Blistering Pattern and Formation of Nanofibers in Capillary Thinning of Polymer Solutions

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 nm thickness remains, which is essentially permanent.

Figure 1

The minimum radius $h_{\min }$ as a function of time. Not all data points are shown. Between numbers 1 and 3, the curve is well described by $h_{\min }(t)=h_0\exp (-t/\tau )$ with $\tau =130\pm 30\mathrm{ms}$ (red, straight line). A plateau is reached between 3 and 4 which is associated with an instability near the end plates, followed by rapid pinching. Between 5 and 6 the curve can be approximated with two linear laws (dotted blue and dashed green lines). For further explanation see text.

Figure 2

Growth of a sinusoidal instability of the viscoelastic filament that develops into a group of droplets on the thinning filament. The spacing of the pictures is ${300}^{-1}\mathrm{s}$. The time window between 4 and 5 in Fig. 1 is represented by the images up to 0.287 s showing the range of exponential growth.

Figure 3

Main: The growth of the amplitude of a sinusoidal surface deformation on a filament of radius $R_0=10\mu \mathrm{m}$. The origin of the time axis has been shifted relatively to Fig. 1. Circles and crosses are experimental data of two different runs; from the latter we were able to detect amplitudes as low as 80 nm. The straight line and the dotted line are exponential fits, giving an inverse growth rate of $\omega =9.3\pm 0.1\mathrm{ms}$. Inset: The sinusoidal surface deformation at $t=18.7\mathrm{ms}$. Points are experimental data and the solid line is a fit with a sine and a linear offset. The selected wavelength is $\lambda /R_0=12\pm 0.9$.

Figure 4

(a) The final state of the filament. Beads are formed off center relative to the thread. (b) SEM image of two beads, connected by a thread (intermediate resolution). The structure was caught and dried upon the substrate (c) Another example of the structure, the red box indicating a close-up at high magnification shown in (d). The diameter of the fiber can be as small as 70 nm.

Figure 5

Trajectories of two bubbles in the filament; they move in parallel, indicating uniform flow inside the filament. First the bubbles are convected by the extensional flow produced by the thinning. Then their position undergoes a sequence of plateaus, associated with consecutive contractions and relaxations—the “breathing” at the very end of the filament, shown in the inset. The breathing correspondents to the red shaded region between 2 and 3 in Fig. 1. At 3, the bubbles run out of the field of view.