From Molecular Constraints to Macroscopic Dynamics in Associative Networks Formed by Ionizable Polymers: A Neutron Spin Echo and Molecular Dynamics Simulations Study

The association of ionizable polymers strongly affects their motion in solutions, where the constraints arising from clustering of the ionizable groups alter the macroscopic dynamics. The interrelation between the motion on multiple length and time scales is fundamental to a broad range of complex fluids including physical networks, gels, and polymer-nanoparticle complexes where long-lived associations control their structure and dynamics. Using neutron spin echo and fully atomistic, multimillion atom molecular dynamics (MD) simulations carried out to times comparable to that of chain segmental motion, the current study resolves the dynamics of networks formed by suflonated polystryene solutions for sulfonation fractions 0 ≤ f ≤ 0.09 across time and length scales. The experimental dynamic structure factors were measured and compared with computational ones, calculated from MD simulations, and analyzed in terms of a sum of two exponential functions, providing two distinctive time scales. These time constants capture confined motion of the network and fast dynamics of the highly solvated segments. A unique relationship between the polymer dynamics and the size and distribution of the ionic clusters was established and correlated with the number of polymer chains that participate in each cluster. The correlation of dynamics in associative complex fluids across time and length scales, enabled by combining the understanding attained from reciprocal space through neutron spin echo and real space, through large scale MD studies, addresses a fundamental long-standing challenge that underline the behavior of soft materials and affect their potential uses.

From ionic clusters dynamics to network constraints in ionic polymer solutions

Physical networks formed by ionizable polymers with ionic clusters as crosslinks are controlled by coupled dynamics that transcend from ionic clusters through chain motion to macroscopic response. Here, the coupled dynamics, across length scales, from the ionic clusters to the networks in toluene swollen polystyrene sulfonate networks, were directly correlated, as the electrostatic environment of the physical crosslinks was altered. The multiscale insight is attained by coupling neutron spin echo measurements with molecular dynamics simulations, carried out to times typical of relaxation of polymers in solutions. The experimental dynamic structure factor is in outstanding agreement with the one calculated from computer simulations, as the networks are perturbed by elevating the temperature and changing the electrostatic environment. In toluene, the long-lived clusters remain stable over hundreds of ns across a broad temperature range, while the polymer network remains dynamic. Though the size of the clusters changes as the dielectric constant of the solvent is modified through the addition of ethanol, they remain stable but morph, enhancing the polymer chain dynamics.

Inducing stratification of colloidal mixtures with a mixed binary solvent

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.

Response of ionizable block copolymer assemblies to solvent dielectrics: A molecular dynamics study

Ionizable copolymers assembly in solutions is driven by the formation of ionic clusters. Fast clustering of the ionizable blocks often leads to the formation of far-from equilibrium assemblies that ultimately impact the structure of polymer membranes and affect their many applications. Using large-scale atomistic molecular dynamics simulations, we probe the effects of electrostatics on the formation of ionizable copolymer micelles that dominate their solution structure, with the overarching goal of defining the factors that control the assembly of structured ionizable copolymers. A symmetric pentablock ionizable copolymer, with a randomly sulfonated polystyrene center tethered to polyethylene-r-propylene block, terminated by poly(t-butyl styrene), in solvents of varying dielectric constants from 2 to 20, serves as the model system. We find that independent of the solvents, this polymer forms a core-shell micelle with the ionizable segment segregating to the center of the assembly. The specific block conformation, however, strongly depends on the sulfonation levels and the dielectric constant and the polarity of the solvents.

Fractal dimensions of jammed packings with power-law particle size distributions in two and three dimensions

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 -β. The static structure factor exhibits diverging power-law behavior for small wave numbers, allowing us to identify a structural fractal dimension d_{f}. In three dimensions, d_{f}≈2.0 for 2.5≤β≤3.8, such that each of the structure factors can be collapsed onto a universal curve. In two dimensions, we instead find 1.0≲d_{f}≲1.34 for 2.1≤β≤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.

Unexpected Slow Relaxation Dynamics in Pure Ring Polymers Arise from Intermolecular Interactions

Ring polymers have fascinated scientists for decades, but experimental progress has been challenging due to the presence of linear chain contaminants that fundamentally alter dynamics. In this work, we report the unexpected slow stress relaxation behavior of concentrated ring polymers that arises due to ring-ring interactions and ring packing structure. Topologically pure, high molecular weight ring polymers are prepared without linear chain contaminants using cyclic poly(phthalaldehyde) (cPPA), a metastable polymer chemistry that rapidly depolymerizes from free ends at ambient temperatures. Linear viscoelastic measurements of highly concentrated cPPA show slow, non-power-law stress relaxation dynamics despite the lack of linear chain contaminants. Experiments are complemented by molecular dynamics (MD) simulations of unprecedentedly high molecular weight rings, which clearly show non-power-law stress relaxation in good agreement with experiments. MD simulations reveal substantial ring-ring interpenetrations upon increasing ring molecular weight or local backbone stiffness, despite the global collapsed nature of single ring conformation. A recently proposed microscopic theory for unconcatenated rings provides a qualitative physical mechanism associated with the emergence of strong inter-ring caging which slows down center-of-mass diffusion and long wavelength intramolecular relaxation modes originating from ring-ring interpenetrations, governed by the onset variable N/ND, where the crossover degree of polymerization ND is qualitatively predicted by theory. Our work overcomes challenges in achieving ring polymer purity and by characterizing dynamics for high molecular weight ring polymers. Overall, these results provide a new understanding of ring polymer physics.

Polydots, soft nanoparticles, at membrane interfaces

Soft nanoparticles (NPs) are emerging candidates for nano medicine, particularly for intercellular imaging and targeted drug delivery. Their soft nature, manifested in their dynamics, allows translocation into organisms without damaging their membranes. A crucial step towards incorporating soft dynamic NPs in nano medicine, is to resolve their interrelation with membranes. Here using atomistic molecular dynamics (MD) simulations we probe the interaction of soft NPs formed by conjugated polymers with a model membrane. These NPs, often termed polydots, are confined to their nano dimensions without any chemical tethers, forming dynamic long lived nano structures. Specifically, polydots formed by dialkyl para poly phenylene ethylene (PPE), with a varying number of carboxylate groups tethered to the alkyl chains to tune the interfacial charge of the surface of the NP are investigated at the interface with a model membrane that consists of di-palmitoyl phosphatidylcholine (DPPC). We find that even though polydots are controlled only by physical forces, they retain their NP configuration as they transcend the membrane. Regardless of their size, neutral polydots spontaneously penetrate the membrane whereas carboxylated polydots must be driven in, with a force that depends on the charge at their interface, all without significant disruption to the membrane. These fundamental results provide a means to control the position of the nanoparticles with respect to the membrane interfaces, which is key to their therapeutic use.

Entropic Mixing of Ring/Linear Polymer Blends

The topological constraints of nonconcatenated ring polymers force them to form compact loopy globular conformations with much lower entropy than unconstrained ideal rings. The closed-loop structure of ring polymers also enables them to be threaded by linear polymers in ring/linear blends, resulting in less compact ring conformations with higher entropy. This conformational entropy increase promotes mixing rings with linear polymers. Here, using molecular dynamics simulations for bead-spring chains, ring/linear blends are shown to be significantly more miscible than linear/linear blends and that there is an entropic mixing, negative χ, for ring/linear blends compared to linear/linear and ring/ring blends. In analogy with small angle neutron scattering, the static structure function S(q) is measured, and the resulting data are fit to the random phase approximation model to determine χ. In the limit that the two components are the same, χ = 0 for the linear/linear and ring/ring blends as expected, while χ < 0 for the ring/linear blends. With increasing chain stiffness, χ for the ring/linear blends becomes more negative, varying reciprocally with the number of monomers between entanglements. Ring/linear blends are also shown to be more miscible than either ring/ring or linear/linear blends and stay in single phase for a wider range of increasing repulsion between the two components.

Molecular dynamics simulations of binary sphere mixtures

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 3.6×10^{6} 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.

Modeling Solution Drying by Moving a Liquid-Vapor Interface: Method and Applications

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.

Large-scale frictionless jamming with power-law particle size distributions

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 4 000 000 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 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 nonrattler particles attains the frictionless isostatic value of six in all cases. The size distribution of nonrattler 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.

Superstretchable Elastomer from Cross-linked Ring Polymers

The stretchability of polymeric materials is critical to many applications such as flexible 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 trapped entanglements as in cross-linked linear polymers. The more compact conformation of ring polymers before deformation also contributes to the increase in stretchability.

Overlap Concentration of Sodium Polystyrene Sulfonate in Solution

The overlap concentration c* of sodium polystyrene sulfonate in water is calculated using multichain atomistic and coarse grained (CG) simulations for a range of chain lengths. Fully atomistic molecular dynamics simulations are carried out for N = 32-192 monomers. The CG model was parameterized to match the end-to-end distance from the atomistic simulations at small N and allows us to simulate a much larger N. Treating the hydrophobic backbone by inclusion of attraction between monomers is an essential addition to the CG model. The simulation c* are in agreement with experimental data, yet at c*, the chains are not fully stretched, even for N as large as 1200. This implies that none of the experimental systems are in the scaling regime and to reach the scaling regime for NaPSS chains much longer than N = 1200 are required.

Flow and arrest in stressed granular materials

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.

Shear Is Not Always Simple: Rate-Dependent Effects of Flow Type on Granular Rheology

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.

Effects of interaction strength of associating groups on linear and star polymer dynamics

A small number of associating groups incorporated onto a polymer backbone have dramatic effects on the mobility and viscoelastic response of the macromolecules in melts. These associating groups assemble, driving the formation of clusters, whose lifetime affects the properties of the polymers. Here, we probe the effects of the interaction strength on the structure and dynamics of two topologies, linear and star polymer melts, and further investigate blends of associative and non-associating polymers using molecular dynamics simulations. Polymer chains of approximately one entanglement length are described by a bead-spring model, and the associating groups are incorporated in the form of interacting beads with an interaction strength between them that is varied from 1 to 20 k_BT. We find that, for all melts and blends, interaction of a few k_BT between the associating groups drives cluster formation, where the size of the clusters increases with increasing interaction strength. These clusters act as physical crosslinkers, which slow the chain mobility. Blends of chains with and without associating groups macroscopically phase separate for interaction strength between the associating groups of a few k_BT and above. For weakly interacting associating groups, the static structure function S(q) is well fit by functional form predicted by the random phase approximation where a clear deviation occurs as phase segregation takes place, providing a quantitative assessment of phase segregation.

Assembly of Polymer-Grafted Nanoparticles in Polymer Matrices

Leibler pioneered the idea that long enough matrix polymers of length P will spontaneously dewet a chemically identical polymer layer, comprising chains of length N, densely end-grafted to a flat surface ("brush"). This entropically driven idea is routinely used to explain experiments in which 10-20 nm diameter nanoparticles (NPs) densely grafted with polymer chains are found to phase separate from chemically identical melts for P/N ≳4. At lower grafting densities, these effects are also thought to underpin the self-assembly of grafted NPs into a variety of structures. To explore the validity of this picture, we conducted large-scale molecular dynamics simulations of grafted NPs in a chemically identical polymer melt. For the NPs we consider, in the ≈5 nm diameter range, we find no phase separation even for P/N = 10 in the absence of attractions. Instead, we find behavior that more closely parallels experiments when all of the chain monomers are equally attractive to each other but repel the NPs. Our results thus imply that experimental situations investigated to date are dominated by the surfactancy of the NPs, which is driven by the chemical mismatch between the inorganic core and the organic ligands (the graft and free chains are chemically identical). Entropic effects, that is, the translational entropy of the NPs and the matrix, the entropy of mixing of the grafts and the matrix, and the conformational entropy of the chains appear to thus have a second-order effect even in the context of these model systems.

Threading-Unthreading Transition of Linear-Ring Polymer Blends in Extensional Flow

Adding small amounts of ring polymers to a matrix of their linear counterparts is known to increase the zero-shear-rate viscosity because of linear-ring threading. Uniaxial extensional rheology measurements show that, unlike its pure linear and ring constituents, the blend exhibits an overshoot in the stress growth coefficient. By combining these measurements with ex-situ small-angle neutron scattering and nonequilibrium molecular dynamics simulations, this overshoot is shown to be driven by a transient threading-unthreading transition of rings embedded within the linear entanglement network. Prior to unthreading, embedded rings deform affinely with the linear entanglement network and produce a measurably stronger elongation of the linear chains in the blend compared to the pure linear melt. Thus, rings uniquely alter the mechanisms of transient elongation in linear polymers.

Granular packings with sliding, rolling, and twisting friction

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 or 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.

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.

Topological Linking Drives Anomalous Thickening of Ring Polymers in Weak Extensional Flows

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 depends nonmonotonically on Wi, increasing to a maximum when Wi∼1 before rapidly decreasing when the strain rate approaches 1/τ_{e}.

Brush-Like Polymers and Entanglements: From Linear Chains to Filaments

Dynamics of melts and solutions of high molecular weight polymers and biopolymers is controlled by topological constraints (entanglements) imposing a sliding chain motion along an effective confining tube. For linear chains, the tube size is determined by universal packing number P_e, the number of polymer strands within a confining tube that is required for chains to entangle. Here we show that in melts of brush-like (graft) polymers, consisting of linear chain backbones with grafted side chains, P_e is not a universal number and depends on the molecular architecture. In particular, we use coarse-grained molecular dynamics simulations to demonstrate that the packing number is a nonmonotonic function of the ratio R_nsc/R_ng of the size of the side chains R_nsc to that of the backbone spacer between neighboring grafting points R_ng. This parameter characterizes the degree of mutual interpenetration between side chains of the same macromolecule. We show that P_e of brush-like polymers first decreases with increasing side chain grafting density in the dilute side chain regime (R_nsc < R_ng), then begins to increase in the regime of overlapping side chains (R_nsc > R_ng), approaching the value for linear chains in the limit of densely grafted side chains. This dependence of the packing number reflects a crossover from chain-like entanglements in systems with loosely grafted side chains (comb-like polymers) to entanglements between flexible filaments (bottlebrush-like polymers). Our simulation results are in agreement with the experimental data for the dependence of a plateau modulus on the molecular architecture of graft poly(n-butyl acrylates) and poly(norbornene)-graft-poly(lactide) melts.

Random walks on jammed networks: Spectral properties

Using random walk analyses we explore diffusive transport on networks obtained from contacts between isotropically compressed, monodisperse, frictionless sphere packings generated over a range of pressures in the vicinity of the jamming transition p→0. For conductive particles in an insulating medium, conduction is determined by the particle contact network with nodes representing particle centers and edges contacts between particles. The transition rate is not homogeneous, but is distributed inhomogeneously due to the randomness of packing and concomitant disorder of the contact network, e.g., the distribution of the coordination number. A narrow escape time scale is used to write a Markov process for random walks on the particle contact network. This stochastic process is analyzed in terms of spectral density of the random, sparse, Euclidean and real, symmetric, positive, semidefinite transition rate matrix. Results show network structures derived from jammed particles have properties similar to ordered, euclidean lattices but also some unique properties that distinguish them from other structures that are in some sense more homogeneous. In particular, the distribution of eigenvalues of the transition rate matrix follow a power law with spectral dimension 3. However, quantitative details of the statistics of the eigenvectors show subtle differences with homogeneous lattices and allow us to distinguish between topological and geometric sources of disorder in the network.

Control of Stratification in Drying Particle Suspensions via Temperature Gradients

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.

Flow-Arrest Transitions in Frictional Granular Matter

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.

Effect of Chain Length Dispersity on the Mobility of Entangled Polymers

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 (Đ_{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 Đ_{M}=1.0 to 1.16, were studied for times of 600-800  μs 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 Đ_{M}=1.0 and Đ_{M}=1.02, the shortest chains move significantly faster than the longest ones offering a constraint release pathway for the melts for larger Đ_{M}.

Stratification in Drying Films Containing Bidisperse Mixtures of Nanoparticles

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 Pe _sϕ _s ≳ c with c ∼ 1, where Pe _s is the Péclet number and ϕ _s is the volume fraction of the smaller particles. This threshold of Pe _sϕ _s for "small-on-top" is larger by a factor of ∼α² than the prediction of the model treating solvent as an implicit viscous background, where α 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 Pe _sϕ _s above the threshold when Pe _s is large but ϕ _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.

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.

Effect of an external field on capillary waves in a dipolar fluid

The role of an external field on capillary waves at the liquid-vapor interface of a dipolar fluid is investigated using molecular dynamics simulations. For fields parallel to the interface, the interfacial width squared increases linearly with respect to the logarithm of the size of the interface across all field strengths tested. The value of the slope decreases with increasing field strength, indicating that the field dampens the capillary waves. With the inclusion of the parallel field, the surface stiffness increases with increasing field strength faster than the surface tension. For fields perpendicular to the interface, the interfacial width squared is linear with respect to the logarithm of the size of the interface for small field strengths, and the surface stiffness is less than the surface tension. Above a critical field strength that decreases as the size of the interface increases, the interface becomes unstable due to the increased amplitude of the capillary waves.

Structured Ionomer Thin Films at Water Interface: Molecular Dynamics Simulation Insight

Controlling the structure and dynamics of thin films of ionizable polymers at water interfaces is critical to their many applications. As the chemical diversity within one polymer is increased, controlling the structure and dynamics of the polymer, which is a key to their use, becomes a challenge. Here molecular dynamics simulations (MD) are used to obtain molecular insight into the structure and dynamics of thin films of one such macromolecule at the interface with water. The polymer consists of an ABCBA topology with randomly sulfonated polystyrene (C), tethered symmetrically to flexible poly(ethylene-r-propylene) blocks (B), and end-capped by a poly(t-butylstyrene) block (A). The compositions of the interfacial and bulk regions of thin films of the ABCBA polymers are followed as a function of exposure time to water. We find that interfacial rearrangements take place where buried ionic segments migrate toward the water interface. The hydrophobic blocks collapse and rearrange to minimize their exposure to water. The water that initially drives interfacial reengagements breaks the ionic clusters within the film, forming a dynamic hydrophilic internal network within the hydrophobic segments.

Polymers at Liquid/Vapor Interface

Polymers confined to the liquid/vapor interface are studied using molecular dynamics simulations. We show that for polymers which are weakly immiscible with the solvent, the density profile perpendicular to the liquid/vapor interface is strongly asymmetric. On the vapor side of the interface, the density distribution falls off as a Gaussian with a decay length on the order of the bead diameter, whereas on the liquid side, the density profile decays as a simple exponential. This result differs from that of a polymer absorbed from a good solvent with the density profile decaying as a power law. As the surface coverage increases, the average end-to-end distance and chain mobility systematically decreases toward that of the homopolymer melt.

Coarse-Grained Modeling of Polyethylene Melts: Effect on Dynamics

The distinctive viscoelastic behavior of polymers results from a coupled interplay of motion on multiple length and time scales. Capturing the broad time and length scales of polymer motion remains a challenge. Using polyethylene (PE) as a model macromolecule, we construct coarse-grained (CG) models of PE with three to six methyl groups per CG bead and probe two critical aspects of the technique: pressure corrections required after iterative Boltzmann inversion (IBI) to generate CG potentials that match the pressure of reference fully atomistic melt simulations and the transferability of CG potentials across temperatures. While IBI produces nonbonded pair potentials that give excellent agreement between the atomistic and CG pair correlation functions, the resulting pressure for the CG models is large compared with the pressure of the atomistic system. We find that correcting the potential to match the reference pressure leads to nonbonded interactions with much deeper minima and slightly smaller effective bead diameter. However, simulations with potentials generated by IBI and pressure-corrected IBI result in similar mean-square displacements (MSDs) and stress autocorrelation functions G(t) for PE melts. While the time rescaling factor required to match CG and atomistic models is the same for pressure- and non-pressure-corrected CG models, it strongly depends on temperature. Transferability was investigated by comparing the MSDs and stress autocorrelation functions for potentials developed at different temperatures.

Nanoparticle Motion in Entangled Melts of Linear and Nonconcatenated Ring Polymers

The motion of nanoparticles (NPs) in entangled melts of linear polymers and nonconcatenated ring polymers are compared by large-scale molecular dynamics simulations. The comparison provides a paradigm for the effects of polymer architecture on the dynamical coupling between NPs and polymers in nanocomposites. Strongly suppressed motion of NPs with diameter d larger than the entanglement spacing a is observed in a melt of linear polymers before the onset of Fickian NP diffusion. This strong suppression of NP motion occurs progressively as d exceeds a and is related to the hopping diffusion of NPs in the entanglement network. In contrast to the NP motion in linear polymers, the motion of NPs with d > a in ring polymers is not as strongly suppressed prior to Fickian diffusion. The diffusion coefficient D decreases with increasing d much slower in entangled rings than in entangled linear chains. NP motion in entangled nonconcatenated ring polymers is understood through a scaling analysis of the coupling between NP motion and the self-similar entangled dynamics of ring polymers.

Communication: Polymer entanglement dynamics: Role of attractive interactions

The coupled dynamics of entangled polymers, which span broad time and length scales, govern their unique viscoelastic properties. 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 polymer melts is explored for the first time over a wide temperature range. Attractive interactions have little effect on the local packing for all temperatures T and on the chain mobility for T higher than about twice the glass transition T_g. These results, across a broad range of molecular weight, show that to study the dynamics of entangled polymer 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.

Soft nanoparticles: nano ionic networks of associated ionic polymers

Directing the formation of nanostructures that serve as building blocks of membranes presents an immense step towards engineering controlled polymeric ion transport systems. Using the exquisite atomic detail captured by molecular dynamics simulations, we follow the assembly of a co-polymer that consists of polystyrene sulfonate tethered symmetrically to hydrophobic blocks, realizing a new type of long lived solvent-responsive soft nanoparticle.