field lines concentrate toward the knife‐edge and the jet tends to follow the direction of the electric field. As the disk rotates (~1000 rpm), the fibers wind continuously along the knife‐edge with a pitch of 1–2 μm (Ramakrishna 2005). To improve the alignment, the fibers must be collected before the onset of the whipping instability. Auxiliary electrodes can be used to suppress the whipping instability (Carnell et al. 2008). Alternatively, using solvents with low dielectric constants and high purity can suppress the whipping instability (Ogata et al. 2007). Practically, the highly aligned fibers are achieved for a short period of time ~ minutes after which alignment decreases, which may be attributed to fiber repulsion due to charge accumulation. Therefore, for complex patterns, mechanical drawing techniques that avoid the electric field and whipping stability are preferable (Nain and Wang 2013).
Nanofiber yarns have also been of interest. To produce yarns, electrospun nanofibers can be deposited on water. As the nanofibers are lifted off the water, the surface of tension bundles the fibers into a yarn. Collecting on water flowing in the form of a vortex is a means to achieving continuous yarn production. The disadvantage of this approach is that the yarn must then be dried. Self‐bundling nanofibers have been achieved using AC power. The jet splits and contains both negative and positive segments which bundle together midflight. Twisting the fibers can improve yarn strength. Such twisting can be achieved by collecting on two parallel ring electrodes and rotating one of the rings. Although simple, the length of the yarn is limited using this approach (Abbasipour and Khajavi 2013).
1.4 Effect of Solution Parameters
1.4.1 Polymer Solution Properties (Molecular Weight, Concentration, Viscosity, and Elasticity)
The effect of polymer solution properties is generally more significant than process and setup parameters on electrospinning and the resultant fibers. The solution properties, namely viscosity and viscoelasticity, surface tension, and conductivity are affected by the polymer, solvent(s), and additives (e.g. salts, surfactants).
Although the electrospinning process is relatively easy to implement on a lab scale, many polymer solutions do not form uniform fibers. Issues electrospinning uniform fibers arise when the polymer solution is too dilute and is limited by polymer solubility or when the polymer chains are short or rigid. Electrospinning new materials is typically done ad hoc varying solution properties and process variables; there are no generalizable approaches to predict if a polymer/solvent system will form nanofibers when electrospun. Significant efforts have yielded useful semiempirical approaches for predicting electrospinnability, i.e. production uniform fibers.
It is commonly observed that viscosity influences electrospinning and resulting fiber properties. The viscosity is affected by the molecular weight of the polymer, polymer concentration, and solvent quality. Generally, the higher the molecular weight, the higher the viscosity of the polymer solution. Increasing the polymer concentration also increases the viscosity of the solution. A frequent observation has been that at low viscosities/polymer concentrations, the electrospinning jet breaks up into droplets, rather than stretching to form a fiber. With increasing concentration, there is a transition to beaded fibers and a second transition to uniform fibers (Figure 1.3). The ability to form uniform fibers has been frequently attributed to polymer entanglement (Andrady 2008; Ramakrishna 2005; Li and Wang 2013).
Figure 1.3 Specific viscosity as a function of polymer concentration to determine entanglement concentration for PEO of various molecular weights. Scanning electron microscopy (SEM) (PEO 600 kDa) showing the transition from beaded fibers to uniforms as the polymer concentration increases above the entanglement concentration. For neutral polymers in a good solvent, e.g. aqueous PEO, concentrations above ~2.5× the entanglement concentration form uniform fibers.
Source: Image of beaded fibers is reprinted from Fong et al. (1999). Copyright (1999), with permission from Elsevier.
To quantify the degree of entanglement required to achieve uniform fibers, semiempirical relationships have been used (Shenoy et al. 2005; McKee et al. 2004, 2006). The entanglement concentration can be determined by measuring the viscosity (zero‐shear) as a function of polymer concentration and examining the scaling relationship between the specific viscosity and concentration. Note that the specific viscosity (ηsp) accounts for the viscosity of the solvent
(1.9)
where η 0 is the zero‐shear viscosity of the polymer solution and ηs is the viscosity of the solvent. Upon the onset of polymer entanglement, there is a sharp increase in the scaling relationship based on the theory for semidilute solutions, below the entanglement concentration ηsp α [C]1.25 and above the entanglement concentration ηsp α [C]4.8. For linear, neutral polymers in a good solvent, the transition from beaded fibers to uniform fibers generally occurs at a polymer concentration ~2–2.5× the entanglement concentration (Figure 1.3). This approach has worked well for a number of polymer systems, e.g. polyvinyl alcohol (aqueous), PEO (aqueous), polystyrene in tetrahydrofuran, poly(D‐lactic acid) in DMF, and poly(L‐lactic acid) in dichloromethane (Shenoy et al. 2005; McKee et al. 2004). Analogous approaches have been developed for polyelectrolyte solutions. Polyelectrolytes transition from droplets to fibers at ~8 × Ce. The viscosity scaling relationships for polyelectrolytes to determine the entanglement concentration are an increase in the scaling relationship from ηsp α [C]0.5 to ηsp α [C]1.5 (McKee et al. 2006).
The entanglement concentration can also be used to predict nanofiber diameter based on polymer concentration. A master curve for fiber diameter (df) as a function of concentration φ can be constructed as follows:
(1.10)
where df,e is the diameter of the fibers electrospun at the entanglement concentration φe. This result agrees well with the theoretical scaling of 2.3 (Wang et al. 2016). Long and coworkers showed comparable results with multiple polymers including linear, randomly branched, highly branched, and star polymers (McKee et al. 2004). This approach, which considers polymer concentration, viscosity, and polymer molecular weight (because the entanglement concentration decreases as polymer molecular weight increases), is convenient (Andrady 2008). Due to the high deformation rates, the entangled polymer solutions behave like elastic swollen gels. The rapid stretching of the gel has recently been considered the main mechanism of fiber formation. These results imply that the elasticity of the entangled polymer solution rather than the viscosity influences the final fiber diameter (Wang et al. 2016).
Rutledge and coworkers attribute ability to form uniform fibers to elasticity of the polymer solution noting that the presence of entanglements is a sufficient but not necessary condition for the fluid polymer to demonstrate strong elastic properties. A lack of sufficient elasticity leads to droplets or beaded fibers. To prevent beaded fibers, Rayleigh's breakup instability must be suppressed. The instability can be slowed down or suppressed by the viscoelasticity of the polymer solution. The timescales for instability and the viscoelasticity can be quantified with the Deborah number (De), i.e. the ratio of the fluid relaxation time and instability growth time. Using blends of poly(ethylene oxide) and poly(ethylene glycol) of various molecular weights to
