DYNAMICS OF REGULAR STAR POLYMERS - THE INTRINSIC-VISCOSITY

The dynamics of a regular star polymer is investigated under good-solv ent and Theta conditions. A self-consistent approach to the equilibriu m and dynamics is proposed within the Gaussian approximation in terms of the polymer normal modes, i.e., suitable statistically-independent linear combinations of the bond vectors. The equilibrium normal modes used to study the star expansion through self-consistent free-energy m inimization (see Allegra, G.; Colombo, E.; Ganazzoli, F. Macromolecule s 1993, 26, 330) form a first-order approximation to the dynamical nor mal modes under partial-draining conditions. The latter modes are obta ined by diagonalization of a matrix that depends on the intramolecular elasticity and on the hydrodynamic interaction in the preaveraging ap proximation, the effect of chain expansion on both being easily accoun ted for. If the equilibrium normal modes are used, the relaxation time s, from which the intrinsic viscosity is calculated, are somewhat in e rror only for the collective modes describing the concerted motion of the arms, unlike those related with the independent motion of the arms ; on the other hand, they yield the intrinsic viscosity to a very good approximation, thus avoiding the lengthy diagonalization. Numerical r esults for regular stars and linear chains are summarized by analytica l equations giving the mean-square radius of gyration (S-2), the hydro dynamic radius R(H) and the intrinsic viscosity [eta] The influence of the topology is expressed through the ratios g(Q) = Q(star/)Q(lin), Q being any of the above quantities. In a good solvent, the star is onl y slightly more expanded than the linear chain, and so the g ratios ar e very close to the theoretical phantom-chain value both for (S-2) and for RH. Conversely, [eta] increases less in the star than in the Line ar chain because of the different rate of change with expansion of the intramolecular elasticity and of the hydrodynamic interaction, and so the corresponding g ratio is lower than the phantom-chain value. In t he Theta state, the residual three-body interactions give a finite exp ansion to the star, unlike the linear chain. Therefore, we have g(Q)(p h) less than or similar to g(Q) < g(Q)(Theta) for (S-2) and R(H), in agreement with experiment (the asterisk refers to the good-solvent con ditions); on the other hand, we get g(eta) < g(eta)(ph) < g(eta)(Thet a), whereas the experimental finding is g(eta) < g(eta)(Theta) < g(et a)(ph). The reason for this discrepancy is attributed to the preaverag ing approximation, which becomes questionable for stars in the Theta s tate because of their large density near the branch point.