Abstract
Dissipative particle dynamics (DPD) with bond uncrossability shows a great potential in studying entangled polymers, however relatively little is known of applicability range of entangled DPD model to be use as a model for ideal chains and properly describe the full dynamics of entangled melts. Therefore, we perform a comprehensive study on structure, dynamics and linear viscoelasticity of a typical DPD entangled model system, semiflexible linear polymer melt. These polymers obey Flory’s ideality hypothesis in chain dimensions, but their local structure exhibits nonideal behavior due to weak correlated hole effect. Both monomer motion and viscoelasticity relaxation reproduce the full pictures as predicted by reptation theory. The stronger chain length dependent diffusion coefficient and relaxation time as well as dynamic moduli are in close agreement with predictions of modern tube model that accounts for additional relaxation mechanisms besides chain reptation. However, an anomalous sub-diffusive center of mass motion is observed both before and after the intermediate reptation regime and the cross-correlation between chains is not negligible even these polymers obey stress-optical law, indicating limitations of the reptation theory. Hence semiflexible linear entangled DPD model can correctly describe statics and dynamics of entangled polymer melts.
Similar content being viewed by others
References
Doi, M.; Edwards, S. F., The theory of polymer dynamics. Oxford: Oxford University Press: 1986.
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.
Fritz, D.; Koschke, K.; Harmandaris, V. A.; van der Vegt, N. F. A.; Kremer, K. Multiscale modeling of soft matter: scaling of dynamics. Phys. Chem. Chem. Phys. 2011, 13, 10412–10420.
Kremer, K.; Grest, G. S. Dynamics of entangled linear polymer melts: a molecular-dynamics simulation. J. Chem. Phys. 1990, 92, 5057–5086.
Likhtman, A. E. Viscoelasticity and molecular rheology. Polym. Sci.: A Compr. Ref. Elsevier, 2012, 1, pp. 133–179.
Flory, P. J. Statistical mechanics of chain molecules. Wiley, New York, 1969.
Beckrich, P.; Johner, A.; Semenov, A. N.; Obukhov, S. P.; Benoît, H.; Wittmer, J. P. Intramolecular form factor in dense polymer systems: systematic deviations from the debye formula. Macromolecules 2007, 40, 3805–3814.
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.
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.
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.
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.
Hsu, H. P.; Kremer, K. Static and dynamic properties of large polymer melts in equilibrium. J. Chem. Phys. 2016, 144, 154907.
Jabbari-Farouji, S. Static and dynamic scaling behavior of a polymer melt model with triple-well bending potential. J. Polym. Sci.; Part B: Polym. Phys. 2018, 56, 1376–1392.
Harmandaris, V. A.; Adhikari, N. P.; Vegt, N. F. A. v. d.; Kremer, K. Hierarchical modeling of polystyrene: from atomistic to coarsegrained simulations. Macromolecules 2006, 39, 6708–6719.
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.
de Gennes, P. G. Reptation of a polymer chain in the presence of fixed obstacles. J. Chem. Phys. 1971, 55, 572–579.
Doi, M.; Edwards, S. F. Dynamics of concentrated polymer systems. Part 1.—Brownian motion in the equilibrium state. J. Chem. Soc. Faraday Trans. 2 1978, 74, 1789–1801.
Doi, M.; Edwards, S. F. Dynamics of concentrated polymer systems. Part 2.—Molecular motion under flow. J. Chem. Soc. Faraday Trans. 2 1978, 74, 1802–1817.
Doi, M.; Edwards, S. F. Dynamics of concentrated polymer systems. Part 3.—The constitutive equation. J. Chem. Soc. Faraday Trans. 2 1978, 74, 1818–1832.
Doi, M.; Edwards, S. F. Dynamics of concentrated polymer systems. Part 4.—Rheological properties. J. Chem. Soc. Faraday Trans. 2 1979, 75, 38–54.
Moreira, L. A.; Zhang, G.; Müller, F.; Stuehn, T.; Kremer, K. Direct equilibration and characterization of polymer melts for computer simulations. Macromol. Theory Simul. 2015, 44, 419–431.
Wang, Z.; Likhtman, A. E.; Larson, R. G. Segmental dynamics in entangled linear polymer melts. Macromolecules 2012, 45, 3557–3570.
Hall, K. W.; Sirk, T. W.; Klein, M. L.; Shinoda, W. A coarse-grain model for entangled polyethylene melts and polyethylene crystallization. J. Chem. Phys. 2019, 150, 244901.
Salerno, K. M.; Agrawal, A.; Perahia, D.; Grest, G. S. Resolving dynamic properties of polymers through coarse-grained computational studies. Phys. Rev. Lett. 2016, 116, 058302.
Peters, B. L.; Salerno, K. M.; Ge, T.; Perahia, D.; Grest, G. S. Viscoelastic response of dispersed entangled polymer melts. Macromolecules 2020, 53, 8400–8405.
Lodge, T. P. Reconciliation of the molecular weight dependence of diffusion and viscosity in entangled polymers. Phys. Rev. Lett. 1999, 83, 3218–3221.
Watanabe, H. Viscoelasticity and dynamics of entangled polymers. Prog. Polym. Sci. 1999, 24, 1253–1403.
McLeish, T. C. B. Tube theory of entangled polymer dynamics. Adv. Phys. 2002, 57, 1379–1527.
Feng, L.; Gao, P.; Guo, H. Retardation on blending in the entangled binary blends of linear polyethylene: a molecular dynamics simulation study. Macromolecules 2019, 52, 3404–3416.
Milner, S. T.; McLeish, T. C. B. Reptation and contour-length fluctuations in melts of linear polymers. Phys. Rev. Lett. 1998, 81, 725–728.
M. Doi, Explanation for the 3.4-power law for viscosity of polymeric liquids on the basis of the tube model. J. Polym. Sci. Part B: Polym. Phys. 1983, 21, 667–684.
Likhtman, A. E.; McLeish, T. C. B. Quantitative theory for linear dynamics of linear entangled polymers. Macromolecules 2002, 35, 6332–6343.
Rubinstein, M.; Colby, R. H. Self-consistent theory of polydisperse entangled polymers: linear viscoelasticity of binary blends. J. Chem. Phys. 1988, 89, 5291–5306.
Viovy, J. L.; Rubinstein, M.; Colby, R. H. Constraint release in polymer melts: tube reorganization versus tube dilation. Macromolecules 1991, 24, 3587–3596.
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.
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.
Cao, J.; Likhtman, A. E. Time-dependent orientation coupling in equilibrium polymer melts. Phys. Rev. Lett. 2010, 104, 207801.
Likhtman, A. E.; Sukumaran, S. K.; Ramirez, J. Linear viscoelasticity from molecular dynamics simulation of entangled polymers. Macromolecules 2007, 40, 6748–6757.
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.
Chappa, V. C.; Morse, D. C.; Zippelius, A.; Muller, M. Translationally invariant slip-spring model for entangled polymer dynamics. Phys Rev Lett 2012, 109, 148302.
Sgouros, A. P.; Megariotis, G.; Theodorou, D. N. Slip-spring model for the linear and nonlinear viscoelastic properties of molten polyethylene derived from atomistic simulations. Macromolecules 2017, 50, 4524–4541.
Masubuchi, Y.; Uneyama, T. Comparison among multi-chain models for entangled polymer dynamics. Soft Matter 2018, 14, 5986–5994.
Behbahani, A. F.; Schneider, L.; Rissanou, A.; Chazirakis, A.; Bačová, P.; Jana, P. K.; Li, W.; Doxastakis, M.; Polińska, P.; Burkhart, C.; Müller, M.; Harmandaris, V. A. Dynamics and rheology of polymer melts via hierarchical atomistic, coarsegrained, and slip-spring simulations. Macromolecules 2021, 54, 2740–2762.
Nikunen, P.; Vattulainen, I.; Karttunen, M. Reptational dynamics in dissipative particle dynamics simulations of polymer melts. Phys. Rev. E 2007, 75, 036713.
Kumar, S.; Larson, R. G. Brownian dynamics simulations of flexible polymers with spring-spring repulsions. J. Chem. Phys. 2001, 774, 6937–6941.
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.
Ouyang, Y.; Hao, L.; Ma, Y.; Guo, H. Dissipative particle dynamics thermostat: a novel thermostat for molecular dynamics simulation of liquid crystals with Gay-Berne potential. Sci. China Chem. 2014, 58, 694–707.
Ruan, Y.; Lu, Y.; An, L.; Wang, Z. G. Nonlinear rheological behaviors in polymer melts after step shear. Macromolecules 2019, 52, 4103–4110.
Ruan, Y.; Lu, Y.; An, L.; Wang, Z. G. Shear banding in entangled polymers: stress plateau, banding location, and lever rule. ACS Macro Lett. 2021, 10, 1517–1523.
Mohagheghi, M.; Khomami, B. Molecular processes leading to shear banding in well entangled polymeric melts. ACS Macro Lett. 2015, 4, 684–688.
Mohagheghi, M.; Khomami, B. Elucidating the flow-microstructure coupling in the entangled polymer melts. Part I: single chain dynamics in shear flow. J. Rheol. 2016, 60, 849–859.
Mohagheghi, M.; Khomami, B. Elucidating the flow-microstructure coupling in entangled polymer melts. Part II: molecular mechanism of shear banding. J. Rheol. 2016, 60, 861–872.
Mohagheghi, M.; Khomami, B. Molecularly based criteria for shear banding in transient flow of entangled polymeric fluids. Phys. Rev. E 2016, 93, 062606.
Hoogerbrugge, P. J.; Koelman, J. M. V. A. Simulating microscopic hydrodynamic phenomena with dissipative particle dynamics. EPL 1992, 19, 155–160.
Español, P.; Warren, P. Statistical mechanics of dissipative particle dynamics. EPL 1995, 30, 191–196.
Groot, R. D.; Madden, T. J. Dynamic simulation of diblock copolymer microphase separation. J. Chem. Phys. 1998, 108, 8713–8724.
Guskova, O. A.; Seidel, C. Mesoscopic simulations of morphological transitions of stimuli-responsive diblock copolymer brushes. Macromolecules 2011, 44, 671–682.
Xu, D.; Shi, R.; Sun, Z. Y.; Lu, Z. Y. Mechanism of periodic field driven self-assembly process. J. Chem. Phys. 2021, 154, 144904.
Guo, F.; Li, K.; Wu, J.; Wang, Y.; Zhang, L. Sliding dynamics of ring chain on a knotted polymer in rotaxane. Polymer 2021, 235, 124226.
Bai, Z.; Guo, H. Interfacial properties and phase transitions in ternary symmetric homopolymer-copolymer blends: a dissipative particle dynamics study. Polymer 2013, 54, 2146–2157.
Zhang, Z. M.; Guo, H. X. A computer simulation study of the anchoring transitions driven by rod-coil amphiphiles at aqueous-liquid crystal interfaces. Soft Matter 2012, 8, 5168–5174.
Sumer, Z.; Striolo, A. Manipulating molecular order in nematic liquid crystal capillary bridges via surfactant adsorption: guiding principles from dissipative particle dynamics simulations. Phys. Chem. Chem. Phys. 2018, 20, 30514–30524.
Liu, Y.; Widmer-Cooper, A. A dissipative particle dynamics model for studying dynamic phenomena in colloidal rod suspensions. J. Chem. Phys. 2021, 154, 104120.
Zhou, Y.; Huang, M.; Lu, T.; Guo, H. Nanorods with different surface properties in directing the compatibilization behavior and the morphological transition of immiscible polymer blends in both shear and shear-free conditions. Macromolecules 2018, 51, 3135–3148.
Huang, M.; Guo, H. The intriguing ordering and compatibilizing performance of Janus nanoparticles with various shapes and different dividing surface designs in immiscible polymer blends. Soft Matter 2011, 9, 7356–7368.
Chang, H. Y.; Lin, Y. L.; Sheng, Y. J.; Tsao, H. K. Structural characteristics and fusion pathways of onion-like multilayered polymersome formed by amphiphilic comb-like graft copolymers. Macromolecules 2013, 46, 5644–5656.
Wu, S.; Guo, H. Simulation study of protein-mediated vesicle fusion. J. Phys. Chem. 2009, 113, 589–591.
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.
Plimpton, S. Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys. 1995, 117, 1–19.
Shanbhag, S.; Kröger, M. Primitive path networks generated by annealing and geometrical methods: insights into differences. Macromolecules 2007, 40, 2897–2903.
Karayiannis, N.; Kroger, M. Combined molecular algorithms for the generation, equilibration and topological analysis of entangled polymers: methodology and performance. Int. J. Mol. Sci. 2009, 10, 5054–89.
Hoy, R. S.; Foteinopoulou, K.; Kroger, M. Topological analysis of polymeric melts: chain-length effects and fast-converging estimators for entanglement length. Phys. Rev. E 2009, 80, 031803.
Fujita, H.; Norisuye, T. Some topics concerning the radius of gyration of linear polymer molecules in solution. J. Chem. Phys. 1970, 52, 1115–1120.
Lhuillier, D. A simple model for polymeric fractals in a good solvent and an improved version of the Flory approximation. J. Phys. France 1988, 49, 705–710.
León, 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.
Semenov, A. N.; Obukhov, S. P. Fluctuation-induced long-range interactions in polymer systems. J. Phys.: Condens. Matter 2005, 17, S1747–S1775.
Obukhov, S. P.; Semenov, A. N. Long-range interactions in polymer melts: the anti-Casimir effect. Phys. Rev. Lett. 2005, 95, 038305.
Hsu, H. P. Lattice Monte Carlo simulations of polymer melts. J. Chem. Phys. 2014, 141, 234901.
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, 204905.
Smith, G. D.; Paul, W.; Monkenbusch, M.; Richter, D. A comparison of neutron scattering studies and computer simulations of polymer melts. Chem. Phys. 2000, 261, 61–74.
Paul, W.; Smith, G. D. Structure and dynamics of amorphous polymers: computer simulations compared to experiment and theory. Rep. Prog. Phys. 2004, 67, 1117–1185.
Farago, J.; Meyer, H.; Semenov, A. N. Anomalous diffusion of a polymer chain in an unentangled melt. Phys. Rev. Lett. 2011, 107, 178301.
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.
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.
Farago, J.; Meyer, H.; Baschnagel, J.; Semenov, A. N. Hydrodynamic and viscoelastic effects in polymer diffusion. J. Phys.: Cond. Matter 2012, 24, 284105.
Soddemann, T.; Dunweg, B.; Kremer, K. Dissipative particle dynamics: a useful thermostat for equilibrium and nonequilibrium molecular dynamics simulations. Phys. Rev. E 2003, 68, 046702.
Harmandaris, V. A.; Mavrantzas, V. G.; Theodorou, D. N.; Kröger, M.; Ramírez, 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.
Tsolou, G.; Mavrantzas, V. G.; Theodorou, D. N. Detailed atomistic molecular dynamics simulation of cis-1,4- poly(butadiene). Macromolecules 2005, 38, 1478–1492.
Yu, W.; Li, R.; Zhou, C. Rheology and phase separation of polymer blends with weak dynamic asymmetry. Polymer 2011, 52, 2693–2700.
Watanabe, H.; Chen, Q.; Kawasaki, Y.; Matsumiya, Y.; Inoue, T.; Urakawa, O. Entanglement dynamics in miscible polyisoprene/poly(p-tert-butylstyrene) blends. Macromolecules 2011, 44, 1570–1584.
Liu, C. Y.; Keunings, R.; Bailly, C. Do deviations from reptation scaling of entangled polymer melts result from single- or many-chain effects. Phys. Rev. Lett. 2006, 97, 246001.
Wang, S. Q. Chain dynamics in entangled polymers: diffusion versus rheology and their comparison. J. Polym. Sci., Part B: Polym. Phys. 2003, 41, 1589–1604.
Yohji K.; W. H.; Takashi U. A note for Kohlrausch-Williams-Watts relaxation function. Nihon Reoroji Gakk. 2011, 39, 127–131.
Wu, Z.; Milano, G.; Muller-Plathe, F. Combination of hybrid particle-field molecular dynamics and slip-springs for the efficient simulation of Coarse-grained polymer models: static and dynamic properties of polystyrene melts. J. Chem. Theory Comput. 2021, 77, 474–487.
Colby, R. H.; Fetters, L. J.; Graessley, W. W. Melt viscosity-molecular weight relationship for linear polymers. Macromolecules 1987, 20, 2226–2237.
Doi, M. Molecular rheology of concentrated polymer systems. I. J. Polym. Sci. Polym. Phys. Ed. 1980, 18, 1005–1020.
Maurel, G.; Schnell, B.; Goujon, F.; Couty, M.; Malfreyt, P. Multiscale modeling approach toward the prediction of viscoelastic properties of polymers. J. Chem. Theory Comput. 2012, 8, 4570–4579.
Boudara, V. A. H.; Read, D. J.; Ramírez, J. Reptate rheology software: toolkit for the analysis of theories and experiments. J. Rheol. 2020, 64, 709–722.
Li, W.; Jana, P. K.; Behbahani, A. F.; Kritikos, G.; Schneider, L.; Polińska, P.; Burkhart, C.; Harmandaris, V. A.; Müller, M.; Doxastakis, M. Dynamics of long entangled polyisoprene melts via multiscale modeling. Macromolecules 2021, 54, 8693–8713.
Schneider, J.; Fleck, F.; Karimi-Varzaneh, H. A.; Müller-Plathe, F. Simulation of elastomers by slip-spring dissipative particle dynamics. Macromolecules 2021, 54, 5155–5166.
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.
Masubuchi, Y.; Sukumaran, S. K. Cross-correlation contributions to orientational relaxations in primitive chain network simulations. Nihon Reoroji Gakk. 2013, 41, 1–6.
Masubuchi, Y.; Amamoto, Y. Effect of osmotic force on orientational cross-correlation in primitive chain network simulation. Nihon Reoroji Gakk. 2016, 44, 219–222.
Acknowledgments
This work was financially supported by the National Natural Science Foundation of China (Nos. 21790343, 21574142 and 21174154) and the National Key Research and Development Program of China (No. 2016YFB1100800).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
The authors declare no interest conflict.
Electronic Supplementary Information
10118_2023_2931_MOESM1_ESM.pdf
Statics, Dynamics and Linear Viscoelasticity from Dissipative Particle Dynamics Simulation of Entangled Linear Polymer Melts
Rights and permissions
About this article
Cite this article
Wang, F., Feng, LK., Li, YD. et al. Statics, Dynamics and Linear Viscoelasticity from Dissipative Particle Dynamics Simulation of Entangled Linear Polymer Melts. Chin J Polym Sci 41, 1392–1409 (2023). https://doi.org/10.1007/s10118-023-2931-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10118-023-2931-5