Table of Contents Author Guidelines Submit a Manuscript
International Journal of Polymer Science
Volume 2015 (2015), Article ID 469353, 12 pages
http://dx.doi.org/10.1155/2015/469353
Review Article

Highlight on the Mathematical Modeling of Controlled Free Radical Polymerization

Department of Chemical Engineering, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia

Received 15 October 2014; Accepted 8 March 2015

Academic Editor: Frederik Wurm

Copyright © 2015 Mamdouh A. Al-Harthi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. A. Goto and T. Fukuda, “Kinetics of living radical polymerization,” Progress in Polymer Science, vol. 29, no. 4, pp. 329–385, 2004. View at Publisher · View at Google Scholar · View at Scopus
  2. K. A. Davis and K. Matyjaszewski, “Statistical, gradient, block, and graft copolymers by controlled/living radical polymerizations,” Advances in Polymer Science, vol. 159, pp. 1–13, 2002. View at Google Scholar · View at Scopus
  3. M. Kamigaito, T. Ando, and M. Sawamoto, “Metal-catalyzed living radical polymerization,” Chemical Reviews, vol. 101, no. 12, pp. 3689–3745, 2001. View at Publisher · View at Google Scholar · View at Scopus
  4. K. Matyjaszewski, “Macromolecular engineering: from rational design through precise macromolecular synthesis and processing to targeted macroscopic material properties,” Progress in Polymer Science, vol. 30, no. 8-9, pp. 858–875, 2005. View at Publisher · View at Google Scholar · View at Scopus
  5. D. Benoit, V. Chaplinski, R. Braslau, and C. J. Hawker, “Development of a universal alkoxyamine for ‘living’ free radical polymerizations,” Journal of the American Chemical Society, vol. 121, no. 16, pp. 3904–3920, 1999. View at Publisher · View at Google Scholar · View at Scopus
  6. M. Rodlert, E. Harth, I. Rees, and C. J. Hawker, “End-group fidelity in nitroxide-mediated living free-radical polymerizations,” Journal of Polymer Science, Part A: Polymer Chemistry, vol. 38, pp. 4749–4763, 2000. View at Publisher · View at Google Scholar · View at Scopus
  7. G. Moad, J. Chiefary, Y. K. Chong et al., “Living free radical polymerization with reversible addition—fragmentation chain transfer (the life of RAFT),” Polymer International, vol. 49, pp. 993–1001, 2000. View at Google Scholar
  8. J. Chiefari, Y. K. Chong, F. Ercole et al., “Living free-radical polymerization by reversible addition−fragmentation chain transfer:  the RAFT process,” Macromolecules, vol. 31, no. 16, pp. 5559–5562, 1998. View at Publisher · View at Google Scholar · View at Scopus
  9. K. Matyjaszewski and J. Xia, “Atom transfer radical polymerization,” Chemical Reviews, vol. 101, no. 9, pp. 2921–2990, 2001. View at Publisher · View at Google Scholar · View at Scopus
  10. E. Borsig, M. Lazár, M. Čapla, and Š. Florián, “Reinitiation reactions of poly(methyl methacrylate) with labile bound fragments of initiator,” Die Angewandte Makromolekulare Chemie, vol. 9, no. 1, pp. 89–95, 1969. View at Publisher · View at Google Scholar
  11. T. Otsu and M. Yoshida, “Role of initiator-transfer agent-terminator (iniferter) in radical polymerizations: polymer design by organic disulfides as inferters,” Makromolekulare Chemie: Rapid Communications, vol. 3, pp. 127–132, 1982. View at Google Scholar
  12. T. Otsu and A. Kuriyama, “Polymer design by iniferter technique in radical polymerization: synthesis of ab and aba block copolymers containing random and alternating copolymer sequences,” Polymer Journal, vol. 17, no. 1, pp. 97–104, 1984. View at Google Scholar · View at Scopus
  13. M. Lee and Y. Minoura, “Polymerization of vinyl monomers initiated by chromium(II) acetate + organic peroxides,” Journal of the Chemical Society, Faraday Transactions 1: Physical Chemistry in Condensed Phases, vol. 74, pp. 1726–1737, 1978. View at Publisher · View at Google Scholar · View at Scopus
  14. W. A. Braunecker and K. Matyjaszewski, “Controlled/living radical polymerization: features, developments, and perspectives,” Progress in Polymer Science, vol. 32, no. 1, pp. 93–146, 2007. View at Publisher · View at Google Scholar · View at Scopus
  15. M. Sawamoto and M. Kamigaito, “Living radical polymerization mediated by transition metals: recent advances,” in Controlled Radical Polymerization, vol. 685 of ACS Symposium Series, chapter 18, pp. 296–304, American Chemical Society, 1998. View at Publisher · View at Google Scholar
  16. D. H. Solomon, E. Rizzardo, and P. Cacioli, “Read/write system for optical disc apparatus with fiber optics,” US Patent 4,581,529, 1985.
  17. M. K. Georges, R. P. N. Veregin, P. M. Kazmaier, and G. K. Hamer, “Narrow molecular weight resins by a free-radical polymerization process,” Macromolecules, vol. 26, no. 11, pp. 2987–2988, 1993. View at Publisher · View at Google Scholar · View at Scopus
  18. J. Chiefari, Y. K. Chong, F. Ercole et al., “Living free-radical polymerization by reversible addition—fragmentation chain transfer: the RAFT process,” Macromolecules, vol. 31, no. 16, pp. 5559–5562, 1998. View at Publisher · View at Google Scholar · View at Scopus
  19. R. P. N. Veregin, P. G. Odell, L. M. Michalak, and M. K. Georges, “Molecular weight distributions in nitroxide-mediated living free radical polymerization: kinetics of the slow equilibria between growing and dormant chains,” Macromolecules, vol. 29, no. 10, pp. 3346–3352, 1996. View at Publisher · View at Google Scholar · View at Scopus
  20. T. Fukuda, Y. Tsujii, and T. Miyamoto, “Book of abstracts,” in Proceedings of the 213th ACS National Meeting, San Francisco, Calif, USA, April 1997.
  21. J. He, H. Zhang, J. Chen, and Y. Yang, “Monte Carlo simulation of kinetics and chain length distributions in living free-radical polymerization,” Macromolecules, vol. 30, no. 25, pp. 8010–8018, 1997. View at Publisher · View at Google Scholar · View at Scopus
  22. D. A. Shipp and K. Matyjaszewski, Polymer Preprints, vol. 40, Division of Polymer Chemistry, American Chemical Society, 1999.
  23. J. He, L. Li, and Y. Yang, “Monte Carlo simulation on rate enhancement of nitroxide-mediated living free-radical polymerization,” Macromolecular Theory and Simulations, vol. 9, no. 8, pp. 463–468, 2000. View at Publisher · View at Google Scholar · View at Scopus
  24. H. Fischer, “Unusual selectivities of radical reactions by internal suppression of fast modes,” Journal of the American Chemical Society, vol. 108, no. 14, pp. 3925–3927, 1986. View at Publisher · View at Google Scholar · View at Scopus
  25. D. Rueegge and H. Fischer, “Unusual selectivities of radical reactions. Experimental studies on alkyl versus phenoxyl reaction systems,” International Journal of Chemical Kinetics, vol. 21, no. 8, pp. 703–714, 1989. View at Publisher · View at Google Scholar · View at Scopus
  26. H. Fischer, “The persistent radical effect in ‘living’ radical polymerization,” Macromolecules, vol. 30, no. 19, pp. 5666–5672, 1997. View at Publisher · View at Google Scholar · View at Scopus
  27. T. Kothe, S. Marque, R. Martschke, M. Popov, and H. Fischer, “Radical reaction kinetics during homolysis of N-alkoxyamines: verification of the persistent radical effect,” Journal of the Chemical Society, Perkin Transactions 2, no. 7, pp. 1553–1559, 1998. View at Google Scholar · View at Scopus
  28. T. Kothe, R. Martschke, and H. Fischer, “Photoreactions of the decatungstate anion W10O324- with organic substrates in solution studied by EPR and kinetic absorption spectroscopy: an example for the persistent radical effect,” Journal of the Chemical Society. Perkin Transactions 2, no. 3, pp. 503–507, 1998. View at Google Scholar · View at Scopus
  29. H. Fischer, “The persistent radical effect in controlled radical polymerizations,” Journal of Polymer Science Part A: Polymer Chemistry, vol. 37, no. 13, pp. 1885–1901, 1999. View at Publisher · View at Google Scholar · View at Scopus
  30. J. Bonilla, E. Saldívar, A. Flores-Tlacuahuac, E. Vivaldo-Lima, R. Pfaendner, and F. Tiscareño-Lechuga, “Detailed modeling, simulation, and parameter estimation of nitroxide mediated living free radical polymerization of styrene,” Polymer Reaction Engineering, vol. 10, no. 4, pp. 227–263, 2002. View at Publisher · View at Google Scholar · View at Scopus
  31. T. Schulte, C. A. Knoop, and A. Studer, “Nitroxide-mediated living free-radical polymerization of styrene: a systematic study of the variation of the alkoxyamine concentration,” Journal of Polymer Science, Part A: Polymer Chemistry, vol. 42, no. 13, pp. 3342–3351, 2004. View at Publisher · View at Google Scholar · View at Scopus
  32. Y. Guillaneuf, D. Gigmes, S. R. A. Marque, P. Tonlo, and D. Bertin, “Nitroxide-mediated polymerization of methyl methacrylate using an SG1-based alkoxyamine: how the penultimate effect could lead to uncontrolled and unliving polymerization,” Macromolecular Chemistry and Physics, vol. 207, no. 14, pp. 1278–1288, 2006. View at Publisher · View at Google Scholar · View at Scopus
  33. D. Gigmes, D. Bertin, C. Lefay, and Y. Guillaneuf, “Kinetic modeling of nitroxide-mediated polymerization: conditions for living and controlled polymerization,” Macromolecular Theory and Simulations, vol. 18, no. 7-8, pp. 402–419, 2009. View at Publisher · View at Google Scholar · View at Scopus
  34. R. Lemoine-Nava, A. Flores-Tlacuahuac, and E. Saldívar-Guerra, “Non-linear bifurcation analysis of the living nitroxide-mediated radical polymerization of styrene in a CSTR,” Chemical Engineering Science, vol. 61, no. 2, pp. 370–387, 2006. View at Publisher · View at Google Scholar · View at Scopus
  35. M. Zhang and W. H. Ray, “Modeling of ‘living’ free-radical polymerization processes. I. Batch, semibatch, and continuous tank reactors,” Journal of Applied Polymer Science, vol. 86, no. 7, pp. 1630–1662, 2002. View at Publisher · View at Google Scholar · View at Scopus
  36. Y. Fu, M. F. Cunningham, and R. A. Hutchinson, “Modeling of nitroxide-mediated semibatch radical polymerization,” Macromolecular Reaction Engineering, vol. 1, no. 2, pp. 243–252, 2007. View at Publisher · View at Google Scholar
  37. M. Asteasuain, M. Soares, M. K. Lenzi et al., “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. View at Google Scholar
  38. M. Asteasuain, M. Soares, M. K. Lenzi et al., “‘Living’ radical polymerization in tubular reactors, 2—process optimization for tailor-made molecular weight distributions,” Macromolecular Reaction Engineering, vol. 2, no. 5, pp. 414–421, 2008. View at Publisher · View at Google Scholar
  39. M. Roa-Luna, A. Nabifar, N. T. McManus, E. Vivaldo-Lima, L. M. F. Lona, and A. Penlidis, “Effect of the addition of inert or TEMPO-capped prepolymer on polymerization rate and molecular weight development in the nitroxide-mediated radical polymerization of styrene,” Journal of Applied Polymer Science, vol. 109, no. 6, pp. 3665–3678, 2008. View at Publisher · View at Google Scholar · View at Scopus
  40. J. Belincanta-Ximenes, P. V. R. Mesa, L. M. F. Lona, E. Vivaldo-Lima, N. T. McManus, and A. Penlidis, “Simulation of styrene polymerization by monomolecular and bimolecular nitroxide-mediated radical processes over a range of reaction conditions,” Macromolecular Theory and Simulations, vol. 16, no. 2, pp. 194–208, 2007. View at Publisher · View at Google Scholar · View at Scopus
  41. L. Li, J. P. He, and Y. L. Yang, “Monte Carlo simulation on living radical polymerization with RAFT process,” Chemical Journal of Chinese Universities (Chinese Edition), vol. 21, pp. 1146–1148, 2000. View at Google Scholar
  42. M. Zhang and W. H. Ray, “Modeling of ‘living’ free-radical polymerization with RAFT chemistry,” Industrial & Engineering Chemistry Research, vol. 40, no. 20, pp. 4336–4352, 2001. View at Publisher · View at Google Scholar · View at Scopus
  43. P. Vana, T. P. Davis, and C. Barner-Kowollik, “Kinetic analysis of reversible addition fragmentation chain transfer (RAFT) polymerizations: conditions for inhibition, retardation, and optimum living polymerization,” Macromolecular Theory and Simulations, vol. 11, no. 8, pp. 823–835, 2002. View at Publisher · View at Google Scholar · View at Scopus
  44. C. Barner-Kowollik, J. F. Quinn, D. R. Morsley, and T. P. Davis, “Modeling the reversible addition-fragmentation chain transfer process in cumyl dithiobenzoate-mediated styrene homopolymerizations: assessing rate coefficients for the addition-fragmentation equilibrium,” Journal of Polymer Science Part A: Polymer Chemistry, vol. 39, no. 9, pp. 1353–1365, 2001. View at Publisher · View at Google Scholar · View at Scopus
  45. P. Vana, T. P. Davis, and C. Barner-Kowollik, “Kinetic analysis of reversible addition fragmentation chain transfer (RAFT) polymerizations: conditions for inhibition, retardation, and optimum living polymerization,” Macromolecular Theory and Simulations, vol. 11, no. 8, pp. 823–835, 2002. View at Google Scholar · View at Scopus
  46. M. Wulkow, M. Busch, T. P. Davis, and C. Barner - Kowollik, “Implementing the reversible addition-fragmentation chain transfer process in PREDICI,” Journal of Polymer Science Part A: Polymer Chemistry, vol. 42, no. 6, pp. 1441–1448, 2004. View at Google Scholar
  47. J. Pallares, J. Gabriel, F. Citlalli, L. E. Vivaldo, L. M. F. Lona, and A. Penlidis, “Comparison of reaction mechanisms for reversible additionfragmentation chain transfer polymerization using modeling tools,” Journal of Macromolecular Science A, vol. 43, pp. 1293–1322, 2006. View at Google Scholar
  48. G. Jaramillo-Soto, M. L. Castellanos-Cárdenas, P. R. García-Morán, E. Vivaldo-Lima, G. Luna-Bárcenas, and A. Penlidis, “Simulation of RAFT dispersion polymerization in supercritical carbon dioxide,” Macromolecular Theory and Simulations, vol. 17, no. 6, pp. 280–289, 2008. View at Publisher · View at Google Scholar · View at Scopus
  49. A. R. Wang and S. Zhu, “Modeling the reversible addition-fragmentation transfer polymerization process,” Journal of Polymer Science A: Polymer Chemistry, vol. 41, no. 11, pp. 1553–1566, 2003. View at Publisher · View at Google Scholar · View at Scopus
  50. A. R. Wang and S. Zhu, “Calculations of monomer conversion and radical concentration in reversible addition-fragmentation chain transfer radical polymerization,” Macromolecular Theory and Simulations, vol. 12, no. 9, pp. 663–668, 2003. View at Publisher · View at Google Scholar · View at Scopus
  51. S. W. Prescott, “Chain-length dependence in living/controlled free-radical polymerizations: physical manifestation and monte carlo simulation of reversible transfer agents,” Macromolecules, vol. 36, no. 25, pp. 9608–9621, 2003. View at Publisher · View at Google Scholar · View at Scopus
  52. Y. Ao, J. He, X. Han et al., “Kinetic analysis of the cross reaction between dithioester and alkoxyamine by a Monte Carlo simulation,” Journal of Polymer Science, Part A: Polymer Chemistry, vol. 45, no. 3, pp. 374–387, 2007. View at Publisher · View at Google Scholar · View at Scopus
  53. H. Tobita and F. Yanase, “Monte Carlo simulation of controlled/living radical polymerization in emulsified systems,” Macromolecular Theory and Simulations, vol. 16, no. 4, pp. 476–488, 2007. View at Publisher · View at Google Scholar · View at Scopus
  54. M. Drache, K. Drees, and G. Schmidt-Naake, “Implementation of a Kinetic model of the RAFT polymerization with a Monte Carlo method,” in Proceedings of the 8th International Workshop on Polymer Reaction Engineering, October 2004.
  55. M. Drache, P. Vana, and G. Schmidt-Naake, “Modeling RAFT polymerization kinetics via Monte-Carlo methods,” in Proceedings of the 7th World Congress of Chemical Engineering, 84560/1, Glasgow, Scotland, July 2005.
  56. A. D. Peklak, A. Butté, G. Storti, and M. Morbidelli, “Gel effect in the bulk reversible addition-fragmentation chain transfer polymerization of methyl methacrylate: modeling and experiments,” Journal of Polymer Science A: Polymer Chemistry, vol. 44, no. 3, pp. 1071–1085, 2006. View at Publisher · View at Google Scholar · View at Scopus
  57. D. Konkolewicz, B. S. Hawkett, A. Gray-Weale, and S. Perrier, “RAFT polymerization kinetics: combination of apparently conflicting models,” Macromolecules, vol. 41, no. 17, pp. 6400–6412, 2008. View at Publisher · View at Google Scholar · View at Scopus
  58. D. A. Shipp and K. Matyjaszewski, “Kinetic analysis of controlled/‘living’ radical polymerizations by simulations. 1. The importance of diffusion-controlled reactions,” Macromolecules, vol. 32, no. 9, pp. 2948–2955, 1999. View at Publisher · View at Google Scholar · View at Scopus
  59. S. Zhu, “Modeling of modular weight development in atom transfer radical polymerization,” Macromolecular Theory and Simulations, vol. 8, no. 1, pp. 29–37, 1999. View at Publisher · View at Google Scholar · View at Scopus
  60. K. Matyjaszewski, M. J. Ziegler, S. V. Arehart, D. Greszta, and T. Pakula, “Gradient copolymers by atom transfer radical copolymerization,” Journal of Physical Organic Chemistry, vol. 13, no. 12, pp. 775–786, 2000. View at Publisher · View at Google Scholar · View at Scopus
  61. J.-F. Lutz and K. Matyjaszewski, “Kinetic modeling of the chain-end functionality in atom transfer radical polymerization,” Macromolecular Chemistry and Physics, vol. 203, no. 10-11, pp. 1385–1395, 2002. View at Publisher · View at Google Scholar · View at Scopus
  62. M. Zhang and W. H. Ray, “Modeling of ‘living’ free-radical polymerization processes. II: tubular reactors,” Journal of Applied Polymer Science, vol. 86, no. 5, pp. 1047–1056, 2002. View at Publisher · View at Google Scholar · View at Scopus
  63. M. Al-Harthi, J. B. P. Soares, and L. C. Simon, “Dynamic Monte Carlo simulation of atom-transfer radical polymerization,” Macromolecular Materials and Engineering, vol. 291, no. 8, pp. 993–1003, 2006. View at Publisher · View at Google Scholar · View at Scopus
  64. M. Al-Harthi, J. B. P. Soares, and L. C. Simon, “Mathematical modeling of atom-transfer radical polymerization using bifunctional initiators,” Macromolecular Theory and Simulations, vol. 15, no. 3, pp. 198–214, 2006. View at Publisher · View at Google Scholar · View at Scopus
  65. M. Al-Harthi, J. B. P. Soares, and L. C. Simon, “Modeling of atom transfer radical polymerization with bifunctional initiators: diffusion effects and case studies,” Macromolecular Chemistry and Physics, vol. 207, no. 5, pp. 469–483, 2006. View at Publisher · View at Google Scholar · View at Scopus
  66. M. Al-Harthi, J. Soares, and L. Simon, “Dynamic Monte Carlo simulation of ATRP with bifunctional initiators,” Macromolecular Reaction Engineering, vol. 1, no. 1, pp. 95–105, 2007. View at Publisher · View at Google Scholar
  67. M. Al-Harthi, L. S. Cheng, J. B. P. Soares, and L. C. Simon, “Atom-transfer radical polymerization of styrene with bifunctional and monofunctional initiators: Experimental and mathematical modeling results,” Journal of Polymer Science A: Polymer Chemistry, vol. 45, no. 11, pp. 2212–2224, 2007. View at Publisher · View at Google Scholar · View at Scopus
  68. M. Al-Harthi, A. Sardashti, J. B. P. Soares, and L. C. Simon, “Atom transfer radical polymerization (ATRP) of styrene and acrylonitrile with monofunctional and bifunctional initiators,” Polymer, vol. 48, no. 7, pp. 1954–1961, 2007. View at Publisher · View at Google Scholar · View at Scopus
  69. M. Al-Harthi, J. Soares, and L. Simon, “Mathematical modeling of atom-transfer radical copolymerization,” Macromolecular Reaction Engineering, vol. 1, no. 4, pp. 468–479, 2007. View at Publisher · View at Google Scholar
  70. M. Al-Harthi, J. B. P. Soares, and L. C. Simon, “Dynamic Monte Carlo simulation of graft copolymers made with ATRP and metallocene catalysts,” Macromolecular Symposia, vol. 243, pp. 83–90, 2006. View at Publisher · View at Google Scholar · View at Scopus
  71. H. Tobita, “Molecular weight distribution of living radical polymers,” Macromolecular Theory and Simulations, vol. 15, no. 1, pp. 23–31, 2006. View at Publisher · View at Google Scholar · View at Scopus
  72. H. Chaffey-Millar, D. Stewart, M. M. T. Chakravarty, G. Keller, and C. Barner-Kowollik, “A parallelised high performance Monte Carlo simulation approach for complex polymerisation kinetics,” Macromolecular Theory and Simulations, vol. 16, no. 6, pp. 575–592, 2007. View at Publisher · View at Google Scholar · View at Scopus
  73. R. Wang, Y. Luo, B.-G. Li, and S. Zhu, “Control of gradient copolymer composition in ATRP using semibatch feeding policy,” AIChE Journal, vol. 53, no. 1, pp. 174–186, 2007. View at Publisher · View at Google Scholar · View at Scopus
  74. Y. Zhao, Y.-W. Luo, C. Ye, B.-G. Li, and S. Zhu, “Model-based design and synthesis of gradient MMA/tBMA copolymers by computer-programmed semibatch atom transfer radical copolymerization,” Journal of Polymer Science, Part A: Polymer Chemistry, vol. 47, no. 1, pp. 69–79, 2009. View at Publisher · View at Google Scholar · View at Scopus
  75. O. Delgadillo-Velázquez, E. Vivaldo-Lima, I. A. Quintero-Ortega, and S. Zhu, “Effects of diffusion-controlled reactions on atom-transfer radical polymerization,” AIChE Journal, vol. 48, no. 11, pp. 2597–2608, 2002. View at Publisher · View at Google Scholar · View at Scopus
  76. Q. Yu, Z. Qin, J. Li, and S. Zhu, “Diffusion-controlled atom transfer radical polymerization with crosslinking,” Polymer Engineering and Science, vol. 48, no. 7, pp. 1254–1260, 2008. View at Publisher · View at Google Scholar · View at Scopus
  77. D. Zhou, X. Gao, W.-J. Wang, and S. Zhu, “Termination of surface radicals and kinetic modeling of ATRP grafting from flat surfaces by addition of deactivator,” Macromolecules, vol. 45, no. 3, pp. 1198–1207, 2012. View at Publisher · View at Google Scholar · View at Scopus
  78. X. Gao, W. Feng, S. Zhu, H. Sheardown, and J. L. Brash, “Kinetic modeling of surface-initiated atom transfer radical polymerization,” Macromolecular Reaction Engineering, vol. 4, no. 3-4, pp. 235–250, 2010. View at Publisher · View at Google Scholar · View at Scopus
  79. D. Zhou, E. Mastan, and S. Zhu, “Termination of surface radicals and kinetic analysis of surface-initiated RAFT polymerization on flat surfaces,” Macromolecular Theory and Simulations, vol. 21, no. 9, pp. 602–614, 2012. View at Publisher · View at Google Scholar · View at Scopus
  80. Y. Fu, M. F. Cunningham, and R. A. Hutchinson, “Atom-transfer radical batch and semibatch polymerization of styrene,” Macromolecular Reaction Engineering, vol. 1, pp. 425–429, 2007. View at Google Scholar
  81. M. Najafi, V. Haddadi-Asl, M. Salami-Kalajahi, and H. R. Mamaghani, “Application of the Monte Carlo simulation method to the investigation of the effect of chain-length-dependent bimolecular termination on ATRP,” E-Polymers, vol. 9, no. 1, pp. 355–374, 2013. View at Publisher · View at Google Scholar · View at Scopus
  82. M. Najafi, H. Roghani-Mamaqani, V. Haddadi-Asl, and M. Salami-Kalajahi, “A simulation of kinetics and chain length distribution of styrene FRP and ATRP: chain-length-dependent termination,” Advances in Polymer Technology, vol. 30, no. 4, pp. 257–268, 2011. View at Publisher · View at Google Scholar · View at Scopus
  83. M. Najafi, H. Roghani-Mamaqani, M. Salami-Kalajahi, and V. Haddadi-Asl, “A comprehensive Monte Carlo simulation of styrene atom transfer radical polymerization,” Chinese Journal of Polymer Science, vol. 28, no. 4, pp. 483–497, 2010. View at Publisher · View at Google Scholar · View at Scopus
  84. M. Najafi, H. Roghani-Mamaqani, M. Salami-Kalajahi, and V. Haddadi-Asl, “An exhaustive study of chain-length-dependent and diffusion-controlled free radical and atom-transfer radical polymerization of styrene,” Journal of Polymer Research, vol. 18, no. 6, pp. 1539–1555, 2011. View at Publisher · View at Google Scholar · View at Scopus
  85. M. Al-Harthi, M. J. Khan, S. H. Abbasi, and J. B. P. Soares, “Gradient copolymers by ATRP in semibatch reactors: dynamic Monte Carlo simulation,” Macromolecular Reaction Engineering, vol. 3, no. 4, pp. 148–159, 2009. View at Publisher · View at Google Scholar · View at Scopus
  86. M. A. Al-Harthi, J. K. Masihullah, S. H. Abbasi, and J. B. P. Soares, “Dynamic Monte Carlo simulation of ATRP in a batch reactor,” Macromolecular Theory and Simulations, vol. 18, no. 6, pp. 307–316, 2009. View at Publisher · View at Google Scholar · View at Scopus
  87. Y.-N. Zhou, Z.-H. Luo, and J.-H. Chen, “Theoretical modeling coupled with experimental study on the preparation and characterization comparison of fluorinated copolymers: effect of chain structure on copolymer properties,” AIChE Journal, vol. 59, no. 8, pp. 3019–3033, 2013. View at Publisher · View at Google Scholar · View at Scopus
  88. P. Polanowski, J. K. Jeszka, and K. Matyjaszewski, “Star polymer synthesis and gelation in ATRP copolymerization: Monte Carlo simulations,” Polymer, vol. 54, no. 8, pp. 1979–1986, 2013. View at Publisher · View at Google Scholar · View at Scopus