Dartmouth Events

Physics and Astronomy Colloquium

Professor Scott Milner, William H. Joyce Professor, The Pennsylvania State University, Department of Chemical Engineering

Friday, May 2, 2014
Wilder 104
Intended Audience(s): Public
Categories: Lectures & Seminars

Title:  "Finding the Tube Without Touching the Chains"

Abstract:  The tube is the key concept in modern theories of entangled polymer dynamics.  The tube has been ``destructively'' visualized in simulations, using chain-shrinking methods to reduce the primitive path to a sequence of straight segments between entanglement points.  Instead, we use isoconfigurational averaging to find the tube without touching the chains.  In this way, we can measure properties such as tube diameter, entanglement molecular weight, confining potential, and persistence length.  By applying compression and extension to a melt of long entangled rings (as a proxy for cross-linked rubbers or long entangled melts), we observe that the primitive paths deform almost affinely for moderate strains.  We have also studied the tubes of entangled chains in strong flows by topologically equilibrating a melt of linear chains under constant tension.  We find the tube diameter decreases with increasing tension, which we can account for by extending the Lin-Noolandi ansatz to oriented and stretched chains.  Ultimately, the tube must be of topological origin, resulting from uncross ability of polymer chains.  We propose two definitions of the entanglement length (Ne) in terms of topological properties of topologically equilibrated melts of rings:  1) the probability of a ring of length Ne in a melt being unknotted is a constant; 2) the topological entropy is 3/2kB per Ne for long rings.  To test these ideas, we simulated rings with chain-crossing moves to equilibrate the topological states.  We identified and counted different knotted states by computing the Jones polynomial.  Our topological estimates of Ne are consistent with previous values based on heuristic chain-shrinking methods.

Bio: Scott Milner earned his PhD in physics at Harvard in 1986, under the direction of Paul Martin.  He worked as a postdoc at Exxon Corporate Research with Tom Witten and Sam Safran, then as a postdoc at AT&T Bell Labs, before joining Exxon (now ExxonMobil) Corporate Research in 1989 as a research physicist.  He won the 1994 John H. Dillon Medal from the American Physical Society for his work in polymer brushes.  In addition to over 120 publications, he is an author of seven patents, several of which are practiced worldwide at ExxonMobil butyl plants.  Milner has been active in the Polymer Division of APS, serving on the executive committee and as division councilor.  Since 2008, he has held the William H. Joyce Chair of Chemical Engineering at Penn State University.


For more information, contact:
Tressena Manning

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