Scaling laws in electrospinning of polystyrene solutions

By tuning the processing variables and solution properties using four different solvents (dimethylformamide, o-dichlorobeneze, tetrahydrofuran, and chloroform), polystyrene (PS) fibers were prepared by the electrospinning process to study the effects of these governing parameters on the morphological changes of the charged cone and jet, as well as the diameter and birefringence of the fibers collected. Both jet diameter (d_j) and fiber diameter (d_f) were scaled with the processing variables, i.e., solution flow-rate (Q), applied voltage (V) and working distance (H), with a power law model. Knowledge of these exponents provided insight into how to manipulate the electrified jet and spun fibers for a given solution. Results showed that Q was the dominant factor in determining the fiber diameter and the Q dependences of d_j and d_f were approximately scaled with: d_j ∼ Q^0.5 and d_f ∼ Q^0.25. The applied electric field (V/H) did affect the cone volume and the length of the electrified jet. Either increasing V or decreasing H produced a slightly thinner jet and smaller fiber, but the effects were not significant due to the limited processing range available for the stable cone-jet mode, and the nonuniformity of the electric field resulting from the point-to-plate electrode configuration used in this study. Regardless of the variations of the processing variables (Q, V, and H), a master curve between d_j and d_f was found for a solution with fixed properties, from which a simple equation was obtained and expressed by: d_f ∼ md_j^0.45 where m was a prefactor depending upon solution properties, such as the viscosity (η₀), conductivity (κ) and surface tension. Values of m were found to be lower for solutions with lower viscosity and/or higher conductivity, and were successfully scaled to be as follows: m ∼η_o^0.38κ^-0.12. As far as the solution properties were concerned, the concentration emerged as the most important parameter because of its interaction with all aspects of the electrospinning process. The rheological properties of the polymer solution showed a significant effect on the formation of smooth electrospun fibers. On the basis of the Graessley's concentration-molecular weight diagram, various PS fiber morphologies were discussed and the minimum polymer concentration at a given polymer molecular weight required for preparing smooth PS fibers could be estimated. For the present PS solutions, a scaling law was found between the fiber diameter and solution viscosity: d_f ∼ η _o^0.41, if other governing parameters (Q, V, H, κ, and surface tension) were fixed.