Electrostatics in ionic solution : work and energy, charge regulation, and inhomogeneous surfaces

Abstract

This thesis concerns the electrostatic properties of charged objects that are immersed into an ionic solvent, for example water with dissolved salt. Typically, the ions inside such a solvent form layers of countercharge close to the charged objects, causing `screening' of the charges. By employing Density Functional Theory (DFT) one is able integrate out the degrees of freedom of the ions and find relations that describe the effective electrostatic properties of the charged objects. One finds that for a large parameter regime the electrostatic potential everywhere in the solvent should satisfy the well established Poisson-Boltzmann equation. We study the electrostatic capacity of porous electrodes in salt water, and derive a method to reversibly extract electric energy from salinity gradients that occur for example at an estuary where sea- and river water meet. However, in the main part of this thesis we consider charged colloidal particles, and study the effect of internal porosity as well as heterogeneities in the surface-charge density (patchy particles) on colloid-colloid interactions. In a far-field analysis we derive equations that describe these interactions for particles with nonvanishing multipole moments, for example `Janus' colloids with a strong dipole component. If such particles locally have a high surface charge density, then the nonlinear dependence of the counterion density on the local charge density leads to a generalisation of charge renormalisation from purely monopolar to dipolar, quadrupolar, etc., including `mode couplings'. In a more detailed approach, which turns out to be important for colloidal particles at smaller distances from each other, we consider the chemical processes that lead to surface charge, and specify a parameter regime in which charging can be described by a single `chargeability' parameter. As we show in this thesis, the phase diagrams we obtain within this regime have many similarities with a `constant surface potential' surface model. The charging of patches on a surface is often much stronger than bulk surface, measured per area. We find a characteristic increase of the charge density close to the edges of a patch. Although the interaction energy between homogeneously charged surfaces is expected to decay exponentially within Poisson-Boltzmann theory, we find that the interactions of patched surfaces can behave totally different at distances that are smaller than the length scale that is set by the size of the patches. For the case of negatively chargeable surfaces with positively chargeable patches, we find that the net force between the surfaces can change from repulsive at larger distances to attractive at short distances. The strength of the forces and the location of the transition can be tuned with the patch size and the bulk and patch chargeability