Icosahedral packing of polymer-tethered nanospheres and stabilization of the gyroid phase

Effect of shape anisotropy on the precipitation of dimeric nanoparticles

We use grand canonical transition matrix Monte Carlo simulations to study the precipitation of dimeric nanoparticles. The dimers are composed of two particles having different chemical features and separated by a fixed distance. The non-attractive and attractive parts of the dimer are modeled using hard-sphere and square-well potentials, respectively. The shape anisotropy is altered by changing the relative sizes of the two particles. We observe that the stability of the nanosuspension increases with the increase in the size of the non-attractive part of the dimer. The precipitates of dimers having larger non-attractive parts have lower packing densities, contain large cavities, and show evidence of self-assembly in the bulk and on the surface. We also use the results from our simulations and the classical nucleation theory to study the kinetics of precipitation. At a given temperature and relative supersaturation, the rate of homogeneous nucleation increases with the increase in the size of the non-attractive parts. Finally, we use an example to show how our results can guide the design of nanosuspensions containing chemically anisotropic dimers that are stable under particular conditions.

Deep learning potential of mean force between polymer grafted nanoparticles

Grafting polymer chains on the surfaces of nanoparticles is a well-known route to control their self-assembly and distribution in a polymer matrix. A wide variety of self-assembled structures are achieved by changing the grafting patterns on the surface of an individual nanoparticle. However, an accurate estimation of the effective potential of mean force between a pair of grafted nanoparticles that determines their assembly and distribution in a polymer matrix is an outstanding challenge in nanoscience. We address this problem via deep learning. As a proof of concept, here we report a deep learning framework that learns the interaction between a pair of single-chain grafted spherical nanoparticles from their molecular dynamics trajectory. Subsequently, we carry out the deep learning potential of mean force-based molecular simulation that predicts the self-assembly of a large number of single-chain grafted nanoparticles into various anisotropic superstructures, including percolating networks and bilayers depending on the nanoparticle concentration in three-dimensions. The deep learning potential of mean force-predicted self-assembled superstructures are consistent with the actual superstructures of single-chain polymer grafted spherical nanoparticles. This deep learning framework is very generic and extensible to more complex systems including multiple-chain grafted nanoparticles. We expect that this deep learning approach will accelerate the characterization and prediction of the self-assembly and phase behaviour of polymer-grafted and unfunctionalized nanoparticles in free space or a polymer matrix.

The emergence of valency in colloidal crystals through electron equivalents

Colloidal crystal engineering of complex, low-symmetry architectures is challenging when isotropic building blocks are assembled. Here we describe an approach to generating such structures based upon programmable atom equivalents (nanoparticles functionalized with many DNA strands) and mobile electron equivalents (small particles functionalized with a low number of DNA strands complementary to the programmable atom equivalents). Under appropriate conditions, the spatial distribution of the electron equivalents breaks the symmetry of isotropic programmable atom equivalents, akin to the anisotropic distribution of valence electrons or coordination sites around a metal atom, leading to a set of well-defined coordination geometries and access to three new low-symmetry crystalline phases. All three phases represent the first examples of colloidal crystals, with two of them having elemental analogues (body-centred tetragonal and high-pressure gallium), while the third (triple double-gyroid structure) has no known natural equivalent. This approach enables the creation of complex, low-symmetry colloidal crystals that might find use in various technologies.

Following the nucleation pathway from disordered liquid to gyroid mesophase

Mesophases have order intermediate between liquids and crystals and arise in systems with frustration, such as surfactants, block copolymers, and Janus nanoparticles. The gyroid mesophase contains two interpenetrated, nonintersecting chiral networks that give it properties useful for photonics. It is challenging to nucleate a gyroid from the liquid. Elucidating the reaction coordinate for gyroid nucleation could assist in designing additives that facilitate the formation of the mesophase. However, the complexity of the gyroid structure and the extreme weakness of the first-order liquid to gyroid transition make this a challenging quest. Here, we investigate the pathway and transition states for the nucleation of a gyroid from the liquid in molecular simulations with a mesogenic binary mixture. We find that the gyroid nuclei at the transition states have a large degree of positional disorder and are not compact, consistent with the low surface free energy of the liquid-gyroid interface. A combination of bond-order parameters for the minor component is best to describe the passage from liquid to gyroid, among those we consider. The committor analyses, however, show that this best coordinate is not perfect and suggests that accounting for the relative ordering of the two interpenetrated networks in infant nuclei, as well as for signatures of ordering in the major component of the mesophase, would improve the accuracy of the reaction coordinate for gyroid formation and its use to evaluate nucleation barriers. To our knowledge, this study is the first to investigate the reaction coordinate and critical nuclei for the formation of any mesophase from an amorphous phase.

Molecular dynamics simulations of mono-tethered particles at solid surfaces

We use molecular dynamics simulations to study the behavior of mono-tethered nanoparticles on solid surfaces. In our model particle-particle and particle-chain interactions are repulsive, while chain-chain interactions are attractive. Two surfaces are considered: the first one attracts particles and the other attracts chains. Excess adsorption isotherms are presented for both the surfaces and different lengths of tethers. The mechanism of adsorption is discussed. We find that depending on the assumed parameters the mono-tethered particles can be adsorbed as single particles or as different aggregates. Our main goal is to explore the structure of surface films. We show that the morphology of the adsorbed layer depends mainly on the type of the surface but the influence of the particle diameter, the chain length and the density is also important. We prove that the shape of aggregates changes near the substrate. For certain parameters the aggregates can break under the influence of the surface.

Why Is Gyroid More Difficult to Nucleate from Disordered Liquids than Lamellar and Hexagonal Mesophases?

Block copolymers, surfactants, and biomolecules form lamellar, hexagonal, and gyroid mesophases. Across these systems, the nucleation of lamellar from the disordered liquid is the easiest and the nucleation of gyroid the most challenging. This poses the question of what are the factors that determine the rates of nucleation of the mesophases and whether they are controlled by the complexity of the structures or the thermodynamics of nucleation. Here, we use molecular simulations to investigate the nucleation and thermodynamics of lamellar, hexagonal, and gyroid in a binary mixture of particles that produces the same mesophases as those of surfactants and block copolymers. We demonstrate that a combination of averaged bond-order parameters q̅₂ and q̅₈ identifies and distinguishes the three mesophases. We use these parameters to track the microscopic process of nucleation of each mesophase and investigate the existence of heterogeneous nucleation (cross-nucleation) between mesophases. We estimate the surface tensions of the liquid/mesophase interfaces from nucleation rates using classical nucleation theory and find that they are comparable for the three mesophases with values that are about a third of those expected for liquid-crystal interfaces. The driving forces for nucleation, on the other hand, are quite different and increase in the order gyroid < hexagonal < lamellar at any temperature. We find that the nucleation rates of the mesophases follow the order of their driving forces. We conclude that the difficulty to nucleate the gyroid originates in its lower temperature of melting and extremely low entropy of melting compared to those of the hexagonal and lamellar mesophases.

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.

Self-assembly of polymer-linked nanoparticles and scaling behavior in the assembled phase

An entropic depletion-driven phase separation is known to be observed for mixtures of polymers and nanoparticles. While polymer-linked nanoparticles have been synthesized, their phase behavior has only been predicted for chemically specific interactions. We use integral equation theory to determine the structure and phase behavior of chemically isotropic polymer-linked nanoparticles at high densities. When each end of a linear polymer is grafted to a nanoparticle, we predict an entropy-driven microphase separation of locally segregated polymer-rich and nanoparticle-rich domains. The formation of these self-assembled structures is purely a consequence of the shape of the polymer-linked particle species. The depletion-driven demixing of ungrafted polymer-nanoparticle composites (with small amounts of nanoparticles) is enhanced as particle diameter (D) grows compared to the polymer radius of gyration (R_g). However, this study shows that for polymer-linked nanoparticle systems, the transition from a liquid to microphase separated state shifts to higher densities (i.e. is inhibited) as D/R_g increases. The transition volume fractions attain a unique value (of ∼0.69) at D/R_g ∼ 1.13. The repeating length scale (L*) is 1.4-2.2 times the size of the entire species (D + R_g). Surprisingly, L*/(D + R_g) is a non-monotonic function of the polymer radius of gyration. The repeating length scale also displays a remarkable scaling behavior, as a function of the particle diameter and the polymer density. Additionally, our study implies that two different mechanisms of transitioning to the microphase separated state are possible for these systems, which has important implications for the transition density and the kinds of structures formed.

Self-Assembly of Colloidal Nanocrystals: From Intricate Structures to Functional Materials

Chemical methods developed over the past two decades enable preparation of colloidal nanocrystals with uniform size and shape. These Brownian objects readily order into superlattices. Recently, the range of accessible inorganic cores and tunable surface chemistries dramatically increased, expanding the set of nanocrystal arrangements experimentally attainable. In this review, we discuss efforts to create next-generation materials via bottom-up organization of nanocrystals with preprogrammed functionality and self-assembly instructions. This process is often driven by both interparticle interactions and the influence of the assembly environment. The introduction provides the reader with a practical overview of nanocrystal synthesis, self-assembly, and superlattice characterization. We then summarize the theory of nanocrystal interactions and examine fundamental principles governing nanocrystal self-assembly from hard and soft particle perspectives borrowed from the comparatively established fields of micrometer colloids and block copolymer assembly. We outline the extensive catalog of superlattices prepared to date using hydrocarbon-capped nanocrystals with spherical, polyhedral, rod, plate, and branched inorganic core shapes, as well as those obtained by mixing combinations thereof. We also provide an overview of structural defects in nanocrystal superlattices. We then explore the unique possibilities offered by leveraging nontraditional surface chemistries and assembly environments to control superlattice structure and produce nonbulk assemblies. We end with a discussion of the unique optical, magnetic, electronic, and catalytic properties of ordered nanocrystal superlattices, and the coming advances required to make use of this new class of solids.

Tube-graft-Sheet Nano-Objects Created by A Stepwise Self-Assembly of Polymer-Polyoxometalate Hybrids

In this work, we report the preparation of complex nano-objects by means of a stepwise self-assembly of two polymer-polyoxometalate hybrids (PPHs) in solution. The PPHs are designed and synthesized by tethering two linear poly(ε-caprolactone)s (PCL) of different molecular weights (MW) on a complex of a Wells-Dawson-type polyoxometalate (POM) cluster and its countraions. The higher MW PCL-POM self-assembled into nanosheets, while the lower MW PCL-POM assembled into nanotubes just by altering the ratio of water in the DMF-water mixed solvent system. The two nano-objects have a similar membrane structure in which a PCL layer is sandwiched by the two POM-based complex layers. The PCL layer in the nanosheets is semicrystalline, while the PCL layer in the nanotubes is amorphous. We further exploited this MW-dependence to self-assemble the nanotubes on the nanosheet edges to create complex tube-graft-sheet nano-objects. We found that the nanotubes nucleate on the four {110} faces of the PCL crystal and then further grow along the crystallographic b-axis of the PCL crystal. Our findings offer hope for the further development of nano-objects with increasing complexity.

Weak links between fast mobility and local structure in molecular and atomic liquids

We investigate by molecular-dynamics simulations, the fast mobility-the rattling amplitude of the particles temporarily trapped by the cage of the neighbors-in mildly supercooled states of dense molecular (linear trimers) and atomic (binary mixtures) liquids. The mixture particles interact by the Lennard-Jones potential. The non-bonded particles of the molecular system are coupled by the more general Mie potential with variable repulsive and attractive exponents in a range which is a characteristic of small n-alkanes and n-alcohols. Possible links between the fast mobility and the geometry of the cage (size and shape) are searched. The correlations on a per-particle basis are rather weak. Instead, if one groups either the particles in fast-mobility subsets or the cages in geometric subsets, the increase of the fast mobility with both the size and the asphericity of the cage is revealed. The observed correlations are weak and differ in states with equal relaxation time. Local forces between a tagged particle and the first-neighbour shell do not correlate with the fast mobility in the molecular liquid. It is concluded that the cage geometry alone is unable to provide a microscopic interpretation of the known, universal link between the fast mobility and the slow structural relaxation. We suggest that the particle fast dynamics is affected by regions beyond the first neighbours, thus supporting the presence of collective, extended fast modes.

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.

Nanoparticle role on the repeatability of stimuli-responsive nanocomposites

Repeatability of the responsiveness with time is one important concern for effective durable functions of stimuli-responsive materials. Although the increase in the yield and tensile strength of the hybrid composite materials by nanoparticle (NP) incorporation has been reported, exact NP effect on stimuli-responsiveness is rarely reported. In this study, a set of nanoscale actuating system is demonstrated by a thermo-sensitive process operated by polyethylene glycol (PEG) linked by gold nanoparticle (AuNP). This designed nanocomposite exclusively provides an artificial on/off gate function for selective passages of permeate molecules. The results demonstrate high repetition efficiency with sharp responding in a timely manner. In terms of the morphology changes induced by repeated swelling-deswelling mechanics, the nanocomposite exhibits phase separation between AuNP clusters and PEG domains. This leads to a delay in responsiveness in a cumulative way with time. Acting as stable junction points in the nanocomposite network structures, the incorporated AuNPs contribute to maintain repeatability in responsiveness. This study contributes to new-concept smart material design and fundamental understanding on the hybrid nanomaterials for various applications in terms of a dynamic mechanical behavior.

Polymer directed aggregation and dispersion of anisotropic nanoparticles

The aggregation and dispersion of two anisotropic nanoparticles (NPs), cubes and tetrahedrons, in a polymer matrix are studied in this work using coarse-grained molecular dynamics simulations. We present the phase diagrams of NP-polymer composites, depicting microscopically phase-separated, dispersed, and bridged cubes and tetrahedrons in a polymer matrix, which depend on the interaction between the NPs and polymer (εnp), along with the NPs' volume fraction (ϕ). The microscopic phase separation occurs at very low εnp, where NPs self-organize into multidimensional structures, depending on ϕ. In particular, for tetrahedrons, a cross-over from an ordered spherical aggregate to a disordered sheet-like aggregate is observed with increasing ϕ. In the case of cubes, a transition from cubic array → square column → square array (sheet) is identified with increasing ϕ. The clusters of NPs are characterized by their asphericity and principal radii of gyration. The free energy profile for a structured assembly is estimated, which clearly shows that the successful assembly of NPs is energetically favorable at a lower temperature. However, there exists an energy barrier for the successful assembly of all the NPs in the system. At intermediate εnp, a transition from a clustered state to a state comprising dispersed cubes and tetrahedrons in a polymer matrix is observed. At higher εnp, a further transition takes place, where gas-like dispersed NPs form a liquid-like aggregate via polymer layers. Therefore, the findings in this work illustrate that the effective interaction between anisotropic NPs in a polymer matrix is very diverse, which can generate multidimensional structured assemblies, with the disordered clustering, dispersion, and bridging-induced aggregation of NPs.

Phase behavior and complex crystal structures of self-assembled tethered nanoparticle telechelics

Motivated by growing interest in the self-assembly of nanoparticles for applications such as photonics, organic photovoltaics, and DNA-assisted designer crystals, we explore the phase behavior of tethered spherical nanoparticles. Here, a polymer tether is used to geometrically constrain a pair of nanoparticles creating a tethered nanoparticle "telechelic". Using simulation, we examine how varying architectural features, such as the size ratio of the two end-group nanospheres and the length of the flexible tether, affects the self-assembled morphologies. We demonstrate not only that this hybrid building block maintains the same phase diversity as linear triblock copolymers, allowing for a variety of nanoparticle materials to replace polymer blocks, but also that new structures not previously reported are accessible. Our findings imply a robust underlying ordering mechanism is common among these systems, thus allowing flexibility in synthesis approaches to achieve a target morphology.

Self-assembly of polymer-grafted nanoparticles in thin films

We use large-scale molecular dynamics simulations with a coarse-grained model to investigate the self-assembly of solvent-free grafted nanoparticles into thin free-standing films. Two important findings are highlighted. First, for appropriately chosen values of system parameters the nanoparticles spontaneously assemble into monolayer thick films. Further, the nanoparticles self-assemble into a variety of morphologies ranging from dispersed particles, finite stripes, long strings, to percolating networks. The main driving force for these morphologies is the competition between strong short-range attractions of the particle cores and long-range entropic repulsions of the grafted chains. The grafted nanoparticle systems provide practical means to realize two-length-scale systems that have been previously seen, using a simple two-dimensional model [G. Malescio and G. Pellicane, Nat. Mater., 2003, 2, 97], to generate a variety of morphologies. However, there are only relatively narrow ranges of interaction strengths and chain lengths for which anisotropic self-assembly is possible.

Theory and simulation studies of effective interactions, phase behavior and morphology in polymer nanocomposites

Polymer nanocomposites are a class of materials that consist of a polymer matrix filled with inorganic/organic nanoscale additives that enhance the inherent macroscopic (mechanical, optical and electronic) properties of the polymer matrix. Over the past few decades such materials have received tremendous attention from experimentalists, theoreticians, and computational scientists. These studies have revealed that the macroscopic properties of polymer nanocomposites depend strongly on the (microscopic) morphology of the constituent nanoscale additives in the polymer matrix. As a consequence, intense research efforts have been directed to understand the relationships between interactions, morphology, and the phase behavior of polymer nanocomposites. Theory and simulations have proven to be useful tools in this regard due to their ability to link molecular level features of the polymer and nanoparticle additives to the resulting morphology within the composite. In this article we review recent theory and simulation studies, presenting briefly the methodological developments underlying PRISM theories, density functional theory, self-consistent field theory approaches, and atomistic and coarse-grained molecular simulations. We first discuss the studies on polymer nanocomposites with bare or un-functionalized nanoparticles as additives, followed by a review of recent work on composites containing polymer grafted or functionalized nanoparticles as additives. We conclude each section with a brief outlook on some potential future directions.

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.

Effect of nanoparticle polydispersity on the self-assembly of polymer tethered nanospheres

Recent simulations predict that aggregating nanospheres functionalized with polymer "tethers" can self-assemble to form a cylinder, perforated lamellae, lamellae, and even the double gyroid phase, which are phases also seen in block copolymer and surfactant systems. Nanoparticle size polydispersity is likely to be a characteristic of these systems. If too high, polydispersity may destabilize a phase. Using multiple thermodynamic paths to explore the phase diagram as a function of temperature and polydispersity, we explore the effect of nanosphere size polydispersity on the phase diagram. We show that in the portions of the phase diagram characterized by an icosahedral local nanoparticle packing motif, a low amount of polydispersity lowers the energy and a large amount of polydispersity raises the energy of the system by disrupting the icosahedral packing. In general, regions of the phase diagram characterized by liquid-like icosahedral packing have high terminal polydispersities from 15% to more than 30%. In the regions of the phase diagram characterized by crystalline local packing, polydispersity raises the energy of the system and induces a phase transition from crystalline to liquid-like ordering within the nanosphere rich regions of the microphase. We find the bilayer crystalline lamellae phase has a terminal polydispersity of 6%, but may still be partially crystalline up to 12%.

Role of polytetrahedral structures in the elongation and rupture of gold nanowires

We report comprehensive high-accuracy molecular dynamics simulations using the ReaxFF force field to explore the structural changes that occur as Au nanowires are elongated, establishing trends as a function of both temperature and nanowire diameter. Our simulations and subsequent quantitative structural analysis reveal that polytetrahedral structures (e.g., icosahedra) form within the "amorphous" neck regions, most prominently for systems with small diameter at high temperature. We demonstrate that the formation of polytetrahedra diminishes the conductance quantization as compared to systems without this structural motif. We demonstrate that use of the ReaxFF force field, fitted to high-accuracy first-principles calculations of Au, combines the accuracy of quantum calculations with the speed of semiempirical methods.

Average relaxation time of internal spectrum for carbosilane dendrimers: nuclear magnetic resonance studies

A new theoretical description of the interior mobility of carbosilane dendrimers has been tested. Experiments were conducted using measurements of the (1)H NMR spin-lattice relaxation time, T(1H), of two-, three- and four-generation carbosilane dendrimers with three different types of terminal groups in dilute chloroform solutions. Temperature dependences of the NMR relaxation rate, 1/T(1H), were obtained for the internal CH(2)-groups of the dendrimers in the range of 1/T(1H) maximum, allowing us to directly evaluate the average time of the internal spectrum for each dendrimer. It was found that the temperature of 1/T(1H) maximum is practically independent of the number of generations, G; therefore, the theoretical prediction was confirmed experimentally. In addition, the average time of the internal spectrum of carbosilane dendrimers was found to be near 0.2 ns at room temperature, and this value correlates well with the values previously obtained for other dendrimer structures using other experimental techniques.

Structural transitions of solvent-free oligomer-grafted nanoparticles

Novel structural transitions of solvent-free oligomer-grafted nanoparticles are investigated by using molecular dynamics simulations of a coarse-grained bead-spring model. Variations in core size and grafting density lead to self-assembly of the nanoparticles into a variety of distinct structures. At the boundaries between different structures, the nanoparticle systems undergo thermoreversible transitions. This structural behavior, which has not been previously reported, deviates significantly from that of simple liquids. The reversible nature of these transitions in solvent-free conditions offers new ways to control self-assembly of nanoparticles at experimentally accessible conditions.

Design of polymer nanocomposites in solution by polymer functionalization

Polymer nanocomposites, materials combining polymers and inorganic components such as nanosized crystallites or nanoparticles have attracted significant attention in recent years. A successful strategy for designing polymer nanocomposites is polymer functionalization via attaching functional groups with specific affinity for the inorganic component. In this paper, a systematic investigation by molecular dynamics of polymer functionalization for design of composites combining nanosize crystallites with multiblock polymers in solution is presented. It is shown that functionalization is an example of active self-assembly, where the resulting polymer nanocomposite exhibits a different type of order than the original pure polymer system (without inorganic components). Optimal polymer architectures and concentrations are identified appropriate for different applications, alongside an in-depth analysis on the origin and stability of the resulting phases as well as its experimental implications.

Coarse-grained models of tethers for fast self-assembly simulations

Long molecular ligands or "tethers" play an important role in the self-assembly of many nanoscale systems. These tethers, whose only interaction may be a hard-core repulsion, contribute significantly to the free energy of the system because of their large conformational entropy. Here, we investigate how simple approximate models can be developed and used to quickly determine the configurations into which tethers will self assemble in nanoscale systems. We derive criteria that determine when these models are expected to be accurate. Finally, we propose a generalized two-body approximation that can be used as a toy model for the self-assembly of tethers in systems of arbitrary geometry and apply this to the self-assembly of self-assembled monolayers on a planar surface. We compare our results to those in the literature obtained via atomistic and dissipative particle dynamics simulations.

Complex crystal structures formed by the self-assembly of ditethered nanospheres

We report the results from a computational study of the self-assembly of amphiphilic ditethered nanospheres using molecular simulation. As a function of the interaction strength and directionality of the tether-tether interactions, we predict the formation of four highly ordered phases not previously reported for nanoparticle systems. We find a double diamond structure comprised of a zinc blende (binary diamond) arrangement of spherical micelles with a complementary diamond network of nanoparticles (ZnS/D), a phase of alternating spherical micelles in a NaCl structure with a complementary simple cubic network of nanoparticles to form an overall crystal structure identical to that of AlCu2Mn (NaCl/SC), an alternating tetragonal ordered cylinder phase with a tetragonal mesh of nanoparticles described by the [8,8,4] Archimedean tiling (TC/T), and an alternating diamond phase in which both diamond networks are formed by the tethers (AD) within a nanoparticle matrix. We compare these structures with those observed in linear and star triblock copolymer systems.