X-ray scattering is a structural characterization tool that has impacted diverse fields of study. It is unique in its ability to examine materials in real time and under realistic sample environments, enabling researchers to understand morphology at nanometer and angstrom length scales using complementary small and wide angle X-ray scattering (SAXS, WAXS), respectively. Herein, we focus on the use of SAXS to examine nanoscale particulate systems. We provide a theoretical foundation for X-ray scattering, considering both form factor and structure factor, as well as the use of correlation functions, which may be used to determine a particle's size, size distribution, shape, and organization into hierarchical structures. The theory is expanded upon with contemporary use cases. Both transmission and reflection (grazing incidence) geometries are addressed, as well as the combination of SAXS with other X-ray and non-X-ray characterization tools. We conclude with an examination of several key areas of research where X-ray scattering has played a pivotal role, including in situ nanoparticle synthesis, nanoparticle assembly, and operando studies of catalysts and energy storage materials. Throughout this review we highlight the unique capabilities of X-ray scattering for structural characterization of materials in their native environment.

Directional bonding interactions in solid-state atomic lattices dictate the unique symmetries of atomic crystals, resulting in a diverse and complex assortment of three-dimensional structures that exhibit a wide variety of material properties. Methods to create analogous nanoparticle superlattices are beginning to be realized, but the concept of anisotropy is still largely underdeveloped in most particle assembly schemes. Some examples provide interesting methods to take advantage of anisotropic effects, but most are able to make only small clusters or lattices that are limited in crystallinity and especially in lattice parameter programmability. Anisotropic nanoparticles can be used to impart directional bonding interactions on the nanoscale, both through face-selective functionalization of the particle with recognition elements to introduce the concept of valency, and through anisotropic interactions resulting from particle shape. In this work, we examine the concept of inherent shape-directed crystallization in the context of DNA-mediated nanoparticle assembly. Importantly, we show how the anisotropy of these particles can be used to synthesize one-, two- and three-dimensional structures that cannot be made through the assembly of spherical particles.

Crystallization is a fundamental and ubiquitous process much studied over the centuries. But although the crystallization of atoms is fairly well understood, it remains challenging to predict reliably the outcome of molecular crystallization processes that are complicated by various molecular interactions and solvent involvement. This difficulty also applies to nanoparticles: high-quality three-dimensional crystals are mostly produced using drying and sedimentation techniques that are often impossible to rationalize and control to give a desired crystal symmetry, lattice spacing and habit (crystal shape). In principle, DNA-mediated assembly of nanoparticles offers an ideal opportunity for studying nanoparticle crystallization: a well-defined set of rules have been developed to target desired lattice symmetries and lattice constants, and the occurrence of features such as grain boundaries and twinning in DNA superlattices and traditional crystals comprised of molecular or atomic building blocks suggests that similar principles govern their crystallization. But the presence of charged biomolecules, interparticle spacings of tens of nanometres, and the realization so far of only polycrystalline DNA-interconnected nanoparticle superlattices, all suggest that DNA-guided crystallization may differ from traditional crystal growth. Here we show that very slow cooling, over several days, of solutions of complementary-DNA-modified nanoparticles through the melting temperature of the system gives the thermodynamic product with a specific and uniform crystal habit. We find that our nanoparticle assemblies have the Wulff equilibrium crystal structure that is predicted from theoretical considerations and molecular dynamics simulations, thus establishing that DNA hybridization can direct nanoparticle assembly along a pathway that mimics atomic crystallization.

Due to their potential for creating 'designer materials,' the 3D assembly of nanoparticle building blocks into macroscopic structures with well-defi ned order and symmetry remains one of the most important challenges in materials science. [1][2][3][4][5] Furthermore, superlattices consisting of noble-metal nanoparticles have emerged as a new platform for the bottom-up design of plasmonic metamaterials. [6][7][8] The allure of optical metamaterials is that they provide a means for altering the temporal and spatial propagation of electromagnetic fi elds, resulting in materials that exhibit many properties that do not exist in nature. [9][10][11][12][13] With the vast array of nanostructures now synthetically realizable, computational methods play a crucial role in identifying the assemblies that exhibit the most exciting properties. [ 14 ] Once target assemblies are identifi ed, the synthesis of nanometer-scale structures for use at optical and IR wavelengths must be taken into account. Many of the current methods to fabricate metamaterials in the optical range use serial lithographic-based approaches. [ 6 ] The challenge of controlled assembly into well-defi ned architectures has kept bottom-up methods that rely on the self-organization of colloidal metal nanoparticles from being fully explored for metamaterial applications. [ 8 ] DNA-mediated assembly of nanoparticles has the potential to help overcome this challenge. The predictability and programmability of DNA makes it a powerful tool for the rational assembly of plasmonic nanoparticles with tunable nearest-neighbor distances and symmetries. [ 1,[15][16][17][18] Herein, we combine theory and experiment to study a new class of plasmonic superlattices-fi rst using electrodynamics simulations to identify that superlattices of spherical silver nanoparticles (Ag NPs) have the potential to exhibit emergent metamaterial properties, including epsilon-near-zero (ENZ) behavior, [ 13 ] and a region with an 'optically metallic' response.Optically metallic materials are DC insulators that refl ect in the visible spectrum. This behavior can be described as the opposite of the common touch-screen material, indium tin oxide (ITO), which is transparent in the visible spectrum, but conducts electricity. We then synthesize the fi rst examples of silver nanoparticle superlattices using DNA-mediated assembly and characterize their optical properties with both ensemble measurements and measurements of individual superlattices using spectroscopy. Furthermore, we expand beyond monometallic nanoparticle superlattices to create novel binary superlattices of gold and silver nanoparticle building blocks and observe a Fano-like interference between the two components, leading to a signifi cant dampening of the plasmonic response.ENZ materials [ 19 ] are a new class of metamaterials that allow for the tunneling of light through a barrier and present the opportunity for arbitrary phase manipulation of light. [ 13,[20][21][22] With the global progression of optical fi bers and the potential ...

DNA-functionalized gold nanoparticles can be used to induce the formation and control the unit cell parameters of highly ordered face-centered cubic crystal lattices. Nanoparticle spacing increases linearly with longer DNA interconnect length, yielding maximum unit cell parameters of 77 nm and 0.52% inorganic-filled space for the DNA constructs studied. In general, we show that longer DNA connections result in a decrease in the overall crystallinity and order of the lattice due to greater conformational flexibility.

The assembly of DNA-programmable colloidal crystals is presented, where the sizes of nanoparticles used vary from 5 to 80 nm and the lattice parameters of the resulting crystals vary from 25 to 225 nm. A predictable and mathematically definable relationship between particle size and DNA length is demonstrated to dictate the assembly and crystallization processes, creating a set of design rules for DNA-based nanoscale assembly. ** We acknowledge George Schatz for helpful discussions regarding the theoretical calculations of DNA flexibility and relative DNA concentrations in aggregates. C. A. M. acknowledges the NSF-NSEC and the AFOSR for grant support. He also is grateful for a NIH Director's Pioneer Award and an NSSEF Fellowship from the DoD. R. J. M. acknowledges Northwestern University for a Ryan Fellowship. M. R. J.

We present an analysis of the key steps involved in the DNAdirected assembly of nanoparticles into crystallites and polycrystalline aggregates. Additionally, the rate of crystal growth as a function of increased DNA linker length, solution temperature, and self-complementary versus non-self-complementary DNA linker strands (1-versus 2-component systems) has been studied. The data show that the crystals grow via a 3-step process: an initial ''random binding'' phase resulting in disordered DNA-AuNP aggregates, followed by localized reorganization and subsequent growth of crystalline domain size, where the resulting crystals are well-ordered at all subsequent stages of growth.DNA materials ͉ SAXS ͉ self assembly T he chemical and physical properties of most materials are determined by the placement of individual atoms relative to one another (1-4). These atom-atom interactions include forces such as covalent and ionic bonds, Van der Waals forces and London dispersion forces. However, in the field of nanomaterials, the length scales of particle assembly are significantly larger and the assembly process is governed by a more complicated set of interactions (5-7). The tailorable arrangement of nanoscale materials through directed-mechanisms has proven to be the most practical method to create ordered arrangements of nanoparticles in solution (8-15); crystalline nanoparticle aggregates have potential implications for the development of materials with unique plasmonic (16, 17), photonic (18, 19), electrical (20), and magnetic properties (21). Previous strategies developed to create well-ordered nanoscale assemblies have used electrostatic interactions (11, 12), hydrogen bonding networks (10, 13), and peptide recognition properties (9). Over a decade ago, we introduced the concept of synthetically programmable particle assembly through the use of DNA and polyvalent oligonucleotide nanoparticle conjugates (22). Recently, we (23,24) and the Gang group (25) independently used these principles to construct highly-ordered nanoparticle crystallites via DNA hybridization, where crystal type and lattice parameters can be programmed through design of DNA linker.The formation of these crystals involves multiple types of molecular interactions that are highly dependent and predictable based on the DNA base sequence (22,(26)(27)(28), where the hybridization of the DNA linkers drives the crystallization process. Moreover, the ultimate structure formed is typically the one that maximizes the number of hybridization events, and therefore, if enough thermal energy is provided, the system will typically equilibrate to this structure (23,25,29,30). Indeed, only highly-ordered crystalline aggregates present the thermodynamically most stable arrangement of nanoparticles, because they allow for a maximum of nearestneighbor complementary DNA interactions.Previous work has shown that the complexity of the nanoparticle systems studied thus far necessitates significant thermal annealing to create the thermodynamically favorable crystal structu...

Colloidal crystals can be assembled using a variety of entropic, [1][2][3] depletion, [4,5] electrostatic, [6][7][8] or biorecognition forces [9][10][11][12] and provide a convenient model system for studying crystal growth. Although superlattices with diverse geometries can be assembled in solution and on surfaces, the incorporation of specific bonding interactions between particle building blocks and a substrate would significantly enhance control over the growth process. Herein, we use a stepwise growth process to systematically study and control the evolution of a body-centered cubic (bcc) crystalline thinfilm comprised of nanoparticle building blocks functionalized with DNA on a complementary DNA substrate. We examine crystal growth as a function of temperature, number of layers, and substrate-particle bonding interactions. Importantly, the judicious choice of DNA interconnects allows one to tune the interfacial energy between various crystal planes and the substrate, and thereby control crystal orientation and size in a stepwise fashion using chemically programmable attractive forces. This is a unique approach since prior studies involving superlattice assembly typically rely on repulsive interactions between particles to dictate structure, and those that rely on attractive forces (e.g. ionic systems) still maintain repulsive particle-substrate interactions.In addition to providing a model for crystallization, the field of particle assembly has garnered considerable interest because materials generated from ordered particle arrays can have novel optical, [1,3,[13][14][15][16][17] electronic, [13,18] and magnetic properties. [19,20] These properties can be sensitive to the composition, symmetry, and distance between nanoparticles, in addition to the number of layers and orientation. [9,15,16] DNA-mediated nanoparticle crystallization is particularly attractive for preparing these materials because the nanoparticle building blocks can be considered a type of "pro-