FloryStarProof
This problem deals with controlling polydispersity and enhancing molecular weight in
condensation polymers. If one is willing to have a “star polymer” rather than a linear one,
then condensation polymerization can actually produce high molecular weights and
reasonably sharp fractions. Consider polymerization of AB (e.g., a hydroxyacid like
HOOC-(CH2)6-COOH) in the presence of 0.1 mol% of a star functional (e.g., something
like this six-functional alcohol below).
We find that the expression we had for mole fraction of linear polymers, xi=(1-p)pi-1 must
be modified to include a degeneracy factor and to account for the fact that, in the sixarmed star, there are six unreacted sites per molecule (one at the end of each arm of the
star). The revised expression is
(1  p ) 6 p i
(5  i )!
5! i!
Part I. Explain the degeneracy term (5+i)!/5!i!
Part II. Using algebra and/or computational tools, along with appropriate relations
between w and n, show that the expression for polydispersity ratio is:
Mw w
1

 1 = 1.17. It may actually be easier to show it for the general case of an
Mn n
6
f-functional star, in which case PDI = 1 + 1/f.