Colloids as Big Atoms

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Science  07 May 2004:
Vol. 304, Issue 5672, pp. 830-831
DOI: 10.1126/science.1097964

Colloid science is important for applications ranging from drugs to dairy products. Less well known is that it can also illuminate basic physics questions, because in certain crucial respects, colloids behave as “big atoms.” The report on page 847 of this issue by Aarts et al. (1) beautifully illustrates this approach, which was pioneered by Einstein. In particular, the results show that phenomena at the interface between a liquid and a vapor can be studied with a colloidal model.

Beginning with his doctoral thesis, Einstein showed that the incessant, random jiggling of colloidal particles known as Brownian movement was the visible manifestation of the “graininess”—the molecular nature—of the surrounding liquid. One consequence is that the density of particles as a function of height in a dilute suspension in sedimentation equilibrium is given by an equation that depends on the particle's buoyant mass, the gravitational acceleration, Boltzmann's constant, and the absolute temperature. It turns out that this equation also expresses the distribution of gas molecules in a constant-temperature atmosphere in gravity, where it is known as the barometric distribution. In other words, colloids made up of relatively large particles can behave in the same way as much smaller counterparts in the molecular world; for some purposes, colloids behave as “big atoms.” Jean-Baptiste Perrin's experimental verification of the “colloidal barometric distribution” contributed toward his 1926 physics Nobel Prize and the widespread acceptance of the reality of molecules.

Today, the study of colloids is throwing new light on fundamental problems of condensed matter physics, from the kinetics of crystallization (2) to the nature of glassy states [(3, 4); see (5) for a review]. In their work, Aarts et al. (1) use colloids to study the vapor-liquid interface. At conditions far from the critical point (the temperature and pressure beyond which vapor and liquid do not exist separately), such interfaces are macroscopically flat. Microscopically, however, thermal energy excites ripples in the interface. These capillary waves (which, like capillary rise, are governed by the surface tension) are important in diverse fields such as oceanography (where wind-excited capillary ripples amplify to giant waves) and the rupture of polymer films (which is bad for coatings). After a century of study, these ripples still hold surprises. Thus, recent x-ray scattering from capillary waves in organic liquids (6) shows that as we move down to molecular length scales, the surface tension first decreases and then increases again; the decrease is probably caused by the long-range nature of the dispersion (that is, van der Waals) forces between the molecules.

Vapor-liquid coexistence reflects a tug of war between intermolecular attraction and repulsion. Aarts et al. used inert polymers to induce attraction between hard-sphere colloids of diameter d ≈ 140 nm. Polymer coils are excluded from the region between the surfaces of two nearby particles, creating an unbalanced osmotic pressure pushing them together—the particles effectively attract each other (see the figure, A). The range and strength of this so-called depletion attraction is directly proportional to the size and the concentration of the inert polymers, respectively (see the figure, B).

Colloidal coexistence.

A schematic illustration of the origin of the polymer-induced depletion attraction between hard spheres. (A) The centers of mass of the polymer coils with radius of gyration (rg) (blue) are excluded from a thin shell (white) surrounding each particle of radius R (green). There is no polymer in the lens-shaped region (red) between two nearby particles, leading to a net osmotic force pushing them together. (B) The depletion potential, U(r), for a polymer that is ∼60% the size of the colloids (with diameter 2R set to unity). (C) A colloid-polymer mixture showing coexisting colloidal liquid (lower) and colloidal vapor (upper) phases. Note the macroscopically sharp interface. Aarts et al. (1) obtained images of the interface in a similar system at near-single-particle resolution.


The study of such colloid-polymer mixtures has yielded many new insights [see (7) for a review]. In particular, it has been verified that attraction is necessary but not sufficient for vapor-liquid coexistence. An attraction of long enough range is needed—something like a quarter of the size of the particles or larger. Thus, by adding sufficiently large polymers to a suspension (Aarts et al. used polymers that were 60% the size of their particles), it is possible to create colloidal vapor-liquid coexistence—thermodynamically stable phases of dilute and dense disordered arrangements of diffusing particles, separated by an interface (see the figure, C).

The colloidal vapor-liquid interface has many of the properties one expects from its molecular analog. For example, Wijting et al. have demonstrated that the colloidal interface shows a curved meniscus next to a wall as a result of capillary rise (8). Now Aarts et al. have studied the capillary waves at this interface. To understand why their work is feasible and beautiful, we need to know that the surface tension scales as the inverse square of the particle diameter, d. Thus, colloids, with d ≈ 10 nm to 1 μm, give very low values of surface tension indeed, from micronewtons per meter down to nanonewtons per meter (compare this with the surface tension of water at 70 mN/m). This made the task of Wijting et al. (8) rather difficult because capillary rise is proportional to surface tension. On the other hand, the low surface tensions in colloid-polymer mixtures mean that the capillary wave amplitude and velocity have values of ∼0.1 to 1 μm and ∼1 to 10 μm/s, respectively, in the system of Aarts et al. This made it possible for them to catch capillary waves “in the act” by real-time imaging using fluorescent particles and a confocal microscope.

Their observations confirmed various features expected of classical capillary waves, including a dramatic increase in amplitude near the critical point [see the bottom part of figure 1 in (1)] and certain predictions for the interfacial roughness and dynamics. The full power of this approach, however, emerges with the observation by Aarts et al. of capillary waves roughening up the surface of droplets, leading to their coalescence [figure 3C of (1)]. That capillary waves have this role has long been suspected; their small amplitudes and fast speeds in molecular systems, however, have hampered experimentation.

The longer term significance of the work of Aarts et al. lies in the possibilities it opens up. An optical microscope can resolve submicrometer features. By using somewhat larger particles, one could image capillary waves down to the single-particle level. In this case, the depletion attraction has strictly finite range, so we may expect that the decrease in surface tension with length scale observed in molecular systems (6) will not occur in the colloidal system. On the other hand, Wijting et al. have found evidence for wetting transitions in a similar system (8); high-resolution imaging should be a powerful technique for investigating these transitions in the future. In any case, Aarts et al. have demonstrated again the continued fecundity of Einstein's and Perrin's approach to “colloids as (big) atoms.”


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