(363i) Self-Entanglement of a Single Polymer Chain Confined in a Cubic Box
We study the self-entanglement of a single linear polymer chain confined to a cubic box (L * L * L) using the bond-fluctuation lattice model and primitive path analysis. We probe chains with number of monomers between N = 30 and 750, and degree of confinement L/Rg0 between 0.4 and 12, where Rg0 is the radius of gyration of an unconfined polymer. We found that the conformational properties Rg/Rg0 and Lp/Rg0, where Lp is the average primitive path length, collapsed onto a single master curve as a function of the degree of confinement. In the strongly confined regime, L/Rg0 << 1, we found that Rg/Rg0 ~ (L/Rg0)0.8, and Lp/Rg0 ~ (L/Rg0)-2. We verify that simulation methodology used is quantitatively consistent with experimental data and the Colby-Rubinstein entanglement model for unconfined concentrated polymer solutions. The most significant difference between unconfined and confined systems is the variation of Lp with monomer density φ; Lp ~ φ5/9, in the former, and Lp ~ φ2/3, in the latter.