On the description of the microdomains within carbon fiber precursory mesophase pitch: a mesoscopic continuum approach

Abstract

The present paper proposes a mesoscopic continuum approach in order to describe the behavior of microdomains within carbon fiber precursory mesophase pitch. The microdomains are assumed to have an orientation, which is determined by the average orientation of the particles that form it. On the mesoscopic space, balance equations for the microdomains are presented. Evolution equations for the density and for the orientation of the crystalline microdomains are proposed. In order to determine the temporal variation of the microdomain density, it was deduced a quite simple relation between mass production, critical density of microdomains and a mesoscopic operator acting on the orientation distribution function. As presented in the present work, the mass production can be determined by the crystallization kinetics theory via the steady-state nucleation rate. Specific forms for the mesoscopic operator are proposed in this work, although they may be extended to other models that describe oriented microstructures. There are not yet enough experimental data to test the mesoscopic model deduced here, but in turn, it is presented as a new tool for experimental studies, since it can estimate the time rate of microdomain property changes. Possible extensions of this model could be applied to describe mechanical and rheological properties of carbon fibers.