Web Release Date: April 17,
Ring-Chain Equilibrium in Reversibly Associated Polymer Solutions: Monte Carlo Simulations
Department of Macromolecular Science and Engineering, Case Western Reserve University, Cleveland, Ohio 44106
Received September 19, 2003
Revised Manuscript Received March 2, 2004
Abstract:
Living polymers formed by reversible association of spacers (oligomers) terminated by one
donor and one acceptor group at the ends are studied by means of Monte Carlo simulations (using the
bond-fluctuation model). To account for the different chemical nature of the associating groups and spacers,
we considered three cases of flexible, semiflexible, and rigid polymers. Rigid polymers have both intrinsic
rigidity of spacers and rigidity (entropic penalty) imparted by end groups association. Semiflexible polymers
possess only the latter, and flexible polymers do not have any type of rigidity. We have studied the average
degree of association for all types of polymers as a function of concentration and spacer length and
compared the results with a simple analytical model. We found that above some crossover concentration
the association behaviors of all chains follow the same pattern, well-described by the analytical model
and depending mainly on the number density of donor/acceptor groups. Below the crossover concentration,
the association is governed by the individual characteristics of spacers and differs for chains of different
rigidity and chain length. Defined in this way the crossover concentration, ccr, is a measure of the ring-to-chain transition: below ccr ring formation is most favorable, while above ccr linear chain formation
dominates. We found that the rigidity (entropic penalty) imparted by end group association defines the
behavior above the ccr: the total degree of association of semiflexible chains is much smaller than that
for flexible chains of the same concentration and practically coincides with that for rigid chains (despite
different spacer rigidity). The crossover concentration, ccr, is a function of spacer length and strongly
differs for chains of different rigidity: 
< 
. The rigidity of the spacer has a much stronger
impact on ccr compared to the end group rigidity imparted by association.
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