  When a dilute polymer solution experiences capillary thinning, it forms an
almost uniformly cylindrical thread, which we study experimentally. In the last
stages of thinning, when polymers have become fully stretched, the filament
becomes prone to instabilities, of which we describe two: A novel "breathing"
instability, originating from the edge of the filament, and a sinusoidal
instability in the interior, which ultimately gives rise to a "blistering"
pattern of beads on the filament. We describe the linear instability with a
spatial resolution of 80 nm in the disturbance amplitude. For sufficiently high
polymer concentrations, the filament eventually separates out into a "solid"
phase of entangled polymers, connected by fluid beads. A solid polymer fiber of
about 100 nanometer thickness remains, which is essentially permanent.
