Niels Boon

‘Blue energy’ from ion adsorption and electrode charging in sea and river water

A huge amount of entropy is produced at places where fresh water and seawater mix, for example at river mouths. This mixing process is a potentially enormous source of sustainable energy, provided it is harnessed properly, for instance by a cyclic charging and discharging process of porous electrodes immersed in salt and fresh water, respectively [D. Brogioli, Phys. Rev. Lett. 103, 058501 (2009)]. Here we employ a modified Poisson–Boltzmann free-energy density functional to calculate the ionic adsorption and desorption onto and from the charged electrodes, from which the electric work of a cycle is deduced. We propose optimal (most efficient) cycles for two given salt baths involving two canonical and two grand-canonical (dis)charging paths, in analogy to the well-known Carnot cycle for heat-to-work conversion from two heat baths involving two isothermal and two adiabatic paths. We also suggest a slightly modified cycle which can be applied in cases that the stream of fresh water is limited.

Phase diagrams of colloidal spheres with a constant zeta-potential

We study suspensions of colloidal spheres with a constant zeta-potential within Poisson-Boltzmann theory, quantifying the discharging of the spheres with increasing colloid density and decreasing salt concentration. We use the calculated renormalized charge of the colloids to determine their pairwise effective screened-Coulomb repulsions. Bulk phase diagrams in the colloid concentration-salt concentration representation follow, for various zeta-potentials, by a mapping onto published fits of phase boundaries of point-Yukawa systems. Although the resulting phase diagrams do feature face-centered cubic and body-centered cubic phases, they are dominated by the (re-entrant) fluid phase due to the colloidal discharging with increasing colloid concentration and decreasing salt concentration.

Charge regulation and ionic screening of patchy surfaces

The properties of surfaces with charge-regulated patches are studied using nonlinear Poisson-Boltzmann theory. Using a mode expansion to solve the nonlinear problem efficiently, we reveal the charging behavior of Debye-length sized patches. We find that the patches charge up to higher charge densities if their size is relatively small and if they are well separated. The numerical results are used to construct a basic analytical model which predicts the average surface charge density on surfaces with patchy chargeable groups.

Effective charges and virial pressure of concentrated macroion solutions

Significance Colloids constitute the basic components of many everyday products and are integrated into the fabric of modern society. Understanding their assembly is key for nanotechnological and biotechnological advances. At the single-particle level, colloids commonly possess electric charge. Consequently, the structure to which they conform is strongly influenced by electrostatic interactions. In solution, these interactions are modified by the presence of ions. We have developed a model for computing the corresponding effective electrostatic interactions as well as the osmotic pressure. Our model extends the applicability of Derjaguin−Landau−Verwey−Overbeek theory to dense systems in which many-body effects are crucial. This will allow previously impossible, mesoscale studies of colloidal assembly to be performed analytically or by simulation with implicit ions models. The stability of colloidal suspensions is crucial in a wide variety of processes, including the fabrication of photonic materials and scaffolds for biological assemblies. The ionic strength of the electrolyte that suspends charged colloids is widely used to control the physical properties of colloidal suspensions. The extensively used two-body Derjaguin−Landau−Verwey−Overbeek (DLVO) approach allows for a quantitative analysis of the effective electrostatic forces between colloidal particles. DLVO relates the ionic double layers, which enclose the particles, to their effective electrostatic repulsion. Nevertheless, the double layer is distorted at high macroion volume fractions. Therefore, DLVO cannot describe the many-body effects that arise in concentrated suspensions. We show that this problem can be largely resolved by identifying effective point charges for the macroions using cell theory. This extrapolated point charge (EPC) method assigns effective point charges in a consistent way, taking into account the excluded volume of highly charged macroions at any concentration, and thereby naturally accounting for high volume fractions in both salt-free and added-salt conditions. We provide an analytical expression for the effective pair potential and validate the EPC method by comparing molecular dynamics simulations of macroions and monovalent microions that interact via Coulombic potentials to simulations of macroions interacting via the derived EPC effective potential. The simulations reproduce the macroion−macroion spatial correlation and the virial pressure obtained with the EPC model. Our findings provide a route to relate the physical properties such as pressure in systems of screened Coulomb particles to experimental measurements.

Charge reversal of moisturous porous silica colloids by take-up of protons

The net charge of porous Stöber silica colloids is studied using a modified Poisson-Boltzmann theory in a spherical cell, with a focus on the case of water-filled porous silica particles suspended in a non-aqueous solvent. We show that the silicas usual negative surface charge, due to deprotonisation of the Si-OH group, is counteracted by an excess uptake of protons in the water-filled pores of the particle at low enough pH. A small volume fraction of pores suffices to induce a point of zero charge at pH≈4. Based on the difference in Donnan potential between the porous medium and the solvent a relation can be constructed that describes the location of the point of zero charge analytically. The accuracy of this relation is confirmed by numerical calculations. For Stöber silica in water we find a charge reversal below pH≈3, which is in this case solely a result of the selective uptake of cations in the porous network.