In this work we use Monte Carlo simulations to study the phase behavior of spherical caps confined between two parallel hard walls separated by a distance H. The particle model consists of a hard sphere of diameter σ cut off by a plane at a height χ, and it is loosely based on mushroom cap-shaped particles whose phase behavior was recently studied experimentally [E. K. Riley and C. M. Liddell, Langmuir, 26, 11648 (2010)]. The geometry of the particles is characterized by the reduced height χ * = χ/σ, such that the model extrapolates between hard spheres for χ * → 1 and infinitely thin hard platelets for χ * → 0. Three different particle shapes are investigated: (a) three-quarter height spherical caps (χ * = 3 /4), (b) one-half height spherical caps or hemispheres (χ * = 1 /2), and (c) one-quarter height spherical caps (χ * = 1 /4). These three models are used to rationalize the effect of particle shape, obtained by cutting off spheres at different heights, on the entropy-driven self-assembly of the particles under strong confinements; i.e., for 1 < H/χ < 2.5. As H is varied, a sequence of crystal structures are observed, including some having similar symmetry as that of the structures observed in confined hard spheres on account of the remaining spherical surface in the particles, but with additional features on account of the particle shapes having intrinsic anisotropy and orientational degrees of freedom. The χ * = 3 /4 system is found to exhibit a phase diagram that is most similar to the one obtained experimentally for the confined mushroom cap-shaped colloidal particles under. A qualitative global phase diagram is constructed that helps reveal the interrelations among different phases for all the particle shapes and confinements studied.

wileyonlinelibrary.com COMMUNICATIONsubwavelength imaging (superlens). [ 12,13 ] In addition, doping sphere-based photonic crystals with rare earths, lanthanides, organic dyes and quantum dots has established properties such as suppression or enhancement of spontaneous emission and photonic crystal lasing due to multiple refl ections and high density of states at the photonic band gap edges. [14][15][16] Only a handful of experimental reports address uniform nonspherical colloidal building blocks (i.e., size range between 400 nm and 1.5 micrometers for photonic crystals in the visible and nearinfrared regimes) with an active optical functionality (i.e., luminescence) at the single particle level.The present work develops fullerene microcrystals as a new materials platform, suitable for 'active' light emitting elements in colloid-based photonic crystals. The materials support singlet excited states that tend to be self-trapped by localized lattice deformation (i.e., Jahn-Teller distortion) and recombine to produce a characteristic red photoluminescence (PL). [17][18][19][20] These high refractive index and transparent building blocks (λ > 560 nm) may also support photonic band gaps in direct structures as compared to the common silica and polymer sphere-based structures which must be backfi lled with semiconductors such as Si and GaAs. [ 11 ] Fullerene molecular crystals have previously been synthesized in a variety of bulk to mesoscale forms including thick and thin fi lms, [ 21 ] wire arrays, [ 22 ] whiskers [ 23 ] and platelets. [ 24 ] Micrometer and sub-micrometer crystals have also been prepared with anisotropic morphology using solution-based techniques such as precipitation at the interface between immiscible liquids (LLIP, liquid-liquid interfacial precipitation), [24][25][26] and evaporation-assisted growth from drops on a substrate. [27][28][29][30] Control of size and shape dispersity with these methods is still lacking. In contrast, microcrystal growth in emulsifi ed solvent-nonsolvent mixtures (co-solvent precipitation) has yielded colloidal particles with tunable shapes, crystal structure and monodispersity. [31][32][33][34] Droplet shrinkage over time in miscible liquids causes local supersaturation of the fullerenes and leads to particle nucleation. The solvent properties (i.e., molecular shape, fullerene solubility, dipole moment, miscibility, interdiffusion rate, etc.), solvent-antisolvent ratio, concentration, temperature and mixing conditions determine the colloidal chemistry and morphology. [31][32][33][34][35] For example, crystallization of C 60 with CS 2 in 2-propanol resulted in bipyramidal-shaped particles, C 70 crystallized with CS 2 in 1-propanol produced rugby ball shapes as well as rhombic dodecahedra, and C 70 with mesitylene in 2-propanol solution produced cubes. [ 31,32 ] Here, we report the synthesis of shape diverse and monodisperse microcrystal solvates using co-solvent precipitation with C 60 and C 70 fullerene-methylbenzene solutions in 2-propanol as a poor solvent. The photol...

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Inspired by self-assembly of binary colloidal mixtures, we simulate the photonic properties of Archimedean tilings composed of triangular and square cross-section rods. Large isotropic photonic bandgaps up to 29.6% (TE) and 29.3% (TM) are found for the 32·4·3·4 Archimedean tiling due to its high rotational symmetry. For each particle geometry, the relative dielectric contrasts were varied independently over the range ε = 2 to 16, consistent with the assembly of binary materials. Mode field distributions indicate that the bandgaps originate from Lorenz-Mie scattering for high dielectric particles in an air matrix (i.e., direct structures). For the inverted structures, bandgaps arise due to the redistribution of the mode field into air pores or into complementary regions of the high dielectric material. Equifrequency contour analysis and finite difference time domain simulations are performed for direct structures with high ε square rods and low ε triangular rods and vice versa. Negative refraction occurs at nearly all angles of incidence for a relative frequency of 0.27, and sub-wavelength imaging is demonstrated for the photonic crystal flatlens with a half-wave distance of 0.45λ. Self-collimation is observed for incident angles in the range (−45°, 45°). Additionally, a waveguide with the 32·4·3·4 structure displays slow light-based signal enhancement.

Colloidal aperiodic phases (i.e., entropy stabilized degenerate crystals, DCs) are realized via self-assembly of hollow fluorescent silica dimers under wedge-cell confinement. The dimer building blocks approximate two tangent spheres and their arrangements are studied via laser scanning confocal microscopy. In the DCs, the individual lobes tile a lattice and five distinct DC arrangements with square, triangular or rectangular layer symmetry are determined as a function of confinement height. Moreover, Monte Carlo simulations are used to construct the phase diagram for DCs up to two layer confinements and to analyze structural order in detail. Just as for spheres, the DC structural transitions under confinement are attributed to the ability or frustration to accommodate an integral number of particle layers between hard walls. Unlike spheres, dimers can also experience transitions involving changes in orientation. DCs are among the unconventional structures (e.g., semi-regular tilings, quasicrystals, plastic crystals) expected to enhance the properties of photonic solids.