# Like charged particles at liquid interfaces

Original Entry by Holly McIlwee, AP225 Fall 09

## Overview

Like charged particles at liquid interfaces, M. G. Nikolaides, A. R. Bausch, M. F. Hsu, A. D. Dinsmore, M. P. Brenner, C. Gay, D. A. Weitz. Brief Communications, Nature, 424, August, (2003).

## Abstract

Joanna Aizenberg *et al*. wrote a communication in response to an article Nikolaids *et al*. published in Nature in 2002. In the original paper, it was proposed that the attraction between micron-sized particles and an aqueous interface they are absorbed on is caused by a distortion of the liquid interface due to the dipolar electric field of the particles inducing capillary action. Aizenberg *et al*. were compelled to challenge this claim on the basis that they believed that this explanation for the observed attraction does not adhere to force balance laws.

## Keywords

Surface tension, Electric field, Capillary action

## Soft Matter

Nikolaides *et al.* assume that the sum of electrostatic pressure acting on the liquid interface is equal to an external force, F, acting on the particle resulting in:

U(r) = <math>F^ 2</math>/2*<math>\pi</math>*<math>\gamma</math>)ln(r/<math>r_o</math>)

Where: <math>\gamma</math> is surface tension r is particle distance <math>r_o</math> is a constant

This equation implies that the force acts on the particle and water at the same time. As Aizenberg *et al.* explains, this cannot be the case because the force is balanced by surface tension creating a dimple in the water (as seen in Figure 1) which is governed by the Young-LaPlace equation:

[(1/<math>R_1</math>) + (1/<math>R_2</math>)]<math>\gamma</math> = <math>\Delta</math>p

They go on to say that capillary attraction between spheres is caused by the overlap of their dimples reducing the total surface area of the water. This results in, for large (r):

U(r) = -(<math>F^ 2</math>/<math>\pi</math><math>\gamma</math>)(<math>r_c</math>/r)^6

This is much shorter range than, U(r) = <math>F^ 2</math>/2*<math>\pi</math>*<math>\gamma</math>)ln(r/<math>r_o</math>), and shorter than dipole-dipole repulsion between like-charged particles proportional to 1/<math>r^ 3</math>, revealing that no attraction exists and is thermodynamically insignificant, contributing 1.8 x <math>10^-5</math>kT to interaction potential. In conclusion, they believe that the mystery of the origin of the attraction remains unsolved.

In their rebuttal, it is admitted that, U(r) = <math>F^ 2</math>/2*<math>\pi</math>*<math>\gamma</math>)ln(r/<math>r_o</math>) accounts for the electrostatic stressed while neglecting the force that the electric field exerts on the particle itself. Detailed calculations, not shown, reveal the interfacial force pulling the particle out of the fluid is canceled by the electrical force pushing the particle into the fluid.

The data does show that there is a long range repulsive interaction because of charges. Also the attractive interactions balances the electrostatic repulsion. If it decays as a power law it must be slower than 1/<math>r^ 3</math>. Still, the most likely interaction with sufficient range is capillary distortion at the interface. This can only occur if there is an imbalance between the forces pushing the particle into the water and the interface outwards towards the oil.

The interesting factor left is the charge on the particles on the oil side. The density of free charges is much less in oil than water and the screening length is larger. These factors extend the range of force imbalance and can account for the experimental observations. The capillary distortion remains electrostatic in nature.

Further experiments confirm the measurable charge in oil increasing the screening length to values greater than particle separation allowing force imbalance to persist far enough for significant interfacial distortion to exist at scales comparable to interparticle separation.

Therefore it is believed that electric-field-induced capillary distortion remains the likely culprit for the attractive interaction between like-charged interfacial particles.

## References

M. G. Nikolaides, A. R. Bausch, M. F. Hsu, A. D. Dinsmore, M. P. Brenner, C. Gay, D. A. Weitz. *Nature*, **424**, August, (2003).

M. G. Nikolaides *et al*. *Nature* **420**, 299-301 (2002).

Stamou, D., Dushi, C. and Johannsmann, D. *Phys. Rev E* **54**, 5263-5272, (2000).

Aveyard, R *et al. Phys. Rev. Lett*. **88**, 246102-1-4 (2002).