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

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

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

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

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

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

Coherent Hydrodynamic Coupling for Stochastic Swimmers

A recently developed theory of stochastic swimming is used to study the notion of coherence in active systems that couple via hydrodynamic interactions. It is shown that correlations between various modes of deformation in stochastic systems play the same role as the relative internal phase in deterministic systems. An example is presented where a simple swimmer can use these correlations to hunt a non-swimmer by forming a hydrodynamic bound state of tunable velocity and equilibrium separation. These results highlight the significance of coherence in the collective behavior of nano-scale stochastic swimmers.Comment: 6 pages, 3 figure

Shear Viscosity of Clay-like Colloids in Computer Simulations and Experiments

Dense suspensions of small strongly interacting particles are complex systems, which are rarely understood on the microscopic level. We investigate properties of dense suspensions and sediments of small spherical Al_2O_3 particles in a shear cell by means of a combined Molecular Dynamics (MD) and Stochastic Rotation Dynamics (SRD) simulation. We study structuring effects and the dependence of the suspension's viscosity on the shear rate and shear thinning for systems of varying salt concentration and pH value. To show the agreement of our results to experimental data, the relation between bulk pH value and surface charge of spherical colloidal particles is modeled by Debye-Hueckel theory in conjunction with a 2pK charge regulation model.Comment: 15 pages, 8 figure

Ground state of classical bilayer Wigner crystals

We study the ground state structure of electronic-like bilayers, where different phases compete upon changing the inter-layer separation or particle density. New series representations with exceptional convergence properties are derived for the exact Coulombic energies under scrutiny. The complete phase transition scenario --including critical phenomena-- can subsequently be worked out in detail, thereby unifying a rather scattered or contradictory body of literature, hitherto plagued by the inaccuracies inherent to long range interaction potentials

Renormalization Group Functions of the \phi^4 Theory in the Strong Coupling Limit: Analytical Results

The previous attempts of reconstructing the Gell-Mann-Low function \beta(g) of the \phi^4 theory by summing perturbation series give the asymptotic behavior \beta(g) = \beta_\infty g^\alpha in the limit g\to \infty, where \alpha \approx 1 for the space dimensions d = 2,3,4. It can be hypothesized that the asymptotic behavior is \beta(g) ~ g for all values of d. The consideration of the zero-dimensional case supports this hypothesis and reveals the mechanism of its appearance: it is associated with a zero of one of the functional integrals. The generalization of the analysis confirms the asymptotic behavior \beta(g)=\beta_\infty g in the general d-dimensional case. The asymptotic behavior of other renormalization group functions is constant. The connection with the zero-charge problem and triviality of the \phi^4 theory is discussed.Comment: PDF, 17 page