Challenges in multiscale modeling of polymer dynamics

Polymers

Volumn 5, Issue 2, 2013, Pages 751-832

  Li, Ying ^a   Abberton, Brendan C ^a   Kröger, Maartin ^b   Liu, Wing Kam ^a  

^a Northwestern University   (United States)

^b ETH ZURICH   (Switzerland)

Author keywords

Coarse grained molecular dynamics; Entanglement; Multiscale modeling; Polymer; Primitive path; Rheology; Tube model; Viscoelasticity

Indexed keywords

COARSE-GRAINED MOLECULAR DYNAMICS; ENTANGLEMENT; MULTI-SCALE MODELING; PRIMITIVE PATH; TUBE MODEL;

COMPUTATIONAL CHEMISTRY; ELASTICITY; RHEOLOGY; VISCOELASTICITY;

POLYMERS;

EID: 84883303199     PISSN: None     EISSN: 20734360     Source Type: Journal    
DOI: 10.3390/polym5020751     Document Type: Review

References (401)

1. Rouse, P.E., Jr. A theory of the linear viscoelastic properties of dilute solutions of coiling polymers. J. Chem. Phys. 1953, 21, 1272-1280.
2. Mondello, M.; Grest, G.S.; Webb, E.B.; Peczak, P. Dynamics of n-alkanes: Comparison to Rouse model. J. Chem. Phys. 1998, 109, 798-805.
3. Harmandaris, V.A.; Doxastakis, M.; Mavrantzas, V.G.; Theodorou, D.N. Detailed molecular dynamics simulation of the self-diffusion of n-alkane and cis-1, 4 polyisoprene oligomer melts. J. Chem. Phys. 2002, 116, 436-446.
4. Fleischer, G.; Appel, M. Chain length and temperature dependence of the self-diffusion of polyisoprene and polybutadiene in the melt. Macromolecules 1995, 28, 7281-7283.
5. De Gennes, P.G. Scaling Concepts in Polymer Physics; Cornell University Press: Ithaca, NY, USA, 1979.
6. Doi, M.; Edwards, S.F. The Theory of Polymer Dynamics; Oxford University Press New York, NY, USA, 1988; Volume 73.
7. McLeish, T.C.B. Tube theory of entangled polymer dynamics. Adv. Phys. 2002, 51, 1379-1527.
8. Doi, M. Explanation for the 3. 4-power law for viscosity of polymeric liquids on the basis of the tube model. J. Polym. Sci. Polym. Lett. 1983, 21, 667-684.
9. Needs, R.J. Computer simulation of the effect of primitive path length fluctuations in the reptation model. Macromolecules 1984, 17, 437-441.
10. Watanabe, H. Viscoelasticity and dynamics of entangled polymers. Progr. Polym. Sci. 1999, 24, 1253-1403.
11. Schweizer, K.S.; Curro, J.G. Integral equation theories of the structure, thermodynamics, and phase transitions of polymer fluids. Adv. Chem. Phys. 1997, 98, 1-142.
12. Schweizer, K.S.; Fuchs, M.; Szamel, G.; Guenza, M.; Tang, H. Polymer-mode-coupling theory of the slow dynamics of entangled macromolecular fluids. Macromol. Theory Simul. 1997, 6, 1037-1117.
13. Dealy, J.M.; Larson, R.G. Structure and Rheology of Molten Polymers From Structure to Flow Behavior and Back again; Hanser Gardner Publications Heidelberg, Germany, 2006.
14. Likhtman, A.E.; McLeish, T.C.B. Quantitative theory for linear dynamics of linear entangled polymers. Macromolecules 2002, 35, 6332-6343.
15. Hou, J.X.; Svaneborg, C.; Everaers, R.; Grest, G.S. Stress relaxation in entangled polymer melts. Phys. Rev. Lett. 2010, 105, 0683011-0683014.
16. Kröger, M. Simple models for complex nonequilibrium fluids. Phys. Rep. 2004, 390, 453-551.
17. Larson, R.G.; Zhou, Q.; Shanbhag, S.; Park, S.J. Advances in modeling of polymer melt rheology. AIChE J. 2007, 53, 542-548.
18. Likhtman, A.E. Viscoelasticity and Molecular Rheology. In Comprehensive Polymer Science; Elsevier Amsterdam, The Netherlands, 2011.
19. Fang, J.; Kröger, M.; Ottinger, H.C. A thermodynamically admissible reptation model for fast flows of entangled polymers. II. Model predictions for shear and extensional flows. J. Rheol. 2000, 44, 1293-1317.
20. Shanbhag, S. Analytical rheology of polymer melts State of the art. ISRN Mater. Sci. 2012, 2012, 7321761-73217624.
21. Edwards, S.F.; Vilgis, T.A. The tube model theory of rubber elasticity. Rep. Progr. Phys. 1999, 51, 243-297.
22. Edwards, S. The statistical mechanics of polymerized material. Proc. Phys. Soc. 1967, 92, 9-16.
23. Edwards, S. Statistical mechanics with topological constraints I. Proc. Phys. Soc. 1967, 91, 513-519.
24. Edwards, S. Statistical mechanics with topological constraints II. J. Phys. A 1968, 1, 15-28.
25. De Gennes, P.G. Reptation of a polymer chain in the presence of fixed obstacles. J. Chem. Phys. 1971, 55, 572-579.
26. Rubinstein, M.; Panyukov, S. Nonaffine deformation and elasticity of polymer networks. Macromolecules 1997, 30, 8036-8044.
27. Rubinstein, M.; Panyukov, S. Elasticity of polymer networks. Macromolecules 2002, 35, 6670-6686.
28. Arruda, E.M.; Boyce, M.C. A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials. J. Mech. Phys. Solids 1993, 41, 389-412.
29. Miehe, C.; Göktepe, S.; Lulei, F. A micro-macro approach to rubber-like materials. Part I The non-affine micro-sphere model of rubber elasticity. J. Mech. Phys. Solids 2004, 52, 2617-2660.
30. Miehe, C.; Göktepe, S. A micro-macro approach to rubber-like materials. Part II The micro-sphere model of finite rubber viscoelasticity. J. Mech. Phys. Solids 2005, 53, 2231-2258.
31. Göktepe, S.; Miehe, C. A micro-macro approach to rubber-like materials Part III The micro-sphere model of anisotropic Mullins-type damage. J. Mech. Phys. Solids 2005, 53, 2259-2283.
32. Tang, S.; Greene, M.S.; Liu, W.K. Two-scale mechanism-based theory of nonlinear viscoelasticity. J. Mech. Phys. Solids 2012, 60, 199-226.
33. Jensen, M.K.; Khaliullin, R.; Schieber, J.D. Self-consistent modeling of entangled network strands and linear dangling structures in a single-strand mean-field slip-link model. Rheol. Acta 2012, 51, 21-35.
34. Gee, R.H.; Lacevic, N.; Fried, L.E. Atomistic simulations of spinodal phase separation preceding polymer crystallization. Nat. Mater. 2005, 5, 39-43.
35. Baschnagel, J.; Binder, K.; Doruker, P.; Gusev, A.; Hahn, O.; Kremer, K.; Mattice, W.; Müller-Plathe, F.; Murat, M.; Paul, W.; et al. Bridging the Gap between Atomistic and Coarse-grained Models of Polymers Status and Perspectives. In Viscoelasticity, Atomistic Models, Statistical Chemistry; Springer Berlin, Germany, 2000; pp. 41-156.
36. Kremer, K.; Müller-Plathe, F. Multiscale simulation in polymer science. Mol. Simul. 2002, 28, 729-750.
37. Faller, R. Automatic coarse graining of polymers. Polymer 2004, 45, 3869-3876.
38. Müller-Plathe, F. Coarse-graining in polymer simulation From the atomistic to the mesoscopic scale and back. ChemPhysChem 2002, 3, 754-769.
39. Müller-Plathe, F. Scale-hopping in computer simulations of polymers. Soft Mater. 2002, 1, 1-31.
40. Paul, W.; Smith, G.D. Structure and dynamics of amorphous polymers Computer simulations compared to experiment and theory. Rep. Progr. Phys. 2004, 67, 1117-1185.
41. Padding, J.T.; Briels, W.J. Systematic coarse-graining of the dynamics of entangled polymer melts The road from chemistry to rheology. J. Phys. Condens. Matter 2011, 23, 2331011-23310117.
42. Karimi-Varzaneh, H.A.; van der Vegt, N.F.A.; Müller-Plathe, F.; Carbone, P. How good are coarse-grained polymer models? A comparison for atactic polystyrene. ChemPhysChem 2012, 13, 3428-3439.
43. Brini, E.; Algaer, E.A.; Ganguly, P.; Li, C.; Rodríguez-Ropero, F.; van der Vegt, N.F. Systematic coarse-graining methods for soft matter simulations-A review. Soft Matter 2013, 9, 2108-2119.
44. Holm, C.; Kremer, K. Advanced computer simulation approaches for soft matter sciences I. Adv. Polym. Sci. 2005, 173, 1-275.
45. Holm, C.; Kremer, K. Advanced computer simulation approaches for soft matter sciences II. Adv. Polym. Sci. 2005, 185, 1-250.
46. Holm, C.; Kremer, K. Advanced computer simulation approaches for soft matter sciences III. Adv. Polym. Sci. 2009, 221, 1-237.
47. Voth, G.A. Coarse-Graining of Condensed Phase and Biomolecular Systems; CRC Press Cambridge, UK, 2009.
48. Faller, R. Biomembrane Frontiers Nanostructures, Models, and the Design of Life; Springer Berlin, Germany, 2009; Volume 2.
49. Scheutjens, J.M.H.M.; Fleer, G.J. Statistical theory of the adsorption of interactingchain molecules. 1. Partition-function, segment density distribution, and adsoprtion-isotherms. J. Phys. Chem. 1979, 83, 1619-1635.
50. Boris, D.; Rubinstein, M. A self-consistent mean field model of a starburst dendrimer Dense core vs. dense shell. Macromolecules 1996, 29, 7251-7260.
51. Lai, P.Y.; Binder, K. Structure and dynamics of polymer brushes near the theta point-A Monte Carlo simulation. J. Chem. Phys. 1992, 97, 586-595.
52. Szleifer, I.; Carignano, M.A. Tethered polymer layers. Adv. Chem. Phys. 1996, 94, 165-260.
53. Detcheverry, F.A.; Kang, H.M.; Daoulas, K.C.; Müller, M.; Nealey, P.F.; de Pablo, J.J. Monte Carlo simulations of a coarse grain model for block copolymers and nanocomposites. Macromolecules 2008, 41, 4989-5001.
54. Zhulina, E.B.; Wolterink, J.K.; Borisov, O.V. Screening effects in a polyelectrolyte brush Self-consistent-field theory. Macromolecules 2000, 33, 4945-4953.
55. Müller, M. Phase diagram of a mixed polymer brush. Phys. Rev. E 2002, 65, 0308021-0308024.
56. Stuart, M.A.C.; Huck, W.T.S.; Genzer, J.; Müller, M.; Ober, C.; Stamm, M.; Sukhorukov, G.B.; Szleifer, I.; Tsukruk, V.V.; Urban, M.; et al. Emerging applications of stimuli-responsive polymer materials. Nat. Mater. 2010, 9, 101-113.
57. Halperin, A.; Kröger, M. Theoretical considerations on mechanisms of harvesting cells cultured on thermoresponsive polymer brushes. Biomaterials 2012, 33, 4975-4987.
58. Peleg, O.; Tagliazucchi, M.; Kröger, M.; Rabin, Y.; Szleifer, I. Morphology control of hairy nanopores. ACS Nano 2011, 5, 4737-4747.
59. Tagliazucchi, M.; Peleg, O.; Kröger, M.; Rabin, Y.; Szleifer, I. Effect of charge, hydrophobicity and sequence of nucleoporins on the translocation of model particles through the nuclear pore complex. Proc. Natl. Acad. Sci. USA 2013, 110, 3363-3368.
60. Csányi, G.; Albaret, T.; Payne, M.; de Vita, A. "Learn on the fly" A hybrid classical and quantum-mechanical molecular dynamics simulation. Phys. Rev. Lett. 2004, 93, 1755031-1755034.
61. Johnston, K.; Harmandaris, V. Properties of benzene confined between two Au (111) surfaces using a combined density functional theory and classical molecular dynamics approach. J. Phys. Chem. C 2011, 115, 14707-14717.
62. Johnston, K.; Nieminen, R.M.; Kremer, K. A hierarchical dualscale study of bisphenol-A-polycarbonate on a silicon surface Structure, dynamics and impurity diffusion. Soft Matter 2011, 7, 6457-6466.
63. Johnston, K.; Harmandaris, V. Properties of short polystyrene chains confined between two gold surfaces through a combined density functional theory and classical molecular dynamics approach. Soft Matter 2012, 8, 6320-6332.
64. Ilett, S.M.; Orrock, A.; Poon, W.; Pusey, P. Phase behavior of a model colloid-polymer mixture. Phys. Rev. E 1995, 51, 1344-1352.
65. Müller, M.; Binder, K. Computer simulation of asymmetric polymer mixtures. Macromolecules 1995, 28, 1825-1834.
66. Müller, M.; Schmid, F. Incorporating Fluctuations and Dynamics in Self-consistent Field Theories for Polymer Blends. In Advanced Computer Simulation Approaches for Soft Matter Sciences II; Springer Berlin, Germany, 2005; pp. 1-58.
67. Deutsch, H.P.; Binder, K. Interdiffusion and self-diffusion in polymer mixtures A Monte Carlo study. J. Chem. Phys. 1991, 94, 2294-2304.
68. Faller, R. Correlation of static and dynamic inhomogeneities in polymer mixtures A computer simulation of polyisoprene and polystyrene. Macromolecules 2004, 37, 1095-1101.
69. Qian, H.J.; Carbone, P.; Chen, X.; Karimi-Varzaneh, H.A.; Liew, C.C.; Müller-Plathe, F. Temperature-transferable coarse-grained potentials for ethylbenzene, polystyrene, and their mixtures. Macromolecules 2008, 41, 9919-9929.
70. Murat, M.; Kremer, K. From many monomers to many polymers Soft ellipsoid model for polymer melts and mixtures. J. Chem. Phys. 1998, 108, 4340-4348.
71. McCarty, J.; Guenza, M.G. Multiscale modeling of binary polymer mixtures Scale bridging in the athermal and thermal regime. J. Chem. Phys. 2010, 133, 0949041-09490415.
72. McCarty, J.; Lyubimov, I.Y.; Guenza, M.G. Effective soft-core potentials and mesoscopic simulations of binary polymer mixtures. Macromolecules 2010, 43, 3964-3979.
73. Yatsenko, G.; Sambriski, E.J.; Nemirovskaya, M.A.; Guenza, M. Analytical soft-core potentials for macromolecular fluids and mixtures. Phys. Rev. Lett. 2004, 93, 2578031-2578034.
74. Baig, C.; Stephanou, P.S.; Tsolou, G.; Mavrantzas, V.G.; Kröger, M. Understanding dynamics in binary mixtures of entangled cis-1, 4-polybutadiene melts at the level of primitive path segments by mapping atomistic simulation data onto the tube model. Macromolecules 2010, 43, 8239-8250.
75. Harmandaris, V.A.; Kremer, K.; Floudas, G. Dynamic heterogeneity in fully miscible blends of polystyrene with oligostyrene. Phys. Rev. Lett. 2013, 110, 1657011-1657015.
76. Harmandaris, V.A.; Mavrantzas, V.G.; Theodorou, D.N.; Kröger, M.; Ramirez, J.; Öttinger, H.C.; Vlassopoulos, D. Crossover from the Rouse to the entangled polymer melt regime Signals from long, detailed atomistic molecular dynamics simulations, supported by rheological experiments. Macromolecules 2003, 36, 1376-1387.
77. Carmesin, I.; Kremer, K. The bond fluctuation method A new effective algorithm for the dynamics of polymers in all spatial dimensions. Macromolecules 1988, 21, 2819-2823.
78. Grest, G.S.; Kremer, K. Molecular dynamics simulation for polymers in the presence of a heat bath. Phys. Rev. A 1986, 33, 3628-3631.
79. Kremer, K.; Grest, G.S. Dynamics of entangled linear polymer melts A molecular-dynamics simulation. J. Chem. Phys. 1990, 92, 5057-5086.
80. Hua, C.C.; Schieber, J.D. Segment connectivity, chain-length breathing, segmental stretch, and constraint release in reptation models. I. Theory and single-step strain predictions. J. Chem. Phys. 1998, 109, 10018-10027.
81. Hua, C.C.; Schieber, J.D.; Venerus, D.C. Segment connectivity, chain-length breathing, segmental stretch, and constraint release in reptation models. II. Double-step strain predictions. J. Chem. Phys. 1998, 109, 10028-10032.
82. Tschöp, W.; Kremer, K.; Batoulis, J.; Bürger, T.; Hahn, O. Simulation of polymer melts. I. Coarse-graining procedure for polycarbonates. Acta Polym. 1998, 49, 61-74.
83. Meyer, H.; Biermann, O.; Faller, R.; Reith, D.; Müller-Plathe, F. Coarse graining of nonbonded inter-particle potentials using automatic simplex optimization to fit structural properties. J. Chem. Phys. 2000, 113, 6264-6275.
84. Padding, J.T.; Briels, W.J. Uncrossability constraints in mesoscopic polymer melt simulations Non-Rouse behavior of C120H242. J. Chem. Phys. 2001, 115, 2846-2859.
85. Padding, J.T.; Briels, W.J. Time and length scales of polymer melts studied by coarse-grained molecular dynamics simulations. J. Chem. Phys. 2002, 117, 925-943.
86. Kindt, P.; Briels, W.J. A single particle model to simulate the dynamics of entangled polymer melts. J. Chem. Phys. 2007, 127, 1349011-13490112.
87. Guenza, M.G. Theoretical models for bridging timescales in polymer dynamics. J. Phys. Condens. Matter 2007, 20, 0331011-03310124.
88. McCarty, J.; Lyubimov, I.Y.; Guenza, M.G. Multiscale modeling of coarse-grained macromolecular liquids. J. Phys. Chem. B 2009, 113, 11876-11886.
89. Stephanou, P.S.; Baig, C.; Tsolou, G.; Mavrantzas, V.G.; Kröger, M. Quantifying chain reptation in entangled polymer melts Topological and dynamical mapping of atomistic simulation results onto the tube model. J. Chem. Phys. 2010, 132, 1249041-12490416.
90. Ilg, P.; Öttinger, H.C.; Kröger, M. Systematic time-scale-bridging molecular dynamics applied to flowing polymer melts. Phys. Rev. E 2009, 79, 0118021-0118027.
91. De, S.; Fish, J.; Shephard, M.S.; Keblinski, P.; Kumar, S.K. Multiscale modeling of polymer rheology. Phys. Rev. E 2006, 74, 0308011-0308014.
92. Li, Y.; Tang, S.; Abberton, B.; Kröger, M.; Burkhart, C.; Jiang, B.; Papakonstantopoulos, G.; Poldneff, M.; Liu, W.K. A predictive multiscale computational framework for viscoelastic properties of linear polymers. Polymer 2012, 53, 5935-5952.
93. Wittmer, J.P.; Cavallo, A.; Xu, H.; Zabel, J.E.; Polinska, P.; Schulmann, N.; Meyer, H.; Farago, J.; Johner, A.; Obukhov, S.P.; Baschnagel, J. Scale-free static and dynamical correlations in melts of monodisperse and Flory-distributed homopolymers. A review of recent bond-fluctuation model studies. J. Statist. Phys. 2011, 145, 1017-1126.
94. Paul, W.; Binder, K.; Heermann, D.W.; Kremer, K. Dynamics of polymer solutions and melts. Reptation predictions and scaling of relaxation times. J. Chem. Phys. 1991, 95, 7726-7740.
95. Binder, K.; Paul, W. Monte Carlo simulations of polymer dynamics Recent advances. J. Polym. Sci. B 1997, 35, 1-31.
96. Shaffer, J.S. Effects of chain topology on polymer dynamics Bulk melts. J. Chem. Phys. 1994, 101, 4205-4213.
97. Everaers, R.; Sukumaran, S.K.; Grest, G.S.; Svaneborg, C.; Sivasubramanian, A.; Kremer, K. Rheology and microscopic topology of entangled polymeric liquids. Science 2004, 303, 823-826.
98. Doi, M.; Kuzuu, N.Y. Rheology of star polymers in concentrated solutions and melts. J. Polym. Sci. Polym. Phys. 1980, 18, 775-780.
99. Paul, W.; Binder, K.; Kremer, K.; Heermann, D.W. Structure-property correlation of polymers, a Monte Carlo approach. Macromolecules 1991, 24, 6332-6334.
100. Paul, W.; Pistoor, N. A mapping of realistic onto abstract polymer models and an application to two bisphenol polycarbonates. Macromolecules 1994, 27, 1249-1255.
101. Tries, V.; Paul, W.; Baschnagel, J.; Binder, K. Modeling polyethylene with the bond fluctuation model. J. Chem. Phys. 1997, 106, 738-748.
102. Baschnagel, J.; Binder, K.; Paul, W.; Laso, M.; Suter, U.W.; Batoulis, I.; Jilge, W.; Bürger, T. On the construction of coarse-grained models for linear flexible polymer chains Distribution functions for groups of consecutive monomers. J. Chem. Phys. 1991, 95, 6014-6025.
103. Weeks, J.D.; Chandler, D.; Andersen, H.C. Role of repulsive forces in determining the equilibrium structure of simple liquids. J. Chem. Phys. 1971, 54, 5237-5247.
104. Hess, S.; Kröger, M.; Voigt, H. Thermo-mechanical properties of the WCA-Lennard-Jones model system in its fluid and solid states. Physica A 1998, 250, 58-82.
105. Pütz, M.; Kremer, K.; Grest, G.S. What is the entanglement length in a polymer melt? EPL (Europhys. Lett.) 2000, 49, 735-739.
106. Kröger, M.; Hess, S. Rheological evidence for a dynamical crossover in polymer melts via nonequilibrium molecular dynamics. Phys. Rev. Lett. 2000, 85, 1128-1131.
107. Kremer, K.; Binder, K. Dynamics of polymer chains confined into tubes Scaling theory and Monte Carlo simulations. J. Chem. Phys. 1984, 81, 6381-6394.
108. Cifre, J.G.H.; Hess, S.; Kröger, M. Linear viscoelastic behavior of unentangled polymer melts via non-equilibrium molecular dynamics. Macromol. Theory Simul. 2004, 13, 748-753.
109. Ferry, J.D. Viscoelastic Properties of Polymers; Wiley New York, NY, USA, 1980; Volume 641.
110. Cox, W.P.; Merz, E.H. Correlation of dynamic and steady flow viscosities. J. Polym. Sci. Polym. Phys. 1958, 28, 619-622.
111. Antonietti, M.; Coutandin, J.; Sillescu, H. Diffusion of linear polystyrene molecules in matrixes of different molecular weights. Macromolecules 1986, 19, 793-798.
112. Higgins, J.S.; Roots, J.E. Effects of entanglements on the single-chain motion of polymer molecules in melt samples observed by neutron scattering. J. Chem. Soc. Faraday Trans. II 1985, 81, 757-767.
113. Pearson, D.S.; Fetters, L.J.; Graessley, W.W.; Ver Strate, G.; von Meerwall, E. Viscosity and self-diffusion coefficient of hydrogenated polybutadiene. Macromolecules 1994, 27, 711-719.
114. Smith, S.W.; Hall, C.K.; Freeman, B.D. Molecular dynamics study of entangled hard-chain fluids. J. Chem. Phys. 1996, 104, 5616-5637.
115. Faller, R. Influence of chain stiffness on structure and dynamics of polymers in the melt. Ph.D. thesis, University of Mainz, Mainz, Germany, 2000.
116. Affouard, F.; Kröger, M.; Hess, S. Molecular dynamics of model liquid crystals composed of semiflexible molecules. Phys. Rev. E 1996, 54, 5178-5186.
117. Kröger, M.; Peleg, O.; Ding, Y.; Schlüter, A.D.; Öttinger, H.C. Formation of double helical and filamentous structures in models of physical and chemical gels. Soft Matter 2008, 4, 18-28.
118. Harasim, M.; Wunderlich, B.; Peleg, O.; Kröger, M.; Bausch, A. Direct observation of the dynamics of semiflexible polymers in shear flow. Phys. Rev. Lett. 2013, 110, 1083021-1083025.
119. Sukumaran, S.K.; Grest, G.S.; Kremer, K.; Everaers, R. Identifying the primitive path mesh in entangled polymer liquids. J. Polym. Sci. B 2005, 43, 917-933.
120. Uchida, N.; Grest, G.S.; Everaers, R. Viscoelasticity and primitive path analysis of entangled polymer liquids From F-actin to polyethylene. J. Chem. Phys. 2008, 128, 0449021-0449026.
121. Hoy, R.S.; Robbins, M.O. Strain hardening of polymer glasses Effect of entanglement density, temperature, and rate. J. Polym. Sci. B 2006, 44, 3487-3500.
122. Hoy, R.S.; Robbins, M.O. Strain hardening in polymer glasses Limitations of network models. Phys. Rev. Lett. 2007, 99, 1178011-1178014.
123. Hoy, R.S. Why is understanding glassy polymer mechanics so difficult? J. Polym. Sci. B 2011, 49, 979-984.
124. Halverson, J.D.; Lee, W.B.; Grest, G.S.; Grosberg, A.Y.; Kremer, K. Molecular dynamics simulation study of nonconcatenated ring polymers in a melt. I. Statics. J. Chem. Phys. 2011, 134, 2049041-20490413.
125. Halverson, J.D.; Lee, W.B.; Grest, G.S.; Grosberg, A.Y.; Kremer, K. Molecular dynamics simulation study of nonconcatenated ring polymers in a melt. II. Dynamics. J. Chem. Phys. 2011, 134, 2049051-20490510.
126. Halverson, J.D.; Grest, G.S.; Grosberg, A.Y.; Kremer, K. Rheology of ring polymer melts From linear contaminants to ring-linear blends. Phys. Rev. Lett. 2012, 108, 0383011-0383015.
127. Baljon, A.R.C.; van Weert, M.H.M.; DeGraaff, R.B.; Khare, R. Glass transition behavior of polymer films of nanoscopic dimensions. Macromolecules 2005, 38, 2391-2399.
128. Morita, H.; Tanaka, K.; Kajiyama, T.; Nishi, T.; Doi, M. Study of the glass transition temperature of polymer surface by coarse-grained molecular dynamics simulation. Macromolecules 2006, 39, 6233-6237.
129. Peter, S.; Meyer, H.; Baschnagel, J.; Seemann, R. Slow dynamics and glass transition in simulated free-standing polymer films A possible relation between global and local glass transition temperatures. J. Phys. Condens. Matter 2007, 19, 2051191-20511911.
130. Barrat, J.L.; Baschnagel, J.; Lyulin, A. Molecular dynamics simulations of glassy polymers. Soft Matter 2010, 6, 3430-3446.
131. Kröger, M.; Makhloufi, R. Wormlike micelles under shear flow A microscopic model studied by nonequilibrium molecular dynamics computer simulations. Phys. Rev. E 1996, 53, 2531-2536.
132. Li, S.F.; Sheng, N. On multiscale non-equilibrium molecular dynamics simulations. Int. J. Numer. Meth. Eng. 2010, 83, 998-1038.
133. Huang, C.C.; Ryckaert, J.P.; Xu, H. Structure and dynamics of cylindrical micelles at equilibrium and under shear flow. Phys. Rev. E 2009, 79, 0415011-04150113.
134. Padding, J.T.; Briels, W.J.; Stukan, M.R.; Boek, E.S. Review of multi-scale particulate simulation of the rheology of wormlike micellar fluids. Soft Matter 2009, 5, 4367-4375.
135. Lukyanov, A.; Likhtman, A. Dynamic surface tension effects from molecular dynamics simulations. Bull. Am. Phys. Soc. 2010, 55, Abstract ID BAPS.2011.DFD.S26.9.
136. Peter, S.; Napolitano, S.; Meyer, H.; Wubbenhorst, M.; Baschnagel, J. Modeling dielectric relaxation in polymer glass simulations Dynamics in the bulk and in supported polymer films. Macromolecules 2008, 41, 7729-7743.
137. Yokomizo, K.; Banno, Y.; Kotaki, M. Molecular dynamics study on the effect of molecular orientation on polymer welding. Polymer 2012, 53, 4280-4286.
138. Ge, T.; Pierce, F.; Perahia, D.; Grest, G.S.; Robbins, M.O. Molecular dynamics simulations of polymer welding Strength from interfacial entanglements. Phys. Rev. Lett. 2013, 110, 0983011-0983015.
139. Shanbhag, S.; Larson, R.G.; Takimoto, J.; Doi, M. Deviations from dynamic dilution in the terminal relaxation of star polymers. Phys. Rev. Lett. 2001, 87, 1955021-1955024.
140. Doi, M.; Takimoto, J.I. Molecular modelling of entanglement. Phil. Trans. R. Soc. Lond. A 2003, 361, 641-652.
141. Likhtman, A.E. Single-chain slip-link model of entangled polymers Simultaneous description of neutron spin-echo, rheology, and diffusion. Macromolecules 2005, 38, 6128-6139.
142. Indei, T.; Schieber, J.D.; Takimoto, J.i. Effects of fluctuations of cross-linking points on viscoelastic properties of associating polymer networks. Rheol. Acta 2012, 51, 1021-1039.
143. Schieber, J.D.; Indei, T.; Steenbakkers, R.J.A. Fluctuating entanglements in single-chain mean-field models. Polymers 2013, 5, 643-678.
144. Masubuchi, Y.; Takimoto, J.I.; Koyama, K.; Ianniruberto, G.; Marrucci, G.; Greco, F. Brownian simulations of a network of reptating primitive chains. J. Chem. Phys. 2001, 115, 4387-4394.
145. Masubuchi, Y.; Ianniruberto, G.; Greco, F.; Marrucci, G. Entanglement molecular weight and frequency response of sliplink networks. J. Chem. Phys. 2003, 119, 6925-6930.
146. Masubuchi, Y.; Ianniruberto, G.; Greco, F.; Marrucci, G. Molecular simulations of the long-time behaviour of entangled polymeric liquids by the primitive chain network model. Model. Simul. Mater. Sci. Eng. 2004, 12, S91. doi10.1088/0965-0393/12/3/S03.
147. Masubuchi, Y.; Ianniruberto, G.; Greco, F.; Marrucci, G. Quantitative comparison of primitive chain network simulations with literature data of linear viscoelasticity for polymer melts. J. Non-Newtonian Fluid Mech. 2008, 149, 87-92.
148. Yaoita, T.; Isaki, T.; Masubuchi, Y.; Watanabe, H.; Ianniruberto, G.; Greco, F.; Marrucci, G. Highly entangled polymer primitive chain network simulations based on dynamic tube dilation. J. Chem. Phys. 2004, 121, 126501-126505.
149. Uneyama, T.; Masubuchi, Y. Multi-chain slip-spring model for entangled polymer dynamics. J. Chem. Phys. 2012, 137, 1549021-15490213.
150. Masubuchi, Y.; Ianniruberto, G.; Greco, F.; Marrucci, G. Primitive chain network simulations for branched polymers. Rheol. Acta 2006, 46, 297-303.
151. Yaoita, T.; Isaki, T.; Masubuchi, Y.; Watanabe, H.; Ianniruberto, G.; Greco, F.; Marrucci, G. Statics, linear, and nonlinear dynamics of entangled polystyrene melts simulated through the primitive chain network model. J. Chem. Phys. 2008, 128, 1549011-15490111.
152. Yaoita, T.; Isaki, T.; Masubuchi, Y.; Watanabe, H.; Ianniruberto, G.; Marrucci, G. Primitive chain network simulation of elongational flows of entangled linear chains Role of finite chain extensibility. Macromolecules 2011, 44, 9675-9682.
153. Yaoita, T.; Isaki, T.; Masubuchi, Y.; Watanabe, H.; Ianniruberto, G.; Marrucci, G. Primitive chain network simulation of elongational flows of entangled linear chains Stretch/orientation-induced reduction of monomeric friction. Macromolecules 2012, 45, 2773-2782.
154. Masubuchi, Y.; Watanabe, H.; Ianniruberto, G.; Greco, F.; Marrucci, G. Comparison among slip-link simulations of bidisperse linear polymer melts. Macromolecules 2008, 41, 8275-8280.
155. Lay, S.; Sommer, J.U.; Blumen, A. Monte Carlo study of the microphase separation of cross-linked polymer blends. J. Chem. Phys. 2000, 113, 11355-11363.
156. Masubuchi, Y.; Ianniruberto, G.; Greco, F.; Marrucci, G. Primitive chain network model for block copolymers. J. Non-Cryst. Solids 2006, 352, 5001-5007.
157. Okuda, S.; Inoue, Y.; Masubuchi, Y.; Uneyama, T.; Hojo, M. Wall boundary model for primitive chain network simulations. J. Chem. Phys. 2009, 130, 2149071-2149077.
158. Chappa, V.C.; Morse, D.C.; Zippelius, A.; Müller, M. Translationally invariant slip-spring model for entangled polymer dynamics. Phys. Rev. Lett. 2012, 109, 1483021-1483025.
159. Ramírez-Hernández, A.; Müller, M.; de Pablo, J.J. Theoretically informed entangled polymer simulations Linear and non-linear rheology of melts. Soft Matter 2013, 9, 2030-2036.
160. Hess, B.; Holm, C.; van der Vegt, N. Osmotic coefficients of atomistic NaCl (aq) force fields. J. Chem. Phys. 2006, 124, 1645091-1645098.
161. Hess, B.; Holm, C.; van der Vegt, N. Modeling multibody effects in ionic solutions with a concentration dependent dielectric permittivity. Phys. Rev. Lett. 2006, 96, 1478011-1478014.
162. Wang, Y.; Noid, W.; Liu, P.; Voth, G.A. Effective force coarse-graining. Phys. Chem. Chem. Phys. 2009, 11, 2002-2015.
163. Brini, E.; Marcon, V.; van der Vegt, N.F. Conditional reversible work method for molecular coarse graining applications. Phys. Chem. Chem. Phys. 2011, 13, 10468-10474.
164. Ganguly, P.; Mukherji, D.; Junghans, C.; van der Vegt, N.F. Kirkwood-buff coarse-grained force fields for aqueous solutions. J. Chem. Theory Comput. 2012, 8, 1802-1807.
165. Lyubartsev, A.P.; Laaksonen, A. Calculation of effective interaction potentials from radial distribution functions A reverse Monte Carlo approach. Phys. Rev. E 1995, 52, 3730-3737.
166. Shell, M.S. The relative entropy is fundamental to multiscale and inverse thermodynamic problems. J. Chem. Phys. 2008, 129, 1441081-1441087.
167. Mullinax, J.; Noid, W. Reference state for the generalized Yvon-Born-Green theory Application for coarse-grained model of hydrophobic hydration. J. Chem. Phys. 2010, 133, 1241071-12410711.
168. Ercolessi, F.; Adams, J.B. Interatomic potentials from first-principles calculations The force-matching method. EPL (Europhys. Lett.) 1994, 26, 583-588.
169. Izvekov, S.; Voth, G.A. A multiscale coarse-graining method for biomolecular systems. J. Phys. Chem. B 2005, 109, 2469-2473.
170. Izvekov, S.; Voth, G.A. Multiscale coarse graining of liquid-state systems. J. Chem. Phys. 2005, 123, 1341051-13410513.
171. Noid, W.G.; Chu, J.W.; Ayton, G.S.; Voth, G.A. Multiscale coarse-graining and structural correlations Connections to liquid-state theory. J. Phys. Chem. B 2007, 111, 4116-4127.
172. Noid, W.G.; Chu, J.W.; Ayton, G.S.; Krishna, V.; Izvekov, S.; Voth, G.A.; Das, A.; Andersen, H.C. The multiscale coarse-graining method. I. A rigorous bridge between atomistic and coarse-grained models. J. Chem. Phys. 2008, 128, 2441141-24411411.
173. Noid, W.G.; Liu, P.; Wang, Y.; Chu, J.W.; Ayton, G.S.; Izvekov, S.; Andersen, H.C.; Voth, G.A. The multiscale coarse-graining method. II. Numerical implementation for coarse-grained molecular models. J. Chem. Phys. 2008, 128, 2441151-24411520.
174. Rühle, V.; Junghans, C.; Lukyanov, A.; Kremer, K.; Andrienko, D. Versatile object-oriented toolkit for coarse-graining applications. J. Chem. Theory Comput. 2009, 5, 3211-3223.
175. Hansen, J.P.; McDonald, I.R. Theory of Simple Liquids; Academic Press Waltham, MA, USA, 2006.
176. Tschöp, W.; Kremer, K.; Hahn, O.; Batoulis, J.; Bürger, T. Simulation of polymer melts II From coarse-grained models back to atomistic description. Acta Polym. 1998, 49, 75-79.
177. Tschöp, W.; Kremer, K.; Batoulis, J.; Bürger, T.; Hahn, O. Simulation of polymer melts I Coarse-graining procedure for polycarbonates. Acta Polym. 1999, 49, 61-74.
178. Li, Y.; Kröger, M.; Liu, W.K. Primitive chain network study on uncrosslinked and crosslinked cis-polyisoprene polymers. Polymer 2011, 52, 5867-5878.
179. Accelrys, 2012. Available online http//accelrys.com/products/materials-studio/ (accessed on 7 June 2013).
180. Sun, H. COMPASS An ab initio force-field optimized for condensed-phase applications overview with details on alkane and benzene compounds. J. Phys. Chem. B 1998, 102, 7338-7364.
181. Doxastakis, M.; Mavrantzas, V.; Theodorou, D. Atomistic Monte Carlo simulation of cis-1,4 polyisoprene melts I Single temperature end-bridging Monte Carlo simulations. J. Chem. Phys. 2001, 115, 113391-1133913.
182. Faller, R.; Müller-Plathe, F.; Doxastakis, M.; Theodorou, D.N. Local structure and dynamics of trans-polyisoprene oligomers. Macromolecules 2001, 34, 1436-1448.
183. Faller, R.; Müller-Plathe, F. Modeling of poly (isoprene) melts on different scales. Polymer 2002, 43, 621-628.
184. Faller, R.; Reith, D. Properties of poly (isoprene) Model building in the melt and in solution. Macromolecules 2003, 36, 5406-5414.
185. Sun, Q.; Faller, R. Systematic coarse-graining of atomistic models for simulation of polymeric systems. Comp. Chem. Eng. 2005, 29, 2380-2385.
186. Sun, Q.; Faller, R. Systematic coarse-graining of a polymer blend Polyisoprene and polystyrene. J. Chem. Theor. Comput. 2006, 2, 607-615.
187. Ramachandran, G.N.; Ramakrishnan, C.; Sasisekharan, V. Stereochemistry of polypeptide chain configurations. J. Mol. Biol. 1963, 7, 95-99.
188. Harmandaris, V.A.; Reith, D.; van der Vegt, N.F.A.; Kremer, K. Comparison between coarse-graining models for polymer systems Two mapping schemes for polystyrene. Macromol. Chem. Phys. 2007, 208, 2109-2120.
189. McCoy, J.D.; Curro, J.G. Mapping of explicit atom onto united atom potentials. Macromolecules 1998, 31, 9362-9368.
190. Akkermans, R.L.C.; Briels, W.J. A structure-based coarse-grained model for polymer melts. J. Chem. Phys. 2001, 114, 1020-1031.
191. Reith, D.; Meyer, H.; Müller-Plathe, F. Mapping atomistic to coarse-grained polymer models using automatic simplex optimization to fit structural properties. Macromolecules 2001, 34, 2335-2345.
192. Hahn, O.; Site, L.D.; Kremer, K. Simulation of polymer melts From spherical to ellipsoidal beads. Macromol. Theory Simul. 2001, 10, 288-303.
193. Xie, G.; Zhang, Y.; Huang, S. Glass formation of n-butanol Coarse-grained molecular dynamics simulations using Gay-Berne potential model. Chin. J. Chem. Phys. 2012, 25, 177-185.
194. Abrams, C.F.; Kremer, K. Combined coarse-grained and atomistic simulation of liquid bisphenol A-polycarbonate Liquid packing and intramolecular structure. Macromolecules 2003, 36, 260-267.
195. Müller-Plathe, F. Local structure and dynamics in solvent-swollen polymers. Macromolecules 1996, 29, 4782-4791.
196. Milano, G.; Goudeau, S.; Müller-Plathe, F. Multicentered Gaussian-based potentials for coarse-grained polymer simulations Linking atomistic and mesoscopic scales. J. Polym. ScI B 2005, 43, 871-885.
197. Milano, G.; Müller-Plathe, F. Mapping atomistic simulations to mesoscopic models A systematic coarse-graining procedure for vinyl polymer chains. J. Phys. Chem. B 2005, 109, 18609-18619.
198. Spyriouni, T.; Tzoumanekas, C.; Theodorou, D.; Müller-Plathe, F.; Milano, G. Coarse-grained and reverse-mapped united-atom simulations of long-chain atactic polystyrene melts Structure, thermodynamic properties, chain conformation, and entanglements. Macromolecules 2007, 40, 3876-3885.
199. Fetters, L.J.; Lohse, D.J.; Richter, D.; Witten, T.A.; Zirkel, A. Connection between polymer molecular weight, density, chain dimensions, and melt viscoelastic properties. Macromolecules 1994, 27, 4639-4647.
200. Sun, Q.; Faller, R. Crossover from unentangled to entangled dynamics in a systematically coarse-grained polystyrene melt. Macromolecules 2006, 39, 812-820.
201. Harmandaris, V.A.; Adhikari, N.P.; van Der Vegt, N.F.A.; Kremer, K. Hierarchical modeling of polystyrene From atomistic to coarse-grained simulations. Macromolecules 2006, 39, 6708-6719.
202. Mulder, T.; Harmandaris, V.A.; Lyulin, A.V.; van der Vegt, N.F.A.; Vorselaars, B.; Michels, M.A.J. Equilibration and deformation of amorphous polystyrene Scale-jumping simulational approach. Macromol. Theory Simul. 2008, 17, 290-300.
203. Mulder, T.; Harmandaris, V.A.; Lyulin, A.V.; van der Vegt, N.F.A.; Kremer, K.; Michels, M.A.J. Structural properties of atactic polystyrene of different thermal history obtained from a multiscale simulation. Macromolecules 2009, 42, 384-391.
204. Harmandaris, V.A.; Kremer, K. Dynamics of polystyrene melts through hierarchical multiscale simulations. Macromolecules 2009, 42, 791-802.
205. Harmandaris, V.A.; Kremer, K. Predicting polymer dynamics at multiple length and time scales. Soft Matter 2009, 5, 3920-3926.
206. Varzaneh, H.A.K.; Chen, X.; Carbone, P.; Qian, H.J.; Müller-Plathe, F. 2008. Available online http//www.theo.chemie.tu-darmstadt.de/ibisco/IBISCO.html (accessed on 7 June 2013).
207. Karimi-Varzaneh, H.A.; Qian, H.J.; Chen, X.; Carbone, P.; Müller-Plathe, F IBIsCO A molecular dynamics simulation package for coarse-grained simulation. J. Comput. Chem. 2011, 32, 1475-1487.
208. Luo, C.; Sommer, J.U. Coding coarse grained polymer model for LAMMPS and its application to polymer crystallization. Comput. Phys. Commun. 2009, 180, 1382-1391.
209. Plimpton, S. Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys. 1995, 117, 1-19.
210. Faller, R.; Schmitz, H.; Biermann, O.; Müller-Plathe, F. Automatic parameterization of force fields for liquids by simplex optimization. J. Comput. Chem. 1999, 20, 1009-1017.
211. Reith, D.; Meyer, H.; Müller-Plathe, F. CG-OPT A software package for automatic force field design. Comput. Phys. Commun. 2002, 148, 299-313.
212. Reith, D.; Pütz, M.; Müller-Plathe, F. Deriving effective mesoscale potentials from atomistic simulations. J. Comput. Chem. 2003, 24, 1624-1636.
213. Murtola, T.; Falck, E.; Karttunen, M.; Vattulainen, I Coarse-grained model for phospholipid/cholesterol bilayer employing inverse Monte Carlo with thermodynamic constraints. J. Chem. Phys. 2007, 126, 0751011-07510114.
214. Wang, Q.; Keffer, D.J.; Nicholson, D.M.; Thomas, J.B. Use of the Ornstein-Zernike Percus-Yevick equation to extract interaction potentials from pair correlation functions. Phys. Rev. E 2010, 81, 0612041-0612049.
215. Wang, Q.; Keffer, D.J.; Nicholson, D.M.; Thomas, J.B. Coarse-grained molecular dynamics simulation of polyethylene terephthalate (PET). Macromolecules 2010, 43, 10722-10734.
216. Batchelor, G.K. An Introduction to Fluid Dynamics; Cambridge University Press New York, NY, USA, 2000.
217. Lyubimov, IY.; McCarty, J.; Clark, A.; Guenza, M.G. Analytical rescaling of polymer dynamics from mesoscale simulations. J. Chem. Phys. 2010, 132, 2249031-2249035.
218. Lyubimov, I; Guenza, M.G. First-principle approach to rescale the dynamics of simulated coarse-grained macromolecular liquids. Phys. Rev. E 2011, 84, 0318011-03180119.
219. Harmandaris, V.A.; Floudas, G.; Kremer, K. Temperature and pressure dependence of polystyrene dynamics through molecular dynamics simulations and experiments. Macromolecules 2010, 44, 393-402.
220. Fritz, D.; Harmandaris, V.A.; Kremer, K.; van Der Vegt, N.F.A. Coarse-grained polymer melts based on isolated atomistic chains Simulation of polystyrene of different tacticities. Macromolecules 2009, 42, 7579-7588.
221. Leon, S.; van Der Vegt, N.; Delle Site, L.; Kremer, K. Bisphenol A polycarbonate Entanglement analysis from coarse-grained MD simulations. Macromolecules 2005, 38, 8078-8092.
222. Depa, P.K.; Maranas, J.K. Speed up of dynamic observables in coarse-grained molecular-dynamics simulations of unentangled polymers. J. Chem. Phys. 2005, 123, 0949011-0949017.
223. Depa, P.K.; Maranas, J.K. Dynamic evolution in coarse-grained molecular dynamics simulations of polyethylene melts. J. Chem. Phys. 2007, 126, 0549031-0549038.
224. Chen, C.; Depa, P.; Sakai, V.G.; Maranas, J.K.; Lynn, J.W.; Peral, I; Copley, J.R.D. A comparison of united atom, explicit atom, and coarse-grained simulation models for poly (ethylene oxide). J. Chem. Phys. 2006, 124, 2349011-23490111.
225. Chen, C.; Depa, P.; Maranas, J.K.; Garcia Sakai, V. Comparison of explicit atom, united atom, and coarse-grained simulations of poly (methyl methacrylate). J. Chem. Phys. 2008, 128, 1249061-12490612.
226. Strauch, T.; Yelash, L.; Paul, W. A coarse-graining procedure for polymer melts applied to 1, 4-polybutadiene. Phys. Chem. Chem. Phys. 2009, 11, 1942-1948.
227. Karimi-Varzaneh, H.; Müller-Plathe, F. Coarse-Grained Modeling for Macromolecular Chemistry In Multiscale Molecular Methods in Applied Chemistry; Springer New York, NY, USA, 2012; pp. 295-321.
228. Colmenero, J.; Arbe, A. Segmental dynamics in miscible polymer blends Recent results and open questions. Soft Matter 2007, 3, 1474-1485.
229. Roland, C.; Ngai, K. Dynamical heterogeneity in a miscible polymer blend. Macromolecules 1991, 24, 2261-2265.
230. Louis, A.A. Beware of density dependent pair potentials. J. Phys. Condens. Matter 2002, 14, 9187-9206.
231. Fukunaga, H.; Takimoto, J.; Doi, M. A coarse-graining procedure for flexible polymer chains with bonded and nonbonded interactions. J. Chem. Phys. 2002, 116, 8183-8190.
232. Carbone, P.; Varzaneh, H.A.K.; Chen, X.; Müller-Plathe, F. Transferability of coarse-grained force fields The polymer case. J. Chem. Phys. 2008, 128, 0649041-06490411.
233. Marrink, S.J.; de Vries, A.H.; Mark, A.E. Coarse grained model for semiquantitative lipid simulations. J. Phys. Chem. B 2004, 108, 750-760.
234. Harmandaris, V.A.; Adhikari, N.P.; van der Vegt, N.F.A.; Kremer, K.; Mann, B.A.; Voelkel, R.; Weiss, H.; Liew, C.C. Ethylbenzene diffusion in polystyrene United atom atomistic/coarse grained simulations and experiments. Macromolecules 2007, 40, 7026-7035.
235. Hess, B.; León, S.; van Der Vegt, N.; Kremer, K. Long time atomistic polymer trajectories from coarse grained simulations Bisphenol-A polycarbonate. Soft Matter 2006, 2, 409-414.
236. Öttinger, H.C. Systematic coarse graining Four lessons and a caveat from nonequilibrium statistical mechanics. MRS Bull. 2007, 32, 936-940.
237. Vettorel, T.; Meyer, H. Coarse graining of short polythylene chains for studying polymer crystallization. J. Chem. Theory Comput. 2006, 2, 616-629.
238. Yelash, L.; Müller, M.; Paul, W.; Binder, K. How well can coarse-grained models of real polymers describe their structure? the case of polybutadiene. J. Chem. Theory Comput. 2006, 2, 588-597.
239. Eslami, H.; Karimi-Varzaneh, H.A.; Müller-Plathe, F. Coarse-grained computer simulation of nanoconfined polyamide-6, 6. Macromolecules 2011, 44, 3117-3128.
240. Bayramoglu, B.; Faller, R. Coarse-grained modeling of polystyrene in various environments by iterative Boltzmann inversion. Macromolecules 2012, 45, 9205-9219.
241. Pérez-Aparicio, R.; Colmenero, J.; Alvarez, F.; Padding, J.T.; Briels, W.J. Chain dynamics of poly (ethylene-alt-propylene) melts by means of coarse-grained simulations based on atomistic molecular dynamics. J. Chem. Phys. 2010, 132, 0249041-02490411.
242. Hoy, R.; Foteinopoulou, K.; Kröger, M. Topological analysis of polymeric melts Chain-length effects and fast-converging estimators for entanglement length. Phys. Rev. E 2009, 80, 0318031-03180313.
243. Padding, J.T.; Briels, W.J. Zero-shear stress relaxation and long time dynamics of a linear polyethylene melt A test of Rouse theory. J. Chem. Phys. 2001, 114, 8685-8693.
244. Malkin, A.; Semakov, A.; Kulichikhin, V. Macroscopic modeling of a single entanglement at high deformation rates of polymer melts. Appl. Rheol. 2012, 22, 325751-325759.
245. Padding, J.T.; Briels, W.J. TWENTANGLEMENT User's Manual; Twente University Enschede, the Netherlands, 2000.
246. Nikunen, P.; Vattulainen, I; Karttunen, M. Reptational dynamics in dissipative particle dynamics simulations of polymer melts. Phys. Rev. E 2007, 75, 0367131-0367137.
247. Karatrantos, A.; Clarke, N.; Composto, R.J.; Winey, K.I. Topological entanglement length in polymer melts and nanocomposites by a DPD polymer model. Soft Matter 2013, 9, 3877-3884.
248. Karatrantos, A.; Composto, R.J.; Winey, K.I; Kröger, M.; Clarke, N. Entanglements and dynamics of polymer melts near a SWCNT. Macromolecules 2012, 45, 7274-7281.
249. Goujon, F.; Malfreyt, P.; Tildesley, D.J. Mesoscopic simulation of entanglements using dissipative particle dynamics Application to polymer brushes. J. Chem. Phys. 2008, 129, 034902.
250. Kumar, S.; Larson, R.G. Brownian dynamics simulations of flexible polymers with spring-spring repulsions. J. Chem. Phys. 2001, 114, 6937-6941.
251. Pearson, D.S.; Ver Strate, G.; von Meerwall, E.; Schilling, F.C. Viscosity and self-diffusion coefficient of linear polyethylene. Macromolecules 1987, 20, 1133-1141.
252. Paul, W.; Smith, G.D.; Yoon, D.Y. Static and dynamic properties of an-C100H202 melt from molecular dynamics simulations. Macromolecules 1997, 30, 7772-7780.
253. D'Adamo, G.; Pelissetto, A.; Pierleoni, C. Coarse-graining strategies in polymer solutions. Soft Matter 2012, 8, 5151-5167.
254. D'Adamo, G.; Pelissetto, A.; Pierleoni, C. Polymers as compressible soft spheres. J. Chem. Phys. 2012, 136, 2249051-2249059.
255. Vettorel, T.; Besold, G.; Kremer, K. Fluctuating soft-sphere approach to coarse-graining of polymer models. Soft Matter 2010, 6, 2282-2292.
256. Zhang, G.; Daoulas, K.C.; Kremer, K. A new coarse grained particle-to-mesh scheme for modeling soft matter. Macromol. Chem. Phys. 2013, 214, 214-224.
257. Briels, W.J. Theory of Polymer Dynamics In Lecture Notes; Uppsala University Uppsala, Sweden, 1994.
258. Zhu, Y.L.; Liu, H.; Lu, Z.Y. A highly coarse-grained model to simulate entangled polymer melts. J. Chem. Phys. 2012, 136, 1449031-1449037.
259. Briels, W.J. Transient forces in flowing soft matter. Soft Matter 2009, 5, 4401-4411.
260. Kröger,M.; Ramirez, R.; Öttinger, H.C. Projection from an atomistic chain contour to its primitive path. Polymer 2002, 43, 477-487.
261. Sprakel, J.; Padding, J.T.; Briels, W.J. Transient forces and non-equilibrium states in sheared polymer networks. EPL (Europhys. Lett.) 2011, 93, 580031-580036.
262. Savin, T.; Briels, W.J.; Öttinger, H.C. Thermodynamic formulation of flowing soft matter with transient forces. Rheol. Acta 2013, 52, 23-32.
263. Sprakel, J.; Spruijt, E.; van der Gucht, J.; Padding, J.T.; Briels, W.J. Failure-mode transition in transient polymer networks with particle-based simulations. Soft Matter 2009, 5, 4748-4756.
264. Padding, J.T.; van Ruymbeke, E.; Vlassopoulos, D.; Briels, W.J. Computer simulation of the rheology of concentrated star polymer suspensions. Rheol. Acta 2010, 49, 473-484.
265. Padding, J.T.; Mohite, L.V.; Auhl, D.; Briels, W.J.; Bailly, C. Mesoscale modeling of the rheology of pressure sensitive adhesives through inclusion of transient forces. Soft Matter 2011, 7, 5036-5046.
266. Padding, J.T.; Mohite, L.V.; Auhl, D.; Schweizer, T.; Briels, W.J.; Bailly, C. Quantitative mesoscale modeling of the oscillatory and transient shear rheology and the extensional rheology of pressure sensitive adhesives. Soft Matter 2012, 8, 7967-7981.
267. Savin, T.; Briels, W.J.; Öttinger, H.C. Thermodynamic formulation of flowing soft matter with transient forces. Rheol. Acta 2013, 52, 23-32.
268. Clark, A.J.; Guenza, M.G. Mapping of polymer melts onto liquids of soft-colloidal chains. J. Chem. Phys. 2010, 132, 0449021-04490212.
269. McCarty, J.; Guenza, M. How reliable are soft potentials? Ensuring thermodynamic consistency between hierarchical models of polymer melts. Bull. Am. Phys. Soc. 2012, 57, Abstract ID BAPS.2012.MAR.W48.2.
270. McCarty, J.; Clark, A.J.; Lyubimov, IY.; Guenza, M.G. Thermodynamic consistency between analytic integral equation theory and coarse-grained molecular dynamics simulations of homopolymer melts. Macromolecules 2012, 45, 8482-8493.
271. Clark, A.J.; McCarty, J.; Lyubimov, IY.; Guenza, M.G. Thermodynamic consistency in variable-level coarse graining of polymeric liquids. Phys. Rev. Lett. 2012, 109, 1683011-1683015.
272. Lyubimov, IY.; Guenza, M.G. Theoretical reconstruction of realistic dynamics of highly coarse-grained cis-1,4-polybutadiene melts. J. Chem. Phys 2013, 138, 12A5461-12A54613.
273. Krakoviack, V.; Hansen, J.P.; Louis, A.A. Relating monomer to centre-of-mass distribution functions in polymer solutions. EPL (Europhys. Lett.) 2007, 58, 53-59.
274. Sambriski, E.J.; Yatsenko, G.; Nemirovskaya, M.A.; Guenza, M.G. Bridging length scales in polymer melt relaxation for macromolecules with specific local structures. J. Phys. Condens. Matter 2007, 19, 2051151-20511511.
275. Kröger, M.; Ramïrez, J.; Christian Öttinger, H. Projection from an atomistic chain contour to its primitive path. Polymer 2002, 43, 477-487.
276. Zhou, Q.; Larson, R.G. Primitive path identification and statistics in molecular dynamics simulations of entangled polymer melts. Macromolecules 2005, 38, 5761-5765.
277. Foteinopoulou, K.; Karayiannis, N.C.; Mavrantzas, V.G.; Kröger, M. Primitive path identification and entanglement statistics in polymer melts Results from direct topological analysis on atomistic polyethylene models. Macromolecules 2006, 39, 4207-4216.
278. Alemán, C.; Karayiannis, N.C.; Curcó, D.; Foteinopoulou, K.; Laso, M. Computer simulations of amorphous polymers From quantum mechanical calculations to mesoscopic models. J. Mol. Struct. 2009, 898, 62-72.
279. Karayiannis, N.C.; Kröger, M. Combined molecular algorithms for the generation, equilibration and topological analysis of entangled polymers Methodology and performance Int. J. Mol. ScI 2009, 10, 5054-5089.
280. Kremer, K.; Sukumaran, S.K.; Everaers, R.; Grest, G.S. Entangled polymer systems. Comput. Phys. Commun. 2005, 169, 75-81.
281. Kröger, M. Shortest multiple disconnected path for the analysis of entanglements in two-and three-dimensional polymeric systems. Comput. Phys. Commun. 2005, 168, 209-232.
282. Tzoumanekas, C.; Theodorou, D.N. From atomistic simulations to slip-link models of entangled polymer melts Hierarchical strategies for the prediction of rheological properties. Curr. Opin. Solid State Mater. ScI 2006, 10, 61-72.
283. Tzoumanekas, C.; Theodorou, D.N. Topological analysis of linear polymer melts A statistical approach. Macromolecules 2006, 39, 4592-4604.
284. Tzoumanekas, C.; Lahmar, F.; Rousseau, B.; Theodorou, D.N. Onset of entanglements revisited. Topological analysis. Macromolecules 2009, 42, 7474-7484.
285. Anogiannakis, S.D.; Tzoumanekas, C.; Theodorou, D.N. Microscopic description of entanglements in polyethylene networks and melts Strong, weak, pairwise, and collective attributes. Macromolecules 2012, 45, 9475-9492.
286. Everaers, R. Topological versus rheological entanglement length in primitive-path analysis protocols, tube models, and slip-link models. Phys. Rev. E 2012, 86, 0228011-0228015.
287. Shanbhag, S.; Kröger, M. Primitive path networks generated by annealing and geometrical methods Insights into differences. Macromolecules 2007, 40, 2897-2903.
288. Khaliullin, R.N.; Schieber, J.D. Analytic expressions for the statistics of the primitive-path length in entangled polymers. Phys. Rev. Lett. 2008, 100, 1883021-1883024.
289. Steenbakkers, R.J.; Schieber, J.D. Derivation of free energy expressions for tube models from coarse-grained slip-link models. J. Chem. Phys. 2012, 137, 0349011-03490119.
290. Steenbakkers, R.J.; Li, Y.; Liu, W.K.; Kröger, M.; Schieber, J.D. Primitive-path statistics of entangled polymers Mapping multi-chain simulations onto single-chain mean-field models. New J. Phys. 2013, submitted for publication.
291. Baig, C.; Mavrantzas, V.G. From atomistic trajectories to primitive paths to tube models Linking atomistic simulations with the reptation theory of polymer dynamics. Soft Matter 2010, 6, 4603-4612.
292. Stephanou, P.S.; Baig, C.; Mavrantzas, V.G. Projection of atomistic simulation data for the dynamics of entangled polymers onto the tube theory Calculation of the segment survival probability function and comparison with modern tube models. Soft Matter 2011, 7, 380-395.
293. Stephanou, P.S.; Baig, C.; Mavrantzas, V.G. Toward an improved description of constraint release and contour length fluctuations in tube models for entangled polymer melts guided by atomistic simulations. Macromol. Theory Simul. 2011, 20, 752-768.
294. Lodge, T.P. Reconciliation of the molecular weight dependence of diffusion and viscosity in entangled polymers. Phys. Rev. Lett. 1999, 83, 3218-3221.
295. Viovy, J.L. Constraint release in the slip-link model and the viscoelastic properties of polymers. J. Phys. 1985, 46, 847-853.
296. Marrucci, G. Relaxation by reptation and tube enlargement A model for polydisperse polymers. J. Polym. ScI Polym. Phys. 1985, 23, 159-177.
297. Pattamaprom, C.; Larson, R.G.; Sirivat, A. Determining polymer molecular weight distributions from rheological properties using the dual-constraint model. Rheol. Acta 2008, 47, 689-700.
298. Pattamaprom, C.; Larson, R.G.; Van Dyke, T.J. Quantitative predictions of linear viscoelastic rheological properties of entangled polymers. Rheol. Acta 2000, 39, 517-531.
299. Ilg, P.; Kröger, M. Molecularly derived constitutive equation for low-molecular polymer melts from thermodynamically guided simulation. J. Rheol. 2010, 55, 69-93.
300. Ilg, P.; Thermodynamically consistent coarse graining the non-equilibrium dynamics of unentangled polymer melts. J. Non-Newtonian Fluid Mech. 2010, 165, 973-979.
301. Ilg, P.; Mavrantzas, V.G.; Öttinger, H.C. Multiscale Modeling and Coarse Graining of Polymer Dynamics Simulations Guided by Statistical Beyond-equilibrium Thermodynamics In Modeling and Simulations in Polymers; Wiley-VCH Weinheim, Germany, 2010.
302. Jelić, A.; Ilg, P.; Öttinger, H.C. Bridging length and time scales in sheared demixing systems From the Cahn-Hilliard to the Doi-Ohta model. Phys. Rev. E 2010, 81, 0111311-01113113.
303. Ilg, P. Enhanced Landau-de Gennes potential for nematic liquid crystals from a systematic coarse-graining procedure. Phys. Rev. E 2012, 85, 0617091-0617099.
304. Ilg, P.; Hütter, M.; Kröger, M Ideal contribution to the macroscopic, quasiequilibrium entropy of anisotropic fluids. Phys. Rev. E 2011, 83, 0617131-0617137.
305. Ilg, P.; Karlin, IV.; Kröger, M.; Hess, S. Canonical distribution functions in polymer dynamics II Liquid-crystalline polymers. Physica A 2003, 319, 134-150.
306. Gupta, B.; Ilg, P. Energetic and entropic contributions to the Landau-de Gennes Potential for Gay-Berne Models of Liquid Crystals. Polymers 2013, 5, 328-343.
307. Ilg, P.; Kröger, M.; Hess, S. Magnetoviscosity of semi-dilute ferrofluids and the role of dipolar interactions Comparison of molecular simulation and dynamical mean-field theory. Phys. Rev. E 2005, 71, 0312051-03120511.
308. Kröger, M.; Ilg, P.; Hess, S. Magnetoviscous model fluids. J. Phys. Condens. Matter 2003, 15, S1403-S1423.
309. Öttinger, H.C. Beyond Equilibrium Thermodynamics; Wiley-Interscience Hoboken, NJ, USA, 2005.
310. Kröger, M.; Hütter, M. Automated symbolic calculations in nonequilibrium thermodynamics. Comput. Phys. Commun. 2010, 181, 2149-2157.
311. Larson, R.G. The structure and Rheology of Complex Fluids; Oxford University Press New York, NY, USA, 1999.
312. Öttinger, H.C. General projection operator formalism for the dynamics and thermodynamics of complex fluids. Phys. Rev. E 1998, 57, 1416-1420.
313. Ilg, P. Macroscopic thermodynamics of flowing polymers derived from systematic coarse-graining procedure. Physica A 2008, 387, 6484-6496.
314. Hu, Y.; Wang, S.Q.; Jamieson, A.M. Rheological and flow birefringence studies of a shear-thickening complex fluid-A surfactant model system. J. Rheol. 1993, 37, 531-546.
315. Tapadia, P.; Wang, S.Q. Yieldlike constitutive transition in shear flow of entangled polymeric fluids. Phys. Rev. Lett. 2003, 91, 1983011-1983014.
316. Larson, R.G. Constitutive Equations for Polymer Melts and Solutions; Butterworths London, UK, 1988; p. 364.
317. Bird, R.B.; Curtiss, C.F.; Armstrong, R.C.; Hassager, O. Dynamics of Polymeric Liquids. Volume 2 Kinetic Theory; Wiley-Interscience New York, NY, USA, 1987; p. 450.
318. Baig, C.; Mavrantzas, V.G. Multiscale simulation of polymer melt viscoelasticity Expanded-ensemble Monte Carlo coupled with atomistic nonequilibrium molecular dynamics. Phys. Rev. B 2009, 79, 1443021-14430217.
319. Baig, C.; Edwards, B.J. Analysis of the configurational temperature of polymeric liquids under shear and elongational flows using nonequilibrium molecular dynamics and Monte Carlo simulations. J. Chem. Phys. 2010, 132, 1849061-18490619.
320. Lees, A.W.; Edwards, S.F. The computer study of transport processes under extreme conditions. J. Phys. C 1972, 5, 1921-1929.
321. Zhou, M. A new look at the atomic level virial stress On continuum-molecular system equivalence. Proc. R. Soc. Lond. A 2003, 459, 2347-2392.
322. Chen, W.; Fish, J. A mathematical homogenization perspective of virial stress Int. J. Numer. Math. Eng. 2006, 67, 189-207.
323. Fish, J.; Chen, W.; Li, R. Generalized mathematical homogenization of atomistic media at finite temperatures in three dimensions. Comput. Meth. Appl. Mech. Eng. 2007, 196, 908-922.
324. Kröger, M.; Loose, W.; Hess, S. Rheology and structural changes of polymer melts via nonequilibrium molecular dynamics. J. Rheol. 1993, 37, 1057-1079.
325. Bergström, J.S.; Boyce, M.C. Constitutive modeling of the large strain time-dependent behavior of elastomers. J. Mech. Phys. Solids 1998, 46, 931-954.
326. Bergström, J.S.; Boyce, M.C. Large strain time-dependent behavior of filled elastomers. Mech. Mater. 2000, 32, 627-644.
327. Belytschko, T.; Liu, W.K.; Moran, B. Nonlinear Finite Elements for Continua and Structures; Wiley New York, NY, USA, 2000; Volume 26.
328. Li, Y.; Kröger, M.; Liu, W.K. Nanoparticle geometrical effect on structure, dynamics and anisotropic viscosity of polyethylene nanocomposites. Macromolecules 2012, 45, 2099-2112.
329. Li, Y.; Kröger, M.; Liu, W.K. Nanoparticle effect on the dynamics of polymer chains and their entanglement network. Phys. Rev. Lett. 2012, 109, 1180011-1180015.
330. Foteinopoulou, K.; Karayiannis, N.C.; Laso, M.; Kröger, M. Structure, dimensions, and entanglement statistics of long linear polyethylene chains. J. Phys. Chem. B 2009, 113, 442-455.
331. Milner, S.T.; McLeish, T.C.B. Reptation and contour-length fluctuations in melts of linear polymers. Phys. Rev. Lett. 1998, 81, 725-728.
332. Abdel-Goad, M.; Pyckhout-Hintzen, W.; Kahle, S.; Allgaier, J.; Richter, D.; Fetters, L.J. Rheological properties of 1, 4-polyisoprene over a large molecular weight range. Macromolecules 2004, 37, 8135-8144.
333. Lion, A.; Kardelky, C. The Payne effect in finite viscoelasticity Constitutive modelling based on fractional derivatives and intrinsic time scales Int. J. Plast. 2004, 20, 1313-1345.
334. Ramos, J.; Vega, J.F.; Theodorou, D.N.; Martinez-Salazar, J. Entanglement relaxation time in polyethylene Simulation versus experimental data. Macromolecules 2008, 41, 2959-2962.
335. Vega, J.F.; Rastogi, S.; Peters, G.W.M.; Meijer, H.E.H. Rheology and reptation of linear polymers. Ultrahigh molecular weight chain dynamics in the melt. J. Rheol. 2004, 48, 663-678.
336. Qin, J.; So, J.; Milner, S.T. Tube diameter of stretched and compressed permanently entangled polymers. Macromolecules 2012, 45, 9816-9822.
337. Wen, Q.; Basu, A.; Janmey, P.A.; Yodh, A.G. Non-affine deformations in polymer hydrogels. Soft Matter 2012, 8, 8039-8049.
338. Sommer, J.U.; Lay, S. Topological structure and nonaffine swelling of bimodal polymer networks. Macromolecules 2002, 35, 9832-9843.
339. Basu, A.; Wen, Q.; Mao, X.M.; Lubensky, T.C.; Janmey, P.A.; Yodh, A.G. Nonaffine displacements in flexible polymer networks. Macromolecules 2011, 44, 1671-1679.
340. Peter, C.; Kremer, K. Multiscale simulation of soft matter systems-from the atomistic to the coarse-grained level and back. Soft Matter 2009, 5, 4357-4366.
341. Tschöp, W.; Kremer, K.; Hahn, O.; Batoulis, J.; Bürger, T. Simulation of polymer melts II From coarse-grained models back to atomistic description. Acta Polym. 1999, 49, 75-79.
342. Santangelo, G.; Di Matteo, A.; Müller-Plathe, F.; Milano, G. From mesoscale back to atomistic models A fast reverse-mapping procedure for vinyl polymer chains. J. Phys. Chem. B 2007, 111, 2765-2773.
343. Chen, X.; Carbone, P.; Santangelo, G.; di Matteo, A.; Milano, G.; Müller-Plathe, F. Backmapping coarse-grained polymer models under sheared nonequilibrium conditions. Phys. Chem. Chem. Phys. 2009, 11, 1977-1988.
344. Wagner, G.J.; Liu, W.K. Coupling of atomistic and continuum simulations using a bridging scale decomposition. J. Comput. Phys. 2003, 190, 249-274.
345. Xiao, S.P.; Belytschko, T. A bridging domain method for coupling continua with molecular dynamics. Comput. Meth. Appl. Mech. Eng. 2004, 193, 1645-1669.
346. Liu, W.K.; Karpov, E.G.; Zhang, S.; Park, H.S. An introduction to computational nanomechanics and materials. Comput. Meth. Appl. Mech. Eng. 2004, 193, 1529-1578
347. Liu, W.K.; Karpov, E.G.; Park, H.S. Nano Mechanics and Materials Theory, Multiscale Methods and Applications; John Wiley Chichester, UK, 2006.
348. Park, H.S.; Liu, W.K. An introduction and tutorial on multiple-scale analysis in solids. Comput. Meth. Appl. Mech. Eng. 2004, 193, 1733-1772.
349. Park, H.S.; Karpov, E.G.; Liu, W.K.; Klein, P.A. The bridging scale for two-dimensional atomistic/continuum coupling. Phil. Mag. 2005, 85, 79-113.
350. Liu, W.K.; Park, H.S.; Qian, D.; Karpov, E.G.; Kadowaki, H.; Wagner, G.J. Bridging scale methods for nanomechanics and materials. Comput. Meth. Appl. Mech. Eng. 2006, 195, 1407-1421.
351. Qian, D.; Wagner, G.J.; Liu, W.K. A multiscale projection method for the analysis of carbon nanotubes. Comput. Meth. Appl. Mech. Eng. 2004, 193, 1603-1632.
352. Xu, M.; Tabarraei, A.; Paci, J.T.; Oswald, J.; Belytschko, T. A coupled quantum/continuum mechanics study of graphene fracture Int. J. Fract. 2012, 173, 1-11.
353. Moseley, P.; Oswald, J.; Belytschko, T. Adaptive atomistic-to-continuum modeling of propagating defects Int. J. Numer. Math. Eng. 2012, 92, 835-856.
354. Xu, M.; Paci, J.T.; Oswald, J.; Belytschko, T. A constitutive equation for graphene based on density functional theory Int. J. Solids Struct. 2012, 49, 2582-2589.
355. Boukany, P.E.; Wang, S.Q.; Wang, X. Step shear of entangled linear polymer melts New experimental evidence for elastic yielding. Macromolecules 2009, 42, 6261-6269.
356. Liu, G.; Sun, H.; Rangou, S.; Ntetsikas, K.; Avgeropoulos, A.; Wang, S.Q. Studying the origin of strain hardening Basic difference between extension and shear. J. Rheol. 2013, 57, 89-104.
357. Cheng, S.; Wang, S.Q. Is shear banding a metastable property of well-entangled polymer solutions? J. Rheol. 2012, 56, 1413-1428.
358. Cao, J.; Likhtman, A.E. Shear banding in molecular dynamics of polymer melts. Phys. Rev. Lett. 2012, 108, 283021-283025.
359. Baig, C.; Harmandaris, V.A. Quantitative analysis on the validity of a coarse-grained model for nonequilibrium polymeric liquids under flow. Macromolecules 2010, 43, 3156-3160.
360. Malkin, A.Y. The state of the art in the rheology of polymers Achievements and challenges. Polym. ScI A 2009, 51, 80-102.
361. Ahlrichs, P.; Everaers, R.; Dünweg, B. Screening of hydrodynamic interactions in semidilute polymer solutions A computer simulation study. Phys. Rev. E 2001, 64, 0405011-0405014.
362. Hoogerbrugge, P.J.; Koelman, J.M.V.A. Simulating microscopic hydrodynamic phenomena with dissipative particle dynamics. EPL (Europhys. Lett.) 1992, 19, 155-160.
363. Winkler, R.G.; Mussawisade, K.; Ripoll, M.; Gompper, G. Rod-like colloids and polymers in shear flow A multi-particle-collision dynamics study. J. Phys. Condens. Matter 2004, 16, S3941-S3954.
364. Gompper, G.; Ihle, T.; Kroll, D.; Winkler, R.G. Multi-particle Collision Dynamics A Particle-based Mesoscale Simulation Approach to the Hydrodynamics of Complex Fluids In Advanced Computer Simulation Approaches for Soft Matter Sciences; Springer London, UK, 2009; Volume III, pp. 1-87.
365. Succi, S. The Lattice Boltzmann Equation for Fluid Dynamics and Beyond In Numerical Mathematics and Scientific Computation; Oxford University Press New York, NY, USA, 2001.
366. Dünweg, B.; Ladd, A. Lattice Boltzmann Simulations of Soft Matter Systems In Advanced Computer Simulation Approaches for Soft Matter Sciences III; Springer London, UK, 2009; Volume 221, pp. 89-166.
367. Kopacz, A.M.; Patankar, N.A.; Liu, W.K. The immersed molecular finite element method. Comput. Meth. Appl. Mech. Eng. 2012, 233-236, 28-39.
368. Atzberger, P.J. Stochastic eulerian-lagrangian methods for fluid-structure interactions with thermal fluctuations and shear boundary conditions. J. Comput. Phys. 2011, 230, 282-2837.
369. Toth, R.; Voom, D.J.; Handgraaf, J.W.; Fraaje, J.G.E.M.; Fermeglia, M.; Pricl, S.; Posocco, P. Multiscale computer simulation studies of water-based montmorillonite/poly(ethylene oxide). Macromolecules 2009, 42, 8250-8270.
370. Montes, H.; Lequeux, F.; Berriot, J. Influence of the glass transition temperature gradient on the nonlinear viscoelastic behavior in reinforced elastomers. Macromolecules 2003, 36, 8107-8118.
371. Ellison, C.J.; Torkelson, J.M. The distribution of glass-transition temperatures in nanoscopically confined glass formers. Nat. Mater. 2003, 2, 695-700.
372. Yang, Z.; Fujii, Y.; Lee, F.K.; Lam, C.H.; Tsui, O.K.C. Glass transition dynamics and surface layer mobility in unentangled polystyrene films. Science 2010, 328, 1676-1679.
373. Martin, J.; Krutyeva, M.; Monkenbusch, M.; Arbe, A.; Allgaier, J.; Radulescu, A.; Falus, P.; Maiz, J.; Mijangos, C.; Colmenero, J.; et al. Direct observation of confined single chain dynamics by neutron scattering. Phys. Rev. Lett. 2010, 104, 1978011-1978014.
374. Nusser, K.; Schneider, G.J.; Richter, D. Microscopic origin of the terminal relaxation time in polymer nanocomposites An experimental precedent. Soft Matter 2011, 7, 7988-7991.
375. Schneider, G.J.; Nusser, K.; Willner, L.; Falus, P.; Richter, D. Dynamics of entangled chains in polymer nanocomposites. Macromolecules 2011, 44, 5857-5860.
376. Papon, A.; Saalwächter, K.; Schäler, K.; Guy, L.; Lequeux, F.; Montes, H. Low-field NMR investigations of nanocomposites Polymer dynamics and network effects. Macromolecules 2011, 44, 913-922.
377. Starr, F.W.; Schrøder, T.B.; Glotzer, S.C. Molecular dynamics simulation of a polymer melt with a nanoscopic particle. Macromolecules 2002, 35, 4481-4492.
378. Colmenero, J.; Arbe, A. Recent progress on polymer dynamics by neutron scattering From simple polymers to complex materials. J. Polym. ScI B 2013, 51, 87-113.
379. Harmandaris, V.A.; Daoulas, K.C.; Mavrantzas, V.G. Molecular dynamics simulation of a polymer melt/solid interface Local dynamics and chain mobility in a thin film of polyethylene melt adsorbed on graphite. Macromolecules 2005, 38, 5796-5809.
380. Harmandaris, V.A.; Daoulas, K.C.; Mavrantzas, V.G. Molecular dynamics simulation of a polymer melt/solid interface Local dynamics and chain mobility in a thin film of polyethylene melt adsorbed on graphite. Macromolecules 2005, 38, 5796-5809.
381. Hooper, J.B.; Schweizer, K.S. Theory of phase separation in polymer nanocomposites. Macromolecules 2006, 39, 5133-5142.
382. Cordeiro, R.M.; Zschunke, F.; Muller-Plathe, F. Mesoscale molecular dynamics simulations of the force between surfaces with grafted poly (ethylene oxide) chains derived from atomistic simulations. Macromolecules 2010, 43, 1583-1591.
383. Bogoslovov, R.B.; Roland, C.M.; Ellis, A.R.; Randall, A.M.; Robertson, C.G. Effect of silica nanoparticles on the local segmental dynamics in poly (vinyl acetate). Macromolecules 2008, 41, 1289-1296.
384. Krutyeva, M.; Wischnewski, A.; Monkenbusch, M.; Willner, L.; Maiz, J.; Mijangos, C.; Arbe, A.; Colmenero, J.; Radulescu, A.; Holderer, O.; Ohl, M.; Richter, D. Effect of nanoconfinement on polymer dynamics Surface layers and interphases. Phys. Rev. Lett. 2013, 110, 1083031-1083035.
385. Eslami, H.; Müller-Plathe, F. How thick is the interphase in an ultrathin polymer film? Coarse grained molecular dynamics simulations of polyamide-6, 6 on graphene. J. Phys. Chem. C 2013, 117, 5249-5257.
386. Hooper, J.; Schweizer, K.; Desai, T.; Koshy, R.; Keblinski, P. Structure, surface excess and effective interactions in polymer nanocomposite melts and concentrated solutions. J. Chem. Phys. 2004, 121, 6986-6997.
387. Hooper, J.B.; Schweizer, K.S. Contact aggregation, bridging, and steric stabilization in dense polymer-particle mixtures. Macromolecules 2005, 38, 8858-8869.
388. Hooper, J.B.; Schweizer, K.S. Real space structure and scattering patterns of model polymer nanocomposites. Macromolecules 2007, 40, 6998-7008.
389. Jayaraman, A.; Schweizer, K.S. Effective interactions, structure, and phase behavior of lightly tethered nanoparticles in polymer melts. Macromolecules 2008, 41, 9430-9438.
390. Jayaraman, A.; Schweizer, K.S. Effective interactions and self-assembly of hybrid polymer grafted nanoparticles in a homopolymer matrix. Macromolecules 2009, 42, 8423-8434.
391. Hall, L.M.; Jayaraman, A.; Schweizer, K.S. Molecular theories of polymer nanocomposites. Curr. Opin. Solid State Mater. ScI 2010, 14, 38-48.
392. Payne, A.R. The dynamic properties of carbon black-loaded natural rubber vulcanizates. Part I J. Appl. Polym. ScI 2003, 6, 57-63.
393. Payne, A.R. The dynamic properties of carbon black loaded natural rubber vulcanizates. Part II J. Appl. Polym. ScI 2003, 6, 368-372.
394. Lion, A.; Kardelky, C.; Haupt, P. On the frequency and amplitude dependence of the Payne effect Theory and experiments. Rubber Chem. Technol. 2003, 76, 533-547.
395. Greene, M.S. Mechanics and Physics of Solids, Uncertainy, and the Archetype-Genome Exemplar. Ph.D. thesis, Northwestern University, Evanston, IL, USA, 2012.
396. Haward, R.N.; Thackray, G.; Haward, R.N.; Thackray, G. The use of a mathematical model to describe isothermal stress-strain curves in glassy thermoplastics. Proc. R. Soc. Lond. A 1968, 302, 453-472.
397. Arruda, E.M.; Boyce, M.C. Evolution of plastic anisotropy in amorphous polymers during finite straining Int. J. Plast. 1993, 9, 697-720.
398. Akutagawa, K.; Yamaguchi, K.; Yamamoto, A.; Heguri, H.; Jinnai, H.; Shinbori, Y. Mesoscopic mechanical analysis of filled elastomer with 3D-finite element analysis and transmission electron microtomography. Rubber Chem. Technol. 2008, Si, 182-189.
399. Gonzalez, J.; Knauss, W.G. Strain inhomogeneity and discontinuous crack growth in a particulate composite. J. Mech. Phys. Solids 1998, 46, 1981-1995.
400. Simo, J.C. On a fully three-dimensional finite-strain viscoelastic damage model Formulation and computational aspects. Comput. Meth. Appl. Mech. Eng. 1987, 60, 153-173.
401. Lion, A. On the large deformation behaviour of reinforced rubber at different temperatures. J. Mech. Phys. Solids 1997, 45, 1805-1834