Modeling the Electrostatics of Hollow Shell Suspensions: Ion Distribution, Pair Interactions, and Many-Body Effects

Abstract

Electrostatic interactions play a key role in hollow shell suspensions as they determine their structure, stability, thermodynamics, and rheology and also the loading capacity of small charged species for nanoreservoir applications. In this work, fast, reliable modeling strategies aimed at predicting the electrostatics of hollow shells for one, two, and many colloids are proposed and validated. The electrostatic potential inside and outside a hollow shell with a finite thickness and a specific permittivity is determined analytically in the Debye-Hückel (DH) limit. An expression for the interaction potential between two such hollow shells is then derived and validated numerically. It follows a classical Yukawa form with an effective charge depending on the shell geometry, permittivity, and inner and outer surface charge densities. The predictions of the Ornstein-Zernike (OZ) equation with this pair potential to determine equations of state are then evaluated by comparison to results obtained with a Brownian dynamics algorithm coupled to the resolution of the linearized Poisson-Boltzmann and Laplace equations (PB-BD simulations). The OZ equation based on the DLVO-like potential performs very well in the dilute regime as expected, but also quite well, and more surprisingly, in the concentrated regime in which full spheres exhibit significant many-body effects. These effects are shown to vanish for shells with small thickness and high permittivity. For highly charged hollow shells, we propose and validate a charge renormalization procedure. Finally, using PB-BD simulations, we show that the cell model predicts the ion distribution inside and outside hollow shells accurately in both electrostatically dilute and concentrated suspensions. We then determine the shell loading capacity as a function of salt concentration, volume fraction, and surface charge density for nanoreservoir applications such as drug delivery, sensing, or smart coatings.

Tunability of Interactions between the Core and Shell in Rattle-Type Particles Studied with Liquid-Cell Electron Microscopy

“…In Figure c, it is shown that the potential from the surface of the inner shell wall (right-hand side of the plot) decays more slowly than that of a spherical particle; the difference is more pronounced when the core is off-center (Supporting Information). This is due to the concave geometry of the shell as found previously for hollow shells . This slow decay of the electric potential is the reason for the long-ranged interaction in a sphere–shell system.…”

“…This is due to the concave geometry of the shell as found previously for hollow shells. 74 This slow decay of the electric potential is the reason for the long-ranged interaction in a sphere–shell system. Furthermore, it is likely a reason why the core particle was stable at 250 mM concentration of LiCl.…”

Electrostatic Directed Assembly of Colloidal Microparticles Assisted by Convective Flow

“…More details on the numerical solver can be found in refs. 20,21 Note that the experiments reported in Figure 2a were carried out pulling the stage at a speed of 80 μm•s −1 and that convection was not included in the simulations. This is not a problem because at these large dragging speeds the hydrodynamic flow is parallel to the substrate, inducing advective flows of particles parallel to the substrate, whereas assembly on the substrate is driven by particle flows essentially normal to the substrate (diffusion and electrostatic repulsions).…”

Tunability of Interactions Between the Core and Shell in Rattle-Type Particles Studied with Liquid-Cell Electron Microscopy

“…This is due to the concave geometry of the shell as found previously for hollow shells. 75 This slow decay of the electric potential is the reason for the long-ranged interaction in a sphere-shell system. Furthermore, it is likely a reason why the core particle was stable at 250 mM concentration of LiCl.…”