We briefly review recent theoretical and simulation studies of charged colloidal dispersions in alternating electric fields (AC fields). The response of single colloid to an external field can be characterized by a complex polarizability, which describes the dielectric properties of the colloid and its surrounding electrical double layer. We present computer simulation studies of single spherical colloid, using a coarse-grained mesoscale approach that accounts in full for hydrodynamic and electrostatic interactions as well as for thermal fluctuations. We investigate systematically a number of controlling parameters, such as the amplitude and frequency of the AC-fields. The results are in good agreement with recent theoretical predictions.
We study the response of single nanosized spherical colloids in electrolyte solution to an alternating electric field (AC field) by computer simulations. We use a coarse-grained mesoscopic simulation approach that accounts in full for hydrodynamic and electrostatic interactions as well as for thermal fluctuations. The solvent is modeled as a fluid of single Dissipative Particle Dynamics (DPD) beads, and the colloidal particle is modeled as a rigid body made of DPD beads. We compute the mobility and the polarizability of a single colloid and investigate systematically the effect of amplitude an…
Physical properties of colloidal materials can be modified by addition of nanoparticles. Within a model of like-charged mixtures of particles governed by effective electrostatic interactions, we explore the influence of charged nanoparticles on the structure and thermodynamic phase stability of charge-stabilized colloidal suspensions. Focusing on salt-free mixtures of particles of high size and charge asymmetry, interacting via repulsive Yukawa effective pair potentials, we perform molecular dynamics simulations and compute radial distribution functions and static structure factors. Analysis o…
Thermally driven colloidal transport is, to a large extent, due to the thermoelectric or Seebeck effect of the charged solution.We show that, contrary to the generally adopted single-particle picture, the transport coefficient depends on the colloidal concentration. For solutions that are dilute in the hydrodynamic sense, collective effects may significantly affect the thermophoretic mobility. Our results provide an explanation for recent experimental observations on polyelectrolytes and charged particles and suggest that for charged colloids collective behavior is the rule rather than the exc…
We study the behavior of negatively charged colloids with two positively charged polar caps close to a planar patterned surface. The competition between the different anisotropic components of the particle-particle interaction patterns is able by itself to give rise to a rich assembly scenario: colloids with charged surface patterns form different crystalline domains when adsorbed to a homogeneously charged substrate. Here we consider substrates composed of alternating (negative/neutral, positive/neutral and positive/negative) parallel stripes and, by means of Monte Carlo simulations, we inves…
We introduce the Poisson-Boltzmann cell model for spherical colloidal particles with a heterogeneous surface charge distribution. This model is obtained by generalizing existing cell models for mixtures of homogeneously charged colloidal spheres. Our new model has similar features as Onsager's second-virial theory for liquid crystals, but it predicts no orientational ordering if there is no positional ordering. This implies that all phases of heterogeneously charged colloids that are liquid-like with respect to translational degrees of freedom are also isotropic with respect to particle orient…
A mesoscopic colloid model is developed in which a spherical colloid is represented by many interacting sites on its surface. The hydrodynamic interactions with thermal fluctuations are taken accounts in full using Dissipative Particle Dynamics, and the electrostatic interactions are simulated using Particle-Particle-Particle Mesh method. This new model is applied to investigate the electrophoretic mobility of a charged colloid under an external electric field, and the influence of salt concentration and colloid charge are systematically studied. The simulation results show good agreement with…
We study the thermal diffusion coefficient DT of a charged colloid in a temperature gradient, and find that it is to a large extent determined by the thermoelectric response of the electrolyte solution. The thermally induced salinity gradient leads in general to a strong increase with temperature. The difference of the heat of transport of coions and counterions gives rise to a thermoelectric field that drives the colloid to the cold or to the warm, depending on the sign of its charge. Our results provide an explanation for recent experimental findings on thermophoresis in colloidal suspension…
Binary mixture of oppositely charged of colloids can be used to stabilize water-in-oil or oil-in-water emulsions. A Monte Carlo simulation study to address the effect of charge ratio of colloids on the stability of Pickering emulsions is presented. The colloidal particles at the interface are modeled as aligned dipolar hard spheres, with attractive interactions between unlike-charged and repulsive interaction between like-charged particles. The optimum composition (fraction of positively charged particles) required for the stabilization corresponds to a minimum in the interaction energy per pa…
Charged colloids can behave as Yukawa systems, with similar phase behaviour. Using particle- resolved studies, we consider a system with an unusually long Debye screening length which forms crystals at low colloid volume fraction ϕ ~ 0.01. We quantitatively compare this system with the Yukawa model and find that its freezing point is compatible with the theoretical prediction but that the crystal polymorph is not always that expected. In particular we find body-centred cubic crystals where face-centred cubic crystals are expected.
We study the inverse problem of tuning interaction parameters between charged colloidal particles interacting with a hard-core repulsive Yukawa potential, so that they assemble into specified crystal structures. Here, we target the body-centered-cubic (bcc) structure which is only stable in a small region in the phase diagram of charged colloids and is, therefore, challenging to find. In order to achieve this goal, we use the statistical fluctuations in the bond orientational order parameters to tune the interaction parameters for the bcc structure, while initializing the system in the fluid p…
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 s…
Phase diagrams of binary mixtures of oppositely charged colloids are calculated theoretically. The proposed mean-field-like formalism interpolates between the limits of a hard-sphere system at high temperatures and the colloidal crystals which minimize Madelung-like energy sums at low temperatures. Comparison with computer simulations of an equimolar mixture of oppositely charged, equally sized spheres indicate semi-quantitative accuracy of the proposed formalism. We calculate global phase diagrams of binary mixtures of equally sized spheres with opposite charges and equal charge magnitude in …
We examine the translation and rotation of an uncharged spheroidal colloid in polar solvents (water) near a charged flat surface. We solve the nonlinear Poisson-Boltzmann equation outside of the colloid in two dimensions for all tilt angles $θ$ with respect to the surface normal. The colloid's size is assumed to be comparable to the Debye's length and hence field gradients are essential. The Maxwell stress tensor, including the ideal gas pressure of ions, is integrated over the colloid's surface to give the total force and torque on the colloid. From the torque we calculate the effective angul…
We study the electrophoretic flow of suspensions of charged colloids with a mesoscopic method that allows to model generic experimental conditions. We show that for highly charged colloids their electrophoretic mobility increases significantly and displays a mobility maximum on increasing the colloidal charge for all salt concentrations. The electrophoretic mobility of highly charged colloids is also enhanced significantly when ion advection is dominant, leading to a strong heterogeneity in the local electrophoretic response especially at low salt concentration, when ion diffuse layers overlap…
We present a theory of effective electrostatic interactions in polydisperse suspensions of charged macroions, generalizing to mixtures a theory previously developed for monodisperse suspensions. Combining linear response theory with a random phase approximation for microion correlations, we coarse-grain the microion degrees of freedom to derive general expressions for effective macroion-macroion pair potentials and a one-body volume energy. For model mixtures of charged hard-sphere colloids, we give explicit analytical expressions. The resulting effective pair potentials have the same general …
The ion distribution around charged colloids in solution has been investigated intensely during the last decade. However, few theoretical approaches have included the influence of variation in the dielectric permittivity within the system, let alone in the surrounding solvent. In this article, we introduce two relatively new methods that can solve the Poisson equation for systems with varying permittivity. The harmonic interpolation method (HIM) approximately solves the Green's function in terms of a spherical harmonics series, and thus provides analytical ion-ion potentials for the Hamiltonia…
Charge and Salt Driven Reentrant Order-Disorder and Gas-Solid Transitions in Charged Colloids
蒙特卡罗模拟已被执行的含水带电胶体悬浮液作为一个功能的电荷密度的颗粒和盐浓度。我们在我们的模拟中在一定范围内改变电荷密度，其中Yamanaka等人已经报道了二氧化硅和聚合物胶乳颗粒悬浮液中的重入固-液转变[Phys. Rev. Lett. 80 5806（1998）]。我们表明，在低离子强度的均匀液体状有序悬浮液进行结晶时，增加电荷密度。电荷密度的进一步增加再次导致无序状态，这与实验观察一致。除了这种可重入的有序无序过渡，我们观察到一个不均匀的均匀过渡在我们的模拟时，盐被添加到无序的不均匀状态。这种从非均匀到均匀的无序转变类似于原子系统的固-气转变，但在带电胶体中尚未观察到。根据目前的模拟结果，带电胶体悬浮液的实验观察报告进行了讨论。
Computer simulations are used to investigate the response of a charged colloid and its surrounding microion cloud to an external electric field. Both static fields (DC) and alternating fields (AC) are considered. A mesoscopic simulation method is implemented to account in full for hydrodynamic and electrostatic interactions. The response of the system can be characterized by two quantities: the mobility and the polarizability. Due to the interplay of the electrostatic attraction and hydrodynamic drag, the response of the microions close to the colloid surface is different from that of the micr…
Gas-Solid Coexistence in Highly Charged Colloidal Suspensions
采用静态光散射（SLS）和共聚焦激光扫描显微镜（CLSM）研究了不同体积分数的高电荷聚苯乙烯颗粒的水悬浮液的结构有序性和相行为。在去离子条件下，高电荷密度胶体颗粒的悬浮液保持无序，而相对低电荷密度的悬浮液通过对可见光表现出彩虹色而显示结晶。虽然对于肉眼结晶悬浮液出现均匀，静态光散射测量和CLSM观察揭示了其不均匀的性质，在共存的形式的空隙与致密有序的区域。CLSM调查无序悬浮液显示其不均匀性的形式共存的空隙与密集的无序（无定形）区域。我们对高电荷胶体的研究证实了气-固转变的发生，并且与使用具有长程吸引项的对势的蒙特卡罗模拟的预测一致[Mohanty和Tata，Journal of Colloid and Interface Science 2003，264，101]。基于我们的实验和模拟结果，我们认为，所报道的重入无序态[Yamanaka et al Phys. Rev. Lett. 1998，80，5806和Toyotama等人，Langmuir，2003，19，3236]在高电荷密度下观察到的带电胶体中存在气固共存状态。
We calculate the ion and composition distributions around colloid particles in an aqueous mixture, accounting for preferential adsorption, electrostatic interaction, selective solvation among ions and polar molecules, and composition-dependent ionization. On the colloid surface, we predict a precipitation transition induced by strong preference of hydrophilic ions to water and a prewetting transition between weak and strong adsorption and ionization. These transition lines extend far from the solvent coexistence curve in the plane of the interaction parameter χ(or the temperature) and the aver…
Hydrophobic PMMA colloidal particles, when dispersed in oil with a relatively high dielectric constant, can become highly charged. In the presence of an interface with a conducting aqueous phase, image charge effects lead to strong binding of colloidal particles to the interface, even though the particles are wetted very little by the aqueous phase. In this paper, we study both the behavior of individual colloidal particles as they approach the interface, and the interactions between particles that are already interfacially bound. We demonstrate that using particles which are minimally wetted …
It is general wisdom that the pair potential of charged colloids in a liquid may be closely approximated by a Yukawa interaction, as predicted by the classical Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. We experimentally determine the effective forces in a binary mixture of like-charged particles, of species 1 and 2, with blinking optical tweezers. The measured forces are consistent with a Yukawa pair potential but the (12) cross-interaction is not equal to the geometric mean of the (11) and (22) like-interactions, as expected from DLVO. The deviation is a function of the electrostatic sc…
Machine-Learned Many-Body Potentials for Charged Colloids reveal Gas-Liquid Spinodal Instabilities only in the strong-coupling regime of Primitive Models
We generalize the inverse patchy colloid model that was originally developed for heterogeneously charged particles with two identical polar patches and an oppositely charged equator to a model that can have a considerably richer surface pattern. Based on a Debye-Hueckel framework, we propose a coarse-grained description of the effective pair interactions that is applicable to particles with an arbitrary patch decoration. We demonstrate the versatility of this approach by applying it to models with (i) two differently charged and/or sized patches, and (ii) three, possibly different patches.
The ability to dictate colloid motion is an important challenge in fields ranging from materials science to living systems. Here, by embedding energy landscapes in confined nematic liquid crystals, we design a versatile platform to define colloidal migration. This is achieved by placing a wavy wall, with alternating hills and wells, in nematic liquid crystals, to impose a smooth elastic energy field with alternating splay and bend distortions. This domain generates (meta) stable loci that act as attractors and unstable loci that repel colloids over distances large compared to the colloid radiu…
Dynamic processes in dispersions of charged spherical particles are of importance both in fundamental science, and in technical and bio-medical applications. There exists a large variety of charged-particles systems, ranging from nanometer-sized electrolyte ions to micron-sized charge-stabilized colloids. We review recent advances in theoretical methods for the calculation of linear transport coefficients in concentrated particulate systems, with the focus on hydrodynamic interactions and electrokinetic effects. Considered transport properties are the dispersion viscosity, self- and collective…
Charged colloidal particles - both on the nano and micron scales - have been instrumental in enhancing our understanding of both atomic and colloidal crystals. These systems can be straightforwardly realized in the lab, and tuned to self-assemble into body-centered cubic (BCC) and face-centered cubic (FCC) crystals. While these crystals will always exhibit a finite number of point defects, including vacancies and interstitials - which can dramatically impact their material properties - their existence is usually ignored in scientific studies. Here, we use computer simulations and free-energy c…
Designing and fabricating self-assembled open colloidal crystals have become one major direction in soft matter community because of many promising applications associated with open colloidal crystals. However, most of the self-assembled crystals found in experiments are not open but close-packed. Here by using computer simulation, we systematically investigate the self-assembly of oppositely charged colloidal hard spheres confined between two parallel hard walls, and we find that the confinement can stabilize multi-layer NaCl-like (simple cubic) open crystals. The maximal layers of stable NaC…
We study the phase behavior of a system of charged colloidal particles that are electrostatically bound to an almost flat interface between two fluids. We show that, despite the fact that our experimental system consists of only $10^{3}$ - $10^{4}$ particles, the phase behavior is consistent with the theory of melting due to Kosterlitz, Thouless, Halperin, Nelson and Young (KTHNY). Using spatial and temporal correlations of the bond-orientational order parameter, we classify our samples into solid, isotropic fluid, and hexatic phases. We demonstrate that the topological defect structure we obs…
The Seebeck and Soret coefficients of ionically stabilized suspension of maghemite nanoparticles in dimethyl sulfoxide are experimentally studied as a function of nanoparticle volume fraction. In the presence of a temperature gradient, the charged colloidal nanoparticles experience both thermal drift due to their interactions with the solvent molecules and electric forces proportional to the internal thermoelectric field. The resulting thermodiffusion of nanoparticles is observed through Forced Rayleigh scattering, while the thermoelectric field is accessed through voltage measurements in a th…
Anisotropic particles oriented in a specific direction can act as artificial atoms and molecules, and their controlled assembly can result in a wide variety of ordered structures. Towards this, we demonstrate the orientation transitions of uncharged peanut-shaped polystyrene colloids, suspended in a non-ionic aprotic polar solvent, near a flat surface whose potential is static or time-varying. The charged surface is coated with an insulating dielectric layer to suppress electric currents. The transition between several orientation states such as random, normal or parallel orientation with resp…
We study the Soret effect of charged polystyrene particles as a function of temperature and electrolyte composition. As a main result we find that the Soret coefficient is determined by charge effects, and that non-ionic contributions are small. In view of the well-kown electric-double layer interactions, our thermal field-flow fractionation data lead us to the conclusion that the Soret effect originates to a large extent from diffusiophoresis in the salt gradient and from the electrolyte Seebeck effect, both of which show strong specific-ion effects. Moreover, we find that thermophoresis of p…
We report the formation of alternating strings and clusters in a binary suspension of repulsive charged colloids with double layers larger than the particle size. Within a binary cell model we include many-body and charge-regulation effects under the assumption of a constant surface potential, and consider their repercussions on the two-particle interaction potential. We find that the formation of induced dipoles close to a charge-reversed state may explain the formation of these structures. Finally, we will touch upon the formation of dumbbells and small clusters in a one-component system, wh…
Recent studies on confined crystals of charged colloidal particles are reviewed, both in equilibrium and out of equilibrium. We focus in particular on direct comparisons of experiments (light scattering and microscopy) with lattice sum calculations and computer simulations. In equilibrium we address buckling and crystalline multilayering of charged systems in hard and soft slit confinement. We discuss also recent crystalline structures obtained for charged mixtures. Moreover, we put forward possibilities to apply external perturbations, in order to drive the system out of equilibrium. These in…
