A mesoscopic thermodynamic approach for microstructures within the carbon fibers precursory mesophase pitch*

The present study employs a thermodynamic approach different from the conventional one to analyze, describe, and predict thermodynamic and mechanical properties of carbon fibers.  On the mesoscopic space, new balance equations for the microdomains are deduced by considering their size and orientation as internal degrees of freedom.  Evolution equations for the size and orientation of crystalline microdomains are also proposed. Compared to the usual continuum theory, additional fluxes into an orientation and direction space occur. These are constitutive functions, like internal energy, heat flux and stress tensor. By considering a modified form of the microdomain size evolution equation, it is possible to describe the low and intermediate shear rate regions. The overall evolution of the microdomain size, in both the shear inception and relaxation processes, is well described in agreement with phenomenological observations. Moreover, the calculations of steady shear flow properties such as viscosity, anisotropy, and primary normal stress difference, establish a new scheme for the mesophase pitch rheology in the low shear rate region.