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Chin. Phys. B, 2011, Vol. 20(8): 086801    DOI: 10.1088/1674-1056/20/8/086801

Kinetics of catalytically activated aggregation–fragmentation process

Gao Yan(高艳)a), Wang Hai-Feng(王海锋) a)†, Lin Zhen-Quan(林振权)b), and Xue Xin-Ying(薛新英) a)
a Key Laboratory of Ecophysics and Department of Physics, College of Science, Shihezi University, Shihezi 832003, China; b Department of Physics, Wenzhou University, Wenzhou 325027, China
Abstract  We propose a catalytically activated aggregation—fragmentation model of three species, in which two clusters of species A can coagulate into a larger one under the catalysis of B clusters; otherwise, one cluster of species A will fragment into two smaller clusters under the catalysis of C clusters. By means of mean-field rate equations, we derive the asymptotic solutions of the cluster-mass distributions ak(t) of species A, which is found to depend strongly on the competition between the catalyzed aggregation process and the catalyzed fragmentation process. When the catalyzed aggregation process dominates the system, the cluster-mass distribution ak(t) satisfies the conventional scaling form. When the catalyzed fragmentation process dominates the system, the scaling description of ak(t) breaks down completely and the monodisperse initial condition of species A would not be changed in the long-time limit. In the marginal case when the effects of catalyzed aggregation and catalyzed fragmentation counteract each other, ak(t) takes the modified scaling form and the system can eventually evolve to a steady state.
Keywords:  aggregation      fragmentation      catalytically activated reaction      rate equation  
Received:  02 November 2010      Revised:  20 February 2011      Accepted manuscript online: 
PACS:  68.43.Jk (Diffusion of adsorbates, kinetics of coarsening and aggregation)  
  82.20.-w (Chemical kinetics and dynamics)  
  89.75.Da (Systems obeying scaling laws)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 10275048 and 10875086) and by the Science Foundation of Shihezi University (Grant No. RCZX200745).

Cite this article: 

Gao Yan(高艳), Wang Hai-Feng(王海锋), Lin Zhen-Quan(林振权), and Xue Xin-Ying(薛新英) Kinetics of catalytically activated aggregation–fragmentation process 2011 Chin. Phys. B 20 086801

[1] Seinfeld J H and Pandis S N 1998 Atmospheric Chemistry and Physics (New York: Wiley)
[2] Stockmayer W H 1943 J. Chem. Phys. 11 45
[3] Flory P J 1953 Principles of Polymer Chemistry (Ithaca: Cornell University Press)
[4] Anderson P W, Arrow K J and Pines D 1988 The Economy as an Evolving Complex System (Redwood: Addison-Wesley)
[5] Brenner Y S, Reijnders J P G and Spithoven A H G M 1988 The Theory of Income and Wealth Distribution (New York: St. Martin Press)
[6] Ispolatov S, Krapivsky P L and Redner S 1998 Eur. Phys. J. B 2 267
[7] Leyvraz F and Redner S 2002 Phys. Rev. Lett. 88 068301
[8] Ben-Naim E and Redner S 2005 J. Stat. Mech. L11002
[9] Shi H P, Ke J H, Sun C and Lin Z Q 2009 Acta Phys. Sin. 58 1 (in Chinese)
[10] Liang X M, Ma L J and Tang M 2009 Acta Phys. Sin. 58 83 (in Chinese)
[11] Ke J H, Chen X S and Lin Z Q 2010 Chin. Phys. B 19 026802
[12] Shinnar R 1961 J. Fluid Mech. 10 259
[13] Chase K C, Bhattacharyya P and Mekjian A Z 1998 Phys. Rev. C 57 822
[14] McGrady E D and Ziff R M 1987 Phys. Rev. Lett. 58 892
[15] Ishii T and Matsushita M 1992 J. Phys. Soc. Jpn. 61 3474
[16] Oddershede L, Dimon P and Bohr J 1993 Phys. Rev. Lett. 71 3107
[17] Ziff R M and McGrady E D 1985 J. Phys. A: Math. Gen. 18 3027
[18] Family F, Meakin P and Deutch J M 1986 Phys. Rev. Lett. 57 727
[19] Wang L, Vigil R D and Fox R O 2005 J. Colloid Interface Sci. 285 167
[20] Vigil R D, Vermeersch I and Fox R O 2006 J. Colloid Interface Sci. 302 149
[21] Straube R and Falcke M 2007 Phys. Rev. E 76 010402
[22] Ben-Naim E and Krapivsky P L 2008 Phys. Rev. E 77 061132
[23] Ke J H, Wang X H, Lin Z Q and Zhuang Y Y 2004 Physica A 338 356
[24] Ke J H, Lin Z Q and Chen X S 2008 J. Phys. A: Math. Theor. 41 285005
[25] Shen W W, Li P P and Ke J H 2010 Acta Phys. Sin. 59 6681 (in Chinese)
[26] Bond G C 1987 Heterogeneous Catalysis: Principles and Applications (Oxford: Clarendon)
[27] Oshanin G and Burlatsky S F 2002 J. Phys. A: Math. Gen. 35 L695
[28] Benichou O, Coppey M, Moreau M and Oshanin G 2005 J. Chem. Phys. 123 194506
[29] Chen Y, Han A J, Ke J H and Lin Z Q 2006 Chin. Phys. 15 1896
[30] Wang H F, Lin Z Q, Gao Y and Xu C 2009 Chin. Phys. B 18 3577
[31] Lin Z Q, Ke J H and Ye G X 2006 Phys. Rev. E 74 046113
[32] Wang H F, Lin Z Q and Ke J H 2007 Phys. Rev. E 75 046108
[33] Cheng Z and Redner S 1990 J. Phys. A: Math. Gen. 23 1233
[34] Ernst M H, Hendriks E M and Ziff R M 1982 J. Phys. A: Math. Gen. 15 L743
[35] Ziff R M, Ernst M H and Hendriks E M 1983 J. Phys. A: Math. Gen. 16 2293
[36] Ke J H and Lin Z Q 2002 Phys. Rev. E 66 062101
[37] Krapivsky P L 1993 Physica A 198 135
[38] Ben-Naim E and Krapivsky P L 1995 Phys. Rev. E 52 6066
[39] Ke J H, Cai X O and Lin Z Q 2004 Phys. Lett. A 331 281
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