Researchers at the Center for Nanophase Materials Sciences, a US Department of Energy (DOE) Office of Science User Facility located at DOE’s Oak Ridge National Laboratory (ORNL), used high-performance computing to verify experiments that challenge a 40-year-old theory in soft-matter physics. The findings, published in ACS Macro Letters, add to the body of evidence suggesting one of the most successful theories for describing the flow behavior of polymers needs to be revisited.
Polymers—long chains of entangled molecules that form plastic and rubber materials—are ubiquitous in consumer products, found in everything from appliances to electronics to car parts. Their versatility stems from their molecular pliancy. During processing, polymers can be stretched, pulled, and squeezed into useful shapes without breaking. Theoretical modeling of this process has enabled practical predictions for the manufacturing of plastic materials, but a complete description of polymer dynamics continues to elude scientists.
To better understand what happens to the spaghetti-like molecules during processing, a team of ORNL researchers simulated a highly entangled system of polymers undergoing stretching and watched how the molecules relaxed following the deformation. They conducted the simulation on the Titan supercomputer, the leadership-class system of the Oak Ridge Leadership Computing Facility (OLCF), another DOE Office of Science User Facility at ORNL.
The detailed simulation supplied key measurements that conflict with a popular hypothesis to explain polymer motion put forth by physicists Masao Doi and Sam Edwards in 1978. The so-called Doi-Edwards theory predicts that polymer size will decrease in all directions following deformation; however, the ORNL team found no such evidence. The findings back up the results of neutron scattering experiments the team conducted in 2017 at ORNL’s Spallation Neutron Source and the National Institute of Standards and Technology.
“With computer simulation, we can directly examine polymer structure in real space,” said ORNL researcher and team leader Yangyang Wang. “This gives us a lot of details that cannot be resolved by experiment. In this case, molecular dynamics simulations allowed us to accurately determine the size of the polymer and see how closely it aligned with theory.”
Improved understanding of polymer behavior could lead to better control of materials and aid design of materials with novel characteristics.
A molecular dynamics simulation of a well-entangled polymer melt under uniaxial extension. Simulations were performed on the OLCF’s Titan supercomputer using LAMMPS. Images for making the video were rendered on the Rhea supercomputer.
Taking on the Tube Model
In the 1970s, Nobel Prize laureate Pierre-Gilles de Gennes pioneered the tube model, a theory describing how string-like polymers respond to being deformed. The theory posited that polymer movements are generally restricted to narrow tunnels of space—“tubes”—because of entanglements with their neighbors. In short, a polymer can move more freely along the direction of its length than it can move side-to-side.
The theory proved useful when describing molecular diffusion but was insufficient to account for large deformations to polymer systems. The deficiency inspired Doi and Edwards to propose the idea of “chain retraction” to explain how the shapes of polymers change as they relax after being stressed. According to Doi and Edwards, deformation causes polymer strings to stretch—like a taut rubber band—to a degree that mirrors the greater material itself. In response, the molecules retract, or pull back, along their tube pathways until they return to a stress-free state.
Evidence of retraction should be observable by a decrease in molecular size in all directions during relaxation; however, small-angle neutron scattering experiments that Wang’s team conducted did not agree with theoretical predictions.
In neutron scattering, scientists probe materials indirectly by bombarding them with neutrons and analyzing the scattering patterns produced as a result. “It’s an indirect way of checking the structure,” Wang said. “That’s the inherent limitation of the technique.”
Molecular dynamics, a simulation method for studying physical systems, isn’t limited in this way. Trajectories of atoms and molecules can be tracked directly and precisely for as long as computing resources and practical time limits allow.
Using the Cray XK7 Titan and the molecular dynamics code LAMMPS, ORNL postdoctoral researcher Wen-Sheng Xu simulated a rectangular box containing 250 entangled polymers, with each polymer chain composed of 2,000 coarse-grained atoms. Because of the molecules’ exceptional length, the team needed to run the system for an extended amount of simulation time—1 billion time steps, the equivalent of 35 days in real time—to observe the relaxation process, Xu explained.
The aggregation was sufficient to capture long-term relaxation behavior that showed no decrease in polymer size perpendicular to stretching as predicted by Doi and Edwards. The finding suggests there is more work to do to sufficiently understand polymer motion, Wang said.
“We need modifications or maybe a new theory to explain the flow behavior of polymers,” he said.
The team is continuing studies of polymer systems with neutron scattering and has plans to run larger polymer simulations in the future. Because of the cross-disciplinary nature of the project—which brings together experts in neutron scattering, computational science, polymer chemistry, and other areas—ORNL is well positioned to lead the way, Wang said.
“We have this wonderful environment that brings scientists of different backgrounds together,” Wang said. “That’s what makes our work possible.”
Related publications: Wen-Sheng Xu, Jan-Michael Y. Carrillo, Christopher N. Lam, Bobby G. Sumpter, and Yangyang Wang, “Molecular Dynamics Investigation of the Relaxation Mechanism of Entangled Polymers after a Large Step Deformation.” ACS Macro Letters 7 (2018): 190–195.
Zhe Wang, Christopher N. Lam, Wei-Ren Chen, Weiyu Wang, Jianning Liu, Yun Liu, Lionel Porcar, et al., “Fingerprinting Molecular Relaxation in Deformed Polymers.” Physical Review X 7, no. 3 (2017): 031003.
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