**Two-dimensional scattering patterns of polymers in elongated polymer
networks and composites**

K Hagita, POLYMER, 147, 247-259 (2018).

DOI: 10.1016/j.polymer.2018.06.016

The two-dimensional scattering patterns (2DSPs) of elongated polymer networks were investigated by coarse-grained molecular dynamics simulations based on the Kremer-Grest model. To specifically focus on behaviors of polymers in filler-filled polymer nanocomposites, polymer network models with a Poisson's ratio of less than 0.5 were considered. Direct correspondences between nanovoids and the flame patterns in the 2DSPs were confirmed. For a Poisson's ratio of less than 0.5, flame patterns were observed in the ultra-small-angle region of 2D small-angle and wide-angle X-ray scattering patterns. In the stretching simulations for d lambda/dr 0.02%/tau with a Poisson's ratio of 0.46, which is the value for filler-filled rubber, the elongation ratio lambda(c )at which the nanovoids could be observed was approximately 310% and 275% for the cases without and with crosslinks, respectively. These values are consistent with the experimental values for filler-filled rubber. From the stretching simulations with a Poisson's ratio of 0.4, it was confirmed that the elongation ratio lambda(c) becomes smaller as the crosslink density increases. It was also found that the fast stretching simulations with d lambda/dr 0.2%/tau appear to be sufficient for detecting the elongation ratio at which nanovoids can be observed. (C) 2018 Elsevier Ltd. All rights reserved.

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