# Difference between revisions of "Reverse Micelles Enable Strong Electrostatic Interactions Between Colloidal Particles in Nonpolar Solvents"

Charge Stabilization in Nonpolar Solvents

M.F. Hsu, E. R. Dufresne, and D. A. Weitz

Langmuir 21 (2005) 4881-4887

wiki entry by Emily Russell, Fall 2010

The article can be found here.

Note: the citation on Eric Dufresne's page on the wiki is for the earlier arXiv version of this paper; this wiki entry is on the final version published in Langmuir. A brief glance shows the two versions to be similar, although the Langmuir paper is longer and has more figures.

## Contents

This paper discusses the crucial role of surfactants in allowing charge effects to be introduced into nonpolar solvents. The small dielectric constant of a nonpolar solvent means that it takes a good deal of energy to separate ions, so that salts would not be expected to dissociate and charge effects would be predicted to be negligible. Added surfactants, however, form reverse micelles, the cores of which can become charged; this allows colloidal particles to also obtain a charge. Because screening lengths in the low-dielectric solvents can be quite long compared to those in water, once a charge is stabilized, the effects can be significant. The authors point out that these charge interactions in nonpolar solvents have wide applications in electrophoretic inks (such as the Amazon Kindle uses).

## Experimental Methods

Figure 1. Charge stabilization of a nonpolar suspension: (a) optical micrographs of PMMA particles in pure dodecane and (b) with 12 mM AOT. Field of view: 135 × 108 μm^2.

The experiments in this paper were performed on sterically stabilized colloidal PMMA particles, of radius 780 nm, in dodecane. Aerosol-OT (AOT) was added in varying quantities as the surfactant. Significant care was taken to minimize the introduction of water into the system; preparations were performed in a dry glovebox.

The primary experiments were imaging and analysis of quasi-two-dimensional systems; the suspension was loaded into a thin, wedge-shaped sample cell, and bright-field images were taken in a region of the wedge where the colloidal particles were confined to move mainly in-plane. Particle location using the standard Crocker and Grier algorithms allowed calculation of the radial distribution function g(r); this was then inverted, using some slightly clever algorithms, to obtain the pair potential u(r). Experiments were done at several concentrations of the surfactant.

## Results

Figure 2. (a) Pair-correlation function, g(r), at 50 mM AOT, h = 9 +/- 1 μm, diamonds. Simulated hard-sphere g(r) at the same number density, solid line. Simulated g(r) using the potential extracted from data using the Orstein-Zernike equation, dashed line. (b) Interaction potential, u(r), extracted from the above g(r) using the Orstein-Zernike equation, diamonds. A screened Coulomb fit to the data is plotted as a dashed line. For comparison, a hard-sphere potential is plotted as a solid line.

In pure dodecane, without surfactant, the particles aggregated; upon addition of AOT above the critical micellar concentration (CMC), the particles dispersed, indicating a long-range, non-steric repulsive potential (Fig. 1 and 2). This potential was well described by a screened Coulomb potential, as predicted by the DLVO theory for charged colloids in solution. The charge on the particles was found to be roughly independent of surfactant concentration (so long as the concentration was above the CMC), around 300 electron charges. The screening length of the potential decreased with increasing AOT concentration (Fig. 3); screening lengths measured from the g(r) compared well with those calculated from DLVO theory using independent conductivity measurements. The origin of the screening is the presence of charged surfactant micelles in the solution, which act as counterions. Because of the low dielectric constant, screening lengths of greater than one micron were seen, much greater than those usually seen in aqueous solutions.

Figure 3. Inverse screening lengths as inferred from conductivity, κEK (solid circles), and interparticle potentials, κEQ (open symbols). Inset: the ratio κEQ/κEK for each concentration of AOT, with a solid line at κEQ/κEK = 1 for comparison.

The authors presented a thermodynamic argument for the formation of pairs of charged micelles, supporting the observation that the ratio of ionic to total micelles remained roughly constant at $1.2 \times 10^{-5}$. This implied a cost of ionization of about 12kT; a much less energetically favorable ionization than the dissociation of salts in aqueous solution, but still a low enough energy barrier that sufficient ionic micelles are created to stabilize charge effects. The authors also discuss the energetics of charging the colloidal particles themselves, by neutralizing a charged micelle or ionizing a micelle to become oppositely charged. They make the important point that not only the energetics, but the entropic contribution of the charges distributed on the particle surface is significant.

## Discussion

This paper draws nice parallels between charged particles in aqueous and in nonpolar solutions, with salt ions in aqueous solutions replaced by charged micelles in nonpolar solutions. The authors present a clear model for how charge effects can be extremely important in nonpolar solvents, although this seems at first counterintuitive. The combination of good experimental results and simple but effective thermodynamic models and arguments makes for a smooth and interesting read.