conventional electrospinning setup and overview of process, setup, and solution parameters that affect fiber and mat properties."/>
Figure 1.1 Schematic of conventional electrospinning setup and overview of process, setup, and solution parameters that affect fiber and mat properties.
Source: Photograph of mat reprinted from Dror et al. (2008). Copyright (2008). American Chemical Society.
1.2 Effect of Process Parameters
Electrospun fibers from 30 nm to 10 μm in diameter have been reported (Greiner and Wendorff 2007). Despite its widespread use, electrospinning of new materials is typically done ad hoc varying polymer concentration and process variables. Although the nanofiber properties, namely fiber diameter, could be ideally controlled by varying the process parameters, precise control over the fiber diameter remains a technical bottleneck. The effect of process variables on fiber characteristics has been widely examined theoretically and experimentally.
1.2.1 Theoretical Analysis
To avoid the cost and time of experimental trial and error, modeling and theoretical analysis have been applied to predict how process parameters affect fiber diameter. Reneker and coworkers have developed a theoretical model based on simulating jet flow as bead‐springs. Their model describes the entire electrospinning process and accounts for solution viscoelasticity, electric forces, solvent evaporation and solidification, surface tension, and jet–jet interactions. Performing sensitivity analysis of 13 model input parameters, they determined that initial jet radius, tip‐to‐collector distance, volumetric charge density, and solution rheology, i.e. relaxation time and elongational viscosity, had strong effect on final fiber size. Initial polymer concentration, perturbation frequency, solvent vapor pressure, solution density, and electric potential had a moderate effect, whereas vapor diffusivity, relative humidity, and surface tension had minor effects on fiber diameter (Thompson et al. 2007).
Using a simple analytical model focusing on the whipping of the jet treats the jet as a slender viscous object. Rutledge and coworkers assume that the final fiber diameter is dictated by an equilibrium between Coulombic charge repulsion on the surface of the jet and the surface tension of the liquid jet. The model predicts that terminal jet radius (rj)
where Q is the volumetric flow rate, I is the electric current, γ is the surface tension,
Recently, Stepanyan and coworkers developed an electrohydrodynamic model of the jet elongation in which kinetics of elongation and evaporation govern the nanofiber diameter. Using the timescale of elongation to nondimensionalize the force balance, the timescale of solvent evaporation, and concentration‐dependent material functions (e.g. relaxation time), they predict the scaling relationship for the final fiber radius (rf) is
where k is the solvent evaporation rate, ρs is the solution density, ηo is the solution viscosity, Q is the volumetric flow rate, and I is the electric current. The result for Eq. (1.2) reduces to Eq. (1.1) in the limit of very slow evaporation. The viscosity dependence, ηo 1/3, and (Q/I)2/3 agree with experimental results. Using polyvinylpyrrolidone (PVP) in various alcohol solutions as well as polyamide/polyacrylonitrile in dimethylformamide (DMF) solutions, the fiber diameter was experimentally observed to scale with the evaporation rate, k, to the 1/3 power (Stepanyan et al. 2014, 2016).
The current in electrospinning (I) and the volumetric charge density (Q/I) is commonly used in modeling and theoretical approaches. Experimental investigations by Yarin and coworkers determined that
(1.3)
(1.4)
(1.5)
where V is applied voltage, Q is flow rate, C polymer concentration, M molecular weight, and H tip to collector distance. Using PEO/water/ethanol mixtures, the solvent properties also slightly affect the current and volumetric charge density. From this work, it is evident that the fiber size is affected by applied electric field strength (applied voltage and time to collector distance), flow rate, and polymer solution (Thompson et al. 2007). Thus, these predictions for fiber size rely on several model parameters that cannot be easily related to measurable variables.
In another work by Rutledge and coworkers, they experimentally determined that the total current in electrospinning, given by
(1.6)
varies electric field (E), volumetric flow rate (Q), and solution conductivity (K). In electrospray, the measured current scales linearly with Q. The authors attributed the observed Q 0.5 dependence on combined jet and spray arising from secondary jetting. Secondary jetting was considered a mechanism for dynamic removal of charge from the surface of the jet which affects final fiber diameter and reducing jet stretching due to surface charge repulsion. The secondary jetting can be minimized by reducing the volumetric flow rate or solution conductivity (Bhattacharjee et al. 2010).
Alternative scaling analyses based on the spinning solution properties and electrospinning operating conditions alone have been developed. Based on electrohydrodynamic theory, the Taylor–Melcher slender body theory relates jet kinematics to measurable fluid properties and process variables. Helgeson et al. validated the electrohydrodynamic model with measurements of the jet radius and velocity via in situ high‐speed photography and velocimetry in the straight portion of viscoelastic electrospinning jet and PEO/NaCl as a model system. Dimensional analysis of the validated model involves two important quantities the electroviscous number characterizing the electromechanical stress relative to shear stress and the Ohnesorge number (Oh). The relationship for the final fiber diameter was determined to be
(1.7)
where wp
