Surface reactions, modeling

R. J. Gelten et al. Monte Carlo simulation of a surface reaction model showing spatio-temporal pattern formations and oscillations. J Chem Phys 705 5921-5934, 1998. 

R. M. Zilf, E. Gulari, Y. Barshad. Kinetic phase transitions in an irreversible surface-reaction model. Phys Rev Lett 56 2553-2556, 1986. 

E. V. Aibano. Determination of the order-parameter critical exponent of an irreversible dimer-monomer surface reaction model. Phys Rev E 49 1738-1739, 1994. 

I. Jensen, H. C. Fogedby, R. Dickman. Critical exponents for an irreversible surface reaction model. Phys Rev A 47. 3411-3414, 1990. 

C. A. Voigt, R. M. Zilf. Epidemic analysis of the second-order transition in the Zilf Gulari Barshad surface-reaction model. Phys Rev. E 56 R6241-R6244, 1997. 

J. Satulovsky, E. V. Albano. The influence of lateral interactions on the critical behavior of a dimer-monomer surface reaction model. J Chem Phys 97 9440-9446, 1992. 

M. Tammaro, J. W. Evans. Monomer-dimer surface reaction models Influence of the dimer adsorption mechanism. Phys Rev E 52 2310-2317, 1995. 

J. W. Evans. ZGB surface reaction model with high diffusion rates. J Chem Phys 95 2463-2465, 1993. 

B. J. Brosilow, E. Gulari, R. Ziff. Boundary effects in a surface reaction model for CO oxidation. J Chem Phys 99 1-5, 1993. 

J. W. Evans, T. R. Ray. Interface propagation and nucleation phenomena for discontinuous poisoning transitions in surface reaction models. Phys Rev E 50 4302 314, 1994. 

E. V. Albano. The critical behavior of dimer-dimer surface reaction models. Monte Carlo and finite-size scaling investigation. J Stat Phys 69 643-666,1992. 

A. Maltz, E. V. Albano. Kinetic phase transitions in dimer-dimer surface reaction models studied by means of mean-field and Monte Carlo methods. Surf Sci 277-A A-42S, 1992. 

J. Zhuo, S. Redner, H. Park. Critical behavior of an interacting surface reaction model. J Phys A (Math Gen) 26 4197-4213, 1993. 

E. Clement, P. Leroux-Hugon, L. M. Sander. Analytical solution of an irreversible surface reaction model. J Stat Phys 65 915-939, 1991. 

Application to Methane Oxidation. This selection of an appropriate initial model can be accomplished as shown here for the complete oxidation of methane. A general representation of the surface reaction model is (K12)... 

The problem of specifying an adequate model will now be to determine (1) the exponent n by a C2 analysis and (2) the denominator terms required by a C, analysis. Depending upon the particular surface-reaction model considered, the terms within Eq. (98) can change greatly. For any surface-reaction model, however, C2 remains the same. Equating Eqs. (97) and (99) provides an equation with two unknown parameters, B and rt. Estimating n in this way from the reaction data will specify the power of the denominator of Eq. (94). Generally, the selection of any of the models with the appropriate n will eliminate the difficulties represented by Eq. (93) and hence allow an effective C, analysis. 

Fig. 12.4. Stationary-state solutions and limit cycles for surface reaction model in presence of catalyst poison K3 = 9, k2 = 1, k3 = 0.018. There is a Hopf bifurcation on the lowest branch p = 0.0237. The resulting stable limit cycle grows as the dimensionless partial pressure increases and forms a homoclinic orbit when p = 0.0247 (see inset). The saddle-node bifurcation point is at...

McKarnin, M. A., Aris, R., and Schmidt, L. D. (1988). Autonomous bifurcations of a simple biomolecular surface-reaction model. Proc. R. Soc., A415, 363-87. 

Three model kinetic schemes have been studied relatively intensively with periodic forcing the first-order non-isothermal CSTR of chapter 7 the Brusselator model, which is closely related to the cubic autocatalysis of chapters 2 and 3 and the surface reaction model discussed in 12.6. We will use the last of these to introduce some of the general features. 

A comparative study was done by Kevrekidis and published as I. G. Kevrekidis, L. D. Schmidt, and R. Aris. Some common features of periodically forced reacting systems. Chem. Eng. Sci. 41,1263-1276 (1986). See also two papers by the same authors Resonance in periodically forced processes Chem. Eng. Sci. 41, 905-911 (1986) The stirred tank forced. Chem. Eng. Sci. 41,1549-1560 (1986). A full study of the Schmidt-Takoudis vacant site mechanism is to be found in M. A. McKamin, L. D. Schmidt, and R. Aris. Autonomous bifurcations of a simple bimolecular surface-reaction model. Proc. R. Soc. Lond. A 415,363-387 (1988) Forced oscillations of a self-oscillating bimolecular surface reaction model. Proc. R. Soc. Lond. A 415,363-388 (1988). 

K. Autonomous Bifurcations of a Simple Bimolecular Surface-Reaction Model... 

AUTONOMOUS BIFURCATIONS OF A SIMPLE BIMOLECULAR SURFACE-REACTION MODEL... 

The effects of forced oscillations in the partial pressure of a reactant is studied in a simple isothermal, bimolecular surface reaction model in which two vacant sites are required for reaction. The forced oscillations are conducted in a region of parameter space where an autonomous limit cycle is observed, and the response of the system is characterized with the aid of the stroboscopic map where a two-parameter bifurcation diagram for the map is constructed by using the amplitude and frequency of the forcing as bifurcation parameters. The various responses include subharmonic, quasi-peri-odic, and chaotic solutions. In addition, bistability between one or more of these responses has been observed. Bifurcation features of the stroboscopic map for this system include folds in the sides of some resonance horns, period doubling, Hopf bifurcations including hard resonances, homoclinic tangles, and several different codimension-two bifurcations. 

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