Entropic Mixing of Ring/Linear Polymer Blends

The closed-loop structure of ring polymers enables them to be threaded by linear polymers. This results in an entropic mixing (negative χ) compared to linear/linear and ring/ring blends. Results from molecular dynamics (MD) simulations for bead-spring chains of length 50 - 400 for linear/linear, ring/ring and ring/linear blends will be presented.  These chains are long enough that the rings are threaded by multiple linear chains. The phase boundary for the linear/linear and ring/ring blends is determined by MD simulations, supplemented with a Monte Carlo chain exchange process.  In analogy with SANS data, we measured the static structure function S(q) in which the scattering lengths b_i = ± 1 for the two components and fit the resulting data to the random phase approximation (RPA) to determine χ.  In the limit that the two components are equal, χ = 0 for the linear/linear and ring/ring blends, while χ < 0 for the ring/linear blends.  As the incompatibility of the two components increases, the number of linear chains threading each ring decreases, and χ increases but remains less than for the linear/linear and ring/ring blends.  Eventually, the linear chains de-thread the ring polymers and the ring/linear blends phase separate into two macroscopic phases.