Theory and Simulation of Texture Formation in Mesophase Carbon Fibers
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Theory and Simulation of Texture Formation in Mesophase Carbon Fibers J. Yan and A. D. Rey* Department of Chemical Engineering, Mcgill University, 3610 University Street, Montreal, PQ H3A 2B2, Canada Abstract Carbonaceous mesophases are spun into high performance carbon fibers using the melt spinning process. The spinning process produces a range of fiber textures whose origins are not well understood. Planar polar (PP) and planar radial (PR) textures are two ubiquitous ones. A model that describes the formation process of the PP texture based on the Landau-de Gennes mesoscopic theory for discotic liquid crystals, including defect nucleation, defect migration, and overall texture geometry, is presented, solved, and validated. The computed PP and PR textures phase diagram, given in terms of temperature and fiber radius, is presented to establish the processing conditions and geometric factors that lead to the selection of these textures. The influence of elastic anisotropy to the textures’ formation and structure is also characterized. Introduction Carbonaceous mesophases (CMs), such as coal tar and petroleum pitches, are used in the industrial manufacturing of high performance mesophase carbon fibers (MCF). The thermodynamic phase that describes CMs is the discotic nematic liquid crystal (DNLC) state [1] in which the partial orientational order of the molecular unit normal u is along the average orientation or director n (n·n=1). The industrial fabrication of MCF using the conventional melt spinning process typically produces micrometer-sized cylindrical filaments whose cross sectional area displays a variety of transverse textures [2], that is, different spatial arrangements of the average orientation n on the plane perpendicular to the fiber axis. Due to the strong structureproperties correlations, the texture selection mechanisms are essential for product optimization [1,2]. It is known [2] that the observed cross-section fiber textures belong to a numbers of families, such as onion, radial, mixed, PAN-AM, to name a few. The two cross-sectional textures considered in this work are the planar radial (PR) and planar polar (PP). Texture Formation Mesoscopic Model Carbonaceous mesophases are anisotropic viscoelastic textured DNLC materials. The three types of elastic deformations in DNLCs are splay, twist, and bend, and their corresponding modulus K11, K22, and K33, are known as the Frank elasticity constants [3]. The bulk Frank free energy density is given by: 1 1 1 2 2 2 f n = K 11 (∇ ⋅ n ) + K 22 (n ⋅ ∇ × n ) + K 33 n × (∇ × n ) (1) 2 2 2 Thermodynamic stability requires: K 11 > 0; K 22 > 0; K 33 > 0 (2) For DNLCs, the following inequalities hold [4]: U5.6.1
(3) K 22 > K 11 ; K 22 > K 33 which indicates that planar deformations are favored, and twist deformation avoided. While eqn.(1) is useful to model the macroscopic features of CMs textures, it can not the presence of topological defects. To overcome this shortcoming, we use a mesoscopic model based on the Landau-de Gennes free energy [3]. The bulk energy den
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