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The effect of topology on the collapse transition and instantaneous shape ofan energy polydisperse polymer (a model heteropolymer) is studied by means ofcomputer simulations. In particular, we consider three different chaintopology, namely, linear (L), ring (R) and trefoil knot (T). The heteropolymeris modeled by assigning each monomer an interaction parameter, $\varepsilon_i$,drawn randomly from a Gaussian distribution. Through chain size scaling thetransition temperature, $\theta$, is located and compared among the chains ofdifferent topogies. The influence of topology is reflected in the value of$\theta$ and observed that $\theta(\text{L}) > \theta(\text{R}) >\theta(\text{T})$ in a similar fashion to that of the homopolymer counterpart.Also studied chain size distributions, and the shape changes across thetransition temperature characterised through shape parameters based on theeigenvalues of the gyration tensor. It is observed that, for the modelheteropolymer, in addition to chain topology the $\theta$-temperature alsodepends on energy polydispersity.

Effect of topology on the collapse transition and the instantaneous shape of a model heteropolymer