# Electrostatics at the oil–water interface, stability, and order in emulsions and colloids

Original entry: Sujit S. Datta, APPHY 225, Fall 2009.

## Reference

M. E. Leunissen, A. van Blaaderen, A. D. Hollingsworth, M. T. Sullivan, P. M. Chaikin, PNAS 104, 2585 (2007).

## Keywords

electrostatics, apolar, charging, emulsion, wigner crystals

## Key Points

A significant amount of recent work has begun to focus on the electrostatics of colloidal systems in non-polar media, such as various oils with low dielectric constants (e.g. 2-6, versus 80 for water). Because of this low dielectric constant, the energy needed to separate unlike charges is much larger in an apolar medium than in a polar medium, like water -- at equilibrium, this energy is thermal (kT). This leads to a number of rich effects: (i) for very apolar media, colloidal particles will tend to be uncharged, since spontaneous dissociation of charged species at the colloidal surface requires more energy than is available by kT; (ii) at equilibrium, apolar media tend to have a very small concentration of free ions, because the energy required to separate the charges is much larger than kT. This leads to large (from several to hundreds of micrometers) screening lengths.

In this work, the dielectric constant of the solvent (~5.6) is sufficiently large such that spontaneous colloidal charging does occur, and the screening length is on the order of micrometers. However, when the suspension was placed in contact with water, colloidal particles in the solvent near the water-apolar solvent interface formed Wigner crystals with lattice constants up to tens of micrometers, suggesting an effective screening length over an order of magnitude larger than one would expect.

The explanation for this effect comes from the simple observation that the energy required to place a charged ion of size a and charge q (the "self energy") in a dielectric medium is given by $q^{2}/2\epsilon_{r}\epsilon_{0} a$, where $\epsilon_{r}$ is the dielectric constant of the medium. Thus, the ions in the solvent of dielectric constant 5.6 can greatly reduce their energy by "partitioning" into the water phase with dielectric constant 80 -- that is, the water phase will act as an "ion sink", reducing the ionic concentration in the apolar solvent even further and leading to a much larger effective screening length.

There are subtleties which make the physics even richer.

1. Because of the details of the interactions between the water and the free ions in the apolar solvent, the water "ion sink" tends to take up more positive ions, and thus the water phase becomes charged. Indeed, Leunissen et al. use this effect to produce colloid particle-free water-in-oil emulsions that are stable against coalescence, due to the fact that the water droplets are charged. This is a unique emulsion system that is free of any (surfactant or particle) stabilizers, leading to potential applications of emulsion systems that do not require any stabilizer.

2. Because the water phase is charged, a region spanning tens of micrometers in the oil phase, right next to the oil-water interface, exists from which colloidal particles are depleted. This is due to electrostatic repulsion. However, colloidal particles were bound right at the interface; this is because they are attracted to their image charges in the water phase. This could have potential insight into the mechanisms behind particles binding to oil-water interfaces in "Pickering" emulsions, since the particles used in these experiments had wetting properties that do not favor their binding to the oil-water interface.