Scaling relations in nonlinear viscoelastic behavior of aqueous PEO solutions under large amplitude oscillatory shear flow

Abstract

We have found empirical scaling relations in nonlinear viscoelasticity of poly(ethylene oxide) (PEO) solutions under large amplitude oscillatory shear flow. The scaling relations superpose dimensionless nonlinear viscoelastic functions, such as the normalized amplitudes of elastic and viscous stresses and normalized Fourier intensities, measured at different strain amplitudes and frequencies on a single curve irrespective of the molecular weight and the concentration of the polymer solutions. The scaling relations reveal that the nonlinear viscoelastic functions are functions of dimensionless variable ζ≡γo cos δ(ω), where δ is the phase lag of linear viscoelasticity. The validity of our superposition was checked for PEO aqueous solutions under the conditions that concentration:3<c/ce<7; molecular weight: 400 kg/mol<M<1000kg/mol; τmω<10. We suggest some material parameters, which are expected to indicate chain architecture as well as to measure the strength of nonlinearity because the parameters are independent of the test conditions and compositions of the polymer solutions.

Geometric insights on viscoelasticity: Symmetry, scaling and superposition of viscoelastic functions

“…It is interesting that and contain only storage modulus while and contain only loss modulus. How to obtain analytical series solution for the K-BKZ model is described in the appendix of Cho et al (2010). Ewoldt et al (2008) reformulated Eq.…”

“…As time-temperature superposition, development of strain-frequency superposition may be done by intuition before supported by theoretical base. Cho et al (2010) found that some of dimensionless functions of LAOS can be superposed on a single curve when they are plotted as function of dimensionless variable such that (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16) where δ is the phase angle of linear viscoelasticity. They showed strain-frequency superposition for the PEO aqueous solutions made of various molecular weights and concentrations.…”

“…It means that shear stress changes its direction according to that of strain, and it is commonly cross lips as having odd symmetry. From the concept of dimensionless variables, the scaling rules for large amplitude oscillatory shear flow have been suggested (Cho et al 2010). The scaling relations show that the dimensionless variables make the superposition possible regardless of frequency and strain amplitude.…”

Preliminary Mathematics

“…Economized power series was applied to obtain the analytical solution of the K-BKZ model for LAOS by Cho et al (2010). They needed a power series approximation of the damping function of the K-BKZ model.…”

Effect of temporary network structure on linear and nonlinear viscoelasticity of polymer solutions

“…It is helpful to understand the nonlinear behavior for wider range of frequency or time domain. Cho et al (2010) developed a convenient tool which simplifies such complexity, called strain-frequency superposition (SFS). The SFS was obtained from PEO (poly ethylene oxide) aqueous solutions which are fully entangled polymer solutions.…”