CHAIN COLLAPSE OF STAR POLYMERS

The self-consistent approach to free-energy optimization is applied to regular star polymers in bad solvents (T < THETA); the Gaussian appro ximation and the Zimm-Kilb description of Fourier modes are both warra nted under these conditions leading to chain collapse. As currently do ne in this approach, the interatomic-contact free energy is taken to b e a single-valued function of the mean-square radius of gyration [S2], whence the universal plots of the mean-square distances between two a toms and between the atoms and the center of mass are obtained as a fu nction of the contraction ratio alpha(S)2 = [S2]/[S2]0 (the zero subsc ript denotes the unperturbed state at T = THETA) and of the degree of branching. The density as a function of the distance from the center o f mass as well as the equilibrium structure factor are likewise evalua ted. The decrease of alpha(S) with an increase of the undercooling (TH ETA - T) at a fixed molecular weight is sharper with a smaller number of arms, being sharpest with the linear chain. The relative fluctuatio n of the radius of gyration, expressed as ([S4] - [S2]2)/[S2]2, increa ses at first with the undercooling, showing a maximum close to the tra nsition temperature which is more pronounced the smaller is the degree of branching, then decreases sharply at strong contraction. The avera ge 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[S2]. Conversely, the mean-sq uare distance of the branch point from the center of mass if 2[S2]/f, f being the number of arms.