Solution (source code)

= Solution

This is the second printed “(vi)”, concerning solvent <temperature>. \b[The coil is expected to expand, so its <radius of gyration> increases.] For the usual upper-critical-solution-temperature behavior of polystyrene in cyclohexane, heating above the stated theta condition improves <solvent quality>. Effective repulsion between segments favors more expanded conformations than the ideal coil.

In a <Flory–Huggins solution theory> description, the theta condition corresponds approximately to interaction parameter $\chi=1/2$, whereas a <good solvent> has a positive effective <excluded volume>. The asymptotic size dependence crosses toward $R_g\propto N^\nu$ with $\nu$ near $0.59$ for a flexible chain in three dimensions. These scaling ideas establish the expected direction, not a numerical expansion factor for a ten-degree <temperature> change. Its value would require measured solvent-interaction data or a calibrated crossover model.