1932

Abstract

To optimize automation for polymer processing, attempts have been made to simulate the flow of entangled polymers. In industry, fluid dynamics simulations with phenomenological constitutive equations have been practically established. However, to account for molecular characteristics, a method to obtain the constitutive relationship from the molecular structure is required. Molecular dynamics simulations with atomic description are not practical for this purpose; accordingly, coarse-grained models with reduced degrees of freedom have been developed. Although the modeling of entanglement is still a challenge, mesoscopic models with a priori settings to reproduce entangled polymer dynamics, such as tube models, have achieved remarkable success. To use the mesoscopic models as staging posts between atomistic and fluid dynamics simulations, studies have been undertaken to establish links from the coarse-grained model to the atomistic and macroscopic simulations. Consequently, integrated simulations from materials chemistry to predict the macroscopic flow in polymer processing are forthcoming.

Loading

Article metrics loading...

/content/journals/10.1146/annurev-chembioeng-060713-040401
2014-06-07
2024-03-29
Loading full text...

Full text loading...

/deliver/fulltext/chembioeng/5/1/annurev-chembioeng-060713-040401.html?itemId=/content/journals/10.1146/annurev-chembioeng-060713-040401&mimeType=html&fmt=ahah

Literature Cited

  1. Tadmor Z, Gogos CG. 1.  2006. Principles of Polymer Processing. New York: John Wiley & Sons, 2nd.984
  2. Harry DH, Parrott RG. 2.  1970. Numerical simulation of injection mold filling. Polym. Eng. Sci. 10:4209–14 [Google Scholar]
  3. Laroche D, Kabanemi KK, Pecora L, Diraddo RW. 3.  1999. Integrated numerical modeling of the blow molding process. Polym. Eng. Sci. 39:71223–33 [Google Scholar]
  4. Kaye A. 4.  1962. Non-Newtonian Flow in Incompressible Fluids, Note No. 134. Cranfield, UK: Coll. Aeronaut.
  5. Bernstein B, Kearsley EA, Zapas LJ. 5.  1963. A study of stress relaxations with finite strain. Trans. Soc. Rheol. 7:391–410 [Google Scholar]
  6. Bird RB, Curtiss C, Armstrong RC, Hassager O. 6.  1987. Dynamics of Polymeric Liquids. Vol. 2 New York: Wiley
  7. Baumgärtner A, Binder K. 7.  1981. Dynamics of entangled polymer melts: a computer simulation. J. Chem. Phys. 75:62994–3005 [Google Scholar]
  8. Kremer K, Grest GS, Carmesin I. 8.  1988. Crossover from Rouse to reptation dynamics: a molecular-dynamics simulation. Phys. Rev. Lett. 61:5566–69 [Google Scholar]
  9. Kremer K, Grest GS. 9.  1990. Dynamics of entangled linear polymer melts: a molecular-dynamics simulation. J. Chem. Phys. 92:85057–86 [Google Scholar]
  10. Likhtman AE, Sukumaran SK, Ramirez J. 10.  2007. Linear viscoelasticity from molecular dynamics simulation of entangled polymers. Macromolecules 40:186748–57 [Google Scholar]
  11. Kröger M, Loose W, Hess S. 11.  1993. Rheology and structural changes of polymer melts via nonequilibrium molecular dynamics. J. Rheol. 37:61057–79 [Google Scholar]
  12. Kröger M, Hess S. 12.  2000. Rheological evidence for a dynamical crossover in polymer melts via nonequilibrium molecular dynamics. Phys. Rev. Lett. 85:51128–31 [Google Scholar]
  13. Hou J-X, Svaneborg C, Everaers R, Grest GS. 13.  2010. Stress relaxation in entangled polymer melts. Phys. Rev. Lett. 105:6068301 [Google Scholar]
  14. Harmandaris VA, Mavrantzas VG, Theodorou DN, Kröger M, Ramírez J. 14.  et al. 2003. Crossover from the Rouse to the entangled polymer melt regime: signals from long, detailed atomistic molecular dynamics simulations, supported by rheological experiments. Macromolecules 36:41376–87 [Google Scholar]
  15. Baig C, Mavrantzas VG, Kröger M. 15.  2010. Flow effects on melt structure and entanglement network of linear polymers: results from a nonequilibrium molecular dynamics simulation study of a polyethylene melt in steady shear. Macromolecules 43:166886–902 [Google Scholar]
  16. Stephanou PS, Baig C, Tsolou G, Mavrantzas V, Kroeger M. 16.  2010. Quantifying chain reptation in entangled polymer melts: topological and dynamical mapping of atomistic simulation results onto the tube model. J. Chem. Phys. 132:12124904 [Google Scholar]
  17. Harmandaris VA, Kremer K. 17.  2009. Dynamics of polystyrene melts through hierarchical multiscale simulations. Macromolecules 42:3791–802 [Google Scholar]
  18. Padding JT, Briels WJ. 18.  2001. Uncrossability constraints in mesoscopic polymer melt simulations: non-Rouse behavior of C120H242. J. Chem. Phys. 115:62846–59 [Google Scholar]
  19. Padding JT, Briels WJ. 19.  2002. Time and length scales of polymer melts studied by coarse-grained molecular dynamics simulations. J. Chem. Phys. 117:2925 [Google Scholar]
  20. Padding JT, Briels WJ. 20.  2003. Coarse-grained molecular dynamics simulations of polymer melts in transient and steady shear flow. J. Chem. Phys. 118:2210276 [Google Scholar]
  21. Kumar S, Larson RG. 21.  2001. Brownian dynamics simulations of flexible polymers with spring–spring repulsions. J. Chem. Phys. 114:156937 [Google Scholar]
  22. Pan G, Manke CW. 22.  2003. Developments toward simulation of entangled polymer melts by dissipative particle dynamics (DPD). Int. J. Mod. Phys. B 17:1–2231–35 [Google Scholar]
  23. Lahmar F, Tzoumanekas C, Theodorou DN, Rousseau B. 23.  2009. Onset of entanglements revisited. Dynamical analysis. Macromolecules 42:197485–94 [Google Scholar]
  24. Yamanoi M, Pozo O, Maia JM. 24.  2011. Linear and non-linear dynamics of entangled linear polymer melts by modified tunable coarse-grained level dissipative particle dynamics. J. Chem. Phys. 135:4044904 [Google Scholar]
  25. Chappa V, Morse D, Zippelius A, Müller M. 25.  2012. Translationally invariant slip-spring model for entangled polymer dynamics. Phys. Rev. Lett. 109:141–5 [Google Scholar]
  26. Langeloth M, Masubuchi Y, Böhm MC, Müller-Plathe F. 26.  2013. Recovering the reptation dynamics of polymer melts in dissipative particle dynamics simulations via slip-springs. J. Chem. Phys. 138:10104907 [Google Scholar]
  27. Ronca G. 27.  1983. Frequency spectrum and dynamic correlations of concentrated polymer liquids. J. Chem. Phys. 79:21031 [Google Scholar]
  28. Hess W. 28.  1988. Generalized Rouse theory for entangled polymeric liquids. Macromolecules 21:82620–32 [Google Scholar]
  29. Schweizer KS, Fuchs M, Szamel G, Guenza M, Tang H. 29.  1997. Polymer-mode-coupling theory of the slow dynamics of entangled macromolecular fluids. Macromol. Theory Simul. 6:61037–117 [Google Scholar]
  30. Li Y, Abberton B, Kröger M, Liu W. 30.  2013. Challenges in multiscale modeling of polymer dynamics. Polymers 5:2751–832 [Google Scholar]
  31. Edwards SF. 31.  1967. The statistical mechanics of polymerized material. Proc. Phys. Soc. 92:19–16 [Google Scholar]
  32. de Gennes PG. 32.  1971. Reptation of a polymer chain in the presence of fixed obstacles. J. Chem. Phys. 55:2572 [Google Scholar]
  33. Doi M, Edwards SF. 33.  1978. Dynamics of concentrated polymer systems. Part 1—Brownian motion in the equilibrium state. J. Chem. Soc. Faraday Trans. 2 74:1789–801 [Google Scholar]
  34. Doi M, Edwards SF. 34.  1978. Dynamics of concentrated polymer systems. Part 3—the constitutive equation. J. Chem. Soc. Faraday Trans. 2 74:1818–32 [Google Scholar]
  35. Doi M. 35.  1983. Explanation for the 3.4-power law for viscosity of polymeric liquids on the basis of the tube model. J. Polym. Sci. 21:5667–84 [Google Scholar]
  36. Milner S, McLeish T. 36.  1998. Reptation and contour-length fluctuations in melts of linear polymers. Phys. Rev. Lett. 81:3725–28 [Google Scholar]
  37. Likhtman AE, McLeish TCB. 37.  2002. Quantitative theory for linear dynamics of linear entangled polymers. Macromolecules 35:166332–43 [Google Scholar]
  38. Tsenoglou C. 38.  1987. Viscoelasticity of binary polymer blends. ACS Polym. Prepr. 28:185–86 [Google Scholar]
  39. des Cloizeaux J. 39.  1988. Double reptation versus simple reptation in polymer melts. Europhys. Lett. 5:5437–42 [Google Scholar]
  40. Graessley W. 40.  1982. Entangled linear, branched and network polymer systems—molecular theories. Adv. Polym. Sci. 47:67–117 [Google Scholar]
  41. Marrucci G. 41.  1985. Relaxation by reptation and tube enlargement: a model for polydisperse polymers. J. Polym. Sci. 23:1159–77 [Google Scholar]
  42. Wasserman SH, Graessley WW. 42.  1992. Effects of polydispersity on linear viscoelasticity in entangled polymer melts. J. Rheol. 36:4543 [Google Scholar]
  43. Carrot C, Revenu P, Guillet J. 43.  1996. Rheological behavior of degraded polypropylene melts: from MWD to dynamic moduli. J. Appl. Polym. Sci. 61:111887–97 [Google Scholar]
  44. Léonardi F, Majesté J-C, Allal A, Marin G. 44.  2000. Rheological models based on the double reptation mixing rule: the effects of a polydisperse environment. J. Rheol. 44:4675 [Google Scholar]
  45. Rubinstein M, Colby RH. 45.  1988. Self-consistent theory of polydisperse entangled polymers: linear viscoelasticity of binary blends. J. Chem. Phys. 89:85291 [Google Scholar]
  46. Pattamaprom C, Larson RG, Van Dyke TJ. 46.  2000. Quantitative predictions of linear viscoelastic rheological properties of entangled polymers. Rheol. Acta 39:6517–31 [Google Scholar]
  47. Park SJ, Larson RG. 47.  2004. Tube dilation and reptation in binary blends of monodisperse linear polymers. Macromolecules 37:2597–604 [Google Scholar]
  48. Struglinski MJ, Graessley WW. 48.  1985. Effects of polydispersity on the linear viscoelastic properties of entangled polymers. 1. Experimental observations for binary mixtures of linear polybutadiene. Macromolecules 18:122630–43 [Google Scholar]
  49. van Ruymbeke E, Keunings R, Bailly C. 49.  2005. Prediction of linear viscoelastic properties for polydisperse mixtures of entangled star and linear polymers: modified tube-based model and comparison with experimental results. J. Non-Newton. Fluid Mech. 128:17–22 [Google Scholar]
  50. Doi M, Kuzuu NY. 50.  1980. Rheology of star polymers in concentrated solutions and melts. J. Polym. Sci. 18:12775–80 [Google Scholar]
  51. Pearson DS, Helfand E. 51.  1984. Viscoelastic properties of star-shaped polymers. Macromolecules 17:4888–95 [Google Scholar]
  52. Ball RC, McLeish TCB. 52.  1989. Dynamic dilution and the viscosity of star-polymer melts. Macromolecules 22:41911–13 [Google Scholar]
  53. Milner ST, McLeish TCB. 53.  1997. Parameter-free theory for stress relaxation in star polymer melts. Macromolecules 30:72159–66 [Google Scholar]
  54. Colby RH, Rubinstein M. 54.  1990. Two-parameter scaling for polymers in Θ solvents. Macromolecules 23:102753–57 [Google Scholar]
  55. McLeish TCB. 55.  1988. Hierarchical relaxation in tube models of branched polymers. Europhys. Lett. 6:6511–16 [Google Scholar]
  56. McLeish TCB. 56.  1988. Molecular rheology of H-polymers. Macromolecules 21:41062–70 [Google Scholar]
  57. McLeish TCB, Allgaier J, Bick DK, Bishko G, Biswas P. 57.  et al. 1999. Dynamics of entangled H-polymers: theory, rheology, and neutron-scattering. Macromolecules 32:206734–58 [Google Scholar]
  58. Daniels DR, McLeish TCB, Crosby BJ, Young RN, Fernyhough CM. 58.  2001. Molecular rheology of comb polymer melts. 1. Linear viscoelastic response. Macromolecules 34:207025–33 [Google Scholar]
  59. Larson RG. 59.  2001. Combinatorial rheology of branched polymer melts. Macromolecules 34:134556–71 [Google Scholar]
  60. Frischknecht AL, Milner ST, Pryke A, Young RN, Hawkins R, McLeish TCB. 60.  2002. Rheology of three-arm asymmetric star polymer melts. Macromolecules 35:124801–20 [Google Scholar]
  61. van Ruymbeke E, Bailly C, Keunings R, Vlassopoulos D. 61.  2006. A general methodology to predict the linear rheology of branched polymers. Macromolecules 39:186248–59 [Google Scholar]
  62. Das C, Inkson NJ, Read DJ, Kelmanson MA, McLeish TCB. 62.  2006. Computational linear rheology of general branch-on-branch polymers. J. Rheol. 50:2207 [Google Scholar]
  63. Wang Z, Chen X, Larson RG. 63.  2010. Comparing tube models for predicting the linear rheology of branched polymer melts. J. Rheol. 54:2223 [Google Scholar]
  64. Shanbhag S, Joon Park S, Wang Z. 64.  2012. Superensembles of linear viscoelastic models of polymer melts. J. Rheol. 56:2279 [Google Scholar]
  65. Doi M, Edwards SF. 65.  1978. Dynamics of concentrated polymer systems. Part 2. Molecular motion under flow. J. Chem. Soc. Faraday Trans. 2 74:1802–17 [Google Scholar]
  66. Marrucci G, Grizzuti N. 66.  1988. Fast flows of concentrated polymers: predictions of the tube model on chain stretching. Gazz. Chim. Ital. 118:3179–85 [Google Scholar]
  67. Marrucci G. 67.  1996. Dynamics of entanglements: a nonlinear model consistent with the Cox-Merz rule. J. Non-Newton. Fluid Mech. 62:2–3279–89 [Google Scholar]
  68. Ianniruberto G, Marrucci G. 68.  1996. On compatibility of the Cox-Merz rule with the model of Doi and Edwards. J. Non-Newton. Fluid Mech. 65:2–3241–46 [Google Scholar]
  69. Ianniruberto G, Marrucci G. 69.  2001. A simple constitutive equation for entangled polymers with chain stretch. J. Rheol. 45:61305 [Google Scholar]
  70. Ianniruberto G, Marrucci G. 70.  2000. Convective orientational renewal in entangled polymers. J. Non-Newton. Fluid Mech. 95:2–3363–74 [Google Scholar]
  71. Mead DW, Larson RG, Doi M. 71.  1998. A molecular theory for fast flows of entangled polymers. Macromolecules 31:227895–914 [Google Scholar]
  72. Graham RS, Likhtman AE, McLeish TCB, Milner ST. 72.  2003. Microscopic theory of linear, entangled polymer chains under rapid deformation including chain stretch and convective constraint release. J. Rheol. 47:51171 [Google Scholar]
  73. Read DJ, Jagannathan K, Likhtman AE. 73.  2008. Entangled polymers: constraint release, mean paths, and tube bending energy. Macromolecules 41:186843–53 [Google Scholar]
  74. Leygue A, Bailly C, Keunings R. 74.  2006. A tube-based constitutive equation for polydisperse entangled linear polymers. J. Non-Newton. Fluid Mech. 136:11–16 [Google Scholar]
  75. Mead DW. 75.  2006. Development of the “binary interaction” theory for entangled polydisperse linear polymers. Rheol. Acta 46:3369–95 [Google Scholar]
  76. Read DJ, Jagannathan K, Sukumaran SK, Auhl D. 76.  2012. A full-chain constitutive model for bidisperse blends of linear polymers. J. Rheol. 56:4823 [Google Scholar]
  77. Likhtman AE, Graham RS. 77.  2003. Simple constitutive equation for linear polymer melts derived from molecular theory: Rolie-Poly equation. J. Non-Newton. Fluid Mech. 114:11–12 [Google Scholar]
  78. Marrucci G, Ianniruberto G. 78.  2003. Flow-induced orientation and stretching of entangled polymers. Philos. Trans. Ser. A 361:1805677–87; discussion 687–88 [Google Scholar]
  79. McLeish T, Larson R. 79.  1998. Molecular constitutive equations for a class of branched polymers: the pom-pom polymer. J. Rheol. 42:181–110 [Google Scholar]
  80. Bishko G, McLeish T, Harlen O, Larson R. 80.  1997. Theoretical molecular rheology of branched polymers in simple and complex flows: the pom-pom model. Phys. Rev. Lett. 79:122352–55 [Google Scholar]
  81. Verbeeten WMH, Peters GWM, Baaijens FPT. 81.  2001. Differential constitutive equations for polymer melts: the extended Pom-Pom model. J. Rheol. 45:4823 [Google Scholar]
  82. Inkson NJ, McLeish TCB, Harlen OG, Groves DJ. 82.  1999. Predicting low density polyethylene melt rheology in elongational and shear flows with “pom-pom” constitutive equations. J. Rheol. 43:4873 [Google Scholar]
  83. Read DJ, Auhl D, Das C, den Doelder J, Kapnistos M. 83.  et al. 2011. Linking models of polymerization and dynamics to predict branched polymer structure and flow. Science 333:60511871–74 [Google Scholar]
  84. Hua CC, Schieber JD. 84.  1998. Segment connectivity, chain-length breathing, segmental stretch, and constraint release in reptation models. I. Theory and single-step strain predictions. J. Chem. Phys. 109:2210018 [Google Scholar]
  85. Shanbhag S, Larson RG, Takimoto J, Doi M. 85.  2001. Deviations from dynamic dilution in the terminal relaxation of star polymers. Phys. Rev. Lett. 87:19195502 [Google Scholar]
  86. Doi M, Takimoto J. 86.  2003. Molecular modelling of entanglement. Philos. Trans. Ser. A 361:1805641–52 [Google Scholar]
  87. Schieber JD, Neergaard J, Gupta S. 87.  2003. A full-chain, temporary network model with sliplinks, chain-length fluctuations, chain connectivity and chain stretching. J. Rheol. 47:1213–33 [Google Scholar]
  88. Khaliullin R, Schieber J. 88.  2009. Self-consistent modeling of constraint release in a single-chain mean-field slip-link model. Macromolecules 42:197504–17 [Google Scholar]
  89. Likhtman AE. 89.  2005. Single-chain slip-link model of entangled polymers: simultaneous description of neutron spin-echo, rheology, and diffusion. Macromolecules 38:146128–39 [Google Scholar]
  90. Watanabe H, Ishida S, Matsumiya Y, Inoue T. 90.  2004. Test of full and partial tube dilation pictures in entangled blends of linear polyisoprenes. Macromolecules 37:176619–31 [Google Scholar]
  91. Masubuchi Y, Takimoto J, Koyama K, Ianniruberto G, Marrucci G, Greco F. 91.  2001. Brownian simulations of a network of reptating primitive chains. J. Chem. 115:94387–94 [Google Scholar]
  92. Marrucci G, Greco F, Ianniruberto G. 92.  2000. Possible role of force balance on entanglements. Macromol. Symp. 158:57–64 [Google Scholar]
  93. Masubuchi Y, Yaoita T, Matsumiya Y, Watanabe H, Matsumiya Y. 93.  2011. Primitive chain network simulations for asymmetric star polymers. J. Chem. Phys. 134:19194905 [Google Scholar]
  94. Masubuchi Y, Ianniruberto G, Greco F, Marrucci G. 94.  2004. Molecular simulations of the long-time behaviour of entangled polymeric liquids by the primitive chain network model. Model. Simul. Mater. Sci. Eng. 12:3S91–S100 [Google Scholar]
  95. Yaoita T, Isaki T, Masubuchi Y, Watanabe H, Ianniruberto G, Marrucci G. 95.  2012. Primitive chain network simulation of elongational flows of entangled linear chains: stretch/orientation-induced reduction of monomeric friction. Macromolecules 45:62773–82 [Google Scholar]
  96. Uneyama T, Masubuchi Y. 96.  2012. Multi-chain slip-spring model for entangled polymer dynamics. J. Chem. Phys. 137:15154902 [Google Scholar]
  97. Ramírez-Hernández A, Müller M, de Pablo JJ. 97.  2013. Theoretically informed entangled polymer simulations: linear and non-linear rheology of melts. Soft Matter 9:2030–36 [Google Scholar]
  98. Kindt P, Briels WJ. 98.  2007. A single particle model to simulate the dynamics of entangled polymer melts. J. Chem. Phys. 127:13134901 [Google Scholar]
  99. Padding JT, Mohite LV, Auhl D, Schweizer T, Briels WJ, Bailly C. 99.  2012. Quantitative mesoscale modeling of the oscillatory and transient shear rheology and the extensional rheology of pressure sensitive adhesives. Soft Matter 8:307967–81 [Google Scholar]
  100. Byutner O, Smith GD. 100.  2001. Prediction of the linear viscoelastic shear modulus of an entangled polybutadiene melt from simulation and theory. Macromolecules 34:1134–39 [Google Scholar]
  101. Fetters L, Lohse D, Graessley W. 101.  1999. Chain dimensions and entanglement spacings in dense macromolecular systems. J. Polym. Sci. 37:101023–33 [Google Scholar]
  102. Ramos J, Vega JF, Theodorou DN, Martinez-Salazar J. 102.  2008. Entanglement relaxation time in polyethylene: simulation versus experimental data. Macromolecules 41:82959–62 [Google Scholar]
  103. Sukumaran SK, Likhtman AE. 103.  2009. Modeling entangled dynamics: comparison between stochastic single-chain and multichain models. Macromolecules 42:124300–9 [Google Scholar]
  104. Kröger M, Ramírez J, Öttinger HC. 104.  2002. Projection from an atomistic chain contour to its primitive path. Polymer 43:2477–87 [Google Scholar]
  105. Yamamoto R, Onuki A. 105.  2004. Entanglements in quiescent and sheared polymer melts. Phys. Rev. E 70:4041801 [Google Scholar]
  106. Everaers R, Sukumaran SK, Grest GS, Svaneborg C, Sivasubramanian A, Kremer K. 106.  2004. Rheology and microscopic topology of entangled polymeric liquids. Science 303:5659823–26 [Google Scholar]
  107. León S, van der Vegt N, Delle Site L, Kremer K. 107.  2005. Bisphenol A polycarbonate: entanglement analysis from coarse-grained MD simulations. Macromolecules 38:198078–92 [Google Scholar]
  108. Zhou Q, Larson RG. 108.  2006. Direct calculation of the tube potential confining entangled polymers. Macromolecules 39:196737–43 [Google Scholar]
  109. Kröger M. 109.  2005. Shortest multiple disconnected path for the analysis of entanglements in two- and three-dimensional polymeric systems. Comput. Phys. Commun. 168:3209–32 [Google Scholar]
  110. Foteinopoulou K, Karayiannis NC, Mavrantzas VG, Kröger M. 110.  2006. Primitive path identification and entanglement statistics in polymer melts: results from direct topological analysis on atomistic polyethylene models. Macromolecules 39:124207–16 [Google Scholar]
  111. Shanbhag S, Larson RG. 111.  2006. Identification of topological constraints in entangled polymer melts using the bond-fluctuation model. Macromolecules 39:62413–17 [Google Scholar]
  112. Tzoumanekas C, Theodorou DN. 112.  2006. Topological analysis of linear polymer melts: a statistical approach. Macromolecules 39:134592–604 [Google Scholar]
  113. Anogiannakis SD, Tzoumanekas C, Theodorou DN. 113.  2012. Microscopic description of entanglements in polyethylene networks and melts: strong, weak, pairwise, and collective attributes. Macromolecules 45:239475–92 [Google Scholar]
  114. Bisbee W, Qin J, Milner ST. 114.  2011. Finding the tube with isoconfigurational averaging. Macromolecules 44:228972–80 [Google Scholar]
  115. Keunings R. 115.  2003. Finite element methods for integral viscoelastic fluids. Rheol. Rev. 2003:167–95 [Google Scholar]
  116. Baaijens FPT. 116.  1998. Mixed finite element methods for viscoelastic flow analysis: a review. J. Non-Newton. Fluid Mech. 79:2–3361–85 [Google Scholar]
  117. Yuan XF, Ball RC, Edwards SF. 117.  1993. A new approach to modelling viscoelastic flow. J. Non-Newton. Fluid Mech. 46:2–3331–50 [Google Scholar]
  118. Rasmussen HK, Hassager O. 118.  1993. Simulation of transient viscoelastic flow. J. Non-Newton. Fluid Mech. 46:2–3289–305 [Google Scholar]
  119. Rasmussen HK. 119.  2002. Lagrangian viscoelastic flow computations using a generalized molecular stress function model. J. Non-Newton. Fluid Mech. 106:2–3107–20 [Google Scholar]
  120. Wagner MH, Schaeffer J. 120.  1992. Nonlinear strain measures for general biaxial extension of polymer melts. J. Rheol. 36:11 [Google Scholar]
  121. Hassager O, Bisgaard C. 121.  1983. A Lagrangian finite element method for the simulation of flow of non-Newtonian liquids. J. Non-Newton. Fluid Mech. 12:2153–64 [Google Scholar]
  122. Peters EAJF, Hulsen MA, van den Brule BHAA. 122.  2000. Instationary Eulerian viscoelastic flow simulations using time separable Rivlin–Sawyers constitutive equations. J. Non-Newton. Fluid Mech. 89:1–2209–28 [Google Scholar]
  123. van Heel APG, Hulsen MA, van den Brule BHAA. 123.  1999. Simulation of the Doi–Edwards model in complex flow. J. Rheol. 43:51239 [Google Scholar]
  124. Peters EAJF, van Heel APG, Hulsen MA, van den Brule BHAA. 124.  2000. Generalization of the deformation field method to simulate advanced reptation models in complex flow. J. Rheol. 44:4811 [Google Scholar]
  125. Wapperom P, Keunings R. 125.  2000. Simulation of linear polymer melts in transient complex flow. J. Non-Newton. Fluid Mech. 95:167–83 [Google Scholar]
  126. Wapperom P. 126.  2001. Numerical simulation of branched polymer melts in transient complex flow using pom-pom models. J. Non-Newton. Fluid Mech. 97:2–3267–81 [Google Scholar]
  127. Marrucci G, Greco F, Ianniruberto G. 127.  2001. Integral and differential constitutive equations for entangled polymers with simple versions of CCR and force balance on entanglements. Rheol. Acta 40:298–103 [Google Scholar]
  128. Laso M, Öttinger HC. 128.  1993. Calculation of viscoelastic flow using molecular models: the CONNFFESSIT approach. J. Non-Newton. Fluid Mech. 47:1–20 [Google Scholar]
  129. Hua CC, Schieber JD. 129.  1996. Application of kinetic theory models in spatiotemporal flows for polymer solutions, liquid crystals and polymer melts using the CONNFFESSIT approach. Chem. Eng. Sci. 51:91473–85 [Google Scholar]
  130. Murashima T, Taniguchi T. 130.  2011. Multiscale simulation of history-dependent flow in entangled polymer melts. Europhys. Lett. 96:118002 [Google Scholar]
  131. De S, Fish J, Shephard M, Keblinski P, Kumar S. 131.  2006. Multiscale modeling of polymer rheology. Phys. Rev. E 74:31–4 [Google Scholar]
  132. Bonvin J, Picasso M. 132.  1999. Variance reduction methods for CONNFFESSIT-like simulations. J. Non-Newton. Fluid Mech. 84:2–3191–215 [Google Scholar]
  133. Masubuchi Y, Uneyama T, Saito K. 133.  2012. A multiscale simulation of polymer processing using parameter-based bridging in melt rheology. J. Appl. Polym. Sci. 125:42740–47 [Google Scholar]
  134. Graham RS. 134.  2010. Molecular modelling of flow-induced crystallisation in polymers. J. Eng. Math. 71:3237–51 [Google Scholar]
  135. Shanbhag S. 135.  2012. Analytical rheology of polymer melts: state of the art. ISRN Mater. Sci. 2012:1–24 [Google Scholar]
  136. Ferry JD. 136.  1980. Viscoelastic Properties of Polymers. New York: John Wiley & Sons, 3rd ed..
  137. Karimi-Varzaneh HA, van der Vegt NFA, Müller-Plathe F, Carbone P. 137.  2012. How good are coarse-grained polymer models? A comparison for atactic polystyrene. ChemPhysChem 13:153428–39 [Google Scholar]
  138. Grmela M, Öttinger H. 138.  1997. Dynamics and thermodynamics of complex fluids. I. Development of a general formalism. Phys. Rev. E 56:66620–32 [Google Scholar]
  139. Öttinger HC, Beris AN. 139.  1999. Thermodynamically consistent reptation model without independent alignment. J. Chem. Phys. 110:146593 [Google Scholar]
  140. Öttinger HC. 140.  2001. Thermodynamic admissibility of the Pom-Pom model for branched polymers. Rheol. Acta 40:4317–21 [Google Scholar]
  141. Schieber JD. 141.  2003. GENERIC compliance of a temporary network model with sliplinks, chain-length fluctuations, segment-connectivity and constraint release. J. Non-Equilib. Thermodyn. 28:2179–88 [Google Scholar]
  142. Ilg P, Mavrantzas V, Ottinger HC. 142.  2010. Multiscale modeling and coarse graining of polymer dynamics: simulations guided by statistical beyond-equilibrium thermodynamics. Modeling and Simulation in Polymers PD Gujrati, AI Leonov 343–83 Weinheim, Ger.: Wiley-VCH Verlag GmbH & Co. KGaA [Google Scholar]
  143. Watanabe H, Ishida S, Matsumiya Y. 143.  2002. Rheodielectric behavior of entangled cis-polyisoprene under fast shear. Macromolecules 35:238802–18 [Google Scholar]
  144. Teixeira RE, Dambal AK, Richter DH, Shaqfeh ESG, Chu S. 144.  2007. The individualistic dynamics of entangled DNA in solution. Macromolecules 40:72461–76 [Google Scholar]
  145. Uneyama T, Masubuchi Y, Horio K, Matsumiya Y, Watanabe H. 145.  et al. 2009. A theoretical analysis of rheodielectric response of type-A polymer chains. J. Polym. Sci. B 47:111039–57 [Google Scholar]
  146. Uneyama T, Horio K, Watanabe H. 146.  2011. Anisotropic mobility model for polymers under shear and its linear response functions. Phys. Rev. E 83:6061802 [Google Scholar]
  147. Huang Q, Mednova O, Rasmussen HK, Alvarez NJ, Skov AL. 147.  et al. 2013. Concentrated polymer solutions are different from melts: role of entanglement molecular weight. Macromolecules 46:125026–35 [Google Scholar]
  148. Wagner MH, Kheirandish S, Hassager O. 148.  2005. Quantitative prediction of transient and steady-state elongational viscosity of nearly monodisperse polystyrene melts. J. Rheol. 49:61317 [Google Scholar]
  149. Marrucci G, Ianniruberto G. 149.  2004. Interchain pressure effect in extensional flows of entangled polymer melts. Macromolecules 37:103934–42 [Google Scholar]
  150. Shima T, Kuni H, Okabe Y, Doi M, Yuan XF, Kawakatsu T. 150.  2003. Self-consistent-field theory of viscoelastic behavior of inhomogeneous dense polymer systems. Macromolecules 36:249199–204 [Google Scholar]
/content/journals/10.1146/annurev-chembioeng-060713-040401
Loading
/content/journals/10.1146/annurev-chembioeng-060713-040401
Loading

Data & Media loading...

  • Article Type: Review Article
This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error