On the evolution of the exclusion zone produced by hydrophilic surfaces: A contracted description.

After exciting scientific debates about its nature, the development of the exclusion zone, a region near hydrophilic surfaces from which charged colloidal particles are strongly expelled, has been finally traced back to the diffusiophoresis produced by unbalanced ion gradients. This was done by numerically solving the coupled Poisson equation for electrostatics, the two stationary Stokes equations for low Reynolds numbers in incompressible fluids, and the Nernst-Planck equation for mass transport. Recently, it has also been claimed that the leading mechanism behind the diffusiophoretic phenomenon is electrophoresis [Esplandiu et al., Soft Matter 16, 3717 (2020)]. In this paper, we analyze the evolution of the exclusion zone based on a one-component interaction model at the Langevin equation level, which leads to simple analytical expressions instead of the complex numerical scheme of previous works, yet being consistent with it. We manage to reproduce the evolution of the exclusion zone width and the mean-square displacements of colloidal particles we measure near Nafion, a perfluorinated polymer membrane material, along with all characteristic time regimes, in a unified way. Our findings are also strongly supported by complementary experiments using two parallel planar conductors kept at a fixed voltage, mimicking the hydrophilic surfaces, and some computer simulations.

Effects of the curvature gradient on the distribution and diffusion of colloids confined to surfaces.

The properties and behavior of colloids confined to move on curved surfaces offer a fertile ground for analysis since the geometric constraints induce specific features that are not available in flat spaces. Given their pertinence for biological and physicochemical processes, both with potential useful applications, the development of the concepts and methodology necessary for a deeper understanding of these unconventional systems is indeed an essential pursuit. The present study discusses a general and rigorous algorithm for the implementation of Brownian dynamics simulations that solves underlying difficulties and shortcomings inherent to conventional first-order schemes. Still based on the Ermak-McCammon recipe, our approach complements it with the higher-order geodesical projections of the elementary jumps generated on the associated tangent plane. This strategy, which warrants the locally isotropic propagation of non-interacting particles, is tested with a model system of colloidal particles interacting through a screened Coulomb potential while confined to move on ellipsoidal surfaces. This allows us to measure the effects prompted by the curvature gradient on the static and dynamic properties of this system. The varying curvature thus induces energetically favorable configurations in which the particles maximize their Euclidean distancing by crowding the regions with the largest Gaussian curvature, while withdrawing from those with the lowest. In turn, these inhomogeneous distributions provoke the anisotropic self-diffusion of the confined colloids, which is examined by exploiting the pertinent geodesic radial coordinates. The proficient methods under consideration thus allows dealing with the rich and remarkable new phenomena generated by any distinctive surface geometry.

Structural and dynamic inhomogeneities induced by curvature gradients in elliptic colloidal halos of paramagnetic particles.

Paramagnetic colloidal particles distributed along an ellipse are used as a model system to study the effects of curvature gradients on the structure and dynamics of colloids in curved manifolds. Unlike what happens for circular and spherical systems, in the present case, the equilibrium one-particle distribution function displays inhomogeneities due to the changing curvature along the ellipse. The ensuing effects on the two-body correlations are also analyzed, leading to the observation of anisotropic and long-ranged effects. Another noticeable consequence is the slowing down of the self-diffusion of these particles, which for large eccentricities may induce metastable states; this is evaluated by means of the time-dependent self-distribution.

Formation and structure of colloidal halos in two-dimensional suspensions of paramagnetic particles.

Different Monte Carlo simulation approaches are used here to study the static structure induced by a spherical neutral substrate inserted in the midst of a two-dimensional suspension of paramagnetic particles. It is then observed that in some instances some of these particles are adsorbed to the surface of the substrate, forming colloidal halos. We investigate the necessary conditions for the formation of these halos and the dependence of the number of adsorbed particles on the relevant parameters of the system. The angular distribution of the adsorbed particles around the perimeter of the substrate is analyzed here too.

Structure and effective interactions in parallel monolayers of charged spherical colloids.

We study the microstructure and the effective interactions of model suspensions consisting of Yukawa-like colloidal particles homogeneously distributed in equally spaced parallel planar monolayers. All the particles interact with each other, but particle transfer between monolayers is not allowed. The spacing between the layers defines the effective system dimensionality. When the layer spacing is comparable to the particle size, the system shows quasi-three-dimensional behavior, whereas for large distances the layers behave as effective two-dimensional systems. We find that effective attractions between like-charged particles can be triggered by adjusting the interlayer spacing, showing that the distance between adjacent layers is an excellent control parameter for the effective interparticle interactions. Our study is based on Brownian dynamics simulations and the integral equations theory of liquids. The effective potentials are accounted for by exploiting the invariance of the Ornstein-Zernike matrix equation under contractions of the description, and on assuming that the difference between bare and effective bridge functions can be neglected. We find that the hypernetted chain approximation does not account properly for the effective interactions in layered systems.

Two-body correlations among particles confined to a spherical surface: packing effects.

The two-point correlation functions among particles confined to move within a spherical two-dimensional space are studied here using Monte Carlo simulations in the canonical ensemble and the corresponding liquid theory concepts. This work takes a simple model system with soft-sphere interactions among the particles lying on the spherical surface. We focus this study on the ordering induced by the particle packing and the restrictions imposed by the system topology. The corresponding grand canonical results are obtained from the canonical Monte Carlo data using the standard statistical mechanics formulas. These grand canonical ensemble results show that as the strength of the interactions increases, the system transits between liquidlike states and crystal-like states as the average number of particles on the spherical surface matches certain specific values. The crystal-like states correspond to sharp minima in the plot of the standard deviation in the number of particles on the spherical surface versus the average value of this number. We also test the validity of the integral equation approaches for this kind of closed but boundless systems: It is found that the Percus-Yevick approximation overestimates the correlations for this system in a liquid state, whereas the hypernetted-chain approximation underestimates these correlations.

Entropic forces in dilute colloidal systems.

Depletion forces can be accounted for by a contraction of the description in the framework of the integral equations theory of simple liquids. This approach includes, in a natural way, the effects of the concentration on the depletion forces, as well as energetic contributions. In this paper we systematically study this approach in a large variety of dilute colloidal systems composed of spherical and nonspherical hard particles, in two and in three dimensions, in the bulk and in front of a hard wall with a relief pattern. We show by this way the form in which concentration and geometry determine the entropic interaction between colloidal particles. The accuracy of our results is corroborated by comparison with computer simulations.

A reference interaction site model approach to depletion forces induced by hard rodlike particles.

We study the effective interactions among large hard spherical colloidal particles induced by small hard rodlike particles and compare them with those induced by small hard spherical particles to highlight the specific effects due to the anisotropic shape of the former. This is done by determining the effective pair potentials within the framework of the reference interaction site model approach. The rodlike particles are modeled as N nonoverlapping spherical units arranged in a straight line, so that their total length is N times their transversal diameter. These results are compared against those obtained in the Asakura-Oosawa limit.

Photonic properties of strongly correlated colloidal liquids.

The optical and structural properties of dense colloidal suspensions in the presence of long-range electrostatic repulsion are determined from both light and small-angle neutron scattering experiments. Short-range structural order induces an enhancement of the scattering strength while at the same time the total transmission shows strong wavelength dependence, reminiscent of a photonic crystal. Interestingly, the interplay between diffusive scattering and local order leads to negative values of the scattering anisotropy parameter. The tunable optical properties of these liquids furthermore suggest potential applications such as transparency switches or filters.

Energetic contributions to wall-particle depletion forces.

Recently, depletion forces were accounted for by a contraction of the description based on the integral equations theory of simple liquids [Phys. Rev. E 61, 4095 (2000)]. The extension of those results to the case of inhomogeneous systems is reported here. Besides, the energetic contributions to the wall-particle depletion forces are studied, as they arise as soon as charge is put on some of the components of a binary mixture of hard spheres on the front of a hard wall. By charging the small particles the amplitude of the depletion attraction between wall and large particles is reduced, and can even become a repulsion. A similar effect is observed if an attractive interaction between wall and small particles is present.