Self-assembly of patchy particles into polymer chains: a parameter-free comparison between Wertheim theory and Monte Carlo simulation

The authors numerically study a simple fluid composed of particles having a hard-core repulsion, complemented by two short-ranged attractive (sticky) spots at the particle poles, which provides a simple model for equilibrium polymerization of linear chains. The simplicity of the model allows for a close comparison, with no fitting parameters, between simulations and theoretical predictions based on the Wertheim perturbation theory. This comparison offers a unique framework for the analytic prediction of the properties of self-assembling particle systems in terms of molecular parameters and liquid state correlation functions. The Wertheim theory has not been previously subjected to stringent tests against simulation data for ordering across the polymerization transition. The authors numerically determine many of the thermodynamic properties governing this basic form of self-assembly (energy per particle, order parameter or average fraction of particles in the associated state, average chain length, chain length distribution, average end-to-end distance of the chains, and the static structure factor) and find that predictions of the Wertheim theory accord remarkably well with the simulation results.     

Reversible self-assembly of patchy particles into monodisperse icosahedral clusters

We systematically study the design of simple patchy sphere models that reversibly self-assemble into monodisperse icosahedral clusters. We find that the optimal patch width is a compromise between structural specificity (the patches must be narrow enough to energetically select the desired clusters) and kinetic accessibility (they must be sufficiently wide to avoid kinetic traps). Similarly, for good yields the temperature must be low enough for the clusters to be thermodynamically stable, but the clusters must also have enough thermal energy to allow incorrectly formed bonds to be broken. Ordered clusters can form through a number of different dynamic pathways, including direct nucleation and indirect pathways involving large disordered intermediates. The latter pathway is related to a reentrant liquid-to-gas transition that occurs for intermediate patch widths upon lowering the temperature. We also find that the assembly process is robust to inaccurate patch placement up to a certain threshold and that it is possible to replace the five discrete patches with a single ring patch with no significant loss in yield.     

Self-assembly of rod-coil molecules into molecular length-dependent organization

A series of rod-coil molecules (n-x, where n represents the number of repeating units in a PPO coil and x the number of phenyl groups in a rod segment) with variation in the molecular length, but an identical rod to coil volume ratio was synthesized, and their self-assembling behavior was investigated by using DSC and X-ray scatterings. The molecule with a short rod-coil molecule (16-4) shows a 3-D tetragonal structure based on a body-centered symmetry of the discrete bundles in addition to a lamellar structure. This 3-D lattice, on heating, collapses to generate a disordered micellar structure. Remarkably, the molecules based on longer molecular length (21-5 and 24-6) were observed to self-organize into, on heating, lamellar, tetagonally perforated lamellar, 2-D hexagonal columnar and finally disordered micellar structures. Further increase in the molecular length as in the case of 29-7 and 32-8 induces a 3-D hexagonally perforated lamellar structure as an intermediate structure between the lamellar and tetragonally perforated lamellar structures. Consequently, these systems demonstrate the ability to regulate the domain nanostructure, from 2-dimensionally continuous layers, long strips to discrete bundles via periodic perforated layers by small changes in the molecular length, at an identical rod-to-coil volume fraction.     

Quantitative description of the self-assembly of patchy particles into chains and rings

We numerically study a simple fluid composed of particles having a hard-core repulsion complemented by two patchy attractive sites on the particle poles. An appropriate choice of the patch angular width allows for the formation of ring structures which, at low temperatures and low densities, compete with the growth of linear aggregates. The simplicity of the model makes it possible to compare simulation results and theoretical predictions based on the Wertheim perturbation theory, specialized to the case in which ring formation is allowed. Such a comparison offers a unique framework for establishing the quality of the analytic predictions. We find that the Wertheim theory describes remarkably well the simulation results.     

Self-assembly of beta-D glucose-stabilized Pt nanocrystals into nanowire-like structures

In this work we demonstrate the self-assembly of beta-D glucose-protected Pt nanocrystals (average particle size = 4.1 nm) into nanowire-like assemblies under ambient conditions.     

Self-assembly of viral particles

Viruses, as typical bionanoparticles from nature, possess many superb properties, such as exquisite symmetry, uniformity of size and shape, well-characterized surface chemistry that governs the potential interparticle interactions. These features make viral particles ideal building blocks for self-assembly studies and novel materials development. This review outlines some of the recent research activities in the area of controlled self-assembly of viruses and its potential use as materials. One particular application of the assembled viruses, especially for biomaterials, is also briefly discussed.     

Self-assembly of molecular dumbbells into organized bundles with tunable size

Dumbbell-shaped molecules consisting of three biphenyls connected through vinyl linkages as a conjugated rod segment and aliphatic polyether dendritic wedges with different cross-sections (i.e., dibranch (1), tetrabranch (2) and hexabranch (3)) were synthesized and characterized. The molecular dumbbells self-assemble into discrete bundles that organize into three-dimensional superlattices. Molecule 1, based on a dibranched dendritic wedge, organizes into primitive monoclinic-crystalline and body-centered, tetragonal liquid crystalline structures, while molecules 2 and 3, based on tetra- and hexabranched dendritic wedges, respectively, form only body-centered, tetragonal liquid crystalline structures. X-ray diffraction experiments and density measurements showed that the rod-bundle cross-sectional area decreases with increasing cross-section of the dendritic wedges. The influences of supramolecular structure on the bulk-state optical properties were investigated by measuring the UV/Vis absorption and steady state fluorescence spectroscopies. As the cross-section of the dendritic wedge of the molecule increases, the absorption and emission maxima shift to higher energy. This can be attributed to a quantum size effect of the three-dimensionally confined nanostructure.     

Crystallization of tetrahedral patchy particles in silico

We investigate the competition between glass formation and crystallization of open tetrahedral structures for particles with tetrahedral patchy interactions. We analyze the outcome of such competition as a function of the potential parameters. Specifically, we focus on the separate roles played by the interaction range and the angular width of the patches, and show that open crystal structures (cubic and hexagonal diamond and their stacking hybrids) spontaneously form when the angular width is smaller than about 30°. Evaluating the temperature and density dependence of the chemical potential of the fluid and of the crystal phases, we find that adjusting the patch width affects the fluid and crystal in different ways. As a result of the different scaling, the driving force for spontaneous self-assembly rapidly grows as the fluid is undercooled for small-width patches, while it only grows slowly for large-width patches, in which case crystallization is pre-empted by dynamic arrest into a network glass.     

Self-assembly of dendritic structures

There have been some impressive achievements in the past 1–2 years in the area of self-assembled dendritic structures. The most notable include self-assembly by non-covalent interactions as reported by Zimmerman, Fréchet, and others, Percec's ground-breaking discovery of self-assembling liquid crystalline materials based on dendritic compounds, and the accomplishments of Crooks, among others, in the area of dendritic self-assembled monolayers. © 1999 Elsevier Science Ltd.     

Template-assisted fabrication of patchy particles with uniform patches

Patchy particles with uniform patches of specific shape and size have been predicted to have a rich potential in fabricating new structures; however, an effective method to control the patch shape and size is still missing. In the method presented here, a template is used to assist the fabrication of patchy particles with patches of uniform shape and controlled size by use of the glancing angle deposition method (GLAD). Uniform shadowing effects are caused by the wall of the grooves carved into the surface of a silicon wafer. The ratio of template dimension to particle diameter and the angle of incidence of the metal vapor rays determine the patch shape and size. Mathematical calculations are applied to predict the patch shape and size. Scanning electron microscopy is used to demonstrate the efficiency of the method. Scaling analysis shows that the template-assisted GLAD method leads to a 3100-fold increase in patchy particle fabrication volumes compared to the template-free GLAD method.     

Self-assembly of lanthanide helicate coordination polymers into 3D metal-organic framework structures

Pyridine-2,6-dicarboxylic acid (pdcH(2) ) reacts with nitrate salts of La(III), Ce(III), and Nd(III) under hydrothermal conditions to form three-dimensional network structures, 1-4. All the compounds crystallize in the monoclinic space group P2(1)/c with the following lattice parameters: [La(2)(pdc)(3).3H(2)O] 1, a = 10.966(3) A, b = 17.534(4) A, c = 13.578(2) A, beta = 100.23(3) degrees, V( )()= 2569.3(9) A(3), Z = 4, R1 = 0.052, wR2 = 0.143, S = 1.06; [Ce(2)(pdc)(3).3H(2)O] 2, a = 12.701(3) A, b = 9.979(1) A, c = 19.401(4) A, beta = 97.73(2) degrees, V( )()= 2436.6(8) A(3), Z = 4, R1 = 0.039, wR2 = 0.117, S = 1.30; [Ce(2)(pdc)(3).3H(2)O] 3, a = 10.961(5) A, b = 17.523(5) A, c = 13.505(2) A, beta = 100.89(3) degrees, V( )()= 2547.2(8) A(3), Z = 4, R1 = 0.040, wR2 = 0.103, S = 1.08; [Nd(2)(pdc)(3).3H(2)O] 4, a = 10.944(3) A, b = 17.448(5) A, c = 13.397(2) A, beta = 101.19(3) degrees, V( )()= 2569.3(9) A(3), Z = 4, R1 = 0.052, wR2 = 0.143, S = 1.06. Compounds 1, 3, and 4 form infinite single helical chains with large widths and pitches containing four metal ions per turn while 2 forms a different helix with smaller width and pitch containing two metal ions per turn. Each helix is further bonded on either side via carboxylate bridging producing three-dimensional metal-organic framework structures.     

Self-assembly of model amphiphilic Janus particles

We apply molecular dynamics simulations to investigate the structure formation of amphiphilic Janus particles in the bulk phase. The Janus particles are modeled as (soft) spheres composed of a hydrophilic and hydrophobic part. Their orientation is described by a vector representing an internal degree of freedom. Investigating energy fluctuations and cluster size distributions, we determine the aggregation line in a temperature-density-diagram, where the reduced temperature is an inverse measure for the anisotropic coupling. Below this aggregation line clusters of various sizes depending on density and reduced temperature are found. For low densities in the range ρ? ≤ 0.3, the cluster size distribution has a broad maximum, indicating simultaneous existence of various cluster sizes between 5 and 10. We find no hint of a condensation transition of these clustered systems. In the case of higher densities (ρ? = 0.5 and 0.6), the cluster size distribution shows an extremely narrow peak at clusters of size 13. In these icosahedrons, the particles are arranged in a closed-packed manner, thereby maximizing the number of bonds. Analyzing the translational mean-square displacement we also observe indications of hindered diffusion due to aggregation.     

NMR investigations into heterogeneous structures of thermosensitive microgel particles

The internal properties of submicron poly(N‐isopropylmethacrylamide) latex particles were investigated as a function of the methylene bisacrylamide (MBA) concentration used as a crosslinker. Two experimental approaches were performed. First, quasi‐electric light scattering measurements provided the size variation of the particles as a function of temperature, from which the swelling capacity of the particles as a function of MBA were estimated. In addition, the broadening and lowering effects of the volume phase transition temperature were detected from the turbidity of the solutions versus the MBA concentration. Second, observations of the transverse relaxation of protons gave evidence for heterogeneous structures inside the particles; several structural parts were discriminated from one another from different proton mobilities detected through magnetic relaxation rates. Corresponding to the concentration gradients of the crosslinker, the internal particle structures were looser and looser from the core to the shell. The state of the gelation of the polymer particles was governed by the initial amount of the crosslinker introduced into the latex recipe. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 889–898, 2000     

Self-assembly of chiral molecular polygons

Treatment of 2,2'-diacetyl-1,1'-binaphthyl-6,6'-bis(ethyne), L-H2, with 1 equiv of trans-Pt(PEt3)2Cl2 led to a mixture of different sizes of chiral metallocycles [trans-(PEt3)2Pt(L)]n (n = 3-8, 1-6). Each of the chiral molecular polygons 1-6 was purified by silica gel column chromatography and characterized by 1H, 13C{1H}, and 31P{1H} NMR spectroscopy, MS, IR, UV-vis, and circular dichroism spectroscopies, and microanalysis. The presence of tunable cavities (1.4-4.3 nm) and chiral functionalities in these molecular polygons promises to make them excellent receptors for a variety of guests.     

Formation of dodecagonal quasicrystals in two-dimensional systems of patchy particles

The behaviour of two-dimensional patchy particles with five and seven regularly arranged patches is investigated by computer simulation. For higher pressures and wider patch widths, hexagonal crystals have the lowest enthalpy, whereas at lower pressures and for narrower patches, lower density crystals with five nearest neighbours that are based on the (3(2),4,3,4) tiling of squares and triangles become lower in enthalpy. Interestingly, in regions of parameter space near to that where the hexagonal crystals become stable, quasicrystalline structures with dodecagonal symmetry form on cooling from high temperature. These quasicrystals can be considered as tilings of squares and triangles and are probably stabilized by the large configurational entropy associated with all the different possible such tilings. The potential for experimentally realizing such structures using DNA multi-arm motifs is also discussed.     

Self-assembly of DNA double-double crossover complexes into high-density, doubly connected, planar structures

We designed a molecular complex, the double-double crossover, consisting of four DNA double helices connected by six reciprocal exchanges. Atomic force micrographs suggest that double-double crossover complexes self-assemble into high-density, doubly connected, two-dimensional, planar structures. Such structures may be suitable as substrates for the deposition of nanomaterials in the creation of high-density electrical and quantum devices. We speculate about a modified double-double crossover complex that might self-assemble into high-density, doubly connected, three-dimensional structures.     

Self-assembly of a molecular figure-of-eight strip

A hexanuclear copper(ii) complex with a figure-of-eight strip topology is formed by metal-directed self-assembly of tritopic ligand L, bis-bidentate glycine hydroxamic acid and Cu(ii) ions in a 2:2:6 ratio.