Nanoparticle Motion in Entangled Melts of Linear and Nonconcatenated Ring Polymers

Force transmission during repose of flexible granular chains

We study the mechanics of standing columns formed during the repose of flexible granular chains. It is one of the many intriguing behaviours exhibited by granular materials when links capable of transmitting tension exist between particles. We develop and calibrate a discrete element method contact model to simulate the mechanics of the macroscopic flexible granular chains and conduct simulations of the angle of repose experiments of these chains by extracting a chain-filled cylinder and allowing the material to flow out under gravity and repose. We evaluate various micro-mechanical, topological and macroscopic parameters to elucidate the mechanics of the repose behaviour of chain ensembles. It is the ability of the links connecting the individual particles to transmit tensile forces along the chain backbone that provides lateral stability to the column, enabling them to stand. In particular, the contact force rearrangement inside the columns generates a self-confining radial stress near the base of the columns, which provides an important stabilizing stress.

Triggering Gaussian-to-Exponential Transition of Displacement Distribution in Polymer Nanocomposites via Adsorption-Induced Trapping

In many disordered systems, the diffusion of classical particles is described by a displacement distribution P(x, t) that displays exponential tails instead of Gaussian statistics expected for Brownian motion. However, the experimental demonstration of control of this behavior by increasing the disorder strength has remained challenging. In this work, we explore the Gaussian-to-exponential transition by using diffusion of poly(ethylene glycol) (PEG) in attractive nanoparticle-polymer mixtures and controlling the volume fraction of the nanoparticles. In this work, we find "knobs", namely nanoparticle concentration and interaction, which enable the change in the shape of P(x,t) in a well-defined way. The Gaussian-to-exponential transition is consistent with a modified large deviation approach for a continuous time random walk and also with Monte Carlo simulations involving a microscopic model of polymer trapping via reversible adsorption to the nanoparticle surface. Our work bears significance in unraveling the fundamental physics behind the exponential decay of the displacement distribution at the tails, which is commonly observed in soft materials and nanomaterials.

Structure and Dynamics of Hybrid Colloid-Polyelectrolyte Coacervates: Insights from Molecular Simulations

Electrostatic interactions in polymeric systems are responsible for a wide range of liquid-liquid phase transitions that are of importance for biology and materials science. Such transitions are referred to as complex coacervation, and recent studies have sought to understand the underlying physics and chemistry. Most theoretical and simulation efforts to date have focused on oppositely charged linear polyelectrolytes, which adopt nearly ideal-coil conformations in the condensed phase. However, when one of the coacervate components is a globular protein, a better model of complexation should replace one of the species with a spherical charged particle or colloid. In this work, we perform coarse-grained simulations of colloid-polyelectrolyte coacervation using a spherical model for the colloid. Simulation results indicate that the electroneutral cell of the resulting (hybrid) coacervates consists of a polyelectrolyte layer adsorbed on the colloid. Power laws for the structure and the density of the condensed phase, which are extracted from simulations, are found to be consistent with the adsorption-based scaling theory of hybrid coacervation. The coacervates remain amorphous (disordered) at a moderate colloid charge, Q, while an intra-coacervate colloidal crystal is formed above a certain threshold, at Q > Q*. In the disordered coacervate, if Q is sufficiently low, colloids diffuse as neutral nonsticky nanoparticles in the semidilute polymer solution. For higher Q, adsorption is strong and colloids become effectively sticky. Our findings are relevant for the coacervation of polyelectrolytes with proteins, spherical micelles of ionic surfactants, and solid organic or inorganic nanoparticles.

Force-driven active dynamics of thin nanorods in unentangled polymer melts

Recent advances in the functional material and biomedical applications of nanorods call for a fundamental understanding of the active motion of nanorods in a viscoelastic medium. Molecular dynamics simulations are performed to investigate a model system consisting of force-driven active thin nanorods in a melt of unentangled polymers. The activeness of a thin nanorod arises from a constant external force applied uniformly along the rod. The simulations demonstrate that the active force overcomes the randomness of the diffusive motion and results in a ballistic motion along the direction of the applied force at long timescales. The constant speed of the force-driven ballistic motion is determined by the balance of the active force and the friction from the coupling of the nanorod with the polymer viscosity. The friction coefficient, which is computed as the ratio of the active force and the speed, decreases as the active force increases. The origin of the reduction in the friction coefficient is the high speed that allows the nanorod to renew its local environment faster than the relaxation time of melt chains. A scaling theory is developed to quantify the dependence of the friction coefficient on the strength of the active force. The simulations also demonstrate that the force-driven ballistic motion suppresses the rotational diffusion of the rod and cuts off the de-correlation of the rod axis with time. On the scaling level, the long-time trajectory of a force-driven active nanorod piercing through unentangled polymers may be described as a stretched array of "active blobs", where the short-time random-walk trajectory within an active blob is unperturbed by the active force.

Diffusion of polymer-grafted nanoparticles with dynamical fluctuations in unentangled polymer melts

The dynamics of polymer-grafted nanoparticles (PGNPs) in melts of unentangled linear chains were investigated by means of coarse-grained molecular dynamics simulations. The results demonstrated that the graft monomers closer to the particle surface relax more slowly than those farther away due to the constraint of the grafted surface and the confinement of the neighboring chains. Such heterogeneous relaxations of the surrounding environment would perturb the particle motion, making them fluctuating around their centers before they can diffuse through the melt. During such intermediate-time stage, the dynamics is subdiffusive while the distribution of particle displacements is Gaussian, which can be described by the popular fractional Brownian motion model. For the long-time Fickian diffusion, we found that the diffusivity D decreases with increasing grafting density Σ_g, grafted chain length N_g, and matrix chain length N_m. This is due to the fact that the diffusivity is controlled by the viscous drag of an effective core, consisting of the NP and the non-draining layer of graft segments, and that of the free-draining graft layer outside the "core". With increasing Σ_g, the PGNPs become harder with greater effective size and thinner free draining layer, resulting in a reduction in D. At extremely high Σ_g, the diffusivity can even be estimated by the diameter-renormalized Stokes-Einstein (SE) relation. With increasing N_g, both the effective core size and the thickness of the free-draining layer increase, leading to a reduction in diffusivity by D ∼ N-γg with 0.5 < γ < 1. Increasing N_m would lead to the enlargement of the effective core size but meanwhile result in the reduction of the free-draining layer thickness due to autophobic dewetting. The counteraction between these two opposite effects leads to only a slight reduction in the diffusivity, significantly different from the typical SE behavior where D ∼ N_m^-1. These findings bear significance in unraveling the fundamental physics of the anomalous dynamics of PGNPs in various polymers, including biological and synthetic.

Exploration of Ion Transport in Blends of an Ionic Liquid and a Polymerized Ionic Liquid Graft Copolymer

In this study, we prepared a composite membrane consisting of a poly(1-butyl-3-vinylimidazolium-tetrafluoroborate) (poly([BVIM]-[BF₄])) polymerized ionic liquid graft copolymer (PILGC) and a blend of PILGC and 1-butyl-3-methylimidazolium tetrafluoroborate ([BMIM]-[BF₄]) ionic liquid (IL) to explore techniques for improving the conductivity of PILGCs, which is normally three orders of magnitude lower than that of ILs. PILGCs, which are environmentally friendly, have attracted much interest. To gain a better understanding of ion transport in composites, the mechanisms of ion transport in composite components should be explored. We investigated anion transport in ILs and PILGCs and were able to obtain the correct ion transport mechanisms in IL-PILGC blends based on a previous work. We performed molecular dynamics (MD) simulations, which are commonly used to investigate molecular mechanisms. According to the MD simulation results, in most IL-PILGC blends of various compositions, the contributions of cations are greater than those of anions. This is one reason that blends have higher conductivities than their component PILGCs. To the best of our knowledge, we are the first to identify ion transport mechanisms in PILGCs and their blends with ILs by exploring subdiffusive ion motion regimes. The ratio of the number of cages with more than three cationic branch chains in the blend with 50 wt % PILGC, the blend with 80 wt % PILGC, and the PILGC was 0.26:0.39:0.65. Therefore, the ratio of firm cages gets a promotion as the PILGC content increases. Because the ratio of fast ions decreases as the ratio of firm cages increases, the blend with 80 wt % PILGC has lower anion diffusivities than the blend with 50 wt % PILGC. It was inappropriate to probe ion transport in PILGCs (or IL-PILGC blends) solely via analyzing ion association interactions. Analysis of only ion association interactions led to the incorrect conclusion that the time scales of ion transport in PILGCs are given by the continuous ion association time, which is the time when the ion association remains paired rather than the time when an ion is caught inside a cage. Proper methods should be used to obtain more accurate theories.

Nanorheology of active-passive polymer mixtures differentiates between linear and ring polymer topology

We study the motion of dispersed nanoprobes in entangled active-passive polymer mixtures. By comparing the two architectures of linear vs. unconcatenated and unknotted circular polymers, we demonstrate that novel, rich physics emerge. For both polymer architectures, nanoprobes of size smaller than the entanglement threshold of the solution move faster as activity is increased and more energy is pumped in the system. For larger nanoprobes, a surprising phenomenon occurs: while in linear solutions they move qualitatively as before, in active-passive ring solutions nanoprobes decelerate with respect to the purely passive conditions. We rationalize this effect in terms of the non-equilibrium, topology-dependent association (clustering) of nanoprobes to the cold component of the ring mixture reminiscent of the recently discovered [Weber et al., Phys. Rev. Lett., 2016, 116, 058301] phase separation in scalar active-passive mixtures. We conclude with a potential connection to the microrheology of the chromatin in the nuclei of the cells.

Effects of Tethered Polymers on Dynamics of Nanoparticles in Unentangled Polymer Melts

Polymer-tethered nanoparticles (NPs) are commonly added to a polymer matrix to improve material properties. Critical to the fabrication and processing of such composites is the mobility of the tethered NPs. Here we study the motion of tethered-NPs in unentangled polymer melts using molecular dynamics simulations, which offer a precise control of the grafted chain length N _g and the number z of grafted chains per particle. As N _g increases, there is a crossover from particle-dominated to tethered-chain-dominated terminal diffusion of NPs with the same z. The mean squared displacement of loosely tethered NPs in the case of tethered-chain dominated terminal diffusion exhibits two sub-diffusive regimes at intermediate time scales for small z. The first one at shorter time scales arises from the dynamical coupling of the particle and matrix chains, while the one at longer time scales is due to the participation of the particle in the dynamics of the tethered chains. The friction of loosely grafted chains in unentangled melts scales linearly with the total number of monomers in the chains, as the frictions of individual monomers are additive in the absence of hydrodynamic coupling. As more chains are grafted to a particle, hydrodynamic interactions between grafted chains emerge. As a result, there is a non-draining layer of hydrodynamically coupled chain segments surrounding the bare particle. Outside the non-draining layer is a free-draining layer of grafted chain segments with no hydrodynamic coupling. The boundary of the two layers is the stick surface where the shear stress due to the relative melt flow is balanced by the friction between grafted and melt chains in the interpenetration layer. The stick surface is located further away from the bare surface of the particle with higher grafting density.

Nanoparticle diffusion in polymer melts: Molecular dynamics simulations and mode-coupling theory

Nanoparticle diffusion in polymer melts is studied by the combination of Molecular Dynamics (MD) simulations and Mode-Coupling Theory (MCT). In accord with earlier experimental, simulation, and theoretical studies, we find that the Stokes-Einstein (SE) hydrodynamic relation D_n ∼ 1/R_n holds when the nanoparticle radius R_n is greater than the polymer gyration radius R_g, while in the opposite regime, the measured nanoparticle diffusion coefficient D_n exceeds the SE value by as much as an order of magnitude. The MCT values of D_n are found to be consistently higher than the MD simulation values. The observed discrepancy is attributed to the approximations involved in constructing the microscopic friction as well as to the approximate forms for dynamic structure factors used in MCT. In a thorough test of underlying MCT assumptions and approximations, various structural and dynamical quantities required as input for MCT are obtained directly from MD simulations. We present the improved MCT approach, which involves splitting of the microscopic time-dependent friction into two terms: binary (originating from short-time dynamics) and collective (due to long-time dynamics). Using MD data as input in MCT, we demonstrate that the total friction is largely dominated by its binary short-time term, which, if neglected, leads to severe overestimation of D_n. As a result, the revised version of MCT, in agreement with the present MD data, predicts 1/R_n ² scaling of the probe diffusion coefficient in a non-hydrodynamic regime when R_n < R_g. If the total friction is dominated by the collective long-time component, one would observe 1/R_n ³ scaling of D_n in accordance with previous studies.

The interfacial structure and dynamics in a polymer nanocomposite containing small attractive nanoparticles: a full atomistic molecular dynamics simulation study

We study the interfacial structure and dynamics of a polymer nanocomposite (PNC) composed of octaaminophenyl polyhedral oligomeric silsesquioxane (OAPS) and poly(2-vinylpyridine) (P2VP) by performing full atomistic molecular dynamics simulations. There are eight aminophenyl groups grafted on the surface of the OAPS particle and the particle has a size comparable to the Kuhn segment of P2VP. These aminophenyl groups can form hydrogen bonds (HBs) with pyridine rings from surrounding P2VP chains. We found that OAPS can form ∼2 HBs on average with surrounding polymer chains. The effect of the HBs is investigated in detail by either switching on or off these HBs in our simulation. By analyzing the interfacial static packing structure and dynamic properties, we demonstrate that the system has an ∼1 nm interface width, similar to the OAPS particle size. We also found that HBs can prevent the further penetration of polymers into the inner zone (grafting layer) of the OAPS, and therefore keep the P2VP chains in the outer layer (>1 nm), remaining bulk-like, which is well consistent with experimental results. In addition, we found that NP diffusion is coupled to the absorbed polymer chains, which also dramatically slows down the diffusion of polymer segments in return. The core-shell model in which the NP and absorbed polymers diffuse as a single object is validated here at the full atomistic level. These results provide atomistic insights into the unique structure and dynamics in the small attractive NP-polymer interfacial region. We hope these results will be helpful for the understanding of peculiar phenomena in attractive polymer nanocomposites containing small NPs.

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.

Unexpected entanglement dynamics in semidilute blends of supercoiled and ring DNA

Blends of polymers of different topologies, such as ring and supercoiled, naturally occur in biology and often exhibit emergent viscoelastic properties coveted in industry. However, due to their complexity, along with the difficulty of producing polymers of different topologies, the dynamics of topological polymer blends remains poorly understood. We address this void by using both passive and active microrheology to characterize the linear and nonlinear rheological properties of blends of relaxed circular and supercoiled DNA. We characterize the dynamics as we vary the concentration from below the overlap concentration c* to above (0.5c* to 2c*). Surprisingly, despite working at the dilute-semidilute crossover, entanglement dynamics, such as elastic plateaus and multiple relaxation modes, emerge. Finally, blends exhibit an unexpected sustained elastic response to nonlinear strains not previously observed even in well-entangled linear polymer solutions.

Determine Mesh Size through Monomer Mean-Square Displacement

A dynamic method to determine the main parameter of the tube theory through monomer mean-square displacement is discussed in this paper. The tube step length can be measured from the intersection of the slope-12 line and the slope-14 line in log-log plot, and the tube diameter can be obtained by recording the time at which g1 data start to leave the slope-12 regime. According to recent simulation data, the ratio of the tube step length to the tube diameter was found to be about 2 for different entangled polymer systems. Since measuring the tube diameter does not require g1 data to reach the slope-14 regime, this could be the best way to find the entanglement length from microscopic consideration.

Driven spheres, ellipsoids and rods in explicitly modeled polymer solutions

Understanding the transport of driven nano- and micro-particles in complex fluids is of relevance for many biological and technological applications. Here we perform hydrodynamic multiparticle collision dynamics simulations of spherical and elongated particles driven through polymeric fluids containing different concentrations of polymers. We determine the mean particle velocities which are larger than expected from Stokes law for all particle shapes and polymer densities. Furthermore we measure the fluid flow fields and local polymer density and polymer conformation around the particles. We find that polymer-depleted regions close to the particles are responsible for an apparent tangential slip velocity which accounts for the measured flow fields and transport velocities. A simple two-layer fluid model gives a good match to the simulation results.

Probing the organization and dynamics of two DNA chains trapped in a nanofluidic cavity

Here we present a pneumatically-actuated nanofluidic platform that has the capability of dynamically controlling the confinement environment of macromolecules in solution. Using a principle familiar from classic devices based on soft-lithography, the system uses pneumatic pressure to deflect a thin nitride lid into a nanoslit, confining molecules in an array of cavities embedded in the slit. We use this system to quantify the interactions of multiple confined DNA chains, a key problem in polymer physics with important implications for nanofluidic device performance and DNA partitioning/organization in bacteria and the eukaryotes. In particular, we focus on the problem of two-chain confinement, using differential staining of the chains to independently assess the chain conformation, determine the degree of partitioning/mixing in the cavities and assess coupled diffusion of the chain center-of-mass positions. We find that confinement of more than one chain in the cavity can have a drastic impact on the polymer dynamics and conformation.

A Review of the Synthesis and Applications of Polymer–Nanoclay Composites

Recent advancements in material technologies have promoted the development of various preparation strategies and applications of novel polymer–nanoclay composites. Innovative synthesis pathways have resulted in novel polymer–nanoclay composites with improved properties, which have been successfully incorporated in diverse fields such as aerospace, automobile, construction, petroleum, biomedical and wastewater treatment. These composites are recognized as promising advanced materials due to their superior properties, such as enhanced density, strength, relatively large surface areas, high elastic modulus, flame retardancy, and thermomechanical/optoelectronic/magnetic properties. The primary focus of this review is to deliver an up-to-date overview of polymer–nanoclay composites along with their synthesis routes and applications. The discussion highlights potential future directions for this emerging field of research.

Effect of copolymer sequence on structure and relaxation times near a nanoparticle surface

We simulate a simple nanocomposite consisting of a single spherical nanoparticle surrounded by coarse-grained polymer chains. The polymers are composed of two different monomer types that differ only in their interaction strengths with the nanoparticle. We examine the effect of adjusting copolymer sequence on the structure as well as the end-to-end vector autocorrelation, bond vector autocorrelation, and self-intermediate scattering function relaxation times as a function of distance from the nanoparticle surface. We show how the range and magnitude of the interphase of slowed dynamics surrounding the nanoparticle depend strongly on sequence blockiness. We find that, depending on block length, blocky copolymers can have faster or slower dynamics than a random copolymer. Certain blocky copolymer sequences lead to relaxation times near the nanoparticle surface that are slower than those of either homopolymer system. Thus, tuning copolymer sequence could allow for significant control over the nanocomposite behavior.

Chemical heterogeneity in interfacial layers of polymer nanocomposites

It is well-known that particle-polymer interactions strongly control the adsorption and conformations of adsorbed chains. Interfacial layers around nanoparticles consisting of adsorbed and free matrix chains have been extensively studied to reveal their rheological contribution to the behavior of nanocomposites. This work focuses on how chemical heterogeneity of the interfacial layers around the particles governs the microscopic mechanical properties of polymer nanocomposites. Low glass-transition temperature composites consisting of poly(vinyl acetate) coated silica nanoparticles in poly(ethylene oxide) and poly(methyl acrylate) matrices, and of poly(methyl methacrylate) silica nanoparticles in a poly(methyl acrylate) matrix are examined using rheology and X-ray photon correlation spectroscopy. We demonstrate that miscibility between the adsorbed and matrix chains in the interfacial layers led to the observed unusual reinforcement. We suggest that packing of chains in the interfacial regions may also contribute to the reinforcement in the polymer nanocomposites. These features may be used in designing mechanically adaptive composites operating at varying temperature.

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.

Adsorption Behavior of Polymer Chain with Different Topology Structure at the Polymer-Nanoparticle Interface

The effect of the polymer chain topology structure on the adsorption behavior in the polymer-nanoparticle (NP) interface is investigated by employing coarse-grained molecular dynamics simulations in various polymer-NP interaction and chain stiffness. At a weak polymer-NP interaction, ring chain with a closed topology structure has a slight priority to occupy the interfacial region than linear chain. At a strong polymer-NP interaction, the “middle” adsorption mechanism dominates the polymer local packing in the interface. As the increase of chain stiffness, an interesting transition from ring to linear chain preferential adsorption behavior occurs. The semiflexible linear chain squeezes ring chain out of the interfacial region by forming a helical structure and wrapping tightly the surface of NP. In particular, this selective adsorption behavior becomes more dramatic for the case of rigid-like chain, in which 3D tangent conformation of linear chain is absolutely prior to the 2D plane orbital structure of ring chain. The local packing and competitive adsorption behavior of bidisperse matrix in polymer-NP interface can be explained based on the adsorption mechanism of monodisperse (pure ring or linear) case. These investigations may provide some insights into polymer-NP interfacial adsorption behavior and guide the design of high-performance nanocomposites.

Exploration of bulk and interface behavior of gas molecules and 1-butyl-3-methylimidazolium tetrafluoroborate ionic liquid using equilibrium and nonequilibrium molecular dynamics simulation and quantum chemical calculation

Ionic liquids (ILs) show brilliant performance in separating gas impurities, but few researchers have performed an in-depth exploration of the bulk and interface behavior of penetrants and ILs thoroughly. In this research, we have performed a study on both molecular dynamics (MD) simulation and quantum chemical (QC) calculation to explore the transport of acetylene and ethylene in the bulk and interface regions of 1-butyl-3-methylimidazolium tetrafluoroborate ([BMIM]-[BF4]). The diffusivity, solubility and permeability of gas molecules in the bulk were researched with MD simulation first. The subdiffusion behavior of gas molecules is induced by coupling between the motion of gas molecules and the ions, and the relaxation processes of the ions after the disturbance caused by gas molecules. Then, QC calculation was performed to explore the optical geometry of ions, ion pairs and complexes of ions and penetrants, and interaction potential for pairs and complexes. Finally, nonequilibrium MD simulation was performed to explore the interface structure and properties of the IL-gas system and gas molecule behavior in the interface region. The research results may be used in the design of IL separation media.

Nanorheology of Entangled Polymer Melts

We use molecular simulations to probe the local viscoelasticity of an entangled polymer melt by tracking the motion of embedded nonsticky nanoparticles (NPs). As in conventional microrheology, the generalized Stokes-Einstein relation is employed to extract an effective stress relaxation function G_{GSE}(t) from the mean square displacement of NPs. G_{GSE}(t) for different NP diameters d are compared with the stress relaxation function G(t) of a pure polymer melt. The deviation of G_{GSE}(t) from G(t) reflects the incomplete coupling between NPs and the dynamic modes of the melt. For linear polymers, a plateau in G_{GSE}(t) emerges as d exceeds the entanglement mesh size a and approaches the entanglement plateau in G(t) for a pure melt with increasing d. For ring polymers, as d increases towards the spanning size R of ring polymers, G_{GSE}(t) approaches G(t) of the ring melt with no entanglement plateau.

Molecular insight into the Mullins effect: irreversible disentanglement of polymer chains revealed by molecular dynamics simulations

The debate regarding the possible molecular origins of the Mullins effect has been ongoing since its discovery. Molecular dynamics (MD) simulations were carried out to elucidate the underlying mechanism of the Mullins effect. For the first time, the key characteristics associated with the Mullins effect, including (a) the majority of stress softening occurring in the first stretch, (b) continuous softening with stress increase, (c) a permanent set, and (d) recovery with heat treatment, are captured by molecular modeling. It is discovered that the irreversible disentanglement of polymer chains is physically sufficient to interpret these key characteristics, providing molecular evidence for this long-controversial issue. Our results also reveal that filled polymers exhibit three distinct regimes, i.e., the polymer matrix, the interface, and the filler. When subjected to external strain, the polymer matrix suffers from excess deformation, indicating strong heterogeneity within the filled polymer, which offers molecular insight for the formulation of physics-based constitutive relations for filled polymers.

Dynamics of Nanoparticles in Entangled Polymer Solutions

The mean square displacement ⟨r²⟩ of nanoparticle probes dispersed in simple isotropic liquids and in polymer solutions is interrogated using fluorescence correlation spectroscopy and single-particle tracking (SPT) experiments. Probe dynamics in different regimes of particle diameter (d), relative to characteristic polymer length scales, including the correlation length (ξ), the entanglement mesh size (a), and the radius of gyration (R_g), are investigated. In simple fluids and for polymer solutions in which d ≫ R_g, long-time particle dynamics obey random-walk statistics ⟨r²⟩:t, with the bulk zero-shear viscosity of the polymer solution determining the frictional resistance to particle motion. In contrast, in polymer solutions with d < R_g, polymer molecules in solution exert noncontinuum resistances to particle motion and nanoparticle probes appear to interact hydrodynamically only with a local fluid medium with effective drag comparable to that of a solution of polymer chain segments with sizes similar to those of the nanoparticle probes. Under these conditions, the nanoparticles exhibit orders of magnitude faster dynamics than those expected from continuum predictions based on the Stokes-Einstein relation. SPT measurements further show that when d > a, nanoparticle dynamics transition from diffusive to subdiffusive on long timescales, reminiscent of particle transport in a field with obstructions. This last finding is in stark contrast to the nanoparticle dynamics observed in entangled polymer melts, where X-ray photon correlation spectroscopy measurements reveal faster but hyperdiffusive dynamics. We analyze these results with the help of the hopping model for particle dynamics in polymers proposed by Cai et al. and, on that basis, discuss the physical origins of the local drag experienced by the nanoparticles in entangled polymer solutions.

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.

Comparing gas transport in three polymers via molecular dynamics simulation

Molecular dynamics (MD) simulation was employed to study the transport of methane and n-butane molecules in the bulk and interface region of polyethylene (PE), poly(4-methyl-2-pentyne) (PMP) and polydimethylsiloxane (PDMS).

Solvent-Driven Infiltration of Polymer (SIP) into Nanoparticle Packings

Despite their wide potential utility, the manufacture of polymer-nanoparticle (NP) composites with high filler fractions presents significant challenges because of difficulties associated with dispersing and mixing high volume fractions of NPs in polymer matrices. Polymer-infiltrated nanoparticle films (PINFs) circumvent these issues, allowing fabrication of functional composites with extremely high filler fractions (>50 vol %). In this work, we present a one-step, room-temperature method for porous PINF fabrication through solvent-driven infiltration of polymer (SIP) into NP packings from a bilayer film composed of a densely packed layer of NPs atop a polymer film. Upon exposure to solvent vapor, capillary condensation occurs in the NP packing, leading to plasticization of the polymer layer and subsequent infiltration of polymer into the NP layer. This process results in a porous PINF without the need for energy-intensive processes. We show that the extent of polymer infiltration depends on the quality of solvent and the duration of solvent annealing as well as the molecular weight of the polymer. SIP can also be induced using a slightly poor solvent, which offers a great advantage of inducing SIP via liquid solvent annealing, eliminating potential hazards associated with solvent vapor annealing. The SIP process circumvents challenges associated with dispersing high concentrations of nanoparticles in a polymer matrix to prepare a nanocomposite film with high filler fraction. Thus, SIP is a potentially scalable method that can be used for the manufacturing of porous PINFs of a wide range of compositions, structures, and functionalities for applications in structural and barrier coatings as well as electrodes for energy storage and conversion devices.

Tuning Adsorption Duration To Control the Diffusion of a Nanoparticle in Adsorbing Polymers

Controlling the nanoparticle (NP) diffusion in polymers is a prerequisite to obtain polymer nanocomposites (PNCs) with desired dynamical and rheological properties and to achieve targeted delivery of nanomedicine in biological systems. Here we determine the suppression mechanism of direct NP-polymer attraction to hamper the NP mobility in adsorbing polymers and then quantify the dependence of the effective viscosity η_eff felt by the NP on the adsorption duration τ_ads of polymers on the NP using scaling theory analysis and molecular dynamics simulations. We propose and confirm that participation of adsorbed chains in the NP motion break up at time intervals beyond τ_ads due to the rearrangement of polymer segments at the NP surface, which accounts for the onset of Fickian NP diffusion on a time scale of t ≈ τ_ads. We develop a power law, η_eff ∼ (τ_ads)^ν, where ν is the scaling exponent of the dependence of polymer coil size on the chain length, which leads to a theoretical basis for the design of PNCs and nanomedicine with desired applications through tuning the polymer adsorption duration.