Chain collapse of star polymers

The self‐consistent approach to free‐energy optimization is applied to regular star polymers in bad solvents ( T < Θ); the Gaussian approximation and the Zimm‐Kilb description of Fourier modes are both warranted under these conditions leading to chain collapse. As currently done in this approach, the interatomic‐contact free energy is taken to be a single‐valued function of the mean‐square radius of gyration 〈 S 2 〉, whence the universal plots of the mean‐square distances between two atoms and between the atoms and the center of mass are obtained as a function of the contraction ratio α   2 S= 〈 S 2 〉/〈 S 2 〉 0 (the zero subscript denotes the unperturbed state at T = Θ) and of the degree of branching. The density as a function of the distance from the center of mass as well as the equilibrium structure factor are likewise evaluated. The decrease of α s with an increase of the undercooling (Θ − T ) at a fixed molecular weight is sharper with a smaller number of arms, being sharpest with the linear chain. The relative fluctuation of the radius of gyration, expressed as (〈 S 4 〉 − 〈 S 2 〉 2 )/〈 S 2 〉 2 , increases at first with the undercooling, showing a maximum close to the transition temperature which is more pronounced the smaller is the degree of branching, then decreases sharply at strong contration. The average location of the free ends of the collapsed molecule is close to, or even outside, the surface of the resulting globule, their mean‐square distance from the center of mass being 2 〈 S 2 〉. Conversely, the mean‐square distance of the branch point from the center of mass if 2〈 S 2 〉/ f , f being the number of arms.