Nanocrystal Assemblies: Current Advances and Open Problems.

We explore the potential of nanocrystals (a term used equivalently to nanoparticles) as building blocks for nanomaterials, and the current advances and open challenges for fundamental science developments and applications. Nanocrystal assemblies are inherently multiscale, and the generation of revolutionary material properties requires a precise understanding of the relationship between structure and function, the former being determined by classical effects and the latter often by quantum effects. With an emphasis on theory and computation, we discuss challenges that hamper current assembly strategies and to what extent nanocrystal assemblies represent thermodynamic equilibrium or kinetically trapped metastable states.

Emergence of catalytic function in prebiotic information-coding polymers.

Life as we know it relies on the interplay between catalytic activity and information processing carried out by biological polymers. Here we present a plausible pathway by which a pool of prebiotic information-coding oligomers could acquire an early catalytic function, namely sequence-specific cleavage activity. Starting with a system capable of non-enzymatic templated replication, we demonstrate that even non-catalyzed spontaneous cleavage would promote proliferation by generating short fragments that act as primers.

Symmetry-specific characterization of bond orientation order in DNA-assembled nanoparticle lattices.

Bond-orientational order in DNA-assembled nanoparticles lattices is explored with the help of recently introduced Symmetry-specific Bond Order Parameters (SymBOPs). This approach provides a more sensitive analysis of local order than traditional scalar BOPs, facilitating the identification of coherent domains at the single bond level. The present study expands the method initially developed for assemblies of anisotropic particles to the isotropic ones or cases where particle orientation information is unavailable.

Mitigation of SARS-CoV-2 transmission at a large public university.

In Fall 2020, universities saw extensive transmission of SARS-CoV-2 among their populations, threatening health of the university and surrounding communities, and viability of in-person instruction. Here we report a case study at the University of Illinois at Urbana-Champaign, where a multimodal "SHIELD: Target, Test, and Tell" program, with other non-pharmaceutical interventions, was employed to keep classrooms and laboratories open. The program included epidemiological modeling and surveillance, fast/frequent testing using a novel low-cost and scalable saliva-based RT-qPCR assay for SARS-CoV-2 that bypasses RNA extraction, called covidSHIELD, and digital tools for communication and compliance.

Geometric and topological entropies of sphere packing.

We present a statistical mechanical description of randomly packed spherical particles, where the average coordination number is treated as a macroscopic thermodynamic variable. The overall packing entropy is shown to have two contributions: geometric, reflecting statistical weights of individual configurations, and topological, which corresponds to the number of topologically distinct states. Both of them are computed in the thermodynamic limit for isostatic and weakly underconstrained packings in 2D and 3D.

Symmetry-specific orientational order parameters for complex structures.

A comprehensive framework of characterizing complex self-assembled structures with a set of orientational order parameters is presented. It is especially relevant in the context of using anisotropic building blocks with various symmetries. Two classes of tensor order parameters are associated with polyhedral nematic and bond orientational order.

Controlling morphology in hybrid isotropic/patchy particle assemblies.

Brownian dynamics is used to study self-assembly in a hybrid system of isotropic particles (IPs), combined with anisotropic building blocks that represent special "designer particles." Those are modeled as spherical patchy particles (PPs) with binding only allowed between their patches and IPs. In this study, two types of PPs are considered: Octahedral PPs (Oh-PPs) and Square PPs (Sq-PPs), with octahedral and square arrangements of patches, respectively.

Stochastic social behavior coupled to COVID-19 dynamics leads to waves, plateaus, and an endemic state.

It is well recognized that population heterogeneity plays an important role in the spread of epidemics. While individual variations in social activity are often assumed to be persistent, that is, constant in time, here we discuss the consequences of dynamic heterogeneity. By integrating the stochastic dynamics of social activity into traditional epidemiological models, we demonstrate the emergence of a new long timescale governing the epidemic, in broad agreement with empirical data.

Time-dependent heterogeneity leads to transient suppression of the COVID-19 epidemic, not herd immunity.

Epidemics generally spread through a succession of waves that reflect factors on multiple timescales. On short timescales, superspreading events lead to burstiness and overdispersion, whereas long-term persistent heterogeneity in susceptibility is expected to lead to a reduction in both the infection peak and the herd immunity threshold (HIT). Here, we develop a general approach to encompass both timescales, including time variations in individual social activity, and demonstrate how to incorporate them phenomenologically into a wide class of epidemiological models through reparameterization.

Structured sequences emerge from random pool when replicated by templated ligation.

The central question in the origin of life is to understand how structure can emerge from randomness. The Eigen theory of replication states, for sequences that are copied one base at a time, that the replication fidelity has to surpass an error threshold to avoid that replicated specific sequences become random because of the incorporated replication errors [M. Eigen, 58 (10), 465-523 (1971)].

Entropic elasticity and negative thermal expansion in a simple cubic crystal.

While most solids expand when heated, some materials show the opposite behavior: negative thermal expansion (NTE). In polymers and biomolecules, NTE originates from the entropic elasticity of an ideal, freely jointed chain. The origin of NTE in solids has been widely believed to be different.

Onset of natural selection in populations of autocatalytic heteropolymers.

Reduction of information entropy along with ever-increasing complexity is among the key signatures of life. Understanding the onset of such behavior in the early prebiotic world is essential for solving the problem of the origin of life. Here we study a general problem of heteropolymers capable of template-assisted ligation based on Watson-Crick-like hybridization.

Communication: Programmable self-assembly of thin-shell mesostructures.

We study numerically the possibility of programmable self-assembly of various thin-shell architectures. They include clusters isomorphic to fullerenes C and C, finite and infinite sheets, tube-shaped and toroidal mesostructures. Our approach is based on the recently introduced directionally functionalized nanoparticle platform, for which we employ a hybrid technique of Brownian dynamics with stochastic bond formation.

Layer-by-layer assembly of patchy particles as a route to nontrivial structures.

We propose a strategy for robust high-quality self-assembly of nontrivial periodic structures out of patchy particles and investigate it with Brownian dynamics simulations. Its first element is the use of specific patch-patch and shell-shell interactions between the particles, which can be implemented through differential functionalization of patched and shell regions with specific DNA strands. The other key element of our approach is the use of a layer-by-layer protocol that allows one to avoid the formation of undesired random aggregates.

Generic phase diagram of binary superlattices.

Emergence of a large variety of self-assembled superlattices is a dramatic recent trend in the fields of nanoparticle and colloidal sciences. Motivated by this development, we propose a model that combines simplicity with a remarkably rich phase behavior applicable to a wide range of such self-assembled systems. Those systems include nanoparticle and colloidal assemblies driven by DNA-mediated interactions, electrostatics, and possibly, controlled drying.

Self-organized architectures from assorted DNA-framed nanoparticles.

The science of self-assembly has undergone a radical shift from asking questions about why individual components self-organize into ordered structures, to manipulating the resultant order. However, the quest for far-reaching nanomanufacturing requires addressing an even more challenging question: how to form nanoparticle (NP) structures with designed architectures without explicitly prescribing particle positions. Here we report an assembly concept in which building instructions are embedded into NPs via DNA frames.

In situ microscopy of the self-assembly of branched nanocrystals in solution.

Solution-phase self-assembly of nanocrystals into mesoscale structures is a promising strategy for constructing functional materials from nanoscale components. Liquid environments are key to self-assembly since they allow suspended nanocrystals to diffuse and interact freely, but they also complicate experiments. Real-time observations with single-particle resolution could have transformative impact on our understanding of nanocrystal self-assembly.

Sequential programmable self-assembly: Role of cooperative interactions.

We propose a general strategy of "sequential programmable self-assembly" that enables a bottom-up design of arbitrary multi-particle architectures on nano- and microscales. We show that a naive realization of this scheme, based on the pairwise additive interactions between particles, has fundamental limitations that lead to a relatively high error rate. This can be overcome by using cooperative interparticle binding.

Diamond family of nanoparticle superlattices.

Diamond lattices formed by atomic or colloidal elements exhibit remarkable functional properties. However, building such structures via self-assembly has proven to be challenging because of the low packing fraction, sensitivity to bond orientation, and local heterogeneity. We report a strategy for creating a diamond superlattice of nano-objects via self-assembly and demonstrate its experimental realization by assembling two variant diamond lattices, one with and one without atomic analogs.

Chromatic patchy particles: Effects of specific interactions on liquid structure.

We study the structural and thermodynamic properties of patchy particle liquids, with a special focus on the role of "color," i.e., specific interactions between individual patches.

Spontaneous emergence of autocatalytic information-coding polymers.

Self-replicating systems based on information-coding polymers are of crucial importance in biology. They also recently emerged as a paradigm in material design on nano- and micro-scales. We present a general theoretical and numerical analysis of the problem of spontaneous emergence of autocatalysis for heteropolymers capable of template-assisted ligation driven by cyclic changes in the environment.

Two-dimensional DNA-programmable assembly of nanoparticles at liquid interfaces.

DNA-driven assembly of nanoscale objects has emerged as a powerful platform for the creation of materials by design via self-assembly. Recent years have seen much progress in the experimental realization of this approach for three-dimensional systems. In contrast, two-dimensional (2D) programmable nanoparticle (NP) systems are not well explored, in part due to the difficulties in creating such systems.

Precursors of order in aggregates of patchy particles.

We study computationally the local structure of aggregated systems of patchy particles. By calculating the probability distribution functions of various rotational invariants we can identify the precursors of orientation order in amorphous phase. Surprisingly, the strongest signature of local order is observed for four-patch particles with tetrahedral symmetry, not for six-patch particles with the cubic one.

DNA-programmed mesoscopic architecture.

We study the problem of the self-assembly of nanoparticles (NPs) into finite mesoscopic structures with a programmed local morphology and complex overall shape. Our proposed building blocks are NPs that are directionally functionalized with DNA. The combination of directionality and selectivity of interactions allows one to avoid unwanted metastable configurations, which have been shown to lead to slow self-assembly kinetics even in much simpler systems.

Linear mesostructures in DNA--nanorod self-assembly.

The assembly of molecules and nanoscale objects into one-dimensional (1D) structures, such as fibers, tubules, and ribbons, typically results from anisotropic interactions of the constituents. Conversely, we found that a 1D structure can emerge via a very different mechanism, viz, the spontaneous symmetry breaking of underlying interparticle interactions during structure formation. For systems containing DNA-decorated nanoscale rods, this mechanism, driven by flexible DNA chains, results in the formation of 1D ladderlike mesoscale ribbons with a side-by-side rod arrangement.