Thermotropic liquid crystalline polymer fibers

Super-strength, lightweight materials used in bullet-proof vests, high-perf ormance cables and tires, and stealth airplanes are built from liquid cryst alline polymer ( LCP) fibers. The remarkable strength properties are domina ted by molecular alignment achieved as a result of the complex interactions at play in ber processes. The ber manufacturing process begins with a high temperature liquid phase of rigid rod macromolecules, whose orientation co uples to the strong elongational free surface ow. The ow exits at a prescri bed radius and velocity (v(0)), tapers and cools as it evolves downstream, and solidi es along some free boundary, below which a take-up velocity (v(1 ) > v(0)) is imposed at a fixed location. Our goal in this paper is a model for this process which realistically couples the hydrodynamics, the LCP dy namics, and the temperature field, along with the free surface and boundary conditions. Moreover, we aim for a model, by necessity complex, that provi des nontrivial ber process predictions and that admits a linearized stabili ty analysis of steady ber processes. We rst generalize three-dimensional Do i-Edwards averaged kinetic equations to include temperature-dependent mater ial behavior and a coupled energy equation. From this formulation we genera lize previous isothermal hydrodynamic, isotropic viscoelastic, and anisotro pic viscoelastic models, incorporating temperature-dependent material respo nse. The model, its nontrivial boundary value solutions, and their lineariz ed stability are presented, along with the translation of these mathematica l results, to industrially relevant issues of ber performance properties an d bounds on stable spinning speeds.