Abstract
It is well known that the relaxation spectrum characterizing the linear viscoelastic properties of a polymer melt or solution is not directly accessible by an experiment. Therefore, it must be calculated from data for a material function. With Tikhonov regularization the relaxation spectrum in the terminal and plateau region can be calculated from data for a material function in the corresponding region. Serious difficulties arise however, if the spectrum should be determined in a larger range. These difficulties are caused by the considerably different contributions at short and long relaxation times. We show that these difficulties can be avoided by a nonlinear regularization method.
Similar content being viewed by others
References
Baumgaertel M, Schausberger A, Winter HH (1990) The relaxation of polymers with linear flexible chains of uniform length. Rheol Acta 29:400–408
Elster C, Honerkamp J (1991) Modified maximum entropy method and its applications to creep data. Macromolecules 24:310 - 314
Elster C, Honerkamp J, Weese J (1992) Using regularization methods for the determination of relaxation and retardation spectra of polymeric liquids. Rheol Acta 31:161–174
Ferry JD (1980) Viscoelastic properties of polymers. J Wiley & Sons, New York
Friedrich Ch, Hofmann B (1983) Nichtkorrekte Aufgaben in der Rheometrie. Rheol Acta 22:425–434
Groetsch CW (1984) The theory of Tikhonov regularization for Fredholm equations of the first kind. Pitman, London
Honerkamp J (1989) Ill-posed problems in rheology. Rheol Acta 28:363 - 371
Honerkamp J, Weese J (1989) Determination of the relaxation spectrum by a regularization method. Macromolecules 22:4372 - 4377
Honerkamp J, Weese J (1990) Tikhonovs regularization method for ill-posed problems: A comparison of different methods for the determination of the regularization parameter. Continuum Mech Thermodyn 2:17 - 30
Honerkamp J, Weese J (1993) A note on estimating mastercurves. Rheol Acta 32:57 - 64
Schausberger A, Schindlauer G, Janeschitz-Kriegl H (1985) Linear elasticoviscous properties of molten standard polystyrenes: I. Presentation of complex moduli; role of short range structural parameters. Rheol Acta 24:220 - 227
Weese J (1992) A reliable and fast method for the solution of Fredholm integral equations of the first kind based on Tikhonov regularization. Comput Phys Commun 69:99–111
Weese J (in preparation) A regularization method for nonlinear ill-posed problems
Wiff DR, Gehatia M (1975) Inferring mechanical relaxation spectra as an ill-posed problem. J Appl Phys 46 (10):4231–4234
Wiff DR (1978) RQP method of inferring a mechanical relaxation spectrum. J Rheol 22 (6):589 - 597
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Honerkamp, J., Weese, J. A nonlinear regularization method for the calculation of relaxation spectra. Rheologica Acta 32, 65–73 (1993). https://doi.org/10.1007/BF00396678
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00396678