Hydrodynamics of Linear Macromolecules. I. Finite Segment Length

Abstract

According to the ideal necklace model for the linear macromolecule, as introduced by Rouse, the macromolecule and its segments expand to infinite length if subjected to larger and larger shear stress. A more realistic model has to take into account that the segment has a finite maximum length b ∞ which cannot be exceeded even at largest stress. Therefore, the elastic restoring forces transmitted by the segment and acting on the ends of the segment have to be assumed to increase more than linearly with the distance b and to become infinitely large at b ∞, yielding a modification of the eigenvalues of the corresponding restoring‐force matrix. The eigenfunctions are considered to be the same as in the original Rouse model. With the new set of eigenvalues the segment deformation of the linear molecule in laminar flow is claculated as a function of the flow parameter β. Saturation effects show up which are missing in the original model. The results obtained are formally identical with those of the original Rouse model if β is replaced by a modified β*=β/(E 0 *+½R). E 0 * is the nonlinearity factor of restoring force in solution at rest depending on the b ∞/b 0 ratio, and R is the maximum increase of this factor taking place in the central segment of the model and depending on β. Intrinsic viscosity and birefringenceextinction angle are calculated for some b ∞/b 0 ratios and compared with the corresponding values of the dumbbell model.