APS March Meeting 2014
Volume 59, Number 1
Monday–Friday, March 3–7, 2014;
Denver, Colorado
Session F56: Invited Session: Polymer Physics Prize Symposium
8:00 AM–11:00 AM,
Tuesday, March 4, 2014
Room: Four Seasons Ballroom 4
Sponsoring
Unit:
DPOLY
Chair: Tom Witten, University of Chicago
Abstract ID: BAPS.2014.MAR.F56.3
Abstract: F56.00003 : Path-Integration Computation of the Transport Properties of Polymers Nanoparticles and Complex Biological Structures
9:12 AM–9:48 AM
Preview Abstract
Abstract
Author:
Jack Douglas
(Material Science and Engineering Division, NIST)
One of the things that puzzled me when I was a PhD student working under
Karl Freed was the curious unity between the theoretical descriptions of
excluded volume interactions in polymers, the hydrodynamic properties of
polymers in solution, and the critical properties of fluid mixtures, gases
and diverse other materials (magnets, superfluids,etc.) when these problems
were formally expressed in terms of Wiener path integration and the
interactions treated through a combination of epsilon expansion and
renormalization group (RG) theory. It seemed that only the interaction
labels changed from one problem to the other. What do these problems have in
common?
Essential clues to these interrelations became apparent when Karl Freed,
myself and Shi-Qing Wang together began to study polymers interacting with
hyper-surfaces of continuously variable dimension where the Feynman
perturbation expansions could be performed through infinite order so that we
could really understand what the RG theory was doing. It is evidently simply
a particular method for resuming perturbation theory, and former ambiguities
no longer existed. An integral equation extension of this type of exact
calculation to ``surfaces'' of arbitrary fixed shape finally revealed the
central mathematical object that links these diverse physical models- the
capacity of polymer chains, whose value vanishes at the critical dimension
of 4 and whose magnitude is linked to the friction coefficient of polymer
chains, the virial coefficient of polymers and the 4-point function of the
phi-4 field theory,\textellipsis Once this central object was recognized, it
then became possible solve diverse problems in material science through the
calculation of capacity, and related ``virials'' properties, through Monte
Carlo sampling of random walk paths.
The essential ideas of this computational method are discussed and some
applications given to non-trivial problems: nanotubes treated as either
rigid rods or ensembles worm-like chains having finite cross-section, DNA,
nanoparticles with grafted chain layers and knotted polymers. The
path-integration method, which grew up from research in Karl Freed's group,
is evidently a powerful tool for computing basic transport properties of
complex-shaped objects and should find increasing application in polymer
science, nanotechnological applications and biology.
To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2014.MAR.F56.3