Sanat K. Kumar

Nanocomposites: Structure, Phase Behavior, and Properties

It is well recognized that nanocomposites formed by adding nanoparticles to polymers can have significantly enhanced properties relative to the native polymer. This review focuses on three aspects that are central to the outstanding problem of realizing these promised property improvements. First, we ask if there exist general strategies to control nanoparticle spatial distribution. This is an important question because it is commonly accepted that the nanoparticle dispersion state crucially affects property improvements. Because ideas on macroscale composites suggest that optimizing different properties requires different dispersion states, we next ask if we can predict a priori the particle dispersion and organization state that can optimize one (or more) properties of the resulting nanocomposite. Finally, we examine the role that particle shape plays in affecting dispersion and hence property control. This review focuses on recent advances concerning these underpinning points and how they affect measurable properties relevant to engineering applications.

Molecular dynamics simulations of polymer transport in nanocomposites

Molecular dynamics simulations on the Kremer-Grest bead-spring model of polymer melts are used to study the effect of spherical nanoparticles on chain diffusion. We find that chain diffusivity is enhanced relative to its bulk value when polymer-particle interactions are repulsive and is reduced when polymer-particle interactions are strongly attractive. In both cases chain diffusivity assumes its bulk value when the chain center of mass is about one radius of gyration R(g) away from the particle surface. This behavior echoes the behavior of polymer melts confined between two flat surfaces, except in the limit of severe confinement where the surface influence on polymer mobility is more pronounced for flat surfaces. A particularly interesting fact is that, even though chain motion is strongly speeded up in the presence of repulsive boundaries, this effect can be reversed by pinning one isolated monomer onto the surface. This result strongly stresses the importance of properly specifying boundary conditions when the near surface dynamics of chains are studied.

Direct determination of phase behavior of square-well fluids

We have combined Gibbs ensemble Monte Carlo simulations with the aggregation volume-biased method in conjunction with the Gibbs-Duhem method to provide the first direct estimates for the vapor-solid, vapor-liquid, and liquid-solid phase coexistences of square-well fluids with three different ranges of attraction. Our results are consistent with the previous simulations and verify the notion that the vapor-liquid coexistence behavior becomes metastable for cases where the attraction well becomes smaller than 1.25 times the particle diameter. In these cases no triple point is found.

End grafted polymer nanoparticles in a polymeric matrix: Effect of coverage and curvature

It has recently been proposed that the miscibility of nanoparticles with a polymer matrix can be controlled by grafting polymer chains to the nanoparticle surface. We examine this hypothesis using molecular dynamics simulations on a single nanoparticle of radius R (4σ ≤ R ≤ 16σ, where σ is the diameter of a polymer monomer) grafted with chains of length 500 in a polymer melt of chains of length 1000. The grafting density Σ is varied between 0.04–0.32 chains/σ2. To facilitate equilibration a Monte Carlo double-bridging algorithm is applied - new bonds are formed across a pair of chains, creating two new chains each substantially different from the original. For the long brush chains studied here, the structure of the brush assumes its large particle limit even for R as small as 8σ, which is consistent with recent experimental findings and the small chain lattice simulations of Klos and Pakula. We study autophobic dewetting of the melt from the brush as a function of increasing Σ. Even these long brush and matrix chains of lengths 6 and 12 Ne, respectively, (the entanglement length is Ne ∼ 85) give somewhat ambiguous results for the interfacial width, showing that studies of two or more nanoparticles are necessary to properly understand these miscibility issues. Entanglement between the brush and melt chains is identified using path analysis. We find that the number of entanglements between the brush and melt chains scale simply with the product of the local monomer densities of brush and melt chains.

Modeling the anisotropic self-assembly of spherical polymer-grafted nanoparticles

Recent experimental results demonstrated that polymer grafted nanoparticles in solvents display self-assembly behavior similar to the microphase separation of block copolymers and other amphiphiles. We present a mean-field theory and complementary computer simulations to shed light on the parametric underpinnings of the experimental observations. Our theory suggests that such self-assembled structures occur most readily when the nanoparticle size is comparable to the radius of gyration of the polymer brush chains. Much smaller particle sizes are predicted to yield uniform particle dispersions, while larger particles are expected to agglomerate due to phase separation from the solvent. Selected aspects of our theoretical predictions are corroborated by computer simulations.

Mechanical properties of thin glassy polymer films filled with spherical polymer-grafted nanoparticles

It is commonly accepted that the addition of spherical nanoparticles (NPs) cannot simultaneously improve the elastic modulus, the yield stress, and the ductility of an amorphous glassy polymer matrix. In contrast to this conventional wisdom, we show that ductility can be substantially increased, while maintaining gains in the elastic modulus and yield stress, in glassy nanocomposite films composed of spherical silica NPs grafted with polystyrene (PS) chains in a PS matrix. The key to these improvements are (i) uniform NP spatial dispersion and (ii) strong interfacial binding between NPs and the matrix, by making the grafted chains sufficiently long relative to the matrix. Strikingly, the optimal conditions for the mechanical reinforcement of the same nanocomposite material in the melt state is completely different, requiring the presence of spatially extended NP clusters. Evidently, NP spatial dispersions that optimize material properties are crucially sensitive to the state (melt versus glass) of the polymeric material.

Effective interactions between grafted nanoparticles in a polymer matrix

Molecular dynamics simulations were used to delineate the separation dependent forces between two polymer-grafted nanoparticles in a polymer melt, the associated potential of mean force (PMF), and the molecular origins of these forces. The nanoparticle radius (=5, in units of the size of the chain monomers) and grafted brush length (=10) were held constant, while the grafting density and the polymer matrix length were varied systematically in a series of simulations. We first show that simulations of a single nanoparticle do not reveal any signatures of the expected autophobic dewetting of the brush with increasing polymer matrix length. In fact, density distributions of the matrix and grafted chains around a single nanoparticle appear to only depend on the grafting density but not on the matrix chain length in the regime where autophobic dewetting is expected, i.e., when the matrix chain length is equal to or longer than the graft chain length. We thus conjecture that two nanoparticle simulations might be more illuminating in these situations. Indeed, the calculated forces between two nanoparticles in a melt show that increasing the matrix chain length from 10 to 70 causes the inter-nanoparticle potential of mean force (PMF) to go from purely repulsive to attractive with a well depth on the order of kBT. These results are purely entropic in origin and arise from a competition between brush-brush repulsion and an attractive inter-nanoparticle interaction caused by matrix depletion from the inter-nanoparticle zone. The matrix-induced Asakura-Oosawa type inter-nanoparticle attraction, which dominates at intermediate nanoparticle separations especially in the case of long matrix chains, is thus implicated as the essential player in the autophobic dewetting phenomenon, which drives phase separation in these situations.

Mesoscale model of polymer melt structure : Self-consistent mapping of molecular correlations to coarse-grained potentials

Development and application of coarse-graining methods to condensed phases of macromolecules is an active area of research. Multiscale modeling of polymeric systems using coarse-graining methods presents unique challenges. Here we apply a coarse-graining method that self-consistently maps structural correlations from detailed molecular dynamics (MD) simulations of alkane oligomers onto coarse-grained potentials using a combination of MD and inverse Monte Carlo methods. Once derived, the coarse-grained potentials allow computationally efficient sampling of ensemble of conformations of significantly longer polyethylene chains. Conformational properties derived from coarse-grained simulations are in excellent agreement with experiments. The level of coarse graining provides a control over the balance of computational efficiency and retention of chemical identity of the underlying polymeric system. Challenges to extension and application of this and similar structure-based coarse-graining methods to model dynamics and phase behavior in polymeric systems are briefly discussed.

Stabilizing colloidal crystals by leveraging void distributions

Colloids often crystallize into polymorphic structures, which are only separated by marginal differences in free energy. Due to this fact, the face-centred cubic and hexagonal close-packed hard-sphere morphologies, for example, usually crystallize simultaneously from a supersaturated solution. The resulting lack of long-range order in these polymorphic structures has been a significant barrier to the widespread application of these crystals in, for instance, photonic bandgap materials. Here, we report a simple method to stabilize one out of two competing polymorphs by exploiting the fact that they have significantly different spatial distributions of voids. We use a variety of polymeric additives whose geometries can be tuned such that their entropy loss, which is related to crystal void symmetries, is different in the two competing polymorphs. This, in turn, controls which polymorph is most thermodynamically stable, providing a generalizable means to stabilize a selected crystal polymorph from a suite of competing structures.

First-principles study of the effects of polytype and size on energy gaps in SiC nanoclusters

We have studied the band-gap variation and stability energy in silicon carbide (SiC) nanoclusters of different polytypes using density functional theory (DFT) based on a gradient-corrected approximation. We have obtained a series of spherical SiC nanoclusters with dimensions up to 2 nm from bulk 2H, 3C, and 4H polytype crystals. All clusters with diameters smaller than 1 nm exhibit similar energy-gap-size variations, while energy gaps for clusters larger than 1 nm show a distinct size dependence with different polytypes and approach their bulk gaps with an increase in cluster size. In contrast to their bulk behavior, the binding energy difference between polytypes of clusters within the diameter range 0.5 nm−2 nm is found to be negligible, suggesting that the problems associated with the synthesis of polytypes of SiC in bulk may disappear for small clusters. The convergence of the energy gap and binding energy with different polytypes at small size clusters and the transition between the clusters to bulk ...