What is the size of a ring polymer in a ring-linear blend?

Abstract

In melts, ring polymers assume more compact conformations compared to linear chains with the same degree of polymerization N_r, i.e. R_r ~ N_r^ν with ν ≈ 0.4, where R_r is the radius of gyration. Upon gradually substituting some of the ring polymers with linear chains, the ring molecules swell. In the limit of infinite dilution, their size scales as R_r ~ N_r^0.5. We present a scaling argument based on the blob model to capture this transition. Ring-linear blends are modeled as a semidilute solution of ring polymers in a ν-solvent consisting of linear chains. The model predicts that the size of the ring polymer remains unchanged up to the overlap concentration c^∗_t. Beyond c^∗_t the size of the ring shrinks according to R_r c_r^β, where β = 2ν - 1 = -1/5 for ν = 0.4. The overlap concentration depends on the degree of polymerization of the ring according to c^∗_t~ 1/ √N_τ. These predictions were tested by performing Monte Carlo simulations of ring-linear blends using the bond-fluctuation model. The results of the simulation for N_r = 150 and 300 blended at different concentrations with linear chains of the same degree of polymerization validate the scaling model.