Reptation of a Polymer Chain in the Presence of Fixed Obstacles
Abstract
We discuss possible motions for one polymer molecule P (of mass M) performing wormlike displacements inside a strongly crosslinked polymeric gel G. The topological requirement that P cannot intersect any of the chains of G is taken into account by a rigorous procedure: The only motions allowed for the chain are associated with the displacement of certain "defects" along the chain. The main conclusions derived from this model are the following:
(a) There are two characteristic times for the chain motion: One of them (T_{d}) is the equilibration time for the defect concentration, and is proportional to M^{2}. The other time (T_{r}) is the time required for complete renewal of the chain conformation, and is proportional to M^{3}.
(b) The overall mobility and diffusion coefficients of the chain P are proportional to ^{M2. }
(c) At times t < T_{r} the mean square displacement of one monomer of P increases only like <(r_{t}  r0)^{2}> = const t^{1/4}.
These results may also turn out to be useful for the (more difficult) problem of entanglement effects in unlinked molten polymers.
 Publication:

Journal of Chemical Physics
 Pub Date:
 July 1971
 DOI:
 10.1063/1.1675789
 Bibcode:
 1971JChPh..55..572D