# 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 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.