Entropic Repulsions

The original is currently in the collection of the Materials Science and Engineering Department at MIT.
Entropy drives Thermodynamic processes. Entropy can have a variety of phenomenological features, and is often expressed mathematically using different terms. For example, there is the chemical entropy associated with changing the nature of reactant molecules into product molecules. There is the mixing entropy we learn about in High School Chemistry classes. There are exotic sounding components to entropy, such as the quantum entropy that is invoked in discussions of the very small and very large and gravitational.

There is also entropy associated with the shape and flexibility of molecules and particles, called configurational entropy. Configurational entropy describes the number of accessible "shapes" or configurations that a molecule can explore. A long floppy molecule, a polymer or oligomer, can explore a large number of possible "shapes" or configurations, when it is completely unimpeded in a dilute solution. If the long floppy molecule impinges upon another long floppy molecule, each is restricted by the need to twine around one another where they meet. This impingement reduces their configurational entropy.

When a long floppy molecule impinges upon a hard immovable surface (no possibility of intertwining), the number of configurations available to the floppy molecule is severely restricted. It loses a lot of configurational entropy. This idea has been used to keep small particles from clumping and caking in flows. If the particles are coated with polymers (chemically attached to the surface), then the polymer surface coating will lose configurational entropy when the particles approach each other too closely. The particles repel each other, due to the phenomenon called "Entropic Repulsion"

In the drawing, particles are depicted with curvy linear halos – the polymer coatings. Where two particles start to impinge, the polymers adopt less random shapes as they intertwine. Of course some phenomena are exaggerated (density differences, for example) and I've made fast a loose with scale to make the drawing "work". It is nevertheless, a pretty decent depiction of the phenomenon in an engaging semi-surreal abstract art format.