Molecular Dynamics Simulations of Fullerene Diffusion in Polymer Melts

Abstract

We employ all-atom molecular dynamics simulations up to microsecond time scales to study diffusion of fullerene nanoparticles (C60 and its derivative PCBM) in a polyimide matrix above its glass transition temperature. A detailed examination of the fullerene mobility in the embedding polymer system reveals the presence of different diffusion regimes (ballistic, subdiffusive, and normal diffusive). The microscopic origin of the observed subdiffusive regime is discussed by comparing the behavior to the one displayed by different anomalous diffusion processes, namely, continuous time random walk (CTRW), random walk on a fractal (RWF), and fractional Langevin equation (FLE). A series of statistical tests suggests that the FLE framework is the more appropriate one to describe subdiffusion of fullerenes in our system. Furthermore, a comprehensive analysis of the self-part of the van Hove function shows that the normal diffusion regime observed at long times displays a nonclassical behavior characterized by the simultaneous presence of several Gaussian peaks. We ascribe this behavior to a mechanism of diffusion by hopping. Until recently, it was commonly believed that hopping of tracer particles in polymer systems is only relevant for particle sizes that are of the order of the reptation tube diameter (d T), while smaller particles are considered to slip through the entanglement mesh. However, our results provide direct evidence for hopping as a relevant mechanism for diffusion of particles whose sizes are commensurate with the correlation length (ξ) of the polymer system. These results emphasize the importance of local interactions at the atomic level for the understanding of nanoparticle dynamics in polymer melts.

RETRACTED ARTICLE: Comparing ion transport in ionic liquids and polymerized ionic liquids

“…Such FLE processes are widely associated with modeling of stochastic transport in viscoelastic environments. FLE equations can be postulated but may also arise as an effective description of more complex multiparticle Markovian dynamics 64 . 64 , which is incurred by the coupling between the motions of fullerene molecules and the molten polymers or fullerene molecules nearby.…”

“…RWF model can describe the effect of geometric constraints arising in complex geometries, is not space-filling, and displays non-Gaussian propagators 64 . Figure 6(c) shows one example of the RWF process, where penetrants can only "walk" along certain passages.…”

Tracer Diffusion in Tightly-Meshed Homogeneous Polymer Networks: A Brownian Dynamics Simulation Study

“…Although several factors influence the dynamics of a tracer particle in polymer networks, such as interactions between a tracer particle and polymer segments [8,19,33], aggregation of polymer segments of the network [30], and network heterogeneity [19,31,32], we solely focus on the size-dependent obstructive effect of small meshes by investigating the diffusion of an inert, nonsticky tracer particle in homogeneous polymer networks. Similar with those in polymer solutions and melts [24,34,35], the dynamics of a tracer particle in polymer networks can be distinguished by the relative mesh size to that of a tracer particle, ξ/σ tr [36]. For large ξ/σ tr , the network confinement has a negligible influence on tracer diffusion with the mean-square displacement (MSD) proportional to time (MSD∼t 1 ).…”

Процессы Агрегации Фуллерена С-=sub=-60-=/Sub=- В Композитах Полимер--Фуллерен

“…B работе [12] с помощью компьютерного моделирования с использованием атомистических моделей были установлены особенности диффузии фуллеренов С 60 в расплаве ароматических полиэфиримидов при T = 600 K (T g = 479 K). Было показано наличие трех режимов диффузии -баллистического, субдиффузионного и нормального.…”

“…Подобное же моделирование было проведено в [3] для композитов полистирол(ПС)−С 60 и полипропилен(ПП)−С 60 при T = 500 K. Из результатов этого моделирования следует, что коэффициент диффузии C 60 в ПС -1 • 10 −8 cm 2 /s, а в ПП -0.9 • 10 −5 cm 2 /s. Отметим, что в обеих работах [3,12] моделирование было проведено для температур, превышающих температуру стеклования соответствующих полимеров более чем на 100 K. Возможно, поэтому расчеты [3,12] дали столь высокие значения коэффициента диффузии С 60 в соответствующих полимерах.…”