(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/R_g0 between 0.4 and 12, where R_g0 is the radius of gyration of an unconfined polymer. We found that the conformational properties R_g/R_g0 and L_p/R_g0, where L_p 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/R_g0 << 1, we found that R_g/R_{g0 ~} (L/R_g0)^0.8, and L_p/R_g0 ~ (L/R_g0)^-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 L_p with monomer density φ; L_p ~ φ^5/9, in the former, and L_p ~ φ^2/3, in the latter.