Self Assembly of Soft Matter Quasicrystals and Their Approximants

The surprising recent discoveries of quasicrystals and their approximants in soft matter systems poses the intriguing possibility that these structures can be realized in a broad range of nano- and micro-scale assemblies. It has been theorized that soft matter quasicrystals and approximants are largely entropically stabilized, but the thermodynamic mechanism underlying their formation remains elusive. Here, we use computer simulation and free energy calculations to demonstrate a simple design heuristic for assembling quasicrystals and approximants in soft matter systems. Our study builds on previous simulation studies of the self-assembly of dodecagonal quasicrystals and approximants in minimal systems of spherical particles with complex, highly-specific interaction potentials. We demonstrate an alternative entropy-based approach for assembling dodecagonal quasicrystals and approximants based solely on particle functionalization and shape, thereby recasting the interaction-potential-based assembly strategy in terms of simpler-to-achieve bonded and excluded-volume interactions. Here, spherical building blocks are functionalized with mobile surface entities to encourage the formation of structures with low surface contact area, including non-close-packed and polytetrahedral structures. The building blocks also possess shape polydispersity, where a subset of the building blocks deviate from the ideal spherical shape, discouraging the formation of close-packed crystals. We show that three different model systems with both of these features -- mobile surface entities and shape polydispersity -- consistently assemble quasicrystals and/or approximants. We argue that this design strategy can be widely exploited to assemble quasicrystals and approximants on the nano- and micro- scales. In addition, our results further elucidate the formation of soft matter quasicrystals in experiment.Comment: 12 pages 6 figure

Derivation of coarse-grained potentials via multistate iterative Boltzmann inversion

In this work, an extension to the standard iterative Boltzmann inversion (IBI) method to derive coarse-grained potentials is proposed. It is shown that the inclusion of target data from multiple states yields a less state-dependent potential, and is thus better suited to simulate systems over a range of thermodynamic states than the standard IBI method. The inclusion of target data from multiple states forces the algorithm to sample regions of potential phase space that match the radial distribution function at multiple state points, thus producing a derived potential that is more representative of the underlying potential interactions. It is shown that the algorithm is able to converge to the true potential for a system where the underlying potential is known. It is also shown that potentials derived via the proposed method better predict the behavior of n-alkane chains than those derived via the standard method. Additionally, through the examination of alkane monolayers, it is shown that the relative weight given to each state in the fitting procedure can impact bulk system properties, allowing the potentials to be further tuned in order to match the properties of reference atomistic and/or experimental systems

Icosahedral packing of polymer-tethered nanospheres and stabilization of the gyroid phase

We present results of molecular simulations that predict the phases formed by the self-assembly of model nanospheres functionalized with a single polymer "tether", including double gyroid, perforated lamella and crystalline bilayer phases. We show that microphase separation of the immiscible tethers and nanospheres causes confinement of the nanoparticles, which promotes local icosahedral packing that stabilizes the gyroid and perforated lamella phases. We present a new metric for determining the local arrangement of particles based on spherical harmonic "fingerprints", which we use to quantify the extent of icosahedral ordering.Comment: 8 pages, 4 figure

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

Large-Scale Atomistic Simulations of Environmental Effects on the Formation and Properties of Molecular Junctions

Using an updated simulation tool, we examine molecular junctions comprised of benzene-1,4-dithiolate bonded between gold nanotips, focusing on the importance of environmental factors and inter-electrode distance on the formation and structure of bridged molecules. We investigate the complex relationship between monolayer density and tip separation, finding that the formation of multi-molecule junctions is favored at low monolayer density, while single-molecule junctions are favored at high density. We demonstrate that tip geometry and monolayer interactions, two factors that are often neglected in simulation, affect the bonding geometry and tilt angle of bridged molecules. We further show that the structures of bridged molecules at 298 and 77 K are similar.Comment: To appear in ACS Nano, 30 pages, 5 figure

Perfluoropolyethers: Development of an All-Atom Force Field for Molecular Simulations and Validation with New Experimental Vapor Pressures and Liquid Densities

A force field for perfluoropolyethers (PFPEs) based on the general optimized potentials for liquid simulations all-atom (OPLS-AA) force field has been derived in conjunction with experiments and ab initio quantum mechanical calculations. Vapor pressures and densities of two liquid PFPEs, perfluorodiglyme (CF3−O−(CF2−CF2−O)2−CF3) and perfluorotriglyme (CF3−O−(CF2−CF2−O)3−CF3), have been measured experimentally to validate the force field and increase our understanding of the physical properties of PFPEs. Force field parameters build upon those for related molecules (e.g., ethers and perfluoroalkanes) in the OPLS-AA force field, with new parameters introduced for interactions specific to PFPEs. Molecular dynamics simulations using the new force field demonstrate excellent agreement with ab initio calculations at the RHF/6-31G* level for gas-phase torsional energies (<0.5 kcal mol−1 error) and molecular structures for several PFPEs, and also accurately reproduce experimentally determined densities (<0.02 g cm−3 error) and enthalpies of vaporization derived from experimental vapor pressures (<0.3 kcal mol−1). Additional comparisons between experiment and simulation show that polyethers demonstrate a significant decrease in enthalpy of vaporization upon fluorination unlike related molecules (e.g., alkanes and alcohols). Simulation suggests this phenomenon is a result of reduced cohesion in liquid PFPEs due to a reduction in localized associations between backbone oxygen atoms and neighboring molecules

Complex crystal structures formed by the self assembly of di-tethered nanospheres

We report the results from a computational study of the self-assembly of amphiphilic di-tethered nanospheres using molecular simulation. As a function of the interaction strength and directionality of the tether-tether interactions, we predict the formation of four highly ordered phases not previously reported for nanoparticle systems. We find a double diamond structure comprised of a zincblende (binary diamond) arrangement of spherical micelles with a complementary diamond network of nanoparticles (ZnS/D); a phase of alternating spherical micelles in a NaCl structure with a complementary simple cubic network of nanoparticles to form an overall crystal structure identical to that of AlCu_2Mn (NaCl/SC); an alternating tetragonal ordered cylinder phase with a tetragonal mesh of nanoparticles described by the [8,8,4] Archimedean tiling (TC/T); and an alternating diamond phase in which both diamond networks are formed by the tethers (AD) within a nanoparticle matrix. We compare these structures with those observed in linear and star triblock copolymer systems