What Is the Size of a Ring Polymer in a Ring−Linear Blend?

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 ϑ-solvent consisting of linear chains. The model predicts that the size of the ring polymer remains unchanged up to the overlap concentration . Beyond 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 ∼ 1/ . 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.