Thermotropic Liquid Crystalline Polymer Fibers
نویسندگان
چکیده
Super-strength, lightweight materials used in bullet-proof vests, high-performance cables and tires, and stealth airplanes are built from liquid crystalline polymer (LCP) bers. The remarkable strength properties are dominated 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 couples to the strong elongational free surface ow. The ow exits at a prescribed radius and velocity (v 0), tapers and cools as it evolves downstream, solidiies along some free boundary, below which a take-up velocity (v 1 > v 0) is imposed at a xed location (Figure 1). Our goal in this paper is a model for this process which realistically couples the hydrodynamics, the LCP dynamics, the temperature eld, along with the free surface and boundary conditions. Moreover, we aim for a model, by necessity complex, that provides nontrivial ber process predictions, and which admits a linearized stability analysis of steady ber processes. We rst generalize 3-D Doi-Edwards averaged kinetic equations 6, 12, 13, 15] to include temperature-dependent material behavior and a coupled energy equation. From this formulation we generalize previous models, incorporating temperature-dependent material response. The model, its nontrivial boundary-value solutions, and their linearized stability, are presented, along with the translation of these mathematical results to industrially relevant issues of ber performance properties and bounds on stable spinning speeds.
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عنوان ژورنال:
- SIAM Journal of Applied Mathematics
دوره 60 شماره
صفحات -
تاریخ انتشار 2000