The effects of solvent quality and core wetting on the circularization of star polymers

We simulate the formation of cyclical arms in star polymers, focusing on the effects of solvent quality on their resulting linking complexity and gyration radius. We find that polymers circularized in bad solvent present a higher degree of linking among arms with respect to those circularized in good solvent. When both are transported to good solvent, this results in a smaller gyration radius of the former with respect to the latter. This effect is magnified when the polymers present a sufficiently small number of arms (or functionality $f$): in this case, in bad solvent, all arms tend to clump together on one side of the central core, due to circularization, and can hence all interact with each other. Instead, when $f$ is large enough, the whole surface of the core is wetted by the arms, whose distribution becomes radially symmetric. This hinders interactions between faraway arms and reduces the probability of inter-arm linking. Interestingly, we find that both the critical $f_c$ at which the clump transition happens and the minimal arm length $n_c$ for which the transition appears depend on the core size: the grafting density of the arms must be larger than a certain constant $\rho_g^c$, while their length must be sufficient to stretch for, at least, half of the core's circumference.