Problem $38.0\mathrm{.}1$ grams of $M=2{10}^6\frac{g}{m}ol$ polystyrene is dissolved in $1$ liter of

cyclohexane at $34C,$ which is a theta $()$ solvent.

a$.$ Determine whether this solution is in the dilute limit$.$

b$.$ A light scattering instrument can resolve the angles $0<<150$ with ${}_0=488nm.$

Plot the relative intensity on a logarithmic basis as a function of $q$ that would be

obtained from this instrument. Assume $n_s=1\mathrm{.}42.$ Note that because the concentratior

is constant and the solvent is a theta solvent, $I(q)P(q).$

c$.$ The temperature is rapidly lowered resulting in an increase in $.$ Assuming the

polystyrene molecules collapse into dense $(1\frac{g}{c}{m}^3)$ spheres, plot $I(q)$ on the same

plot. Assume each sphere contains only one polymer. Hint: Ignore the second virial

coefficient $($i$.$e$.,$ assume it is zero$).$