Skip to main content
SpringerLink
Log in

Exploring bimodal HDPE synthesis using single- and dual-site metallocene catalysts: a comprehensive review of the Monte Carlo method and AI-based approaches

  • Review paper
  • Published:
Journal of Polymer Research Aims and scope Submit manuscript

Abstract

The alteration of the molecular weight distribution (MWD) in high-density polyethylenes (HDPEs) can effectively address processing challenges. However, widening the MWD may have an adverse effect on the mechanical properties. To overcome this, the generation of a bimodal MWD involving low and high molecular weight polymers simultaneously is preferred. Catalytic polymerization and macromolecular engineering design offer viable approaches to achieve this objective. This study explores various production methods, including gas phase, slurry, and solution processes, for synthesizing HDPE with bimodal MWD. It investigates critical variables such as pressure, temperature, initial reactant concentrations (monomer, co-monomer, hydrogen), as well as the utilization of single- and dual-site metallocene catalysts and co-catalysts, which significantly impact the microstructure of bimodal HDPE. In addition, a comprehensive examination of simulation approaches for HDPE synthesis with bimodal MWD is presented, employing deterministic and stochastic methodologies such as moment equations, Monte Carlo simulations, and artificial intelligence (AI) techniques. Detailed insight is provided regarding the simulation algorithms specifically developed for ethylene copolymerization with various co-monomers. A comparative analysis of the advantages and disadvantages of each method is conducted, along with a discussion on the potential application of these methods in future research endeavors.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16

Similar content being viewed by others

References

  1. Soares JBP, McKenna TFL (2013) Polyolefin reaction engineering. John Wiley & Sons

    Google Scholar 

  2. Alkatheri MA (2015) Catalytic olefin polymerization: modelling of heterogeneous kinetics and single-particle growth. Petroleum Institute

    Google Scholar 

  3. Liu J, Rytter E (2001) Bimodal polyethylenes obtained with a dual-site metallocene catalyst system. Effect of trimethylaluminium addition. Macromol Rapid Commun 22:952–956

    Article  CAS  Google Scholar 

  4. Chu K-J, Soares JBP, Penlidis A (2000) Effect of hydrogen on ethylene polymerization using in-situ supported metallocene catalysts. Macromol Chem Phys 201:552–557

    Article  CAS  Google Scholar 

  5. Paredes B, van Grieken R, Carrero A et al (2012) Chromium oxide/metallocene binary catalysts for bimodal polyethylene: Hydrogen effects. Chem Eng J 213:62–69

    Article  CAS  Google Scholar 

  6. Wang M (2016) Synthesis of half-sandwich group 4 transition metal catalysts for tandem ring-opening metathesis/vinyl insertion polymerization

  7. Chung TCM (2002) Functionalization of polyolefins. Elsevier

    Google Scholar 

  8. Arabiourrutia M, Elordi G, Lopez G et al (2012) Characterization of the waxes obtained by the pyrolysis of polyolefin plastics in a conical spouted bed reactor. J Anal Appl Pyrolysis 94:230–237

    Article  CAS  Google Scholar 

  9. Ahvenainen A, Sarantila K, Andtsjo H et al (1994) Multi-stage process for producing polyethylene

  10. Al-Shamrani AA (2010) Characterization, optimization and modelling of PE blends for pipe applications. Loughborough University

    Google Scholar 

  11. Dominguez C, Robledo N, Paredes B, Garcia-Muñoz RA (2020) Strain hardening test on the limits of slow crack growth evaluation in high resistance polyethylene resins: effect of comonomer type. Polym Test 81:106155

    Article  CAS  Google Scholar 

  12. Gahleitner M, Severn JR (2008) Designing polymer properties

  13. Liu H-T, Davey CR, Shirodkar PP (2003) Bimodal polyethylene products from UNIPOLTM single gas phase reactor using engineered catalysts. Macromolecular symposia. pp 309–316

    Google Scholar 

  14. Makaryan IA, Sedov IV (2021) State of the global market of bimodal polyethylenes and the basic technologies for their production. Russ J Gen Chem 91:571–581

    Article  CAS  Google Scholar 

  15. Dengfei W, Jian W, Feng G et al (2016) Progress in technology and catalysts for gas phase polyethylene processes. Adv Sci an d Eng 8:25–31

    Google Scholar 

  16. Jiang B, Ye J, Liao Z et al (2018) Experimental investigation on mechanisms of fine particles generation for the Borealis Borstar multistage olefin polymerization process. J Appl Polym Sci 135:46589

    Article  Google Scholar 

  17. Chen K, Tian Z, Luo N, Liu B (2014) Modeling and simulation of borstar bimodal polyethylene process based on a rigorous PC-SAFT equation of state model. Ind Eng Chem Res 53:19905–19915

    Article  CAS  Google Scholar 

  18. Thakur AK, Gupta SK, Chaudhari P (2020) Slurry-phase ethylene polymerization processes: a review on multiscale modeling and simulations. Rev Chem Eng 38:539–568

    Article  Google Scholar 

  19. Fekete T, Subert J, Jónap K et al (2009) Production of bimodal polyethylene

  20. Touloupidis V (2010) Mathematical modelling and simulation of an industrial α-olefins catalytic slurry phase loop-reactor series. Univ Thessaloniki

    Google Scholar 

  21. Smith M (2005) Chevron Phillips slurry-loop-reactor process for polymerizing linear polyethylene. Handb Petrochemicals Prod Process Robert A Meyers, Ed McGraw-Hill

  22. Wang D, Yang G, Guo F et al (2018) Progress in technology and catalysts for continuous stirred tank reactor type slurry phase polyethylene processes. Pet Chem 58:264–273

    Article  CAS  Google Scholar 

  23. Soares JBP, McKenna TFL (2012) Polyolefin reaction engineering. Wiley Online Library

    Book  Google Scholar 

  24. Kissin YV (1989) Homogeneous interpretation of ethylene polymerization kinetics with supported ziegler-natta catalysts. J Mol Catal 56:220–236

    Article  CAS  Google Scholar 

  25. Gray SD, Coffy TJ, Shamshoum ES, Chen H (2005) Polyolefin catalysts, production thereof and method of use

  26. Samson JJC, van Middelkoop B, Weickert G, Westerterp KR (1999) Gas-phase polymerization of propylene with a highly active ziegler-natta catalyst. AIChE J 45:1548–1558

    Article  CAS  Google Scholar 

  27. Alizadeh M, Mostoufi N, Pourmahdian S, Sotudeh-Gharebagh R (2004) Modeling of fluidized bed reactor of ethylene polymerization. Chem Eng J 97:27–35

    Article  CAS  Google Scholar 

  28. Abbasi MR, Shamiri A, Hussain MA (2016) Dynamic modeling and Molecular Weight Distribution of ethylene copolymerization in an industrial gas-phase Fluidized-Bed Reactor. Adv Powder Technol 27:1526–1538

    Article  CAS  Google Scholar 

  29. Kusolsongtawee T, Bumroongsri P (2018) Two-stage modeling strategy for industrial fluidized bed reactors in gas-phase ethylene polymerization processes. Chem Eng Res Des 140:68–81

    Article  CAS  Google Scholar 

  30. Raufast C (1987) Polymerization in several stages of alpha-olefins in the gas phase

  31. Abbasi MR, Shamiri A, Hussain MA (2019) A review on modeling and control of olefin polymerization in fluidized-bed reactors. Rev Chem Eng 35:311–333

    Article  CAS  Google Scholar 

  32. Albunia AR (2019) Multimodal polymers with supported catalysts: design and production. Springer

    Book  Google Scholar 

  33. McCoy JT, Soares JBP, Rawatlal R (2013) Analysis of slurry phase co-polymerization of Ethylene and 1-Butene by Ziegler-Natta catalysts. Macromol React Eng 7:350–361

    Article  CAS  Google Scholar 

  34. Chen X, Liu D, Wang H (2010) Synthesis of bimodal polyethylene using Ziegler-Natta catalysts by multiple H2 concentration switching in a single slurry reactor. Macromol React Eng 4:342–346

    Article  CAS  Google Scholar 

  35. Gao K, Yi J, Yuan Y et al (2012) Progress in slurry process and catalyst for polyethylene with bimodal molecular weight distribution [J]. Polym Bull 4

  36. Vantomme A, Bernard P, Michel J et al (2018) Metallocene-catalyzed polyethylene

  37. Junling GZYDZ, Baoyun J (2008) Industrial application of BCE catalyst in slurry process for polyethylene with bimodal relative molecular mass distribution [J]. Petrochemical Technol 9

  38. Zifang G, Wei C, Junling Z, Hongxu Y (2009) Novel high performance Ziegler-Natta catalyst for ethylene slurry polymerization. Chin J Chem Eng 17:530–534

    Article  Google Scholar 

  39. Suhm J, Schneider MJ, Mülhaupt R (1998) Influence of metallocene structures on ethene copolymerization with 1-butene and 1-octene. J Mol Catal A Chem 128:215–227

    Article  CAS  Google Scholar 

  40. Jandaghian MH, Maddah Y, Nikzinat E et al (2021) Investigation of the effect of Mg (OEt) 2 manipulation on the ethylene and 1-butene co-polymerization performance of Ziegler-Natta catalysts. J Macromol Sci Part A 58:492–498

    Article  CAS  Google Scholar 

  41. Pérez O, Soares JBP, Garcia M et al (2013) Heterogeneous ethylene and alpha-olefin copolymerization using zirconocene aluminohydride complexes. Macromolecular symposia. pp 71–76

    Google Scholar 

  42. Dornik HP, Luft G, Rau A, Wieczorek T (2003) Metallocene-catalyzed solution polymerization of ethene at elevated pressure. Macromol Mater Eng 288:558–561

    Article  CAS  Google Scholar 

  43. de Camargo Forte MM, da Cunha FOV, dos Santos JHZ, Zacca JJ (2003) Ethylene and 1-butene copolymerization catalyzed by a Ziegler-Natta/metallocene hybrid catalyst through a 23 factorial experimental design. Polymer (Guildf) 44:1377–1384

    Article  Google Scholar 

  44. Bruaseth I, Rytter E (2003) Dual site ethene/1-hexene copolymerization with MAO activated (1, 2, 4-Me3Cp) 2ZrCl2 and (Me5Cp) 2ZrCl2 catalysts. Possible transfer of polymer chains between the sites. Macromolecules 36:3026–3034

    Article  Google Scholar 

  45. Heiland K, Kaminsky W (1992) Comparison of zirconocene and hafnocene catalysts for the polymerization of ethylene and 1-butene. Die Makromol Chemie Macromol Chem Phys 193:601–610

    Article  CAS  Google Scholar 

  46. Zhu B, Guo C, Liu Z, Yin Y (2004) In situ copolymerization of ethylene to produce linear low-density polyethylene by Ti (OBu) 4/AlEt3-MAO/SiO2/Et (Ind) 2ZrCl2. J Appl Polym Sci 94:2451–2455

    Article  CAS  Google Scholar 

  47. Ahmadjo S, Dehghani S, Zohuri GH et al (2015) Thermal behavior of polyethylene reactor alloys polymerized by Ziegler-Natta/late transition metal hybrid catalyst. Macromol React Eng 9:8–18

    Article  CAS  Google Scholar 

  48. Mortazavi SMM, Jafarian H, Ahmadi M, Ahmadjo S (2016) Characteristics of linear/branched polyethylene reactor blends synthesized by metallocene/late transitional metal hybrid catalysts. J Therm Anal Calorim 123:1469–1478

    Article  CAS  Google Scholar 

  49. Maddah Y, Ahmadjo S, Mortazavi SMM et al (2020) Control over branching topology by introducing a dual catalytic system in coordinative chain transfer polymerization of olefins. Macromolecules 53:4312–4322

    Article  CAS  Google Scholar 

  50. Hassanian-Moghaddam D, Mortazavi SMM, Ahmadjo S et al (2022) Resolving long-chain branch formation in tandem catalytic coordinative chain transfer polymerization of ethylene via thermal analysis. J Polym Res 29:1–10

    Article  Google Scholar 

  51. Zhou J-M, Li N-H, Bu N-Y et al (2003) Gas-phase ethylene polymerization over polymer-supported metallocene catalysts. J Appl Polym Sci 90:1319–1330

    Article  CAS  Google Scholar 

  52. Wegner MM, Ott AK, Rieger B (2010) Gas phase polymerization of ethylene with supported α-diimine nickel (II) catalysts. Macromolecules 43:3624–3633

    Article  CAS  Google Scholar 

  53. Rahaman M, Parvez MA, Soares JBP, Hussein IA (2014) Effect of polymerization conditions on thermal and mechanical properties of ethylene/1-butene copolymer made with Ziegler-Natta catalysts. Int J Polym Sci 2014

  54. Li W, Guan C, Xu J et al (2014) Bimodal/broad polyethylene prepared in a disentangled state. Ind Eng Chem Res 53:1088–1096

    Article  CAS  Google Scholar 

  55. Sedov IV, Russiyan LN, Blinova LN et al (2014) Dual-site hybrid catalysts for production of linear low-density polyethylene. J Polym Res 21:1–4

    Article  CAS  Google Scholar 

  56. Mattos Neto AG, Freitas MF, Nele M, Pinto JC (2005) Modeling ethylene/1-butene copolymerizations in industrial slurry reactors. Ind Eng Chem Res 44:2697–2715

    Article  CAS  Google Scholar 

  57. Chatzidoukas C, Kanellopoulos V, Kiparissides C (2007) On the production of polyolefins with bimodal molecular weight and copolymer composition distributions in catalytic gas-phase fluidized-bed reactors. Macromol Theory Simulations 16:755–769

    Article  CAS  Google Scholar 

  58. Xie T, McAuley KB, Hsu JCC, Bacon DW (1994) Gas phase ethylene polymerization: Production processes, polymer properties, and reactor modeling. Ind Eng Chem Res 33:449–479

    Article  CAS  Google Scholar 

  59. Ogunnaike BA (1994) On-line modelling and predictive control of an industrial terpolymerization reactor. Int J Control 59:711–729

    Article  Google Scholar 

  60. Kozub DJ, MacGregor JF (1992) Feedback control of polymer quality in semi-batch copolymerization reactors. Chem Eng Sci 47:929–942

    Article  CAS  Google Scholar 

  61. DesLauriers PJ, Rohlfing DC (2009) Estimating slow crack growth performance of polyethylene resins from primary structures such as molecular weight and short chain branching. Macromolecular symposia. pp 136–149

    Google Scholar 

  62. DesLauriers PJ, Rohlfing DC (2011) System and method for estimating density of a polymer

  63. Tian Z, Chen K-R, Liu B-P et al (2015) Short-chain branching distribution oriented model development for Borstar bimodal polyethylene process and its correlation with product performance of slow crack growth. Chem Eng Sci 130:41–55

    Article  CAS  Google Scholar 

  64. Ehrenstein GW (2012) Polymeric materials: structure, properties, applications. Carl Hanser Verlag GmbH Co KG

  65. Furukawa T, Sato H, Kita Y et al (2006) Molecular structure, crystallinity and morphology of polyethylene/polypropylene blends studied by Raman mapping, scanning electron microscopy, wide angle X-ray diffraction, and differential scanning calorimetry. Polym J 38:1127–1136

    Article  CAS  Google Scholar 

  66. Samuel AZ, Lai B-H, Lan S-T et al (2017) Estimating percent crystallinity of polyethylene as a function of temperature by Raman spectroscopy multivariate curve resolution by alternating least squares. Anal Chem 89:3043–3050

    Article  CAS  PubMed  Google Scholar 

  67. Moyassari A, Gkourmpis T, Hedenqvist MS, Gedde UW (2019) Molecular dynamics simulations of short-chain branched bimodal polyethylene: topological characteristics and mechanical behavior. Macromolecules 52:807–818

    Article  CAS  Google Scholar 

  68. McAuley KB, MacGregor JF, Hamielec AE (1990) A kinetic model for industrial gas-phase ethylene copolymerization. AIChE J 36:837–850

    Article  CAS  Google Scholar 

  69. Spitz R (1987) Molecular weight distribution in Ziegler-Natta olefin polymerization. Recent advances in mechanistic and synthetic aspects of polymerization. Springer, pp 485–502

    Chapter  Google Scholar 

  70. Bremner T, Rudin A, Cook DG (1990) Melt flow index values and molecular weight distributions of commercial thermoplastics. J Appl Polym Sci 41:1617–1627

    Article  CAS  Google Scholar 

  71. Narkchamnan K, Anantawaraskul S, Soares JBP (2011) Bimodality criterion for the chemical composition distribution of ethylene/1-olefin copolymers: theoretical development and experimental validation. Macromol React Eng 5:198–210

    Article  CAS  Google Scholar 

  72. Nele M, Pinto JC (2002) Molecular-Weight Multimodality of Multiple Flory Distributions. Macromol theory simulations 11:293–307

    Article  CAS  Google Scholar 

  73. Soares JBP, Kim JD (2000) Copolymerization of ethylene and $α$-olefins with combined metallocene catalysts. I. A formal criterion for molecular weight bimodality. J Polym Sci Part A Polym Chem 38:1408–1416

    Article  CAS  Google Scholar 

  74. Daftaribesheli M (2009) Comparison of catalytic ethylene polymerization in slurry and gas phase. Univ Twente

  75. Aigner P, Paulik C, Krallis A, Kanellopoulos V (2016) Optimal catalyst and cocatalyst precontacting in industrial ethylene copolymerization processes. J Polym 2016

  76. Yiagopoulos A, Yiannoulakis H, Dimos V, Kiparissides C (2001) Heat and mass transfer phenomena during the early growth of a catalyst particle in gas-phase olefin polymerization: the effect of prepolymerization temperature and time. Chem Eng Sci 56:3979–3995

    Article  CAS  Google Scholar 

  77. Michaels AS, Bixler HJ (1961) Solubility of gases in polyethylene. J Polym Sci 50:393–412

    Article  CAS  Google Scholar 

  78. Pladis P, Baltsas A, Meimaroglou D, Kiparissides C (2018) A dynamic simulator for slurry-phase catalytic olefin copolymerization in a series of CSTRs: prediction of distributed molecular and rheological properties. Macromol React Eng 12:1800017

    Article  Google Scholar 

  79. Hutchinson RA, Ray WH (1990) Polymerization of olefins through heterogeneous catalysis. VIII. Monomer sorption effects. J Appl Polym Sci 41:51–81

    Article  CAS  Google Scholar 

  80. Sun J, Wang H, Chen M et al (2017) Solubility measurement of hydrogen, ethylene, and 1-hexene in polyethylene films through an intelligent gravimetric analyzer. J Appl Polym Sci 134:44507

    Article  Google Scholar 

  81. Kulkarni SS, Stern SA (1983) The diffusion of CO2, CH4, C2H4, and C3H8 in polyethylene at elevated pressures. J Polym Sci Polym Phys Ed 21:441–465

    Article  CAS  Google Scholar 

  82. Moore SJ, Wanke SE (2001) Solubility of ethylene, 1-butene and 1-hexene in polyethylenes. Chem Eng Sci 56:4121–4129

    Article  CAS  Google Scholar 

  83. Kröner S, Minjiong W, Bartke M (2011) Thermodynamic data of ethylene-propane mixtures in condensed and supercritical state. Macromol React Eng 5:563–574

    Article  Google Scholar 

  84. Burriss WL, Hsu NT, Reamer HH, Sage BH (1953) Phase behavior of the hydrogen-propane system. Ind Eng Chem 45:210–213

    Article  CAS  Google Scholar 

  85. Poling BE (2004) The properties of gases and liquids

  86. Zhuze TP, Zhurba AS (1960) Solubilities of ethylene in hexane, cyclohexane, and benzene under pressure. Bull Acad Sci USSR Div Chem Sci 9:335–337

    Article  Google Scholar 

  87. Snijder ED, Versteeg GF, van Swaaij WPM (1994) Some properties of LaNi5-xAlx metal alloys and the diffusion coefficient and solubility of hydrogen in cyclohexane. J Chem Eng Data 39:405–408

    Article  CAS  Google Scholar 

  88. Habashi RB, Najafi M, Zarghami R (2024) An exact and vigorous kinetic Monte Carlo simulation to determine the properties of bimodal HDPE synthesized with a dual-site metallocene catalyst. J Mol Graph Model 126:108668

    Article  CAS  PubMed  Google Scholar 

  89. Xie T, McAuley KB, Hsu JCC, Bacon DW (1995) Modeling molecular weight development of gas-phase α-olefin copolymerization. AIChE J 41:1251–1265

    Article  CAS  Google Scholar 

  90. Kröner S, Eloranta K, Bergstra MF, Bartke M (2007) Kinetic study of the copolymerisation of ethylene with a single site catalyst in propane slurry polymerisation. Macromolecular symposia. pp 284–294

    Google Scholar 

  91. Soares JBP (2001) Mathematical modelling of the microstructure of polyolefins made by coordination polymerization: a review. Chem Eng Sci 56:4131–4153

    Article  CAS  Google Scholar 

  92. Chakravarti S, Ray WH (2001) Kinetic study of olefin polymerization with a supported metallocene catalyst. II. Ethylene/1-hexene copolymerization in gas phase. J Appl Polym Sci 80:1096–1119

    Article  CAS  Google Scholar 

  93. Soares JBP (2004) Polyolefins with long chain branches made with single-site coordination catalysts: a review of mathematical modeling techniques for polymer microstructure. Macromol Mater Eng 289:70–87

    Article  CAS  Google Scholar 

  94. Mastan E, Zhu S (2015) Method of moments: A versatile tool for deterministic modeling of polymerization kinetics. Eur Polym J 68:139–160

    Article  CAS  Google Scholar 

  95. Ali MA, Ajbar EAA, Alhumaizi K (2010) Control of molecular weight distribution of polyethylene in gas-phase fluidized bed reactors. Korean J Chem Eng 27:364–372

    Article  CAS  Google Scholar 

  96. Ali MA, Ali EM (2011) Effect of monomer feed and production rate on the control of molecular weight distribution of polyethylene in gas phase reactors. Comput Chem Eng 35:2480–2490

    Article  Google Scholar 

  97. Kazerooni NM, Eslamloueyan R, Biglarkhani M (2019) Dynamic simulation and control of two-series industrial reactors producing linear low-density polyethylene. Int J Ind Chem 10:107–120

    Article  CAS  Google Scholar 

  98. Young M-J, Ma C-CM (2002) Polymerization kinetics and modeling of slurry ethylene polymerization process with metallocene/MAO catalysts. Polym Plast Technol Eng 41:601–618

    Article  CAS  Google Scholar 

  99. Ahmadi M, Nekoomanesh M, Jamjah R et al (2007) Modeling of slurry polymerization of ethylene using a soluble Cp2ZrCl2/MAO catalytic system. Macromol Theory Simulations 16:557–565

    Article  CAS  Google Scholar 

  100. Touloupides V, Kanellopoulos V, Pladis P et al (2010) Modeling and simulation of an industrial slurry-phase catalytic olefin polymerization reactor series. Chem Eng Sci 65:3208–3222

    Article  CAS  Google Scholar 

  101. Khorasani MM, Saeb MR, Mohammadi Y, Ahmadi M (2014) The evolutionary development of chain microstructure during tandem polymerization of ethylene: A Monte Carlo simulation study. Chem Eng Sci 111:211–219

    Article  CAS  Google Scholar 

  102. Zhang J, Fan H, Li B-G, Zhu S (2008) Modeling and kinetics of tandem polymerization of ethylene catalyzed by bis (2-dodecylsulfanyl-ethyl) amine-CrCl3 and Et (Ind) 2ZrCl2. Chem Eng Sci 63:2057–2065

    Article  CAS  Google Scholar 

  103. Brandão ALT, Soares JBP, Pinto JC, Alberton AL (2015) When polymer reaction engineers play dice: applications of Monte Carlo models in PRE. Macromol React Eng 9:141–185

    Article  Google Scholar 

  104. Meimaroglou D, Kiparissides C (2014) Review of Monte Carlo methods for the prediction of distributed molecular and morphological polymer properties. Ind Eng Chem Res 53:8963–8979

    Article  CAS  Google Scholar 

  105. Bruns W, Motoc I, O’Driscoll KF (2012) Monte Carlo applications in polymer science. Springer Science & Business Media

    Google Scholar 

  106. Golshan S, Zarghami R, Mostoufi N (2019) A hybrid deterministic–stochastic model for spouted beds. Particuology 42:104–113

    Article  Google Scholar 

  107. Gillespie DT (1977) Exact stochastic simulation of coupled chemical reactions. J Phys Chem 81:2340–2361

    Article  CAS  Google Scholar 

  108. Platkowski K, Reichert K-H (1999) Application of Monte Carlo methods for modelling of polymerization reactions. Polymer (Guildf) 40:1057–1066

    Article  CAS  Google Scholar 

  109. Habashi RB, Najafi M, Mostafaei P, Shojaei B (2021) A detailed description of methyl methacrylate free radical polymerization using different heating policies under isothermal and non-isothermal conditions: a kinetic Monte Carlo simulation. Int J Model Simul 41:101–119

    Article  Google Scholar 

  110. Wilding NB, Müller M (1994) Accurate measurements of the chemical potential of polymeric systems by Monte Carlo simulation. J Chem Phys 101:4324–4330

    Article  CAS  Google Scholar 

  111. Ling J, Ni X, Zhang Y, Shen Z (2000) Monte Carlo simulation of gas phase polymerization of 1, 3-butadiene Part I. Modeling and programming Polymer (Guildf) 41:8703–8707

    Article  CAS  Google Scholar 

  112. Mavrantzas VG (2021) Using Monte Carlo to simulate complex polymer systems: Recent progress and outlook. Front Phys 9:661367

    Article  Google Scholar 

  113. Demirel Özçam D, Teymour F (2017) Chain-by-chain Monte Carlo simulation: a novel hybrid method for modeling polymerization. Part I. Linear controlled radical polymerization systems. Macromol React Eng 11:1600042

    Article  Google Scholar 

  114. Matsumoto M, Nishimura T (1998) Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator. ACM Trans Model Comput Simul 8:3–30

    Article  Google Scholar 

  115. Khubi-Arani Z, Salami-Kalajahi M, Najafi M et al (2010) Simulation of styrene free radical polymerization over bi-functional initiators using Monte Carlo simulation method and comparison with mono-functional initiators. Polym Sci Ser B 52:184–192

    Article  Google Scholar 

  116. Najafi M, Haddadi-Asl V, Mohammadi Y (2007) Application of the Monte Carlo simulation method to the investigation of peculiar free-radical copolymerization reactions: Systems with both reactivity ratios greater than unity (rA> 1 and rB> 1). J Appl Polym Sci 106:4138–4147

    Article  CAS  Google Scholar 

  117. Mohammadi Y, Najafi M, Haddadi-Asl V (2005) Comprehensive study of free radical copolymerization using a Monte Carlo simulation mthod, 1e. Macromol theory simulations 14:325–336

    Article  CAS  Google Scholar 

  118. Najafi M, Roghani-Mamaqani H, Haddadi-Asl V, Salami-Kalajahi M (2011) A simulation of kinetics and chain length distribution of styrene FRP and ATRP: Chain-length-dependent termination. Adv Polym Technol 30:257–268

    Article  CAS  Google Scholar 

  119. Najafi M, Roghani-Mamaqani H, Salami-Kalajahi M, Haddadi-Asl V (2010) A comprehensive Monte Carlo simulation of styrene atom transfer radical polymerization. Chinese J Polym Sci 28:483–497

    Article  CAS  Google Scholar 

  120. Saeb MR, Mohammadi Y, Ahmadi M et al (2015) A Monte Carlo-based feeding policy for tailoring microstructure of copolymer chains: Reconsidering the conventional metallocene catalyzed polymerization of α-olefins. Chem Eng J 274:169–180

    Article  CAS  Google Scholar 

  121. Salami-Kalajahi M, Najafi M, Haddadi-Asl V (2009) Application of Monte Carlo simulation method to polymerization kinetics over Ziegler-Natta catalysts. Int J Chem Kinet 41:45–56

    Article  CAS  Google Scholar 

  122. Taheri AR, Najafi M, Motahari S (2020) Prediction of branch on branch and topological characteristics of low-density polyethylene polymerization by a novel stochastic approach. Polym Adv Technol 31:1067–1076

    Article  CAS  Google Scholar 

  123. Brandão ALT, Alberton AL, Pinto JC, Soares JBP (2017) Copolymerization of Ethylene with 1,9-Decadiene: Part I - prediction of average molecular weights and long-chain branching frequencies. Macromol Theory Simulations 26:1–18

    Google Scholar 

  124. Brandão ALT, Alberton AL, Pinto JC, Soares JBP (2017) Copolymerization of Ethylene with 1, 9-Decadiene: Part II—prediction of molecular weight distributions. Macromol Theory Simulations 26:1700040

    Article  Google Scholar 

  125. Simon LC, Soares JBP (2005) Monte Carlo simulation of long-chain branched polyolefins made with dual catalysts: a classification of chain structures in topological branching families. Ind Eng Chem Res 44:2461–2468

    Article  CAS  Google Scholar 

  126. Beigzadeh D (2003) Monte Carlo simulation of long-chain branched polyethylene chains synthesized with dual-site-type catalyst systems. Macromol Theory Simul 12:174–183

    Article  CAS  Google Scholar 

  127. Sivanandam SN, Deepa SN (2006) Introduction to neural networks using Matlab 6.0. Tata McGraw-Hill Education

    Google Scholar 

  128. Yousef BF, Mourad A-HI, Hilal-Alnaqbi A (2013) Modeling of the mechanical behavior of polyethylene/polypropylene blends using artificial neural networks. Int J Adv Manuf Technol 64:601–611

    Article  Google Scholar 

  129. Ahmadi M, Nekoomanesh M, Arabi H (2009) New approach in modeling of metallocene-catalyzed olefin polymerization using artificial neural networks. Macromol Theory Simul 18:195–200

    Article  CAS  Google Scholar 

  130. Hagan MT, Menhaj MB (1994) Training feedforward networks with the Marquardt algorithm. IEEE Trans Neural Networks 5:989–993

    Article  CAS  PubMed  Google Scholar 

  131. Charoenpanich T, Anantawaraskul S, Soares JBP (2017) On the robustness of forward and inverse artificial neural networks for the simulation of ethylene/1-butene copolymerization. Macromol Theory Simul 26:1700042

    Article  Google Scholar 

  132. Wilamowski BM, Irwin JD (2011) The industrial electronics handbook: Intelligent Systems. CRC Press Boca Raton, Florida, United States

    Google Scholar 

  133. He S, Sepehri N, Unbehauen R (2001) Modifying weights layer-by-layer with levenberg-marquardt backpropagation algorithm. Intell Autom Soft Comput 7:233–247

    Article  Google Scholar 

  134. Charoenpanich T, Anantawaraskul S, Soares JBP (2016) Estimation of polymerization conditions needed to make ethylene/1-olefin copolymers with specific microstructures using artificial neural networks. Macromol React Eng 10:215–232

    Article  CAS  Google Scholar 

  135. Atashrouz S, Rahmani M, Balzadeh Z, Nasernejad B (2020) Mathematical modeling of ethylene polymerization over advanced multisite catalysts: an artificial intelligence approach. SN Appl Sci 2:356

    Article  CAS  Google Scholar 

  136. Rizkin BA, Hartman RL (2019) Supervised machine learning for prediction of zirconocene-catalyzed α-olefin polymerization. Chem Eng Sci 210:115224

    Article  CAS  Google Scholar 

  137. Anantawaraskul S, Toungsetwut M, Pinyapong R (2008) Determination of operating conditions of ethylene/1-octene copolymerization using artificial neural network (ANN). Macromolecular symposia. pp 157–162

    Google Scholar 

  138. Amnuaykijvanit O, Anantawaraskul S, Rakthanmanon T (2022) Estimation of ethylene/1-butene copolymerization conditions using the autoencoder model. J Phys Conf Ser 12028

  139. Charoenpanich T, Anantawaraskul S, Soares JBP (2020) Using artificial intelligence techniques to design ethylene/1-olefin copolymers. Macromol Theory Simulations 2000048

  140. Atashrouz S, Rahmani M, Nasernejad B, Balzade Z (2020) Kinetic prediction of molecular weight distribution in bimodal polyethylene from heterogeneous post-metallocene catalysis. Mater Chem Phys 255:123466

    Article  CAS  Google Scholar 

  141. Wulkow M (1996) The simulation of molecular weight distributions in polyreaction kinetics by discrete Galerkin methods. Macromol Theory Simul 5:393–416

    Article  CAS  Google Scholar 

  142. Lu J, Zhang H, Yang Y (1993) Monte Carlo simulation of kinetics and chain-length distribution in radical polymerization. Macromol Theory Simul 2:747–760

    Article  CAS  Google Scholar 

  143. He J, Zhang H, Chen J, Yang Y (1997) Monte Carlo simulation of kinetics and chain length distributions in living free-radical polymerization. Macromolecules 30:8010–8018

    Article  CAS  Google Scholar 

  144. Binder K, Müller M (2000) Monte Carlo simulation of block copolymers. Curr Opin Colloid Interface Sci 5:314–322

    Article  Google Scholar 

  145. Taheri AR, Najafi M, Motahari S (2020) A New Monte Carlo simulation of low-density-polyethylene polymerization for prediction of its microstructure as a result of various process conditions. J Macromol Sci Part B 59:457–478

    Article  CAS  Google Scholar 

  146. Al-Harthi M, Soares JBP, Simon LC (2007) Dynamic Monte Carlo simulation of ATRP with bifunctional initiators. Macromol React Eng 1:95–105

    Article  CAS  Google Scholar 

  147. Shah JK, Marin-Rimoldi E, Mullen RG et al (2017) Cassandra: an open source Monte Carlo package for molecular simulation

  148. Brandl F, Drache M, Beuermann S (2018) Kinetic Monte Carlo simulation based detailed understanding of the transfer processes in semi-batch iodine transfer emulsion polymerizations of vinylidene fluoride. Polymers (Basel) 10:1008

    Article  PubMed  Google Scholar 

  149. Zhang J (2004) A reliable neural network model based optimal control strategy for a batch polymerization reactor. Ind Eng Chem Res 43:1030–1038

    Article  CAS  Google Scholar 

  150. Curteanu S, Leon F, Furtuna R et al (2010) Comparison between different methods for developing neural network topology applied to a complex polymerization process. The 2010 International Joint Conference on Neural Networks (IJCNN), pp 1–8

    Google Scholar 

  151. Mohammadi Y, Saeb MR, Penlidis A et al (2019) Intelligent machine learning: tailor-making macromolecules. Polymers 11:579

    Article  PubMed  PubMed Central  Google Scholar 

  152. Zhang Z, Friedrich K (2003) Artificial neural networks applied to polymer composites: a review. Compos Sci Technol 63:2029–2044

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Polymer Engineering, School of Chemical Engineering, College of Engineering, University of Tehran, P.O. Box 11155-4563, Tehran, Iran

    Ramin Bairami Habashi & Mohammad Najafi

  2. School of Chemical Engineering, College of Engineering, University of Tehran, P.O. Box 11155- 4563, Tehran, Iran

    Reza Zarghami

Authors
  1. Ramin Bairami Habashi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mohammad Najafi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Reza Zarghami
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mohammad Najafi.

Ethics declarations

Conflict of interest

We hereby state that there is no conflict of interest.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary Information

Below is the link to the electronic supplementary material.

Supplementary Material 1

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Habashi, R.B., Najafi, M. & Zarghami, R. Exploring bimodal HDPE synthesis using single- and dual-site metallocene catalysts: a comprehensive review of the Monte Carlo method and AI-based approaches. J Polym Res 31, 76 (2024). https://doi.org/10.1007/s10965-024-03895-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10965-024-03895-8

Keywords

Search

Navigation