Citation: Yao, P.; Feng, L. K.; Guo, H. X. Combined molecular dynamics simulation and rouse model analysis of static and dynamic properties of unentangled polymer melts with different chain architectures. Chinese J. Polym. Sci. 2021, 39, 512–524 doi: 10.1007/s10118-020-2489-4 shu

Combined Molecular Dynamics Simulation and Rouse Model Analysis of Static and Dynamic Properties of Unentangled Polymer Melts with Different Chain Architectures

  • Corresponding author: Hong-Xia Guo, E-mail: hxguo@iccas.ac.cn
  • Received Date: 2020-07-18
    Available Online: 2020-09-29

Figures(6) / Tables(1)

  • Chain architecture effect on static and dynamic properties of unentangled polymers is explored by molecular dynamics simulation and Rouse mode analysis based on graph theory. For open chains, although they generally obey ideal scaling in chain dimensions, local structure exhibits nonideal behavior due to the incomplete excluded volume (EV) screening, the reduced mean square internal distance (MSID) can be well described by Wittmer’ theory for linear chains and the resulting chain swelling is architecture dependent, i.e., the more branches a bit stronger swelling. For rings, unlike open chains they are compact in term of global sizes. Due to EV effect and nonconcatenated constraints their local structure exhibits a quite different non-Gaussian behavior from open chains, i.e., reduced MSID curves do not collapse to a single master curve and fail to converge to a chain-length-independent constant, which makes the direct application of Wittmer’s theory to rings quite questionable. Deviation from ideality is further evidenced by limited applicability of Rouse prediction to mode amplitude and relaxation time at high modes as well as the non-constant and mode-dependent scaled Rouse mode amplitudes, while the latter is architecture-dependent and even molecular weight dependent for rings. The chain relaxation time is architecture-dependent, but the same scaling dependence on chain dimensions does hold for all studied architectures. Despite mode orthogonality at static state, the role of cross-correlation in orientation relaxation increases with time and the time-dependent coupling parameter rises faster for rings than open chains even at short time scales it is lower for rings.
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    1. [1]

      Hadjichristidis, N.; Pitsikalis, M.; Pispas, S.; Iatrou, H. Polymers with complex architecture by living anionic polymerization. Chem. Rev. 2001, 101, 3747−92. doi: 10.1021/cr9901337

    2. [2]

      Hadjichristidis, N.; Iatrou, H.; Pitsikalis, M.; Mays, J. Macromolecular architectures by living and ontrolled/living polymerizations. Prog. Polym. Sci. 2006, 31, 1068−1132. doi: 10.1016/j.progpolymsci.2006.07.002

    3. [3]

      Grubbs, R. B.; Grubbs, R. H. 50th Anniversary perspective: living polymerization—emphasizing the molecule in macromolecules. Macromolecules 2017, 50, 6979−6997. doi: 10.1021/acs.macromol.7b01440

    4. [4]

      Paul, W.; Smith, G. D.; Yoon, D. Y. Static and dynamic properties of a n-C100H202 melt from molecular dynamics simulations. Macromolecules 1997, 30, 7772−7780. doi: 10.1021/ma971184d

    5. [5]

      Masubuchi, Y.; Takata, H.; Amamoto, Y.; Yamamoto, T. Relaxation of rouse modes for unentangled polymers obtained by molecular simulations. Nihon Reoroji Gakk 2018, 46, 171−178. doi: 10.1678/rheology.46.171

    6. [6]

      Fatkullin, N. F.; Shakirov, T. M.; Balakirev, N. A. Why does the rouse model fairly describe the dynamic characteristics of polymer melts at molecular masses below critical mass? Polym. Sci., Ser. A 2010, 52, 72−81. doi: 10.1134/S0965545X10010104

    7. [7]

      Vasile, C.; Pascu, M. Practical guide to polyethylene. Rapra Technology Limited, 2005.

    8. [8]

      Flory, P. J. Statistical mechanics of chain molecules. Interscience: New York, 1969.

    9. [9]

      Auhl, R.; Everaers, R.; Grest, G. S.; Kremer, K.; Plimpton, S. J. Equilibration of long chain polymer melts in computer simulations. J. Chem. Phys. 2003, 119, 12718−12728. doi: 10.1063/1.1628670

    10. [10]

      Zhang, G. J.; Moreira, L. A.; Stuehn, T.; Daoulas, K. C.; Kremer, K. Equilibration of high molecular weight polymer melts: a hierarchical strategy. ACS Macro Lett. 2014, 3, 198−203. doi: 10.1021/mz5000015

    11. [11]

      Moreira, L. A.; Zhang, G. J.; Muller, F.; Stuehn, T.; Kremer, K. Direct equilibration and characterization of polymer melts for computer simulations. Macromol. Theory Simul. 2015, 24, 419−431. doi: 10.1002/mats.201500013

    12. [12]

      Svaneborg, C.; Karimi-Varzaneh, H. A.; Hojdis, N.; Fleck, F.; Everaers, R. Multiscale approach to equilibrating model polymer melts. Phys. Rev. E 2016, 94, 032502. doi: 10.1103/PhysRevE.94.032502

    13. [13]

      Sliozberg, Y. R.; Kroger, M.; Chantawansri, T. L. Fast equilibration protocol for million atom systems of highly entangled linear polyethylene chains. J. Chem. Phys. 2016, 144, 154901. doi: 10.1063/1.4946802

    14. [14]

      Kreer, T.; Baschnagel, J.; Müller, M.; Binder, K. Monte Carlo simulation of long chain polymer melts: crossover from Rouse to reptation dynamics. Macromolecules 2001, 34, 1105−1117. doi: 10.1021/ma001500f

    15. [15]

      Hsu, H. P. Lattice Monte Carlo simulations of polymer melts. J. Chem. Phys. 2014, 141, 234901. doi: 10.1063/1.4903506

    16. [16]

      Wittmer, J. P.; Beckrich, P.; Johner, A.; Semenov, A. N.; Obukhov, S. P.; Meyer, H.; Baschnagel, J. Why polymer chains in a melt are not random walks. Europhys. Lett. 2007, 77, 56003. doi: 10.1209/0295-5075/77/56003

    17. [17]

      Wittmer, J. P.; Beckrich, P.; Meyer, H.; Cavallo, A.; Johner, A.; Baschnagel, J. Intramolecular long-range correlations in polymer melts: the segmental size distribution and its moments. Phys. Rev. E 2007, 76, 011803.

    18. [18]

      Wittmer, J. P.; Meyer, H.; Baschnagel, J.; Johner, A.; Obukhov, S.; Mattioni, L.; Muller, M.; Semenov, A. N. Long range bond-bond correlations in dense polymer solutions. Phys. Rev. Lett. 2004, 93, 147801. doi: 10.1103/PhysRevLett.93.147801

    19. [19]

      Tsolou, G.; Stratikis, N.; Baig, C.; Stephanou, P. S.; Mavrantzas, V. G. Melt structure and dynamics of unentangled polyethylene rings rouse theory, atomistic molecular dynamics simulation, and comparison with the linear analogues. Macromolecules 2010, 43, 0692−10713.

    20. [20]

      Doi, M., Edwards, S. F. The theory of polymer dynamics. Oxford University Press, 1988.

    21. [21]

      Gurtovenko, A. A.; Blumen, A. Generalized gaussian structures: models for polymer systems with complex topologies. Adv. Polym. Sci. 2005, 182, 171−282.

    22. [22]

      Dolgushev, M.; Blumen, A. Dynamics of semiflexible treelike polymeric networks. J. Chem. Phys. 2009, 131, 044905. doi: 10.1063/1.3184797

    23. [23]

      Dolgushev, M.; Berezovska, G.; Blumen, A. Cospectral polymers: differentiation via semiflexibility. J. Chem. Phys. 2010, 133, 154905. doi: 10.1063/1.3505147

    24. [24]

      Dolgushev, M.; Berezovska, G.; Blumen, A. Branched semiflexible polymers: theoretical and simulation aspects. Macromol. Theory Simul. 2011, 20, 621−644. doi: 10.1002/mats.201100049

    25. [25]

      Paul, W.; Smith, G. D.; Yoon, D. Y.; Farago, B.; Rathgeber, S.; Zirkel, A.; Willner, L.; Richter, D. Chain motion in an unentangled polyethylene melt: a critical test of the rouse model by molecular dynamics simulations and neutron spin echo spectroscopy. Phys. Rev. Lett. 1998, 80, 2346−2349. doi: 10.1103/PhysRevLett.80.2346

    26. [26]

      Kalathi, J. T.; Kumar, S. K.; Rubinstein, M.; Grest, G. S. Rouse mode analysis of chain relaxation in homopolymer melts. Macromolecules 2014, 47, 6925−6931. doi: 10.1021/ma500900b

    27. [27]

      Colmenero, J. A generalized rouse incoherent scattering function for chain dynamics of unentangled polymers in dynamically asymmetric blends. Macromolecules 2013, 46, 5363−5370. doi: 10.1021/ma400309c

    28. [28]

      Smith, G. D.; Paul, W.; Monkenbusch, M.; Richter, D. On the non-gaussianity of chain motion in unentangled polymer melts. J. Chem. Phys. 2001, 114, 4285−4288. doi: 10.1063/1.1348032

    29. [29]

      Graf, R.; Heuer, A.; Spiess, H. W. Chain-order effects in polymer melts probed by 1H double-quantum NMR spectroscopy. Phys. Rev. Lett. 1998, 80, 5738−5741. doi: 10.1103/PhysRevLett.80.5738

    30. [30]

      Ylitalo, C. M.; Kornfield, J. A.; Fuller, G. G.; Pearson, D. S. Molecular-weight dependence of component dynamics in bidisperse melt rheology. Macromolecules 1991, 24, 749−758. doi: 10.1021/ma00003a019

    31. [31]

      Likhtman, A. E.; Sukumaran, S. K.; Ramirez, J. Linear viscoelasticity from molecular dynamics simulation of entangled polymers. Macromolecules 2007, 40, 6748−6757. doi: 10.1021/ma070843b

    32. [32]

      Cao, J.; Likhtman, A. E. Time-dependent orientation coupling in equilibrium polymer melts. Phys. Rev. Lett. 2010, 104, 207801. doi: 10.1103/PhysRevLett.104.207801

    33. [33]

      Masubuchi, Y.; Pandey, A.; Amamoto, Y.; Uneyama, T. Orientational cross correlations between entangled branch polymers in primitive chain network simulations. J. Chem. Phys. 2017, 147, 184903. doi: 10.1063/1.5001960

    34. [34]

      Qi, Y.; Dolgushev, M.; Zhang, Z. Dynamics of semiflexible recursive small-world polymer networks. Sci. Rep. 2014, 4, 7576.

    35. [35]

      Yang, Y. Z.; Qiu, F.; Zhang, H. D.; Yang, Y. L. The rouse dynamic properties of dendritic chains: a graph theoretical method. Macromolecules 2017, 50, 4008−4022.

    36. [36]

      Hsu, H. P.; Kremer, K. Detailed analysis of rouse mode and dynamic scattering function of highly entangled polymer melts in equilibrium. Eur. Phys. J. Spec. Top. 2017, 226, 693−703. doi: 10.1140/epjst/e2016-60322-5

    37. [37]

      Likhtman, A. E.; Ponmurugan, M. Microscopic definition of polymer entanglements. Macromolecules 2014, 47, 1470−1481. doi: 10.1021/ma4022532

    38. [38]

      Downey, J. P. Static and dynamic scaling properties of single, self-avoiding polymer chains in two dimensions via the bond fluctuation method of Monte Carlo simulation. Macromolecules 1994, 27, 2929−2932. doi: 10.1021/ma00089a006

    39. [39]

      Panja, D.; Barkema, G. T. Rouse modes of self-avoiding flexible polymers. J. Chem. Phys. 2009, 131, 154903. doi: 10.1063/1.3244678

    40. [40]

      Rauscher, P. M.; Rowan, S. J.; de Pablo, J. J. Topological effects in isolated poly[n]catenanes: molecular dynamics simulations and rouse mode analysis. ACS Macro Lett. 2018, 7, 938−943. doi: 10.1021/acsmacrolett.8b00393

    41. [41]

      Kremer, K.; Grest, G. S. Dynamics of entangled linear polymer melts:  a molecular-dynamics simulation. J. Chem. Phys. 1990, 92, 5057−5086. doi: 10.1063/1.458541

    42. [42]

      Kopf, A.; Dünweg, B.; Paul, W. Dynamics of polymer “isotope” mixtures: molecular dynamics simulation and rouse model analysis. J. Chem. Phys. 1997, 107, 6945−6955. doi: 10.1063/1.474934

    43. [43]

      Khabaz, F.; Khare, R. Effect of chain architecture on the size, shape, and intrinsic viscosity of chains in polymer solutions: a molecular simulation study. J. Chem. Phys. 2014, 141, 214904. doi: 10.1063/1.4902052

    44. [44]

      Plimpton, S. Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys. 1995, 117, 1. doi: 10.1006/jcph.1995.1039

    45. [45]

      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. doi: 10.1126/science.1091215

    46. [46]

      Hou, J. X.; Svaneborg, C.; Everaers, R.; Grest, G. S. Stress relaxation in entangled polymer melts. Phys. Rev. Lett. 2010, 105, 068301. doi: 10.1103/PhysRevLett.105.068301

    47. [47]

      Xu, X.; Chen, J.; An, L. Simulation studies on architecture dependence of unentangled polymer melts. J. Chem. Phys. 2015, 142, 074903. doi: 10.1063/1.4908262

    48. [48]

      West, D. B. Introduction to graph theory. Prentice hall Upper Saddle River, 2001.

    49. [49]

      Lang, M. Ring conformations in bidisperse blends of ring polymers. Macromolecules 2013, 46, 1158−1166. doi: 10.1021/ma301359b

    50. [50]

      Ramirez, J.; Sukumaran, S. K.; Vorselaars, B.; Likhtman, A. E. Efficient on the fly calculation of time correlation functions in computer simulations. J. Chem. Phys. 2010, 133, 154103. doi: 10.1063/1.3491098

    51. [51]

      Arkin, H.; Janke, W. Gyration tensor based analysis of the shapes of polymer chains in an attractive spherical cage. J. Chem. Phys. 2013, 138, 054904. doi: 10.1063/1.4788616

    52. [52]

      Blavatska, V.; Janke, W. Shape anisotropy of polymers in disordered environment. J. Chem. Phys. 2010, 133, 184903. doi: 10.1063/1.3501368

    53. [53]

      Brereton, M. G.; Vilgis, T. A. The statistical mechanics of a melt of polymer rings. J. Phys. A: Math. Gen. 1995, 28, 1149−1167. doi: 10.1088/0305-4470/28/5/007

    54. [54]

      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, 204904. doi: 10.1063/1.3587137

    55. [55]

      Brown, S.; Szamel, G. Computer simulation study of the structure and dynamics of ring polymers. J. Chem. Phys. 1998, 109, 6184−6192. doi: 10.1063/1.477247

    56. [56]

      Obukhov, S.; Johner, A.; Baschnagel, J.; Meyer, H.; Wittmer, J. P. Melt of polymer rings: the decorated loop model. Europhys. Lett. 2014, 105, 48005. doi: 10.1209/0295-5075/105/48005

    57. [57]

      Hsu, H. P.; Kremer, K. Static and dynamic properties of large polymer melts in equilibrium. J. Chem. Phys. 2016, 144, 154907. doi: 10.1063/1.4946033

    58. [58]

      Brodeck, M.; Alvarez, F.; Arbe, A.; Juranyi, F.; Unruh, T.; Holderer, O.; Colmenero, J.; Richter, D. Study of the dynamics of poly(ethylene oxide) by combining molecular dynamic simulations and neutron scattering experiments. J. Chem. Phys. 2009, 130, 094908. doi: 10.1063/1.3077858

    59. [59]

      Hu, Y. F.; Xue, K. L.; Yu, X. C.; Hou, J. X. The relaxation times of unentangled polymer melts with different molecular architectures. J. Polym. Res. 2019, 26, 192. doi: 10.1007/s10965-019-1861-y

    60. [60]

      Takahashi, K. Z.; Yamato, N.; Yasuoka, K.; Masubuchi, Y. Critical test of bead-spring model to resolve the scaling laws of polymer melts: a molecular dynamics study. Mol. Simul. 2017, 43, 1196−1201. doi: 10.1080/08927022.2017.1334883

    61. [61]

      Takahashi, K. Z.; Nishimura, R.; Yasuoka, K.; Masubuchi, Y. Molecular dynamics simulations for resolving scaling laws of polyethylene melts. Polymers 2017, 9, 24. doi: 10.3390/polym9010024

    62. [62]

      Tsalikis, D. G.; Alatas, P. V.; Peristeras, L. D.; Mavrantzas, V. G. Scaling laws for the conformation and viscosity of ring polymers in the crossover region around Me from detailed molecular dynamics simulations. ACS Macro Lett. 2018, 7, 916−920. doi: 10.1021/acsmacrolett.8b00437

    63. [63]

      Kolinski, A.; Skolnick, J.; Yaris, R. Does reptation describe the dynamics of entangled, finite length polymer systems? A model simulation. J. Chem. Phys. 1987, 86, 1567−1585. doi: 10.1063/1.452196

    64. [64]

      Svaneborg, C.; Everaers, R. Characteristic time and length scales in melts of kremer-grest bead-spring polymers with wormlike bending stiffness. Macromolecules 2020, 53, 1917−1941. doi: 10.1021/acs.macromol.9b02437

    65. [65]

      Doxastakis, M.; Theodorou, D. N.; Fytas, G.; Kremer, F.; Faller, R.; Muller-Plathe, F.; Hadjichristidis, N. Chain and local dynamics of polyisoprene as probed by experiments and computer simulations. J. Chem. Phys. 2003, 119, 6883−6894. doi: 10.1063/1.1603720

    66. [66]

      Farago, J.; Semenov, A. N.; Meyer, H.; Wittmer, J. P.; Johner, A.; Baschnagel, J. Mode-coupling approach to polymer diffusion in an unentangled melt. I. The effect of density fluctuations. Phys. Rev. E 2012, 85, 051806. doi: 10.1103/PhysRevE.85.051806

    67. [67]

      Farago, J.; Meyer, H.; Baschnagel, J.; Semenov, A. N. Mode-coupling approach to polymer diffusion in an unentangled melt. II. The effect of viscoelastic hydrodynamic interactions. Phys. Rev. E 2012, 85, 051807. doi: 10.1103/PhysRevE.85.051807

    68. [68]

      Farago, J.; Meyer, H.; Semenov, A. N. Anomalous diffusion of a polymer chain in an unentangled melt. Phys. Rev. Lett. 2011, 107, 178301. doi: 10.1103/PhysRevLett.107.178301

    69. [69]

      Ramirez, J.; Sukumaran, S. K.; Likhtman, A. E. Significance of cross correlations in the stress relaxation of polymer melts. J. Chem. Phys. 2007, 126, 244904. doi: 10.1063/1.2746867

    70. [70]

      Masubuchi, Y.; Sukumaran, S. K. Cross-correlation contributions to orientational relaxations in primitive chain network simulations. Nihon Reoroji Gakkaishi 2013, 41, 1−6. doi: 10.1678/rheology.41.1

    71. [71]

      Masubuchi, Y.; Pandey, A.; Amamoto, Y. Inter-chain cross-correlation in multi-chain slip-link simulations without force balance at entanglements. Nihon Reoroji Gakk 2017, 45, 175−180. doi: 10.1678/rheology.45.175

    72. [72]

      Masubuchi, Y.; Amamoto, Y. Effect of osmotic force on orientational cross-correlation in primitive chain network simulation. Nihon Reoroji Gakk 2016, 44, 219−222. doi: 10.1678/rheology.44.219

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    1. [1]

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      Gustavo A. Carri . A Modern Approach to the Solution and Analysis of the Simha-Somcynsky Model for the Description of Pressure-Volume-Temperature Properties of Polymer Fluids. Chinese J. Polym. Sci, 2015, 33(4): 523-539. doi: 10.1007/s10118-015-1601-7

    3. [3]

      . ARCHITECTURE OF LADDER,TUBULAR AND SIEVE-PLATE POLYMERS PREPARED BY STEPWISE COUPLING POLYMERIZATION. Chinese J. Polym. Sci, 2000, 18(3): 195-206.

    4. [4]

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      Hao TangJin TangYi ShenWen-Xuan GuoMin ZhouRui-Hua WangNi JiangZhi-Hua GanQing-Song Yu . Comb-like Poly(N-(2-hydroxypropyl) methacrylamide) Doxorubicin Conjugates: The Influence of Polymer Architecture and Composition on the Biological Properties. Chinese J. Polym. Sci, 2018, 36(11): 1225-1238. doi: 10.1007/s10118-018-2159-y

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      Jian-Hua ChenLi-Qun LuHong-Xia ZhaoYong YangXin ShuQian-Ping Ran . Conformational Properties of Comb-shaped Polyelectrolytes with Negatively Charged Backbone and Neutral Side Chains Studied by a Generic Coarse-grained Bead-and-Spring Model. Chinese J. Polym. Sci, 2020, 38(4): 371-381. doi: 10.1007/s10118-020-2350-9

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      Jia-hao XiaYing JiangShi-ming GongZhen SunYing-han Wang . Effects of Side Chains with Similar Lengths and Different Structures of Polyimides on Liquid Crystal Alignment Behavior. Chinese J. Polym. Sci, 2014, 32(12): 1610-1619. doi: 10.1007/s10118-014-1550-6

    10. [10]

      O. RafilM. TamineB. BourahlaR. TigrineS. AmoudacheA. Khater . PHONONS IN POLYACENIC CHAINS. Chinese J. Polym. Sci, 2006, 24(3): 229-236.

    11. [11]

      . SHAPE OF POLYMER CHAINS ON A TETRAHEDRAL LATTICE*. Chinese J. Polym. Sci, 2000, 18(5): 419-422.

    12. [12]

      ZHANG XinshengCHEN SumingSHI Lianghe . STUDIES ON REGULARITY OF POLY PHENYLSILSESQUIOXANE CHAINS. Chinese J. Polym. Sci, 1987, 5(2): 162-168.

    13. [13]

      WAN Meixiang . MEASUREMENT METHOD AND PHYSICAL MODEL OF VSC CONDUCTIVITY AND ITS APPLICATIONS IN CONDUCTING POLYMERS. Chinese J. Polym. Sci, 1989, 7(4): 330-339.

    14. [14]

      ZHOU ZhipingYAN Deyue . AN INVESTIGATION ON FOLD STRUCTURE IN POLYETHYLENE LAMELLA WITH DIAMOND LATTICE MODEL*. Chinese J. Polym. Sci, 1998, 16(2): 133-141.

    15. [15]

      . BRITTLE-DUCTILE TRANSITION OF POLYMERS AND ITS PERCOLATION MODEL*. Chinese J. Polym. Sci, 2003, 21(2): 129-133.

    16. [16]

      . A RHEOLOGICAL MODEL FOR POLYMER MELTS WITH INTERNAL STRUCTURE IN FLOW FIELDS*. Chinese J. Polym. Sci, 1999, 17(2): 151-158.

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