Models of Liquid Crystalline Polymer Fibers

Abstract

In this chapter, a variety of one- and two-dimensional models for the melt spinning of thermotropic liquid crystalline polymer (LCP) and liquid semi-crystalline polymer fibers including single-core, hollow, compound, and hollow-compound fibers, is presented. These models couple the hydrodynamics of the polymer, the thermal field, and the LCP dynamics and, therefore, account for the polymer rheology and the molecular orientation/alignment that result from the complex interactions that are at play in fiber spinning processes. A special emphasis is placed on the modeling of the crystallization and molecular orientation and their effects on the polymer’s rheology under both quiescent and flow conditions. Several crystallization models are reviewed and compared, and kinetic, mesoscopic and macroscopic approaches to the modeling of the molecular orientation are described. Several methods for the development of one-dimensional models of melt spinning of liquid semi-crystalline polymer fibers are discussed and their limitations are indicated. The chapter also presents the most relevant two-dimensional models of fiber spinning of LCP that have been developed to-date and indicates the main difficulties that may be encountered when implementing numerically these models. Hybrid models that combine one-dimensional approximations for the fiber’s geometry and average axial velocity component and two-dimensional ones for the temperature, stresses, molecular orientation and/or crystallization are also reviewed. Some one- and two-dimensional sample results of the fiber spinning of thermotropic LCP are presented, and future work on modeling is suggested.