Schloegl's second model for autocatalysis with particle diffusion: Lattice-gas realization exhibiting generic two-phase coexistence

Journal of Chemical Physics

Volumn 130, Issue 7, 2009, Pages

  Guo, Xiaofang ^a,b   Liu, Da Jiang ^a   Evans, J W ^a,b  

^a IOWA STATE UNIVERSITY   (United States)

^b IOWA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFUSION IN SOLIDS; STOCHASTIC MODELS;

ANNIHILATION RATES; AUTOCATALYTIC; CONTACT PROCESS; CRITICAL VALUES; DIFFUSIVITIES; DISCONTINUOUS EQUILIBRIUMS; FINITE POPULATIONS; LATTICE GAS; METASTABILITY; NON-EQUILIBRIUM PHASE TRANSITIONS; PARTICLE DIFFUSIONS; PHASE COEXISTENCES; SQUARE LATTICES; STEADY STATE; THERMODYNAMIC SYSTEMS;

PHASE TRANSITIONS;

EID: 60749088867     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3074308     Document Type: Article

References (57)

1. G. Nicolis and I. Prigogine, Self-Organization in Non-Equilibrium Systems (Wiley, New York, 1977).
2. P. Gray and S. K. Scott, Chemical Oscillations and Instabilities (Clarendon, Oxford, 1994).
3. A. S. Mikhailov, Foundations of Synergetics I (Springer, Berlin, 1990).
4. Chemical Waves and Patterns, edited by, R. Kapral, and, K. Showalter, (Kluwer, Amsterdam, 1995).
5. N. G. Van Kampen, Stochastic Processes in Physics and Chemistry (North Holland, Amsterdam, 1981).
6. A. S. Mikhailov and A. Yu. Loskutov, Foundations of Synergetics II (Springer, Berlin, 1996).
7. J. Garcia-Ojalvo and J. M. Sancho, Noise in Spatially Extended Systems (Springer, Berlin, 1999).
8. M. Hildebrand, A. S. Mikhailov, and G. Ertl, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.81.2602 81, 2602 (1998).
9. D. T. Gillespie and L. Petzold, in System Modeling in Cellular Biology, edited by, Z. Szallasi, J. Stelling, and, V. Periwal, (MIT Press, Cambridge, 2006), p. 331.
10. R. Imbihl, Prog. Surf. Sci. 0079-6816 10.1016/0079-6816(93)90086-B 44, 185 (1993).
11. R. Imbihl and G. Ertl, Chem. Rev. (Washington, D.C.) 0009-2665 10.1021/cr00035a012 95, 697 (1995).
12. Y. Suchorski, J. Beben, E. W. James, J. W. Evans, and R. Imbihl, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.82.1907 82, 1907 (1999).
13. D. -J. Liu and J. W. Evans, J. Phys.: Condens. Matter 0953-8984 10.1088/0953-8984/19/6/065129 19, 065129 (2007).
14. J. Starke, C. Reichert, M. Eiswirth, H. H. Rotermund, and G. Ertl, Europhys. Lett. 0295-5075 10.1209/epl/i2005-10492-4 73, 820 (2006).
15. D. Dab, A. Lawniczak, J. P. Boon, and R. Kapral, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.64.2462 64, 2462 (1990).
16. J. P. Boon, D. Dab, R. Kapral, and A. Lawniczak, Phys. Rep. 0370-1573 10.1016/0370-1573(95)00080-1 273, 55 (1996).
17. J. Marro and R. Dickman, Nonequilibrium Phase Transitions in Lattice Models (Cambridge University Press, Cambridge, 1999).
18. H. Hinrichsen, Adv. Phys. 0001-8732 10.1080/00018730050198152 49, 815 (2000).
19. G. Odor, Rev. Mod. Phys. 0034-6861 10.1103/RevModPhys.76.663 76, 663 (2004).
20. R. M. Ziff, E. Gulari, and Y. Barshad, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.56.2553 56, 2553 (1986).
21. J. W. Evans and T. R. Ray, Phys. Rev. E 1063-651X 10.1103/PhysRevE.50. 4302 50, 4302 (1994).
22. R. H. Goodman, D. S. Graff, L. M. Sander, P. Leroux-Hugon, and E. Cĺment, Phys. Rev. E 1063-651X 10.1103/PhysRevE.52.5904 52, 5904 (1995).
23. J. W. Evans and M. S. Miesch, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.66.833 66, 833 (1991).
24. E. Loscar and E. V. Albano, Rep. Prog. Phys. 0034-4885 10.1088/0034-4885/66/8/203 66, 1343 (2003).
25. E. Machado, G. M. Buendia, and P. A. Rikvold, Phys. Rev. E 1063-651X 10.1103/PhysRevE.71.031603 71, 031603 (2005).
26. D. -J. Liu and J. W. Evans, Surf. Sci., DOI:10.1016/j.susc.2008.10.058 (2009).
27. F. Schlögl, Z. Phys. 0044-3328 10.1007/BF01379769 253, 147 (1972).
28. P. Grassberger, Z. Phys. B: Condens. Matter 47, 365 (1982).
29. R. Durrett, SIAM Rev. 0036-1445 10.1137/S0036144599354707 41, 677 (1999).
30. D. -J. Liu, X. Guo, and J. W. Evans, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.98.050601 98, 050601 (2007).
31. X. Guo, D. -J. Liu, and J. W. Evans, Phys. Rev. E 1063-651X 10.1103/PhysRevE.75.061129 75, 061129 (2007).
32. C. Bezuidenhout and L. Gray, Ann. Probab. 22, 1160 (1994). 0091-1798
33. A. L. Toom, in Multicomponent Random Systems, edited by, R. L. Dobrushin, and, Y. G. Sinai, (Dekker, New York, 1980).
34. C. H. Bennett and G. Grinstein, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.55.657 55, 657 (1985).
35. G. Grinstein, IBM J. Res. Dev. 48, 5 (2004). 0018-8646
36. M. A. Munoz, F. de los Santos, and M. M. T. da Gama, Eur. Phys. J. B 1434-6028 10.1140/epjb/e2005-00029-3 43, 73 (2005).
37. D. Mollison, J. R. Stat. Soc. Ser. B (Methodol.) 39, 283 (1977).
38. X. Guo, J. W. Evans, and D. -J. Liu, Physica A 387, 177 (2008). 0378-4371
39. X. Guo, D. -J. Liu, and J. W. Evans, " Schloegl's second model for autocatalysis on a square lattice with particle diffusion: analytic treatment.."
40. Interchange the role of particles and empty sites in the QCP (Refs.). Then, one has spontaneous creation of particles at empty sites, and their autocatalytic removal given suitable empty pairs of sites. The former mimics monomer adsorption in the ZGB model, and the latter mimics reactive monomer removal (which requires empty pairs sites to allow dimer adsorption).
41. R. M. Ziff and B. J. Brosilow, Phys. Rev. A 1050-2947 10.1103/PhysRevA.46.4630 46, 4630 (1992).
42. D. -J. Liu, J. Stat. Phys., "Generic two-phase coexistence and non-equilibrium criticality in a lattice version of Schloegl's second model for autocatalysis."
43. R. H. Schonmann and S. B. Shlosman, Commun. Math. Phys. 0010-3616 10.1007/s002200050363 194, 389 (1998).
44. S. Shlosman, Physica A 0378-4371 10.1016/S0378-4371(98)00531-7 263, 180 (1999).
45. S. Friedli and C. -E. Pfister, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.92.015702 92, 015702 (2004).
46. P. A. Rikvold, H. Tomita, S. Miyashita, and S. W. Sides, Phys. Rev. E 1063-651X 10.1103/PhysRevE.49.5080 49, 5080 (1994). This study described the spinodal associated with an infinite Ising system as the "mean-field spinodal point" (MFSP) although it cannot be assessed with a simple mean-field theory.
47. M. Avrami, J. Chem. Phys. 0021-9606 10.1063/1.1750380 7, 1103 (1939); M. Avrami, J. Chem. Phys. 0021-9606 10.1063/1.1750631 8, 212 (1940); M. Avrami, J. Chem. Phys. 0021-9606 10.1063/1.1750872 9, 177 (1941).
48. J. Krug and H. Spohn, in Solids Far from Equilibrium: Growth, Morphology and Defects, edited by, C. Godreche, (Cambridge University Press, Cambridge, 1991).
49. A. -L. Barabasi and H. E. Stanley, Fractal Concepts in Surface Growth (Cambridge University Press, Cambridge, 1995).
50. For a planar interface with small slope y/x measured relative to S=1, the normal velocity is denoted V (S=1+h/x). By a Pythagorean construction, the velocity in the y -direction is y/t=V (S=1+h/x) [1+ (h/x) 2] 1/2 ≈ V0 +δV+1/2 V0 (h/x) 2, where V0 =V (S=1), and δV=V (S=1+h/x) -V (S=1) ≈C (h/x) 2 (Ref.). Thus, one has λ=2C+ V0.
51. H. -C. Jeong and E. D. Williams, Surf. Sci. Rep. 0167-5729 10.1016/S0167-5729(98)00010-7 34, 171 (1999).
52. Writing ̃ eff (θ) ≈ av (h) +f (h) cos (4θ), it follows that eff (θ) ≈ av (h) -f (h) cos (4θ) /15. These identities are equivalent to Eqs. noting that ̃ 1 (h) = av (h) -f (h) and g (h) =2f (h).
53. An increasing number of vacuum clusters which nucleate just ahead of the interface can be incorporated into the advancing interface as time progresses corrupting estimation of V.
54. J. D. Gunton and M. Droz, Introduction to the Theory of Metastable and Unstable States, Springer Lecture Notes in Physics (Springer, Berlin, 1983), Vol. 183.
55. A. Matzavinos, X. Guo, D. -J. Liu, and J. W. Evans. " Analysis of coarse-grained stochastic reaction-diffusion equations for Schloegl's second model on a square lattice. Here, ac C1/2 (p+C- C2) 1/2 ac is the nonconserved particle annihilation-creation noise, and diff ∇ [h1/2 C1/2 (1-C) 1/2 diff] is the conserved particle diffusion noise. ac and diff are independent white noises."
56. M. Hildebrand and A. S. Mikhailov, J. Phys. Chem. 0022-3654 10.1021/jp961668w 100, 19089 (1996).
57. D. -J. Liu and J. W. Evans, " Generic two-phase coexistence in lattice-gas reaction-diffusion models.. "