Colloid electrophoresis for strong and weak ion diffusivity

Mesoscopic modelling and simulation of soft matter

The deformability of soft condensed matter often requires modelling of hydrodynamical aspects to gain quantitative understanding. This, however, requires specialised methods that can resolve the multiscale nature of soft matter systems. We review a number of the most popular simulation methods that have emerged, such as Langevin dynamics, dissipative particle dynamics, multi-particle collision dynamics, sometimes also referred to as stochastic rotation dynamics, and the lattice-Boltzmann method. We conclude this review with a short glance at current compute architectures for high-performance computing and community codes for soft matter simulation.

Computer simulations of single particles in external electric fields

Applying electric fields is an attractive way to control and manipulate single particles or molecules, e.g., in lab-on-a-chip devices. However, the response of nanosize objects in electrolyte solution to external fields is far from trivial. It is the result of a variety of dynamical processes taking place in the ion cloud surrounding charged particles and in the bulk electrolyte, and it is governed by an intricate interplay of electrostatic and hydrodynamic interactions. Already systems composed of one single particle in electrolyte solution exhibit a complex dynamical behaviour. In this review, we discuss recent coarse-grained simulations that have been performed to obtain a molecular-level understanding of the dynamic and dielectric response of single particles and single macromolecules to external electric fields. We address both the response of charged particles to constant fields (DC fields), which can be characterized by an electrophoretic mobility, and the dielectric response of both uncharged and charged particles to alternating fields (AC fields), which is described by a complex polarizability. Furthermore, we give a brief survey of simulation algorithms and highlight some recent developments.

Computing the electrophoretic mobility of large spherical colloids by combining explicit ion simulations with the standard electrokinetic model

The electrophoretic mobility of large spherical colloids in different salt solutions of varying valency and concentration is studied via a combination approach of numerically solving the standard electrokinetic model with a ζ potential that has been obtained from explicit ion simulations of the restricted primitive model, thus going beyond the standard mean-field treatment. We compare our theoretical mobility curves to two distinct sets of experimental results and obtain good agreement for monovalent and divalent salt solutions. For the case of the trivalent La(3+) salt, the experimentally obtained mobility reversal at high ionic strengths can be obtained only by adding an additional attractive interaction of 4k(B)T to the potential between the colloid and La(3+), hinting at the presence of a nonelectrostatic binding term for this ion. It is also shown that, contrary to intuition, charge inversion does not necessarily result in mobility reversal.

Counterion condensation on spheres in the salt-free limit

A highly-charged spherical colloid in a salt-free environment exerts such a powerful attraction on its counterions that a certain fraction condenses onto the surface of a particle. The degree of condensation depends on the curvature of the surface. So, for instance, condensation is triggered on a highly-charged sphere only if the radius exceeds a certain critical radius R*. R* is expected to be a simple function of the volume fraction of particles. To test these predictions, we prepare spherical particles which contain a covalently-bound ionic liquid, which is engineered to dissociate efficiently in a low-dielectric medium. By varying the proportion of ionic liquid to monomer we synthesise nonpolar dispersions of highly-charged spheres which contain essentially no free co-ions. The only ions in the system are counterions generated by the dissociation of surface-bound groups. We study the electrophoretic mobility of this salt-free system as a function of the colloid volume fraction, the particle radius, and the bare charge density and find evidence for extensive counterion condensation. At low electric fields, we observe excellent agreement with Poisson-Boltzmann predictions for counterion condensation on spheres. At high electric fields however, where ion advection is dominant, the electrophoretic mobility is enhanced significantly which we attribute to hydrodynamic stripping of the condensed layer of counterions from the surface of the particle.

Numerical homogenization of electrokinetic equations in porous media using lattice-Boltzmann simulations

We report the calculation of all the transfer coefficients which couple the solvent and ionic fluxes through a charged pore under the effect of pressure, electrostatic potential, and concentration gradients. We use a combination of analytical calculations at the Poisson-Nernst-Planck and Navier-Stokes levels of description and mesoscopic lattice simulations based on kinetic theory. In the absence of added salt, i.e., when the only ions present in the fluid are the counterions compensating the charge of the surface, exact analytical expressions for the fluxes in cylindrical pores allow us to validate a new lattice-Boltzmann electrokinetics (LBE) scheme which accounts for the osmotic contribution to the transport of all species. The influence of simulation parameters on the numerical accuracy is thoroughly investigated. In the presence of an added salt, we assess the range of validity of approximate expressions of the fluxes computed from the linearized Poisson-Boltzmann equation by a systematic comparison with LBE simulations.

Charge generation in low-polarity solvents: poly(ionic liquid)-functionalized particles

We present a straightforward strategy for the synthesis of highly charged poly(ionic liquid)-functionalized particles in low-polarity solvents. A series of cationic liquid monomers consisting of a tetraalkyl ammonium cation and a fluorinated tetrakis[phenyl] borate anion linked, via a C3-alkyl chain, to a methacrylate unit were synthesized. The addition of this ionic monomer to a conventional dispersion polymerization of methyl methacrylate and methacrylic acid at 80 °C in a mixed dodecane/hexane solvent yielded spherical, highly monodisperse particles with mean diameters of between ~50 and 2500 nm with high electrophoretic mobility and stability in nonpolar solvents such as dodecane. The surface potential in dodecane could be adjusted in the range from 0 to 180 ± 9 mV by altering the ratio of ionic monomer to methacrylate monomers. The particles open up new opportunities for the electrostatic assembly of nanoparticles and organized structures in nonpolar environments.

AC-field-induced polarization for uncharged colloids in salt solution: a dissipative particle dynamics simulation

We study the response of a spherical colloid under alternating electric fields (AC fields) by mesoscopic simulation method, accounting in full for hydrodynamic and electrostatic interactions. We focus on a special case of uncharged colloids. The main polarization mechanism is the "volume polarization", where ionic currents are deflected by the core of the uncharged colloid. Specifically, we compute the polarizability of a single colloid and systematically investigate the effect of AC field frequency and salt concentration. The simulation results are compared with predictions from classical Maxwell-Wagner theory and electrokinetic theory.