Chemistry Reference
In-Depth Information
the consequence that all linear species disappear. The only reasonable interpre-
tation is the to postulate that cyclic species were exclusively formed in contra-
diction to Flory's premisse of perfectly linear polycondensations. A third example
demonstrating that Flory's equations are inconsistent with p = 1 is given by Eqs.
(
4.7
) and (
4.8
). Flory derived Eq. (
4.8
) from (
4.7
) with p = 1, but for an equimolar
feed ratio (r = 1) DP
n
Goes to infinity. In contrast, Eq. (
4.7
) yields correct results
for all conversions with p
max
= N
a0
-2/N
a0
.
Another problem results from Flory's calculations of polydispersities,
Eqs. (
4.23
) and (
4.32
). Even Flory's concept of cyclization-free step-growth
polymerizations are taken seriously, Eq. (
4.23
) does not give a satisfactory
description of the DP
n
-p correlation, because the final state of a linear polycon-
densation is one giant chain. This means D = 1, whereas Flory's equation yields
D = 2, regardless, if the maximum conversion is defined by p = 1orN
a0
-2/N
a0
.
When the formation of cyclic oligomers and polymers is taken into account, Eqs.
(
4.23
) and (
4.32
) are useless for the calculation of the dispersities of virgin reaction
products. For various KC polycondensations the author has found Ds in the range
of 3-15 [
93
-
96
], and members of E. I. DuPont found for the TC syntheses of
Nylon-6, Nylon-6,6, and PET dispersities in the range of 3-13 [
97
] (for the linear
chains alone a D around 2 was found). The experimental dispersities reported for
several ab
f
(ab
n
) polycondensations also fall into the range of 5-15, whereas
according to Eq. (
4.32
) the dispersity approaches infinity for p = 1. These results
are a consequence of the fact that end-to-end cyclization causes opposite trends for
the dispersities of two-dimensional and three-dimensional polycondensations. In
the former case the presence of cyclics enhances the number of oligomers above
the values predicted by Flory (Eq.
4.3
) and thus, enhances the D, whereas in three-
dimensional polycondensation the limitation of the chain growth due to cyclization
also limits the increase of D.
References
4. Flory PJ (1953) Principles of Polymer Chemistry. Cornell University Press, Ithaca (ISBN O-
8014-0134-8)
5. Flory PJ (1969) Statistical mechanics of chain molecules. In: Interscience (ISBN 0-470-
26495-0), reissued 1989 (ISBN 1-56990-019-1)
6. Flory PJ (1946) Chem. Rev. 39:137
7. Schulz GV, Phys Z (1938) Chem. Ser. A 18:127
8. Huglin MB (1991) Eur. Polym. J. 27:875
9. Elias HG (1978) J Macromol Sci Ser A 12:183
10. Carmichael JB (1969) J Macromol Sci Ser A 3:1021
11. Turner JCR (1973) Polymer 14:462
12. Goodrich FC (1967) In: Cantow HJ (ed) Polymer functionalization. Academic Press, New
York, Chapter 14
