LINEAR AND REGULAR STAR POLYMER IN A GOOD SOLVENT

The conformational expansion problem of a regular star polymer in a good solvent is solved within the Gaussian approximation for the interatomic distances. Taking the Rouse-Zimm-Kilb Fourier coordinates as the basis of the conformational representation, their strain ratios with respect to the unperturbed phantom state are derived via self-consistent minimization of the intramolecular free energy. As usual for polymers above the theta temperature, only the two-atom repulsions are taken into consideration. In the crossover regime, for an overall mean-square expansion up to 3, the off-diagonal strain ratios are less than 1/10 the diagonal terms for a six-arm star and at least 1 order of magnitude smaller for a linear chain, thus indicating that the Fourier coordinates approach the normal modes to within a good approximation. Numerical analysis of the off-diagonal strain ratios is consistent with the expansion being especially large in the vicinity of the branch point, where the intramolecular repulsion is most concentrated. The mean-square expansion of the radius of gyration increases with tauN1/2 (tau = (T - theta)/T, N is the number of atoms in the molecule) in about the same way as in the linear molecule. Bond correlation is largest around the branch point for bond vectors belonging to the same arm, but it tends to vanish if the bonds are on different arms. The normalized Kratky plot of the structure factor vs Q = 4pi sin (theta/2)/lambda increases with increasing expansion at larger Q, consistent with a decrease of the normalized density rho(R)/rho(0) for distances R from the center of mass on the order of the root-mean-square radius of gyration [S2]1/2. The relative fluctuation of [S2], that is, ([S4] - [S2]2)/[S2]2, is also shown to increase with increasing expansion. The present conformational study may be considered as a preliminary step to obtain the dynamic eigenfunctions as well as the relaxation times.