Bortel and Kochanowski
1. (20 points) Bortel and Kochanowski measured the dilute solution properties for a series of
high molecular weight poly(ethylene oxides) in 0.1 M HCl. The light scattering data for
one sample is given in the table, as Kc/R×108 mol/g. Construct a Zimm plot, and find Mw,
Rg, and B; take λ = 546 nm and n = 1.335.
a) How would you assess the solvent quality, based on B and based on the magnitude of
Rg?
θ º c = 1 mg/mL 1.5 mg/mL 2.0 mg/mL 2.5 mg/mL 3.0 mg/mL
45 93 95 104 110 115
60 112 115 120 126 129
75 129 134 139 144 150
90 146 153 158 162 167
105 162 167 170 174 182
120 175 179 184 188 192
135 184 189 191 199 203
b) If 20% of monomers of this polymer are charged (for example, if you copolymerize
poly(ethylene oxide) and poly(amine)), how will B change and how will this be
reflected in the Kc/R values for 1 M ionic strength solutions? Estimate the electrostatic
contribution to B.
2. (10 points) Prove that when ΔH = 0, no phase separation is possible (The sign of ΔG is not
enough, as we discussed in class).
3. (20 points) The Flory-Huggins parameter, χ depends on temperature in a complex way, but
it is also found to depend on the solvent composition for dilute solutions.
a. Why?
For solutions of linear polystyrene in cyclohexane, the interaction parameter
χ = 0.2+ 91/T + 0.3ϕ +0.15ϕ
was determined by R. Koningsveld et al., J. Polym. Sci. A-2 8, 1261(1970).
b. What is the critical temperature for a very high molar mass polystyrene in
cyclohexane with polymer volume fraction ϕ = 0.01?
c. Does the polystyrene/cyclohexane system have a UCST or an LCST?
4. (20 points). Draw and label a phase diagram for a polymer with N = 1000, and χ = 150/T.
Find the critical points. How do you know if it is a UCST or an LCST phase diagram?
What determines the binodal and the spinodal curves? How would you prove this phase
diagram experimentally? How does the phase diagram change if N = 500?
5. (10 points) On the axes below, sketch what you would expect to see for precise measurements
of Π/cRT vs. c for the following polystyrene/cyclohexane systems (B=0 at 35 ºC)
I M = 100,000 g/mol, T= 35 ºC
II M = 100,000 g/mol, T= 75 ºC
III M = 200,000 g/mol, T= 25 ºC
IV M = 50,000 g/mol, T= 75 ºC
Answer the following in 30 words or fewer:
6. (5 points) Light scattering is used to monitor a dilute solution of monomer
that is undergoing slow polymerization. At first, the intensity goes up with time at all
scattering angles, but later on, it actually begins to decrease at high angles while still
increasing at low angles
7. (5 points) Describe how B, v and χ are related
8. (5 points) Why do polymers phase separate?
9. (5 points) Name three ways to measure solvent quality experimentally