Temporal scaling analysis: Viscoelastic properties of star polymers

Abstract

A generalized temporal scaling ansatz for the frequency dependence of the loss and storage moduli and for the shear dependence of the viscosity is tested against studies on entangled solutions of star polymers in good and theta solvents. At lower frequencies or shear rates, the ansatz calls for an exponential or stretched-exponential form [e.g., G0 exp(−αων)] for G″(ω)/ω and G′(ω)/ω2, and correspondingly in κ for η(κ). At higher frequencies, the ansatz indicates that each of these quantities has a power-law dependence on its primary variable. The predicted forms are in excellent agreement with literature data on solutions of poly-α-methylstyrene, polybutadiene, polystyrene, and polyisoprene stars. A power-law correlation α∼G02/3 is observed between the zero-frequency, zero-shear modulus G0 and the low-frequency or low-shear decay constant α of the stretched exponential, the same power-law line describing both star and linear polymers in good solvents.

Viscosity of Hard Sphere Suspensions

“…[2] and [3] within an ansatz that correctly (18,19) predicts G (ω) and G (ω) of polymer solutions. η(φ) is proposed to follow from the Altenberger-Dahler positive function renormalization group (10) method, the form of η(c) being determined by the locally dominant fixed point.…”

The Hydrodynamic Scaling Model for the Dynamics of Non-Dilute Polymer Solutions: A Comprehensive Review

“…Preliminary tests against literature data were highly satisfactory. Further tests reported in Temporal Scaling Analysis: Viscoelastic Properties of Star Polymers [27], Temporal Scaling Analysis: Linear and Crosslinked Polymers [28], and Viscosity of Hard Sphere Suspensions [30] were equally satisfactory. In particular, it was confirmed that the predicted forms, with fitted parameters, agreed with Kronig-Kramers relations.…”

Temporal scaling analysis: Linear and crosslinked polymers

“…The storage modulus is predicted to follow similar low-and high-frequency forms, namely GЉ͑͒ 2 ϭ G 10 exp(Ϫ␣ ) (3) and…”

“…Preliminary tests found good agreement between representative data2 and the predicted frequency dependence of the loss modulus G ″(ω). The ansatz's predictions for G ″(ω), the storage modulus G ′(ω), and the shear‐dependent viscosity η(κ) were systematically compared3 with the experimental literature on solutions of star polymers. Good agreement between predictions and the experiment was found.…”