W. H. Stockmayer and the Role of Equilibration - Polycondensation: History and New Results - page 63

in the calculations of J ? S or Flory and cast serious doubts on the existence of the
crIMC phenomenon.
Furthermore, the role of end-to-end cyclization and the role of self-dilution [ 93 ]
(Eq. ( 5.25 )) of the linear active species La must be taken into account (both
aspects were neither discussed by J ? S nor by Flory). At first, it should be
emphasized, that cyclization via ''back-biting'' is not a hindrance for cyclization
via ''end-biting''. The rings formed by ''end-biting'' will, of course, not maintain
their ring size, because they will be involved in the equilibration process. Yet,
cyclization by ''end-biting'' has a strong influence on the course of the polycon-
densation, because it consumes end groups in contrast to ''back-biting.'' Therefore,
''end-biting'' lowers the concentration of linear chains and their reduced con-
centration favors, in turn, cyclization due to the RZDP.
Furthermore, it may be helpful to compare two hypothetical polycondensation
experiments. In experiment (A) the IMC is 1 mol/L and slightly below the critical
conversion, while in experiment (B) the IMC is 4 mol/L and above the critical
conversion. Close to 100 % conversion the difference in the concentration of linear
species has almost vanished, and only a handful of long chains has survived in
both experiments (see also Fig. 7.2 ). Their concentration is around 10 -23 mol/L,
and thus, the RZDP plays a decisive role. According to the JS theory the chains in
experiment (A) will cyclize when the conversion goes to completion, and at p = 1
all reaction products will be cycles. In experiment (B) the chains are not allowed to
cyclize and form one giant chain at p max (in addition to the much smaller weight
fraction of rings). Hence, the question arises, where do the chains in experiment
(B) know from that they are not allowed to cyclize, although concentration and
reactivity of the end groups are the same as in experiment (A). Of course, the DPn
of the chains in experiment (B) may be slightly higher, and the fraction of the
cycles slightly lower than in experiment (A), but this difference is negligible
considering the extremely low concentration of the chains.
The same problem may be considered from another perspective.
The kinetic probability of end-to-end cyclization is the same in KC and TC
polycondensations because it depends on the same parameters: structure and
conformations of the chains and their molar concentration. Using three different
mathematical approaches Gordon et al. [ 94 ] and Stepto et al. [ 95 ] have shown that
even the longest chains cyclize at high conversions, and at p = 1 all reaction
products are necessarily rings. No influence of a critical IMC was detected.
In this context the experiments of Höcker et al. [ 96 ], Rempp et al. [ 97 ], Roovers
et al. [ 98 ]. and other research groups [ 99 ] should be recalled. Those authors
obtained high yields of cyclic polymers from preformed difunctional polymers
(e.g., bisanionic polystyrene) by polycondensation with difunctional reaction
partners at an IMC of 10 -5 mol/L. The final concentration of chains in experi-
ments (A) and (B) are by a factor 10 -18 lower, and chain growth without any
cyclization is absolutely unlikely: In summary, the existence of the critical IMC is
unproven, it is in contradiction to the results of Kricheldorf et al. [ 46 , 47 ], it is in
conflict with the calculations of Gordon et al. or Stepto et al. (see Chap. 7 ) , and it is
in conflict with the law of self-dilution combined with the RZDP: