Numerical calculation of storage and loss modulus from stress relaxation data for linear viscoelastic materials

Schwarzl, Friedrich Rudolf

doi:10.1007/bf02040437

Cited by 77 publications

(45 citation statements)

References 3 publications

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“…We can translate between G(t) and G * (ω) either by using Schwarzl approximations [231,234] or by extracting the underlying relaxation spectrum h(τ) [62,229,235,236]. The relationships between G(t), G * (ω), and h(τ) are given by…”

Section: Linear Polymersmentioning

confidence: 99%

Analytical Rheology of Polymer Melts: State of the Art

Shanbhag

2012

ISRN Materials Science

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The extreme sensitivity of rheology to the microstructure of polymer melts has prompted the development of "analytical rheology," which seeks inferring the structure and composition of an unknown sample based on rheological measurements. Typically, this involves the inversion of a model, which may be mathematical, computational, or completely empirical. Despite the imperfect state of existing models, analytical rheology remains a practically useful enterprise. I review its successes and failures in inferring the molecular weight distribution of linear polymers and the branching content in branched polymers.

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Section: Linear Polymersmentioning

confidence: 99%

Analytical Rheology of Polymer Melts: State of the Art

Shanbhag

2012

ISRN Materials Science

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“…The higher the value of φ, the lower the temperature at which tan δ peak appears, and the smaller the maximum tan δ value, being similar to the observations in Figure 2. In order to evaluate the relaxation process more accurately, the relaxation spectra (H(τ)) can be calculated based on the Schwarzl and Staverman differential equation 27) as given as in which τ is the relaxation time. Figure Hence, we believe that the ultimate relaxation value of H(τ)…”

Section: Temperature Dependencementioning

confidence: 99%

Linear/Nonlinear Rheological Properties and Percolation Threshold of Polydimethylsiloxane Filled with Calcium Carbonate

Gao

Zheng

Jiang

2007

J. Soc. Rheol., Jpn

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The dynamic rheological properties of hydroxyl-terminated polydimethyllsiloxane (PDMS) filled with calcium carbonate (CaCO 3 ) were investigated systematically over a broad temperature range from −40 to 50°C. The results reveal that with an increase of filler volume fraction (φ), the span of the linear viscoelastic region in which dynamic storage modulus (G′) is constant narrows and the relaxation time of the compounds shifts to longer time scales. Beyond the critical φ (φ c = 0.069), G′ remarkably increases and exhibits a "pseudo solid-like" behavior in the low frequency (ω) region, meanwhile the width and height of the modulus plateau increase with increasing φ. On the other hand, the "ColeCole" plots of G′ against dynamic loss modulus (G″) at different temperatures indicate that the microstructure of compounds with relative high φ is distinct from those of compounds with low φ. The reasons for "pseudo solid-like" behavior are attributed to the agglomeration of filler particles and the formation of percolated filler network structure due to filler-polymer and filler-filler interactions. When φ <φ c , the nonhydrodynamic force of polymer matrix is predominant, while particle-particle interactions play an important role when φ >φ c .

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“…From G(t), we use a Schwarzl transformation [40] to reconstruct the elastic and loss moduli G ′ and G ′′ . In this section the strain applied is small, as a consequence, the system stays in the linear regime and the arms do not stretch (λ = 1).…”

Section: Predictions Of the Model: Linear Regime A Methodsmentioning

confidence: 99%

Stochastic and preaveraged nonlinear rheology models for entangled telechelic star polymers

Boudara

Read

2017

J. Rheol.

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We present a simplified stochastic model designed to exemplify the non-linear rheology of entangled supramolecular polymeric materials. We have developed a simplified stochastic model for the rheology of entangled telechelic star polymers. As a toy model for entanglement effects, we use the Rolie-Poly equations [1] that we decorate with finite extensibility. Additionally, we include a stretch-dependent probability of detachment for the stickers. In both linear and non-linear regimes, we explore the parameter space, indicating the parameter values for which qualitative changes in response to the applied flow are predicted. Theory and results in the linear rheology regime are consistent with previous more detailed work of van Ruymbeke and co-workers [2]. Finally, we develop a pre-averaged version of the stochastic equations described above to obtain a set of non-stochastic coupled equations that produces very similar predictions but requires less computing resources.This pre-averaged model is based on two tensors representing the attached and detached chain populations and a scalar quantity that represents the fraction of these populations. * mmvahb@leeds.ac.uk

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Numerical calculation of storage and loss modulus from stress relaxation data for linear viscoelastic materials

Cited by 77 publications

References 3 publications

Analytical Rheology of Polymer Melts: State of the Art

Analytical Rheology of Polymer Melts: State of the Art

Linear/Nonlinear Rheological Properties and Percolation Threshold of Polydimethylsiloxane Filled with Calcium Carbonate

Stochastic and preaveraged nonlinear rheology models for entangled telechelic star polymers

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