On the description of the microdomains within carbon fiber precursory mesophase pitch: a mesoscopic continuum approach. (English) Zbl 1500.74003

Summary: 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.


74A60 Micromechanical theories
74E15 Crystalline structure
Full Text: DOI


[1] Chand, S., Review carbon fibers for composites, J. Mater. Sci., 35, 6, 1303-1313 (2000)
[2] Cato, AD; Edie, DD, Flow behavior of mesophase pitch, Carbon, 41, 7, 1411-1417 (2003)
[3] Edie, DD; Stoner, EG; Buckley, JD; Edie, DD, Effect of microstructure and shape on carbon fiber properties, Carbon-Carbon Materials and Composites, 41-69 (1993), Park Ridge: Noyes Publications, Park Ridge
[4] Endo, M., Structure of mesophase pitch-based carbon fibres, J. Mater. Sci., 23, 2, 598-605 (1988)
[5] Hamada, T.; Nishida, T.; Sajiki, Y.; Matsumoto, M.; Endo, M., Structures and physical properties of carbon fibers from coal tar mesophase pitch, J. Mater. Res., 2, 6, 850-857 (1987)
[6] Hamada, T.; Nishida, T.; Furuyama, M.; Tomioka, T., Transverse structure of pitch fiber from coal tar mesophase pitch, Carbon, 26, 6, 837-841 (1988)
[7] Goodhew, PJ; Clarke, AJ; Bailey, JE, A review of the fabrication and properties of carbon fibres, Mater. Sci. Eng., 17, 1, 3-30 (1975)
[8] Huang, X., Fabrication and properties of carbon fibers, Materials, 2, 4, 2369-2403 (2009)
[9] Kase, S.; Matsuo, T., Studies on melt spinning. i. fundamental equations on the dynamics of melt spinning, J. Polym. Sci. A, 3, 7, 2541-2554 (1965)
[10] Kase, S.; Matsuo, T., Studies on melt spinning. ii. steady-state and transient solutions of fundamental equations compared with experimental results, J. Appl. Polym. Sci., 11, 2, 251-287 (1967)
[11] Mochida, I.; Yoon, S.; Korai, Y., Mesoscopic structure and properties of liquid crystalline mesophase pitch and its transformation into carbon fiber, Chem. Rec., 2, 2, 81-101 (2002)
[12] de Castro, LD, Anisotropy and mesophase formation towards carbon fibre production from coal tar and petroleum pitches - a review, J. Braz. Chem. Soc., 17, 6, 1096-1108 (2006)
[13] Matsumoto, T., Mesophase pitch and its carbon fibers, Pure Appl. Chem., 57, 11, 1553-1562 (1985)
[14] Edie, DD; Dunham, MG, Melt spinning pitch-based carbon fibers, Carbon, 27, 5, 647-655 (1989)
[15] Florindo, CCF; Papenfuss, C.; Bassi, ABMS, Mesoscopic continuum thermodynamics for mixtures of particles with orientation, J. Math. Chem., 55, 10, 1985-2003 (2017) · Zbl 1387.82022
[16] Blenk, S.; Ehrentraut, H.; Muschik, W., Statistical foundation of macroscopic balances for liquid crystals in alignment tensor formulation, Physica A, 174, 1, 119-138 (1991)
[17] Blenk, S.; Ehrentraut, H.; Muschik, W., Macroscopic constitutive equations for liquid crystals induced by their mesoscopic orientation distribution, Int. J. Eng. Sci., 30, 9, 1127-1143 (1992) · Zbl 0759.76009
[18] Blenk, S.; Ehrentraut, H.; Muschik, W., A continuum theory for liquid crystals describing different degrees of orientational order, Liq. Cryst., 14, 4, 1221-1226 (1993)
[19] Muschik, W.; Papenfuss, C.; Ehrentraut, H., Sketch of the mesoscopic description of nematic liquid crystals, J. Nonnewton. Fluid Mech., 119, 1-3, 91-104 (2004) · Zbl 1070.76008
[20] Papenfuss, C., Theory of liquid crystals as an example of mesoscopic continuum mechanics, Comput. Mater. Sci., 19, 1-4, 45-52 (2000)
[21] Blenk, S.; Muschik, W., Orientational balances for nematic liquid crystals, J. Non-Equilib. Thermodyn., 16, 1, 67-87 (1991) · Zbl 0722.76007
[22] Muschik, W.; Ehrentraut, H.; Papenfuss, C., Concepts of mesoscopic continuum physics with application to biaxial liquid crystals, J. Non-Equilib. Thermodyn., 25, 2, 179-197 (2000) · Zbl 0981.76007
[23] Muschik, W.; Ehrentraut, H.; Papenfuss, C., The connection between Ericksen-Leslie equations and the balances of mesoscopic theory of liquid crystals, Mol. Cryst. Liq. Cryst. Sci. Technol. A, 262, 1, 417-423 (1995) · Zbl 0855.76007
[24] Bourrat, X.; Roche, EJ; Lavin, JG, Structure of mesophase pitch fibers, J. Appl. Polym. Sci., 28, 2-3, 435-446 (1990)
[25] Hamada, T.; Furuyama, M.; Sajiki, Y.; Tomioka, T.; Endo, M., Preferred orientation of pitch precursor fibers, J. Mater. Res., 5, 6, 1271-1280 (1990)
[26] Ehrentraut, H.; Hess, S., Viscosity coefficients of partially aligned nematic and nematic discotic liquid crystals, Phys. Rev. E, 51, 3, 2203-2212 (1995)
[27] Ehrentraut, H.; Muschik, W.; Papenfuss, C., Mesoscopically derived orientation dynamics of liquid crystals, J. Non-Equilib. Thermodyn., 22, 3, 285-298 (1997) · Zbl 0903.76008
[28] C.C.F. Florindo, Mesoscopic continuum thermodynamics for chemical systems. PhD thesis, University of Campinas (April 2016)
[29] Müller, I., Thermodynamics (1985), Boston: Pitman Publishing, Boston
[30] Doi, M., Molecular dynamics and rheological properties of concentrated solutions of Rodlike polymers in isotropic and liquid crystalline phases, J. Polym. Sci. Polym. Phys. Ed., 19, 2, 229-243 (1981)
[31] Schmelzer, JWP; Abyzov, AS; Fokin, VM; Schick, C.; Zanotto, ED, Crystallization of glass-forming liquids: maxima of nucleation, growth, and overall crystallization rates, J. Non-Cryst. Solids, 429, 24-32 (2015)
[32] Schmelzer, JWP; Abyzov, AS, Crystallization of glass-forming liquids: thermodynamic driving force, J. Non-Cryst. Solids, 449, 41-49 (2016)
[33] Schmelzer, JWP; Abyzov, AS, Crystallization of glass-forming liquids: specific surface energy, J. Chem. Phys., 145, 6 (2016)
[34] Gornick, F.; Hoffman, JD, Nucleation in polymers, Ind. Eng. Chem., 58, 2, 41-53 (1966)
[35] Hoffman, JD; Weeks, JJ, Rate of Spherulitic crystallization with chain folds in polychlorotrifluoroethylene, J. Chem. Phys., 37, 8, 1723-1741 (1962)
[36] Wang, M.; Wang, C.; Chen, M.; Li, T.; Hu, Z., Bubble growth in the preparation of mesophase-pitch-based carbon foams, New Carbon Mater., 24, 1, 61-66 (2009)
[37] Yoon, S-H; Korai, Y.; Mochida, I.; Kato, I., The flow properties of mesophase pitches derived from methylnaphthalene and naphthalene in the temperature range of their spinning, Carbon, 32, 2, 273-280 (1994)
[38] Ehrenstein, GW, Polymeric Materials Structure-Properties-Applications (2001), Munich: Carl Hanser Verlag GmbH & Co.KG, Munich
[39] C.C.F. Florindo, A.B.M.S. Bassi, Thermodynamic modelling of mesophase pitch for the development of highperformance carbon fibers, in 11th Triennial Congress of the World Association of Theoretical and Computational Chemists (27 August-1 September 2017 Munich, Germany) (2017)
[40] Mochida, I.; Korai, Y.; Ku, CH; Watanabe, F.; Sakai, Y., Chemistry of synthesis, structure, preparation and application of aromatic-derived mesophase pitch, Carbon, 38, 2, 305-328 (2000)
[41] Avrami, M., Kinetics of phase change. i general theory, J. Chem. Phys., 7, 12, 1103-1112 (1939)
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