Correlations in rheological behavior between large amplitude oscillatory shear and steady shear flow of silica‐filled star‐shaped styrene‐butadiene rubber compounds: Experiment and simulation

Abstract

The large amplitude oscillatory shear (LAOS) and steady shear behavior of star‐shaped SSBR/silica 60 phr (21 vol%) compounds with various filler surface areas was measured and simulated. An SBR gum and SBR compounds containing four different silicas with surface areas of 55, 135, 160, and 195 m2/g were utilized. Rheological behavior indicated clear correlation with surface area. LAOS tests showed an increase in dynamic moduli, shear stress, and higher order harmonic contributions with surface area. Elastic and viscous Lissajous figures showed significant distortion at intermediate and higher strain amplitudes. Additionally, ratios of third and fifth order stress harmonics to the first stress harmonic (I3/1 and I5/1, respectively) showed a ''bump'' at intermediate strain amplitudes for the three highest surface area compounds. With regards to steady shear, all materials showed strong shear thinning behavior, and an increase in shear viscosity with surface area. The Cox‐Merz rule was shown to be valid for the SBR gum but not for the filled compounds. However, the complex viscosity as a function of shear rate amplitude at various frequencies at high strain amplitudes and the steady shear viscosity as a function of shear rate coincided. This correlation, referred to as the Philippoff approach, has important ramifications for the rubber industry, providing quick data for predicting processing behavior. The Simhambhatla‐Leonov model was successfully employed to simulate rheological behavior for the SBR gum and the lowest surface area silica compound, but the model yielded mixed results for the higher surface area silica compounds.

Viscoelasticity of Low-Molecular-Weight Polyelectrolytes

“…are for the storage and loss modulus and reflect the elastic and viscous contributions to the stress response. 48 They are clearly and uniquely defined and are independent of the deformation and the deformation rate. 47,48 The linear viscoelastic regime is in the range γ 0 ∼ 1−10% for homopolymer melts and polymer solutions and γ 0 < 1% for dispersed systems or block copolymer solutions.…”

“…Considering an oscillatory-shear strain (unsteady flow) like a single-harmonic sinusoid (i.e., γ­( t ) = γ 0 sin­( ωt )) allows an investigation of the transient states. , It provides useful information on the materials’ ability to store energy (elastic behavior) and to dissipate heat (viscous behavior). , The general stress response σ xy (ω, t ,γ 0 ) for an arbitrary γ 0 and a given ω = 2 πf ( f the oscillation frequency) can be expressed as a Fourier series. , For small enough γ 0 (i.e., the linear viscoelastic regime), σ xy (ω, t ,γ 0 ) reduces to a single-harmonic sinusoid: ,, where σ xy ,1 , and δ 1 are the stress amplitude of the single harmonic and the phase shift, respectively. and are for the storage and loss modulus and reflect the elastic and viscous contributions to the stress response . They are clearly and uniquely defined and are independent of the deformation and the deformation rate. , The linear viscoelastic regime is in the range γ 0 ∼ 1–10% for homopolymer melts and polymer solutions and γ 0 < 1% for dispersed systems or block copolymer solutions .…”

“… and are for the storage and loss modulus and reflect the elastic and viscous contributions to the stress response . They are clearly and uniquely defined and are independent of the deformation and the deformation rate. , The linear viscoelastic regime is in the range γ 0 ∼ 1–10% for homopolymer melts and polymer solutions and γ 0 < 1% for dispersed systems or block copolymer solutions . σ xy (ω, t ,γ 0 ) deviates from a single-harmonic-sinusoid response at large γ 0 (i.e., the nonlinear viscoelastic regime). , Even if molecular simulations looked feasible in the latter regime, care must be taken because large γ 0 and ω may imply beyond the validity limit of the simulation technique. , Therefore, we restrained our study to mainly the linear viscoelastic regime.…”

“…47 Considering an oscillatory-shear strain (unsteady flow) like a single-harmonic sinusoid (i.e., γ(t) = γ 0 sin(ωt)) allows an investigation of the transient states. 47,48 It provides useful information on the materials' ability to store energy (elastic behavior) and to dissipate heat (viscous behavior). 49,50 The general stress response σ xy (ω,t,γ 0 ) for an arbitrary γ 0 and a given ω = 2πf (f the oscillation frequency) can be expressed as a Fourier series.…”

“…49,50 The general stress response σ xy (ω,t,γ 0 ) for an arbitrary γ 0 and a given ω = 2πf (f the oscillation frequency) can be expressed as a Fourier series. 47,48 For small enough γ 0 (i.e., the linear viscoelastic regime), σ xy (ω,t,γ 0 ) reduces to a single-harmonic sinusoid: 47,48…”