(179e) Ergodicity-Breaking and Glassy Dynamics in the Stretching Flows of Single Polymer Molecules

In this talk, the findings of Schroeder et al. 2003,, 2004 regarding the conformational hysteresis of single molecule dynamics near the coil-stretch transition in extensional flow will be reviewed from the point-of-view of Kramers' rate theory (or the Markovian first passage time). We will demonstrate that the coiled and stretched states are kinetically separated by an activation energy, and moreover that this general picture of polymer dynamics as a first order activated process is far more general than originally thought (e.g. by DeGennes, 1974) if one considers nonlocal or nonlinear flows -- i.e. flows that vary along the molecule's length. These flows have application in microfluidics. We will take two examples in detail and demonstrate that an effective Arrhenius expression for the rate of hopping from coiled to stretched polymer states can be derived analytically and describes the results of large scale computer simulations quantitatively. Furthermore we demonstrate that the activation energy in these Arrhenius expressions grows as N where N is the number of Kuhn steps in the chain and therefore ergodicity is broken in the limit N -> infinity. Thus the idea of glassy dynamic states must be included in any description of the rheology of this class of flows even for isolated chains. Finally, we will extend these ideas to consider ?mixed? flow where there is significant vorticity in the flow, We will demonstrate that the addition of vorticity modifies these theories primarily by changing the size of the fluctuations in polymer length, thus providing a source of convective fluctuations. Thus vorticity in an otherwise extension dominant flow, can increase the ?hopping? rate between conformational states in a manner that can be understood using advective (Taylor) dispersion theory.