Rheological models of rubber-carbon black compounds: low interaction viscoelastic models and high interaction thixotropic - plastic - viscoelastic models

Montes, Sergio A.; White, James L.

doi:10.1016/0377-0257(93)85005-u

Cited by 30 publications

(9 citation statements)

References 32 publications

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“…This result suggests that these As it can be seen, the equation fits the experimental values with a very good accuracy and the predicted yield stress was s y ¼ 491. In a number of experimental and theoretical studies focusing on rheology of concentrated systems and melts with yield stress, the observed stress overshoot in steady shear flows has been related to the structural breakdown [26][27][28]. Figure 7 presents the normalized transient shear stress as a function of strain ðc ¼ _ c 3 tÞ.…”

Section: Linear Melt Viscoelastic Resultsmentioning

confidence: 99%

Linear and nonlinear melt‐state viscoelastic properties of polypropylene/organoclay nanocomposites

Nazockdast

Goharpey

2008

Polymer Engineering & Sci

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Rheological behavior of polypropylene (PP)/organoclay nanocomposites varying in compatibilizer (PP-g-MA) and organoclay concentration was investigated. The samples were prepared by melt intercalation method in an internal mixer. The wide angle X-ray diffraction patterns and results of rheological measurements showed that the compatibilizer had strong influence in increasing the interlayer spacing. The observed low frequency liquid-like to solid-like transition and apparent yield stress in simple shear flows, along with convergence of transient shear stress to nonzero values in stress relaxation after the cessation of flow experiments, were found to be consistent with formation of a physical network in quiescent conditions which could be easily ruptured with applying low shear rates. The values of stress overshoot strain in flow reversal experiments were independent of shear rate, organoclay, and compatibilizer content. From the results of frequency sweep experiments in different nonlinear strain amplitudes it was shown that extended Cox-Merz analogy was valid in nonlinear dynamic deformations while the shear viscosity showed positive deviation from this analogy with higher deviations at lower shear rates. Results of storage modulus recovery and flow reversal experiments at different shear rates suggested that network structure is reformed with a much slower rate compared to the rotational relaxation of organoclay platelets. FIG. 13. The results of flow reversal experiments after various resting periods for PN7.5-3 samples at _ c ¼ 1ð1=sÞ. FIG. 14. Effect of shear rate on microstructure reformation rate in flow reversal experiments for PN7.5-3 samples.

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Section: Linear Melt Viscoelastic Resultsmentioning

confidence: 99%

Linear and nonlinear melt‐state viscoelastic properties of polypropylene/organoclay nanocomposites

Nazockdast

Goharpey

2008

Polymer Engineering & Sci

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“…Rheological properties of CB/polymer compounds and CB suspensions are very important from both academic and industrial points of view. In attempting to elucidate these rheological responses, extensive studies have been carried out for the CB/polymer compounds1–11 and CB suspensions 12–30. The occurrence of both yield stress and thixotropy for these systems has been found.…”

Section: Introductionmentioning

confidence: 99%

Rheological characterization of carbon black/polystyrene solution systems

Aoki

2008

J of Applied Polymer Sci

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Steady-shear measurements of suspensions of carbon blacks (CB) in polystyrene (PS)/di-(butyl phthalate) (DBP) solution were investigated as a function of volume fraction (/) of CB to clarify the effect of the primary particle size and the structure of CB aggregates on the rheological properties. The suspensions show a typical shear-thinning behavior in the range of a shear rate studied. The Casson model was applied to evaluate the viscosity at infinite of shear rate h ' and the yield stress r y for the suspensions. Relative viscosity h ' /h m , (h m : medium viscosity) thus obtained was compared to the high-frequency viscosity for the ideal hard-sphere silica suspensions to evaluate the effective volume fraction / eff of CB aggregates. The / eff value was larger for the higher-structure CB with higher DBP absorption value, irrespective of the primary particle size. The yield stress r y had almost the same / eff dependence for neutral furnace CB/(PS/ DBP) suspensions, although it was larger for acetylene black (AcB)/(PS/DBP) suspensions. These results demonstrated that the effective volume fraction is the most important quantity to characterize the CB aggregates on the rheological properties. It was also found that the correction of the medium viscosity changes due to polymer adsorption on the CB surface is important since neutral furnace CB adsorbs PS polymers but AcB hardly adsorbs PS polymers in the solution.

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“…The rheological properties of the polymer melts is described by the 5‐mode Phan‐Thien‐Tanner (PTT) model, expressed as

true{\begin{matrix} left \\ τ = \sum_{i = 1}^{5} {boldτ}^{(i)} \\ \exp true[\frac{ε_{i} λ_{i}}{η_{i}} tr ({boldτ}^{(i)}) true] {boldτ}^{(i)} + λ_{i} true[(1 - \frac{ξ_{i}}{2}) \overset{\nabla}{{boldτ}^{(i)}} + \frac{ξ_{i}}{2} \overset{Δ}{{boldτ}^{(i)}} true] = 2 η_{i} D \end{matrix}

where the rate of deformation tensor is given by

D = \frac{1}{2} true(L + {boldL}^{boldT} true)

, with the velocity gradient tensor

L = {(\nabla v)}^{boldT}

λ_{i}

is the relaxation time,

η_{i}

is the zero shear viscosity,

ε_{i}

and

ξ_{i}

are parameters controlling the extensional viscosity and the second normal stress difference, respectively. The PTT model is capable of modeling the realistic extrudate swell effect as well as a nonzero second normal stress difference …”

Section: Methodsmentioning

confidence: 99%

An integrated numerical study of coextrusion flow inside and outside the die

Yang¹,

2016

J of Applied Polymer Sci

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The three-dimensional coextrusion flow of two polymer melts is solved over the die-extrudate region using the finite element method. As elastic recovery is known to be the main source of extrudate swelling, a viscoelastic constitutive model (the Phan-Thien-Tanner or PTT model) is adopted to characterize the rheological behavior of the elastomers. A major challenge in the simulation of multilayer flow inside and outside the die is to update multiple moving surfaces (material interface and extrudate free surface) simultaneously. This difficulty is resolved by introducing a two-step updating algorithm which decouples the iterations of the interface and the free surface. The effects of extrudate swelling and bending on interface deformation are investigated herein, together with the interface shape dependency on flow elasticity. The numerical method is also applied to an industrial profile and the simulation result is in quantitative agreement with the experimental coextrusion data. V C 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016, 133, 43522.

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Rheological models of rubber-carbon black compounds: low interaction viscoelastic models and high interaction thixotropic - plastic - viscoelastic models

Cited by 30 publications

References 32 publications

Linear and nonlinear melt‐state viscoelastic properties of polypropylene/organoclay nanocomposites

Linear and nonlinear melt‐state viscoelastic properties of polypropylene/organoclay nanocomposites

Rheological characterization of carbon black/polystyrene solution systems

An integrated numerical study of coextrusion flow inside and outside the die

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