Formulation of a Mathematical Process Model for the Foaming of a Mesophase Carbon Precursor
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FORMULATION OF A MATHEMATICAL PROCESS MODEL FOR THE FOAMING OF A MESOPHASE CARBON PRECURSOR S. S. SANDHU* and J. W. HAGER** *Department of Chemical/Materials Engineering, University of Dayton, Dayton, OH 45469 "**WrightLaboratory, WL/MLBC, Wright-Patterson AFB, OH 45433-6533
ABSTRACT Mathematical equations have been formulated to guide an experimental effort to produce an open-celled mesophase pitch foam. The formulation provides an analytical description of homogeneous bubble nucleation and growth, diffusion of the blowing gas through the liquid to the bubble surface, and the average material thickness between bubbles. Implications of the formulation for the experimental production of mesophase pitch foam are discussed. INTRODUCTION Mesophase pitch is one of the major precursors used in the production of high performance carbon fiber. Carbon fibers derived from mesophase pitch are typically characterized by high tensile strength and, depending on processing, can possess extraordinarily high elastic moduli. These remarkable mechanical properties are generally attributed to the alignment of graphitic planes with the axis of the fiber. The mesophase pitch can be used to manufacture high quality carbon fibers by the alignment of the graphite precursor molecules achieved during the melt spinning process. A similar alignment of precursor molecules occurs during the blowing of an open-celled foam from a mesophase pitch melt. Subsequent stabilization, carbonization and graphitization of a foam produced in this way has been shown to yield a degree of graphitization similar to that achieved in high modulus, carbon fibers [11. Foams produced in this way may become novel reinforcing phases for composite structural materials [2]. We have recently initiated a research activity whose objective is to produce structural carbon foam from a mesophase pitch, Mitsubishi AR® [3], produced via naphthalene synthesis. The foaming process involves the control of temperature and pressure of the nitrogen-saturated pitch. Spontaneous bubble nucleation results from pressure relaxation, and bubble growth is thought to occur by diffusion of the blowing gas through the liquid crystal melt to the bubble nucleation sites. Since the number concentration and final average size of the bubbles influence the mechanical and thermal properties of the carbon foam, it is desirable to have a process model which relates these to the controllable process variables. For example, how is the bubble nucleation density related to the starting pressure and to the pressure release? When should cooling of the pitch melt be initiated and at what rate should cooling be carried out? Fundamental mathematical formulation of the mesophase foaming process described above is envisioned to guide our experimental effort to produce a graphitic foam from the mesophase pitch with desirable mechanical and thermal properties. The current process model formulation considers the initial heating of a fixed amount of the nitrogen-saturated mesophase pitch at a given initial pressure, t
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