Session Q53: Packing, Self-Assembly, and Granular Memory

Cooperative effects in DNA nanotile attachment

In the context of realising a DNA nanotile system capable of exponentially replicating an information string encoded in a tile pattern with the aid of thermal and UV cycling [1], we encountered the problem of predicting the hybridisation transition temperatures of DNA tile pairs with multiple single strand connectors (sticky ends). For the common single-helix hybridisation transition, sufficiently accurate predictions can be derived from SantaLucia's nearest-neighbour parameter analysis [2]. However, the case of several DNA strands hybridising cooperatively while attached to a rigid object is entropically different and we had to develop a method to factor in the resulting phase space restrictions (cf. a similar approach for DNA-covered colloids [3]). We were able to test our thermodynamic model by fluorescently labelling DNA tile pairs with variable numbers of sticky ends and recording the hybridisation transition using FRET. The data fit our prediction within an acceptable parameter range.\\[4pt] [1] T. Wang et al., {\em Nature}, 478(7368):225--228, 2011;\\[0pt] [2] J. SantaLucia, {\em PNAS}, 95(4):1460--1465, 1998\\[0pt] [3] R.~{Dreyfus} et al.; {\em Phys. Rev. Lett.}, 102(4):048301, 2009.   

Minimal energy packings of weakly semiflexible polymers: Application to targeted self-assembly of nanostructures

Using exact enumeration, we characterize how structure, mechanical and thermodynamic stability of minimal energy packings of short ``sticky tangent sphere'' (SHS) polymer chains vary with angular interaction strength $k_b$ and equilibrium bond angle $\theta_0$. While flexible SHS polymers possess highly degenerate ground states (i.\ e.\ many differently ordered ``macrostates'' [1]), angular interactions dramatically break this degeneracy. The macrostate associated with the ground state semiflexible packing changes as $k_b$ and $\theta_0$ are varied. Further degeneracy breaking arises from angular interactions' influence on packing size, asymmetry, and vibrational entropy. The strength of these effects increases with chain length $N$. Our exact analysis provides design principles for self-assembly of polymers into a variety of structures that can be tuned by varying $N$, $k_b$ and $\theta_0$. \\[4pt] [1] R. S. Hoy and C. S. O'Hern, Phys. Rev. Lett. \textbf{105}, 068001 (2010).   

Self-assembly of Low-coordinated Ground States via Monotonic Pair Potentials

Monotonically decreasing radially symmetric pair potentials can lead to the self assembly of unusual low-coordinated ground states. The states include, but are not limited to, the square, honeycomb, and simple cubic crystals in two and three-dimensional Euclidean spaces $R^2$ and $R^3$. We can determine optimal potentials for targeted ground states using inverse statistical mechanical techniques. Using a linear programming method, we are able to search over a wide parameter space while still enforcing constraints such as motonicity and convexity on optimized potentials. The features present in the classes of short-ranged potentials that conform to these constraints suggest sufficient requirements for colloids to self assemble into a desired ground state.   

Dense packings of spheres in cylinders

We develop a simple analytical theory that relates dense hard sphere packings in a cylinder to corresponding disk packings on its surface. It applies for ratios R=D/d (where d and D are the diameters of the hard spheres and the bounding cylinder, respectively) up to R=2.738. Within this range the densest packings are such that all spheres are in contact with the cylindrical boundary. The detailed results elucidate extensive numerical simulations by others and ourselves by identifying the nature of various competing phases. We also present results for the regime R greater than 2.738. These preliminary results explore packings that include internal spheres (i.e. spheres that do not contact the cylinder). This is done through a combination of experiments and numerical simulation (simulated annealing). Our experiments involve the packing of monodisperse bubbles in narrow micron-sized capillaries. Such ``wet foams'' are an excellent model of the hard sphere packing problem and are analyzed by X-ray tomography to provide structural information.   

Novel structures from the densest binary sphere packings

The densest binary sphere packings have historically been very difficult to determine. The only rigorously known packings in the $\alpha$-$x$ plane of small to large sphere radius ratio $\alpha$ and small sphere relative concentration $x$ are at the Kepler limit $\alpha \rightarrow 1$, where packings are monodisperse. Utilizing an implementation of the Torquato-Jiao linear programming algorithm, we find many distinct families of novel densest binary packings and construct a phase diagram for all known densest packings over the $\alpha$-$x$ plane. In particular, these families of densest binary packings are examples of complicated, mechanically stable structures that can appear in colloidal systems without any anisotropic or attractive interactions.   

Random and ordered phases of off-lattice rhombus tiles

We study the covering of the plane by non-overlapping rhombus tiles, a problem well-studied only in the limiting case of dimer coverings of regular lattices. We go beyond this limit by allowing tiles to take any position and orientation on the plane, to be of irregular shape, and to possess different types of attractive interactions. Using extensive numerical simulations we show that at large tile densities there is a phase transition from a fluid of rhombus tiles to a solid packing with broken rotational symmetry. We observe self-assembly of broken-symmetry phases, even at low densities, in the presence of attractive tile-tile interactions. Depending on tile shape and interactions the solid phase can be random, possessing critical orientational fluctuations, or crystalline. Our results suggest strategies for controlling tiling order in experiments involving ``molecular rhombi.''   

Structure and stability of finite sphere packings via exact enumeration

We analyze the geometric structure and mechanical stability of complete sets of isostatic and hyperstatic sphere packings obtained via exact enumeration techniques. The number of nonisomorphic isostatic packings grows exponentially with the number of spheres $N$, and the fraction of packings possessing soft modes (for ``sticky'' spheres with contact attractions) grows faster. The diversity of structure and symmetry increases with $N$ and decreases with the degree of hyperstaticity. We further show that maximally contacting packings are in general neither the densest nor the most symmetric. Our studies of the geometry of complete sets of sphere packings provide a basis for future work on ground and metastable states in systems with hard-core plus short-range attractive interactions including attractive colloids, collapsed proteins, and jammed particulate media.   

Fabrication of sophisticated two-dimensional organic nanoarchitectures thought hydrogen bond mediated molecular self assembly

Complex supramolecular two-dimensional (2D) networks are attracting considerable interest as highly ordered functional materials for applications in nanotechnology. The challenge consists in tailoring the ordering of one or more molecular species into specific architectures over an extended length scale with molecular precision. Highly organized supramolecular arrays can be obtained through self-assembly of complementary molecules which can interlock via intermolecular interactions. Molecules forming hydrogen bonds (H-bonds) are especially interesting building blocks for creating sophisticated organic architectures due to high selectivity and directionality of these bindings. We used scanning tunnelling microscopy to investigate at the atomic scale the formation of H-bonded 2D organic nanoarchitectures on surfaces. We mixed perylene derivatives having rectangular shape with melamine and DNA base having triangular and non symmetric shape respectively. We observe that molecule substituents play a key role in formation of the multicomponent H-bonded architectures. We show that the 2D self-assembly of these molecules can be tailored by adjusting the temperature and molecular ratio. We used these stimuli to successfully create numerous close-packed and porous 2D multicomponent structures.   

Exploiting Mixed Self-Assembled Monolayers for Design and Fabrication of Patchy Particles

Previous computational studies [1,2] explained the formation of patterns (stripes and patches) in binary mixtures of immiscible surfactants adsorbed on gold nanoparticles [3]. These patterns can confer to the particles unexpected properties, including novel wetting behavior [4]. As an extension of those studies, we performed atomistic and mesoscale simulations of ternary and quaternary mixed self-assembled monolayers (SAMs) on nanosphere surfaces. Here we present predictions for new and unexpected patterns for patchy particles that could be synthesized through judicious choice of surfactant architecture, nanoparticle geometry, and SAM stoichiometry. \\[4pt] [1] C. Singh et al. Physical Review Letters 99, 226106 (2007)\\[0pt] [2] C. Singh et al. Nanoscale 3, 3244-3250 (2011)\\[0pt] [3] A.M. Jackson et al. Nature Materials, 3, 330-336 (2004)\\[0pt] [4] J.J. Kuna et al. Nature Materials, 8, 837-842 (2009)   

Entropy density and Mutual Information measures to quantify the complexity of a nanoscale system

Information-theoretic approach is the most general way to quantify complexity of nanoscale systems. In this study the entropy density and mutual information measures were used to identify the optimal interaction parameters between nanoparticles, which lead to the maximum geometric complexity of self-assembled nanostructures. A generalization of complexity measures at a finite temperature and for nonequilibrium systems is also presented. The developed theory can be used for efficient in silico design of new self-assembled nanostructures with a complex geometry not achievable before.   

Road Usage Heterogeneity and Mitigation of Traffic Congestion

Road networks form the backbone of the social and economic life of a city. Until recently, however, data have not been available to study the impact of trip selection on traffic congestion at an urban scale. To that end, we combined the most complete record of daily trips with the detailed road GIS data to analyze the road usage patterns in two US metropolitan areas. We classify the importance of road segments based on their ability to attract drivers from diverse sources and find that most of them are mainly used by drivers from very few sources. Thanks to this heterogeneity, we find that it is possible to design an efficient strategy to largely reduce the travel time in the road system.   

Rippling ``instability'' in granular jet impact is a memory effect

Experiments and simulations of a dense granular jet impacting a target give rise to a collimated outflow despite the lack of cohesion in the system. This outflow eventually breaks up far away from the target. The breakup, however, is not a uniform dilution but rather takes the form of a series of wave-like undulations with a wavelength much larger than the grain scale. We investigate the possibility that this is another continuum hydrodynamic analog reproduced by bulk granular motion using 2D simulations. We find that these waves, unlike a Helmholz instability, cannot readily be nucleated by perturbations of the granular flow surface. Instead, we find that they point to relics of the velocity fluctuations caused by the impact itself. We show that the ripples are an effect of the effectively ballistic flow far from the target remembering these original velocity fluctuations.   

Transient Memories in Non-Equilibrium Disordered Systems

Some non-equilibrium systems can store information of their external driving in an unexpected manner. They ``learn'' multiple driving amplitudes that can subsequently be read out. Notably, only one memory is retained after many driving cycles, even if all of the amplitudes are continually fed in. This behavior has been observed in diverse scenarios such as traveling charge-density waves [1] and simulations of sheared suspensions [2]. Here we explore this latter system experimentally using a suspension of neutrally buoyant non-Brownian particles in a very viscous fluid that is sheared cyclically in a Couette cell geometry. Starting from a random configuration, the particle trajectories are irreversible at first but, as had been shown [3], eventually settle into a configuration where they retrace their paths exactly during each cycle. We show that the resulting configuration comprises a memory of the driving amplitude, which can be read out by measuring the degree of particle reversibility versus shear amplitude. We also discuss this system's capacity for storing multiple memories.\\[4pt] [1] S. N. Coppersmith et al., PRL 78, 3983 (1997).\\[0pt] [2] N. C. Keim, S. R. Nagel, PRL 107, 010603 (2011).\\[0pt] [3] L. Cort{\'e}, P. M. Chaikin, J. P. Gollub, D. J. Pine, Nature Phys. 4, 420 (2008).   

Role of interaction in the formation of memories in paste

A densely packed colloidal suspension with plasticity, called paste, remembers the directions of vibration and flow. These memories in paste can be visualized by the morphology of desiccation crack patterns. We investigate the role of interaction in the formation of memories in paste. First, interparticle attractive forces, such as van der Waals interaction, are needed to construct a macroscopic network structure with plasticity. With the help of attractive interaction, a water-poor paste remembers the direction of vibration and a water-rich paste remembers the flow direction [1]. When particles are charged in water, however, Coulombic repulsive interaction prevents formation of dilute network structure under flow, which leads to the experimental result that a water-rich charged paste cannot remember flow direction. Addition of sodium chloride to such a paste gives the ability to remember flow direction due to the screening effect of Coulombic repulsive interaction between particles [2].\\[4pt] [1] A. Nakahara, Y. Shinohara and Y. Matsuo, J. Phys.: Conf. Ser. 319 (2011) 012014.\\[0pt] [2] Y. Matsuo and A. Nakahara, arXiv:1101.0953v1 [cond- mat.soft].   

Resonances arising from hydrodynamic memory - The Color of Brownian motion

Observation of the Brownian motion of a small probe interacting with its environment is one of the main strategies to characterize soft matter. Initially, the particle is driven by rapid collisions with the surrounding solvent molecules, referred to as thermal noise. Later, the friction between the particle and the viscous solvent damps its motion. Conventionally, thermal force is taken to be characterized by a Gaussian white noise spectrum. The friction is assumed to be given by the Stokes drag, suggesting that motion is overdamped at long times, when inertia becomes negligible. Here, we measured the noise spectrum of the thermal forces by tracking with high resolution a single micron-sized sphere suspended in a fluid, and confined by a stiff optical trap [1]. Coupling between sphere and fluid gives rise to hydrodynamic memory [2] and a resonance, equivalent to a colored peak in the power spectral density of the sphere's thermal fluctuations. Our results reveal that motion is not overdamped, even at long times. In view to exploit the particle-fluid-trap system as a nanomechanical resonator, we disentangle the two regimes in which the detected resonance is either sensitive to the fluid properties or to the particle's mass.\\[4pt] [1] Jeney et al. Nature 2011.\\[0pt] [2] Jeney et al. PRL 2008.