Osmotically driven shape-dependent colloidal separations
by Lidiya Mishchenko
Mason, T.G. Physical Review E 66, 060402(R) 2002
Osmotic pressure, entropy, assembly, micelle, colloid, excluded volume
"The thermally induced motion of nanometer-sized surfactant micelles in water is used to create strong attractive forces between micron-sized disks of wax in a mixed aqueous dispersion of microdisks and microspheres. The short-ranged attractive force due to the depletion of micelles from between the microdisks is much stronger than that between two microspheres of similar size, and is largest when the disks approach face to face, so columns of microdisks form. These columns cream, whereas the spheres remain dispersed, providing a means for shape-dependent colloidal separations driven by an applied micellar osmotic pressure."
Soft Matter Example
This paper utilizes entropically driven assembly first proposed by Asakura and Oosawa in 1954 ("On interaction between two bodies immersed in a solution of macromolecules"). The basic idea is as follows: A mixture of large and small spheres leads to assembly of the larger spheres. This is because these large spheres create area of "excluded volume" around them which small spheres cannot enter (with hard sphere interactions). When two large spheres come into contact, however, they reduce the excluded volume of the smaller spheres, thus increasing the entropy of the system. Another way of understanding this "attractive" force that develops between large spheres is that when they approach each other and exclude small particles between them, the "nonuniform effective pressure of the smaller spheres over the larger spheres creates a net attractive force" (i.e. there's an uncompensated force from the smaller spheres on the outer sides of larger approaching spheres). This is very similar to the driving force in osmosis and is thus called "osmotic pressure".
This paper utilizes the principle above to separate microparticles with different geometries. By mixing spherical colloids and microdisks of same diameters in a micelle solution, they were able to selective assemble only the microdisks and separate them from solution. The micelles were there for the depletion forces (and adsorbed on surfaces for steric stabilization of colloids).
Because the excluded volume of face-to-face microdisks is significantly higher than for two spheres of for side-to-side microdisks (see figure), the microdisks assemble into columns at much lower micelle concentrations than the colloids do. Thus, at an intermediate micelle concentration, the disks assemble into columns, while the colloids are still dispersed. The columnar aggregrates then cream under gravity and can be separated from solution.
Interestingly enough, these aggregates are reversible. If one lowers the micelle concentration, the microdisks redisperse in solution. Despite this property, if one doesn't change the micelle concentration, these columns are very stable against thermal fluctuations.
This type of model is useful for studying a similar biological system: red blood cells. When a polymer is added to blood, osmotic depletion effects cause red blood cells to stacked coin structures.
This method can be generalized for assembly of many systems with dispersed particles of different geometries.