DISTRIBUTION-FUNCTIONS AND DYNAMICAL PROPERTIES OF STIFF MACROMOLECULES

An analytically tractable model for chain molecules with bending stiff ness is presented and the dynamical properties of such chains are inve stigated. The partition function is derived via the maximum entropy pr inciple taking into account the chain connectivity as well as the bend ing restrictions in form of constraints. We demonstrate that second mo ments agree exactly with those known from the Kratky-Porod wormlike ch ain. Moreover, various distribution functions are calculated. In parti cular, the static structure factor is shown to be proportional to 1/q at large scattering vectors q. The equations of motion for a chain in a melt as well as in dilute solution are presented. In the latter case the hydrodynamic interaction is taken into account via the Rotne-Prag er tenser. The dynamical equations are solved by a normal mode analysi s. In the limit of a flexible chain the model reproduces the well-know n Rouse and Zimm dynamics, respectively, on large length scales, where as in the rod limit the eigenfunctions correspond to bending motion on ly. In addition, the coherent and incoherent dynamic structure factor is discussed. For melts we show that at large scattering vectors the i ncoherent dynamic structure factor is a universal function of only the combination q(8/3)tp(1/3), where 1/(2p) is the persistence length of the macromolecules. The comparison of the theoretical results with qua sielastic neutron and light scattering experiments of various polymers in solution and melt exhibits good agreement. Our investigations show that local stiffness strongly influences the dynamics of macromolecul es on small length scales even for long and flexible chains.