Phase diagram of model anisotropic particles with octahedral symmetry

We computed the phase diagram for a system of model anisotropic particles with six attractive patches in an octahedral arrangement. We chose to study this model for a relatively narrow value of the patch width where the lowest-energy configuration of the system is a simple cubic crystal. At this value of the patch width, there is no stable vapour-liquid phase separation, and there are three other crystalline phases in addition to the simple cubic crystal that is most stable at low pressure. Firstly, at moderate pressures, it is more favourable to form a body-centred cubic crystal, which can be viewed as two interpenetrating, and almost non-interacting, simple cubic lattices.Secondly, at high pressures and low temperatures, an orientationally ordered face-centred cubic structure becomes favourable. Finally, at high temperatures a face-centred cubic plastic crystal is the most stable solid phase.Comment: 12 pages,10 figure

Coherent vibrations of submicron spherical gold shells in a photonic crystal

Coherent acoustic radial oscillations of thin spherical gold shells of submicron diameter excited by an ultrashort optical pulse are observed in the form of pronounced modulations of the transient reflectivity on a subnanosecond time scale. Strong acousto-optical coupling in a photonic crystal enhances the modulation of the transient reflectivity up to 4%. The frequency of these oscillations is demonstrated to be in good agreement with Lamb theory of free gold shells.Comment: Error in Eqs.2 and 3 corrected; Tabl. I corrected; Fig.1 revised; a model that explains the dependence of the oscillation amplitude of the transient reflectivity with wavelength adde

The stability of a crystal with diamond structure for patchy particles with tetrahedral symmetry

The phase diagram of model anisotropic particles with four attractive patches in a tetrahedral arrangement has been computed at two different values for the range of the potential, with the aim of investigating the conditions under which a diamond crystal can be formed. We find that the diamond phase is never stable for our longer-ranged potential. At low temperatures and pressures, the fluid freezes into a body-centred-cubic solid that can be viewed as two interpenetrating diamond lattices with a weak interaction between the two sublattices. Upon compression, an orientationally ordered face-centred-cubic crystal becomes more stable than the body-centred-cubic crystal, and at higher temperatures a plastic face-centered-cubic phase is stabilized by the increased entropy due to orientational disorder. A similar phase diagram is found for the shorter-ranged potential, but at low temperatures and pressures, we also find a region over which the diamond phase is thermodynamically favored over the body-centred-cubic phase. The higher vibrational entropy of the diamond structure with respect to the body-centred-cubic solid explains why it is stable even though the enthalpy of the latter phase is lower. Some preliminary studies on the growth of the diamond structure starting from a crystal seed were performed. Even though the diamond phase is never thermodynamically stable for the longer-ranged model, direct coexistence simulations of the interface between the fluid and the body-centred-cubic crystal and between the fluid and the diamond crystal show that, at sufficiently low pressures, it is quite probable that in both cases the solid grows into a diamond crystal, albeit involving some defects. These results highlight the importance of kinetic effects in the formation of diamond crystals in systems of patchy particles.Comment: 15 pages, 13 figure

Photonic crystals of coated metallic spheres

It is shown that simple face-centered-cubic (fcc) structures of both metallic and coated metallic spheres are ideal candidates to achieve a tunable complete photonic bandgap (CPBG) for optical wavelengths using currently available experimental techniques. For coated microspheres with the coating width to plasma wavelength ratio $l_c/\lambda_p \leq 10$ and the coating and host refractive indices $n_c$ and $n_h$, respectively, between 1 and 1.47, one can always find a sphere radius $r_s$ such that the relative gap width $g_w$ (gap width to the midgap frequency ratio) is larger than 5% and, in some cases, $g_w$ can exceed 9%. Using different coatings and supporting liquids, the width and midgap frequency of a CPBG can be tuned considerably.Comment: 14 pages, plain latex, 3 ps figures, to appear in Europhys. Lett. For more info on this subject see http://www.amolf.nl/research/photonic_materials_theory/moroz/moroz.htm

Measuring every particle's size from three-dimensional imaging experiments

Often experimentalists study colloidal suspensions that are nominally monodisperse. In reality these samples have a polydispersity of 4-10%. At the level of an individual particle, the consequences of this polydispersity are unknown as it is difficult to measure an individual particle size from microscopy. We propose a general method to estimate individual particle radii within a moderately concentrated colloidal suspension observed with confocal microscopy. We confirm the validity of our method by numerical simulations of four major systems: random close packing, colloidal gels, nominally monodisperse dense samples, and nominally binary dense samples. We then apply our method to experimental data, and demonstrate the utility of this method with results from four case studies. In the first, we demonstrate that we can recover the full particle size distribution {\it in situ}. In the second, we show that accounting for particle size leads to more accurate structural information in a random close packed sample. In the third, we show that crystal nucleation occurs in locally monodisperse regions. In the fourth, we show that particle mobility in a dense sample is correlated to the local volume fraction.Comment: 7 pages, 5 figure

Commensurate and Incommensurate Vortex States in Superconductors with Periodic Pinning Arrays

As a function of applied field, we find a rich variety of ordered and partially-ordered vortex lattice configurations in systems with square or triangular arrays of pinning sites. We present formulas that predict the matching fields at which commensurate vortex configurations occur and the vortex lattice orientation with respect to the pinning lattice. Our results are in excellent agreement with recent imaging experiments on square pinning arrays [K. Harada et al., Science 274, 1167 (1996)].Comment: 9 pages, 3 figures. Accepted to Physical Review

A simple formula for the L-gap width of a face-centered-cubic photonic crystal

The width $\triangle_L$ of the first Bragg's scattering peak in the (111) direction of a face-centered-cubic lattice of air spheres can be well approximated by a simple formula which only involves the volume averaged $\epsilon$ and $\epsilon^2$ over the lattice unit cell, $\epsilon$ being the (position dependent) dielectric constant of the medium, and the effective dielectric constant $\epsilon_{eff}$ in the long-wavelength limit approximated by Maxwell-Garnett's formula. Apparently, our formula describes the asymptotic behaviour of the absolute gap width $\triangle_L$ for high dielectric contrast $\delta$ exactly. The standard deviation $\sigma$ steadily decreases well below 1% as $\delta$ increases. For example $\sigma< 0.1$ for the sphere filling fraction $f=0.2$ and $\delta\geq 20$. On the interval $\delta\in(1,100)$, our formula still approximates the absolute gap width $\triangle_L$ (the relative gap width $\triangle_L^r$) with a reasonable precision, namely with a standard deviation 3% (4.2%) for low filling fractions up to 6.5% (8%) for the close-packed case. Differences between the case of air spheres in a dielectric and dielectric spheres in air are briefly discussed.Comment: 13 pages, 4 figs., RevTex, two references added. For more info see http://www.amolf.nl/external/wwwlab/atoms/theory/index.htm

Resonance-Induced Effects in Photonic Crystals

For the case of a simple face-centered-cubic photonic crystal of homogeneous dielectric spheres, we examine to what extent single-sphere Mie resonance frequencies are related to band gaps and whether the width of a gap can be enlarged due to nearby resonances. Contrary to some suggestions, no spectacular effects may be expected. When the dielectric constant of the spheres $\epsilon_s$ is greater than the dielectric constant $\epsilon_b$ of the background medium, then for any filling fraction $f$ there exists a critical $\epsilon_c$ above which the lowest lying Mie resonance frequency falls inside the lowest stop gap in the (111) crystal direction, close to its midgap frequency. If $\epsilon_s <\epsilon_b$, the correspondence between Mie resonances and both the (111) stop gap and a full gap does not follow such a regular pattern. If the Mie resonance frequency is close to a gap edge, one can observe a resonance-induced widening of a relative gap width by $\approx 5$.Comment: 14 pages, 3 figs., RevTex. For more info look at http://www.amolf.nl/external/wwwlab/atoms/theory/index.htm

Metallo-dielectric diamond and zinc-blende photonic crystals

It is shown that small inclusions of a low absorbing metal can have a dramatic effect on the photonic band structure. In the case of diamond and zinc-blende photonic crystals, several complete photonic band gaps (CPBG's) can open in the spectrum, between the 2nd-3rd, 5th-6th, and 8th-9th bands. Unlike in the purely dielectric case, in the presence of small inclusions of a low absorbing metal the largest CPBG for a moderate dielectric constant (epsilon<=10) turns out to be the 2nd-3rd CPBG. The 2nd-3rd CPBG is the most important CPBG, because it is the most stable against disorder. For a diamond and zinc-blende structure of nonoverlapping dielectric and metallo-dielectric spheres, a CPBG begins to decrease with an increasing dielectric contrast roughly at the point where another CPBG starts to open--a kind of gap competition. A CPBG can even shrink to zero when the dielectric contrast increases further. Metal inclusions have the biggest effect for the dielectric constant 2<=epsilon<=12, which is a typical dielectric constant at near infrared and in the visible for many materials, including semiconductors and polymers. It is shown that one can create a sizeable and robust 2nd-3rd CPBG at near infrared and visible wavelengths even for a photonic crystal which is composed of more than 97% low refractive index materials (n<=1.45, i.e., that of silica glass or a polymer). These findings open the door for any semiconductor and polymer material to be used as genuine building blocks for the creation of photonic crystals with a CPBG and significantly increase the possibilities for experimentalists to realize a sizeable and robust CPBG in the near infrared and in the visible. One possibility is a construction method using optical tweezers, which is analyzed here.Comment: 25 pp, 23 figs, RevTex, to appear in Phys Rev B. For more information look at http://www.amolf.nl/research/photonic_materials_theory/moroz/moroz.htm

Aniline incorporated silica nanobubbles

We report the synthesis of stearate functionalized nanobubbles of SiO2 with a few aniline molecules inside, represented as C6H5NH2@SiO2@stearate, exhibiting fluorescence with red-shifted emission. Stearic acid functionalization allows the materials to be handled just as free molecules, for dissolution, precipitation, storage etc. The methodology adopted involves adsorption of aniline on the surface of gold nanoparticles with subsequent growth of a silica shell through monolayers, followed by the selective removal of the metal core either using sodium cyanide or by a new reaction involving halocarbons. The material is stable and can be stored for extended periods without loss of fluorescence. Spectroscopic and voltammetric properties of the system were studied in order to understand the interaction of aniline with the shell as well as the monolayer, whilst transmission electron microscopy has been used to study the silica shell