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Single-File Diffusion in Zeolites

Chapter
Part of the Molecular Sieves book series (SIEVES, volume 7)

Abstract

The exclusion of the mutual passage of diffusants in zeolites with one-dimensional channels leads to patterns of molecular transportation which are unknown in amorphous materials or from zeolites with multi-dimensional pore networks. In particular, there is no possibility to describe molecular transport by the well-known Fick's equations of molecular diffusion. Molecular transport in such systems has been termed single-file diffusion. It is characterized by the molecular mean square displacements, which in infinitely extended single-file diffusion is found to increase in proportion with the square root of the observation time rather than with the observation time itself. For finite single-file systems, the rate of molecular exchange between the crystals and their surroundings, representing one of the key parameters for their practical application in heterogeneous catalysis and mass separation, decreases with the third rather than with the second power of the crystal size.

As a consequence of the correlation of the movement of the individual diffusants and the thus-mediated long-range influence of boundaries, the treatment of single-file systems of finite length is particularly complicated. Present attempts of analytical treatment of such systems and the quantification of the boundary conditions do not provide anything more than first approaches. Monte-Carlo simulations supported by analytical approaches reveal striking peculiarities of zeolitic single-file systems. These peculiarities include an enhanced dependence of the intracrystalline mean lifetime, and hence of the effectiveness factor, on the size of the catalyst particle, and the possibility of an enhancement of the apparent activation energy of catalytic reactions under transport control. Though there is still some controversy concerning the evidence obtained by the different methods applied, indications of single-file diffusion in zeolites have been observed by various experimental techniques including pulsed field gradient NMR, quasi-elastic neutron scattering and tracer exchange measurements.

Anomalous diffusion Confinement Diffusion-limited reaction Dynamic Monte Carlo simulation Molecular traffic control Random walk Single-file diffusion  

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References

  1. 1.
    Kärger J, Petzold M, Pfeifer H, Ernst S, Weitkamp J (1992) J Catal 136:283 CrossRefGoogle Scholar
  2. 2.
    Riekert L (1970) Adv Catal 21:281 CrossRefGoogle Scholar
  3. 3.
    Rickert H (1964) Z Phys Chem NF 34:129 Google Scholar
  4. 4.
    Hodkin AL, Keynes RD (1955) J Physiol 128:61 Google Scholar
  5. 5.
    van Bejeren H, Kehr KW, Kutner R (1983) Phys Rev B 28:5711 CrossRefGoogle Scholar
  6. 6.
    Kehr KW, Mussawisade K, Wichmann T (1997) In: Kärger J, Heitjans P, Haberlandt R (eds) Diffusion in Condensed Matter. Vieweg, Wiesbaden, p 265 Google Scholar
  7. 7.
    Fedders PA (1978) Phys Rev B 17:40 CrossRefGoogle Scholar
  8. 8.
    Levitt DG (1973) Phys Rev A 8:3050 CrossRefGoogle Scholar
  9. 9.
    Kehr KW, Binder K (1987) In: Binder K (ed) Applications of the Monte Carlo Method in Statistical Physics. Springer, Berlin, p 181 Google Scholar
  10. 10.
    Hahn K, Kärger J (1995) J Phys A-Math General 28:3061 CrossRefGoogle Scholar
  11. 11.
    Kehr KW, Mussawisade K, Schütz GM, Wichmann T (2005) In: Heitjans P, Kärger J (eds) Diffusion in Condensed Matter – Methods, Materials, Models. Springer, Berlin, p 975 Google Scholar
  12. 12.
    Kärger J (1992) Phys Rev A 45:4173 CrossRefGoogle Scholar
  13. 13.
    Kärger J (1993) Phys Rev E 47:1427 CrossRefGoogle Scholar
  14. 14.
    Kärger J (2008) Diffusion Measurements by NMR Techniques, in this volume Google Scholar
  15. 15.
    Allnatt AR, Lidiard AB (1993) Atomic Transport in Solids. University Press, Cambridge, p 572 CrossRefGoogle Scholar
  16. 16.
    Kärger J, Ruthven DM (1992) Diffusion in Zeolites and Other Microporous Solids. Wiley & Sons, New York Google Scholar
  17. 17.
    Brandani S (1996) J Catal 160:326 CrossRefGoogle Scholar
  18. 18.
    Kärger J, Hahn K (1996) J Catal 160:328 CrossRefGoogle Scholar
  19. 19.
    Roque-Malherbe RM (2002) Microporous Mesoporous Mater 56:322 Google Scholar
  20. 20.
    Roque-Malherbe R, Ivanov V (2001) Microporous Mesoporous Mater 47:25 CrossRefGoogle Scholar
  21. 21.
    Kärger J (2002) Microporous Mesoporous Mater 56:321 CrossRefGoogle Scholar
  22. 22.
    Hahn K, Kärger J (1996) J Phys Chem 100:316 CrossRefGoogle Scholar
  23. 23.
    Leherte L, Vercauteren DP, Derouane EG, Lie GC, Clementi E, André JM (1989) In: Jacobs PA, van Santen RA (eds) Proc 8th Int Zeolite Conf, Amsterdam, The Netherlands, July 10–14, 1989. Elsevier, Amsterdam, 1989, p 773 Google Scholar
  24. 24.
    Leherte L, Vercauteren DP, Derouane EG, Lie GC, Clementi E, André JM (1989) Stud Surf Sci Catal 49:773 CrossRefGoogle Scholar
  25. 25.
    Nowak AK, Denouden CJJ, Pickett SD, Smit B, Cheetham AK, Post MFM, Thomas JM (1991) J Phys Chem 95:848 CrossRefGoogle Scholar
  26. 26.
    Haberlandt R, Fritzsche S, Peinel G, Heinzinger K (1995) Molekulardynamik – Grundlagen und Anwendungen. Vieweg, Braunschweig, p 252 Google Scholar
  27. 27.
    Keffer D, McCormick AV, Davis HT (1996) Molec Phys 87:367 Google Scholar
  28. 28.
    Bhide SY, Yashonath S (2002) J Phys Chem A 106:7130 CrossRefGoogle Scholar
  29. 29.
    Demontis P, Gonzalez JG, Suffritti GB, Tilocca A (2001) J Am Chem Soc 123:5069 CrossRefGoogle Scholar
  30. 30.
    Demontis P, Suffritti GB, Bordiga S, Buzzoni R (1995) J Chem Soc, Faraday Trans 91:525 CrossRefGoogle Scholar
  31. 31.
    Fritzsche S, Haberlandt R, Pfeifer H, Heinzinger K (1993) Chem Phys 174:229 CrossRefGoogle Scholar
  32. 32.
    Fritzsche S, Haberlandt R, Hofmann G, Kärger J, Heinzinger K, Wolfsberg M (1997) Chem Phys Lett 265:253 CrossRefGoogle Scholar
  33. 33.
    Fan JF, Xia QY, Gong XD, Xiao HM (2001) Chinese J Chem 19:251 CrossRefGoogle Scholar
  34. 34.
    Haberlandt R, Fritzsche S, Vörtler HL (2001) In: Nalwa HS (eds) Handbook of Surfaces and Interfaces of Materials. Academic Press, New York, p 357 CrossRefGoogle Scholar
  35. 35.
    Hahn K, Kärger J (1998) J Phys Chem 102:5766 Google Scholar
  36. 36.
    MacElroy JMD, Suh SH (2001) Microporous Mesoporous Mater 48:195 CrossRefGoogle Scholar
  37. 37.
    Mon KK, Percus JK (2002) J Chem Phys 117:2289 CrossRefGoogle Scholar
  38. 38.
    Mao ZG, Sinnott SB (2000) J Phys Chem B 104:4618 CrossRefGoogle Scholar
  39. 39.
    Jakobtorweihen S, Verbeek MG, Lowe CP, Keil FJ, Smit B (2005) Phys Rev Lett 95:044501 CrossRefGoogle Scholar
  40. 40.
    Sholl DS, Fichthorn KA (1997) Phys Rev A 55:7753 Google Scholar
  41. 41.
    Sholl DS, Fichthorn KA (1997) Phys Rev Lett 79:3569 CrossRefGoogle Scholar
  42. 42.
    Sholl DS, Lee CK (2000) J Chem Phys 112:817 CrossRefGoogle Scholar
  43. 43.
    Pitale KK, Rajadhyaksha RA (1988) Curr Sci 57:172 Google Scholar
  44. 44.
    Palekar MG, Rajadhyaksha RA (1995) Chem Eng Sci 40:1085 Google Scholar
  45. 45.
    Kärger J, Pfeifer H, Heink W (1988) Adv Magn Res 12:2 Google Scholar
  46. 46.
    Nelson PH, Auerbach SM (1999) J Chem Phys 110:9235 CrossRefGoogle Scholar
  47. 47.
    Nelson PH, Auerbach SM (1999) Chem Eng J 74:43 CrossRefGoogle Scholar
  48. 48.
    Rödenbeck C, Kärger J (1999) J Chem Phys 110:3970 CrossRefGoogle Scholar
  49. 49.
    Jobic H (1994) In: Imelik B, Vedrine JC (eds) Catalyst Characterization: Physical Techniques for Solid Materials. Plenum Press, New York, p 347 Google Scholar
  50. 50.
    Jobic H, Theodorou DN (2007) Microporous Mesoporous Mater 21:50 Google Scholar
  51. 51.
    Kutner R (1981) Phys Lett 81A:239 Google Scholar
  52. 52.
    Kärger J, Keller W, Pfeifer H, Ernst S, Weitkamp J (1995) Microporous Mater 3:401 CrossRefGoogle Scholar
  53. 53.
    Kocirik M, Zikanova A (1972) Z Phys Chem Leipzig 250:250 Google Scholar
  54. 54.
    Barrer RM (1978) Zeolites and Clay Minerals as Sorbents and Molecular Sieves. Academic Press, London, p 497 Google Scholar
  55. 55.
    Rödenbeck C, Kärger J, Hahn K (1995) J Catal 157:656 CrossRefGoogle Scholar
  56. 56.
    Bräuer P, Fritzsche S, Kärger J, Schütz GM, Vasenkov S (2004) In: Haberlandt R, Michel D, Pöppl A, Stannarius R (eds) Molecules in Interaction with Surfaces and Interfaces. Springer, Berlin, p 511 Google Scholar
  57. 57.
    Vasenkov S, Kärger J (2002) Phys Rev E 66:052601 CrossRefGoogle Scholar
  58. 58.
    Wheeler A (1951) Adv Catal 3:249 CrossRefGoogle Scholar
  59. 59.
    Chen NY, Degnan TF, Smith CM (1994) Molecular Transport and Reaction in Zeolites. VCH, New York, p 309 Google Scholar
  60. 60.
    Bräuer P, Kärger J, Neugebauer N (2001) Europhys Lett 53:8 CrossRefGoogle Scholar
  61. 61.
    Neugebauer N, Bräuer P, Kärger J (2000) J Catal 194:1 CrossRefGoogle Scholar
  62. 62.
    Brzank A, Schutz GM, Brauer P, Kärger J (2004) Phys Rev E 69 Google Scholar
  63. 63.
    Brzank A, Schütz GM (2005) Appl Catal A: General 288:194 CrossRefGoogle Scholar
  64. 64.
    Derouane EG, Gabelica Z (1980) J Catal 65:486 CrossRefGoogle Scholar
  65. 65.
    Weitkamp J, Puppe L (1999) Catalysis and Zeolites. Springer, Berlin Heidelberg, p 564 Google Scholar
  66. 66.
    Snurr RQ, Kärger J (1997) J Phys Chem B 101:6469 CrossRefGoogle Scholar
  67. 67.
    Clark LA, Ye GT, Snurr RQ (2000) Phys Rev Lett 84:2893 CrossRefGoogle Scholar
  68. 68.
    Nedea SV, Jansen APJ, Lukkien JJ, Hilbers PAJ (2002) Phys Rev E 6506:6701 Google Scholar
  69. 69.
    Nedea SV, Jansen APJ, Lukkien JJ, Hilbers PAJ (2002) Phys Rev E 66:066705 CrossRefGoogle Scholar
  70. 70.
    Nedea SV, Jansen APJ, Lukkien JJ, Hilbers PAJ (2003) Phys Rev E 67:046707 CrossRefGoogle Scholar
  71. 71.
    Jansen APJ, Nedea SV, Lukkien JJ (2003) Phys Rev E 67:036104 CrossRefGoogle Scholar
  72. 72.
    Rödenbeck C, Kärger J, Hahn K (1997) Phys Rev 55:5697 Google Scholar
  73. 73.
    Rödenbeck C, Kärger J, Hahn K (1998) Phys Rev E 57:4382 CrossRefGoogle Scholar
  74. 74.
    Rödenbeck C (1997) PhD Thesis, University of Leipzig, Leipzig Google Scholar
  75. 75.
    Kukla V (1997) PhD Thesis, University of Leipzig, Leipzig Google Scholar
  76. 76.
    Rödenbeck C, Kärger J, Hahn K (1997) Collect Czechoslovak Chem Commun 62:995 CrossRefGoogle Scholar
  77. 77.
    Brandani S, Hufton J, Ruthven D (1995) Zeolites 15:624 CrossRefGoogle Scholar
  78. 78.
    Hufton JR, Brandani S, Ruthven DM (1994) In: Weitkamp J, Karge HG, Pfeifer H, Hölderich W (eds) Zeolites and Related Microporous Materials: State of the Art 1994, Proc 10th Int Zeolite Conf, Garmisch-Patenkirchen, Germany, July 17–22, 1994. Elsevier, Amsterdam, p 1323 Google Scholar
  79. 79.
    Hufton JR, Brandani S, Ruthven DM (1994) Stud Surf Sci Catal 84:1323 CrossRefGoogle Scholar
  80. 80.
    Ruthven DM, Post MFM (2001) In: van Bekkum H, Flanigen EM, Jacobs PA, Jansen JC (eds) Introduction to Zeolite Science and Practice, 2nd edn. Elsevier, Amsterdam, p 525 Google Scholar
  81. 81.
    Ruthven DM, Post MFM (2001) Stud Surf Sci Catal 137:525 CrossRefGoogle Scholar
  82. 82.
    Ruthven DM, Brandani S (2000) In: Kanellopoulos NK (ed) Recent Advances in Gas Separation by Microporous Ceramic Membranes. Elsevier, Amsterdam, p 187 CrossRefGoogle Scholar
  83. 83.
    Rödenbeck C, Kärger J, Hahn K (1998) Ber Bunsen-Ges, Phys Chem Chem Phys 102:929 Google Scholar
  84. 84.
    Rödenbeck C, Kärger J, Schmidt H, Rother T, Rödenbeck M (1999) Phys Rev E 60:2737 CrossRefGoogle Scholar
  85. 85.
    Gupta V, Nivarthi SS, McCormick AV, Davis HT (1995) Chem Phys Lett 247:596 CrossRefGoogle Scholar
  86. 86.
    Kukla V, Hahn K, Kärger J, Kornatowksi JJ, Pfeifer H (1995) In: Rozwadowski M (ed) Proc 2nd Polish-German Zeolite Colloquium, Torun. Nicholas Copernicus Univ Press, Torun, p 110 Google Scholar
  87. 87.
    Kukla V, Kornatowski J, Demuth D, Gimus I, Pfeifer H, Rees LVC, Schunk S, Unger KK, Kärger J (1996) Science 272:702 CrossRefGoogle Scholar
  88. 88.
    Hahn K, Kärger J, Kukla V (1996) Phys Rev Lett 76:2762 CrossRefGoogle Scholar
  89. 89.
    Kärger J, Pfeifer H, Rudtsch S, Heink W, Gross U (1988) J Fluorine Chem 39:349 CrossRefGoogle Scholar
  90. 90.
    Fenzke D, Kärger J (1993) Z Phys D 25:345 CrossRefGoogle Scholar
  91. 91.
    Kölsch P, Venzke D, Noack M, Toussaint P, Caro J (1994) J Chem Soc Chem Commun, p 2491 Google Scholar
  92. 92.
    Kärger J, Vasenkov S (2003) In: Laeri F, Schüth F, Simon U, Wark M (eds) Host-Guest Systems Based on Nanoporous Crystals. Wiley-VCH, Weinheim, p 255 Google Scholar
  93. 93.
    Lehmann E, Chmelik C, Scheidt H, Vasenkov S, Staudte B, Kärger J, Kremer F, Zadrozna G, Kornatowski J (2002) J Am Chem Soc 124:8690 CrossRefGoogle Scholar
  94. 94.
    Lehmann E, Vasenkov S, Kärger J, Zadrozna G, Kornatowski J, Weiss Ö, Schüth F (2003) J Phys Chem B 107:4685 CrossRefGoogle Scholar
  95. 95.
    Karge HG, Kärger J (2008) Application of IR Spectroscopy, IR Microscopy and Optical Interference Microscopy on Diffusion Zeolites Google Scholar
  96. 96.
    Nivarthi SS, McCormick AV, Davis HT (1994) Chem Phys Lett 229:297 CrossRefGoogle Scholar
  97. 97.
    Jobic H, Bee M, Kearley GJ (1989) Zeolites 9:312 CrossRefGoogle Scholar
  98. 98.
    Jobic H (2000) In: Kanellopoulos NK (ed) Recent Advances in Gas Separation by Microporous Ceramic Membranes. Elsevier, Amsterdam, p 109 CrossRefGoogle Scholar
  99. 99.
    Jobic H, Kärger J, Bee M (1999) Phys Rev Lett 82:4260 CrossRefGoogle Scholar
  100. 100.
    Jobic H, Methivier A, Ehlers G, Farago B, Haeussler W (2004) Angew Chem Int Ed 43:364 CrossRefGoogle Scholar
  101. 101.
    Hahn K, Jobic H, Kärger J (1999) Phys Rev E 59:6662 CrossRefGoogle Scholar
  102. 102.
    Jobic H, Hahn K, Kärger J, Bée M, Noack M, Grinus I, Tuel A, Kearley GJ (1997) J Phys Chem 101:5834 Google Scholar
  103. 103.
    Schäfer H, Sternin E (1997) Phys Canada 77 Google Scholar
  104. 104.
    Song LJ, Rees LVC (2000) Microporous Mesoporous Mater 41:193 CrossRefGoogle Scholar
  105. 105.
    Onyestyak G, Valyon J, Rees LVC (2001) Solid State Ion 141:93 CrossRefGoogle Scholar
  106. 106.
    Kärger J (1997) In: Ertl G, Knözinger H, Weitkamp J (eds) Handbook of Heterogeneous Catalysis. Wiley-VCH, Weinheim, p 1252 Google Scholar
  107. 107.
    Karge HG, Niessen W (1991) Catal Today 8:451 CrossRefGoogle Scholar
  108. 108.
    Hermann M, Niessen W, Karge HG (1995) In: Beyer HK, Karge HG, Kiricsi I, Nagy JB (eds) Catalysis by Microporous Materials, Proc ZEOCAT '95, Szombathely, Hungary, July 9–13, 1995. Elsevier, Amsterdam, p 131 Google Scholar
  109. 109.
    Hermann M, Niessen W, Karge HG (1995) Stud Surf Sci Catal 94:131 CrossRefGoogle Scholar
  110. 110.
    Karge HG (1998) In: Rozwadowski M (eds) Proc Third Polish-German Zeolite Colloquium. Nicolas Copernicus Univ Press, Torun, p 11 Google Scholar
  111. 111.
    Karge HG, Niessen W, Bludau H (1996) Appl Catal A General 146:339 CrossRefGoogle Scholar
  112. 112.
    Niessen W, Karge HG (1993) Microporous Mater 1:1 CrossRefGoogle Scholar
  113. 113.
    Brandani S, Ruthven DM, Kärger J (1997) Microporous Mater 8:193 CrossRefGoogle Scholar
  114. 114.
    Karge HG, Ladebeck J, Sarbak Z, Hatada K (1982) Zeolites 2:94 CrossRefGoogle Scholar
  115. 115.
    Karge HG, Weitkamp J (1986) Chem Ing Tech 58:946 CrossRefGoogle Scholar
  116. 116.
    Weitkamp J, Ernst S (1994) Catal Today 19:107 CrossRefGoogle Scholar
  117. 117.
    Kapinski Z, Ghandi SN, Sachtler WMH (1993) J Catal 141:337 CrossRefGoogle Scholar
  118. 118.
    Rödenbeck C, Kärger J, Hahn K (1998) J Catal 176:513 CrossRefGoogle Scholar
  119. 119.
    Rödenbeck C, Kärger J, Hahn K, Sachtler W (1999) J Catal 183:409 CrossRefGoogle Scholar
  120. 120.
    Lei GD, Carvill BT, Sachtler WMH (1996) Appl Catal A General 142:347 CrossRefGoogle Scholar
  121. 121.
    Lei GD, Sachtler WMH (1993) J Catal 140:601 CrossRefGoogle Scholar
  122. 122.
    Vanbroekhoven EH, Schoonhoven J, Ponec V (1985) Surf Sci 156:899 CrossRefGoogle Scholar
  123. 123.
    de Gauw FJMM, van Grondelle J, van Santen RA (2001) J Catal 204:53 CrossRefGoogle Scholar
  124. 124.
    Liu H, Lei GD, Sachtler WMH (1996) Appl Catal A General 137:167 CrossRefGoogle Scholar
  125. 125.
    Carvill BT, Lerner BA, Adelman BJ, Tomczak DC, Sachtler WMH (1993) J Catal 144:1 CrossRefGoogle Scholar
  126. 126.
    Ribeiro F, Marcilly C, Guisnet M (1982) J Catal 78:275 CrossRefGoogle Scholar
  127. 127.
    Lutz C, Kollmann M, Leiderer P, Bechinger C (2004) J Phys Condens Matter 16:S4075 CrossRefGoogle Scholar
  128. 128.
    Wei QH, Bechinger C, Leiderer P (2000) Science 287:625 CrossRefGoogle Scholar
  129. 129.
    Lutz C, Kollmann M, Bechinger C (2004) Phys Rev Lett 93:026001 CrossRefGoogle Scholar
  130. 130.
    Adhangale P, Keffer D (2003) Separation Sci Technol 38:977 CrossRefGoogle Scholar
  131. 131.
    Sheintuch M, Efremenko I (2004) Chem Eng Sci 59:4739 CrossRefGoogle Scholar
  132. 132.
    Czaplewski KF, Reitz TL, Kim YJ, Snurr RQ (2002) Microporous Mesoporous Mater 56:55 CrossRefGoogle Scholar
  133. 133.
    Sholl DS, Fichthorn KA (1997) J Chem Phys 107:4384 CrossRefGoogle Scholar
  134. 134.
    Sholl DS, Fichthorn KA (1998) J Chem Phys 109:5693 CrossRefGoogle Scholar
  135. 135.
    Hahn K, Kärger J (1997) J Chem Phys 109:5691 CrossRefGoogle Scholar
  136. 136.
    Caro J, Noack M, Kölsch P, Schäfer R (2000) Microporous Mesoporous Mater 38:3 CrossRefGoogle Scholar
  137. 137.
    Vasenkov S, Kärger J (2002) Phys Rev E 66:052601 CrossRefGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  1. 1.Fakultät für Physik und GeowissenschaftenUniversität LeipzigLeipzigGermany

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