The complex viscosity of Möbius macromolecules

Abstract

Using general rigid bead-rod theory, we explore the effect of twisting a macromolecule on its rheological properties in suspensions. We thus focus on macromolecules having the form of Möbius bands so that the number of twists can be incremented. We call these Möbius macromolecules. When represented in general rigid bead-rod theory, these macromolecules comprise beads whose centers all fall on a Möbius band. From first principles, we calculate the complex viscosity of twisted rings with zero to seven twists. We find that the zero-shear values of the viscosity and first normal stress coefficient increase with twisting. Furthermore, we find that the real part of the complex viscosity descends more rapidly, with frequency, with extent of twist. For the imaginary part of the complex viscosity, the more twisted, the higher the peak. For each part of the dimensionless complex viscosity and the first normal stress coefficient, the results fall on one of just three curves corresponding to zero, even, or odd numbers of twists. We also explore the effects of the length and the aspect ratio of twisted macromolecular suspensions. We close with a worked example for a suspension of triply twisted Möbius annulene.