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Depletion Attraction

March 7, 2011

It's often instructive to think about the absence of things, rather than the things themselves. A philosophical example of this, as attributed first to Augustine, is the idea that evil, itself, does not exist. Evil is really the absence of Good. In a more physical vein, we've discovered that cold is really the absence of hot, and darkness is really the absence of light. In solid state physics, we have the idea of "holes," the absence of negative charge, as a current carriers.

One interesting example of the use of absence in physics is the steady state cosmology of Fred Hoyle, Thomas Gold and Hermann Bondi. In an extreme appeal to the idea that nature abhors a vacuum, the steady state theory proposes an idea of continuous creation of matter. As the universe expands, matter is created to fill the voids. This proposal wasn't as extreme as it appears, since the amount of matter created would be just a single hydrogen atom per cubic meter per billion years. However, the discovery of the cosmic microwave background by Penzias and Wilson confirmed the Big Bang theory, and few today believe in steady state cosmology.

Absence plays a role also in solution chemistry. When we have particles in solution, it's obvious that two particles can't occupy the same space at the same time. This concept doesn't appear too enlightening until we see that in a mixture of large and small particles, one large particle can take the place of many smaller particles. This can be important when there are surface effects. For spheres, the ratio of surface area to volume is a function of 1/r, where r is the sphere radius, so a lot of small spheres filling the same volume as one larger sphere will have a larger surface area exposed to the solution.

One important observation on the differences between large and small particles in solution was published in 1958 by the polymer scientists, Sho Asakura and Fumio Oosawa.[1] They found that there was an attraction between particles suspended in solutions that's not related to any specific force, such as electrostatic attraction. The attractive force was found to be stronger in solutions of macromolecules of dissymmetrical shape.

Larger particles stick to each other, simply because the small particles that push them around in solution can't access the space between closely spaced large particles. Instead, the smaller particles have nothing else to do than to push the larger particles towards each other. It's a purely thermodynamic effect. According to the Asakura-Oosawa model, the free energy change ΔF of the system that favors this process is given as[2]
ΔF ≈ n kB T [1 + 3/2(D/d)]

in which D and d are the diameters of the larger and smaller spheres, T is temperature, kB is Boltzmann's constant, and n is the volume fraction of small spheres. Of course, (1-n) is the volume fraction of large spheres, and the spheres are considered to be perfectly elastic. A more cogent summary of this effect, called depletion attraction, can be found in a paper about cellular organization, reference two.[2]

Arrangement of spheres in space

An artful arrangement of spheres in space.
(Figure by
Jonas De Kooning,
from Wikimedia Commons).

A research group from the New York University Department of Physics and Center for soft Matter Research, led by Professor Jasna Brujic, has utilized this depletion attraction effect as a way to improve emulsions. Their model system was oil droplets in water, which is a proxy for such things as butter, ice cream, milk and various lotions. Their object was to manipulate the way that the oil droplets pack, and thereby modify the material properties.[3]

Unlike the normal depletion attraction process, which is thermal, the colloidal process studied uses the gravitational settling of the colloids as the motive source for the particles. The oil particles in the colloids are large, so they added small polymer particles. This addition affected the jamming behavior of the particles, an effect seen in granular media. This method has the potential of creating a spectrum of material properties from loose to dense. Their work is published in a recent issue of the Proceedings of the National Academy of Sciences.[4]


  1. Sho Asakura and Fumio Oosawa, "Interaction between particles suspended in solutions of macromolecules," Journal of Polymer Science, vol. 33, no. 126 (December, 1958), pp. 183-192.
  2. Davide Marenduzzo, Kieran Finan and Peter R. Cook, "The depletion attraction: an underappreciated force driving cellular organization," J Cell Biol., VOL. 175, NO. 5 (December 4, 2006), PP. 681-686
  3. James Devitt, "NYU Physicists Develop Potent Packing Process," NYU Press Release, February 28, 2011.
  4. Ivane Jorjadze, Lea-Laetitia Pontani, Katherine A. Newhall and Jasna Brujic, "Attractive emulsion droplets probe the phase diagram of jammed granular matter," Proceedings of the National Academy of Sciences, (Online, February 28, 2011).
  5. A. A. Louis, E. Allahyarov, H. Löwen and R. Roth, "Effective forces in colloidal mixtures: From depletion attraction to accumulation repulsion," Phys. Rev. E, vol. 65 (13 June 2002), Document 061407 (11 pages).

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