For more information about this meeting, contact Andrew Belmonte, Hope Shaffer, Tim Reluga.
|Title:||Studying Polymer Melts with Knot Theory|
|Seminar:||The Pritchard Lab Seminar|
|Speaker:||Jian Qin, Dept of Chemical Engineering, Penn State|
|Linear polymers are flexible and one-dimensional molecules with finite thickness. When densely packed, their motions are severely constrained by the uncrossability of surrounding molecules. The molecules are free to change conformations only inside a tube-like region. The tube diameter, or the entanglement length, is the key parameter needed to understand how polymers respond to stress. But a molecular understanding of the origin of the tube diameter is still lacking. Part of the difficulty is to identify the presence of entanglements, and distinguish one entangled state from another. We approach this problem by closing polymers into rings, mapping the molecular configurations into knots, and using knot polynomials as the identifier to the entangled states. The ring configurations are generated by extensive continuum Monte Carlo simulations of a bead-spring model, in which several molecular rebridging moves are incorporated to break the ergodicity barrier among topologically distinct states. We studied systems under both aperiodic and periodic boundary conditions, and implemented a generalization of Jones polynomial to the 2D periodic patterns. We then accumulated the probability distribution of the types of entangled states (knots) and extracted the entanglement length using the ring length dependence of the unknot probability and of the information theoretical entropy associated with the distribution. The two results are consistent, and agree with those obtained using heuristic methods.
Room Reservation Information
|Date:||12 / 06 / 2010|
|Time:||02:30pm - 03:30pm|