PPT Slide
Entropy-driven phase transitions. Hard sphere models. Phase behaviour of hard sphere colloids.
In the pioneering work of Lars Onsager (1949) on the isotropic-nematic phase transition of a system of long hard rods [1], it has became gradually accepted that many first-order phase transitions are driven by entropy alone. An important example, which is particularly relevant for concentrated colloidal suspensions, is the complex phase behaviour of the system of hard spheres.
The first-order solidification transition in hard spheres was first observed in 1957 through MD calculations by B. J. Alder and T. E. Wainwright [2] and in MC simulations by W.Wood and J. D. Jacobson [3]. Hard spheres order when they occupy approximately 50% of the system volume. The onset of freezing immediately produces a solid at the melting volume fraction of f=0.545, and the crystal can be further compressed up to the closest packing density of 0.74 (Fig. 1).
A mixture of hard spheres of two different species exhibits another first-order phase transition: fluid-fluid phase separation. This transition may be driven by the two distinct physical mechanisms [4]. One is the osmotic depletion of the smaller particles. These forces result from the excluded-volume interaction between a large and a small particle. If ss denotes the diameter of the small particles and sl represents the diameter of the large particles, then there is a volume of radius ?= (ss + sl )/2 around every large colloidal particle where the centers of the small particles cannot penetrate (Fig. 2). When two large particles are separated by the distance less than ss, the pressure exerted on them by the small particles is anisotropic and leads to strong effective attraction between them. This mechanism was suggested by Asakura and Oosawa (1958) in order to explain the reversible flocculation observed in colloid-polymer mixtures [5].
These forces turned out to be quite long-ranged in nature [6] (Fig. 3). Close to the attractive depletion well, when the separation between colloids is larger than ss a pronounced repulsive barrier was found.