Fractional diffusion interpretation of simulated single-file systems in microporous materials

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 74, Issue 5, 2006, Pages

  Demontis, Pierfranco ^a   Suffritti, Giuseppe B ^a  

^a UNIVERSITY OF SASSARI   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; CRYSTALLINE MATERIALS; DIFFUSION; MOLECULAR DYNAMICS; SILICATES;

ALUMINOSILICATES; FRACTIONAL DIFFUSION EQUATIONS; SINGLE FILE DIFFUSION PROCESS;

MICROPOROUS MATERIALS;

EID: 33751198975     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.74.051112     Document Type: Article

References (61)

1. F. Gambale, M. Bregante, F. Stragapede, and A. M. Cantu, J. Membr. Biol. JMBBBO 0022-2631 10.1007/s002329900133 154, 69 (1996).
2. C.-Y. Chou, B. C. Eng, and M. Robert, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.2151888 124, 044902 (2006).
3. R. Arratia, Ann. Probab. APBYAE 0091-1798 11, 362 (1983).
4. A. D. Stroock, M. Weck, D. T. Chiu, W. T. S. Huck, P. J. A. Kenis, R. F. Ismagilov, and G. M. Whitesides, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.84.3314 84, 3314 (2000).
5. H. Y. Lee, H. W. Lee, and D. Kim, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.81.1130 81, 1130 (1998).
6. J. Kärger and D. M. Ruthven, Diffusion in Zeolites and Other Microporous Solids (Wiley-Interscience, New York, 1992).
7. P. Demontis, G. Stara, and G. B. Suffritti, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1697382 120, 9233 (2004).
8. P. Demontis, G. Stara, and G. B. Suffritti, Microporous Mesoporous Mater. MIMMFJ 1387-1811 86, 166 (2005).
9. A. Fick, Philos. Mag. PHMAA4 0031-8086 10, 30 (1855).
10. A. Fick, Philos. Mag. PHMAA4 0031-8086 10, 30 (1855);
11. A. Fick, Ann. Phys. Chem. ANPYA2 0003-3804 94, 59 (1855);
12. A. Einstein, Ann. Phys. ANPYA2 0003-3804 17, 549 (1905);
13. J. Crank, The Mathematics of Diffusion (Clarendon Press, Oxford, 1970).
14. R. Metzler and J. Klafter, Phys. Rep. PRPLCM 0370-1573 10.1016/S0370-1573(00)00070-3 339, 1 (2000).
15. V. Balakrishnan, Physica A PHYADX 0378-4371 10.1016/0378-4371(85)90028-7 132, 569 (1985);
16. R. Gorenflo, F. Mainardi, D. Moretti, and P. Paradisi, Nonlinear Dyn. NODYES 0924-090X 29, 129 (2002);
17. F. Mainardi, A. Vivoli, and R. Gorenflo, Fluct. Noise Lett. ZZZZZZ 0219-4775 5, L291 (2005).
18. T. E. Harris, J. Appl. Probab. JPRBAM 0021-9002 10.2307/3212197 2, 323 (1965).
19. D. G. Levitt, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.8.3050 8, 3050 (1973).
20. J. Kärger, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.45.4173 45, 4173 (1992).
21. H. van Beijeren, K. W. Kehr, and R. Kutner, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.28.5711 28, 5711 (1983).
22. M. Kollmann, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90. 180602 90, 180602 (2003).
23. E. Barkai, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.63.046118 63, 046118 (2001).
24. Kwok Sau Fa and E. K. Lenzi, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.72.011107 72, 011107 (2005).
25. M. Abramowitz, and, I. A. Stegun, Eds. Handbook of Mathematical Functions (Dover Pub. Inc., New York, 1972).
26. D. Frenkel and R. Portugal, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/34/17/302 34, 3541 (2001).
27. I. Goychuk, E. Heinsalu, M. Patriarca, G. Schmid, and P. Hänggi, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.73.020101 73, 020101 (R) (2006).
28. E. Heinsalu, M. Patriarca, I. Goychuk, G. Schmid, and P. Hänggi, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.73.046133 73, 046133 (2006).
29. R. Metzler, E. Barkai, and J. Klafter, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.82.3563 82, 3563 (1999).
30. C. Rödenbeck, J. Kärger, and K. Hahn, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.57.4382 57, 4382 (1998).
31. J. M. D. MacElroy and S.-H. Suh, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.473914 106, 8595 (1997).
32. W. Feller, An Introduction to Probability Theory and Its Applications, Vol. 2 (Wiley, New York, 1971).
33. A. Compte, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.55.6821 55, 6821 (1997).
34. J. L. Lebowitz and J. K. Percus, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.155.122 155, 122 (1967).
35. Q.-H Wei, C. Bechinger, and P. Leiderer, Science SCIEAS 0036-8075 10.1126/science.287.5453.625 287, 625 (2000).
36. B. Lin, M. Meron, B. Cui, S. A. Rice, and H. Diamant, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.216001 94, 216001 (2005).
37. C. Lutz, M. Kollmann, and C. Bechinger, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.026001 93, 026001 (2004).
38. K. Hahn, J. Kärger, and V. Kukla, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.76.2762 76, 2762 (1996).
39. C.-Y. Chou, B. C. Eng, and M. Robert, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.2151888 124, 044902 (2006).
40. G. Coupier, M. Saint Jean, and C. Guthmann, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.73.031112 73, 031112 (2006).
41. P. M. Richards, Phys. Rev. B PLRBAQ 0556-2805 10.1103/PhysRevB.16.1393 16, 1393 (1977).
42. J. Kärger, M. Petzold, H. Pfeifer, S. Ernst, and J. Weitkamp, J. Catal. JCTLA5 0021-9517 10.1016/0021-9517(92)90062-M 136, 283 (1992).
43. K. K. Mon and J. K. Percus, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1490337 117, 2289 (2002).
44. D. S. Sholl and K. A. Fichthorn, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.474779 107, 4384 (1997);
45. K. Hahn and J. Kärger, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.476524 109, 5691 (1998);
46. D. S. Sholl and K. A. Fichthorn, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.476525 109, 5693 (1998).
47. K. Hahn and J. Kärger, J. Chem. Phys. JCPSA6 0021-9606 10.1021/jp951807u 100, 316 (1996).
48. S. Pal, G. Srinivas, S. Bhattacharyya, and B. Bagchi, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1461361 116, 5941 (2002).
49. K. K. Mon and J. K. Percus, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1591179 119, 3343 (2003).
50. A. Taloni and F. Marchesoni, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.020601 96, 020601 (2006).
51. S. Vasenkov, A. Shüring, and S. Fritzsche, Langmuir LANGD5 0743-7463 22, 5728 (2006).
52. P. Demontis, G. Stara, and G. B. Suffritti, J. Phys. Chem. B JPCBFK 1089-5647 10.1021/jp0300849 107, 4426 (2003).
53. P. Demontis, S. Spanu, and G. B. Suffritti, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.481432 112, 8267 (2001).
54. A. Chechkin, V. Gonchar, J. Klafter, R. Metzler, and L. Tanatarov, Chem. Phys. CMPHC2 0301-0104 10.1016/S0301-0104(02)00551-7 284, 233 (2002).
55. A. V. Chechkin, J. Klafter, V. Yu. Gonchar, R. Metzler, and L. V. Tanatarov, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.67.010102 67, 010102 (R) (2003).
56. A. V. Chechkin, V. Yu. Gonchar, J. Klafter, R. Metzler, and L. V. Tanatarov, J. Stat. Phys. JSTPBS 0022-4715 10.1023/B:JOSS.0000028067.63365.04 115, 1505 (2004).
57. B. Gorenflo, G. De Fabritiis, and F. Mainardi, Physica A PHYADX 0378-4371 269, 78 (1999);
58. B. Gorenflo, F. Mainardi, D. Moretti, G. Pagnini, and P. Paradisi, Physica A PHYADX 0378-4371 10.1016/S0378-4371(01)00647-1 305, 106 (2002);
59. B. Gorenflo, F. Mainardi, D. Moretti, G. Pagnini, and P. Paradisi, Chem. Phys. CMPHC2 0301-0104 10.1016/S0301-0104(02)00714-0 284, 521 (2002).
60. A. V. Chechkin, R. Gorenflo, and I. M. Sokolov, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.66.046129 66, 046129 (2002);
61. I. M. Sokolov, A. V. Chechkin, and J. Klafter, Acta Phys. Pol. B APOBBB 0587-4254 35, 1323 (2004).