Molecular dynamics simulation study of the role of evenly spaced poly(ethylene oxide) tethers on the aggregation of C60 fullerenes in water

Hierarchical Self-Assembly of Water-Soluble Fullerene Derivatives into Supramolecular Hydrogels

Controlling the self-assembly of nanoparticle building blocks into macroscale soft matter structures is an open question and of fundamental importance to fields as diverse as nanomedicine and next-generation energy storage. Within the vast library of nanoparticles, the fullerenes-a family of quasi-spherical carbon allotropes-are not explored beyond the most common, C60. Herein, a facile one-pot method is demonstrated for functionalizing fullerenes of different sizes (C60, C70, C84, and C90-92), yielding derivatives that self-assemble in aqueous solution into supramolecular hydrogels with distinct hierarchical structures. It is shown that the mechanical properties of these resultant structures vary drastically depending on the starting material. This work opens new avenues in the search for control of macroscale soft matter structures through tuning of nanoscale building blocks.

Solution properties of spherical gold nanoparticles with grafted DNA chains from simulation and theory

There has been a rapidly growing interest in the use of functionalized Au nanoparticles (NPs) as platforms in multiple applications in medicine and manufacturing. The sensing and targeting characteristics of these NPs, and the realization of precisely organized structures in manufacturing applications using such NPs, depend on the control of their surface functionalization. NP functionalization typically takes the form of polymer grafted layers, and a detailed knowledge of the chemical and structural properties of these layers is required to molecularly engineer the particle characteristics for specific applications. However, the prediction and experimental determination of these properties to enable the rational engineering of these particles is a persistent problem in the development of this class of materials. To address this situation, molecular dynamic simulations were performed based on a previously established coarse-grained single-stranded DNA (ssDNA) model to determine basic solution properties of model ssDNA-grafted NP-layers under a wide range of conditions. In particular, we emphasize the calculation of the hydrodynamic radius for ssDNA-grafted Au NPs as a function of structural parameters such as ssDNA length, NP core size, and surface coverage. We also numerically estimate the radius of gyration and the intrinsic viscosity of these NPs, which in combination with hydrodynamic radius estimates, provide valuable information about the fluctuating structure of the grafted polymer layers. We may then understand the origin of the commonly reported variation in effective NP "size" by different measurement methods, and then exploit this information in connection to material design and characterization in connection with the ever-growing number of applications utilizing polymer-grafted NPs.

Hierarchical and synergistic self-assembly in composites of model wormlike micellar-polymers and nanoparticles results in nanostructures with diverse morphologies

Using Monte Carlo simulations, we investigate the self-assembly of model nanoparticles inside a matrix of model equilibrium polymers (or matrix of wormlike micelles) as a function of the polymeric matrix density and the excluded volume parameter between polymers and nanoparticles. In this paper, we show morphological transitions in the system architecture via synergistic self-assembly of nanoparticles and the equilibrium polymers. In a synergistic self-assembly, the resulting morphology of the system is a result of the interaction between the nanoparticles and the polymers and corresponding re-organization of both the assemblies. This is different from the polymer templating method. We report the morphological transition of nanoparticle aggregates from percolating network-like structures to non-percolating clusters as a result of the change in the excluded volume parameter between nanoparticles and polymeric chains. Corresponding to the change in the self-assembled structures of nanoparticles, the matrix of equilibrium polymers also simultaneously shows a transition from a dispersed state to a percolating network-like structure formed by the clusters of polymeric chains. We show that the shape anisotropy of the nanoparticle clusters formed is governed by the polymeric density resulting in rod-like, sheet-like or other anisotropic nanoclusters. It is also shown that the pore shape and the pore size of the porous network of nanoparticles can be changed by changing the minimum approaching distance between nanoparticles and polymers. We provide a theoretical understanding of why various nanostructures with very different morphologies are obtained.

Nanostructuring Single-Molecule Polymeric Nanoparticles via Macromolecular Architecture

Heterogeneous polymer-based nanoparticles comprise a very promising family of materials for a broad range of applications. Here, we present a detailed study of structural heterogeneities in nanostructured single-molecule nanoparticles in various environments by means of atomistic molecular dynamics simulations. The nanoparticles consist of mikto-arm star copolymers with two types of chemically incompatible arms, namely poly(ethylene oxide) (PEO) and polystyrene (PS), (PS) _n,(PEO) _n, where n is the number of arms. The immiscibility between the two components gives rise to intramolecularly nanostructured particles. The nanostructured objects resemble either "Janus-like" or "patchy-like" particles, depending on the number or the length of the arms (or both) as well as the interaction with the surrounding medium. The degree of intramolecular heterogeneity increases with increasing number of arms and with decreasing affinity of star components to the polymer host. We provide a detailed analysis of the internal structure of the star-shaped particles, focusing on the intramolecular packing and the spatial arrangement of the arms. The results of our study can be used to design heterogeneous, internally nanostructured particles with two phases of distinct static properties for challenging specific applications of next-generation materials.

Self-assembly of hairy disks in two dimensions - insights from molecular simulations

We report the results of large scale molecular dynamics simulations conducted for sparsely grafted disks in two-dimensional systems. The main goal of this work is to show how the ligand mobility influences the self-assembly of particles decorated with short chains. We also analyze the impact of the chain length on the structure of dense phases. A crossover between the systems controlled by the core-core or by the segment-segment interactions is discussed. We prove that the ligand mobility determines the structure of the system. The particles with fixed tethers are found to order into different structures, an amorphous phase, hexagonal or honeycomb lattices, and a "spaghetti"-like phase containing single strings of cores, depending on the length of attached chains. The disks with mobile monomers assemble into a hexagonal structure, while the particles with longer mobile chains attached to them form a lamellar phase consisting of double strings of cores.

In-chain functionalized polymer induced assembly of nanoparticles: toward materials with tailored properties

We adopt a molecular dynamics simulation method to describe the self-assembly of nanoparticles in in-chain functionalized polymers. In such novel systems, the organization of nanoparticles is governed by the interplay of the intrinsic attractions between nanoparticles and the entropy of redistributing the functionalized polymers that are adsorbed on the nanoparticles. Our simulations also demonstrate that this approach to nanoparticle assembly enables considerable control for the creation of polymer nanocomposites with tailored properties.

Quantitative analogy between polymer-grafted nanoparticles and patchy particles

We establish a quantitative analogy between polymer grafted nanoparticles (PGNPs) and patchy nanoparticles (NPs). Over much of the experimentally relevant parameter space, we show that PGNPs behave quantitatively like Janus NPs, with the patch size having a universal dependence on the number of grafts and the ratio of the size of the NPs to the grafted chain size. The widely observed anisotropic self-assembly of PGNP into superstructures can thus be understood through simple geometric considerations of single patch models, in the same spirit as the geometry-based surfactant models of Israelachvili.

Understanding the role of grafted polystyrene chain conformation in assembly of magnetic nanoparticles

Polystyrene-grafted iron oxide nanoparticles have been shown to phase separate into ordered morphologies of strings, well-dispersed particles, and spherical aggregates at low graft densities in polymer matrices. In this work, small-angle neutron scattering experiments are performed to reveal the role of grafted chain conformation on nanoparticle assemblies. We demonstrate that chains grafted at low densities follow Gaussian statistics at any dispersion states. These results suggest that grafted chains are not distorted but remain Gaussian when particles are aggregated into strings. Small-angle x-ray and neutron scattering results show that matrix chains do not influence the formation of strings, but have a significant impact on the size and internal structure of aggregated particles. We conclude that spherical aggregates of nanoparticles with low polymer graft densities are akin to interpenetrating networks in which free matrix chains bridge the fractals of particles and control the cluster density.

Fluctuation-driven anisotropic assembly in nanoscale systems

We demonstrate that the self-assembly of spherical nanoparticles (NPs), grafted isotropically with polymeric ligands, into anisotropic structures is a manifestation of the fluctuations inherent in small number statistics. Computer simulations show that the organization of ligand atoms around an individual NP is not spatially isotropic for small numbers of grafts and ligand monomers. This inherent, spatially asymmetric ligand distribution causes the effective, two-body inter-NP potential to have a strong orientational dependence, which reproduces the anisotropic assembly observed ubiquitously for these systems. In contrast, ignoring this angular dependence does not permit us to capture NP self-assembly. This idea of fluctuation-driven behavior should be broadly relevant, and, for example, it should be important for the assembly of ligand-decorated quantum dots into arrays.

One-dimensional assembly of silica nanospheres: effects of nonionic block copolymers

The effects of polymers on the one-dimensional assembly of silica nanospheres (SNSs) in the liquid phase are systematically investigated using nonionic poly(ethylene oxide)-b-poly(propylene oxide)-b-poly(ethylene oxide) (abbreviated as PEO-PPO-PEO) triblock copolymers with varying hydrophilic-lipophilic balance (HLB) values. Scanning electron microscopy is employed for morphological observations of the polymer-mediated assemblies of SNSs on the basis of which the optimal pH for 1D assembly (pH(1D)) is determined. To clarify the polymers' effects on the 1D assembly of SNSs, the relationships between pH(1D) and polymers' HLB values, the numbers of hydrophilic EO and hydrophobic PO units, and the relative ratio of N(PO)/N(EO) are examined. Zeta potential measurements are conducted to investigate the electrostatic repulsion among the SNSs in the presence of block copolymers. It is found that the relative hydrophilicity of the block copolymers greatly affects the balance of interactions in the 1D assembly of SNSs. Block copolymers with large HLB values promote the 1D assembly of SNSs under near-neutral pH conditions, whereas the block copolymers with small HLB values promote 1D assembly under basic pH conditions. Therefore, the 1D assembly of SNSs is achieved over an extensive pH range (7.5-9.5) through the employment of block copolymers of different hydrophilic and hydrophobic block lengths.

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.

Aggregation of polymer-grafted nanoparticles in good solvents: a hierarchical modeling method

Brownian dynamics simulations are carried out to study the aggregation behavior of polymer-grafted nanoparticles (NPs) in good solvents by using the coarse-grained model derived from the all-atom force field, according to the hierarchical modeling strategy, and here PEG-grafted gold nanoparticles (GNPs) were taken as an example. Generally, grafting PEG to the surface of GNPs is to protect them from aggregation in the solution. However, our results reveal that PEG-grafted GNPs may also aggregate when concentration increases. Our simulations indicate that there exists a critical aggregating concentration (CAC), beyond which the PEG-grafted GNPs will aggregate. We further check the effects of grafting density and the length of grafted chains on the aggregation behavior of the grafted GNPs, and find that there exists an optimized length of grafted chain, at which the system has the maximal CAC. Furthermore, the aggregate size of self-assembled mesostructures formed by the grafted GNPs increases with the concentration. Interestingly, it is observed that the aggregation favors to form linear gold nanowires rather than compact gold nanoclusters, and the corresponding mechanism is also addressed. It is expected that this work would provide useful information for the fabrication of metal nanowires and the surface modification of metal nanoparticles.

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.

Theoretical issues relating to thermally reversible gelation by supermolecular fiber formation

Existing models of the thermodynamics and dynamics of self-assembly are summarized to provide a context for discussing the difficulties that arise in modeling supermolecular fiber assembly and the formation of thermally reversible gels through fiber growth and branching. Challenging problems in this field, such as the physical origin of fibers of uniform diameter and fiber twisting, the kinetics of fiber growth, the hierarchical bundling of fibers into "superfibers", fiber branching, gelation through fiber impingement and the associated phenomenon of fractal fiber network and spherulite formation, and the origin and control of structural polymorphism in the fiber and superfiber geometry, are discussed from a personal perspective. Suggestions are made for integrating current research efforts into a more coherent multiscale description of fiber formation and gelation on molecular, mesoscopic, and macroscopic scales.

Anisotropic self-assembly of spherical polymer-grafted nanoparticles

It is easy to understand the self-assembly of particles with anisotropic shapes or interactions (for example, cobalt nanoparticles or proteins) into highly extended structures. However, there is no experimentally established strategy for creating a range of anisotropic structures from common spherical nanoparticles. We demonstrate that spherical nanoparticles uniformly grafted with macromolecules ('nanoparticle amphiphiles') robustly self-assemble into a variety of anisotropic superstructures when they are dispersed in the corresponding homopolymer matrix. Theory and simulations suggest that this self-assembly reflects a balance between the energy gain when particle cores approach and the entropy of distorting the grafted polymers. The effectively directional nature of the particle interactions is thus a many-body emergent property. Our experiments demonstrate that this approach to nanoparticle self-assembly enables considerable control for the creation of polymer nanocomposites with enhanced mechanical properties. Grafted nanoparticles are thus versatile building blocks for creating tunable and functional particle superstructures with significant practical applications.

Supramolecular self-organization in PEO-modified C60 fullerene/water solutions: influence of polymer molecular weight and nanoparticle concentration

Utilizing a first-principles-based coarse-grained implicit solvent model, we have investigated the self-association of C(60) fullerenes that have been symmetrically modified with six grafted poly(ethylene oxide) (PEO) chains in aqueous solution. Despite the highly symmetric nature of the pair interactions between PEO-grafted fullerenes, their supramolecular assemblies are highly anisotropic and resemble the linear clusters formed in Stockmayer fluids. The dipole-like interaction between these symmetrically modified fullerenes results from the shielding of the C(60) fullerenes by PEO, favoring the addition of more PEO-grafted fullerenes to the linear clusters at the relatively unprotected ends. At low nanoparticle concentrations, self-association is dominated by the formation of stable dimers and trimers resulting from fullerene-fullerene contact and favorable PEO-fullerene interactions. With increasing nanoparticle concentration, larger clusters become increasingly probable. The molecular weight of the PEO tethers can be treated as a temperature-like analogue, with a reduction in average cluster size with increasing chain length due to increased steric repulsion, which is qualitatively similar to effects observed in Stockmayer fluids with increasing temperature. The role of PEO in supramolecular self-organization in PEO-modified C(60) fullerene/water solutions is complex, contributing not only to steric stabilization but also to favorable energetic interactions, nanoparticle shielding, and depletion-driven aggregation.

Molecular dynamics simulation study of the structure of poly(ethylene oxide) brushes on nonpolar surfaces in aqueous solution

The structure of poly(ethylene oxide) (PEO, M(w) = 526) brushes of various grafting density (sigma) on nonpolar graphite and hydrophobic (oily) surfaces in aqueous solution has been studied using atomistic molecular dynamics simulations. Additionally, the influence of PEO-surface interactions on the brush structure was investigated by systematically reducing the strength of the (dispersion) attraction between PEO and the surfaces. PEO chains were found to adsorb strongly to the graphite surface due primarily to the relative strength of dispersion interactions between PEO and the atomically dense graphite compared to those between water and graphite. For the oily surface, PEO-surface and water-surface dispersion interactions are much weaker, greatly reducing the energetic driving force for PEO adsorption. This reduction is mediated to some extent by a hydrophobic driving force for PEO adsorption on the oily surface. Reduction in the strength of PEO-surface attraction results in reduced adsorption of PEO for both surfaces, with the effect being much greater for the graphite surface where the strong PEO-surface dispersion interactions dominate. At high grafting density (sigma approximately 1/R(g)(2)), the PEO density profiles exhibited classical brush behavior and were largely independent of the strength of the PEO-surface interaction. With decreasing grafting density (sigma < 1/R(g)(2)), coverage of the surface by PEO requires an increasingly large fraction of PEO segments resulting in a strong dependence of the PEO density profile on the nature of the PEO-surface interaction.