Nanoparticle Motion in Entangled Melts of Linear and Nonconcatenated Ring Polymers

Significance Statement

Research on polymer nanocomposites has been at the frontier of polymer science and engineering in the past few decades.  Polymer nanocomposites integrate nanoparticles into a polymer matrix, and often exhibit excellent thermal, mechanical, electrical and optical features when compared with pure polymeric materials. The fabrication of polymer nanocomposites as well as their processing calls for an in-depth understanding of their viscoelastic properties. At the heart of the viscoelasticity of polymer nanocomposites is the coupling between the motion of nanoparticles and the relaxation dynamics of polymer matrix chains.

Experiments, computer simulations, and theoretical studies have demonstrated that the dynamical coupling between nanoparticles and linear polymers depends on the diameter of the particles with respect to the entanglement mesh size of the polymer.  If the diameter is smaller than the mesh size, the nanoparticle motion is coupled to the unentangled dynamical modes of local chain segments, resulting in subdiffusive motion before Fickian diffusion. If the diameter is larger, the particles are confined by the entanglement mesh for time scales longer than the relaxation time of entanglement strands.

One active research topic is the dynamical coupling between nanoparticles and polymers with non-linear architectures, such as star, branched, and ring polymers. Recently, Prof. Michael Rubinstein and Dr. Ting Ge at the University of North Carolina in the USA studied nanoparticle motion in nonconcatenated ring polymers. “Nonconcatenated ring polymers are of particular interest, owing to their unique topology that gives rise to distinctive conformational and dynamic properties” said Prof. Rubinstein. “Moreover, non-concatenated ring polymers are good models of biopolymers commonly found in many biological systems such as bacterial and mitochondrial genomes, as well as DNA plasmids.” Other researchers contributed to the study included Prof. Jagannathan Kalathi at Indian National Institute of Technology Karnataka in India, Dr. Jonathan Halverson at Max Planck Institute for Polymer Research in Germany, and Dr. Gary S. Grest at Sandia National Laboratories in the USA. The research work is now published in Macromolecules.

The team performed molecular dynamics simulations of nanoparticles in melts of entangled linear and entangled nonconcatenated ring polymers. They employed the bead-spring model to simulate the polymers. Neighboring beads in a polymer were connected by the finitely extensible non-linear elastic (FENE) potential. Nanoparticles were modelled as smooth spheres that interact with each other via repulsive potential. The interactions between nanoparticles and polymers were weakly attractive, so the particles were well dispersed in the polymers. “Our simulations were built on a solid foundation,” said the first author Ting Ge. “Previously, Prof. Kalathi had extensively simulated nanoparticles in linear polymer melts, while Dr. Halverson had performed systematic simulations of pure non-concatenated ring polymers. Dr. Grest, a world-renowned computational physicist, offered invaluable guidance on setting up the new simulations.”

The simulations by the authors revealed the stark contrast between nanoparticle motion in linear polymers and in non-concatenated ring polymers. Nanoparticle motion was strongly suppressed before Fickian diffusion in entangled linear polymers. The strong suppression occurred progressively as the diameter of nanoparticles exceeds the entanglement mesh size. In contrast, the motion of nanoparticles with diameters larger than the entanglement spacing in ring polymers was not as strongly suppressed as in linear polymers. The decrease in the diffusion coefficient with increasing particle diameter in ring polymers was more gradual compared to the steep drop of the coefficient in linear polymers.

The authors analyzed the nanoparticle motion in linear chains on the basis of the hopping diffusion mechanism proposed by Rubinstein’s group. For nanoparticles in rings, the authors developed a scaling theory for the coupling between the nanoparticle motion and the self-similar dynamics of entangled rings. The comparison of nanoparticle motion in linear polymers and non-concatenated ring polymers demonstrated the significance of polymer architecture in the dynamical coupling between nanoparticles and polymers in nanocomposites.

Nanoparticle Motion in Entangled Melts of Linear and Nonconcatenated Ring Polymers- Advances in Engineering

About the author

Dr. Ting Ge is currently a Postdoctoral Research Associate in the Department of Chemistry at the University of North Carolina – Chapel Hill. He performs computational and theoretical research in polymer and soft matter physics. He obtained his Ph.D. from the Department of Physics & Astronomy at Johns Hopkins University in December 2013.

About the author

Gary Grest received his Ph.D. in physics from Louisiana State University in 1974. Grest spend 17 years at Exxon Research and Engineering Company in NJ before moving to Sandia National Laboratories in NM in 1998, where he is Distinguished Member of Technical Staff at their Center for Integrated Nanotechnologies (CINT). In 2008, Grest was elected to the U.S. National Academy of Engineering.

Current research activities are focused on flow and rheology of nanoparticle assemblies, mechanical and viscoelastic properties of polymer nanocomposites, nanoparticle assembly and responsive polymer films.

About the author

Dr. Jagannathan Thimmarajampet Kalathi is an assistant professor at Department of Chemical Engineering, National Institute of Technology Karnataka, India. He earned his doctoral degree in Chemical Engineering from Indian Institute of Technology Madras in year 2011. He worked as a postdoctoral fellow in Prof. Kumar’s Group at Columbia University in the city of New York from year 2011-2013.

His current research interests focus on understanding dynamics of nanoparticles and polymer chains in polymer nanocomposites using molecular simulations, preparation of Janus nanoparticles and core-shell nanoparticles for environmental protection applications, and process intensification using ultrasound.

About the author

Michael Rubinstein received B.S. from Caltech in 1979 and Ph.D. in physics from Harvard University in 1983. After two years as a post-doc at AT&T Bell Laboratories he joined Research Laboratories of Eastman Kodak Company where he worked for 10 years. In 1995 Michael Rubinstein moved to the University of North Carolina at Chapel Hill where he is currently a John P. Barker Distinguished Professor. In 1998 he was Visiting Professor at College de France and in 2013 he was awarded Michelin Science Chair at ESPCI.  In 2003 he published a textbook “Polymer Physics” with R. H. Colby. In 2004 Michael Rubinstein was a co-chair of the Gordon Research Conference on Macromolecular, Colloidal and Polyelectrolyte Solutions. In 2008-2009 he was a Chair of the Division of Polymer Physics of the American Physical Society.

Michael Rubinstein served as Chair of the Editorial Board of Soft Matter and as Associate Editor of Macromolecules. In 2010 he received the Polymer Physics Prize of the American Physical Society. Rubinstein is currently serving as the Chair of the IUPAP Working Group on Soft Matter.


Ting Ge, Jagannathan T. Kalathi, Jonathan D. Halverson, Gary S. Grest, and Michael Rubinstein. Nanoparticle Motion in Entangled Melts of Linear and Nonconcatenated Ring Polymers. Macromolecules 2017, 50, pages 1749−1754.

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