Ring polymers as topological glass, a new phase of matter?

In this thesis the dynamic properties of unknotted ring polymers at high densities is investigated. We hypothesise an unusual type of glass transition which is purely attributed to the topological constraints between the penetrating rings. A mean-field model is developed to describe the strongly constrained ring polymers as ideal lattice trees. Equilibrium properties can be derived within the framework of statistical thermodynamics using an argument based on structural recurrence. Here each ring can be seen as a linear object|as a loop strand with branching protrusions. The ring polymers were simplified as loop strands without any branching. We focused on the constraints emerging from the circular topology, and the polymer dynamics was simulated using a Monte Carlo technique. The degree of inter-ring penetrations essentially controls the slowing of dynamics and represents a universal parameter for the glass transition. The penetrating rings form a percolating network involving reversible quasi-topological entanglements. As such, the stress relaxation of each ring is prolonged by the coupled penetrations which have limited pathways to release constraints from one another. The simulation data suggest the existence of a glassy material exclusively formed by the topological constraints associated with the circular structure. In order to test the picture of topological glass, the uorescence-labelled circular DNA was used to observe its self-diffusion in the entangled state. The experimental method has demonstrated its potential for the future investigation of the dynamics of entangled ring polymers despite the fact that it failed to provide evidence of the glassy state in our experiment