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Polymers are an effective test-bed for studying topological constraints in condensed matter due to a wide array of synthetically-available chain topologies. When linear and ring polymers are blended together, emergent rheological properties are observed as the blend can be more viscous than either of the individual components. This emergent behavior arises since ring-linear blends can form long-lived topological constraints as the linear polymers thread the ring polymers. Here, we demonstrate how the Gauss linking integral can be used to efficiently evaluate the relaxation of topological constraints in ring-linear polymer blends. For majority-linear blends, the relaxation rate of topological constraints depends primarily on reptation of the linear polymers, resulting in the diffusive time $\tau_{d,R}$ for rings of length $N_R$ blended with linear chains of length $N_l$ to scale as $\tau_{d,R}\sim N_R^2N_L^{3.4}$., Comment: 6 pages, 6 figures

Molecular dynamics simulations are used to demonstrate that a binary solvent can be used to stratify colloidal mixtures when the suspension is rapidly dried. The solvent consists of two components, one more volatile than the other. When evaporated at high rates, the more volatile component becomes depleted near the evaporation front and develops a negative concentration gradient from the bulk of the mixture to the liquid-vapor interface while the less volatile solvent is enriched in the same region and exhibit a positive concentration gradient. Such gradients can be used to drive a binary mixture of colloidal particles to stratify if one is preferentially attracted to the more volatile solvent and the other to the less volatile solvent. During solvent evaporation, the fraction of colloidal particles preferentially attracted to the less volatile solvent is enhanced at the evaporation front, whereas the colloidal particles having stronger attractions with the more volatile solvent are driven away from the interfacial region. As a result, the colloidal particles show a stratified distribution after drying, even if the two colloids have the same size., Comment: 11 pages, 6 figures, 1 page Supporting Information with 2 figures

Granular matter takes many paths to pack. Gentle compression, compaction or repetitive tapping can happen in natural and industrial processes. The path influences the packing microstructure, and thus macroscale properties, particularly for frictional grains. We perform discrete element modeling simulations to construct packings of frictional spheres implementing a range of stress-controlled protocols with 3D periodic boundary conditions. A volume-controlled over-compression method is compared to four stress-controlled methods, including over-compression and release, gentle under-compression and cyclical compression and release. The packing volume fraction of each method depends on the pressure, initial kinetic energy and protocol parameters. A non-monotonic pressure dependence in the volume fraction, but not the coordination number occurs when dilute particles initialized with a non-zero kinetic energy are compressed, but can be reduced with the inclusion of drag. The fraction of frictional contacts correlates with the volume fraction minimum. Packings were cyclically compressed 1000 times. Response to compression depends on pressure; low pressure packings have a constant volume fraction regime, while high pressure packings continue to get dense with number of cycles. The capability of stress-controlled, bulk-like particle simulations to capture different protocols is showcased, and the ability to pack at low pressures demonstrates unexpected behavior.

Static structure factors are computed for large-scale, mechanically stable, jammed packings of frictionless spheres (three dimensions) and disks (two dimensions) with broad, power-law size dispersity characterized by the exponent $-\beta$. The static structure factor exhibits diverging power-law behavior for small wavenumbers, allowing us to identify a structural fractal dimension, $d_f$. In three dimensions, $d_f \approx 2.0$ for $2.5 \le \beta \le 3.8 $, such that each of the structure factors can be collapsed onto a universal curve. In two dimensions, we instead find $1.0 \lesssim d_f \lesssim 1.34 $ for $2.1 \le \beta \le 2.9 $. Furthermore, we show that the fractal behavior persists when rattler particles are removed, indicating that the long wavelength structural properties of the packings are controlled by the large particle backbone conferring mechanical rigidity to the system. A numerical scheme for computing structure factors for triclinic unit cells is presented and employed to analyze the jammed packings., Comment: 5 figures, 1 table

A method of simulating the drying process of a soft matter solution with an implicit solvent model by moving the liquid-vapor interface is applied to various solution films and droplets. For a solution of a polymer and nanoparticles, we observe "polymer-on-top" stratification, similar to that found previously with an explicit solvent model. Furthermore, "polymer-on-top" is found even when the nanoparticle size is smaller than the radius of gyration of the polymer chains. For a suspension droplet of a bidisperse mixture of nanoparticles, we show that core-shell clusters of nanoparticles can be obtained via the "small-on-outside" stratification mechanism at fast evaporation rates. "Large-on-outside" stratification and uniform particle distribution are also observed when the evaporation rate is reduced. Polymeric particles with various morphologies, including Janus spheres, core-shell particles, and patchy particles, are produced from drying droplets of polymer solutions by combining fast evaporation with a controlled interaction between the polymers and the liquid-vapor interface. Our results validate the applicability of the moving interface method to a wide range of drying systems. The limitations of the method are pointed out and cautions are provided to potential practitioners on cases where the method might fail., Comment: 14 pages, 7 figures

Explicit simulations of fluid mixtures of highly size-dispersed particles are constrained by numerical challenges associated with identifying pair-interaction neighbors. Recent algorithmic developments have ameliorated these difficulties to an extent, permitting more efficient simulations of systems with many large and small particles of disperse sizes. We leverage these capabilities to perform molecular dynamics simulations of binary sphere mixtures with elastically stiff particles approaching the hard sphere limit and particle size ratios of up to 50, approaching the colloidal limit. The systems considered consist of 500 large particles and up to nearly 3.6 million small particles with total particle volume fractions up to 0.51. Our simulations confirm qualitative predictions for correlations between large particles previously obtained analytically and for simulations employing effective depletion interactions, but also reveal additional insights into the near-contact structure that result from the explicit treatment of the small particle solvent. No spontaneous crystal nucleation was observed during the simulations, suggesting that nucleation rates in the fluid-solid coexistence region are too small to observe crystal nucleation for feasible simulation system sizes and timescales.

Due to significant computational expense, discrete element method simulations of jammed packings of size-dispersed spheres with size ratios greater than 1:10 have remained elusive, limiting the correspondence between simulations and real-world granular materials with large size dispersity. Invoking a recently developed neighbor binning algorithm, we generate mechanically-stable jammed packings of frictionless spheres with power-law size distributions containing up to nearly four million particles with size ratios up to 1:100. By systematically varying the width and exponent of the underlying power laws, we analyze the role of particle size distributions on the structure of jammed packings. The densest packings are obtained for size distributions that balance the relative abundance of large-large/intermediate and small-small particle contacts. Although the proportion of rattler particles and mean coordination number strongly depend on the size distribution, the mean coordination of non-rattler particles attains the frictionless isostatic value of six in all cases. The size distribution of non-rattler particles that participate in the load-bearing network exhibits no dependence on the width of the total particle size distribution beyond a critical particle size for low-magnitude exponent power laws. This signifies that only particles with sizes greater than the critical particle size contribute to the mechanical stability. However, for high-magnitude exponent power laws, all particle sizes participate in the mechanical stability of the packing.

The stretchability of polymeric materials is critical to many applications such as stretchable electronics and soft robotics, yet the stretchability of conventional cross-linked linear polymers is limited by the entanglements between polymer chains. We show using molecular dynamics simulations that cross-linked ring polymers are significantly more stretchable than cross-linked linear polymers. Compared to linear polymers, the entanglements between ring polymers do not act as effective cross-links. As a result, the stretchability of cross-linked ring polymers is determined by the maximum extension of polymer strands between cross-links, rather than between entanglements as in cross-linked linear polymers. The more compact conformation of ring polymers before deformation also contributes to the increase in stretchability.

The flow of frictionless granular particles is studied with stress-controlled discrete element modeling simulations for systems varying in size from 300 to 100,000 particles. The volume fraction and shear stress ratio $\mu$ are relatively insensitive to system size fo a wide range of inertial numbers $I$. Second-order effects in strain rate, such as second normal stress differences, require large system sizes to accurately extract meaningful results, notably a non-monotonic dependence in the first normal stress difference with strain rate. The first-order rheological response represented by the $\mu(I)$ relationship works well at describing the lower-order aspects of the rheology, except near the quasi-static limit of these stress-controlled flows. The pressure is varied over five decades, and a pressure dependence of the coordination number is observed, which is not captured by the inertial number. Large fluctuations observed for small systems $N\le$ 1,000 near the quasi-static limit can lead to arrest of flow resulting in challenges to fitting the data to rheological relationships. The inertial number is also insufficient for capturing the pressure-dependent behavior of property fluctuations. Fluctuations in the flow and microstructural properties are measured in both the quasi-static and inertial regimes, including shear stress, pressure, strain rate, normal stress differences, volume fraction, coordination number and contact fabric anisotropy. The fluctuations in flow properties scale self-similarly with pressure and system size. A transition in the scaling of fluctuations of stress properties and contact fabric anisotropy are measured and proposed as a quantitative identification of the transition from inertial to quasi-static flow.

Despite there being an infinite variety of types of flow, most rheological studies focus on a single type such as simple shear. Using discrete element simulations, we explore bulk granular systems in a wide range of flow types at large strains and characterize invariants of the stress tensor for different inertial numbers and interparticle friction coefficients. We identify a strong dependence on the type of flow which grows with increasing inertial number or friction. Standard models of yielding, repurposed to describe the dependence of the stress on flow type in steady-state flow and at finite rates, are compared with data., Comment: 6 pages, 5 figures

Extensive molecular simulations are applied to characterize the equilibrium dynamics, entanglement topology, and nonlinear extensional rheology of symmetric ring-linear polymer blends with systematically varied ring fraction $\phi_R$. Chains with degree of entanglement $Z\approx14$ mixed to produce 10 well-entangled systems with $\phi_R$ varying from neat linear to neat ring melts. Primitive path analysis are used to visualize and quantify the structure of the composite ring-linear entanglement network. We directly measure the quantity of ring-linear threading and linear-linear entanglement as a function of $\phi_R$, and identify with simple arguments a ring fraction $\phi_R\approx0.4$ where the topological constraints of the entanglement network are maximized. These topological analyses are used to rationalize the $\phi_R$-dependence of ring and linear chain dynamics, conformations, and blend viscosity. Complimentary simulations of startup uniaxial elongation flows demonstrate the extensional stress overshoot observed in recent filament stretching experiments, and characterize how it depends on the blend composition and entanglement topology. The overshoot is driven by an overstretching and recoil of ring polymer conformations that is caused by the convective unthreading of rings from linear chains. This produces significant changes in the entanglement structure of blends that we directly visualize and quantify with primitive path analyses during flow.

By generalizing a geometric argument for frictionless spheres, a model is proposed for the jamming density $\phi_J$ of mechanically stable packings of bidisperse, frictional spheres. The monodisperse, $\mu_s$-dependent jamming density $\phi_J^{\mathrm{mono}}(\mu_s)$ is the only input required in the model, where $\mu_s$ is the coefficient of friction. The predictions of the model are validated by robust estimates of $\phi_J$ obtained from computer simulations of up to $10^7$ particles for a wide range of $\mu_s$, and size ratios up to 40:1. Although $\phi_J$ varies nonmonotonically with the volume fraction of small spheres $f^s$ for all $\mu_s$, its maximum value $\phi_{J,\mathrm{max}}$ at an optimal $f^{s}_{\mathrm{max}}$ are both $\mu_s$-dependent. The optimal $f^{s}_{\mathrm{max}}$ is characterized by a sharp transition in the fraction of small rattler particles., Comment: Accepted version; 5 pages, 4 figures

Flowing granular materials often abruptly arrest if not driven by sufficient applied stresses. Such abrupt cessation of motion can be economically expensive in industrial materials handling and processing, and is significantly consequential in intermittent geophysical phenomena such as landslides and earthquakes. Using discrete element simulations, we calculate states of steady flow and arrest for granular materials under the conditions of constant applied pressure and shear stress, which are also most relevant in practice. Here the material can dilate or compact, and flow or arrest, in response to the applied stress. Our simulations highlight that under external stress, the intrinsic response of granular materials is characterized by uniquely-defined steady states of flow or arrest, which are highly sensitive to interparticle friction. While the flowing states can be equivalently characterized by volume fraction, coordination number or internal stress ratio, to characterize the states of shear arrest, one needs to also consider the structural anisotropy in the contact network. We highlight the role of dilation in the flow-arrest transition, and discuss our findings in the context of rheological transitions in granular materials., Comment: accepted version in Soft Matter. 9 pages, 5 figures

Intuition tells us that a rolling or spinning sphere will eventually stop due to the presence of friction and other dissipative interactions. The resistance to rolling and spinning/twisting torque that stops a sphere also changes the microstructure of a granular packing of frictional spheres by increasing the number of constraints on the degrees of freedom of motion. We perform discrete element modeling simulations to construct sphere packings implementing a range of frictional constraints under a pressure-controlled protocol. Mechanically stable packings are achievable at volume fractions and average coordination numbers as low as 0.53 and 2.5, respectively, when the particles experience high resistance to sliding, rolling and twisting. Only when the particle model includes rolling and twisting friction, were experimental volume fractions reproduced.

This study examines the flow of dense granular materials under external shear stress and pressure using discrete element method simulations. In this method, the material is allowed to strain along all periodic directions and adapt its solid volume fraction in response to an imbalance between the internal state of stress and the external applied stress. By systematically varying the external shear stress and pressure, the steady rheological response is simulated for: (1) rate-independent quasi-static flow; and (2) rate-dependent inertial flow. The simulated flow is viscometric with non-negligible first and second normal stress differences. While both normal stress differences are negative in inertial flows, the first normal stress difference switches from negative to slightly positive, and second normal stress difference tends to zero in quasi-static flows. The first normal stress difference emerges from a lack of coaxiality between a second-rank contact fabric tensor and strain rate tensor in the flow plane, while the second normal stress difference is linked to an excess of contacts in the shear plane compared with the vorticity direction. A general rheological model of second order (in terms of strain rate tensor) is proposed to describe the two types of flow, and the model is calibrated for various values of interparticle friction from simulations on nearly monodisperse spheres. The model incorporates normal stress differences in both regimes of flow and provides a complete viscometric description of steady dense granular flows., Comment: Accepted Version, 28 pages, 8 figures

Molecular dynamics simulations confirm recent extensional flow experiments showing ring polymer melts exhibit strong extension-rate thickening of the viscosity at Weissenberg numbers $Wi<<1$. Thickening coincides with the extreme elongation of a minority population of rings that grows with $Wi$. The large susceptibility of some rings to extend is due to a flow-driven formation of topological links that connect multiple rings into supramolecular chains. Links form spontaneously with a longer delay at lower $Wi$ and are pulled tight and stabilized by the flow. Once linked, these composite objects experience larger drag forces than individual rings, driving their strong elongation. The fraction of linked rings generated by flow depends non-monotonically on $Wi$, increasing to a maximum when $Wi\sim1$ before rapidly decreasing when the strain rate approaches the relaxation rate of the smallest ring loops $\sim 1/\tau_e$., Comment: 5 Pages, 5 Figures

The evolution of the internal granular structure in shear-arrested and shear-flowing states of granular materials is characterized using fabric tensors as descriptors of the internal contact and force networks. When a dilute system of frictional grains is subjected to a constant pressure and shear stress, the bulk stress ratio is well-predicted from the anisotropy of its contact and force networks during transient flow prior to steady shear flow or shear arrest. Although the onset of shear arrest is a stochastic process, the fabric tensors upon arrest are distributed around nearly equal contributions of force and contact network anisotropy to the bulk stress ratio. The distribution becomes seemingly narrower with increasing system size. The anisotropy of the contact network in shear-arrested states is reminiscent of the fabric anisotropy observed in shear-jammed packings., Comment: Accepted Version; 8 pages, 6 figures

The packing and flow of aspherical frictional particles are studied using discrete element simulations. Particles are superballs with shape $|x|^{s}+|y|^{s}+|z|^{s} = 1$ that varies from sphere ($s=2$) to cube ($s=\infty$), constructed with an overlapping-sphere model. Both packing fraction, $\phi$, and coordination number, $z$, decrease monotonically with microscopic friction $\mu$, for all shapes. However, this decrease is more dramatic for larger $s$ due to a reduction in the fraction of face-face contacts with increasing friction. For flowing grains, the dynamic friction $\tilde{\mu}$ - the ratio of shear to normal stresses - depends on shape, microscopic friction and inertial number $I.$ For all shapes, $\tilde{\mu}$ grows from its quasi-static value $\tilde{\mu}_0$ as $(\tilde{\mu}-\tilde{\mu}_0) = dI^\alpha,$ with different universal behavior for frictional and frictionless shapes. For frictionless shapes the exponent $\alpha \approx 0.5$ and prefactor $d \approx 5\tilde{\mu}_0$ while for frictional shapes $\alpha \approx 1$ and $d$ varies only slightly. The results highlight that the flow exponents are universal and are consistent for all the shapes simulated here., Comment: 6 pages, 5 figures

Large scale molecular dynamics simulations are used to study drying suspensions of a binary mixture of large and small particles in explicit and implicit solvents. The solvent is first modeled explicitly and then mapped to a uniform viscous medium by matching the diffusion coefficients and the pair correlation functions of the particles. `Small-on-top' stratification of the particles, with an enrichment of the smaller ones at the receding liquid-vapor interface during drying, is observed in both models under the same drying conditions. With the implicit solvent model, we are able to model much thicker films and study the effect of the initial film thickness on the final distribution of particles in the dry film. Our results show that the degree of stratification is controlled by the P\'{e}clet number defined using the initial film thickness as the characteristic length scale. When the P\'{e}clet numbers of large and small particles are much larger than 1, the degree of `small-on-top' stratification is first enhanced and then weakens as the P\'{e}clet numbers are increased., Comment: 10 pages, 7 figures

A potential strategy for controlling stratification in a drying suspension of bidisperse particles is studied using molecular dynamics simulations. When the suspension is maintained at a constant temperature during fast drying, it can exhibit "small-on-top" stratification with an accumulation (depletion) of smaller (larger) particles in the top region of the drying film, consistent with the prediction of current theories based on diffusiophoresis. However, when only the region near the substrate is thermalized at a constant temperature, a negative temperature gradient develops in the suspension because of evaporative cooling at the liquid-vapor interface. Since the associated thermophoresis is stronger for larger nanoparticles, a higher fraction of larger nanoparticles migrate to the top of the drying film at fast evaporation rates. As a result, stratification is converted to "large-on-top". Very strong "small-on-top" stratification can be produced with a positive thermal gradient in the drying suspension. Here we explore a way to produce a positive thermal gradient by thermalizing the vapor at a temperature higher than that of the solvent. Possible experimental approaches to realize various thermal gradients in a suspension undergoing solvent evaporation, and thus to produce different stratification states in the drying film, are suggested., Comment: 10 pages, 4 figures, supporting information (17 pages, 15 figures)

The transition between shear-flowing and shear-arrested states of frictional granular matter is studied using constant-stress discrete element simulations. By subjecting a dilute system of frictional grains to a constant external shear stress and pressure, friction-dependent critical shear stress and density are clearly identified with both exhibiting a crossover between low and high friction. The critical shear stress bifurcates two nonequilibrium steady states: (i) steady state shear flow characterized by a constant deformation rate, and (ii) shear arrest characterized by temporally decaying creep to a statically stable state. The onset of arrest below critical shear stress occurs at a time $t_{c}$ that exhibits a heavy-tailed distribution, whose mean and variance diverge as a power law at the critical shear stress with a friction-dependent exponent that also exhibits a crossover between low and high friction. These observations indicate that granular arrest near critical shear stress is highly unpredictable and is strongly influenced by interparticle friction.

While nearly all theoretical and computational studies of entangled polymer melts have focused on uniform samples, polymer synthesis routes always result in some dispersity, albeit narrow, of distribution of molecular weights (D_M=M_w/M_n ~ 1.02-1.04). Here the effects of dispersity on chain mobility are studied for entangled, disperse melts using a coarse-grained model for polyethylene. Polymer melts with chain lengths set to follow a Schulz-Zimm distribution for the same average M_w = 36 kg/mol with D_M = 1.0 to 1.16, were studied for times of $600-800$ $\mu$s using molecular dynamics simulations. This time frame is longer than the time required to reach the diffusive regime. We find that dispersity in this range does not affect the entanglement time or tube diameter. However, while there is negligible difference in the average mobility of chains for the uniform distribution D_M=1.0 and D_M = 1.02, the shortest chains move significantly faster than the longest ones offering a constraint release pathway for the melts for larger D_M.

Large scale molecular dynamics simulations for bidisperse nanoparticle suspensions with an explicit solvent are used to investigate the effects of evaporation rates and volume fractions on the nanoparticle distribution during drying. Our results show that ``small-on-top'' stratification can occur when ${\rm Pe}_s\phi_s \gtrsim c$ with $c\sim 1$, where ${\rm Pe}_s$ is the P\'{e}clet number and $\phi_s$ is the volume fraction of the smaller particles. This threshold of ${\rm Pe}_s\phi_s$ for ``small-on-top'' is larger by a factor of $\sim\alpha^2$ than the prediction of the model treating solvent as an implicit viscous background, where $\alpha$ is the size ratio between the large and small particles. Our simulations further show that when the evaporation rate of the solvent is reduced, the ``small-on-top'' stratification can be enhanced, which is not predicted by existing theories. This unexpected behavior is explained with thermophoresis associated with a positive gradient of solvent density caused by evaporative cooling at the liquid-vapor interface. For ultrafast evaporation the gradient is large and drives the nanoparticles toward the liquid/vapor interface. This phoretic effect is stronger for larger nanoparticles and consequently the ``small-on-top'' stratification becomes more distinct when the evaporation rate is slower (but not too slow such that a uniform distribution of nanoparticles in the drying film is produced), as thermophoresis that favors larger particles on the top is mitigated. A similar effect can lead to ``large-on-top'' stratification for ${\rm Pe}_s\phi_s$ above the threshold when ${\rm Pe}_s$ is large but $\phi_s$ is small. Our results reveal the importance of including the solvent explicitly when modeling evaporation-induced particle separation and organization and point to the important role of density gradients brought about by ultrafast evaporation., Comment: 11 pages, 4 figures, supporting information (19 pages, 19 figures)

Ordering nanoparticles into a desired super-structure is often crucial for their technological applications. We use molecular dynamics simulations to study the assembly of nanoparticles in a polymer brush randomly grafted to a planar surface as the solvent evaporates. Initially, the nanoparticles are dispersed in a solvent that wets the polymer brush. After the solvent evaporates, the nanoparticles are either inside the brush or adsorbed at the surface of the brush, depending on the strength of the nanoparticle-polymer interaction. For strong nanoparticle-polymer interactions, a 2-dimensional ordered array is only formed when the brush density is finely tuned to accommodate a single layer of nanoparticles. When the brush density is higher or lower than this optimal value, the distribution of nanoparticles shows large fluctuations in space and the packing order diminishes. For weak nanoparticle-polymer interactions, the nanoparticles order into a hexagonal array on top of the polymer brush as long as the grafting density is high enough to yield a dense brush. An interesting healing effect is observed for a low-grafting-density polymer brush that can become more uniform in the presence of weakly adsorbed nanoparticles., Comment: 9 pages, 6 figures

The coupled dynamics of entangled polymers which span a broad time and length scales govern the unique viscoelastic properties of polymers. To follow chain mobility by numerical simulations from the intermediate Rouse and reptation regimes to the late time diffusive regime, highly coarse grained models with purely repulsive interactions between monomers are widely used since they are computationally the most efficient. Here using large scale molecular dynamics simulations the effect of including the attractive interaction between monomers on the dynamics of entangled polymers melts is explored for the first time over wide temperature range. Attractive interactions has little effect on the local packing for all temperatures T and on the chain mobility for T higher than about twice the glass transition Tg. These results, across a broad range of molecular weight, show that to study the dynamics of entangled polymers melts the interactions can be treated as pure repulsive, confirming a posteriori the validity of previous studies and opening the way to new large scale numerical simulations., Comment: 11 Pages, 5 Figures; Journal of Chemical Physics (accepted)

The crazing behavior of polymer nanocomposites formed by blending polymer grafted nanoparticles with an entangled polymer melt is studied by molecular dynamics simulations. We focus on the three key differences in the crazing behavior of a composite relative to the pure homopolymer matrix, namely, a lower yield stress, a smaller extension ratio and a grafted chain length dependent failure stress. The yield behavior is found to be mostly controlled by the local nanoparticle-grafted polymer interfacial energy, with the grafted polymer-polymer matrix interfacial structure being of little to no relevance. Increasing the attraction between nanoparticle core and the grafted polymer inhibits void nucleation and leads to a higher yield stress. In the craze growth regime, the presence of grafted chain sections of 100 monomers alters the mechanical response of composite samples, giving rise to smaller extension ratios and higher drawing stresses than for the homopolymer matrix. The dominant failure mechanism of composite samples depends strongly on the length of the grafted chains, with disentanglement being the dominant mechanism for short chains, while bond breaking is the failure mode for chain lengths greater than 10Ne, where Ne is the entanglement length., Comment: Accepted for publication Journal of Chemical Physics

Large scale molecular dynamics simulations are used to study the dispersion of nanoparticles (NPs) in a polymer film during solvent evaporation. As the solvent evaporates, a dense polymer-rich skin layer forms at the liquid/vapor interface, which is either NP rich or poor depending on the strength of the NP/polymer interaction. When the NPs are strongly wet by the polymer, the NPs accumulate at the interface and form layers. However when the NPs are only partially wet by the polymer, most NPs are uniformly distributed in the bulk of the polymer film with the dense skin layer serving as a barrier to prevent the NPs from moving to the interface. Our results point to a possible route to employ less favorable NP/polymer interactions and fast solvent evaporation to uniformly disperse NPs in a polymer film, contrary to the common belief that strong NP/polymer attractions are needed to make NPs well dispersed in polymer nanocomposites., Comment: 7 pages, 6 figures

Coupled length and time scales determine the dynamic behavior of polymers and underlie their unique viscoelastic properties. To resolve the long-time dynamics it is imperative to determine which time and length scales must be correctly modeled. Here we probe the degree of coarse graining required to simultaneously retain significant atomistic details and access large length and time scales. The degree of coarse graining in turn sets the minimum length scale instrumental in defining polymer properties and dynamics. Using linear polyethylene as a model system, we probe how coarse graining scale affects the measured dynamics. Iterative Boltzmann inversion is used to derive coarse-grained potentials with 2-6 methylene groups per coarse-grained bead from a fully atomistic melt simulation. We show that atomistic detail is critical to capturing large scale dynamics. Using these models we simulate polyethylene melts for times over 500 {\mu}s to study the viscoelastic properties of well-entangled polymer chains., Comment: 6 pages, 6 figures

Using random walk simulations we explore diffusive transport through monodisperse sphere packings over a range of packing fractions, $\phi$, in the vicinity of the jamming transition at $\phi_{c}$. Various diffusion properties are computed over several orders of magnitude in both time and packing pressure. Two well-separated regimes of normal, "Fickian" diffusion, where the mean squared displacement is linear in time, are observed. The first corresponds to diffusion inside individual spheres, while the latter is the long-time bulk diffusion. The intermediate anomalous diffusion regime and the long-time value of the diffusion coefficient are both shown to be controlled by particle contacts, which in turn depend on proximity to $\phi_{c}$. The time required to recover normal diffusion $t^*$ scales as $(\phi-\phi_c)^{-0.5}$ and the long-time diffusivity $D_\infty \sim (\phi - \phi_c)^{0.5}$, or $D_\infty \sim 1/t^*$. It is shown that the distribution of mean first passage times associated with the escape of random walkers between neighboring particles controls both $t^*$ and $D_\infty$ in the limit $\phi \rightarrow \phi_c$., Comment: Accepted to Phys. Rev. Lett

Large-scale molecular simulations are performed to investigate tensile failure of polymer interfaces as a function of welding time $t$. Changes in the tensile stress, mode of failure and interfacial fracture energy $G_I$ are correlated to changes in the interfacial entanglements as determined from Primitive Path Analysis. Bulk polymers fail through craze formation, followed by craze breakdown through chain scission. At small $t$ welded interfaces are not strong enough to support craze formation and fail at small strains through chain pullout at the interface. Once chains have formed an average of about one entanglement across the interface, a stable craze is formed throughout the sample. The failure stress of the craze rises with welding time and the mode of craze breakdown changes from chain pullout to chain scission as the interface approaches bulk strength. The interfacial fracture energy $G_I$ is calculated by coupling the simulation results to a continuum fracture mechanics model. As in experiment, $G_I$ increases as $t^{1/2}$ before saturating at the average bulk fracture energy $G_b$. As in previous simulations of shear strength, saturation coincides with the recovery of the bulk entanglement density. Before saturation, $G_I$ is proportional to the areal density of interfacial entanglements. Immiscibiltiy limits interdiffusion and thus suppresses entanglements at the interface. Even small degrees of immisciblity reduce interfacial entanglements enough that failure occurs by chain pullout and $G_I \ll G_b$.

Self-healing of polymer films often takes place as the molecules diffuse across a damaged region, above their melting temperature. Using molecular dynamics simulations we probe the healing of polymer films and compare the results with those for thermal welding of homopolymer slabs. The two processes differ in their interfacial structure since damage leads to increased polydispersity and more short chains. A polymer sample was cut into two separate films that were then held together in the melt state. The recovery of the damaged film was followed as time elapsed and polymer molecules diffused across the interface. The mass uptake and formation of entanglements, as obtained from primitive path analysis, are extracted and correlated with the interfacial strength obtained from shear simulations. We find that the interdiffusion is significantly faster in the damaged film compared to welding because of the presence of short chains. Though interfacial entanglements increase more rapidly for the damaged films, a large fraction of them are near chain ends. As a result, the interfacial strength of the healing film increases more slowly than for welding. For both healing and welding, the interfacial strength saturates as the bulk entanglement density is recovered across the interface. However, the saturation strength of the damaged film is below the bulk strength for the polymer sample. At saturation, cut chains remain near the healing interface. They are less entangled and thus mechanically weaken the interface. When the interfacial strength saturates, the number of interfacial entanglements scales with the corresponding bulk entanglement density. Chain stiffness increases the density of entanglements, which increases the interfacial strength. Our results show that a few entanglements across the interface are sufficient to resist interfacial chain pullout and enhance the mechanical strength., Comment: Phys. Rev. E (in press)