Dispersity and spinnability: Why highly polydisperse polymer solutions are desirable for electrospinning

We develop new criteria that describe the minimum concentration limits controlling the spinnability of dilute and semi-dilute flexible polymer solutions with high molecular weight and varying polydispersity. By asserting that the finite and bounded extensional viscosity of the solution is the key material property determining the stability of a filament during spinning, we propose a new scaling relating the minimum necessary concentration of a polymer cspin to its molecular weight M and the quality of the solvent (through the excluded volume exponent n) of the form cspin ⇠ M (n+1). This new scaling differs from the classical interpretation of the coil overlap concentration c⇤ or entanglement concentration ce as the minimum concentration required to increase the viscosity of the spinning dope, and rationalizes the surprising spinnability of high molecular weight polymers at concentrations much lower than ce. Furthermore, we introduce the concept of an extensibility average molecular weight ML as the appropriate average for the description of polydisperse solutions undergoing an extensiondominated spinning process. In particular it is shown that this extensibility average measure, and thus the solution spinnability, is primarily determined by the extensibility of the highest molecular weight fractions. For highly polydisperse systems this leads to an effective lowering of the minimum required concentration for successful fiber spinning (in comparison to narrowly distributed polymer solutions of similar weight average molecular weights). These predictions are validated with experimental observations of the electrospinnablity of monoand polydisperse poly(methyl methacrylate) (PMMA) solutions as well as a model bimodal blend, and through comparison to published literature data on the minimum spinnable polymer concentration for a variety of flexible long chain polymers over a range of molecular weights.