Nanofibers of polymers were electrospun by creating an electrically charged jet of polymer solution at a pendent droplet. After the jet flowed away from the droplet in a nearly straight line, it bent into a complex path and other changes in shape occurred, during which electrical forces stretched and thinned it by very large ratios. After the solvent evaporated, birefringent nanofibers were left. In this article the reasons for the instability are analyzed and explained using a mathematical model. The rheological complexity of the polymer solution is included, which allows consideration of viscoelastic jets. It is shown that the longitudinal stress caused by the external electric field acting on the charge carried by the jet stabilized the straight jet for some distance. Then a lateral perturbation grew in response to the repulsive forces between adjacent elements of charge carried by the jet. The motion of segments of the jet grew rapidly into an electrically driven bending instability. The three-dimensional paths of continuous jets were calculated, both in the nearly straight region where the instability grew slowly and in the region where the bending dominated the path of the jet. The mathematical model provides a reasonable representation of the experimental data, particularly of the jet paths determined from high speed videographic observations.

A localized approximation was developed to calculate the bending electric force acting on an electrified polymer jet, which is a key element of the electrospinning process for manufacturing of nanofibers. Using this force, a far reaching analogy between the electrically driven bending instability and the aerodynamically driven instability was established. Continuous, quasi-one-dimensional, partial differential equations were derived and used to predict the growth rate of small electrically driven bending perturbations of a liquid column. A discretized form of these equations, that accounts for solvent evaporation and polymer solidification, was used to calculate the jet paths during the course of nonlinear bending instability leading to formation of large loops and resulting in nanofibers. The results of the calculations are compared to the experimental data acquired in the present work. Agreement of theory and experiment is discussed.

In addition to round nanofibers, electrospinning a polymer solution can produce thin fibers with a variety of cross-sectional shapes. Branched fibers, flat ribbons, ribbons with other shapes, and fibers that were split longitudinally from larger fibers were observed. The transverse dimensions of these asymmetric fibers were typically 1 or 2 m, measured in the widest direction. A correlation of the branches and bends, observed in high-frame-rate videography of the electrified jets of polymer solutions from which the ribbons and branched fibers were produced, suggest that these phenomena occur at scales ranging from around 1 mm to 1 m. The observation of fibers with these cross-sectional shapes from a number of different kinds of polymers and solvents indicates that fluid mechanical effects, electrical charge carried with the jet, and evaporation of the solvent all contributed to the formation of the fibers. The influence of a skin on the jets of polymer solutions accounts for a number of the observations. The observed shapes can be used as guides for the extension of mathematical or computer-generated models for the electrospinning process.

Sessile and pendant droplets of polymer solutions acquire stable shapes when they are electrically charged by applying an electrical potential difference between the droplet and a flat plate, if the potential is not too large. These stable shapes result only from equilibrium of the electric forces and surface tension in the cases of inviscid, Newtonian, and viscoelastic liquids. In liquids with a nonrelaxing elastic force, that force also affects the shapes. It is widely assumed that when the critical potential φ0* has been reached and any further increase will destroy the equilibrium, the liquid body acquires a conical shape referred to as the Taylor cone, having a half angle of 49.3°. In the present work we show that the Taylor cone corresponds essentially to a specific self-similar solution, whereas there exist nonself-similar solutions which do not tend toward a Taylor cone. Thus, the Taylor cone does not represent a unique critical shape: there exists another shape, which is not self-similar. The experiments of the present work demonstrate that the observed half angles are much closer to the new shape. In this article a theory of stable shapes of droplets affected by an electric field is proposed and compared with data acquired in our experimental work on electrospinning of nanofibers from polymer solutions and melts.

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