Mathematical Modeling of Bivariate Polymer Property Distributions Using 2D Probability Generating Functions, 1 – Numerical Inversion Methods
作者： Mariano Asteasuain , Adriana Brandolin
关键词: Bivariate analysis 、 Chemistry 、 Inversion (meteorology) 、 Polymer 、 Applied mathematics 、 Joint probability distribution 、 Calculus 、 Probability-generating function 、 Inversion methods
摘要: This is the first of two papers presenting a new mathematical method for modeling bivariate distributions polymer properties. It based on transformation infinite mass balances describing evolution two-dimensional distribution using 2D probability generating functions (pgf). A key step this inversion transforms. In work, numerical methods pgfs are developed and carefully validated. The accuracy obtained with both was very satisfactory. formulas simple easy to implement. copolymerization example used show complete procedure from derivation pgf recovery molecular weight distribution.
sci-hub.se 参考文章(24)
Mariano Asteasuain, Matheus Soares, Marcelo K. Lenzi, Robin A. Hutchinson, Michael Cunningham, Adriana Brandolin, José Carlos Pinto, Claudia Sarmoria, “Living” Radical Polymerization in Tubular Reactors, 2 - Process Optimization for Tailor-Made Molecular Weight Distributions Macromolecular Reaction Engineering. ,vol. 2, pp. 414- 421 ,(2008) , 10.1002/MREN.200800015
Latchezar Christov, George Georgiev, An algorithm for determination of the copolymer molecular weight distribution by Markov chain simulation Macromolecular Theory and Simulations. ,vol. 4, pp. 177- 193 ,(1995) , 10.1002/MATS.1995.040040113
Mariano Asteasuain, Matheus Soares, Marcelo K. Lenzi, Michael Cunningham, Claudia Sarmoria, José Carlos Pinto, Adriana Brandolin, “Living” Free Radical Polymerization in Tubular Reactors. I. Modeling of the Complete Molecular Weight Distribution Using Probability Generating Functions Macromolecular Reaction Engineering. ,vol. 1, pp. 622- 634 ,(2007) , 10.1002/MREN.200700026
Dimitrios Meimaroglou, Apostolos Krallis, Vassilis Saliakas, Costas Kiparissides, Prediction of the Bivariate Molecular Weight - Long Chain Branching Distribution in Highly Branched Polymerization Systems Using Monte Carlo and Sectional Grid Methods Macromolecules. ,vol. 40, pp. 2224- 2234 ,(2007) , 10.1021/MA0623439
M. Asteasuain, A. Brandolin, C. Sarmoria, Recovery of molecular weight distributions from transformed domains. Part II. Application of numerical inversion methods Polymer. ,vol. 43, pp. 2529- 2541 ,(2002) , 10.1016/S0032-3861(02)00035-6
Mariano Asteasuain, Adriana Brandolin, Modeling and optimization of a high-pressure ethylene polymerization reactor using gPROMS Computers & Chemical Engineering. ,vol. 32, pp. 396- 408 ,(2008) , 10.1016/J.COMPCHEMENG.2007.02.011
Robin A. Hutchinson, Modeling of Chain Length and Long-Chain Branching Distributions in Free-Radical Polymerization Macromolecular Theory and Simulations. ,vol. 10, pp. 144- 157 ,(2001) , 10.1002/1521-3919(20010301)10:3<144::AID-MATS144>3.0.CO;2-A
M. Asteasuain, C. Sarmoria, A. Brandolin, Recovery of molecular weight distributions from transformed domains. Part I. Application of pgf to mass balances describing reactions involving free radicals Polymer. ,vol. 43, pp. 2513- 2527 ,(2002) , 10.1016/S0032-3861(02)00034-4
Apostolos Krallis, Dimitrios Meimaroglou, Costas Kiparissides, Dynamic prediction of the bivariate molecular weight–copolymer composition distribution using sectional-grid and stochastic numerical methods Chemical Engineering Science. ,vol. 63, pp. 4342- 4360 ,(2008) , 10.1016/J.CES.2008.05.047
Christian-Ulrich Schmidt, Markus Busch, Dieter Lilge, Michael Wulkow, Detailed Molecular Structure Modeling – A Path Forward to Designing Application Properties of ldPE Macromolecular Materials and Engineering. ,vol. 290, pp. 404- 414 ,(2005) , 10.1002/MAME.200400342