Measurement systems for distribution of relaxation and retardation times
Abstract
There is a widespread belief in scientific literature on material research that the distribution of relaxation and retardation times (DRRT) is a non-measurable quantity. In the presented contribution, we try to revise this belief. Based on the recently developed functional filtering approach for DRRT recovery, measurement systems are proposed to develop executing an active measurement experiment by exciting material with the specific stimulus, measuring material's responses sampled geometrically in time- or frequency-domain and processing them by the appropriate DRRT recovery filters. Design and algorithms of DRRT recovery filters are considered and practical implementations of DRRT measurement systems are proposed executing measurement experiments by exploiting the standard excitations, such as the Heaviside step function, the Dirac delta function and the steady-state multi-harmonic one.
References
[1]
J.D. Ferry, Viscoelastic Properties of Polymers, 3rd. ed., J. Wiley and Sons, 1980.
[2]
N.W. Tschoegl, The Phenomenological Theory of Linear Viscoelastic Behavior; Springer-Verlag, 1989.
[3]
N.G. McCrum, B.E. Read, G. Wiliams, Anelastic and Dielectric Effects in Polymer Solids, J. Wiley and Sons, 1967.
[4]
A.K. Jonscher, Dielectric Relaxation in Solids, Chelsea Dielectric, 1983.
[5]
F. Kremer, A. Schonhals, W. Luck, Broadband Dielectric Spectroscopy; Springer-Verlag, 2002.
[6]
C.P. Slichter, Principles of Magnetic Resonance; 3rd. enlarged and updated ed., Springer-Verlag, 1996.
[7]
C. Friedrich, R.J. Loy, R.S. Anderssen, Relaxation time spectrum molecular weight distribution relationships, Rheol. Acta, Vol. 48, 2009, pp. 151-162.
[8]
M.R. Nobile, F. Cocchini, A general relation between MWD and relaxation time spectrum, Rheol. Acta, Vol. 47, 2008, pp. 509-519.
[9]
W. Thimm, C. Friedrich, M. Marth, J. Honerkamp, An analytical relation between relaxation time spectrum and molecular weight distribution, J. Rheol, Vol. 43, 1999, pp. 1663- 1672.
[10]
A.R. Davies, R.S. Anderssen, Sampling localization in determining the relaxation spectrum, J. Non-Newtonian Fluid Mech., Vol. 73, 1997, pp. 163-179.
[11]
A.R. Davies, R.S. Anderssen, Sampling localization and duality algorithms in practice, J. Non-Newtonian Fluid Mech., Vol. 79, 1998, pp. 235-252.
[12]
J.R. Macdonald, On relaxation-spectrum estimation for decades of data: accuracy and sampling-localization considerations, Inverse Problems, Vol. 16, 2000, pp. 1561-1583.
[13]
M. Renardy, On the use of Laplace transform inversion for reconstruction of relaxation spectra, J. Non-Newtonian Fluid Mech., Vol. 154, 2008, pp. 47-51.
[14]
J.R. Macdonald, Comparison of parametric and nonparametric methods for the analysis and inversion of immittance data: Critique of earlier work, J. Comp. Phys., Vol. 157, 2000, pp. 280- 301.
[15]
J.R. Macdonald, E. Tuncer, Deconvolution of immittance data: Some old and new methods, J. Electroanalytical Chem., Vol. 602, 2007, pp. 255- 262.
[16]
F. Aslani, L. Sjögren, Relaxation rate distribution from frequency or time dependent data, Chem. Phys., Vol. 325, 2006, pp. 299-312.
[17]
V. Shtrauss, Determination of the relaxation and retardation spectrum - A view from the up-todate signal processing perspective, Mech. Comp. Mat. (in press).
[18]
V. Shtrauss, Determination of relaxation and retardation spectrum by inverse functional filtering, J. Non-Newtonian Fluid Mech., Vol. 165, 2005, pp. 453-465.
[19]
V. Shtrauss, Digital estimators of relaxation spectra, J. Non-Crystal. Solids, Vol. 353, 2007, pp. 4581-4585.
[20]
V. Shtrauss, Digital signal processing for relaxation data conversion, J. Non-Crystal. Solids, Vol. 351, 2005, pp. 2911-2916.
[21]
V. Shtrauss, Decomposition of Multi-Exponential and Related Signals - Functional Filtering Approach, WSEAS Transactions on Signal Processing, Vol. 4, Issue 7, 2008, pp. 44- 52.
[22]
V. Shtrauss, Sampling and algorithm design for relaxation data conversion, WSEAS Transactions on Signal Processing, Vol. 2, Issue 7, 2006, pp. 984-990.
[23]
V. Shtrauss, Sampling in relaxation data conversion, Proc. 10th WSEAS International Conference on SYSTEMS, Vouliagmeni, Athens, Greece, July 10-12, 2006, pp. 37-42.
[24]
V. Shtrauss, A. Kalpinsh, U. Lomanovskis, Pragmatic approach to designing deconvolution filters, Scientific Proceedings of RTU. Series 7. Telecommunications and Electronics, Vol.9, 2009, pp. 86-95.
[25]
V. Shtrauss, Functional conversion of signals in the study of relaxation phenomena, Signal Processing, Vol. 45, 1995, pp. 293-312.
Index Terms
- Measurement systems for distribution of relaxation and retardation times
Index terms have been assigned to the content through auto-classification.
Recommendations
Recovery of distribution of relaxation and retardation times by measuring amplitudes to multi-harmonic excitations
Proceedings of the 15th WSEAS international conference on SystemsThe paper is devoted to simplifying measurement of the distribution of relaxation and retardation times (DRRT) by determining DRRT from the modulus (absolute value) of a complex frequency-domain material function. It is demonstrated that the problem may ...
Leveraging measurement systems to drive enterprise transformation: Two case studies from the U.S. aerospace industry
The focus of this paper is to depict the role of measurement systems in driving enterprise behavior and guiding enterprise transformation. Although enterprise transformation and performance measurement are separate areas of study, few have made the ...
Utility based framework for optimal network measurement
Packet level measurement is now routinely used to evaluate the loss and delay performance of broadband networks. In active measurement, probe packets provide samples of the loss and delay and from these samples the performance of the traffic as a whole ...
Comments
Information & Contributors
Information
Published In
July 2011
481 pages
ISBN:9781618040237
Publisher
World Scientific and Engineering Academy and Society (WSEAS)
Stevens Point, Wisconsin, United States
Publication History
Published: 14 July 2011
Author Tags
Qualifiers
- Article
Contributors
Other Metrics
Bibliometrics & Citations
Bibliometrics
Article Metrics
- 0Total Citations
- 0Total Downloads
- Downloads (Last 12 months)0
- Downloads (Last 6 weeks)0
Reflects downloads up to 27 Jul 2024