DeGennes 1974 described in his seminal paper the possibility that near the well-known coil-stretch transition of polymers in extensional flows, there could exist two kinetically separated or glassy dynamic states simultaneously at the same applied extension rate. The simultaneously existing coiled and stretched states were postulated as a product of intramolecular hydrodynamic interactions along the chain backbone. Since this original work, many researchers have weighed in on DeGennes theory with no clear consensus and much debate. Thirty years after DeGennes original publication, Schroeder et al. 2003 presented the first clear, unambiguous experimental evidence that conformational hysteresis existed by examining the dynamics of single molecule, genomic length E Coli DNA. Moreover, theoretically, it was demonstrated by Schroeder et al. 2004 that these kinetically separated states were separated by an effective activation energy that could be hundreds of kT.
In this talk, the findings of Schroeder, Babcock, Shaqfeh and Chu 2003, 2004 will be reviewed from the
point-of-view of a conformational Kramers
rate theory. Moreover, we will demonstrate that the presence of glassy or
kinetically separated conformational states is far more general than originally
thought, if one considers nonlocal or nonlinear flows
i.e. flows which vary along a molecules 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 describe the results of large scale
computer simulation quantitatively. Furthermore, we demonstrate that the
activation energy in these Arrhenius expressions becomes infinite in the
thermodynamic limit of 
where 
is the Kuhn step number and therefore ergodicity is broken.
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 flows where there is significant vorticity in the flow. We will demonstrate that the
addition of vorticity modifies these theories
primarily in changing the size of the fluctuations in the polymer length, thus
providing a source of convective fluctuations. Thus vorticity,
in an otherwise extension dominant flow, can increase the hopping rate between
the conformational states in a manner that can be understood using advective (