  The coil-stretch transition in extensional flows of viscoelastic dilute
polymer solutions is known to be associated with a strong hysteresis in
molecular conformations and rheo-optical properties. At infinite dilution,
hysteresis is caused by the large difference in frictional drag coefficient
between undeformed isotropic polymer coils and highly stretched conformations.
At the low extension rates in the hysteresis regime, stretched molecules
pervade larger volumes than equilibrium coils since the flow is too weak to
suppress transverse fluctuations. The onset of intermolecular overlap occurs
for such stretched conformations at polymer concentrations much smaller than
c*, the conventional critical overlap concentration for equilibrium coils.
Therefore, for a range of concentrations c < c*, intramolecular hydrodynamic
interactions may be significantly screened in stretched conformations. Scaling
arguments based on "blob" concepts are used here to argue that the stretched
state drag coefficient can grow strongly with concentration in the dilute
regime. A dumbbell model with conformation-dependent drag model is used to
predict a concomitant strong enhancement of coil-stretch hysteresis with
increasing concentration in the dilute regime. This extensional flow induced
self-concentration leads to a maximum in hysteretic effects around c*, which
progressively diminish in the semi-dilute regime where screening in isotropic
coils reduces the difference in drag coefficient between stretched and coiled
states. It is shown that the concentration dependence observed by Clasen et al.
(2006) of capillary-thinning dynamics in liquid bridges of polymer solutions
provides direct evidence of coil-stretch hysteresis enhancement by
self-concentration.
