# Difference between revisions of "Electric-field-induced capillary attraction between 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 Nature 420, 299-301 (2002).

# Additional Entry: Maja Cassidy, AP225 Fall 2009/2010

## Summary

Figure 1 - (A) Ordering between like-charged colloidal particles under confinement is caused by repulsive interactions. (B) When no confinement is present, ordering of the like-charged colloidal particles can still take place, indicating that an attractive interaction is also present.

The authors present a quantitative investigation into the attraction of like-charged particles at a water-oil interface, and argue that the attraction can be explained by capillary forces. Typically (Fig 1A) like-charged particles at oil-water interfaces are stabilized by Coulombic interactions, and if confined will arrange themselves in the form of a lattice in order to minimize the total energy of the system. Contrary to this, it has also been observed that when there is no confinement, the like-charged particles will also arrange themselves in an ordered manner (Fig 1B) at the interface. The particle stay arranged in this way for long periods of time, and so this is an indication of attractive forces also existing between the particles.

Figure 2 - Secondary interparticle potential minimum derived from experimental observations. The data points are obtained from the particle distribution function of the crystallite shown in Fig. 1b. The minimum at a separation of 5.7 mm produces the observed hexagonal crystallite.
Figure 3 - Sketch of the equipotential lines at the fluid interface and the resulting distortion of the oil–water interface. The distortion of the interface shape is greatly enhanced for clarity.

## Experiment Details

Spherical PMMA particles (1.5um diameter) that are surface stabilized with poly(hydroxosteric) acid are used. The cores of the particles are doped with a green fluorescent dye, which allows their position to be recorded on a CCD camera through a fluorescence microscope.

## Results

The interaction potential of the particles in Fig 1B is determined by measuring the probability distribution P(r) of the center-to-center distance of the center particle to each of the outer particles,

$P(r) \alpha Exp({-V(r)/k_{B}T})$

It can be seen (Fig 2) that the potential is well described by a harmonic equation with minimum at r = 5.7um and spring constant of k = 23kBT um2.

A sketch of the full interparticle potential is shown in the inset in Fig 2. This potential includes the repulsive barrier that stabilizes the particles, and a deep primary minimum at short range that is due to van der Waals attraction. These crystallites were observed to collapse and form a gel after several hours, confirming the presence of the primary minimum and the large repulsive barrier. The authors note that the accessible range of particle separation allows the to explore the shape of the secondary minimum, however the repulsive potential is sufficiently large that they cannot explore the shape or magnitude of the primary attractive well using thermal fluctuations.

The authors interpret the attraction force normal to the interface as being caused by the dipolar fields around each particle that cause electrical stresses that distort the oil-water interface (Figure 3).

## Conclusions and Soft Matter Discussion

The interpretation of these results has been controversial, with Megens and Aizenberg writing a follow up commentary in Nature [1], together with a reply from the authors.

Megens and Aizenberg argue that the explanation of dipolar fields causing a capillary attraction between the particles is inconsistent with Newton's Third Law, and so cannot be the explanation behind this observation. They calculate that capillary deformation of the interface contributes only 1.8e-5 kBT to the interfacial potential, and so it is insignificant thermodynamically.

Understanding of this attractive effect betweeen colloidal particles has many implications for the field of soft matter. As the authors note, adsorption if charged particles at fluid interfaces is a common phenomenon in foods, drugs, oil recovery, and even biology.

[1] M. Megens, J. Aizenberg, Like-Charged Particles at Liquid Interfaces, Nature, 2003, 424, 101

# Original entry: Nan Niu, APPHY 226, Spring 2009

by M. G. Nikolaides, A. R. Bausch, M. F. Hsu, A. D. Dinsmore, M. P. Brenner, C. Gay & D. A. Weitz

## Abstract

In the recent years, scientists are usually interested in nano and micro scale experiments. In this article, the authors examed nanometer and micrometer sized charged particles at aqueous interfaces and showed that they are stabilized by a repulsive Coulomb interaction. Importantly, the authors indicated that when one of the phases forming the interface is a nonpolar substance that cannot sustain a charge, the particles will exhibit long-ranged dipolar repulsion. Moreover, if the interface area is confined, mutual repulsion between the particles can induce ordering and even crystallization. As for capillary forces, the authors discussed that they are typically caused by interface deformations. In the article, the authors did extensive experiments and presented quantitative measurements of attractive interactions between colloidal particles at oil–water interface and showed that the attraction can be explained by capillary forces that arise from a distortion of the interface shape. The author's explanation also suggested that the attractive interactions might be controllable. The mechanism is that by tuning the polarity of one of the interfacial fluids, it should be possible to adjust the electrostatic stresses of the system and hence the interparticle attractions.

## Experiment

The authors presented much information in the article. Those important experimental results and procedures are well illustrated by these four figures. First and foremost, figure 1 shows a fluorescence microscopy image of an ordered structure of colloidal particles at an oil–water interface. The authors use this to demonstrate the long range of the repulsive interaction. Moreover, in the experiment, the authors used poly(methyl methacrylate) (PMMA) particles, sterically stabilized with poly(hydroxystearic acid). The particles are suspended in decahydronaphthalene at a volume fraction of 0.01%. The particle cores are labelled with fluorescent dye. An emulsion of water drops in oil is produced by gently shaking around 2 ml of deionized water in 1ml of the decalin–PMMA mixture. The particles are strongly bound to the interface because of the surface energies. The authors used this to determine the contact angle. All in all, the particles are never observed to escape, which implies that the particles are trapped by a barrier of several tens of kBT. The mean squared displacement measured at short delay times provides a measure of the particle diffusion coefficient, which is intermediate between that for a particle in the water and in the oil. This confirms that the particles are at the interface, partially extending into each of the fluids.

Figure 2 is a scatter plot showing positions of a seven-particle hexagonal crystallite on a water droplet of 24 mm radius. Figure 3 shows secondary interparticle potential minimum derived from experimental observations. The data points are obtained from the particle distribution function of the crystallite shown in Fig. 2. The inset is a sketch of the full interparticle potential and includes the repulsive barrier that stabilizes the particles, and a deep primary minimum at short range that is due to van der Waals attraction. According to the authors, these crystallites were observed to collapse and form a gel after several hours, confirming the presence of the primary minimum and the large repulsive barrier. Figure 4 provides a sketch of the equipotential lines at the fluid interface and the resulting distortion of the oil–water interface.

In this article, the authors believes that the experimental results are useful to convey the essential physics, which is that, first, dipolar electric fields induce surface charges that distort the interface, and second, the dipolar interaction causes repulsion, while the interfacial distortion causes capillary attraction. According to the authors, this finding has broad implication because adsorption of charged particles at fluid interfaces is a common phenomenon in foods, drugs, oil recovery, and even biology.

# Additional Entry: Xu Zhang, AP225 Fall 2009

## Keywords

colloidal particles, oil-water interface, capillary force, dipolar field

## Summary

Figure 1: Interfacial colloidal particle ordering induced by repulsive interactions.
Figure 2: Scatter plot showing positions of a seven-particle hexagonal crystallite on a water droplet of 24μm radius. The inset shows a fluorescent microscope image of the crystallite.
Figure 3: Secondary interparticle potential minimum derived from experimental observations.

Figure 4: Sketch of the equipotential lines at the fluid interface and the resulting distortion of the oil-water interface.

This paper presents quantitative measurements of attractive interactions between colloidal particles at an oil-water interface and shows that the attraction can be explained by capillary forces that arise from a distortion of the interface shape that is due to electrostatic stresses caused by the particles' dipolar field.

Figure 1 shows a configuration of colloidal particles at the interface of a large water drop in oil. The large particle separation shows the long range of the repulsive interaction. Even when the particle coverage is not complete, ordering can still be observed, as illustrated in Figure 2, which shows a group of seven particles in a hexagonal crystalline.This crystalline remained stable for more than 30 minutes. The persistent of this structure over long time is clear evidence of a long-ranged attractive interaction.

The particle distribution function of the crystallite in Figure 2 is used to extract the interaction potential shown in Figure 3. The minimum at a separation of 5.7　μm produces the observed hexagonal crystallite.The inset is a sketch of the full interparticle potential and includes the repulsive barrier that stabilizes the particles, and a deep primary minimum at short range that is due to van der Waals attraction. These crystallites were observed to collapse and form a gel after several hours, confirming the presence of the primary minimum and the large repulsive barrier.

The author then discusses the origin of the observed repulsion and attraction.The conclusion on the working mechanism is reached: Dipolar electric fields induce surface charges that distort the interface; the dipolar interaction causes repulsion, while the interfacial distortion causes capillary attraction.

## Soft Matter Connection

The attractive interaction between particles absorbed at an aqueous interface has always been enigmatic, even though interface deformation is known to give rise to capillary forces and a logarithmic attraction between neighbouring particles. There have been several previous explanation for the deformation of the interface like gravity,wetting of the particles,surface roughness and thermal fluctuations . However, the resulting forces in these models do not scale with the colloidal particle size. This new explanation, which is consistent with all reports on interfacial particle ordering so far, also suggests that the attractive interactions might be controllable: by tuning the polarity of one of the interfacial fluids, it should be possible to adjust the electrostatic stresses of the system and hence the interparticle attractions.

## Reference

1.M.G.Nikolaides et al., Electric-field-induced capillary attraction between like-charged particles at liquid interfaces, Nature 420 (6913):299-301 (2002)

2. M. Megens, J. Aizenberg, Like-Charged Particles at Liquid Interfaces, Nature, 2003, 424, 101