Question 1)

A student observed the following viscometer flow times in triplicate for various solutions of a narrow molecular weight PEG in water:

c (g/cm3) t1 (s) t2 (s) t3 (s)
0 242 242 243
0.0052 266 267 267
0.0188 331 333 332
0.0315 415 415 423
0.0553 595 592 588

(a) Determine the intrinsic viscosity of this polymer using both Huggins and Kraemer plots.

(b) What are the values of the constants k’ and k’’ for the Huggins and Kraemer equations?

(c) Given that for PEG the value for K is known to be 0.0125 and a = 0.78 what is the molecular weight of this polymer?

Question 2)

The following dependence of Tg on M for poly(dimethylsiloxane) was determined:
Mn Tg (K)
240 123.4
310 129.1
530 137.4
630 139.4
810 141.2
990 143.3
1290 144.8
1630 146.1
2260 147.5
2460 148
2920 148.3
4080 149.2
4880 148.8
6330 149.3
7720 149.5
10060 149.5
12290 149.4
14750 149.7
18250 149.8
21390 149.8
25460 149.7

(a) What is the value of Tg for this polymer at infinite molecular weight?

(b) Using the sol-gel reaction shown in the notes for step-growth polymerization, and using the appropriate end-groups, what is the value of Tg for a poly(dimethylsiloxane) with a degree of
polymerization = 47?

(d) An unkown polymer was investigated and the molecular weight values, intrinsic viscosity and zero-shear melt-viscosity (?0) determined. The following numbers were obtained:

Sample Mn Mw [?] ?0
1 17800 19000 0.126 1.70 x103
2 58300 61800 0.289 6.18 x104
3 164400 171000 0.626 1.06 x106
4 339100 393400 1.148 8.51 x106
5 985500 1015000 2.291 1.04 x109

Determine the Mark-Houwink-Sakurada constants for this polymer.

(e) Was the polymer entangled in the melt?

Question 3)
Consider the polymerization of the following monomers:

(a) Draw the repeat unit of the resulting polymer.

(b) Identify the two structural units comprising the repeat unit.

(c) Plot the Mn of the polymer vs. the extent of reaction, where the extent of reaction increases from 0 to 0.95 in intervals of 0.05, and extend the plot include data points for an extent of
reaction = 0.96, 0.97, 0.98, 0.99, and 0.995.

(d) What is the extent of reaction when the molecular weight reaches 30 000 g/mol?

(e) State two conditions that must be ensured for a step growth polymerization to reach high conversion.

Question 4)
The anionic polymerization of styrene was performed using a 1.38 mol/L solution of styrene in cyclohexane at 40 °C. The polymerization was initiated by 100×10-5 mol/L of butyl lithium and a
kinetic order dependence on initiator of 0.5 was observed with an apparent rate constant of 2.4×10-2 observed. The polymerization was run from t = 0 to t = 8000 and a data point collected every t
= 200 intervals.

Using only this information:

(i) Plot [M] vs. time for this reaction.

(ii) Plot Mn vs. p for this reaction.

(iii) Plot PDI vs. p for this reaction.

(iv) Plot ln([M]0/[M]t) vs. time for this reaction.

(v) Consider a scenario when a student shows you the plots for the correct answers to Question 4 parts (ii) and (iv) that they obtained in an experiment. What can you say about the level of
“livingness” and control in this polymerization based on these plots?

(vi) What would it mean if the slope in the plot for Question 4, part v curved downward?

Question 5)

Suddaby et al. (Macromolecules 1997 702-713) determined the chain transfer constant of COBF (a cobalt based chain transfer agent) for the polymerization of methyl methacrylate and styrene and
recorded the following results:

MMA
run [COBF]/[M] x 109 Mn
1 0 970179
2 261 11822
3 522 6980
4 1044 4173
5 2088 2210
STYRENE
run [COBF]/[M] x 109 Mn
1 0 69886
2 5106 10118
3 10212 6604
4 15318 4376
5 20423 3441

(i) Determine the chain transfer constant for COBF for both polymerizations.

(ii) Compare these values to those for n-butyl mercaptan for the same monomers and state qualitatively which chain transfer agent you would choose to produce the lowest molecular weight species.
Question 6)
(a) Draw the mechanism for the first monomer additions of ?-caprolactone to the POSS-diol used by Mather in the viscoelasticity paper discussed in class. For full marks show the activation of the
catalyst.

(b) Draw the generic equilibrium for an ATRP polymerization. Make sure to include all rate constants.

(c) Use this equilibrium to derive an equation for the rate of an ATRP polymerization.
(d) While nitroxide mediated polymerization has been shown to be effective for the polymerization of styrene, it is less so for methacrylate monomers. State why that is, and draw the mechanism for
any side-reactions that you use in your answer.
Question 7.

The compositions of a styrene/acrylonitrile copolymerization are given below:

Fa Fb fa fb
0.65 0.35 0.69 0.31
0.58 0.42 0.52 0.48
0.55 0.45 0.42 0.58
0.52 0.48 0.31 0.69
a) Use the Kelen-Tudos method to determine the reactivity ratios for this polymerization.

b) Based on your answer to part 7a) plot the fraction of styrene in the copolymer vs the fraction of styrene in the feed over the whole composition range (0-1 in 0.01 steps) and on the same graph
plot the copolymer compositions given by calculating the reactivity ratios based on the scheme of Alfrey and Price with the values given in the notes..

Question 8.

Consider the following Fisher diagram for an isotactic polymerization that has proceeded with two stereoerrors:

(a) Perform an analysis of stereoregularity of this polymer w.r.t .dyad and triad sequences.

(b) Did this polymerization occur with catalyst site control or chain end control, and why?

(c) Draw the Fisher diagram for the same polymerization with opposite stereocontrol to the correct answer to part (b), and perform the analysis of dyad and trad stereoregularity on the polymer.
Question 9.

The results of light scattering studies for a styrene copolymer in toluene solution using a 436 nm light source were as follows:
c x 103 (g/cm3) R’(?) x 104 (cm-1)
15° 45° 75°
0.20 1.91 1.47 1.01
0.40 3.55 2.78 1.95
0.60 4.95 3.94 2.80
0.80 6.16 4.96 3.59
1.00 7.19 5.87 4.31

The refractive index of toluene is 1.4976 and the specific refractive index increment of the polymer in toluene is 0.1263 cm3/g.

(a) What is the molecular weight of the polymer?

(b) What is the radius of gyration of the copolymer?
Hint: A useful way to calculate Rg2 is found from the line of a Zimm Plot in the limiting case of c =0. Here;

(c) Calculate the second virial coefficient, A2.

(d) Is toluene a good or poor solvent for the polymer based on your answer to part (c) (Include a rationalization for your answer?
Question 10.

Plot on a single graph, the composition dependence of the free energy of mixing per site (normalized by the thermal energy) of a symmetric polymer blend with NA = NB = 100 using ? = 0, 0.01, 0.02,
0.03, 0.04. Plot the x-axis from a volume fraction of A from 0.01 to 0.99 in 0.01 increments. Which values of ? make the blends miscible in all proportions? Justify your answer.