Phase behaviour of colloidal assemblies on 2D corrugated substrates

We investigate--using Monte Carlo computer simulations--the phase behaviour of dimeric colloidal molecules on periodic substrates with square symmetry. The molecules are formed in a two-dimensional suspension of like charged colloids subject to periodic external confinement, which can be experimentally realized by optical methods. We study the evolution of positional and orientational order by varying the temperature across the melting transition. We propose and evaluate appropriate order parameters as well as the specific heat capacity and show that the decay of positional correlations belongs to a class of crossover transitions while the orientational melting is a second-order phase transition.     

Orientational coupling amplification in ferroelectric nematic colloids

We investigated the physical properties of low concentration ferroelectric nematic colloids, using calorimetry, optical methods, infrared spectroscopy, and capacitance studies. The resulting homogeneous colloids possess a significantly amplified nematic orientational coupling. We find that the nematic orientation coupling increases by approximately 10% for particle concentrations of 0.2%. A manifestation of the increased orientational order is that the clearing temperature of a nematic colloid increases by up to 40 degrees C compared to the pure liquid crystal host. A theoretical model is proposed in which the ferroelectric particles induce local dipoles whose effective interaction is proportional to the square of the orientational order parameter.     

二维胶体玻璃中玻色峰与结构无序度的关联

本文从实验上研究了胶体玻璃在相同面密度下随着体系结构无序程度的增加, 振动态密度和玻色峰的变化规律. 通过调制两种不同粒径的温敏性水凝胶的数量比来改变体系的无序程度. 通过分析无序体系的声子模式得到体系的振动特性. 研究发现, 随着无序度的增加, 态密度在低频区域增强、玻色峰增高、玻色峰的峰值向低频区域移动. 不同无序程度的样品引起玻色峰的低频声子模式都表现出准局域的特点, 且低频准局域声子模式与样品中无序结构存在关联.     

Dynamical ordering and directional locking for particles moving over quasicrystalline substrates

We use molecular dynamics simulations to study the driven phases of particles such as vortices or colloids moving over a decagonal quasiperiodic substrate. In the regime where the pinned states have quasicrystalline ordering, the driven phases can order into moving square or smectic states, or into states with aligned rows of both square and triangular tiling which we term dynamically induced Archimedean-like tiling. We show that when the angle of the drive is varied with respect to the substrate, directional locking effects occur where the particle motion locks to certain angles. It is at these locking angles that the dynamically induced Archimedean tiling appears. We also demonstrate that the different dynamical orderings and locking phases show pronounced changes as a function of filling fraction.     

Effect of electric field on light scattering by aqueous colloids of diamond and graphite

We present the results of our experimental investigation of light scattering by polydisperse colloids of diamond and graphite. The scattering is studied at a random orientation of particles and in an external radiofrequency electric field, which orients particles along the strength. The average dimensions of particles in both colloids are close to each other and comparable with the wavelength of the incident light. The shape of particles and the optical and electrooptical properties of diamond and graphite colloids are significantly different. We analyze the polarization components of scattered light energy when the light incident on the colloids is linearly polarized. We show that the quadrupole light scattering by isotropic diamond particles has the main effect on angular dependences of depolarization of scattered light. For light scattering by anisotropic graphite particles, the depolarization of scattered light is mainly determined by a particular feature of the dipole scattering of particles. It is shown that, in both colloids, the orientational order of particles considerably reduces the depolarization of light scattered by particles. We show that relative changes in the intensity and depolarization of scattered light, which depend on the scattering angle and polarization direction of light, as well as on the parameters of particles, can be used as a measure of electrooptical effects observed in colloids.     

Colloidal dynamics on disordered substrates

Using Langevin simulations, we examine driven colloids interacting with quenched disorder. For weak substrates the colloids form an ordered state and depin elastically. For increasing substrate strength, we find a sharp crossover to inhomogeneous depinning and a substantial increase in the depinning force, analogous to the peak effect in superconductors. The velocity versus driving force curve shows criticality at depinning, with a change in scaling exponent occurring at the order to disorder crossover. Upon application of a sudden pulse of driving force, pronounced transients appear in the disordered regime which are due to the formation of long-lived colloidal flow channels.     

Phase behavior of colloidal molecular crystals on triangular light lattices

We investigate the melting process of a two-dimensional charge-stabilized colloidal system in the presence of a triangular substrate potential. This potential is formed by an optical interference pattern that allows the substrate strength to be varied continuously. By means of an additional scanned optical tweezer the particle density can be adjusted to different numbers m of colloidal particles per substrate minima; here we concentrate on the case of trimers, i.e., m = 3. Because trimers exhibit additional internal degrees of rotational freedom, the phase behavior of such a system is very different from homogeneous or one-dimensional periodic substrate potentials.     

Orientation-dependent depletion interaction in rodlike colloid-polymer mixtures

Depletion interaction in a suspension of rodlike colloids with added non-adsorbing polymer coils is theoretically studied. We calculate an overlap volume of depletion zone between two rodlike colloids, based on the second virial approximation. We examine nematic-isotropic phase transition (NIT) and two-phase coexistence between an isotropic and a nematic phase at low polymer concentrations. We find that the depletion interaction is dependent on the orientational order parameter of rodlike colloids and leads to a decrease in the NIT concentration on the addition of polymer. The coexistence curves have a leaning-chimney shape and are shifted to lower rod concentrations on increasing the polymer concentration. Received 23 May 2001 and Received in final form 18 July 2001     

Patterned colloidal deposition controlled by electrostatic and capillary forces

We use substrates chemically micropatterned with anionic and cationic regions to govern the deposition of charged colloidal particles. The direct observation of the colloidal assembly suggests that this process includes two steps: an initial patterned attachment of colloids to the substrate and an additional ordering of the structure upon drying. The driving forces of the process, i.e. , screened electrostatic and lateral capillary interactions, are discussed. This approach makes it possible to fabricate complex, high-resolution two-dimensional arrays of colloidal particles.     

Shape-induced frustration of hexagonal order in polyhedral colloids

The effect of a nonspherical particle shape and shape polydispersity on the structure of densely packed hard colloidal particles was studied in real space by confocal microscopy. We show that the first layer at the wall of concentrated size-monodisperse but shape-polydisperse polyhedral colloids exhibits significant deviations from a hexagonal lattice. These deviations are identified as bond-orientational fluctuations which lead to percolating "mismatch lines." While the shape-induced geometrical frustration of the hexagonal symmetry suppresses translational order, bond-orientational order is clearly retained, indicating a hexaticlike structure of the polyhedral colloids.     

Comparing light-induced colloidal quasicrystals with different rotational symmetries

Quasicrystals are aperiodic structures with long-range orientational order. Unlike crystals, quasicrystals can, in principle, possess any non-crystallographic rotational symmetry. However, only a few of these rotational symmetries have been observed. By using Monte Carlo simulations of colloidal particles in laser interference patterns with quasicrystalline symmetry, we compare the onset of quasicrystalline order for different rotational symmetries in two dimensions. We find that quasicrystals with 5-, 8-, 10-, and 12-fold rotational axes can be induced with lower laser intensities than quasicrystals with other non-crystallographic rotational symmetries. We relate this finding to the number of local symmetry centers in the respective interference patterns.     

Life at ultralow interfacial tension: wetting, waves and droplets in demixed colloid-polymer mixtures

Mixtures of colloids and polymers display a rich phase behavior, involving colloidal gas (rich in polymer, poor in colloid), colloidal liquid (poor in polymer, rich in colloid) and colloidal crystal phases (poor in polymer, highly ordered colloids). Recently, the colloidal gas-colloidal liquid interface received considerable attention as well. Due to the colloidal length scale the interfacial tension is much lower than in the atomic or molecular analog (nN/m instead of mN/m). This ultra-low interfacial tension has pronounced effects on the kinetics of phase separation, the colloidal gas-liquid profile near a single wall and the thermally induced fluctuations of the interface. The amplitudes of these thermally excited capillary waves are restrained by the interfacial tension and are for that reason of the order of the particle diameter. Therefore, in molecular systems, the capillary waves can only be seen indirectly in scattering experiments. In colloidal systems, however, the wave amplitudes are on a (sub) micrometer scale. This fact enables the direct observation of capillary waves in both real space and real time using confocal scanning laser microscopy. Moreover, the real space technique enables us to demonstrate the strong influence of interface fluctuations on droplet coalescence and droplet break up.     

Topological defect motifs in two-dimensional Coulomb clusters

We study the distribution of topological defects in two-dimensional Coulomb clusters with parabolic lateral confinement. The minima hopping algorithm based on molecular dynamics is used to efficiently locate the ground-?and low-energy metastable states, and their structure is analysed by means of the Delaunay triangulation. The size, structure and distribution of geometry-induced lattice imperfections strongly depends on the system size and the energetic state. Besides isolated disclinations and dislocations, classification of defect motifs includes defect compounds-grain boundaries, rosette defects, vacancies and interstitial particles. Proliferation of defects in metastable configurations destroys the orientational order of the Wigner lattice.     

Colloids as model systems for metals and alloys: a case study of crystallization

Metallic systems are widely used as materials in daily human life. Their properties depend very much on the production route. In order to improve the production process and even develop novel materials a detailed knowledge of all physical processes involved in crystallization is mandatory. Atomic systems like metals are characterized by very high relaxation rates, which make direct investigations of crystallization very difficult and in some cases impossible. In contrast, phase transitions in colloidal systems are very sluggish and colloidal suspensions are optically transparent. Therefore, colloidal systems are often discussed as model systems for metals. In the present work, we study the crystallization process of charged colloidal systems from the very beginning. Charged colloids offer the advantage that the interaction potential can be systematically tuned by a variation of the particle number density and the salt concentration. We apply light scattering and ultra-small angle x-ray scattering to investigate the formation of short-range order in the liquid state even far from equilibrium, crystal nucleation and crystal growth. The results are compared with equivalent studies on metallic systems.     

Mechanical Deformation–Assisted Fabrication of Plasmonic Nanobowties with Broken Symmetry and Tunable Gaps

A symmetry broken and gap tunable gold nanobowtie array is demonstrated by nanosphere lithography performed on a mechanically uniaxially prestretched elastomeric substrate. Due to symmetry breaking of each nanotriangle with its three neighboring nanotriangles once the uniaxial prestretch is released, the structure exhibits polarization-dependent optical properties. In addition, the decrease in the gap between adjacent triangles provided by mechanical relaxation of the substrate enhances the electric field enhancement between adjacent triangles, which in turn results in enhanced Raman scattering from molecules present in the gap. Triangle apex-to-apex gaps as small as 20 nm are generated using a colloidal crystal formed from 500 nm colloids on at 30% prestretched substrate (gaps formed when an unstretched substrate is used are ≈115 nm).     

Gels and glasses in a single system: evidence for an intricate free-energy landscape of glassy materials

In the free-energy landscape picture of glassy systems, their slow dynamics is due to a complicated free-energy landscape with many local minima. We show that for a colloidal glassy material multiple paths can be taken through the free-energy landscape. The evolution of the nonergodicity parameter shows two distinct master curves that we identify as gels and glasses. We show that for a range of colloid concentrations, the transition to nonergodicity can occur in either direction (gel or glass), accompanied by "hesitations" between the two. Thus, colloidal gels and glasses are merely global free-energy minima in the same free-energy landscape, and the paths leading to these minima can be complicated.     

Structure factor of charged colloidal suspensions using Brownian-dynamics simulation: Comparison of Yukawa and Sogami pair potentials

Static structure factorsS(Q) are obtained for dilute charged colloidal systems using Brownian dynamics simulation method for the widely used screened Coulomb repulsive Yukawa potential and the recently proposed Sogami pair potential. The latter potential has, in addition to the usual repulsive part, an attractive term which is necessary to understand the reentrant phase transition reported in these colloids. It is shown for the first time thatS(Q) obtained using the Sogami potential for parameters favourable for liquid-like order agrees well with that measured experimentally. Thus it appears that the Sogami potential explains features of a homogeneous liquid as well as phase separated states, whereas Yukawa potential does not.     

Phase behaviour of a dispersion of charge-stabilised colloidal spheres with added non-adsorbing interacting polymer chains

We present a theory for the phase behaviour of mixtures of charge-stabilised colloidal spheres plus interacting polymer chains in good and θ -solvents within the framework of free-volume theory. We use simple but accurate combination rules for the depletion thickness around a colloidal particle and for the osmotic pressure up to the semi-dilute concentration regime. Hence, we obtain expressions for the free energy for mixtures of charged colloidal particles and non-adsorbing interacting polymers. From that, we calculate the phase behaviour, and discuss its topology in dependence on the competition between the charge-induced repulsion and the polymer-induced attraction. The homogeneous mixture of colloids and polymers becomes more stabilised against demixing when increasing the electrostatic repulsion. This charge-induced stabilisation is strongest for small polymer-to-colloid size ratios and is more pronounced for charged colloids mixed with polymers in a good solvent than for polymers in a θ -solvent. For the weakly charged regime we find that the phase diagram becomes salt-concentration-independent in the protein limit for charged colloids plus polymers in a θ -solvent. The liquid window, i.e., the concentration regimes where a colloidal liquid exists, is narrowed down upon increasing the charge-induced repulsion. Also this effect is more pronounced when charged colloids are mixed with polymer chains in a good solvent. In summary, we demonstrate that the solvent quality significantly influences the phase behaviour of mixtures of charged colloids plus non-adsorbing polymers if the range of the screened electrostatic repulsion becomes of the order of the range of the depletion-induced attraction.     

Lattice models for liquid crystals

A problem in the theory of liquid crystals is to construct a model system which at low temperatures displays long-range orientational order, but not translational order in all directions. We present five lattice models (two two-dimensional and three three-dimensional) of hard-core particles with attractive interactions and prove (using reflection positivity and the Peierls argument) that they have orientational order at low temperatures; the two-dimensional models have no such ordering if the attractive interaction is not present. We cannot prove that these models do not have complete translational order, but their zero-temperature states are such that we are led to conjecture that complete translational order is always absent.Work of EHL supported by U.S. National Science Foundation Grant MCS 75-21684 A02. Financial assistance from the Danish Natural Science Research Council is also gratefully acknowledged.     

Entangled nematic colloidal dimers and wires

It has been predicted, but never confirmed, that colloidal particles in a nematic liquid crystal could be self-assembled by delocalized topological defects and entangled disclinations. We show experimentally and theoretically that colloidal dimers and 1D structures bound by entangled topological defect loops can indeed be created by locally thermally quenching a thin layer of the nematic liquid crystal around selected colloidal particles. The topological entanglement provides a strong stringlike binding, which is ten thousand times stronger compared to water-based colloids. This unique binding mechanism could be used to assemble resonator optical waveguides and robust chiral and achiral structures of topologically entangled colloids that we call colloidal wires.