Formation of microfibers and nanofibers by capillary-driven thinning of drying viscoelastic filaments

Recent experiments have shown that it is possible to self-assemble very uniform polymeric microfibers and nanofibers by exploiting elasto-capillary thinning of macroscopic liquid bridges (Harfenist et al., Nano Lett., 4(10), 2004). We develop a model of this process that describes the simultaneous viscoelasto-capillary thinning and drying of polymeric liquid filaments. A one-dimensional formulation is developed using a slender body approximation to the inertialess equations of motion. The evolution in the kinematics, stress and composition of differential material elements are computed by numerical simulation on a fixed mesh using an explicit Eulerian scheme. The polymer rheology is described by a single-mode Giesekus model with an experimentally-determined concentration-dependent shift factor that accounts for compositional dependence of the zero shear rate viscosity and the relaxation time of the fluid. The numerical simulations are compared to capillary break-up extensional rheometer (CABER) experiments using high molecular weight poly(methyl methacrylate) solutions in chlorobenzene with a range of mass fractions in the concentrated regime. Very large reductions in the radius of the thinning thread spanning two to three orders of magnitude are attainable by careful control of the mass transfer rate, the molecular extensibility of the dissolved polymer and the dynamics of the elasto-capillary thinning process. Simulations show that the fiber formation process can be conveniently parameterized by two dimensionless parameters which compare, respectively, the rate of capillary thinning with the rate of elastic stress relaxation and with the rate of solvent evaporation.