Linear Viscoelasticity of Polymers and Polymer Nanocomposites: Molecular-Dynamics Large Amplitude Oscillatory Shear and Probe Rheology Simulations

  • Theodoros Davris
  • Alexey V. Lyulin
  • Arlette R. C. Baljon
  • Victor M. Nazarychev
  • Igor V. Volgin
  • Sergey V. Larin
  • Sergey V. Lyulin
Part of the Advances in Dielectrics book series (ADVDIELECT)


In this chapter, we discuss coarse-grained and atomistic molecular-dynamics simulation studies of the rheological properties of bulk polymer systems and polymer nanocomposites. Both systems contain monodispersed and non-crosslinked chain molecules. A multiscale strategy is applied to characterize the rheological behavior on different length scales of the systems structural organization. Fully atomistic simulations provide insights in rheological properties on smaller length scales than those accessible through coarse-grained simulations. Different approaches are utilized to obtain rheological moduli at these different length scales. At both levels of description, cyclic shear deformation is performed to characterize macroscopic properties of the systems before and after filler insertion. In the fully atomistic simulations of polyimide R-BAPB, passive microrheology approach is employed in addition to active rheology. To this end, a probe particle is immersed into the atomistic polymer matrix. Then, local rheological properties on the length scales at and beyond the Kuhn length are estimated. Results are compared with macroscopic rheological properties obtained by shear deformation. Additionally, the influence of the strain amplitude on the resulting rheological properties is examined. The reported coarse-grained simulations show a strong decrease of the nanocomposites storage modulus with increasing strain amplitude, which is accompanied by a maximum in the loss modulus (the so-called Payne effect); the onset of the softening is observed in the linear regime of deformation at strain amplitude of about 0.01. Moreover, the dependence of the storage modulus on the instantaneous strain exhibits both softening and hardening regimes, in agreement with recently reported [22] Large Amplitude Oscillatory Shear (LAOS) experiments. The simulations suggest that the observed hardening is caused by the shear-induced decrease of the non-affine diffusion of the polymer segments due to filler particles acting as effective crosslinks between polymeric chains and, hence, hindering diffusion. Moreover, the formation of “glassy” immobile layers at the nanoparticle interface strongly increases the storage modulus at low strain amplitudes. The strain softening with increasing strain amplitude is connected to the mobilization of these glassy layers and an increase in the dynamic heterogeneity of the polymer matrix. A breakup of the network structure plays a role as well.



T. Davris and A. Lyulin acknowledge the FOM Foundation for the support of the presented research. It was also sponsored by the Stichting Nationale Computerfaciliteiten (National Computer Facilities Foundation, NCF) through the usage of its supercomputer facilities, with financial support from the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (Netherlands Organization from Scientific Research, NWO). V. M. Nazarychev, I. V. Volgin, S. V. Larin, and S. V. Lyulin acknowledge the financial support from the Ministry of Education and Science of the Russian Federation under the Contract no. 14.Z50.31.0002 (megagrant of the Government of the Russian Federation according to the Resolution no. 220 of April 9, 2010). The atomistic simulations have been performed using the computational resources of the Institute of Macromolecular Compounds, Russian Academy of Sciences, the equipment of the shared research facilities of HPC computing resources at Lomonosov Moscow State University, and resources of the federal collective usage center Complex for Simulation and Data Processing for Mega-science Facilities at NRC “Kurchatov Institute.” We thank Daniel Bonn, Doros Theodorou, Thijs Michels, Rajesh Khare, as well as the industrial partners at SKF and Michelin for very fruitful discussions.


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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Theodoros Davris
    • 1
  • Alexey V. Lyulin
    • 1
  • Arlette R. C. Baljon
    • 2
  • Victor M. Nazarychev
    • 3
  • Igor V. Volgin
    • 3
  • Sergey V. Larin
    • 3
  • Sergey V. Lyulin
    • 3
  1. 1.Theory of Polymers and Soft Matter, Department of Applied PhysicsTechnische Universiteit EindhovenEindhovenThe Netherlands
  2. 2.Department of PhysicsSan Diego State UniversitySan DiegoUSA
  3. 3.Institute of Macromolecular CompoundsRussian Academy of SciencesSt. PetersburgRussia

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