Sampling localization in determining the relaxation spectrum

Davies, Alison; Anderssen, R. S.

doi:10.1016/s0377-0257(97)00056-6

Cited by 96 publications

(81 citation statements)

References 4 publications

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“…The extraction of h(τ) from G * (ω) is a celebrated inverse problem, with its own chequered past [18,[237][238][239][240][241][242][243][244][245][246][247][248][249][250][251][252][253][254].…”

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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“…Measuring the storage and loss moduli over the v interval 0.001 to 10 s 21 allows the estimated relaxation spectrum to be interpreted safely over the corresponding range of t values 0.5 to 200 s (Davies and Anderssen, 1997). Due to the correlation between neighboring points, induced by the smoothness constraint, this interval may be extended to a t range of 0.1 to 1,000 s, which corresponds to the conventional reliable interval used for interpretation.…”

Section: Fitting Relaxation Spectramentioning

confidence: 99%

Mechanical Properties of Plant Cell Walls Probed by Relaxation Spectra

et al. 2010

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Transformants and mutants with altered cell wall composition are expected to display a biomechanical phenotype due to the structural role of the cell wall. It is often quite difficult, however, to distinguish the mechanical behavior of a mutant's or transformant's cell walls from that of the wild type. This may be due to the plant's ability to compensate for the wall modification or because the biophysical method that is often employed, determination of simple elastic modulus and breakstrength, lacks the resolving power necessary for detecting subtle mechanical phenotypes. Here, we apply a method, determination of relaxation spectra, which probes, and can separate, the viscoelastic properties of different cell wall components (i.e. those properties that depend on the elastic behavior of load-bearing wall polymers combined with viscous interactions between them). A computer program, BayesRelax, that deduces relaxation spectra from appropriate rheological measurements is presented and made accessible through a Web interface. BayesRelax models the cell wall as a continuum of relaxing elements, and the ability of the method to resolve small differences in cell wall mechanical properties is demonstrated using tuber tissue from wild-type and transgenic potatoes (Solanum tuberosum) that differ in rhamnogalacturonan I side chain structure.

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“…On the other hand, when modulus data over x min \x\x max are used in inferring relaxation spectrum, the calculated spectrum is reliable in a shorter interval of This inequality was derived by Davies and Anderssen (1997). Equation (2.77) is called the Davies and Anderssen limit (DA limit).…”

Section: How To Test Algorithmsmentioning

confidence: 99%

Viscoelastic Spectrum

Cho¹

2016

Viscoelasticity of Polymers

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This chapter deals with the mathematical fundamentals and numerical algorithms of relaxation and retardation spectra. The first section consists of the importance of spectrum, the Fuoss-Kirkwood relations, the ill-posedness in inferring viscoelastic spectra and some mathematical formulas related with the spectra. The second and third sections are the introduction to the algorithms of continuous and discrete spectra, respectively.

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Sampling localization in determining the relaxation spectrum

Cited by 96 publications

References 4 publications

Analytical Rheology of Polymer Melts: State of the Art

Analytical Rheology of Polymer Melts: State of the Art

Mechanical Properties of Plant Cell Walls Probed by Relaxation Spectra

Viscoelastic Spectrum

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