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Colloidal crystals have applications in water treatments, including water purification and desalination technologies. It is, therefore, important to understand the interactions between colloids as a function of electrolyte concentration. We study the assembly of DNA-grafted gold nanoparticles immersed in concentrated electrolyte solutions. Increasing the concentration of divalent Ca 2+ ions leads to the condensation of nanoparticles into face-centered-cubic (FCC) crystals at low electrolyte concentrations. As the electrolyte concentration increases, the system undergoes a phase change to body-centered-cubic (BCC) crystals. This phase change occurs as the interparticle distance decreases. Molecular dynamics analysis suggests that the interparticle interactions change from strongly repulsive to short-range attractive as the divalent-electrolyte concentration increases. A thermodynamic analysis suggests that increasing the salt concentration leads to significant dehydration of the nanoparticle environment. We conjecture that the intercolloid attractive interactions and dehydrated states favour the BCC structure. Our results gain insight into salting out of colloids such as proteins as the concentration of salt increases in the solution.

Anisotropic colloidal crystals are materials with novel optical and electronic properties. However, experimental observations of colloidal single crystals have been limited to relatively isotropic habits. Here, we show DNA-mediated crystallization of two types of nanoparticles with different hydrodynamic radii that form highly anisotropic, hexagonal prism microcrystals with AB 2 crystallographic symmetry. The DNA directs the nanoparticles to assemble into a non-equilibrium crystal shape that is enclosed by the highest surface energy facets (AB 2 (10[Formula: see text]0) and AB 2 (0001)). Simulations and theoretical arguments show that this observation is a consequence of large energy barriers between different terminations of the AB 2 (10[Formula: see text]0) facet, which results in a significant deceleration of the (10[Formula: see text]0) facet growth rate. In addition to reporting a hexagonal colloidal crystal habit, this work introduces a potentially general plane multiplicity mechanism for growing non-equilibrium crystal shapes, an advance that will be useful for designing colloidal crystal habits with important applications in both optics and photocatalysis.

Epitaxial growth of DNA-functionalized nanoparticles is used to grow extended superlattices with a preferred orientation for optimizing the physical properties of metamaterials for real applications. Like any solid in nature, superlattices can contain different kinds of structural defects, which significantly alter their physical properties. Further development of these materials requires a deeper understanding of, as well as precise control over, structural defect formation. Here we use Monte Carlo simulations to conduct a systematic study of the equilibrium structures of the adsorbed nanoparticle monolayers by changing the binding energies of different attachment sites. The simulations show two main results. First, the structural defects form one-dimensional clusters with an exponential length distribution. Second, these linear defects exhibit spontaneous symmetry breaking and undergo a liquid crystal phase transition. Subsequently, a mean-field approach is introduced to provide theoretical descriptions for the system. Our theory matches with the simulation results. We anticipate that this theoretical framework will be highly applicable to other two-dimensional assemblies. Our work demonstrates that defects can be engineered to design two-dimensional superlattices with interesting physical properties.

Colloidal crystallization can be programmed using building blocks consisting of a nanoparticle core and DNA bonds to form materials with controlled crystal symmetry, lattice parameters, stoichiometry, and dimensionality. Despite this diversity of colloidal crystal structures, only spherical nanoparticles crystallized with BCC symmetry experimentally yield single crystals with well-defined crystal habits. Here, we use low-symmetry, anisotropic nanoparticles to overcome this limitation and to access single crystals with different equilibrium Wulff shapes: a cubic habit from cube-shaped nanoparticles, a rhombic dodecahedron habit from octahedron-shaped nanoparticles, and an octahedron habit from rhombic dodecahedron-shaped nanoparticles. The observation that one can control the microscopic shape of single crystals based upon control of particle building block and crystal symmetry has important fundamental and technological implications for this novel class of colloidal matter.

In this work, we present a joint experimental and molecular dynamics simulations effort to understand and map the crystallization behavior of polyhedral nanoparticles assembled via the interaction of DNA surface ligands. In these systems, we systematically investigated the interplay between the effects of particle core (via the particle symmetry and particle size) and ligands (via the ligand length) on crystallization behavior. This investigation revealed rich phase diagrams, previously unobserved phase transitions in polyhedral crystallization behavior, and an unexpected symmetry breaking in the ligand distribution on a particle surface. To understand these results, we introduce the concept of a zone of anisotropy, or the portion of the phase space where the anisotropy of the particle is preserved in the crystallization behavior. Through comparison of the zone of anisotropy for each particle we develop a foundational roadmap to guide future investigations., Competing Interests: The authors declare no conflict of interest.

Surface  energy is a fundamental material property that determines important functions such as catalytic, sensing, and imaging properties. Over the past century, various experimental studies and models including the broken bond theory and Wulff construction have been developed to analyze surface  free energies. However, it remains a challenge to measure or predict thermal fluctuation effects on surface  energies. In particular, crystals of functionalized building blocks, such as self-assembling proteins and DNA-functionalized nanoparticles, assembled via the specific surface interactions of the building blocks, are highly sensitive to thermal fluctuations. In the case of DNA-functionalized nanoparticles, it has been shown that the crystals are formed as a result of thermally active hybridizations. We show here that the surface  energy along different planes can be obtained from the ratio of hybridization events. The surface  energy fluctuations in these systems are shown to bear a nearly linear correlation with the fluctuations in DNA hybridization events in the bulk. We further demonstrate that short DNA chains and high DNA loading increase the volume density of the DNA sticky ends. The relationship between thermally active hybridizations and surface  energy found here can be used to aid the design of single crystals of functionalized colloids with active surface groups.

Herein, we report an example of entropy-driven crystallization behavior in DNA-nanoparticle superlattice assembly, marking a divergence from the well-established enthalpic driving force of maximizing nearest-neighbor hybridization connections. Such behavior is manifested in the observation of a non-close-packed, body-centered cubic (bcc) superlattice when using a system with self-complementary DNA linkers that would be predicted to form a close-packed, face-centered cubic (fcc) structure based solely on enthalpic considerations and previous design rules for DNA-linked particle assembly. Notably, this unexpected phase behavior is only observed when employing long DNA linkers with unpaired "flexor" bases positioned along the length of the DNA linker that increase the number of microstates available to the DNA ligands. A range of design conditions are tested showing sudden onsets of this behavior, and these experiments are coupled with coarse-grained molecular dynamics simulations to show that this entropy-driven crystallization behavior is due to the accessibility of additional microstates afforded by using long and flexible linkers.

Small nanoparticles, globular proteins, viral capsids, and other nanoscopic biomolecules usually display dielectric properties that are different from those of the medium in which they are dispersed. These dielectric heterogeneities can significantly influence the surrounding ion distribution, which determines the self-assembly and colloidal stability of these nanoparticles in solution. Here, we study the impact of a dielectric discontinuity in the structural and thermodynamic properties of a spherical nanoparticle made of different dielectric materials when it is immersed in a charge-asymmetric 1:z supporting electrolyte. The mean electrostatic potential, integrated charge, and ionic profiles are analyzed as a function of both the salt concentration and the nanoparticle's valence via Monte Carlo simulations and the nonlinear Poisson-Boltzmann theory. We observe that the electrostatic screening and charge neutralization near the surface of a nanoparticle increase when the nanoparticle's dielectric permittivity increases in all instances. For 1:1 salts, this effect is small and the nonlinear Poisson-Boltzmann theory displays a good agreement with simulation results. Nevertheless, significant deviations are displayed by the mean field scheme regarding simulation results in the presence of multivalent ions. In particular, for trivalent counterions we observe that increasing the dielectric permittivity or the valence of the nanoparticle decreases the critical salt concentration at which occurs a sign inversion of the mean electrostatic potential at the Helmholtz plane, which is closely related to the behavior of the ζ potential and the electrophoretic mobility. Moreover, we observe that the phenomenon of surface charge amplification, or the augmenting of the net charge of a nanoparticle by the adsorption of like-charged ions on its surface, can be promoted by polarization effects in weakly charged spherical nanoparticles with low dielectric permittivity.

The radial distribution of monovalent cations surrounding spherical nucleic acid-Au nanoparticle conjugates (SNA-AuNPs) is determined by in situ small-angle x-ray scattering (SAXS) and classical density functional theory (DFT) calculations. Small differences in SAXS intensity profiles from SNA-AuNPs dispersed in a series of solutions containing different monovalent ions (Na(+), K(+), Rb(+), or Cs(+)) are measured. Using the "heavy ion replacement" SAXS (HIRSAXS) approach, we extract the cation-distribution-dependent contribution to the SAXS intensity and show that it agrees with DFT predictions. The experiment-theory comparisons reveal the radial distribution of cations as well as the conformation of the DNA in the SNA shell. The analysis shows an enhancement to the average cation concentration in the SNA shell that can be up to 15-fold, depending on the bulk solution ionic concentration. The study demonstrates the feasibility of HIRSAXS in probing the distribution of monovalent cations surrounding nanoparticles with an electron dense core (e.g., metals).

Spherical nucleic acid (SNA) nanostructures assemble into a large variety of well-defined crystalline superlattices via DNA-directed hybridization. Crystallities of SNA with various shapes emerge during the assembly process, which coalesce during coarsening, leading to polycrystalline materials. Here, we investigate the growth dynamics of SNAs into body-centered cubic superlattices and the coalescence of SNA aggregates using a colloidal model formulated from the competition of electrostatic core repulsions and localized DNA hybridization attractions. We find that the growth law of isolated SNA crystallities is well-described by the power law t(1/2), in agreement with experimental observations. At later times, coalescence slows the growth dynamics considerably and is dependent on the orientational mismatch (misorientation angle) of the coalescing crystallites. Molecular dynamics simulations show that the misorientation angle decreases continually during the coalescence, which is a signature of the grain rotation induced coalescence mechanism. This mechanism is followed by the coarsening of a "neck" that develops at the boundary between the coalescing crystallites. Remarkably, we find faster coalescence dynamics for larger SNAs compared to smaller SNAs due to their enhanced surface diffusion, which more effectively reduces curvature at the boundary of two superlattices. These findings provide fundamental insight into the relationship between nanoparticle surface chemistry and its crystallite growth and coalescence.

Colloidal particles are ubiquitous in biology and in everyday products such as milk, cosmetics, lubricants, paints, or drugs. The stability and aggregation of colloidal suspensions are of paramount importance in nature and in diverse nanotechnological applications, including the fabrication of photonic materials and scaffolds for biological assemblies, gene therapy, diagnostics, targeted drug delivery, and molecular labeling. Electrolyte solutions have been extensively used to stabilize and direct the assembly of colloidal particles. In electrolytes, the effective electrostatic interactions among the suspended colloids can be changed over various length scales by tuning the ionic concentration. However, a major limitation is gelation or flocculation at high salt concentrations. This is explained by classical theories, which show that the electrostatic repulsion among charged colloids is significantly reduced at high electrolyte concentrations. As a result, these screened colloidal particles are expected to aggregate due to short-range attractive interactions or dispersion forces as the salt concentration increases. We discuss here a robust, tunable mechanism for colloidal stability by which large counterions prevent highly charged nanoparticles from aggregating in salt solutions with concentrations up to 1 M. Large counterions are shown to generate a thicker ionic cloud in the proximity of each charged colloid, which strengthens short-range repulsions among colloidal particles and also increases the corresponding renormalized colloidal charge perceived at larger separation distances. These effects thus provide a reliable stabilization mechanism in a broad range of biological and synthetic colloidal suspensions.

The selectivity of DNA recognition inspires an elegant protocol for designing versatile nanoparticle (NP) assemblies. We use molecular dynamics simulations to analyze dynamic aspects of the assembly process and identify ingredients that are key to a successful assembly of NP superlattices through DNA hybridization. A scale-accurate coarse-grained model faithfully captures the relevant contributions to the kinetics of the DNA hybridization process and is able to recover all experimentally reported to date binary superlattices (BCC, CsCl, AlB2, Cr3Si, and Cs6C60). We study the assembly mechanism in systems with up to 10(6) degrees of freedom and find that the crystallization process is accompanied with a slight decrease of enthalpy. Furthermore, we find that the optimal range of the DNA linker interaction strengths for a successful assembly is 12-16kBT, and the optimal mean lifetime of a DNA hybridization event is 10(-4)-10(-3) of the total time it takes to form a crystal. We also obtain the optimal percentage of hybridized DNA pairs for different binary systems. On the basis of these results, we propose suitable linker sequences for future nanomaterials design.

Motivated by recent experimental findings, we present here a minimal analytical model illustrating that the steric interactions among the ionic components can provide a simple, generic mechanism for like-charge crystallization in prototypical nanoparticle systems with counterions in polar solvents. In particular, the underlying steric interactions among these ionic components arise from the structural organization of the polar solvent molecules surrounding these ions as molecular dipole moments that may cooperatively enhance or counteract existing entropic depletion and electrostatic forces. Phenomenologically capturing these steric effects, we assume only the existence of a short-range pairwise Gaussian interaction, which has already been employed usefully for nanoparticles with hydrophillic surfaces or grafted-polymer coatings, among these ionic components (nanoparticles and counterions). The corresponding Gaussian interaction parameters characterize tunable interaction strengths. Making use of an analytically obtained effective pairwise potential between two nanoparticles, upon the contraction of counterions, we derive phase diagrams for nanoparticle systems of varying charge- and size-ratios as a function of particle densities, and observe crystallization for a range of parameters. We further demonstrate that our minimal model is compatible with the phenomenon of charge asymmetry.

Controlling interactions between proteins and nanoparticles in electrolyte solutions is crucial for advancing biological sciences and biotechnology. The assembly of charged nanoparticles (NPs) and proteins in aqueous solutions can be directed by modifying the salt concentration. High concentrations of monovalent salt can induce the solubilization or crystallization of NPs and proteins. By using a multiscale coarse-grained molecular dynamics approach, we show that, due to ionic correlations in the electrolyte, NPs pairs at high monovalent salt concentrations interact via remarkably strong long-range attractions or repulsions, which can be split into three regimes depending on the surface charge densities of the NPs. NPs with zero-to-low surface charge densities interact via a long-range attraction that is stronger and has a similar range to the depletion attraction induced by polymers with radius of gyrations comparable to the NP diameter. On the other hand, moderately charged NPs with smooth surfaces as well as DNA-functionalized NPs with no possibility of hybridization between them interact via a strong repulsion of range and strength larger than the repulsion predicted by models that neglect ionic correlations, including the Derjaguin-Landau-Vervey-Overbeek (DLVO) model. Interactions between strongly charged NPs (>2 e/nm²), both types smooth and DNA-functionalized NPs, show an attractive potential well at intermediate-to-high salt concentrations, which demonstrates that electrolytes can induce aggregation of strongly charged NPs. Our work provides an improved understanding of the role of ionic correlations in NP assembly and design rules to utilize the salting-out process to crystallize NPs. [ABSTRACT FROM AUTHOR]

Herein, we investigate the use of proteins with tunable DNA modification distributions to modulate nanoparticle superlattice structure. Using beta-galactosidase (βgal) as a model system, we have employed the orthogonal chemical reactivities of surface amines and thiols to synthesize protein-DNA conjugates with 36 evenly distributed or 8 specifically positioned oligonucleotides. When these are assembled into crystalline superlattices with gold nanoparticles, we find that the distribution of DNA modifications modulates the favored structure: βgal with uniformly distributed DNA bonding elements results in body-centered cubic crystals, whereas DNA functionalization of cysteines results in AB2 packing. We probe the role of protein oligonucleotide number and conjugate size on this observation, which revealed the importance of oligonucleotide distribution in this observed assembly behavior. These results indicate that proteins with defined DNA modification patterns are powerful tools for controlling nanoparticle superlattices architecture, and establish the importance of oligonucleotide distribution in the assembly behavior of protein-DNA conjugates. [ABSTRACT FROM AUTHOR]