We study the vibrational spectrum and the low energy modes of a three dimensional colloidal crystal using confocal microscopy. This is done in a two-dimensional cut through a three-dimensional crystal. We find that the observed density of states is incompatible with the standard Debye form in either two or three dimensions. These results are confirmed by numerical simulations. We show that an effective theory for the projections of the modes onto the two-dimensional cut describes the experimental and simulation data in a satisfactory way.
For like charged colloidal particles two mechanisms of attraction between them survive when the interparticle distance is larger than the Debye screening length. One of them is the conventional van der Waals attraction and the second one is the attraction mechanism mediated by thermal fluctuations of particle positions. The latter is related to an effective variable mass (Euler mass) of the particle produced by a fluid motion. The most stronger attraction potential (up to the value of temperature T) corresponds to a situation of uncharged particles and a relatively large Debye screening length…
A method for forming permanent three dimensional structures from colloidal particles using holographic optical trapping is described. Holographic optical tweezers (HOT) are used to selectively position charge stabilized colloidal particles within a flow cell. Once the particles are in the desired location an electrolyte solution is pumped into the cell which reduces the Debye length and induces aggregation caused by the van der Waals attraction. This technique allows for the formation of three dimensional structures both on and away from the substrate that can be removed from solution without …
The pair correlation function of charge stabilized colloidal particles under strongly sheared conditions is studied using the analytical intermediate asymptotics method recently developed in [L. Banetta and A. Zaccone, Phys. Rev. E 99, 052606 (2019)] to solve the steady-state Smoluchowski equation for medium to high values of the Péclet number; the analytical theory works for dilute conditions. A rich physical behaviour is unveiled for the pair correlation function of colloids interacting via the repulsive Yukawa (or Debye-Hückel) potential, in both the extensional and compressional sectors of…
In this dissertation we analyzed the double-layer force interaction between two dielectric charged colloidal spheres of different radii immersed in a solution of ions in water and in thermal equilibrium. In the limit of low electrostatic potential the interaction is governed by the Linearized Poisson-Boltzmann Equation (LPBE). We obtained an analytical solution from the LPBE for the electrostatic interaction via multipole expansion, considering a uniform and fixed surface charge density on the spheres. A code in the Mathematica platform was developed, allowing us to calculate the force between…
We formulate an extension of the Debye-Hueckel-Bjerrum theory [M. E. Fisher and Y. Levin, Phys. Rev. Lett. 71, 3826 (1993)] to the fluid state of a highly asymmetric charged colloid. Allowing for the formation of clusters consisting of one polyion and n condensed counterions, the total Helmholtz free energy of the colloidal suspension is constructed. The thermodynamic properties, such as the cluster-density distribution and the pressure, are obtained by the minimization of the free energy under the constraints of fixed number of polyions and counterions. In agreement with the current experimen…
We investigate - with 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 belon…
Colloidal particles are not simple rigid particles, in general an isolated particle is a system with many degrees of freedom in its own right, e.g., the counterions around a charged colloidal particle.The behaviour of model colloidal particles, with a simple phenomenological model to account for these degrees of freedom, is studied. It is found that the interaction between the particles is not pairwise additive. It is even possible that the interaction between a triplet of particles is attractive while the pair interaction is repulsive. When this is so the liquid phase is either stable only in…
More than 100 years after Debye proposed his model for the dielectric relaxation of monoalcohols (MA), some fundamental questions about their dynamics and its relation with the supramolecular structures created by hydrogen bonding remain not fully understood. The recent detection of the dynamics of hydrogen-bonded aggregates by techniques other than dielectric spectroscopy is leading to novel insights and opening new questions. In particular it was recently reported that the shear response of some MA present three relaxation components, at variance with their apparent bimodal dielectric respon…
Using a geometry-based fundamental measure density functional theory, we calculate bulk fluid phase diagrams of colloidal mixtures of vanishingly thin hard circular platelets and hard spheres. We find isotropic-nematic phase separation with strong broadening of the biphasic region upon increasing the pressure. In mixtures with large size ratio of platelet and sphere diameter, there is also demixing between two nematic phases with differing platelet concentrations. We formulate a fundamental-measure density functional for mixtures of colloidal platelets and freely overlapping spheres, which rep…
One of hallmark features of glass forming ultraviscous liquids is the decoupling between translational and orientational dynamics. This report presents studies of this phenomenon in glycerol, a canonical molecular glass former, heading for the impact of two exogenic factors: high pressures up to extreme 1.5 GPa and silver (Ag) nanoparticles (NP). The analysis is focused on the fractional Debye-Stokes-Einstein (FDSE) relation $σ(T,P)*(τ(T,P))^S = const$, linking DC electric conductivity $(σ)$ and primary $(α)$ relaxation time $(τ_α)$. In glycerol and its nanocolloid (glycerol with Ag-NP) under …
Electrostatic interactions between point charges embedded into interfaces separating dielectric media are omnipresent in soft matter systems and often control their stability. Such interactions are typically complicated and do not resemble their bulk counterparts. For instance, the electrostatic potential of a point charge at an air-water interface falls off as $r^{-3}$, where $r$ is the distance from the charge, exhibiting a dipolar behaviour. This behaviour is often assumed to be generic, and is widely referred to when interpreting experimental results. Here we explicitly calculate the in-pl…
Using a carefully justified development of Debye-Huckel theory for highly asymmetric electrolytes, one finds that a region of expanded phase instability, or miscibility gap, can appear for charge-stabilised colloidal suspensions at high charges and low ionic strengths. It is argued that this is offers a straightforward explanation for the observations of void structures and other anomalies in such suspensions in this region. The nature of the interface between coexisting phases, and general arguments that many-body attractions form a key part of the underlying physical picture, are also examin…
In titration experiments with NaOH we have determined the full phase diagram of charged colloidal spheres in dependence on the particle density n, the particle effective charge Zeff and the concentration of screening electrolyte c using microscopy, light and Ultra Small Angle X-Ray Scattering (USAXS). For sufficiently large n the system crystallizes upon increasing Zeff at constant c and melts upon increasing c at only slightly altered Zeff. In contrast to earlier work equilibrium phase boundaries are consistent with a universal melting line prediction from computer simulation, if the elastici…
We report on the low temperature behaviour of the colloidal electrolyte by means of Molecular Dynamics simulations, where the electrostatic interactions were modeled using effective screened interactions. As in previous works, we have found a region of gas-liquid coexistence located in the low $T$- low $ρ$ region. At temperatures much lower than the critical one, the system cannot reach equilibrium, that is, the gas-liquid transition is arrested. Two different mechanisms have been identified to cause arrest: gelation in the lowest $T$ and crowding at intermediate $T$ values, the latter associa…
We study low-salt, binary aqueous suspensions of charged colloidal spheres of size ratio Phi = 0.57, number densities below the eutectic number density n_E, and number fractions of p = 1.00-0.40. The typical phase obtained by solidification from a homogeneous shear-melt is a substitutional alloy of body centred cubic structure. In strictly gas-tight vials, the polycrystalline solid is stable against melting and further phase transformation for extended times. For comparison, we prepare the same samples also by slow and mechanically undisturbed deionization in commercial slit cells. These cells…
Colloidal photonic crystals display peculiar optical properties which make them particularly suitable for application in different fields. However, the low packing fraction of the targeted structures usually poses a real challenge in the fabrication stage. Here, we propose a novel route to colloidal photonic crystals via a binary mixture of hard tetramers and hard spheres. By combining theory and computer simulations, we calculate the phase diagram as well as the stacking diagram of the mixture, and show that a colloidal analogue of the MgCu2 Laves phase -- which can serve as a precursor of a …
Using simulations we explore the behaviour of two-dimensional colloidal (poly)crystals doped with active particles. We show that these active dopants can provide an elegant new route to removing grain boundaries in polycrystals. Specifically, we show that active dopants both generate and are attracted to defects, such as vacancies and interstitials, which leads to clustering of dopants at grain boundaries. The active particles both broaden and enhance the mobility of the grain boundaries, causing rapid coarsening of the crystal domains. The remaining defects recrystallize upon turning off the …
The vibrational modes of pristine and polycrystalline monolayer colloidal crystals composed of thermosensitive microgel particles are measured using video microscopy and covariance matrix analysis. At low frequencies, the Debye relation for two dimensional harmonic crystals is observed in both crystal types; at higher frequencies, evidence for van Hove singularities in the phonon density of states is significantly smeared out by experimental noise and measurement statistics. The effects of these errors are analyzed using numerical simulations. We introduce methods to correct for these limitati…
I review recent progress in understanding the arrest and flow behaviour of colloidal glasses, based on mode coupling theory (MCT) and related approaches. MCT has had notable recent successes in predicting the re-entrant arrest behaviour of colloids with short range attractions. Developments based upon it offer important steps towards calculating, from rational foundations in statistical mechanics, nonlinear flow parameters such as the yield stress of a colloidal glass. An important open question is why MCT works so well.
We study the effective interaction between differently charged polyelectrolyte-colloid complexes in electrolyte solutions via Monte Carlo simulations. These complexes are formed when short and flexible polyelectrolyte chains adsorb onto oppositely charged colloidal spheres, dispersed in an electrolyte solution. In our simulations the bending energy between adjacent monomers is small compared to the electrostatic energy, and the chains, once adsorbed, do not exchange with the solution, although they rearrange on the particles surface to accomodate further adsorbing chains or due to the electros…
We study the flow of model experimental hard sphere colloidal suspensions at high volume fraction $Φ$ driven through a constriction by a pressure gradient. Above a particle-size dependent limit $Φ_0$, direct microscopic observations demonstrate jamming and unjamming--conversion of fluid to solid and vice versa--during flow. We show that such a jamming flow produces a reduction in colloid concentration $Φ_{x}$ downstream of the constriction. We propose that this `self-filtration' effect is the consequence of a combination of jamming of the particulate part of the system and continuing flow of t…
Complex fluids exhibit a variety of exotic flow behaviours under high stresses, such as shear thickening and shear jamming. Rheology is a powerful tool to characterise these flow behaviours over the bulk of the fluid. However, this technique is limited in its ability to probe fluid behaviour in a spatially resolved way. Here, we utilise high-speed imaging and the free-surface geometry in drop impact to study the flow of colloidal suspensions. We report, for the first time, observations of coexisting solid and liquid phases due to shear jamming caused by impact. In addition to observing Newtoni…
Colloidal particles trapped at an interface between two fluids can form a wide range of different structures. Replacing one of the fluid with a liquid crystal increases the complexity of interactions and results in a greater range of possible structures. New behaviour emerges when colloidal particles interact with defects in the liquid crystal phases. Here we discuss the templating of colloids at a cholesteric isotropic interface.
Electrostatic interactions make a large contribution to solvation free energy in ionic fluids such as electrolytes and colloidal dispersions. The electrostatic contribution to solvation free energy has been ascribed to the self-energy of a charged particle. Here we apply a variational field theory based on lower bound inequality to the inhomogeneous fluids of one-component charged hard-spheres, thereby verifying that the self-energy is given by the difference between the total correlation function and direct correlation function. Based on the knowledge of the liquid state theory, the self-ener…
Brownian dynamics simulations of a coarse-grained bead-spring chain model, with Debye-Hückel electrostatic interactions between the beads, are used to determine the root-mean-square end-to-end vector, the radius of gyration, and various shape functions (defined in terms of eigenvalues of the radius of gyration tensor) of a weakly-charged polyelectrolyte chain in solution, in the limit of low polymer concentration. The long-time diffusivity is calculated from the mean square displacement of the centre of mass of the chain, with hydrodynamic interactions taken into account through the incorporat…
We study the phase behaviour of a fluid composed of particles which interact via a pair potential that is repulsive for large inter-particle distances, is attractive at intermediate distances and is strongly repulsive at short distances (the particles have a hard core). As well as exhibiting gas-liquid phase separation, this system also exhibits phase transitions from the uniform fluid phases to modulated inhomogeneous fluid phases. Starting from a microscopic density functional theory, we develop an order parameter theory for the phase transition in order to examine in detail the phase behavi…
Within the framework of the mode-coupling theory of super-cooled liquids, we investigate new phenomena in colloidal systems on approach to their glass transitions. When the inter-particle potential contains an attractive part, besides the usual repulsive hard core, two intersecting liquid-glass transition lines appear, one of which extends to low densities, while the other one, at high densities, shows a re-entrant behaviour. In the glassy region a new type of transition appears between two different types of glasses. The complex phenomenology can be described in terms of higher order glass tr…
Complex fluids containing low concentrations of slender colloidal rods can display a high viscosity, while little flow is needed to thin the fluid. This feature makes slender rods essential constituents in industrial applications and biology. Though this behaviour strongly depends on the rod-length, so far no direct relation could be identified. We employ a library of filamentous viruses to study the effect of rod size and flexibility on the zero-shear viscosity and shear-thinning behaviour. Rheology and small angle neutron scattering data are compared to a revised version of the standard theo…
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 m…
We study many-particle diffusion in 2D colloidal suspensions with full hydrodynamic interactions through a novel mesoscopic simulation technique. We focus on the behaviour of the effective scaled tracer and collective diffusion coefficients $D_T(ρ) / D_0$ and $D_C(ρ) / D_0$, where $D_0$ is the single-particle diffusion coefficient, as a function of the density of the colloids $ρ$. At low Schmidt numbers $Sc={\cal O}(1)$, we find that hydrodynamics has essentially no effect on the behaviour of $D_T(ρ)/D_0$. At larger $Sc$, $D_T(ρ)/D_0$ is enhanced at all densities, although the differences comp…
Using fundamental measure density functional theory we investigate paranematic-nematic and nematic-nematic phase coexistence in binary mixtures of circular platelets with vanishing thicknesses. An external magnetic field induces uniaxial alignment and acts on the platelets with a strength that is taken to scale with the platelet area. At particle diameter ratio lambda=1.5 the system displays paranematic-nematic coexistence. For lambda=2, demixing into two nematic states with different compositions also occurs, between an upper critical point and a paranematic-nematic-nematic triple point. Incr…
Strongly confined colloidal dispersions under shear can exhibit a variety of dynamical phenomena, including depinning transitions and complex structural changes. Here, we investigate the behaviour of such systems under pure oscillatory shearing with shear rate $\dotγ(t) = \dotγ_0 \cos(ωt)$, as it is a common scenario in rheological experiments. The colloids' depinning behaviour is assessed from a particle level based on trajectories, obtained from overdamped Brownian Dynamics simulations. The numerical approach is complemented by an analytic one based on an effective single-particle model in t…
We study the stability of mixtures of highly screened repulsive charged spheres and non-adsorbing ideal polymer chains in a common solvent using free volume theory. The effective interaction between charged colloids in an aqueous salt solution is described by a screened-Coulomb pair potential, which supplements the pure hard-sphere interaction. The ideal polymer chains are treated as spheres that are excluded from the colloids by a hard-core interaction, whereas the interaction between two ideal chains is set to zero. In addition, we investigate the phase behaviour of charged colloid-polymer m…
We study the dynamic behaviour of concentrated colloidal hard spheres using Time Resolved Correlation, a light scattering technique that can detect the slow evolution of the dynamics in out-of-equilibrium systems. Surprisingly, equilibrium is reached a very long time after sample initialization, the non-stationary regime lasting up to three orders of magnitude more than the relaxation time of the system. Before reaching equilibrium, the system displays unusual aging behaviour. The intermediate scattering function decays faster than exponentially and its relaxation time evolves non-monotonicall…
Phase transitions and collective dynamics of active colloidal suspensions are fascinating topics in soft matter physics, particularly for out-of-equilibrium systems, which can lead to rich rheological behaviours in the presence of steady shear flow. In this article, the role of self-propulsion in the rheological response of a dense colloidal suspension is investigated by using particle-resolved simulations. First, the interplay between activity and shear in the solid to the liquid transition of the suspension is analysed. While both self-propulsion and shear destroy order and melt the system b…
Understanding how colloidal suspensions behave in confined environments has a striking relevance in practical applications. Despite the fact that the behaviour of colloids in the bulk is key to identify the main elements affecting their equilibrium and dynamics, it is only by studying their response under confinement that one can ponder the use of colloids in formulation technology. In particular, confining fluids of anisotropic particles in nanopores provides the opportunity to control their phase behaviour and stabilise a spectrum of morphologies that cannot form in the bulk. By properly sel…
We present a field-theoretic renormalization group (RG) analysis of a single flexible, screened polyelectrolyte chain (a Debye-Hückel chain) in a polar solvent. We point out that the Debye-Hückel chain may be mapped onto a local field theory which has the same fixed point as a generalised $n \to 1$ Potts model. Systematic analysis of the field theory shows that the system is one with two interplaying length-scales requiring the calculation of scaling functions as well as exponents to fully describe its physical behaviour. To illustrate this, we solve the RG equation and explicitly calculate th…
We perform extensive Monte Carlo simulations to investigate the phase behaviour of colloidal suspensions of hard board-like particles (HBPs). While theories restricting particle orientation or ignoring higher ordered phases suggest the existence of a stable biaxial nematic phase, our recent simulation results on monodisperse systems indicate that this is not necessarily the case, even for particle shapes exactly in between prolate and oblate geometries, usually referred to as self-dual shape. Motivated by the potentially striking impact of incorporating biaxial ordering into display applicatio…
Using both dynamical density functional theory and particle-resolved Brownian dynamics simulations, we explore the flow of two-dimensional colloidal solids and fluids driven through a linear channel with a geometric constriction. The flow is generated by a constant external force acting on all colloids. The initial configuration is equilibrated in the absence of flow and then the external force is switched on instantaneously. Upon starting the flow, we observe four different scenarios: a complete blockade, a monotonic decay to a constant particle flux (typical for a fluid), a damped oscillator…
Colloidal gels constitute an important class of materials found in many contexts and with a wide range of applications. Yet as matter far from equilibrium, gels exhibit a variety of time-dependent behaviours, which can be perplexing, such as an increase in strength prior to catastrophic failure. Remarkably, such complex phenomena are faithfully captured by an extremely simple model - "sticky spheres". Here we review progress in our understanding of colloidal gels made through the use of real space analysis and particle resolved studies. We consider the challenges of obtaining a suitable experi…
We study the phase behaviour and the collective dynamics of interacting paramagnetic colloids assembled above a honeycomb lattice of triangular shaped magnetic minima. A frustrated colloidal molecular crystal is realized when filling these potential minima with exactly two particles per pinning site. External in-plane rotating fields are used to anneal the system into different phases, including long range ordered stripes, random fully packed loops, labyrinth and disordered states. At higher amplitude of the annealing field, the dimer lattice displays a two step melting transition where the in…
Computer simulations were used to study the gel transition occurring in colloidal systems with short range attractions. A colloid-polymer mixture was modelled and the results were compared with mode coupling theory expectations and with the results for other systems (hard spheres and Lennard Jones). The self-intermediate scattering function and the mean squared displacement were used as the main dynamical quantities. Two different colloid packing fractions have been studied. For the lower packing fraction, $α$-scaling holds and the wave-vector analysis of the correlation function shows that ge…
We use thermodynamic perturbation theory to calculate the free energies and resulting phase diagrams of binary systems of spherical colloidal particles and interacting polymer coils in good solvent within an effective one-component representation of such mixtures, whereby the colloidal particles interact via a polymer-induced depletion potential. MC simulations are used to test the convergence of the high temperature expansion of the free energy. The phase diagrams calculated for several polymer to colloid size ratios differ considerably from the results of similar calculations for mixtures of…
The quest for designing new self-propelled colloids is fuelled by the demand for simple experimental models to study the collective behaviour of their more complex natural counterparts. Most synthetic self-propelled particles move by converting the input energy into translational motion. In this work we address the question if simple self-propelled spheres can assemble into more complex structures that exhibit rotational motion, possibly coupled with translational motion as in flagella. We exploit a combination of induced dipolar interactions and a bonding step to create permanent linear bead …
We use theory and simulations to investigate the existence of amorphous glassy states in ultrasoft colloids. We combine the hyper-netted chain approximation with mode-coupling theory to study the dynamic phase diagram of soft repulsive spheres interacting with a Hertzian potential, focusing on low temperatures and large densities. At constant temperature, we find that an amorphous glassy state is entered upon compression, as in colloidal hard spheres, but the glass unexpectedly melts when density increases further. We attribute this re-entrant fluid-glass transition to particle softness, and c…
Colloids have a striking relevance in a wide spectrum of industrial formulations, spanning from personal care products to protective paints. Their behaviour can be easily influenced by extremely weak forces, which disturb their thermodynamic equilibrium and dramatically determine their performance. Motivated by the impact of colloidal dispersions in fundamental science and formulation engineering, we have designed an efficient Dynamic Monte Carlo (DMC) approach to mimic their out-of-equilibrium dynamics. Our recent theory, which provided a rigorous method to reproduce the Brownian motion of co…
Colloidal gels consist of percolating networks of interconnected arms. Their mechanical properties depend on the individual arms, and on their collective behaviour. We use numerical simulations to pull on a single arm, built from a model colloidal gel-former with short-ranged attractive interactions. Under elongation, the arm breaks by a necking instability. We analyse this behaviour at three different length scales: a rheological continuum model of the whole arm; a microscopic analysis of the particle structure and dynamics; and the local stress tensor. Combining these different measurements …
Colloidal particles dispersed in a liquid crystal lead to distortions of the director field. The distortions are responsible for long-range effective colloidal interactions whose asymptotic behaviour is well understood. The short distance behaviour of the interaction, however, is sensitive to the structure and dynamics of the topological defects nucleated near the colloidal particles in the strong anchoring regime. The full non-linear theory is required in order to determine the interaction at short separations. Spherical colloidal particles with sufficiently strong planar degenerate anchoring…
Understanding the rheology of colloidal suspensions is crucial in the formulation of a wide selection of industry-relevant products. To characterise the viscoelastic behaviour of these soft materials, one can analyse the microscopic dynamics of colloidal tracers diffusing through the host fluid and generating local deformations and stresses. This technique, referred to as microrheology, links the bulk rheology of fluids to the microscopic dynamics at the particle scale. If tracers are subjected to external forces, rather than freely diffusing, it is called active microrheology. Motivated by th…
We introduce simple prescriptions of the Yukawa potential to describe the effect of size polydispersity and macroion shielding effect in charged colloidal systems. The solid-liquid phase boundaries were presented with the Lindemann criterion based on molecular dynamics simulations. Compared with the Robbins-Kremer-Grest simulation results, a deviation of melting line is observed at small $λ$, which means large macroion screening length. This deviation of phase boundary is qualitatively consistent with the simulation result of the nonlinear Poisson-Boltzmann equation with full many-body interac…
We study experimentally and numerically the motion of a self-phoretic active particle in two-dimensional (2D) loosely-packed colloidal crystals at fluid interfaces. Two scenarios emerge depending on the interaction between the active particle and the lattice: the active particle either navigates throughout the crystal as an interstitial or is part of the lattice and behaves as an active atom. Active interstitials undergo a run-and-tumble motion, with the passive colloids of the crystal acting as tumbling sites. Instead, active atoms exhibit an intermittent motion, which stems from the interpla…
The effects of an externally applied one-dimensional periodic potential on the freezing/melting behaviour of two-dimensional systems of colloidal particles with a short-range attractive interaction are studied using Monte Carlo simulations. In such systems, incommensuration results when the periodicity of the external potential does not match the length-scale at which the minimum of the attractive potential occurs. To study the effects of this incommensuration, we consider two different models for the system. Our simulations for both these models show the phenomenon of reentrant freezing as th…
