A Precise Packing Sequence for Self-Assembled Convex Structures

Molecular simulations of the self-assembly of cone-shaped particles with specific, attractive interactions are performed. Upon cooling from random initial conditions, we find that the cones self assemble into clusters and that clusters comprised of particular numbers of cones (e.g. 4 - 17, 20, 27, 32, 42) have a unique and precisely packed structure that is robust over a range of cone angles. These precise clusters form a sequence of structures at specific cluster sizes- a precise packing sequence - that for small sizes is identical to that observed in evaporation-driven assembly of colloidal spheres. We further show that this sequence is reproduced and extended in simulations of two simple models of spheres self-assembling from random initial conditions subject to certain convexity constraints. This sequence contains six of the most common virus capsid structures obtained in vivo including large chiral clusters, and a cluster that may correspond to several non-icosahedral, spherical virus capsid structures obtained in vivo. Our findings suggest this precise packing sequence results from free energy minimization subject to convexity constraints and is applicable to a broad range of assembly processes.Comment: 23 pages, 3 figure

Simulation studies of self-assembly of end-tethered nanorods in solution and role of rod aspect ratio and tether length

We present temperature versus concentration phase diagrams for “shape amphiphiles” comprised of tethered moderate and low aspect ratio rods. Simulations of moderate aspect ratio rods (first reported by Horsch et al. [Phys. Rev. Lett. 95, 056105 (2005)]) predict their self-assembly into spherical micelles with bcc order, long micelles with nematic order, a racemic mixture of hexagonally ordered chiral cylinders, two perforated phases: one with tetragonal order and one with hexagonal order, and a smectic C lamellar phase. In contrast, we predict here that small aspect ratio tethered rods self-assemble into bcc ordered spherical micelles, hexagonally ordered cylinders, and a smectic C lamellar phase. We compare and contrast the phases obtained for the two aspect ratios and examine in further detail several unusual phases. Our simulations also reveal that for moderate aspect ratio rods there is a tendency toward phases with decreasing interfacial curvature with decreasing coil size, including a double gyroid phase. In addition, we investigate the role of tether length on the assembled structures. Our results are applicable to short rod-coil block copolymers and rodlike nanoparticles with polymer tethers, and to colloidal building blocks comprised of a flexible string of colloids tethered to a rigid string of colloids, with the interactions scaled appropriately.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87867/2/184903_1.pd

Hydrodynamics and microphase ordering in block copolymers: Are hydrodynamics required for ordered phases with periodicity in more than one dimension?

We use Brownian dynamics (BD), molecular dynamics, and dissipative particle dynamics to study the phase behavior of diblock copolymer melts and to determine if hydrodynamics is required in the formation of phases with greater than one-dimensional periodicity. We present a phase diagram for diblock copolymers predicted by BD and provide a relationship between the inverse dimensionless temperature ϵ/kBTϵ/kBT and the Flory–Huggins χ parameter, allowing for a quantitative comparison between methods and to mean field predictions. Our results concerning phase behavior are in good qualitative agreement with the theoretical predictions of Matsen and Bates [M. W. Matsen and F. S. Bates, Macromolecules 29, 1091 (1996)]; however, fluctuation effects arising from finite polymer lengths substantially alter the phase boundaries. Our results pertaining to the hydrodynamics are in contrast to earlier work by Groot et al. [R. D. Groot, T. J. Madden, and D. J. Tildesley, J. Chem. Phys. 110, 9739 (1999); D. Frenkel and B. Smit, Understanding Molecular Simulation, 2nd ed. (Academic, New York, 2001)]. In particular, we obtain the hexagonal ordered cylinder phase with BD, a method that does not include hydrodynamics. © 2004 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69378/2/JCPSA6-121-22-11455-1.pd

Method of Optimal Scheduling of Cascade Reservoirs based on Improved Chaotic Ant Colony Algorithm

On the basis of the analysis of the basic information of the river basin reservoirs and application of chaotic ant swarm algorithm, the medium-and long-term optimization operation model is established, which regards the maximum annual generation capacity of the cascade hydropower stations as the main purpose. The simulation result shows the algorithm improves the total annual power generation of the cascade reservoirs, and is better than the basic chaotic ant colony solving method of reservoir operation model, finally provides an effective solution to solve the cascade reservoirs optimization operation problem