslash$chi $,$ for a given polymer and solvent?

$($b$)(12$ pts$)$ Flory$-$Huggins theory considers only the attractive interactions between the

molecules, therefore, the interaction parameter has only the enthalpy 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?

Take Boltzmann constant, k$=1\mathrm{.}38$x$10-23$ J$/$K$.$

$($c$)(4$ pts$)$ Based on your finding, what solvents listed in Table $7\mathrm{.}1($attached$)$ can dissolve

polystyrene with degree of polymerization $1000.$

$($ d$)(13$ pts$)$ With the help of a sketch, explain briefly how osmotic pressure measurement

work for polymer solutions. The figure below shows the osmotic pressure data obtained

for polystyrene in cyclohexane at three different temperatures. The straight lines are

linear regression fits. Estimate the molecular weight of PS and the second virial

coefficients at each temperature. Is this a number or a weight average molecular weight?

At which temperature, the chains are swollen with respect to the ideal chain

conformation.