Stochastic Modeling of Oxidation of Defected Graphite

Wei-Yin Chen, Leili Gordji, Baharak Sajjadi

Abstract


To portray the experimentally observable stochastic nature of oxidation of defected graphite,
the piecewise linear, two-stage model was derived in the previous work to which the current
contribution is a sequel. The model takes into account all the major features of the classic
deterministic, graphite oxidation model of Nagle and Strickland-Constable (NSC) including the
simultaneous conversion of the identity of an adjacent basal cluster to an edge cluster. The NSC
model assumes that there are secondary reactions in the second stage due to the decrease in basal
clusters. The model, however, contains a noticeable uncertainty as to the identification of the
breaking point caused by the transition between the two linear stages. This uncertainty is eliminated
by incorporating in the nonlinear stochastic model proposed in the present work a parameter which
renders the extent of the secondary reactions proportional to the concentration of basal clusters in
the carbon matrix. The validity of incorporating this parameter has been amply demonstrated by the
fact that the variances around the means, derived through the method of system-size expansion of
the nonlinear master equation of the current model, are appreciably less than those of the previous
model.


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References


Chen, W.Y.; Kulkarni, A.; Milum, J.L.; Fan, L.T. Stochastic Modeling of Carbon Oxidation,

AIChE J., 1999, 45, 2557-2570.

Oppenheim, I.; Shuler, K.E; Weiss, G.H. Stochastic Process in Chemical Physics: The Master

Equation, The MIT Press, Cambridge, MA, 1977.

Gardiner, C.W. Handbook of Stochastic Methods for Physics, Chemistry, and Natural Sciences,

nd ed., Springer-Verlag, Berlin, Germany, 1985.

van Kampen, N.G. Stochastic Process in Physics and Chemistry, 2nd ed., Elsevier, Amsterdam,

Netherlands, 1992.

Blyholder, G.; Binford Jr., J.S.; Eyring, H. A Kinetic Theory for the Oxidation of Carbonized

Filaments, J. Phys. Chem., 1958, 62, 263-267.

Nagle, J.; Strickland-Constable, R.F. Oxidation of Carbon between 1000-2000EC, Proc. 5th Conf.

on Carbon, Vol. 1., Pergamon Press, pp.154-160 (1962).

Chu, X.; Schmidt, L.D. Reactions of NO, O2, H2O, and CO2 with the Basal Plane of Graphite,

Surface Science, 1992, 268, 325-332.

Chu, X.; Schmidt, L.D. Intrinsic Rates of NOx-Carbon Reactions, Ind. Eng. Chem. Res., 1993, 32,

-1366.

van Kampen, N.G. A Power Series Expansion of the Master Equations, Can. J. Phys., 1961, 39,

-567.

van Kampen, N.G. The Expansion of the Master Equation, Adv. Chem. Phys., 1976, 34, 245-310.

Chen W.Y., Bokka S. Stochastic Modeling of Nonlinear Epidemiology. Journal of Theoretical

Biology, 2005, 234, 455-470.

Parzen, E. Stochastic Processes, Holden-Day, San Francisco, CA, 1962.

Shen, B.C.; Fan, L.T.; Chen, W.Y. Stochastic Modeling of Adsorption in a Batch System,

Journal of Hazardous Materials, 1994, 38, 353-371.

Fan, L.T.; Chou, S.T.; Chen, W.Y.; Bai, M.T.; Hsu, J.P. Modeling Fluctuations in the Growth

Rate of a Single Crystal, in Mixing and Crystallization, Shaliza S.; Sen Gupta, B. ed.,

Kluwer Academic Publishers, Dordrecht, The Netherlands, pp.253-265 (2000).

. Petzold, L.R., and A.C. Hindmarsh, “A Systematized collection of ODE Solvers,” Report of

Lawrence Livemore National Laboratory to the U.S. Department of Energy under contract

W-7405-eng-48, also available on web at http://www.netlib.org/odepack, 1997.

Carmichael, H. Statistical Methods in Quantum Optics 1: Master Equations and Fokker-

Planck Equations, Springer, Berlin, pp.158-162 (1999).

Chen, W.Y. and Bokka S.. "Stochastic modeling of nonlinear epidemiology." Journal of

Theoretical Biology 234(4): 455-470, (2005).




DOI: http://dx.doi.org/10.24294/ijmss.v0i0.530

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