Equilibrium sedimentation profile of dilute, salt-free charged colloids

Electrokinetic and dielectric response of a concentrated salt-free colloid: Different approaches to counterion finite-size effects

In the present work, a general model is developed for the electrokinetics and dielectric response of a concentrated salt-free colloid that takes into account the finite size of the counterions released by the particles to the solution. The effects associated with the counterion finite size have been addressed using a hard-sphere model approach elaborated by Carnahan and Starling [N. F. Carnahan and K. E. Starling, Equation of state for nonattracting rigid spheres, J. Chem. Phys. 51, 635 (1969)0021-960610.1063/1.1672048]. A more simple description of the finite size of the counterions based on that by Bikerman has also been considered for comparison. The studies carried out in this work include predictions on the effect of the finite counterion size on the equilibrium properties of the colloid and its electrokinetic and dielectric response when it is subjected to constant or alternating electric fields. The results show how important the counterion finite-size effects are for most of the electrokinetic and dielectric properties of highly charged and concentrated colloids, mainly for the static and dynamic electrophoretic mobilities. Furthermore, new insights are provided on the counterion condensation effect when counterions are allowed to have finite size. Focus is placed on the changes undergone by their concentration in the condensation layer for low-salt and highly charged colloids.

Influence of ion size effects on the electrokinetics of aqueous salt-free colloids in alternating electric fields

Electrokinetics is the science of the physical phenomena appearing at the solid-liquid interface of dispersed particles subjected to external fields. Techniques based on electrokinetic phenomena constitute an important set of tools for the electrical characterization of colloids because of their sensitivity to the properties of particle-solution interfaces. Their rigorous description may require inclusion of the effects of finite size of chemical species in the theoretical models, and, particularly in the case of salt-free (no external salt added) aqueous colloids, also consideration of water dissociation and possible carbon dioxide contamination in the aqueous solution. A new ac electrokinetic model is presented for concentrated salt-free spherical colloids for arbitrary characteristics of the particles and aqueous solution, including finite-size effects of chemical species by appropriate modifications of the chemical reaction equations to include such non-ideal aspects. The numerical solution of the electrokinetic equations in an alternating electric field has also been carried out by using a realistic non-equilibrium scenario accounting for association-dissociation processes in the chemical reactions. The results demonstrate the importance of including finite-size effects in the electrokinetic response of the colloid, mainly at high frequencies of the electric field, and for highly charged colloids. Findings of previous models for pointlike ions or for ideal salt-free colloids including finite ion size effects are recovered with the present model, for the appropriate limiting conditions.

Colloidal Brazil nut effect in microswimmer mixtures induced by motility contrast

We numerically and experimentally study the segregation dynamics in a binary mixture of microswimmers which move on a two-dimensional substrate in a static periodic triangular-like light intensity field. The motility of the active particles is proportional to the imposed light intensity, and they possess a motility contrast, i.e., the prefactor depends on the species. In addition, the active particles also experience a torque aligning their motion towards the direction of the negative intensity gradient. We find a segregation of active particles near the intensity minima where typically one species is localized close to the minimum and the other one is centered around in an outer shell. For a very strong aligning torque, there is an exact mapping onto an equilibrium system in an effective external potential that is minimal at the intensity minima. This external potential is similar to (height-dependent) gravity such that one can define effective "heaviness" of the self-propelled particles. In analogy to shaken granular matter in gravity, we define a "colloidal Brazil nut effect" if the heavier particles are floating on top of the lighter ones. Using extensive Brownian dynamics simulations, we identify system parameters for the active colloidal Brazil nut effect to occur and explain it based on a generalized Archimedes' principle within the effective equilibrium model: heavy particles are levitated in a dense fluid of lighter particles if their effective mass density is lower than that of the surrounding fluid. We also perform real-space experiments on light-activated self-propelled colloidal mixtures which confirm the theoretical predictions.

Induced polar order in sedimentation equilibrium of rod-like nanoswimmers

The active diffusion and sedimentation equilibrium of rod-like nanoswimmers with length L are investigated by dissipative particle dynamics. In the absence of propulsion, the nanorod has the rotational correlation time τθ and mobility μ0, which vary with L. On the basis of the mean squared displacement, the diffusive behavior of rod-like nanoswimmers subject to active force Fa is found to follow (D - D0) ∝ (μ0Fa)(2)τθ, where D0 depicts the Brownian diffusivity. When the nanoswimmer suspension is under the external force Fe, the balance between the downward migration and upward active diffusion yields the sedimentation length δ = D/(μ0Fe), which no longer obeys δ0 = kBT/Fe obtained from the Einstein-Smoluchowski relationship, D0 = μ0kBT. Different from the suspension of passive rods, the polar order is clearly seen for active rods. The local polar order is essentially constant within the distance of about 2δ from the bottom wall but decays as the distance is further increased. In this work, the active Peclet number is small compared to unity and the maximum polar order grows linearly with Fe/Fa. The polar order arises because it is easier for the nanoswimmer with the swimming direction opposite to the external force to escape from the bottom wall.

Structure of polyelectrolyte brushes subject to normal electric fields

Molecular dynamic simulations of salt-free polyelectrolyte brushes subject to external fields applied normal to the grafting substrate reveal the three-dimensional monomer and counterion distributions. It is found that below a critical electric field, local electroneutrality holds for densely grafted brushes and the brush height remains independent of field intensity. Above this critical field (which scales as 1/3 with grafting density) brush height increases smoothly, and the fraction of condensed counterions decreases. The brush bifurcates into two subpopulations of stretched and collapsed chains when the grafting density is not low. At intermediate grafting densities, the majority of chains are stretched and the minority are nonstretched. At high grafting densities bifurcation and brush height growth occur consecutively. The majority of the chains are nonstretched at high grafting densities. Although not observed prior to overstretching of the chain model, it is predicted that the two subpopulations will re-merge to a single highly stretched phase when field intensity reaches a third critical value. The ability to control subpopulations of chains suggests that utilizing electric fields normal to polyelectrolyte brushes holds potential as controllable gates in microfluidic devices.

Sediments of soft spheres arranged by effective density

Colloidal sedimentation has been studied for decades from both thermodynamic and dynamic perspectives. In the present work, binary mixtures of colloidal spheres are observed to separate spontaneously into two distinct layers on sedimentation. Both layers have a high volume fraction and contain distinct compositions of particles. Although predicting these compositions using settling dynamics is challenging, here we show that the compositions are readily predicted thermodynamically by minimizing the gravitational energy of the system. As the random packing fraction of a mixture of spheres exceeds that of monodisperse spheres of either type, the mixture produces a denser suspension that forms the bottom phase. Experimentally, the use of charged particles and low-ionic-strength solutions provides interparticle repulsions that keep the packed particles mobile, avoiding a glassy state that would prevent particles from reaching their equilibrium configuration. We extend this work beyond binary systems, showing similar separated layers for a five-component mixture of particles.