Determination of the relaxation time spectrum from dynamic moduli using an edge preserving regularization method

Roths, Tobias; Maier, D.; Friedrich, Christian; Marth, Michael; Honerkamp, Josef

doi:10.1007/s003970050016

Cited by 67 publications

(37 citation statements)

References 22 publications

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“…By fitting Eqs. 7 and 8 into the recorded data (G 0 , G 00 vs x) and setting N equal to 50, and using edge preserving regularization method described in detail by Roths et al [24], the discrete relaxation times of samples were calculated. The accuracy of obtained relaxation times depends on quality of fitting of experimental storage and loss moduli with calculated values from Eqs.…”

Section: Glve Model Approachmentioning

confidence: 99%

Analysis of dynamic oscillatory rheological properties of PP/EVA/organo-modified LDH ternary hybrids based on generalized Newtonian fluid and generalized linear viscoelastic approaches

et al. 2016

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A comprehensive investigation was performed on single-step melt processed polypropylene (PP)/(ethylene vinyl acetate copolymer (EVA)/organo-modified layered double hydroxide (LDH) counterpart ternary hybrids to explore the effect of LDH loading on small-amplitude oscillatory shear (SAOS) rheological properties and to correlate the properties with microstructure. The rheological results were analyzed in detail from qualitative and quantitative perspectives. Using qualitative interoperation of storage modulus and complex viscosity alteration against LDH loading, and also quantitative analysis by viscosity models based on both the generalized Newtonian fluid (GNF) and generalized linear viscoelastic (GLVE) approaches, detailed predictions were carried out on the microstructure of samples and also partitioning of the organo-modified LDH particles and their intercalation and exfoliation extent within hybrids. By comparing the elasticity and relaxation spectrum of PP-rich/LDH with those of EVA-rich/LDH hybrids, it was predicted that organo-modified LDH platelets, in the case of PP-rich samples, have been located at the interface or within the EVA dispersed particles, while in the case of EVA-rich samples, they mainly localized within the matrix. In addition, the crossover frequency and slope of G 0 and G 00 curve at terminal region were correlated with the extent of intercalated and exfoliated structures of filler. The validity of these predictions on microstructure of the developed hybrids was confirmed visually using transmission electron microscope (TEM) micrographs.

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Section: Glve Model Approachmentioning

confidence: 99%

Analysis of dynamic oscillatory rheological properties of PP/EVA/organo-modified LDH ternary hybrids based on generalized Newtonian fluid and generalized linear viscoelastic approaches

et al. 2016

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“…Since G i , λ i and ω vary in logarithmic scale and are positive, it is convenient to use following notation: (4) Since our method deals with only loss modulus, we are interested in the SSE defined as (5) where (6) Minimization of eq. (5) implies (7) and (8a)…”

Section: Theorymentioning

confidence: 99%

“…Such works includes, to the author's knowledge, regularization methods for continuous spectrum by Honerkamp, J., 1 Honerkamp and Wesse, 2 Elster and Honerkamp, 3 Roths et al, 4 Parsimonious model (PM) by Baumgaertel and Winter, 5 Padé-Laplace method (PL) for discrete spectrum by Fulchiron et al, 6 Simhambhatla and Leonov, 7 simulated annealing (SA) for discrete spectrum by Jensen, 8 and nonlinear iteration (NI) for continuous spectrum by Cho et al. 9 Numerical method for continuous spectrum is to calculate continuous relaxation time spectrum H(λ) for relaxation times λ with very narrow and equal spacing.…”

Section: Introductionmentioning

confidence: 98%

A simple method for determination of discrete relaxation time spectrum

Cho

2010

Macromol. Res.

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A simple method for determining the discrete relaxation time spectrum from loss modulus data was developed. The method is based on the wavelet transform, which is a kind of peak-sharpening processes. Although several methods have been developed, most cannot determine the number of relaxation times in a single step without an adjustable parameter. However, the method suggested here provides a way of determining the number of relaxation times as well as the arrangement of the relaxation times automatically in a single numerical operation.

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“…1) There have been a number of efforts to solve the ill-posed inverse problem of linear viscoelasticity. The remarkable achievements were done by Honerkamp and Weese 2,3,4) , Mead 5) , and Roths et al 6) They used different forms of regularization. Honerkamp and Weese 4) improved their linear regularization method 3) by calculating logarithm of relaxation time distribution instead of the relaxation time distribution itself.…”

Section: Introductionmentioning

confidence: 99%

“…Mead 5) used additional physical constraints such that the zero-shear viscosity is the first moment of the relaxation time distribution. Roths et al 6) used edge preserving regularization in order to make the solution consistent with piecewise smooth BSW/CW spectrum, which is a power-law type empirical spectrum proposed by H. H. Winter and coworkers. 7) These regularization methods need a large number of modes and the optimized regularization parameter.…”

Section: Introductionmentioning

confidence: 99%

An Iterative Nonlinear Mapping Method for the Relaxation Time Distribution

Cho

Ahn

Lee

2004

J. Soc. Rheol., Jpn

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We propose a simple numerical method to calculate the relaxation time distribution, which is not based on the regularization method. This method is as precise as the nonlinear regularization method developed by Honerkamp and Weese 4) , and is simpler in mathematical aspects. Our method is an iterative nonlinear mapping that maps any initial distribution to the set of distribution functions whose element H (n) (τ) generates moduli very close to those generated by the exact distribution, and is smooth whenever the initial distribution is smooth. By the mapping, the initial distribution becomes close to the exact distribution within less than 10 iterations. This implies that the iterative nonlinear mapping itself contains the role as the regularization term used in the existing regularization methods, while the mapping is not formulated by constructing a counterpart of the regularization term. In other words, this method is free from parameters such as regularization parameter used in the previous regularization methods. Furthermore, our method needs no constraint to keep the distribution non-negative.

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Determination of the relaxation time spectrum from dynamic moduli using an edge preserving regularization method

Cited by 67 publications

References 22 publications

Analysis of dynamic oscillatory rheological properties of PP/EVA/organo-modified LDH ternary hybrids based on generalized Newtonian fluid and generalized linear viscoelastic approaches

Analysis of dynamic oscillatory rheological properties of PP/EVA/organo-modified LDH ternary hybrids based on generalized Newtonian fluid and generalized linear viscoelastic approaches

A simple method for determination of discrete relaxation time spectrum

An Iterative Nonlinear Mapping Method for the Relaxation Time Distribution

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