Random Polymers*

Polymer chains can be viewed as random processes interacting with themselves and with their environment. The simplest models are random walks and self-avoiding walks. The latter are used to account for the "excluded-volume effect" (i.e., for the fact that different monomers cannot occupy the same space), and have been the object of intense study since 50 years.

Polymer chains can exhibit interesting phase transitions. For instance, a polymer can change from an "expanded coil" to a "compact ball" when the temperature is decreased, due to self-attraction. Similarly, a polymer can adsorb onto a surface when the temperature is decreased, due to an
attractive interaction with the surface. Furthermore, the polymer can consist of different types of monomers arranged in a random order. Such "random copolymers" exhibit collapse and adsorption transitions as well, and there are challenging questions about how the randomness affects the nature of the phase transition. Random copolymers can also localise at an interface between two immiscible liquids, distributing their monomers between the two liquids so as to optimise their energy, or interact with a random potential field.

During the course, various stochastic models will be described, each dealing with a particular physical or chemical situation of interest. DNA, arguably the most important polymer of all, exhibits several of the phenomena that will be described in the course.

Written  examination. Depending on the number of students, also oral examination (1 hour) is possible.

Exam date: January 19, 2012 10:00-13:00 in room
401, Snellius building in Leiden.