Cole-Cole Relation for Long-Chain Branching From General Rigid Bead-Rod Theory
Coombs, Steacy J.
Kanso, Mona A.
Giacomin, A. Jeffrey
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Empirically, we find that parametric plots of the imaginary versus real parts of the complex viscosity may depend neither on temperature, nor on average molecular weight. Moreover, for fixed polydispersity, these Cole-Cole curves amplify both rightward and upward with long-chain branching content. In this paper, we find that general rigid bead-rod theory [O. Hassager, “Kinetic theory and rheology of bead-rod models for macromolecular solutions. II. Linear unsteady flow properties,” J. Chem. Phys. 60(10), 4001–4008 (1974)] can explain these rightward and upward amplifications. We explore the effects of branching along a straight chain in small-amplitude oscillatory shear flow. Specifically, we explore the number of branches, branch length, branch position and branch distribution.