| The manufacture of carbon fibers from polymer precursors requires oxidative stabilization of the precursor fibers before the final high temperature carbonization or graphitization steps. In the case of polyacrylonitrile precursors, the stabilization step involves highly exothermic reactions and the potential for nonuniform stabilization, resulting from diffusion of oxygen. This investigation developed a series of mathematical and numerical models of stabilization that examines the process at both the multifilament bundle and individual filament scales. Experimental confirmation was conducted and methods were developed to measure the progress of stabilization and to acquire the basic data required by the model.; The mathematical model of stabilization for multifilament bundles of precursor fibers, based on a simplification of the complex stabilization chemistry, is a set of parabolic partial differential equations describing the progress of the major chemical reactions and the temperatures throughout the bundle. The predictions of the model were confirmed experimentally by measuring bundle temperatures during stabilization and measuring the composition of precursor bundles after stabilization. Application of the model showed that radial temperature and composition differences across the bundle are small, and that cross-flow of oven air, small bundles, and staged oven temperature profiles all help maintain control of the bundle temperature. Oven temperature profiles that are low initially, and then increase rapidly, were shown to result in shorter stabilization times, with good control of the bundle temperature.; Single filament stabilization models were developed for filaments with both round and noncircular shapes to understand the influence of oxygen diffusion through the fibers on the uniformity of stabilization. The round filament model showed the effect of the transition from reaction-limited to diffusion-limited behavior on the progress of the stabilization reactions within individual filaments. A complex transient finite element technique, based on Galerkin's method and the method-of-lines, was required to solve the stabilization model for noncircular filaments. When applied to a series of trilobal fiber shapes, this model showed that lobal shaped fibers stabilize faster than round fibers with the same cross-sectional area. In addition, it indicated that the ends of the lobes stabilize faster than the region between the lobes. |
