Colloidal electrophoresis: Scaling analysis, Green-Kubo relation, and numerical results

We consider electrophoresis of a single charged colloidal particle in a finite box with periodic boundary conditions, where added counterions and salt ions ensure charge neutrality. A systematic rescaling of the electrokinetic equations allows us to identify a minimum set of suitable dimensionless parameters, which, within this theoretical framework, determine the reduced electrophoretic mobility. It turns out that the salt-free case can, on the Mean Field level, be described in terms of just three parameters. A fourth parameter, which had previously been identified on the basis of straightforward dimensional analysis, can only be important beyond Mean Field. More complicated behavior is expected to arise when further ionic species are added. However, for a certain parameter regime, we can demonstrate that the salt-free case can be mapped onto a corresponding system containing additional salt. The Green-Kubo formula for the electrophoretic mobility is derived, and its usefulness demonstrated by simulation data. Finally, we report on finite-element solutions of the electrokinetic equations, using the commercial software package COMSOL.Comment: To appear in Journal of Physics: Condensed Matter - special issue on occasion of the CODEF 2008 conferenc

Ground state structure and interactions between dimeric 2D Wigner crystals

We study the ground state ordering and interactions between two two-dimensional Wigner crystals on neutralizing charged plates by means of computer simulation. We consider crystals formed by (i) point-like charges and (ii) charged dimers, which mimic the screening of charged surfaces by elongated multivalent ions such as aspherical globular proteins, charged dendrimers or short stiff polyelectrolytes. Both systems, with point-like and dimeric ions, display five distinct crystalline phases on increasing the interlayer distance. In addition to alteration of translational ordering within the bilayer, the phase transitions in the dimeric system are characterized by alteration of orientational ordering of the ions.Comment: Revised versio

Density-dependent interactions and structure of charged colloidal dispersions in the weak screening regime

We determine the structure of charge-stabilized colloidal suspensions at low ionic strength over an extended range of particle volume fractions using a combination of light and small angle neutron scattering experiments. The variation of the structure factor with concentration is analyzed within a one-component model of a colloidal suspension. We show that the observed structural behavior corresponds to a non-monotonic density dependence of the colloid effective charge and the mean interparticle interaction energy. Our findings are corroborated by similar observations from primitive model computer simulations of salt-free colloidal suspensions.Comment: Revised version, accepted to Phys. Rev. Let

Numerical electrokinetics

A new lattice method is presented in order to efficiently solve the electrokinetic equations, which describe the structure and dynamics of the charge cloud and the flow field surrounding a single charged colloidal sphere, or a fixed array of such objects. We focus on calculating the electrophoretic mobility in the limit of small driving field, and systematically linearise the equations with respect to the latter. This gives rise to several subproblems, each of which is solved by a specialised numerical algorithm. For the total problem we combine these solvers in an iterative procedure. Applying this method, we study the effect of the screening mechanism (salt screening vs. counterion screening) on the electrophoretic mobility, and find a weak non-trivial dependence, as expected from scaling theory. Furthermore, we find that the orientation of the charge cloud (i. e. its dipole moment) depends on the value of the colloid charge, as a result of a competition between electrostatic and hydrodynamic effects.Comment: accepted for publication in Journal of Physics Condensed Matter (proceedings of the 2012 CODEF conference

Electrophoretic mobility of a charged colloidal particle: A computer simulation study

We study the mobility of a charged colloidal particle in a constant homogeneous electric field by means of computer simulations. The simulation method combines a lattice Boltzmann scheme for the fluid with standard Langevin dynamics for the colloidal particle, which is built up from a net of bonded particles forming the surface of the colloid. The coupling between the two subsystems is introduced via friction forces. In addition explicit counterions, also coupled to the fluid, are present. We observe a non-monotonous dependence of the electrophoretic mobility on the bare colloidal charge. At low surface charge density we observe a linear increase of the mobility with bare charge, whereas at higher charges, where more than half of the ions are co-moving with the colloid, the mobility decreases with increasing bare charge.Comment: 15 pages, 8 figure

Stick boundary conditions and rotational velocity auto-correlation functions for colloidal particles in a coarse-grained representation of the solvent

We show how to implement stick boundary conditions for a spherical colloid in a solvent that is coarse-grained by the method of stochastic rotation dynamics. This allows us to measure colloidal rotational velocity auto-correlation functions by direct computer simulation. We find quantitative agreement with Enskog theory for short times and with hydrodynamic mode-coupling theory for longer times. For aqueous colloidal suspensions, the Enskog contribution to the rotational friction is larger than the hydrodynamic one when the colloidal radius drops below 35nm.Comment: new version with some minor change

Polarized Ukraine 2014: Opinion and Territorial Split Demonstrated with the Bounded Confidence XY Model, Parameterized by Twitter Data

Multiple countries have recently experienced extreme political polarization, which in some cases led to escalation of hate crime, violence and political instability. Beside the much discussed presidential elections in the United States and France, Britain’s Brexit vote and Turkish constitutional referendum, showed signs of extreme polarization. Among the countries affected, Ukraine faced some of the gravest consequences. In an attempt to understand the mechanisms of these phenomena, we here combine social media analysis with agent-based modeling of opinion dynamics, targeting Ukraine’s crisis of 2014. We use Twitter data to quantify changes in the opinion divide and parameterize an extended Bounded-Confidence XY Model, which provides a patiotemporal description of the polarization dynamics.We demonstrate that the level of emotional intensity is a major driving force for polarization that can lead to a spontaneous onset of collective behavior at a certain degree of homophily and conformity. We find that the critical level of emotional intensity corresponds to a polarization transition, marked by a sudden increase in the degree of involvement and in the opinion bimodality

Rejection-free Geometric Cluster Algorithm for Complex Fluids

We present a novel, generally applicable Monte Carlo algorithm for the simulation of fluid systems. Geometric transformations are used to identify clusters of particles in such a manner that every cluster move is accepted, irrespective of the nature of the pair interactions. The rejection-free and non-local nature of the algorithm make it particularly suitable for the efficient simulation of complex fluids with components of widely varying size, such as colloidal mixtures. Compared to conventional simulation algorithms, typical efficiency improvements amount to several orders of magnitude

On the nature of long-range contributions to pair interactions between charged colloids in two dimensions

We perform a detailed analysis of solutions of the inverse problem applied to experimentally measured two-dimensional radial distribution functions for highly charged latex dispersions. The experiments are carried out at high colloidal densities and under low-salt conditions. At the highest studied densities, the extracted effective pair potentials contain long-range attractive part. At the same time, we find that for the best distribution functions available the range of stability of the solutions is limited by the nearest neighbour distance between the colloidal particles. Moreover, the measured pair distribution functions can be explained by purely repulsive pair potentials contained in the stable part of the solution.Comment: 6 pages, 5 figure

Optimizing end-labeled free-solution electrophoresis by increasing the hydrodynamic friction of the drag-tag

We study the electrophoretic separation of polyelectrolytes of varying lengths by means of end-labeled free-solution electrophoresis (ELFSE). A coarse-grained molecular dynamics simulation model, using full electrostatic interactions and a mesoscopic Lattice Boltzmann fluid to account for hydrodynamic interactions, is used to characterize the drag coefficients of different label types: linear and branched polymeric labels, as well as transiently bound micelles. It is specifically shown that the label's drag coefficient is determined by its hydrodynamic size, and that the drag per label monomer is largest for linear labels. However, the addition of side chains to a linear label offers the possibility to increase the hydrodynamic size, and therefore the label efficiency, without having to increase the linear length of the label, thereby simplifying synthesis. The third class of labels investigated, transiently bound micelles, seems very promising for the usage in ELFSE, as they provide a significant higher hydrodynamic drag than the other label types. The results are compared to theoretical predictions, and we investigate how the efficiency of the ELFSE method can be improved by using smartly designed drag-tags.Comment: 32 pages, 11 figures, submitted to Macromolecule