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 orientation.
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…
Inverse patchy colloids are nano- to micro-scale particles with a surface divided into differently charged regions. This class of colloids combines directional, selective bonding with a relatively simple particle design: owing to the competitive interplay between the orientation-dependent attraction and repulsion -- induced by the interactions between like/oppositely charged areas -- experimentally accessible surface patterns are complex enough to favor the stabilization of specific structures of interest. Most important, the behavior of heterogeneously charged units can be ideally controlled …
A Case Study of Sedimentation of Charged Colloids: The Primitive Model and the Effective One-Component Approach
本文从理论上和蒙特卡罗模拟两方面计算了电荷稳定胶体悬浮液的沉降-扩散平衡密度分布，其中既包括胶体颗粒通过成对屏蔽库仑排斥相互作用的单组分模型，也包括胶体、阳离子和阴离子与非屏蔽库仑相互作用的三组分模型。我们专注于实验测量可用的状态点[C. P. Royall等人，J.物理学：Cond.马太福音{ \bf 17}，2315（2005）]。尽管从单组分模型和三组分模型中出现了明显不同的图像（在前者中排斥胶体相互推到高空，而在后者中自生电场将胶体推到高空），但我们从理论和模拟中发现两种模型的胶体密度分布相似，从而表明这些图像代表了同一现象的不同观点。从一个有效的单组分模型MC模拟和理论，连同MC模拟的多组分原始模型的沉积配置文件是一致的，但不同的定量结果的理论多组分描述在泊松-玻尔兹曼水平。我们发现，对于小的和中等的胶体电荷的泊松-玻尔兹曼理论给出的配置文件在良好的协议与有效的单组分理论，如果使用一个较小的有效电荷。我们将这种差异归因于泊松-玻尔兹曼理论中对相关性的处理不佳。
Analytical estimate of effective charges at saturation in Poisson-Boltzmann cell models
我们提出了一个简单的近似方案来计算高电荷胶体（球形或圆柱形的无限长）的有效电荷。在非线性Poisson-Boltzmann理论中，我们从无限稀释极限中的有效电荷的表达式开始，该表达式对于大的盐浓度是渐近有效的;然后将该结果扩展到有限的胶体浓度，近似盐分配效应，该效应将悬浮液中的盐含量与透析水库的盐含量相关联。这导致的有效电荷作为胶体体积分数和盐浓度的函数的解析表达式。这些结果与根据Alexander { \it et al.}提出的标准公式数值计算的有效电荷{ \em at saturation}（即在大裸电荷的极限）相比是有利的。在细胞模型中。
A model is presented for the solution of electrokinetic phenomena of colloidal suspensions in fluid mixtures. We solve the discrete Boltzmann equation with a BGK collision operator using the lattice Boltzmann method to simulate binary fluid flows. Solvent-solvent and solvent-solute interactions are implemented using a pseudopotential model. The Nernst-Planck equation, describing the kinetics of dissolved ion species, is solved using a finite difference discretization based on the link-flux method. The colloids are resolved on the lattice and coupled to the hydrodynamics and electrokinetics thr…
The effects of particle roughness and short-ranged non-central forces on colloidal gels are studied using computer simulations in which particles experience a sinusoidal variation in energy as they rotate. The number of minima $n$ and energy scale $K$ are the key parameters; for large $K$ and $n$, particle rotation is strongly hindered, but for small $K$ and $n$ particle rotation is nearly free. A series of systems are simulated and characterized using fractal dimensions, structure factors, coordination number distributions, bond-angle distributions and linear rheology. When particles rotate e…
The effective electrostatic interaction between a pair of colloids, both of them located close to each other at an electrolyte interface, is studied by employing the full, nonlinear Poisson-Boltzmann (PB) theory within classical density functional theory. Using a simplified yet appropriate model, all contributions to the effective interaction are obtained exactly, albeit numerically. The comparison between our results and those obtained within linearized PB theory reveals that the latter overestimates these contributions significantly at short inter-particle separations. Whereas the surface co…
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…
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…
In this paper we develop a simple theory to study the effects of ionic size on ionic distributions around a charged spherical particle. We include a correction to the regular Poisson-Boltzmann equation in order to take into account the size of ions in a mean-field regime. The results are compared with Monte Carlo simulations and a Density Functional Theory based on the Fundamental Measure approach and a second-order bulk expansion which accounts for electrostatic correlations. The agreement is very good even for multivalent ions. Our results show that the theory can be applied with very good a…
In the study of colloidal, biological and electrochemical systems, it is customary to treat surfaces, macromolecules and electrodes as homogeneously charged. This simplified approach is proven successful in most cases, but fails to describe a wide range of heterogeneously charged surfaces commonly used in experiments. For example, recent experiments have revealed a long-range attraction between overall neutral surfaces, locally charged in a mosaic-like structure of positively and negatively charged domains ("patches"). Here we review experimental and theoretical studies addressing the stabilit…
Machine-Learned Many-Body Potentials for Charged Colloids reveal Gas-Liquid Spinodal Instabilities only in the strong-coupling regime of Primitive Models
