Linear viscoelastic models: Part II. Recovery of the molecular weight distribution using viscosity data |
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| Authors: | Tommi Borg Esko J Pääkkönen |
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| Institution: | 1. TomCoat Oy, Koskisenkuja 11, 62500 Evijärvi, Finland;2. Tampere University of Technology, Laboratory of Plastics and Elastomer Technology, P.O. Box 589, 33101 Tampere, Finland;1. Van’t Hoff Institute for Molecular Sciences, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands;2. Dutch Polymer Institute DPI, PO Box 902, 5600 AX Eindhoven, The Netherlands;1. Department of Pharmacal Sciences, Harrison School of Pharmacy, Auburn University, Auburn, AL 36849, USA;2. Department of Pharmaceutical Analytical Chemistry, Faculty of Pharmacy, Alexandria University, Alexandria 21521, Egypt;1. Clermont Université, Université Blaise Pascal, Institut de Chimie de Clermont-Ferrand, BP 10448, F-63000 Clermont-Ferrand, France;2. CNRS, UMR 6296, Institut de Chimie de Clermont-Ferrand, F-63171 Aubière, France;3. Branch of the Talrose Institute for Energy Problems of Chemical Physics of the Russian Academy of Sciences, Chernogolovka, Moscow Region 142432, Russia;4. Université de Pau et des Pays de l’Adour, IPREM/ECP (UMR 5254), Hélioparc, 2 av. Pierre Angot, 64053 Pau cedex 9, France;1. Universidade Federal do Espírito Santo, Departamento de Engenharias e Tecnologias, Programa de Pós-graduação em Energia, Rodovia BR 101 Norte, Km. 60, Bairro Litorâneo, 29932-540 São Mateus, ES, Brazil;2. Illinois Institute of Technology, Amour College of Engineering, Chemical and Biological Engineering Department, Suite 142, Perlstein Hall, 10 West 33rd Street, Chicago, IL 60616, USA;1. Laboratory for Nonlinear Mechanics, Faculty of Mechanical Engineering, University of Ljubljana, Askerceva 6, SI-1000, Ljubljana, Slovenia;2. Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139-4307, United States |
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| Abstract: | The constitutive models for the viscoelasticity of polymers are presented for determining molecular weight distributions (MWDs) from viscosity measurements. The inversion of this model derived from control theory and melt calibration procedure connects the relaxation modulus, viscosity, and other flow properties of a polymer. The linear principle enables simultaneous and accurate modelling of the relaxation modulus and of viscosity flow curves over a wide range. Starting from viscosity measurements, the new model is used to determine the MWD, linear viscoelastic relaxation moduli, and the relaxation spectra of polyethylene of different grades. In addition, two benchmark analyses of bimodal polystyrene are reported, and the capability of the model is proven by the two-box test of Malkin. The error of the modelled viscosity is smaller than that for previously reported models. One of the main features of this work is that no relaxation time or spectrum procedures were used to generate and model linear viscoelasticity. |
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