Anisotropic Three-Particle Interactions between Spherical Polymer-Grafted Nanoparticles in a Polymer Matrix

Self-assembly of nanocrystal checkerboard patterns via non-specific interactions

Checkerboard lattices-where the resulting structure is open, porous, and highly symmetric-are difficult to create by self-assembly. Synthetic systems that adopt such structures typically rely on shape complementarity and site-specific chemical interactions that are only available to biomolecular systems (e.g., protein, DNA). Here we show the assembly of checkerboard lattices from colloidal nanocrystals that harness the effects of multiple, coupled physical forces at disparate length scales (interfacial, interparticle, and intermolecular) and that do not rely on chemical binding. Colloidal Ag nanocubes were bi-functionalized with mixtures of hydrophilic and hydrophobic surface ligands and subsequently assembled at an air-water interface. Using feedback between molecular dynamics simulations and interfacial assembly experiments, we achieve a periodic checkerboard mesostructure that represents a tiny fraction of the phase space associated with the polymer-grafted nanocrystals used in these experiments. In a broader context, this work expands our knowledge of non-specific nanocrystal interactions and presents a computation-guided strategy for designing self-assembling materials.

Three-body interaction of gold nanoparticles: the role of solvent density and ligand shell orientation

Molecular dynamics simulations are used to study the effective interactions of alkanethiol passivated gold nanoparticles in supercritical ethane at two- and three-particle levels with different solvent densities. Effective interaction is calculated as the potential of mean force (PMF) between two nanoparticles, and the three-body effect is estimated as the difference in PMFs calculated at the two- and three-particle levels. The variation in the three-body effect is examined as a function of solvent density. It is found that effective interaction, which is completely repulsive at very high solvent concentrations, progressively turns attractive as solvent density declines. On the other hand, the three-body effect turns out to be repulsive and increases exponentially with decreasing solvent density. Further, the structure of the ligand shell is analyzed as a function of nanoparticle separation, and its relationship with the three-body effect is investigated. It is observed that the three-body effect arises when the ligand shell begins to deform due to van der Waals repulsion between ligand shells. The study provides a deep insight into good understanding of the solvent evaporation-assisted nanoparticle self-assembly and can aid in experiments.

Characterizing the shear response of polymer-grafted nanoparticles

Grafting polymer chains to the surface of nanoparticles overcomes the challenge of nanoparticle dispersion within nanocomposites and establishes high-volume fractions that are found to enable enhanced material mechanical properties. This study utilizes coarse-grained molecular dynamics simulations to quantify how the shear modulus of polymer-grafted nanoparticle (PGN) systems in their glassy state depends on parameters such as strain rate, nanoparticle size, grafting density, and chain length. The results are interpreted through further analysis of the dynamics of chain conformations and volume fraction arguments. The volume fraction of nanoparticles is found to be the most influential variable in deciding the shear modulus of PGN systems. A simple rule of mixture is utilized to express the monotonic dependence of shear modulus on the volume fraction of nanoparticles. Due to the reinforcing effect of nanoparticles, shortening the grafted chains results in a higher shear modulus in PGNs, which is not seen in linear systems. These results offer timely insight into calibrating molecular design parameters for achieving the desired mechanical properties in PGNs.

Coarse-Grained Many-Body Potentials of Ligand-Stabilized Nanoparticles from Machine-Learned Mean Forces

Colloidal nanoparticles self-assemble into a variety of superstructures with distinctive optical, structural, and electronic properties. These nanoparticles are usually stabilized by a capping layer of organic ligands to prevent aggregation in the solvent. When the ligands are sufficiently long compared to the dimensions of the nanocrystal cores, the effective coarse-grained forces between pairs of nanoparticles are largely affected by the presence of neighboring particles. In order to efficiently investigate the self-assembly behavior of these complex colloidal systems, we propose a machine-learning approach to construct effective coarse-grained many-body interaction potentials. The multiscale methodology presented in this work constitutes a general bottom-up coarse-graining strategy where the coarse-grained forces acting on coarse-grained sites are extracted from measuring the vectorial mean forces on these sites in reference fine-grained simulations. These effective coarse-grained forces, i.e., gradients of the potential of mean force or of the free-energy surface, are represented by a simple linear model in terms of gradients of structural descriptors, which are scalar functions that are rotationally invariant. In this way, we also directly obtain the free-energy surface of the coarse-grained model as a function of all coarse-grained coordinates. We expect that this simple yet accurate coarse-graining framework for the many-body potential of mean force will enable the characterization, understanding, and prediction of the structure and phase behavior of relevant soft-matter systems by direct simulations. The key advantage of this method is its generality, which allows it to be applicable to a broad range of systems. To demonstrate the generality of our method, we also apply it to a colloid-polymer model system, where coarse-grained many-body interactions are pronounced.

Discovery of two-dimensional binary nanoparticle superlattices using global Monte Carlo optimization

Binary nanoparticle (NP) superlattices exhibit distinct collective plasmonic, magnetic, optical, and electronic properties. Here, we computationally demonstrate how fluid-fluid interfaces could be used to self-assemble binary systems of NPs into 2D superlattices when the NP species exhibit different miscibility with the fluids forming the interface. We develop a basin-hopping Monte Carlo (BHMC) algorithm tailored for interface-trapped structures to rapidly determine the ground-state configuration of NPs, allowing us to explore the repertoire of binary NP architectures formed at the interface. By varying the NP size ratio, interparticle interaction strength, and difference in NP miscibility with the two fluids, we demonstrate the assembly of an array of exquisite 2D periodic architectures, including AB-, AB₂-, and AB₃-type monolayer superlattices as well as AB-, AB₂-, A₃B₅-, and A₄B₆-type bilayer superlattices. Our results suggest that the interfacial assembly approach could be a versatile platform for fabricating 2D colloidal superlattices with tunable structure and properties.

Controlling the anisotropic self-assembly of polybutadiene-grafted silica nanoparticles by tuning three-body interaction forces

Recently, the significant improvements in polymer composites properties have been mainly attributed to the ability of filler nanoparticles (NPs) to self-assemble into highly anisotropic self-assembled structures. In this work, we investigate the self-assembly of core-shell NPs composed of a silica core grafted with polybutadiene (PB) chains, generating the so-called "hairy" NPs (HNPs), immersed in tetrahydrofuran solvent. While uncoated silica beads aggregate forming uniform compact structures, the presence of a PB shell affects the silica NPs organization to the point that by increasing the polymer density at the corona, they tend to self-assemble into linear chain-like structures. To reproduce the experimental observations, we propose a theoretical model for the two-body that considers the van der Waals attractive energy together with the polymer-induced repulsive steric contribution and includes an additional three-body interaction term. This term arises due to the anisotropic distribution of PB, which increases their concentration near the NPs contact region. The resulting steric repulsion experienced by a third NP approaching the dimer prevents its binding close to the dimer bond and favors the growth of chain-like structures. We find good agreement between the simulated and experimental self-assembled superstructures, confirming that this three-body steric repulsion plays a key role in determining the cluster morphology of these core-shell NPs. The model also shows that further increasing the grafting density leads to low-density gel-like open structures.

Effect of functional anisotropy on the local dynamics of polymer grafted nanoparticles

End-functionalised polymer grafted nanoparticles (PGNs) form bonds when their coronas overlap. The bonded interactions between the overlapping PGNs depend on the energy of the bonds (U). In the present study, oscillatory deformation imposed on a simple system with interacting PGNs placed on the vertices of a triangle is employed to examine the local dynamics as a function of energy of the bonds and the frequency of oscillation relative to the characteristic rupture frequency, ω₀ = 2πν exp(-U/k_BT), of the bonds. In particular, the effect of functional anisotropy is studied by introducing bonds of two different energies between adjacent PGNs. A multicomponent model developed by Kadre and Iyer, Macromol. Theory Simul., 2021, 30, 2100005, that combines the features of effective interactions between PGNs, self-consistent field theory and master equation approach to study bond kinetics is employed to obtain the local dynamics. The resulting force-strain curves are found to exhibit a simple broken symmetry where F_x (γ,) ≠ -F_x (-γ,-) and F_y (γ,) ≠ F_y (-γ,-) in systems with functional anisotropy. Fourier analysis of the dynamic response reveals that functional anisotropy leads to finite even harmonic terms and systematic variation of both the elastic and dissipative response from that of the isotropic systems. Furthermore, the intra-cycle variations in the strain stiffening and shear thickening ratios obtained from the analysis indicate that functional anisotropy leads to anisotropic nonlinear response.

Tunable Orientation and Assembly of Polymer-Grafted Nanocubes at Fluid-Fluid Interfaces

Self-assembly of faceted nanoparticles is a promising route for fabricating nanomaterials; however, achieving low-dimensional assemblies of particles with tunable orientations is challenging. Here, we demonstrate that trapping surface-functionalized faceted nanoparticles at fluid-fluid interfaces is a viable approach for controlling particle orientation and facilitating their assembly into unique one- and two-dimensional superstructures. Using molecular dynamics simulations of polymer-grafted nanocubes in a polymer bilayer along with a particle-orientation classification method we developed, we show that the nanocubes can be induced into face-up, edge-up, or vertex-up orientations by tuning the graft density and differences in their miscibility with the two polymer layers. The orientational preference of the nanocubes is found to be governed by an interplay between the interfacial area occluded by the particle, the difference in interactions of the grafts with the two layers, and the stretching and intercalation of grafts at the interface. The resulting orientationally constrained nanocubes are then shown to assemble into a variety of unusual architectures, such as rectilinear strings, close-packed sheets, bilayer ribbons, and perforated sheets, which are difficult to obtain using other assembly methods. Our work thus demonstrates a versatile strategy for assembling freestanding arrays of faceted nanoparticles with possible applications in plasmonics, optics, catalysis, and membranes, where precise control over particle orientation and position is required.

Modeling of effective interactions between ligand coated nanoparticles through symmetry functions

Ligand coated nanoparticles are complex objects consisting of a metallic or semiconductor core with organic ligands grafted on their surface. These organic ligands provide stability to a nanoparticle suspension. In solutions, the effective interactions between such nanoparticles are mediated through a complex interplay of interactions between the nanoparticle cores, the surrounding ligands, and the solvent molecules. While it is possible to compute these interactions using fully atomistic molecular simulations, such computations are too expensive for studying self-assembly of a large number of nanoparticles. The problem can be made tractable by removing the degrees of freedom associated with the ligand chains and solvent molecules and using the potentials of mean force (PMF) between nanoparticles. In general, the functional dependence of the PMF on the inter-particle distance is unknown and can be quite complex. In this article, we present a method to model the two-body and three-body PMF between ligand coated nanoparticles through a linear combination of symmetry functions. The method is quite general and can be extended to model interactions between different types of macromolecules.

Functional nanoparticle reinforced starch-based adhesive emulsion: Toward robust stability and high bonding performance

Sustainable bio-based adhesive is a promising substitute for petroleum-based adhesives to alleviate serious environmental and health problems. In this work, a nanoengineered starch-based adhesive was fabricated by grafting vinyl acetate (VAc) onto starch molecule and subsequently incorporating the functional nanoparticle [TiO₂-coupling-poly(butyl acrylate, BA), TKB] to overcome the drawbacks present in conventional nanocomposite adhesive. Results showed that the presence of BA altered the surface property of TKB, leading to improved dispersion. In the adhesive with 4% (mass ratio to starch) TKB, TKB aggregates played the role as a sliding bridge, which significantly promoted the storage stability and shear strength in both dry and wet states. Additionally, the latex film with 4% TKB exhibited high compatibility and water resistance due to the promoted hydrophobicity. This study provides a fundamental insight into the improvement of functional nanoparticles on the performance of starch-based adhesive, suggesting a novel strategy for designing high-performance bio-adhesive.

Analytical van der Waals interaction potential for faceted nanoparticles

Our ability to synthesize faceted nanoparticles of tunable shapes and sizes has opened up many intriguing applications of such particles. However, our progress in understanding, modeling, and simulating their collective rheology, phase behavior, and self-assembly has been hindered by the lack of analytical interparticle interaction potentials. Here, we present one of the first analytical models for the van der Waals interaction energy between faceted nanoparticles. The model was derived through various approximations that reduce the usual six-dimensional integral over particle volumes to a series of two-dimensional integrals over particle interaction areas with closed-form solutions. Comparison and analyses of energies obtained from the analytical model with those computed from exact atomistic calculations show that the model approximations lead to insignificant errors in predicted energies across all relevant particle configurations. We demonstrate that the model yields accurate energies for diverse particle shapes including nanocubes, triangular prisms, faceted rods, and square pyramids, while yielding many orders of magnitude improvement in computational efficiency compared to atomistic calculations. To make the model more accessible and to demonstrate its applicability, an open-source graphical user interface application implementing the model for nanocubes in arbitrary configurations has been developed. We expect that the analytical model will accelerate future investigations of faceted nanoparticles that require accurate calculation of interparticle interactions.

Kinetically assembled binary nanoparticle networks

Embedding percolating networks of nanoparticles (NPs) within polymers is a promising approach for mechanically reinforcing polymers and for introducing novel electronic, transport, and catalytic properties into otherwise inert polymers. While such networks may be obtained through kinetic assembly of unary system of NPs, the ensuing structures exhibit limited morphologies. Here, we investigate the possibility of increasing the diversity of NP networks through kinetic assembly of multiple species of NPs. Using lattice Monte Carlo simulations we show that networks obtained from co-assembly of two NP species of different sizes exhibit significantly more diverse morphology than those assembled from a single species. In particular, we achieved considerable variations in the particle spatial distribution, proportions of intra- and interspecies contacts, fractal dimension, and pore sizes of the networks by simply modulating the stoichiometry of the two species and their intra and inter-species affinities. We classified these distinct morphologies into "integrated", "coated", "leaved", and "blocked" phases, and provide relevant phase diagrams for achieving them. Our findings are relevant to controlled and predictable assembly of particle networks for creating multifunctional composites with improved properties.

Orientational phase behavior of polymer-grafted nanocubes

Surface functionalization of nanoparticles with polymer grafts was recently shown to be a viable strategy for controlling the relative orientation of shaped nanoparticles in their higher-order assemblies. In this study, we investigated in silico the orientational phase behavior of coplanar polymer-grafted nanocubes confined in a thin film. We first used Monte Carlo simulations to compute the two-particle interaction free-energy landscape of the nanocubes and identify their globally stable configurations. The nanocubes were found to exhibit four stable phases: those with edge-edge and face-face orientations, and those exhibiting partially overlapped slanted and parallel faces previously assumed to be metastable. Moreover, the edge-edge configuration originally thought to involve kissing edges instead displayed partly overlapping edges, where the extent of the overlap depends on the attachment positions of the grafts. We next formulated analytical scaling expressions for the free energies of the identified configurations, which were used for constructing a comprehensive phase diagram of nanocube orientation in a multidimensional parameter space comprising of the size and interaction strength of the nanocubes and the Kuhn length and surface density of the grafts. The morphology of the phase diagram was shown to arise from an interplay between polymer- and surface-mediated interactions, especially differences in their scalings with respect to nanocube size and grafting density across the four phases. The phase diagram provided insights into tuning these interactions through the various parameters of the system for achieving target configurations. Overall, this work provides a framework for predicting and engineering interparticle configurations, with possible applications in plasmonic nanocomposites where control over particle orientation is critical.

Multiscale Self-Assembly of Mobile-Ligand Molecular Nanoparticles for Hierarchical Nanocomposites

Multiscale hierarchical morphologies are greatly desired for fabricating nanocomposites with tunable macroscopic properties, but challenges remain in precisely manipulating the spatial arrangement of nanoparticles in polymer matrices across multiple length scales. Here, we demonstrate a class of mobile-ligand nanoparticle system built upon 1 nm anionic polyoxometalate molecular nanoparticles and cationic terminated polymer chains by electrostatic interaction. The highly rearrangeable polymer chains can serve as mobile ligands to direct the polyoxometalates to align into sub-10 nm anisotropic superlattice-like nanoarrays in the bulk state. Moreover, these nanoarrays can further serve as structural units to assemble into hierarchically ordered morphologies in polymer matrices, e.g., percolated networks over hundreds of micrometers which are comprised of cylindrically packed polyoxometalate superlattices down to sub-10 nm scale. These hierarchical morphologies enable the nanocomposites with reinforced mechanical performance. The presented mobile-ligand approach can provide a paradigm to design functional polymer nanocomposites with improved properties such as mechanical reinforcement and collective optical and electronic functions.

Interfacial Assembly of Tunable Anisotropic Nanoparticle Architectures

We propose a strategy for assembling spherical nanoparticles (NPs) into anisotropic architectures in a polymer matrix. The approach takes advantage of the interfacial tension between two mutually immiscible polymers forming a bilayer and differences in the compatibility of the two polymer layers with polymer grafts on particles to trap NPs within two-dimensional planes parallel to the interface. The ability to precisely tune the location of the entrapment planes via the NP grafting density, and to trap multiple interacting particles within distinct planes, can then be used to assemble NPs into unconventional arrangements near the interface. We carry out molecular dynamics simulations of polymer-grafted NPs in a polymer bilayer to demonstrate the viability of the proposed approach in both trapping NPs at tunable distances from the interface and assembling them into a variety of unusual nanostructures. We illustrate the assembly of NP clusters, such as dimers with tunable tilt relative to the interface and trimers with tunable bending angle, as well as anisotropic macroscopic phases, including serpentine and branched structures, ridged hexagonal monolayers, and square-ordered bilayers. We also develop a theoretical model to predict the preferred positions and free energies of NPs trapped at or near the interface that could help guide the design of polymer-grafted NPs for achieving target NP architectures. Overall, this work suggests that interfacial assembly of NPs could be a promising approach for fabricating next-generation polymer nanocomposites with potential applications in plasmonics, electronics, optics, and catalysis where precise arrangement of polymer-embedded NPs is required for function.

Stepwise self-assembly of a block copolymer-platinum(ii) complex hybrid in solvents of variable quality: from worm-like micelles to free-standing sheets to vesicle-like nanostructures

The self-assembly process of formation of worm-like micelles of a block copolymer-platinum(ii) complex hybrid is investigated with respect to the influence of solvent quality. When the solvent quality is moderately weakened, unilamellar free-standing sheets are achieved, in which the worm-like micelles snap off to form star micelles together with a few short worms. Extremely worsened solvent quality leads to unilamellar vesicle-like nanostructures, onto which only star micelles emerged. With the intermediate solvent quality, the sheets coexist with the vesicle-like nanostructures. This is well correlated with mechanistic insights regarding the morphological transition from sheet- to vesicle-like nanoassemblies. In these aggregates, short worms and star micelles still hold their core-shell structures. Furthermore, these unconventional superstructures are well interrelated with their luminescence properties. This result challenges the conventional paradigm of the amphiphilic self-assembly of surfactants and block copolymers in selective solvents, where they form bilayered nanostructures and are required universally to be rearranged during the morphological transition from micelles to vesicles.