Evidence and Limits of Universal Topological Surface Segregation of Cyclic Polymers

If you mix lines and circles, what happens at the edge of the mixture? The problem is simply stated, but the answer is not obvious. Twenty years ago it was proposed that a universal topological driving force would drive cyclic chains to enrich the surface of blends of linear and cyclic chains. Here such behavior is demonstrated experimentally for sufficiently long chains and the limit in molecular weight where packing effects dominate over the topological driving force is identified.

Figure 1

(a) Experimentally measured hPS segment volume fraction depth profiles for the $37k$ cyclic-linear (solid curve) and $37k$ linear-linear (dashed curve) blend films after annealing at $180°\mathrm{C}$ for 12 h. (b) Segment volume fraction depth profile for a $37k$ cyclic-linear blend with ideally smooth surface calculated using SCFT, with ${\phi }_{\text{cyclic}}=0.2$, total bulk segment density ${\rho }_b=1.0$, $b=6\AA$, and $v=1b^3$.

Figure 2

(a) Comparison of linear dPS segment volume fraction depth profiles from NR for the $2k$ cyclic-linear blend film (solid curve) and $2k$ linear-linear blend film (dashed curve) after annealing at $120°\mathrm{C}$ for 12 h. (b) Smoothed segment volume fraction profile for the $2k$ cyclic-linear blend with ideally smooth surface calculated using wall-PRISM with ${\phi }_{\text{cyclic}}=0.2$, $N=20$ beads, total bulk segment density ${\rho }_b=1.0$, packing fraction of 0.45, and $80/20$ ratio of linear to cyclic polymers.

Figure 3

Ratio of surface volume fraction to bulk volume fraction for hydrogenous cyclic and hydrogenous linear chains as a function of molecular weight.