Wave propagation in prestretched polymer nanofibers

Wave propagation in prestretched ultrathin polymer fibers (e.g., those as-electrospun polymer nanofibers) are under the influence of prestretch, surface energy, and nonlinear elasticity. A one-dimensional nonlinear elastic model is proposed to take into account such combined influence in the wave propagation phenomenon. In the model, the polymer nanofibers are considered to behave as hyperelastic Mooney-Rivlin solid. For small dynamic disturbance, linearized wave equation is established by superimposing the dynamic displacement as linear disturbance on the prestretched equilibrium state. Explicit wave dispersion relations are obtained and relevant numerical examples are demonstrated in examining the dependency of wave phase speed upon the wave number at varying surface properties, fiber radius, and prestretch. In the limiting case of neglecting the dynamic effect, the present wave equation can yield the governing equation of surface rippling in compliant nanofibers. This governing equation is capable of predicting the initiation condition of surface rippling and the critical fiber radius, below which compliant nanofibers cannot be produced due to surface instability. Results obtained in this study are applicable as the theoretical basis of dynamic characterization of compliant nanowires/nanofibers, nanofiber device design, and nanostructural analysis.