Equilibrium fluid-crystal interfacial free energy of bcc-crystallizing aqueous suspensions of polydisperse charged spheres

The interfacial free energy is a central quantity in crystallization from the meta-stable melt. In suspensions of charged colloidal spheres, nucleation and growth kinetics can be accurately measured from optical experiments. In previous work, from this data effective non-equilibrium values for the interfacial free energy between the emerging bcc-nuclei and the adjacent melt in dependence on the chemical potential difference between melt phase and crystal phase were derived using classical nucleation theory. A strictly linear increase of the interfacial free energy was observed as a function of increased meta-stability. Here, we further analyze this data for five aqueous suspensions of charg…

Polymer induced changes of the crystallization scenario in suspensions of hard sphere like microgel particles

We investigated the crystallization scenario of highly cross linked polystyrene particles dispersed in the good solvent 2-ethylnaphtalene and their mixtures with non-adsorbing low molecular weight polysterene polymer using time resolved static light scattering. The samples were prepared slightly below the melting volume fraction of the polymer free system. For the polymer free samples, we obtained polycrystalline solids via crystallization scenario known from hard sphere suspensions with little competition of wall crystal formation. Addition of non-adsorbing low molecular weight polystyrene polymer leads to a considerably slowing down of the bulk crystallization kinetics. We observed a dela…

Phase transitions in a colloidal dispersion flowing through a cylindrical capillary

The flow of a charged-stabilized colloidal dispersion of crystalline equilibrium structure through a cylindrical capillary is investigated. The simultaneous existence of up to three differently ordered states is observed under conditions of stationary flow. The evolution of their concentric arrangement along the capillary is determined by Bragg microscopy. For sufficient low fluxes, stationary phase distributions are obtained. While the apparent viscosity is non-monotonous and non-Newtonian, the corresponding velocity profiles are found to be piecewise parabolic and are compatible to numerical calculations. Furthermore, we test the assumption of a constant yield stress determining the radia…

Crystallization in charged two-component suspensions

We report on the crystallization of colloidal crystals comprising of charged particles with different size ratio dispersed in thoroughly deionized water. Single components were characterized carefully and their nucleation behavior was investigated before the preparation of mixtures. Mixtures investigated at constant particle number densities showed body centred cubic structure, conductivity, and shear moduli comply with the assumption of a randomly substituted crystal. Most importantly, for the first time we obtain the dependence of the nucleation rate densities in dependence on the composition and (for one fixed composition) the particle number density. The process of nucleation in random …

Probing dynamics of dense suspensions: three-dimensional cross-correlation technique

We describe the realization of a novel three-dimensional (3D) cross-correlation scheme, which provides the possibility to measure dynamic structure factors of highly concentrated colloidal samples without contributions of multiply scattered light. The apparatus is easier to align and more compact than the two-colour cross-correlation apparatus, which is commercially available. This should make the 3D cross-correlation set-up more convenient for routine applications, for example in industrial laboratories. We describe the set-up and discuss some special features of the optical components.

Colloidal electro-phoresis in the presence of symmetric and asymmetric electro-osmotic flow

We characterize the electro-phoretic motion of charged sphere suspensions in the presence of substantial electro-osmotic flow using a recently introduced small angle super-heterodyne dynamic light scattering instrument (ISASH-LDV). Operation in integral mode gives access to the particle velocity distribution over the complete cell cross-section. Obtained Doppler spectra are evaluated for electro-phoretic mobility, wall electro-osmotic mobility and particle diffusion coefficient. Simultaneous measurements of differing electro-osmotic mobilities leading to asymmetric solvent flow are demonstrated in a custom made electro-kinetic cell fitting standard microscopy slides as exchangeable sidewall…

Sheared colloidal crystals in confined geometry: a real space study on stationary structures under shear.

We constructed an optical plate-plate shear cell suitable for the study of aqueous suspensions of charged colloidal spheres under low electrolyte concentrations (10(-6) M). The variable gap height was adjusted to 30 microm corresponding to 15-30 interparticle distances. The concentration of 300 microm diameter polystyrene spheres was chosen around 1 microm(-1) where previous studies had revealed the equilibrium structure to be fluid or body centred cubic. Under shear, layer structures of hexagonal symmetry form, often coexistent with a fluid phase. We used an adapted high resolution video microscope to perform a detailed study of the structure. The central ray of light was prevented from en…

Phase behaviour of binary mixtures of colloidal charged spheres

Abstract As a step towards the modelling of binary metal alloys we here report on the shape of the phase boundary of two deionized charged sphere colloidal suspensions as a function of mixing ratio and particle density. Their size ratios are r = 0.68 and r = 0.56. Both aqueous suspensions of polystyrene copolymer spheres crystallize in a body-centred cubic structure. Interesting differences in the shape of the phase boundary are observed. In the first case a peaked increase of crystal stability was observed for a mixing ratio of p = 0.2–0.3, which gives the fraction of small spheres. Also in the second case the stability of the crystalline phase is larger than expected for an ideal solid so…

Real-space imaging and motion analysis in sheared colloidal crystals

Microscopic imaging of single particles is a powerful tool to investigate the local structure of colloidal suspensions. For single-particle identification with high-resolution microscopy the resolution power is limited by refraction to roughly the wavelength of light. In this case the depth of sharpness is on a scale of less than this limit. For this reason the simultaneous observation of particles in two or more layers of a colloidal crystal seems to be impossible. We report a method with which we can image more than one particle layer in dilute colloidal suspensions with preserved resolution. The analysis of the images obtained, in particular for the investigation of crystal layer motion …

Colloidal crystallization dynamics

At sufficiently strong interparticle interaction, colloidal particles may form ordered crystalline arrays much in analogy to atomic systems. Well characterized model colloidal suspensions have therefore become valuable model systems for the study of the kinetics of crystal nucleation, growth and ripening. Significant progress has been made in this area throughout the past few years. Precise control of interaction parameters and new instrumental developments have allowed for quantitative determination of nucleation rate densities and growth velocities in monodisperse ‘hard’ and ‘soft sphere’ systems. Results confirm classical theories of nucleation and growth adapted to colloidal systems. Th…

Probing slow fluctuations in nonergodic systems: Interleaved sampling technique

We present a new dynamic light scattering scheme to obtain ensemble-averaged correlation functions of slow fluctuations in non-ergodic systems in an efficient way. On a rotating sample, a large set of separate correlation functions is measured in parallel, for each independent orientational component of the sample’ density fluctuations. The ensemble-averaged correlation function spans a lag time range from 1 to 104 s. We describe our first implementation of this technique, discuss its statistical accuracy and show first results. Compared to plain ensemble averaging over a series of N measurements, the total measurement time is usualy reduced by a factor N without significant degradation of …

Electrophoretic flow behaviour and mobility of colloidal fluids and crystals.

We report on measurements of the electrophoretic mobility mu of charged colloidal spheres in the deionized state, where the suspensions show fluid or crystalline order. In the fluid state, parabolic flow profiles are observed due to electro-osmotic solvent flow. In the crystalline state, complex flow profiles occur due to additional crystal cohesion. The mobility mu then may inferred from the flow velocity averaged over the complete cell cross section as performed in our home built super-heterodyne Doppler velocimeter. For two particle species of 68 and 122 nm diameter we measured mu as a function of particle concentration. Starting from a plateau value at low concentration, mu decreases ap…

Independent ion migration in suspensions of strongly interacting charged colloidal spheres

We report on sytematic measurements of the low frequency conductivity in aequous supensions of highly charged colloidal spheres. System preparation in a closed tubing system results in precisely controlled number densities between 1E16/m3 and 1E19/m^3 (packing fractions between 1E-7 and 1E-2) and electrolyte concentrations between 1E-7 and 1E-3 mol/l. Due to long ranged Coulomb repulsion some of the systems show a pronounced fluid or crystalline order. Under deionized conditions we find s to depend linearily on the packing fraction with no detectable influence of the phase transitions. Further at constant packing fraction s increases sublinearily with increasing number of dissociable surfac…

Crystal growth kinetics in deionised two-component colloidal suspensions

We report first measurements of the crystal growth velocity in deionised two-component aqueous suspensions of charged polystyrene latex spheres. The size ratio was 1:1.3 and mixing ratios up to 18% of the larger particle were investigated. For the pure components limiting growth velocities of (V ∞,120 = 4.8 µm s−1 and V ∞,156 = 2.9 µm s−1) were observed. In the mixture v drops with increasing mixing ratio even below (V ∞,156) of the large minority component. Careful monitoring of the deionisation procedure excludes the explanation of enhanced ionic contamination. Alternatives based on the kinetics of particle attachment and the position of the phase boundary are discussed.

Non-Monotonic Concentration Dependence of the Electro-Phoretic Mobility of Charged Spheres in Realistic Salt Free Suspensions

Using super-heterodyne Doppler velocimetry with multiple scattering correction, we extend the opti-cally accessible range of concentrations in experiments on colloidal electro-kinetics. We here meas-ured the electro-phoretic mobility and the DC conductivity of aqueous charged sphere suspensions covering about three orders of magnitude in particle concentrations and transmissions as low as 40%. The extended concentration range for the first time allows the demonstration of a non-monotonic con-centration dependence of the mobility for a single particle species. Our observations reconcile previ-ous experimental observations made on other species over restricted concentration ranges. We com-par…

Crystallization kinetics of colloidal model suspensions: recent achievements and new perspectives

Colloidal model systems allow studying crystallization kinetics under fairly ideal conditions with rather well characterized pair interactions and minimized external influences. In complementary approaches therefore experiment, analytic theory and simulation have been employed to study colloidal solidification in great detail. These studies were based on advanced optical methods, careful system characterization and sophisticated numerical methods. Both the effects of the type, strength and range of the pair-interaction between the colloidal particles and those of the colloid-specific polydispersity were addressed in a quantitative way. Key parameters of crystallization were derived and comp…

Direct observation of a buckling transition during the formation of thin colloidal crystals

We have investigated a colloidal suspension in a thin wedge formed by two glass plates in the presence of a lateral pressure. Starting with a single hexagonal layer, with increasing separation between the glass plates additional layers are added. This process is accompanied by a number of structural transitions necessary to maintain a high packing fraction under the given boundary conditions. Besides the well-known sequence of hexagonal and quadratic phases, we observe two new phases which are identified with the buckling and the rhombic phase recently predicted by other authors.

Seedless assembly of colloidal crystals by inverted micro-fluidic pumping

We propose a simple seedless approach to assemble millimeter sized monolayer single colloidal crystals with desired orientations at predetermined locations on an unstructured charged substrate. This approach utilizes the millimeter-ranged fluid flow on the bottom glass substrate induced by an ion exchange resin (IEX) fixed on top of the closed sample cell. This fluid flow increases with decreasing height of the sample cell and increasing radius R of the IEX. For a single inverted pump, millimeter sized monolayer single crystals of hexagonal close packing can be obtained. For two closely spaced (D ~ 4R) pumps, the formed crystals have a predefined orientation along the line connecting the tw…

Approaching the limits of multiple scattering decorrelation: 3D light-scattering apparatus utilising semiconductor lasers

Light scattering as a function of scattering angle can be regarded as a standard method to investigate the dynamics of dilute colloidal suspensions. Concentrated suspensions, which are of interest if interactions between the particles are to be investigated, usually show strong multiple scattering. Decorrelation of multiple scattered light, which isolates single scattering events at the expense of a reduced signal-to-noise ratio, has been proven to work using the two-colour crosscorrelation scheme.

A comparative study on the phase behaviour of highly charged colloidal spheres in a confining wedge geometry

We studied the structures formed in aqueous dispersions of charged colloidal spheres under a constant low salt concentration of c = 6 × 10−6 mol l−1. Particles of diameter 2a = 1000 nm were confined to a low angle wedge geometry with plate separation 0<S<50 µm and observed with video microscopy. Irrespective of the initial particle density n we reproducibly observe the particles to migrate to the narrow wedge side on the timescale of a few days. Thereby an interface between a crystalline structure and a near particle free region is formed, which propagates slowly until the dilute region is exhausted of particles. While the origin of this separation is still unclear, the final extension of t…

Polymer-enforced crystallization of a eutectic binary hard sphere mixture

We prepared a buoyancy matched binary mixture of polydisperse polystyrene microgel spheres of size ratio 0.785 and at a volume fraction of 0.567 just below the kinetic glass transition. In line with theoretical expectations, a eutectic phase behavior was observed, but only a minor fraction of the samples crystallized at all. By adding a short non-adsorbing polymer we enforce inter-species fractionation into coexisting pure component crystals, which in turn also shows signs of intra-species fractionation. We show that in formerly inaccessible regions of the phase diagram binary hard sphere physics is made observable using attractive hard spheres. Ancillary files: Correction to Soft Matter 20…

Electrophoresis of colloidal dispersions in the low-salt regime

We study the electrophoretic mobility of spherical charged colloids in a low-salt suspension as a function of the colloidal concentration. Using an effective particle charge and a reduced screening parameter, we map the data for systems with different particle charges and sizes, including numerical simulation data with full electrostatics and hydrodynamics and experimental data for latex dispersions, on a single master curve. We observe two different volume fraction-dependent regimes for the electrophoretic mobility that can be explained in terms of the static properties of the ionic double layer.

3D Colloidal photonic crystal fabrication improved by AC fields for frequency conversion enhancement in photovoltaics

We report on the fabrication of high-quality 3D colloidal photonic crystals, whose finality is to modify the emission properties of frequency converters for photovoltaic applications. The band structure of the photonic crystals can be used to enhance the emission of down- and up-converters materials embedded in the 3D structures. However, in order to achieve an efficient conversion the first step is to obtain highly ordered templates with appropriated dimensions. We analyze here the photonic crystals obtained by the dip-coating or vertical deposition method. Moreover, by using perpendicular AC fields during the assembly of the nanospheres, the quality of the packed structures has been impro…

Dynamics of Binary Active Clusters Driven by Ion-Exchange Particles

We present a framework to quantitatively predict the linear and rotational directed motion of synthetic modular microswimmers. To this end, we study binary dimers and characterize their approach motion as effective interactions within a minimal model. We apply this framework to the assembly of small aggregates composed of a cationic ion-exchange particle with up to five passive particles or anionic ion-exchange particles at dilute conditions. Particles sediment and move close to a substrate, above which the ion-exchange particles generate flow. This flow mediates long-range attractions leading to a slow collapse during which long-lived clusters of a few particles assemble. The effective int…

Construction and stability of a close-packed structure observed in thin colloidal crystals

We have characterized a close-packed structure of confined charged colloidal spheres, which has been recently discovered. Using different microscopy experiments, the vertically arranged hexagonal planes of n - hcp perpendicular are found to continuously evolve from the horizontally oriented stacks of n hexagonal planes (nDelta) following the maximum packing criterion, but discontinuously transform to a stack of n+1 square planes [(n+1)[SHAPE OF A SQUARE]]. Large mechanically stable domains with threefold twin structures are regularly observed in the suspended state at packing fractions between 0.4 and 0.58.

Charged colloidal model systems under confinement in slit geometry: a new setup for optical microscopic studies.

A new experimental setup for optical microscopic studies of charged colloidal model systems under confinement between two flat walls is presented. The measurement cell consists of optically flat quartz substrates attached to piezo actuators. Those facilitate fast and flexible adjustment of the confining geometry. Optionally, the local cell height can be quantitatively controlled by in situ interferometric measurements. Proper choice of materials guarantees sufficient chemical inertia against contamination with salt ions. For efficient preparation of charged colloidal suspensions under strongly deionized conditions, the cell can be connected to a conventional pump circuit including a mixed b…

A Multipurpose Instrument To Measure the Vitreous Properties of Charged Colloidal Solids

We present a new high-precision light-scattering setup to study the properties of colloidal solids. It combines static light scattering, dynamic light scattering, and torsional resonance spectroscopy with a flexible and reliable preparational procedure. All three experiments can be performed quasi-simultaneously on the same mechanically undisturbed sample. Thus, unequivocal identification of glassy behavior in a comprehensive characterization dependent on interaction parameters becomes possible. A detailed description of the mechanics is given. We thoroughly tested the new apparatus on dilute colloidal samples and against commercial reference instruments. We performed a first systematic ser…

Self-Assembly of Colloidal Molecules due to Self-Generated Flow.

The emergence of structure through aggregation is a fascinating topic and of both fundamental and practical interest. Here we demonstrate that self-generated solvent flow can be used to generate long-range attractions on the colloidal scale, with subpiconewton forces extending into the millimeter range. We observe a rich dynamic behavior with the formation and fusion of small clusters resembling molecules. The dynamics of this assembly is governed by an effective conservative energy that for large separations r decays as 1/r. Breaking the flow symmetry, these clusters can be made active.

Formation of Laves phases in buoyancy matched hard sphere suspensions.

Colloidal Laves phases (LPs) are promising precursors for photonic materials. Laves phases have not yet been observed to form in experiments on colloidal suspensions of hard spheres (HS), even though they have been reported in computer simulations. LP formation so far has been achieved only for binary mixtures of colloidal charged spheres or ligand-stabilized nano-particles after drying. Using static light scattering, we monitored LP formation and annealing in a binary mixture of buoyant hard sphere approximants (size ratio Γ = 0.77, number or molar fraction of small spheres xS = 0.76) for volume fractions in the fluid-crystal coexistence regions. All samples spontaneously formed MgZn2 type…

Crystallization kinetics of polydisperse hard-sphere-like microgel colloids: Ripening dominated crystal growth above melting.

Highly cross-linked polystyrene microgel colloids dispersed in an index and density matching solvent provide a system with hard-sphere-like interactions, where gravity effects are effectively minimized. They are a suitable target for time-resolved observations of solidification in purely repulsive systems. We have investigated the crystallization kinetics at increasing undercooling using time resolved light scattering. Crystallization starts always with the formation of compressed, structurally heterogeneous precursor domains. In the coexistence region the precursors, after being converted into true crystallites, start growing fast by assimilating particles from the melt. The resulting poly…

Assembly and Speed in Ion-Exchange-Based Modular Phoretic Microswimmers.

We report an experimental study on ion-exchange-based modular microswimmers in low-salt water. Cationic ion-exchange particles and passive cargo particles assemble into self-propelling complexes, showing self-propulsion at speeds of several micrometers per second over extended distances and times. We quantify the assembly and speed of the complexes for different combinations of ion-exchange particles and cargo particles, substrate types, salt types and concentrations, and cell geometries. Irrespective of the experimental boundary conditions, we observe a regular development of the assembly shape with increasing number of cargo. Moreover, the swimming speed increases stepwise upon increasing…

Enhanced crystal stability in a binary mixture of charged colloidal spheres.

We report on the phase behavior of a binary charged sphere mixture of size ratio $\ensuremath{\Gamma}=0.68$ and charge ratio $\ensuremath{\Lambda}\ensuremath{\approx}1$ as a function of composition $p$ and number density $n$. For $p=0.1--0.3$ we observe freezing at densities well below the freezing densities of the pure components. At all compositions our data indicate the formation of substitutional alloy crystals of body centered cubic structure. No indications for compound formation were observed. Rather, our findings point at the first observation of an upper azeotrope. Measurements of the crystallization kinetics reveal a combined density and composition dependence of growth velocities…

Particle Characterization Using Multiple Scattering Decorrelation Methods. Part 1: Standard Latex Particles

To make a glass—avoid the crystal

Colloidal model systems allow for a flexible tuning of particle sizes, particle spacings and mutual interactions at constant temperature. Colloidal suspensions typically crystallize as soon as the interactions get sufficiently strong and long-ranged. Several strategies have been successfully applied to avoid crystallization and instead produce colloidal glasses. Most of these amorphous solids are formed at high particle concentrations. This paper shortly reviews experimental attempts to produce amorphous colloidal solids using strategies based on topological, thermodynamic and kinetic considerations. We complement this overview by introducing a (transient) amorphous solid forming in a thoro…

Electrophoresis of model colloidal spheres in low salt aqueous suspension

We report on comprehensive measurements of the electrophoretic mobility μ of a highly charged spherical colloid in deionized or low salt aqueous suspensions, where fluid and crystalline order develops with increased packing fraction Φ. We propose the existence of a 'universal' shape of the μ(Φ) showing three distinct regimes: a logarithmic increase, a plateau and a logarithmic decrease. The position and the height of the plateau are found to be influenced by the particle surface properties and the electrolyte concentration. In particular, it starts once the counter-ion concentration becomes equal to the concentration of background electrolyte. This coincides only loosely with the range of Φ…

Melting and Freezing Lines for a Mixture of Charged Colloidal Spheres with Spindle-Type Phase Diagram

We have measured the phase behavior of a binary mixture of like-charged colloidal spheres with a size ratio of 0.9 and a charge ratio of 0.96 as a function of particle number density n and composition p. Under exhaustively deionized conditions the aqueous suspension forms solid solutions of body centered cubic structure for all compositions. The freezing and melting lines as a function of composition show opposite behavior and open a wide, spindle shaped coexistence region. Lacking more sophisticated treatments, we model the interaction in our mixtures as an effective one-component pair energy accounting for number weighted effective charge and screening constant. Using this description, we…

Transient Moiré rotation patterns in thin colloidal crystals

A high resolution optical microscopy study on low salt charged sphere suspensions settling under gravity reveals the formation of AB-stacked triangular layers via different transient structures. In particular, metastable triangular Moire rotation patterns (formally corresponding to 1 × 1 Rα super structures) with rotation angles α = 27.8° and α = 38.2° are identified.

Solidification Experiments in Single-Component and Binary Colloidal Melts

Phase behaviour of deionized binary mixtures of charged colloidal spheres.

We review recent work on the phase behaviour of binary charged sphere mixtures as a function of particle concentration and composition. Both size ratios and charge ratios are varied over a wide range. By contrast to hard spheres the long ranged Coulomb interaction stabilizes the crystal phase at low particle concentrations and shifts the occurrence of amorphous solids to particle concentrations considerably larger than the freezing concentration. Depending on size- and charge ratios we observe upper azeotrope, spindle, lower azeotrope and eutectic types of phase diagrams, all known well from metal systems. Most solids are of body centred cubic structure. Occasionally stoichiometric compound…

Modes of motion in a confined colloidal suspension under shear

We investigated aqueous suspensions of charged polystyrene latex spheres at low salt concentration under the combined influence of steady shear and confining walls. Their equilibrium structure was adjusted via the particle and salt concentration to be either fluid or body centred cubic. Using high-resolution real-space microscopy, we here present a first direct observation of collective modes of motion under shear. As a function of either shear rate and/or salt concentration, we find a continuous transition from registered to free sliding of layers accompanied by an equally continuous structural rearrangement lowering the dimensionality of long-ranged order.

Optical experiments on a crystallizing hard-sphere–polymer mixture at coexistence

We report on the crystallization kinetics in an entropically attractive colloidal system using a combination of time resolved scattering methods and microscopy. Hard sphere particles are polystyrene microgels swollen in a good solvent (radius a=380nm, starting volume fraction 0.534) with the short ranged attractions induced by the presence of short polymer chains (radius of gyration rg = 3nm, starting volume fraction 0.0224). After crystallization, stacking faulted face centred cubic crystals coexist with about 5% of melt remaining in the grain boundaries. From the Bragg scattering signal we infer the amount of crystalline material, the average crystallite size and the number density of cry…

Crystallization kinetics of colloidal binary mixtures with depletion attraction.

In this work the crystallization kinetics of colloidal binary mixtures with attractive interaction potential (Asakura–Oosawa) has been addressed. Parameters such as fraction of crystals, linear crystal dimension and crystal packing have been quantified in order to understand how the crystal formation is driven in terms of the depth of the attractive potential and the composition of the binary mixture (described by the number ratio). It was found that inside the eutectic triangle, crystallization is mainly governed by nucleation and the crystal packing is close to the close-packing of hard spheres. Moving out from the eutectic triangle towards small component results in the crystallization o…

Assessment of Shear-Induced Structures by Real Space and Fourier Microscopy

We report preliminary measurements of the shear-induced sliding layer structure in an aqueous suspension of highly charged polystyrene spheres. Particle interaction was controlled by advanced conditioning procedures to result in fluid or body-centred cubic equilibrium structures. Shear was applied in an optical plate-plate shear cell of variable slit width. Fourier microscopy yielded complementary information to real space analysis. The accessible range of scattering vectors was (3.5 ≤ k ≤ 7.2) μm−1 We checked the experimental performance by recording the form factor of a non-interacting suspension and structure factors of less dilute suspensions in dependence on electrolyte concentration c…

Electro-kinetics of charged-sphere suspensions explored by integral low-angle super-heterodyne laser Doppler velocimetry

We investigated the flow behaviour of colloidal charged-sphere suspensions using a newly designed integral low-angle super-heterodyne laser Doppler velocimetry instrument, which combines the advantages of several previous approaches. Sample conditions ranged from strong electrostatic interactions with pronounced short-range order to individual particles with no spatial correlations. The obtained power spectra correspond to diffusion broadened velocity distributions across the complete sample cross section. The excellent performance of the instrument is highlighted in detail by the example of electro-kinetic flow of suspensions in a closed cell of a rectangular cross section. We demonstrate …

Controlled assembly of single colloidal crystals using electro-osmotic micro-pumps.

We assemble charged colloidal spheres at deliberately chosen locations on a charged unstructured glass substrate utilizing ion exchange based electro-osmotic micro-pumps. Using microscopy, a simple scaling theory and Brownian Dynamics simulations, we systematically explore the control parameters of crystal assembly and the mechanisms through which they depend on the experimental boundary conditions. We demonstrate that crystal quality depends crucially on the assembly distance of the colloids. This is understood as resulting from the competition between inward transport by the electro-osmotic pump flow and the electro-phoretic outward motion of the colloids. Optimized conditions include sub…

Non-equilibrium melting of colloidal crystals in confinement

International audience; We report on a novel and flexible experiment to investigate the non-equilibrium melting behaviour of model crystals made from charged colloidal spheres. In a slit geometry polycrystalline material formed in a low salt region is driven by hydrostatic pressure up an evolving gradient in salt concentration and melts at large salt concentration. Depending on particle and initial salt concentration, driving velocity and the local salt concentration complex morphologic evolution is observed. Crystal-melt interface positions and the melting velocity are obtained quantitatively from time resolved Bragg- and polarization microscopic measurements. A simple theoretical model pr…

Correction: Seedless assembly of colloidal crystals by inverted micro-fluidic pumping.

Correction for ‘Seedless assembly of colloidal crystals by inverted micro-fluidic pumping’ by Ran Niu et al., Soft Matter, 2018, 14, 3435–3442.

Crystal nucleation versus vitrification in charged colloidal suspensions

We investigated the solidification behaviour of thoroughly deionised aqueous suspensions of polystyrene latex spheres by various optical scattering methods. We found a dramatic increase in the nucleation rate densities with increasing particle number density. Crystalline and nanocrystalline samples showed two relaxation processes on widely separated time scales. For an index-matched suspension of perfluorinated particles an amorphous state was accessible with the glass-typical signature of frozen long-time relaxation. From our results we propose a route into the amorphous state different to that observed in hard-sphere suspensions. It seems that in charged-sphere systems the increased nucle…

Microscopic investigations of homogeneous nucleation in charged sphere suspensions.

We studied the homogeneous nucleation kinetics of an aqueous suspension of charged colloidal spheres under de-ionized conditions. Samples of equilibrium crystalline structure were shear molten and the metastable melt left to solidify after cessation of shear. At low particle number densities n, corresponding to low metastability of the melt, nucleation was monitored directly via video microscopy. We determined the nucleation rates gamma(t) by counting the number of newly appearing crystals in the observation volume per unit time. Using a suitable discrete adaptation of Avrami's [J. Chem. Phys. 7, 1003 (1939); ibid.8, 212 (1940); ibid.9, 177 (1941)] model for solidification via homogeneous n…

Dynamic light scattering by preserved skimmed cow milk: A comparison of two-colour and three-dimensional cross-correlation experiments

We investigate the dynamic light scattering of preserved skimmed cow milk and compare the performance of a standard two-colour (2C) cross-correlation setup with the recently developed three-dimensional (3D) cross-correlation setup. Undiluted milk could only be investigated using the 3D setup because of too low signal-to-noise ratio of the 2C setup. A tenfold diluted milk, however, could be investigated by both setups, and comparable results for the dynamics of the sample were obtained thus demonstrating the equivalence of the decorrelation schemes. On the other hand, we found that the dynamics of the milk is strongly altered upon dilution. This finding elucidates the benefits of the new 3D …

Heterogeneous nucleation of colloidal melts under the influence of shearing fields

Large, oriented single crystals may be obtained from shear melts of colloidal particles after nucleation at the container walls. We are here interested in the processes occurring during the initial phase of their formation. Using different microscopic and scattering techniques we here studied highly charged suspensions of spherical particles, dispersed in low salt or deionized water, in single and double wall confinement, during and after cessation of shear. While the equilibrium phase of our colloidal solids is body centred cubic, the shear induced precursors of heterogeneous nuclei consist of wall based, oriented, registered or freely sliding layers with in plane hexagonal symmetry. Cessa…

From nuclei to micro-structure in colloidal crystallization: Investigating intermediate length scales by small angle laser light scattering.

Hard sphere suspensions are well recognized model systems of statistical physics and soft condensed matter. We here investigate the temporal evolution of the immediate environment of nucleating and growing crystals and/or their global scale distribution using time resolved Small Angle Light Scattering (SALS). Simultaneously performed Bragg scattering (BS) measurements provide an accurate temporal gauging of the sequence of events. We apply this approach to studies of re-crystallization in several different shear molten hard sphere and attractive hard sphere samples with the focus being on the diversity of observable signal shapes and their change in time. We demonstrate that depending on th…

Colloids as model systems for liquid undercooled metals

Physical review / E 79(1), 4 (2009). doi:10.1103/PhysRevE.79.010501

Electrophoretic mobility of electrostatically interacting colloidal spheres

We have measured the electrophoretic mobility μ = vE/E (where E is the electric field strength and vE the electrophoretic velocity) of highly charged colloidal spheres in deionized aqueous suspension at particle number densities n between 0.15 and 150 µm−3. Under these conditions the system exhibits fluid or crystalline order. We used laser Doppler velocimetry to determine the electrophoretic velocities vE as spatially averaged particle velocities from both integral and spatially resolved measurements. With this approach we were for the first time able to extend measurements far into the crystalline region of the phase diagram. We found μ to be constant at low n while at large n we observe …

Interactions of different hydrocolloids with milk proteins

Abstract To control rheological properties and accomplish perfect sensory properties and mouthfeel, polysaccharides are added to milk-based beverages. However, in contrast to expectations, it is often found that adding low concentrations of xanthan gum or guar gum to milk provokes phase separations of unclear physical origin. From this observation, questions arise regarding the interaction of added polysaccharides and the proteins present in milk – caseins and whey proteins. The focus of this study is to investigate such systems and to understand the basic interactions of caseins and whey proteins with different hydrocolloids. The hydrocolloids used in this study are xanthan gum, guar gum, …

Experimental determination of effective charges in aqueous suspensions of colloidal spheres

Abstract We determined the low frequency conductivity σ , the phase behaviour and the shear modulus G of colloidal fluids, respectively solids prepared from deionised aqueous suspensions of highly charged spherical particles. Conductivity measures the number of freely moving small ions Z * σ and thus relates to the ion condensation process in the electric double layer under conditions of finite macro-ion concentrations. Phase behaviour and elasticity data are consistently described by a Debye–Huckel pair potential assuming pair-wise additive macro-ion interactions. Like Z * σ , also the effective charges Z * G derived from the elasticity data scales with the ratio of macro-ion radius to Bje…

High-resolution particle sizing by optical tracking of single colloidal particles

Abstract The motion of individual Brownian particles is observed using the confocal Tracking Microscope recently introduced by Schatzel (K. Schatzel, W. G. Neumann, J. Muller and B. Materzok, App. Opt. 31 (1992) 770–778). Particles are laterally trapped in a strongly focused laser beam. By evaluating the light-pressure-induced drift velocity and the backscattered intensity we are able to detemine particle size histograms with a resolution better than 2%. This is demonstrated on a mixture of seven species of polystyrene latex spheres in the diameter range between 300 and 450 nm, where six classes of diameters are identified. We discuss the scope of the method and potential applications.

Charged colloidal particles in a charged wedge: do they go in or out?

Using real-space microscopy experiments, theory and computer simulation, we study the behaviour of highly charged colloidal particles which are confined between two highly charged plates forming a wedge geometry. Under low salt conditions it is experimentally observed that colloidal particles accumulate in the cusp of a wedge to form dense fluid or crystalline ordered structures. This behaviour is found for various cell geometries, salt concentrations and gravitational strengths, and even stays stable when additional convection is present in the system. An effort is made to understand this effect qualitatively on the basis of linear screening theory. For a single macro-ion, linear screening…

Growth and anisotropic ripening in twinned colloidal crystals

The heterogeneous crystallization of colloidal suspensions of Yukawa particles on a wall was observed by Bragg microscopy. The growth velocity ν 110 of the fluid-crystal interface can be very well described by a Wilson-Frenkel growth law, while the limiting velocity is found to be lower than in previous investigations. Twinned bcc domains in lateral direction (parallel to the wall) and their ripening behavior are for the first time investigated systematically. A strong anisotropic growth behavior is found: in the direction of the shear flow, which shear melts the suspension prior to the crystallization process, the extension of the domains is much larger than perpendicular to that. The incr…

Unusual crystallization kinetics in a hard sphere colloid-polymer mixture.

We investigated the crystallization kinetics of a hard sphere colloid-polymer mixture at conditions where about 95% of solid coexists with about 5% of fluid. From time resolved Bragg and small angle light scattering, we find that the crystallite size increases with a power law of exponent alpha approximately 1/3 during both the conversion and the coarsening stage. This observation points to a single conserved order parameter for both stages and cannot be explained if the mixture is regarded as an effective one-component system. We alternatively suggest that--based on local geometric demixing--the polymer density takes the role of the conserved order parameter.

Correlation between dynamical and structural heterogeneities in colloidal hard-sphere suspensions

Experiments combining dynamic and static light scattering have probed a colloidal hard-sphere system for the formation of dynamical and structural heterogeneities, which play a role in both forms of solidification: crystallization and vitrification.

Micro-structure evolution of wall based crystals after casting of model suspensions as obtained from Bragg microscopy.

Growth of heterogeneously nucleated, wall based crystals plays a major role in determining the micro-structure during melt casting. This issue is here addressed using a model system of charged colloidal spheres in deionized aqueous suspension observed by Bragg microscopy which is a combination of light scattering and microscopy. We examine the evolution of the three-dimensional size, shape, and orientation of twin domains in monolithic crystals growing from two opposing planar walls into a meta-stable (shear-) melt. At each wall crystal orientation and twinning emerges during nucleation with small domains. During growth these widen and merge. From image analysis we observe the lateral coars…

Colloidal layers in magnetic fields and under shear flow

The behaviour of colloidal mono- and bilayers in external magnetic fields and under shear is discussed and recent progress is summarized. Superparamagnetic colloidal particles form monolayers when they are confined to a air–water interface in a hanging water droplet. An external magnetic field allows us to tune the strength of the mutual dipole–dipole interaction between the colloids and the anisotropy of the interaction can be controlled by the tilt angle of the magnetic field relative to the surface normal of the air–water interface. For sufficiently large magnetic field strength crystalline monolayers are found. The role of fluctuations in these two-dimensional crystals is discussed. Fur…

Crystallizing polystyrene microgel colloids

Spherical microgel particles of sufficiently high degree of internal cross-linking and swollen in a good solvent in many respects behave quite similarly to hard-sphere colloids. Due to solvent uptake they can be refractive-index-matched and density-matched in suitable organic solvents. We present preliminary measurements of the crystallization kinetics of 1:10 cross-linked polystyrene microgel particles. We measured Bragg and small-angle light scattering of the solidifying shear melt. Two different scattering patterns, a set of Debye-Scherrer rings and a second ring pattern at small angles could be observed. We check for similarities and differences compared to previously investigated collo…

Colloidal crystal motion in electric fields

Abstract We report on the short and long time flow behaviour of colloidal crystals subjected to a homogeneous electrical square wave a.c.-field in closed cells of rectangular cross section. Local velocities are determined from Laser Doppler velocimetry, sample structure and morphology were observed by time resolved polarisation microscopy. We observe a complex time dependence of the flow behaviour. After each field reversal we find a transition from an initial parabola-like flow to a final plug-like flow. On the time scale of minutes to hours channel narrowing occurs, i.e. flow initially restricted by the cell walls becomes restricted to the cell centre by wall based stationary crystals. Wi…

Salt concentration and particle density dependence of electrophoretic mobilities of spherical colloids in aqueous suspension.

Using laser Doppler velocimetry in the superheterodyne mode, we conducted a systematic study of the electrophoretic mobility of dispersions of small silica spheres (a=18 nm) suspended in water at different salinities and particle concentrations. The concentration of NaCl was varied from 40 microM up to 16 mM, while the particle concentrations were varied between 4.2x10(18) and 2.1x10(20) m-3. We find a decrease of mobility with increasing salt concentrations and an increase with increased particle number densities. The latter observation is not backed by the standard cell model of electrophoresis with Shilov-Zharkikh boundary conditions. Rather, if the experimental data are interpreted with…

Drude-type conductivity of charged sphere colloidal crystals: Density and temperature dependence

We report on extensive measurements in the low-frequency limit of the ac conductivity of colloidal fluids and crystals formed from charged colloidal spheres suspended in de-ionized water. Temperature was varied in a range of 5 degrees CTheta35 degrees C and the particle number density n between 0.2 and 25 microm(-3) for the larger, respectively, 2.75 and 210 microm(-3) for the smaller of two investigated species. At fixed Theta the conductivity increased linearly with increasing n without any significant change at the fluid-solid phase boundary. At fixed n it increased with increasing Theta and the increase was more pronounced for larger n. Lacking a rigorous electrohydrodynamic treatment f…

Modular approach to microswimming

The field of active matter in general and microswimming in particular has experienced a rapid and ongoing expansion over the last decade. A particular interesting aspect is provided by artificial autonomous microswimmers constructed from individual active and inactive functional components into self-propelling complexes. Such modular microswimmers may exhibit directed motion not seen for each individual component. In this review, we focus on the establishment and recent developments in the modular approach to microswimming. We introduce the bound and dynamic prototypes, show mechanisms and types of modular swimming and discuss approaches to control the direction and speed of modular microsw…

Electrophoretic mobility of charged spheres

The electrophoretic mobility μ of charged 0.3 µm Polystyrene spheres suspended in water was measured over a wide range of salt concentrations c and packing fractions Φ. To observe isolated spheres at packing fractions Φ ≤ 2 × 10−7 a newly developed optical tweezing electrophoresis (OTE) apparatus was used. At deionised conditions μ=2.5 × 10−8 m2V−1s−1, it decreases further upon increasing the salt concentration c. Measurements at larger Φ generally show much larger μ and a qualitatively different dependence on c. At no added salt μ increases in the unordered state but a saturation at μ=6.8 × 10−8 m2V−1s−1 is observed, as the system develops fluid order. The fluid-crystal phase transition is…

Optical tweezing electrophoresis of isolated, highly charged colloidal spheres

Abstract We report on a novel optical tweezing experiment measuring the electrophoretic mobility μ of highly charged spherical particles suspended in water at volume fractions Φ≤2×10 −7 . At deionised conditions μ =2.5×10 −8 m 2 V −1 s −1 , it decreases further upon increasing the salt concentration c . We compare our data to measurements at larger Φ, where generally much larger μ and a qualitatively different dependence on the salt concentration are observed. To characterise the dependence on Φ we performed measurements at no added salt. There the mobility increases in the unordered state but stays constant at μ =6.8×10 −8 m 2 V −1 s −1 as the system develops fluid order. In the ordered re…

Residual order in amorphous dry films of polymer latices: indications of an influence of particle interaction

Abstract We report small angle X-ray scattering and atomic force microscopy measurements on macroscopically thick, dry films of polymer latex particles. While the surface of dried droplets has long range order due to layering effects, the overall bulk structure is amorphous. This holds for both low charge polymethylmetacrylate particles and for highly charged polystyrene particles with additional stabilisation with sodiumdodecylsurfate. In the latter case, however, considerable amounts of residual crystal-like order is observed.

Frustration of structural fluctuations upon equilibration of shear melts

Abstract We report on the formation of amorphous solids from aquaeous suspensions of charged colloidal spheres. Comprehensive light scattering and microscopic studies show that in these systems the nucleation rate density continuously increases to very high values. At the highest particle densities of 47.5 μm −3 (packing fraction Φ =0.146) an amorphous state is observed of only short range order, finite static shear modulus and frozen long time dynamics. This state is composed of a piling of––as we propose pre-critical––nuclei. Differences from the Hard Sphere case are discussed in some detail. There the arrest of density fluctuations is observed and described by Mode Coupling scenarios. In…

Correction: Polymer-enforced crystallization of a eutectic binary hard sphere mixture

Correction for 'Polymer-enforced crystallization of a eutectic binary hard sphere mixture' by Anna Kozina et al., Soft Matter, 2012, 8, 627-630.

Growth of a colloidal crystallite of hard spheres

Abstract We examine the growth of a single nucleus of hard spheres in a super-saturated colloidal dispersion of hard spheres. A model developed by Bruce Ackerson and Klaus Schatzel based on a Wilson-Frenkel growth law is used. Our emphasis is on the profile of the radial density distribution around the growing (but still spherically symmetric) grain and its Fourier transform, the grain's form factor, which can be observed under small scattering angles in a dynamic light scattering experiment. Depending on the value of the supersaturation we can identify two limiting cases of different growth exponents and density profiles: one is the Frank theory of diffusion-limited growth and the other is…

Crystalline multilayers of charged colloids in soft confinement: experiment versus theory.

We combine real-space experiments and lattice sum calculations to investigate the phase diagram of charged colloidal particles under soft confinement. In the experiments we explore the equilibrium phase diagram of charged colloidal spheres in aqueous suspensions confined between two parallel charged walls at low background salt concentrations. Motivated by the experiments, we perform lattice sum minimizations to predict the crystalline ground state of point-like Yukawa particles which are exposed to a soft confining wall potential. In the multilayered crystalline regime, we obtain good agreement between the experimental and numerical findings: upon increasing the density we recover the sequ…

Vitrification in restricted geometry: dry films of colloidal particles

We prepared dry films of colloidal particles from surfactant co-stabilized polystyrene and poly(methyl methacrylate) latex spheres of moderate polydispersity. The film thickness was varied from monolayer to some 20 μm. The average structure and the influence of polydispersity was analyzed by small-angle X-ray scattering. An analysis of local microscopic structures was performed by force microscopy on the least polydisperse sample. Irrespective of the thickness, we observe the formation of only short-ranged order which is rather pronounced but changes its qualitative character in the vicinity of the substrate. The observations suggest a bulk structure of small, defect-rich and stacking fault…

Properties of mixed colloidal crystals

We prepared colloidal crystals from aqueous suspensions of spherical, charged polystyrene spheres under deionised conditions. Using a home-built multipurpose light scattering apparatus we measured the static structure factor, the static shear modulus and the intermediate scattering function. In addition we also monitored also the conductivity as a function of the composition and the particle number density. For the mixture investigated the data are well described assuming the formation of randomly substituted body-centered-cubic crystals.

Active and Passive Motion in Complex pH‐Fields

Phenomenology of colloidal crystal electrophoresis

We studied the motion of polycrystalline solids comprising of charged sub-micron latex spheres suspended in deionized water. These were subjected to a low frequency alternating square wave electric field in an optical cell of rectangular cross section. Velocity profiles in X and Y direction were determined by Laser Doppler Velocimetry. The observed complex flow profiles are time dependent due to the combined effects of electro-osmosis, electrophoresis, crystal elasticity, and friction of the crystals at the cell wall. On small time scales elastic deformation occurs. On long time scales channel formation is observed. At intermediate times steady state profiles are dominated by a solid plug o…

Coupling between bulk- and surface chemistry in suspensions of charged colloids

The ionic composition and pair correlations in fluid phases of realistically salt-free charged colloidal sphere suspensions are calculated in the primitive model. We obtain the number densities of all ionic species in suspension, including low-molecular weight microions, and colloidal macroions with acidic surface groups, from a self-consistent solution of a coupled physicochemical set of nonlinear algebraic equations and non-mean-field liquid integral equations. Here, we study suspensions of colloidal spheres with sulfonate or silanol surface groups, suspended in demineralized water that is saturated with carbon dioxide under standard atmosphere. The only input required for our theoretical…

Crystal growth kinetics in binary mixtures of model charged sphere colloids

From the formation of crystalline materials from their melts is at the heat of many important industrial processes. A rigorous and comprehensive understanding of the crystallization process, however, is still lacking, and its experimental and theoretical investigation has remained a considerable challenge. We studied the crystal growth velocities v of random composition body centred cubic (rc-bcc) colloidal crystals formed from a shear molten binary mixture of charged colloidal spheres suspended in deionized water. We used Bragg microscopy at constant particle number density n and as a function of the number fraction of large particles p. With increasing p the growth velocity v first drops …

Unraveling modular microswimmers: From self-assembly to ion-exchange-driven motors

Active systems contain self-propelled particles and can spontaneously self-organize into patterns making them attractive candidates for the self-assembly of smart soft materials. One key limitation of our present understanding of these materials hinges on the complexity of the microscopic mechanisms driving its components forward. Here, by combining experiments, analytical theory, and simulations we explore such a mechanism for a class of active system, modular microswimmers, which self-assemble from colloids and ion-exchange resins on charged substrates. Our results unveil the self-assembly processes and the working mechanism of the ion-exchange driven motors underlying modular microswimme…

Particle characterization using multiple scattering decorrelation methods: hard-sphere model system

Applying static light scattering experiments, we characterize colloidal particles that are used as model hard-sphere systems in experiments investigating their crystallization kinetics. The particles comprise of a compact core of poly(methyl methacrylate) and short polymer hairs grafted onto the surface. We use a contrast variation procedure to determine the refractive index variation within the particles and observe that one component of the binary mixture used as a solvent penetrates the particles and masks completely the small polymer hairs. Making use of the determined refractive index variation, we obtain the average particle radius and its polydispersity from measurements of the parti…

Forces between colloidal particles in aqueous solutions containing monovalent and multivalent ions

The present article provides an overview of the recent progress in the direct force measurements between individual pairs of colloidal particles in aqueous salt solutions. Results obtained by two different techniques are being highlighted, namely with the atomic force microscope (AFM) and optical tweezers. One finds that the classical theory of Derjaguin, Landau, Verwey, and Overbeek (DLVO) represents an accurate description of the force profiles even in the presence of multivalent ions, typically down to distances of few nanometers. However, the corresponding Hamaker constants and diffuse layer potentials must be extracted from the force profiles. At low salt concentrations, double layer f…

Nucleation and crystal growth in a suspension of charged colloidal silica spheres with bi-modal size distribution studied by time-resolved ultra-small-angle X-ray scattering

A suspension of charged colloidal silica spheres exhibiting a bi-modal size distribution of particles, thereby mimicking a binary mixture, was studied using time-resolved ultra-small-angle synchrotron X-ray scattering (USAXS). The sample, consisting of particles of diameters d(A) = (104.7 ± 9.0) nm and d(B) = (88.1 ± 7.8) nm (d(A)/d(B) ≈ 1.2), and with an estimated composition A(0.6(1))B(0.4(1)), was studied with respect to its phase behaviour in dependance of particle number density and interaction, of which the latter was modulated by varying amounts of added base (NaOH). Moreover, its short-range order in the fluid state and its eventual solidification into a long-range ordered colloidal…

An Improved Empirical Relation to Determine the Particle Number Density of Fluid-Like Ordered Charge-Stabilized Suspensions

Polystyrene as an archetypal charge-stabilized colloid model system was used in this work under well defined preparation conditions. A continuous preparation technique was used to control the suspension parameters salt concentration c and particle number density n. Measurements of n were performed using both conductivity in the completely deionized state and static light scattering. We found a significant deviation between the position of the first maximum of the static structure factor qmax=2π/L and an estimate identifying the relevant length scale L with the average inter-particle distance d¯=n−1/3. Instead, qmax was observed to follow the relation qmax=(2.20±0.03)π/d¯, which is equivalen…

On the electrophoretic mobility of isolated colloidal spheres

We studied the electrophoretic mobility μ of highly charged colloidal spheres in very dilute low salt aqueous suspension. We combined experiments on individual particles and ensemble averaged measurements. In both cases μ was observed to be independent of particle size and surface chemistry. Corresponding effective charges Zμ*, however, scaled with the ratio of particle size to Bjerrum length λB: Zμ* = Aa/λB with a coefficient . Our results are discussed in comparison to other charge determination experiments and charge renormalization theory and with respect to the issue of charge polydispersity.

Microfluidic Pumping by Micromolar Salt Concentrations

An ion-exchange-resin-based microfluidic pump is introduced that utilizes trace amounts of ions to generate fluid flows. We show experimentally that our pump operates in almost deionized water for periods exceeding 24h and induces fluid flows of um/s over hundreds of um. This flow displays a far-field, power-law decay which is characteristic of two-dimensional (2D) flow when the system is strongly confined and of three-dimensional (3D) flow when it is not. Using theory and numerical calculations we demonstrate that our observations are consistent with electroosmotic pumping driven by umol/L ion concentrations in the sample cell that serve as 'fuel' to the pump. Our study thus reveals that t…

Observation of Oriented Close-Packed Lattice Planes in Polycrystalline Hard-Sphere Solids.

We report time-resolved Bragg scattering experiments on solidifying colloidal suspensions of hard spheres. The polar angle-averaged, integrated intensity of the (111) and (311) reflections show a transient, two-step behavior below melting, which depends in a complex way on the volume fraction and is not present for (200) or (220). Detailed analysis of the full two-dimensional scattering pattern reveals intensity maxima of sixfold symmetry close to the position of the (111) and (311) Debye-Scherrer rings. These can be explained assuming oriented crystals with close-packed planes parallel to the container walls. We show that the observed temporal behavior is due to competing homogeneous and h…

Colloidal and molecular electro-optics

The Kerr effect, also known as the quadratic electro-optic effect, was discovered more than a hundred years ago by John Kerr, a Scottish physicist [1]. It describes the change in the refractive index of a material in response to an applied electric field. Around 1950 its application swayed from simple to complex fluids. A strong contribution was made through a number of seminal papers by the French polymer scientist H Benoit [2–4]. These and others initiated wide interest from researchers working on macromolecular solutions or colloidal dispersions. Experimental activities were further boosted by the advent of the laser and theoretical approaches strongly drew from growing computer power. U…

Solidification kinetics of hard-sphere colloidal suspensions

We investigate the solidification dynamics of hard-sphere colloidal suspensions applying simultaneously small-angle and Bragg light scattering. These experiments allow a consistent picture of nucleation and crystal growth on the level of large-scale density fluctuations and of density fluctuations on the level of individual crystallites. We observe a temporally almost constant nucleation rate after an induction time that decreases with supersaturation. The classical expectation for the nucleation rate density as a function of supersaturation is in accordance with our data. We investigate the validity of the Wilson—Frenkel growth law for hard-sphere systems, which also fits our data satisfac…

Qualitative characterisation of effective interactions of charged spheres on different levels of organisation using Alexander’s renormalised charge as reference

Abstract Effective interactions are conveniently determined from experimental or numerical data by fitting a Debye–Huckel potential with an effective charge Z ∗ and an effective electrolyte concentration c ∗ as free parameters. In this contribution we numerically solved the Poisson–Boltzmann equation to obtain the so-called renormalised charge Z PBC ∗ . For sufficiently large bare charge Z one finds a saturation of Z ∗ which scales as Z ∗ = A a / λ B , where a is the particle radius, λ B the Bjerrum length and A a proportionality factor of order (8–10). The saturation value increases with increased total micro-ion concentration and shows a shallow minimum as a function of packing fraction. …

Colloidal crystallization in the quasi-two-dimensional induced by electrolyte gradients.

We investigated driven crystal formation events in thin layers of sedimented colloidal particles under low salt conditions. Using optical microscopy, we observe particles in a thermodynamically stable colloidal fluid to move radially converging towards cation exchange resin fragments acting as seed particles. When the local particle concentration has become sufficiently large, subsequently crystallization occurs. Brownian dynamics simulations of a 2D system of purely repulsive point-like particles exposed to an attractive potential, yield strikingly similar scenarios, and kinetics of accumulation and micro-structure formation. This offers the possibility of flexibly designing and manufactur…

Ripening-dominated crystallization in polydisperse hard-sphere-like colloids

We report on the crystal growth scenario in gravity-matched, polydisperse hard-sphere-like colloids at increasing particle concentration. In the fluid-crystal coexistence region, the crystal size as a function of time shows two separate regimes corresponding to crystal growth and crystal ripening. At higher supersaturation the crystal size grows according to the same power law through the whole experimental window of a few days: crystal growth and ripening merge together. We show that our observations cannot be explained by considering the slowing down of single-particle dynamics due to increasing volume fraction. We suggest that size fractionation occurring at the crystal-fluid interface i…

Effective charges along the melting line of colloidal crystals

The shear modulus G of charged colloidal crystals was measured at several constant particle densities n and varying salt concentrations c up to the melting salt concentration cM using torsional resonance spectroscopy. Far from the phase boundary the samples are polycrystalline and the shear modulus stays roughly constant as a function of c. Upon approaching the melting transition an increasing amount of wall based crystal material is formed surrounding a shrinking polycrystalline core and G drops nearly linearly. When the transition is complete G again stays constant. The morphologic transitions may be scaled upon a single master curve. For the polycrystalline morphology, the elastic data a…