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 C20 and C60, 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. By combining a number of strategies, we were able to achieve a near-perfect yield of the desired structures with a reduced "alphabet" of building blocks. Among those strategies are the following: the use of bending rigidity of the interparticle bond as a control parameter, programming the morphology with a seed architecture, use of chirality-preserving symmetries for reduction of the particle alphabet, and the hierarchic approach.

Nanoparticle Motion in Entangled Melts of Linear and Nonconcatenated Ring Polymers.

The motion of nanoparticles (NPs) in entangled melts of linear polymers and nonconcatenated ring polymers are compared by large-scale molecular dynamics simulations. The comparison provides a paradigm for the effects of polymer architecture on the dynamical coupling between NPs and polymers in nanocomposites. Strongly suppressed motion of NPs with diameter d larger than the entanglement spacing a is observed in a melt of linear polymers before the onset of Fickian NP diffusion. This strong suppression of NP motion occurs progressively as d exceeds a and is related to the hopping diffusion of NPs in the entanglement network. In contrast to the NP motion in linear polymers, the motion of NPs with d > a in ring polymers is not as strongly suppressed prior to Fickian diffusion. The diffusion coefficient D decreases with increasing d much slower in entangled rings than in entangled linear chains. NP motion in entangled nonconcatenated ring polymers is understood through a scaling analysis of the coupling between NP motion and the self-similar entangled dynamics of ring polymers.

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. The cooperativity is a well known feature of many biochemical processes, responsible, e.g., for signaling and regulations in living systems. Here we propose to utilize a similar strategy for high precision self-assembly, and show that DNA-mediated interactions provide a convenient platform for its implementation. In particular, we outline a specific design of a DNA-based complex which we call "DNA spider," that acts as a smart interparticle linker and provides a built-in cooperativity of binding. We demonstrate versatility of the sequential self-assembly based on spider-functionalized particles by designing several mesostructures of increasing complexity and simulating their assembly process. This includes a number of finite and repeating structures, in particular, the so-called tetrahelix and its several derivatives. Due to its generality, this approach allows one to design and successfully self-assemble virtually any structure made of a "GEOMAG" magnetic construction toy, out of nanoparticles. According to our results, once the binding cooperativity is strong enough, the sequential self-assembly becomes essentially error-free.

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. Here we demonstrate the use of charged liquid interfaces for the assembly and reorganization of 2D systems of DNA-coated NPs. The absorption of DNA-coated NPs to the surface is controlled by the interaction between a positively charged lipid layer and the negatively charged DNA shells of particles. At the same time, interparticle interactions are switchable, from electrostatic repulsion between DNA shells to attraction driven by DNA complementarity, by increasing ionic strength. Using in situ surface X-ray scattering methods and ex situ electron microscopy, we reveal the corresponding structural transformation of the NP monolayer, from a hexagonally ordered 2D lattice to string-like clusters and finally to a weakly ordered network of DNA cross-linked particles. Moreover, we demonstrate that the ability to regulate 2D morphology yields control of the interfacial rheological properties of the NP membrane: from viscous to elastic. Theoretical modeling suggests that the structural adaptivity of interparticle DNA linkages plays a crucial role in the observed 2D transformation of DNA-NP systems at liquid interfaces.

From a melt of rings to chromosome territories: the role of topological constraints in genome folding.

We review pro and contra of the hypothesis that generic polymer properties of topological constraints are behind many aspects of chromatin folding in eukaryotic cells. For that purpose, we review, first, recent theoretical and computational findings in polymer physics related to concentrated, topologically simple (unknotted and unlinked) chains or a system of chains. Second, we review recent experimental discoveries related to genome folding. Understanding in these fields is far from complete, but we show how looking at them in parallel sheds new light on both.

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. With numerical simulations, we show that a variety of target mesoscopic objects can be designed and self-assembled in near perfect yield. They include cubes, pyramids, boxes, and even an Empire State Building model. We summarize our findings with a set of design strategies that leads to the successful self-assembly of a wide range of mesostructures.

Rheology of ring polymer melts: from linear contaminants to ring-linear blends.

Ring polymers remain a challenge to our understanding of polymer dynamics. Experiments are difficult to interpret because of the uncertainty in the purity and dispersity of the sample. Using both equilibrium and nonequilibrium molecular dynamics simulations we have investigated the structure, dynamics, and rheology of perfectly controlled ring-linear polymer blends of chains of up to about 14 entanglements per chain, comparable to experimental systems. Linear contaminants increase the zero-shear viscosity of a ring polymer melt by about 10% around one-fifth of their overlap concentration. For equal concentrations of linear and ring polymers, the blend viscosity is about twice that of the pure linear melt. The diffusion coefficient of the rings decreases dramatically, while the linear polymers are mostly unaffected. Our results are supported by a primitive path analysis.

Molecular dynamics simulation study of nonconcatenated ring polymers in a melt. II. Dynamics.

Molecular dynamics simulations were conducted to investigate the dynamic properties of melts of nonconcatenated ring polymers and compared to melts of linear polymers. The longest rings were composed of N = 1600 monomers per chain which corresponds to roughly 57 entanglement lengths for comparable linear polymers. The ring melts were found to diffuse faster than their linear counterparts, with both architectures approximately obeying a D ∼ N(-2.4) scaling law for large N. The mean-square displacement of the center-of-mass of the rings follows a sub-diffusive behavior for times and distances beyond the ring extension [linear span]R(g)(2)[linear span], neither compatible with the Rouse nor the reptation model. The rings relax stress much faster than linear polymers, and the zero-shear viscosity was found to vary as η(0) ∼ N(1.4 ± 0.2) which is much weaker than the N(3.4) behavior of linear chains, not matching any commonly known model for polymer dynamics when compared to the observed mean-square displacements. These findings are discussed in view of the conformational properties of the rings presented in the preceding paper [J. D. Halverson, W. Lee, G. S. Grest, A. Y. Grosberg, and K. Kremer, J. Chem. Phys. 134, 204904 (2011)].

Molecular dynamics simulation study of nonconcatenated ring polymers in a melt. I. Statics.

Molecular dynamics simulations were conducted to investigate the structural properties of melts of nonconcatenated ring polymers and compared to melts of linear polymers. The longest rings were composed of N = 1600 monomers per chain which corresponds to roughly 57 entanglement lengths for comparable linear polymers. For the rings, the radius of gyration squared, [linear span]R(g)(2)[linear span], was found to scale as N(4/5) for an intermediate regime and N(2/3) for the larger rings indicating an overall conformation of a crumpled globule. However, almost all beads of the rings are "surface beads" interacting with beads of other rings, a result also in agreement with a primitive path analysis performed in the next paper [J. D. Halverson, W. Lee, G. S. Grest, A. Y. Grosberg, and K. Kremer, J. Chem. Phys. 134, 204905 (2011)]. Details of the internal conformational properties of the ring and linear polymers as well as their packing are analyzed and compared to current theoretical models.

A molecular dynamics study of the motion of a nanodroplet of pure liquid on a wetting gradient.

The dynamic behavior of a nanodroplet of a pure liquid on a wetting gradient was studied using molecular dynamics simulation. The spontaneous motion of the droplet is induced by a force imbalance at the contact line. We considered a Lennard-Jones system as well as water on a self-assembled monolayer (SAM). The motion of the droplet for the Lennard-Jones case was found to be steady with a simple power law describing its center-of-mass position with time. The behavior of the water droplet was found to depend on the uniformity of the wetting gradient, which was composed of methyl- and hydroxyl-terminated alkanethiol chains on Au(111). When the gradient was nonuniform the droplet was found to become pinned at an intermediate position. However, a uniform gradient with the same overall strength was found to drive a droplet consisting of 2000 water molecules a distance of 25 nm or nearly ten times its initial base radius in tens of nanoseconds. A similar result was obtained for a droplet that was twice as large. Despite the many differences between the Lennard-Jones and water-SAM systems, the two show a similar overall behavior for the motion. Fair agreement was seen between the simulation results for the water droplet speed and the theoretical predictions. When the driving force was corrected for contact angle hysteresis, the agreement was seen to improve.