Page 126 - Carrahers_Polymer_Chemistry,_Eighth_Edition

Molecular Weight of Polymers 89

Specific viscosity: Difference between the relative viscosity and 1.
Weight-average molecular weight: Second power average of molecular weight; dependent on
the size of the particular chains.
Zimm plot: Type of double extrapolation used to determine the weight-average molecular
weight in light-scattering photometry.

EXERCISES

1. Which of the following is polydisperse with respect to chain length: (a) casein, (b) commercial
polystyrene, (c) paraffin wax, (d) cellulose, or (e) Hevea brasiliensis?

2. If the number average molecular weight for LDPE is 1.4 million, what is the corresponding
average chain length?
3. What are the number- and weight-average molecular weights for a mixture of fi ve molecules
6
6
6
6
each having the following molecular weights: 1.25 × 10 ; 1.35 × 10 ; 1.5 × 10 ; 1.75 × 10 ; and
6
2.00 × 10 ?
4. What is the most probable value for the polydispersity index for (a) a monodisperse polymer and
(b) a polydisperse polymer synthesized by a condensation technique?
5. List in increasing values: M , M , M , and M .
z n w v
6. Which of the following provides an absolute measure of the molecular weight of polymers:
(a) viscometry, (b) cryometry, (c) osmometry, (d) light-scattering photometry, and (e) GCP?
7. What is the relationship between the intrinsic viscosity or limiting viscosity number and aver-
age molecular weight?
8. What molecular weight determination techniques can be used to fractionate polydisperse
polymers?
9. Which of the following techniques yield a number-average molecular weight: (a) viscometry,
(b) light-scattering photometry, (c) ultracentrifugation, (e) osmometry, (e) ebulliometry, or
(f) cryometry?
10. What kind of molecular weight do you generally get from light-scattering photometry?
11. What is the value of the exponent a in the Mark–Houwink equation for polymers in theta
solvents?
12. How many amino groups are present in each molecule of nylon-66 made from an excess of
hexamethylenediamine?
13. What is the value of the exponent in the Mark–Houwink equation for a rigid rod?
3
–2
14. If the value of K and a in the Mark–Houwink equation are 1 × 10 cm /g and 0.5, respectively,
what is the average molecular weight of a polymer whose solution has an intrinsic viscosity of
150 cc/g?
15. Which polymer of ethylene will have the highest molecular weight: (a) a trimer, (b) an oligomer,
or (c) a UHMWPE?
16. What is a Zimm plot?
17. What type of molecular weight average, M or M , is based on colligative properties?
n w
18. What principle is used in the determination of molecular weight by vapor pressure
osmometry?
19. Why does the melt viscosity increase faster with molecular weight increase than with other
properties such as tensile strength?
20. In spite of the high cost of processing, ultrahigh molecular weight polyethylene is used for mak-
ing trash cans and other durable goods. Why?
21. Under what conditions are the weight- and number-average molecular weight the same.
22. What is the driving force for polymer solubility?
23. What are the colligative methods for measuring molecular weight and what kind of molecular
weight do you get?
24. What is the advantage of using viscometry to measure molecular weight?

9/14/2010 3:38:01 PM
K10478.indb 89 9/14/2010 3:38:01 PM
K10478.indb 89