Molecular Dynamics Simulations of Fullerene Diffusion in Polymer Melts

Structural and dynamical properties of thermoplastic polyurethane/fullerene nanocomposites: a molecular dynamics simulations study

In this work, the structural and dynamical properties of thermoplastic polyurethane (TPU)/fullerene (C60) nanocomposites are investigated using atomistic molecular dynamics simulations, focusing on the glass transition, thermal expansion, polymer mobility, polymer-C60 interactions, and diffusion behavior of C60. The results show a slight increase in the glass transition temperature (Tg) with increasing C60 weight fraction (wt%), attributed to hindered polymer dynamics, and a remarkable reduction in the coefficient of thermal expansion above Tg. Results of the mean squared displacement and the time decay of bond-reorientation autocorrelation indicate that the mobility of TPU hard segments is more restricted than that of soft segments, owing to the electrostatic attractions and the π-π stacking between isocyanate groups and C60 molecules. Analysis of TPU-C60 interaction energy reveals that the electrostatic interactions are weakened with an increase in the C60 wt%, while the van der Waals contributions become more significant due to the TPU-C60 interfacial characteristics. Further analysis shows that the translational and rotational diffusion of C60 are both increasingly suppressed with the increase of C60 wt%, indicating a violation of Stokes-Einstein (SE) and Stokes-Einstein-Debye (SED) relations, presumably due to the polymer chain-mediated hydrodynamic interactions arising from chain bridges between neighboring C60 particles. This is highlighted by a stronger decoupling of translational-rotational diffusion and a lower ratio of translational-rotational diffusion coefficient (DT/DR) with increasing C60 wt%. This work elucidates an atomistic understanding of the structure and properties of polymer/C60 nanocomposites.

The Effect of Hole Geometry on the Nonlinear Nanomechanics of γ-Graphyne Structures: A Finite Element Analysis

Graphyne is a material that has unique mechanical properties, but little is known about how these properties change when the material has holes. In this work, the effect of hole geometry, considering circular, triangle, and rhombus hole configurations, on the mechanical nonlinear response of γ-graphyne structures is studied. Graphyne, graphdiyne, graphyne-3, and graphyne-4 structures are under investigation. An efficient nonlinear finite element analysis (FEA) method is adequately implemented under large deformations for this purpose. The study varied the size and shape of the holes to understand how these changes affect the nanostructure's mechanical response. The results indicate that the hole geometry significantly impacts the mechanical nonlinear response of γ-graphyne structures. The holes' size and shape affect the structures' elastic behavior, deformation, and strength. The findings can be used to optimize the design of γ-graphyne structures for specific mechanical applications. The study highlights the importance of considering the hole geometries in the design and fabrication of these materials.

Molecular Simulation of Hopping Mechanisms of Nanoparticles in Regular Cross-Linked Polymer Networks

We use coarse-grained simulations to explore the diffusion mechanism of nanoparticles with different sizes at various nanoparticle-polymer interactions in regular cross-linked polymer networks. The long time diffusivities of nanoparticles show a non-monotonic tendency at various nanoparticle-polymer interactions, due to the intermittent hopping of nanoparticles through network cells. The preferred locations of small nanoparticles switch from the cell centers to the corner of cells as they interact with network more strongly, which results in the hopping energy barrier between different cells switching from cell center localization to adsorption on networks. Steric hindrance seriously hampers large nanoparticles from hopping to neighboring network cells, the interactions between nanoparticle and network enhance the network deformability and also affect the hopping of nanoparticles. The multiple constraint mechanisms result in the non-monotonic diffusivities of nanoparticles with different interactions and non-Brownian motions at different time scales. Our work illustrates the hopping mechanisms of nanoparticles in polymer networks from thermodynamic and dynamic points of view.

Calculating diffusion coefficients from molecular dynamics simulations for foam extrusion modelling of polypropylene with CO2, N2 and ethanol

In foaming processes, the blowing agent has a significant influence on the material behaviour and the necessary processing parameters. Low-density polypropylene foam sheets are usually produced with aliphatic hydrocarbons or alkanes as physical blowing agent. Due to the necessary safety precautions and the environmental impact, there is great interest in using alternative blowing agents such as CO2. The sole use of CO2 often leads to corrugation, open cells or surface defects on the foam sheet and therefore requires modifications to the process technology. For this reason, blowing agent mixtures based on CO2 and organic solvents are used for the production of foam sheets. For developing a process model describing the melt flow in the extrusion die and the formation of cells, specific material data like diffusion coefficients are necessary. For CO2 and N2 as sole blowing agent, experimental data exist in the literature. Since no experimental data are available for co-blowing agents such as ethanol at elevated temperatures as they occur in the foam process, these data were calculated using molecular dynamics (MD) simulations. The benefit of MD simulations lies in their ability to reduce the experimental effort and, in particular, to provide data in cases where this data is not available through experimental measurements. The calculated diffusion coefficient values are compared to experimental data from the literature and presented for CO2, N2 and ethanol in polypropylene. The calculated diffusion coefficients of CO2 and N2 are compared with literature results and agree well with them. For the ethanol molecules, the diffusion coefficient is compared relative to the both aforementioned ones considered the larger size of the ethanol molecule compared to N2 and CO2. The results of the diffusion coefficients for ethanol are reasonable compared to the values found for the other two molecules.

Water Dissolved in a Variety of Polymers Studied by Molecular Dynamics Simulation and a Theory of Solutions

The performance of a polymer medium as a separation membrane is determined by the dissolution free energy ΔG and diffusion coefficient D of the permeant. In this work, ΔG and D of water are investigated with all-atom molecular dynamics simulation in a wide variety of polymer species in the amorphous state. The computed ΔG is shown to agree well with the experimental value for linear homopolymers, and the degrees of polymerization of the homopolymers do not affect ΔG when they are beyond ∼10. The copolymers of ethylene-vinylidene difluoride, ethylene-vinyl acetate, and ethylene-acrylamide are then examined by changing the repeating patterns of the constituent monomers in both the periodic and graft forms. It is found that ΔG is determined primarily by the overall compositions of the monomers and is not affected by the copolymerization topology (periodic or graft). The hydrophobicity of the copolymer is enhanced, furthermore, when the hydrophobicity and hydrophilicity of the ethylene and non-ethylene parts are well contrasted and those parts are fragmented along the polymer chain. According to the computed D, the diffusivity of water tends to be larger when the (co)polymer is more hydrophobic and ΔG is more positive. D is actually seen to vary by orders of magnitude with the polymer structures, while the effect of the polymer species on the water permeation is stronger for ΔG than for D.

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

We report Brownian dynamics simulations of tracer diffusion in regularly crosslinked polymer networks in order to elucidate the transport of a tracer particle in polymer networks. The average mesh size of homogeneous polymer networks is varied by assuming different degrees of crosslinking or swelling, and the size of a tracer particle is comparable to the average mesh size. Simulation results show subdiffusion of a tracer particle at intermediate time scales and normal diffusion at long times. In particular, the duration of subdiffusion is significantly prolonged as the average mesh size decreases with increasing degree of crosslinking, for which long-time diffusion occurs via the hopping processes of a tracer particle after undergoing rattling motions within a cage of the network mesh for an extended period of time. On the other hand, the cage dynamics and hopping process are less pronounced as the mesh size decreases with increasing polymer volume fractions. The interpretation is provided in terms of fluctuations in network mesh size: at higher polymer volume fractions, the network fluctuations are large enough to allow for collective, structural changes of network meshes, so that a tracer particle can escape from the cage, whereas, at lower volume fractions, the fluctuations are so small that a tracer particle remains trapped within the cage for a significant period of time before making infrequent jumps out of the cage. This work suggests that fluctuation in mesh size, as well as average mesh size itself, plays an important role in determining the dynamics of molecules and nanoparticles that are embedded in tightly meshed polymer networks.

Comparing ion transport in ionic liquids and polymerized ionic liquids

Polymerized ionic liquids (polyILs) combine the unique properties of ionic liquids (ILs) with macromolecular polymers. But anion diffusivities in polyILs can be three orders of magnitude lower than that in ILs. Endeavors to improve ion transport in polyILs urgently need in-depth insights of ion transport in polyILs. As such in the work we compared ion transport in poly (1-butyl-3-vinylimidazolium-tetrafluoroborate) (poly ([BVIM]-[BF₄])) polyIL and 1-butyl-3-methylimidazolium tetrafluoroborate ([BMIM]-[BF₄]) IL. The diffusivities of ions in the polyIL and IL were measured and computed. According to the results of the molecular dynamics simulations performed, in the IL the coupling motion between an anion and the ions around determines the ion diffusivities, and the ion association lifetime gives the time scale of ion transport. But in the polyIL, the hopping of an anion among cages composed of cationic branch chains determines the diffusivity, and the associated anion transport time scale is the trap time, which is the time when an anion is caught inside a cage, not the ion association lifetime, as Mogurampelly et al. regarded. The calculation results of average displacements (ADs) of the polyIL chains show that, besides free volume fraction, average amplitudes of the oscillation of chains and chain translation speed lead to various diffusivities at various temperatures.

Transport Properties of Thermoplastic R-BAPB Polyimide: Molecular Dynamics Simulations and Experiment

The present work evaluates the transport properties of thermoplastic R-BAPB polyimide based on 1,3-bis(3,3′,4,4′-dicarboxyphenoxy)benzene (dianhydride R) and 4,4′-bis(4-aminophenoxy)biphenyl (diamine BAPB). Both experimental studies and molecular dynamics simulations were applied to estimate the diffusion coefficients and solubilities of various gases, such as helium (He), oxygen (O₂), nitrogen (N₂), and methane (CH₄). The validity of the results obtained was confirmed by studying the correlation of the experimental solubilities and diffusion coefficients of He, O₂, and N₂ in R-BAPB, with their critical temperatures and the effective sizes of the gas molecules, respectively. The solubilities obtained in the molecular dynamics simulations are in good quantitative agreement with the experimental data. A good qualitative relationship between the simulation results and the experimental data is also observed when comparing the diffusion coefficients of the gases. Analysis of the Robeson plots shows that R-BAPB has high selectivity for He, N₂, and CO₂ separation from CH₄, which makes it a promising polymer for developing gas-separation membranes. From this point of view, the simulation models developed and validated in the present work may be put to effective use for further investigations into the transport properties of R-BAPB polyimide and nanocomposites based on it.

Anomalous Dynamics of Water in Polyamide Matrix

Water in polymer matrixes is likely to show anomalous dynamics, a problem that has not been well understood yet. Here, we performed atomistic molecular dynamics simulations to study the water dynamics in a polyamide (PA) matrix, the bulk phase of well-known reverse osmosis membranes. For time-dependent ensemble average, water molecules experienced ballistic diffusion at a shorter time scale, followed by a crossover from subdiffusion to Brownian diffusion at a time scale ∼10 ns, and non-Gaussian diffusion, an indication of anomalous dynamics, sticks on even in the Brownian diffusion region. The anomalous dynamics mainly originates from two distinct motions including small-step continuous diffusion and jumping diffusion. The jumping motion has a mean length of 3.08 ± 0.31 Å and characteristic relaxation time of 0.218 ± 0.040 ns, which dominates the water diffusion in a fully hydrated PA matrix. It comprised low- and high-frequency jumps; the former is almost unchanged, and the latter remarkably increases with the increase of the hydration level. Surrounding neighbors of water strongly affect the jumping frequency, which exponentially or linearly decays with the increase in the number of atoms from the PA matrix. Although the PA matrix is flexible, associated with the water dynamics, the translocation of water is mainly through either tracing the position of neighboring water or jumping into the adjacent accommodation space.

Miscibility and Nanoparticle Diffusion in Ionic Nanocomposites

We investigate the effect of various spherical nanoparticles in a polymer matrix on dispersion, chain dimensions and entanglements for ionic nanocomposites at dilute and high nanoparticle loading by means of molecular dynamics simulations. The nanoparticle dispersion can be achieved in oligomer matrices due to the presence of electrostatic interactions. We show that the overall configuration of ionic oligomer chains, as characterized by their radii of gyration, can be perturbed at dilute nanoparticle loading by the presence of charged nanoparticles. In addition, the nanoparticle's diffusivity is reduced due to the electrostatic interactions, in comparison to conventional nanocomposites where the electrostatic interaction is absent. The charged nanoparticles are found to move by a hopping mechanism.

Interfacial Properties and Hopping Diffusion of Small Nanoparticle in Polymer/Nanoparticle Composite with Attractive Interaction on Side Group

The diffusion dynamics of fullerene (C 60 ) in unentangled linear atactic polystyrene (PS) and polypropylene (PP) melts and the structure and dynamic properties of polymers in interface area are investigated by performing all-atom molecular dynamics simulations. The comparison of the results in two systems emphasises the influence of local interactions exerted by polymer side group on the diffusion dynamics of the nanoparticle. In the normal diffusive regime at long time scales, the displacement distribution function (DDF) follows a Gaussian distribution in PP system, indicating a normal diffusion of C 60 . However, we observe multiple peaks in the DDF curve for C 60 diffusing in PS melt, which indicates a diffusion mechanism of hopping of C 60 . The attractive interaction between C 60 and phenyl ring side groups are found to be responsible for the observed hopping diffusion. In addition, we find that the C 60 is dynamically coupled with a subsection of a tetramer on PS chain, which has a similar size with C 60 . The phenyl ring on PS chain backbone tends to have a parallel configuration in the vicinity of C 60 surface, therefore neighbouring phenyl rings can form chelation effect on the C 60 surface. Consequently, the rotational dynamics of phenyl ring and the translational diffusion of styrene monomers are found to be slowed down in this interface area. We hope our results can be helpful for understanding of the influence of the local interactions on the nanoparticle diffusion dynamics and interfacial properties in polymer/nanoparticle composites.

Translational and rotational dynamics of an ultra-thin nanorod probe particle in linear polymer melts

Translational and rotational dynamics of a single rigid ultra-thin nanorod probe particle in linear polymer melts are investigated using coarse-grained molecular dynamics (CG-MD) simulations.

Molecular dynamics simulations of oligoester brushes: the origin of unusual conformations

We present results from all-atom molecular dynamics simulations for the structural properties of oligomeric lactic acid chains (OLA) grafted to the surface of cellulose nanocrystals (CNCs) and immersed in the melt of polylactic acid (PLA). Earlier, we have found that the distribution of free ends of OLA molecules is bimodal [Glova et al., Polym. Int., 2016, 65(8), 892]. The results cannot be explained within the standard picture of uncharged polymer brushes exposed to the melt of a chemically identical polymer. Although the oligomeric brushes of the OLA chains are uncharged, they have partial polarization charges producing a non-zero dipole moment of the monomeric chain unit. We study the influence of partial charges on the structure of the layer of OLA chains grafted to the CNC surface. A detailed analysis of the conformations of the grafted chains shows that interaction of partial charges in the models causes bending of the OLA molecules toward the cellulose surface, forming a hairpin structure. The observed separation of the grafted chains into two populations increases with grafting density. We demonstrate that hydrogen bonds can be formed between the free ends of the grafted chains and the CNC surface, but they do not affect the brush structure significantly. Thus, dipole-dipole interactions turn out to be the key factor governing the unusual conformations of grafts.