Effect of Topology on the Collapse Transition and the Instantaneous Shape of a Model Heteropolymer

The effect of topology on the collapse transition and instantaneous shape of an energy polydisperse polymer (EPP), a model heteropolymer is studied by means of computer simulations. In particular, three different chain topologies, namely, linear (L), ring (R), and trefoil knot (T), are considered. The heteropolymer is modeled by assigning each monomer an interaction parameter, ε_i, drawn randomly from a Gaussian distribution. Through chain size scaling, the transition temperature, θ, is located and compared among the chains of different topologies. The influence of topology is reflected in the value of θ and observed that θ(L) > θ(R) > θ(T) in a similar fashion to that of the homopolymer counterpart. Also studied chain size distributions, and the shape changes across the transition temperature characterized through shape parameters based on the eigenvalues of the gyration tensor. It is observed that, for the model heteropolymer, in addition to chain topology, the θ-temperature also depends on energy polydispersity.