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Publications on Fractals in Chemistry

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and indicate the publication(s) number(s).

  • 1983 - 1987
  • 1988 - 1992
  • 1993 - 1997
  • 1998 - 2001


    1983 - 1987

    18. D. Avnir, D. Farin and P. Pfeifer
    "New Developments in the Application of Fractal Theory to Surface Geometric Irregularity",
    Book of Extended Abstracts of the 3S'83 Symposium on Surface Science, Obertaun, Austria, January 1983; pp. 233-236.

    19. D. Avnir and P. Pfeifer
    "Fractal Dimension in Chemistry. An Intensive Characteristic of Surface Irregularity",
    Nouv. J. Chem., 7, 71-72 (1983).

    21. P. Pfeifer, D. Avnir and D. Farin
    "Ideally Irregular Surfaces of Dimension Greater Than Two in Theory and Practice",
    Surface Science, 126, 569-572 (1983).

    25. P. Pfeifer and D. Avnir
    "Chemistry in Noninteger Dimensions Between Two and Three. I. Fractal Theory of Heterogeneous Surfaces",
    J. Chem. Phys., 79, 3558-3565 (1983); Erratum , 80, 4573 (1984).

    26. D. Avnir, D. Farin and P. Pfeifer
    "Chemistry in Noninteger Dimensions Between Two and Three. II. Fractal Surfaces of Adsorbents",
    J. Chem. Phys., 79, 3566-3571 (1983).

    31. D. Avnir, D. Farin and P. Pfeifer
    "Molecular Fractal Surfaces",
    Nature, 308, 261-263 (1984).

    35. S. Peleg, J. Naor, R. Hartley and D. Avnir
    "Multiple Resolution Texture Analysis and Classification",
    IEEE Trans. Pattern Anal. Machine Intelligence PAMI-6, 518-523 (1984).

    36. P. Pfeifer, D. Avnir and D. Farin
    "Scaling Behaviour of Surface Irregularity in the Molecular Domain: From Adsorption Studies to Fractal Catalysis",
    J. Stat. Phys., 36, 699-716 (1984). Erratum, 39, 263 (1985).

    43. D. Avnir, D. Farin and P. Pfeifer
    "Fractal Dimensions of Surfaces. The Use of Adsorption Data for the Quantitative Evaluation of Geometric Irregularity",
    Particulate Sci. Technol. Int. J., 2, 27-35 (1984).

    45. D. Avnir, D. Farin and P. Pfeifer,
    "Surface Geometric Irregularity of Particulate Materials: The Fractal Approach",
    J. Coll. Interface Sci., 103, 112-123 (1985).

    46. D. Farin, S. Peleg, D. Yavin and D. Avnir
    "Applications and Limitations of Boundary-Line Fractal Analysis of Irregular Objects",
    Langmuir , 1, 399-407 (1985).

    49. D. Farin, A. Volpert and D. Avnir
    "Determination of Adsorption Conformation from Surface Resolution Analysis",
    J. Am. Chem. Soc., 107, 3368-3370 (1985). Erratum: 5319 (1985).

    55. D. Rojanski, D. Huppert, H. D. Bale, X. Dacai, P.W. Schmidt, D. Farin, A. Seri-Levy and D. Avnir
    " Integrated Fractal Analysis of Silica: Adsorption, Electronic Energy Transfer and Small Angle X-Ray Scattering",
    Phys. Rev. Lett.., 56, 2505-2508 (1986).

    56. M. Silverberg, D. Farin, A. Ben-Shaul and D. Avnir
    "Chemically Active Fractals. 1. The Dissolution of Fractal Objects",
    Ann. Isr. Phys. Soc., 8, 451-457, 549-550, 553-555 (1986).
    (Proc. F3 Conference on Fragmentation Form and Flow in Fractured Media, R. Englman and Z. Yaeger, Ed's, Israel, Jan. 1986).

    58. A.Y. Meyer, D. Farin and D. Avnir
    "Cross Sectional Areas of Alkanoic Acids. A Comparative Study Applying Fractal Theory of Adsorption and Considerations of Molecular Shape",
    J. Am. Chem. Soc., 108, 7897-7905 (1986).

    60. D. Avnir
    "Fractal Aspects of Surface Science - An Interim Report",
    in: Better Ceramics Through Chemistry, C.J. Brinker, D.E. Clark and D.R. Ulrich, Ed's., Material Res. Soc. Symp. Proc., 73, 321-329 (1986).

    61. D. Avnir
    "Fractal analysis of silica surfaces and of their interactions with ground state and excited state adsorbates",
    Book of extended Abstracts of the EUCHEM conference on Silica from preparation to applications, Strasbourg, 1986, pp.1-4


    62. E. Wellner, D. Pines-Rojanski, M. Ottolenghi, D. Huppert, D. Farin and D. Avnir
    "Chemical Reactivity on Fractal Surfaces: Structure Sensitivity in Catalysis and Screening Effect in Reactive Dissolution",
    Proc. Mat. Res. Soc. Symp. on Fractal Aspects of Materials, D.W. Schaefer, R.B. Laibowitz, B.B. Mandelbrot and S. H. Liu, et. al., ed's., Boston, December 1986, pp. 118-120 (Extended Abstract of invited lecture).

    68. D. Avnir
    "The Geometry Factor in Photoprocesses on Irregular (Fractal) Surfaces. Part 1: Static Considerations",
    J. Am. Chem. Soc. 109, 2931-2938 (1987).

    71. D. Farin and D. Avnir
    "Accessibility of Irregular (Fractal) Surfaces to Silylation Reactions",
    J. Chromatog., 406, 317-324 (1987) (Special Vol. honoring E. Kovats).

    72. D. Farin and D. Avnir
    "The Fractal Nature of Molecule-Surface Chemical Activities and Physical Interactions in Porous Materials", in:- Studies in Surface Science and Catalysis Vol.39: Characterization of Porous Solids, K.K. Unger, J. Rouquerol, K.S.W. Sing and H. Kral, Ed's, Elsevier, Amsterdam, 1988; pp. 421-432.

    73. D. Pines-Rojanski, D. Huppert and D. Avnir
    "Pore Size Effects on the Fractal Distribution of Adsorbed Acceptor Molecules As Revealed by Electronic Energy Transfer on Silica Surfaces",
    Chem. Phys. Lett., 139, 109-115 (1987).

    74. D. Farin and D. Avnir
    "Reactive Fractal Surfaces",
    J. Phys. Chem., 91, 5517-5521 (1987).

    75. D. Farin and D. Avnir
    "The Reaction Dimension in Catalysis on Dispersed Metals",
    J. Am. Chem. Soc., 110, 2039-2045 (1988).

    1988 - 1992

    77. A. Hohr, H.-B. Neuman, M. Steiner, P.W. Schmidt and D. Avnir
    "Fractal Surface and Cluster Structure of Controlled-Pore Glasses and Vycor Porous Glass as Revealed by Small Angle X-Ray Scattering and Neutron Scattering",
    Phys. Rev B, 38, 1462-1467 (1988).

    79. D. Farin and D. Avnir
    "Structure Sensitivity Scaling Laws in Heterogeneous Catalysis on Dispersed Metals. 2. Fractal and Non-Fractal Interpretations of the Reaction Dimension", in:- Proc. 9th Intern. Congr. Catal., M.J. Phillips and M. Ternan, Ed's, Vol. 3, "Characterization and Metal Catalysts", Chem. Inst. Ottawa, 1988; pp. 998-1005.

    80. D. Pines, D. Huppert and D. Avnir
    "The Fractal Nature of the Surfaces of Porous Silicas as Revealed in Electronic Energy Transfer between Adsorbates. Comparison of Three Donor/Acceptor Pairs",
    J. Chem. Phys., 89, 1177-1180 (1988).

    82. D. Farin and D. Avnir
    "The Effects of the Fractal Geometry of Surfaces on the Adsorption Conformation of Polymers at Monolayer Coverage. I. The Case of Polystyrene",
    Coll. Surf., 32, 155-170 (1989). (Special issue on "Recent Advances of Adsorption", S. Kondo, Ed.)

    83. D. Farin and D. Avnir
    "The Fractal Nature of Molecule-Surface Interactions and Reactions",
    in:- The Fractal Approach to Heterogeneous Chemistry, D. Avnir, Ed., Wiley, Chichester, 1989; Chap. 4.1.2., pp 271- 293

    83a. David Avnir
    Preface,
    In The Fractal Approach to Heterogeneous Chemistry: Surfaces, Colloids, Polymers
    Wiley, Chichester, 1989, pp. xv xvii

    84. D. Farin, J. Kiwi and D. Avnir
    "Size Effects in Photoprocesses on Dispersed Metals",
    J. Phys. Chem., 93, 5851-5854 (1989).

    88. Proc. 2nd Int. Conf. Unconventional Photoactive Solids, Cleveland, 1985, H. Scher, Ed., Plenum Press, N.Y., 1988:

    1. D. Rojanski-Pines, D. Huppert, H.B. Bale, X. Dacai, P.W. Schmidt, D. Farin, A. Seri-Levy and D. Avnir
      "An Integrated Fractal Analysis of Silica: Electronic Energy Transfer, Small Angle X-Ray Scattering and Adsorption", pp. 171- 178.

    2. Vered R. Kaufman and David Avnir
      "Structural Changes and Oscillations During the Sol/Gel Transition in Silica Gel Glass Probed by Pyrene Excimerization", pp. 179-183.

    3. David Levy and David Avnir
      "Isolation and Trapping of Organic Photoactive Molecules in Silica Glass Matrices at Room Temperature", pp. 193-196.


    89. P.W. Schmidt, A. Hohr, H.-B. Neuman, H. Kaiser, D. Avnir and J.S. Lin
    "Small Angle X-Ray Scattering Study of the Fractal Morphology of Porous Silicas",
    J. Chem. Phys., 90, 5016-5023 (1989).

    91. A. Seri-Levy, J. Samuel, D. Farin and D. Avnir
    "Photoprocesses on Fractal Surfaces",
    in:- Studies in Surface Science and Catalysis Vol. 47: Photochemistry on Solid Surfaces , M. Anpo and T. Matsuura, Ed's, Elsevier, Amsterdam, 1989; pp. 353- 374.

    93. D. Avnir, A. Seri-Levy, D. Farin and O. Citri,
    "A Fractal Approach to the Geometry Factor in Heterogeneous Catalysis: Surface Effects, Memory Effects and Size Effects",
    Proceedings of the 23rd Biannual Conference of the Royal Spanish Society of Chemistry, A. San-Feliciano, M. Grande and J. Casado, Ed.s, Salamanca, Spain (23-28, Sept. 1990), 309-319 (1991).
    94. D. Avnir, O. Citri, D. Farin, M. Ottolenghi, J. Samuel and A. Seri-Levy
    "Optimization of Heterogeneous-Catalyst Structures: Simulations and Experiments with Fractal and Non-Fractal Systems",
    in:- Optimal Structures in Heterogeneous Reaction Systems, Peter J. Plath, Ed., Springer Ser. Synergetics, Vol. 44, pp. 65-81, 1989, Springer, Berlin.

    95. D. Avnir and D. Farin,
    "Fractal Scaling Laws in Heterogeneous Chemistry: Part I- Adsorptions, Chemisorptions and Interactions between Adsorbates",
    New J. Chem., 14, 197-206 (1990).

    97. D. Avnir and M. Jaroniec
    "An Isotherm Equation for Adsorption on Fractal Surfaces of Heterogeneous Porous Materials",
    Langmuir, 5, 1431-1433 (1989).

    99. D. Farin and D. Avnir,
    "Crystallite Size Effects in Chemisorption on Dispersed Metals",
    J. Catal., 120, 55-67 (1989).

    104. P.W. Schmidt, D. Avnir, D. Levy, A. Hohr, M. Steiner and A. Roll
    "Small Angle X-Ray Scattering From the Surfaces of Reversed Phase Silicas: Power-Law Scattering Exponents of Magnitudes Greater than Four",
    J. Chem. Phys., 94, 1474-1479 (1991).(For an Extended Abstract see 104a)

    104a. P.W. Schmidt, D. Levy, A. Hohr, M. Steiner and D. Avnir
    "Small Angle X-Ray Scattering From the Surfaces of Reversed Phase Silicas: Power-Law Scattering Exponents of Magnitudes Greater than Four",
    in: "Fractal Aspects of Materials", Materials Research Society Extended Abstracts, EA-20, (MRS Meeting, Boston, Nov. 1989), J.H. Kaufman, J.E. Martin and P.W. Schmidt, Ed's, MRS, Pittsburgh, 1989, pp. 159-162.

    105. Paul W. Schmidt, David Avnir, Armin Hohr and David M. Nelson
    "Small Angle X-Ray Scattering of Bone Porosity",
    in: "Fractal Aspects of Materials", Materials Research Society Extended Abstracts, EA-20, (MRS Meeting, Boston, Nov. 1989), J.H. Kaufman, J.E. Martin and P.W. Schmidt, Ed's, MRS, Pittsburgh, 1989, pp. 155-158.

    106. R. Gutfraind, M. Sheintuch and D. Avnir
    "Multifractal Scaling of Diffusion Limited Reactions on Devils Staircase and Cantor Set Catalytic Structures",
    Chem. Phys. Lett., 147, 8-12 (1990).

    107. M. Jaroniec, X. Lu, R. Madey and D. Avnir
    "Thermodynamics of Gas Adsorption on Fractal Surfaces of Heterogeneous Microporous Solids",
    J. Chem. Phys., 92, 7589-7595 (1990).

    108. Dina Farin and David Avnir
    "Surface Geometry Effects on the Activity of Porous Catalysts",
    Preprints of the IUPAC Symposium on Characterization of Porous Solids (COPS II), Alicante, Spain, May 1990, pp. 172-174.

    109. J. Samuel, D. Avnir and M. Ottolenghi
    "Diffusion Controlled Processes at Solid-Liquid Interfaces of Porous Glasses",
    Preprints of the IUPAC Symposium on Characterization of Porous Solids (COPS II), Alicante, Spain, May 1990, pp. 23-25.

    113. J. Samuel, M. Ottolenghi and D. Avnir
    "Diffusion Limited Reactions at Solid-Liquid Interfaces: Effects of Surface Geometry",
    J. Phys. Chem., 95 1890-1895 (1991).

    116. T. Elias-Kohav, M. Sheintuch and D. Avnir
    "Steady State Diffusion and Reactions in Catalytic Fractal Porous Media",
    Chem. Eng. Sci., 46, 2787-2798 (1991).

    117. D. Avnir and M. Ottolenghi
    "Photoprocesses in Environments of Complex Geometry: Fractal and Porous Materials",
    in: Photochemistry in Organized and Constrained Media. V. Ramamurthy, Ed., VCH, N.Y., 1991, pp. 535-562.

    118. D. Avnir, J.J. Carberry, O. Citri, D. Farin, M. Gratzel and A.J. McEvoy
    "Fractal Analysis of Size Effects and Surface Morphology Effects in Catalysis and Electrocatalysis"
    Chaos, 1, 397-410 (1991)

    119. D. Avnir, D. Farin and P. Pfeifer
    "A Discussion of Some Aspects of Surface Fractality and of Its Determination"
    New J. Chem., 16, 439-449 (1992).

    120. D. Farin and D. Avnir
    "Study of the Effects of Surface Morphology on Drug Dissolution Using Fractal Geometry Approach",
    J. Pharm. Sci., 81, 54-57 (1991).

    121. A. Seri-Levy and D. Avnir
    "Fractal Analysis of Surface Geometry Effects on Catalytic Reactions",
    Surf. Sci., 248, 258-170 (1991).

    125. Peter Pfeifer, David Avnir and Dina Farin
    "Complex Surface Geometry in Nano-Structure Solids: Fractal Versus Bernal-Type Models",
    in: Large Scale Molecular Systems - Quantum and Stochastic Aspects, W. Gans, A. Blumen and A. Amann, Eds., NATO ASI Ser. B, Plenum, New-York, 1991, pp 215-229.

    127. R. Gutfraind, M. Sheintuch and D. Avnir
    "Fractal and Multifractal Analysis of the Sensitivity of Catalytic Reactions to Catalyst Structure",
    J. Chem. Phys., 95 , 6100-6111 (1991).

    129. D. Avnir "Fractal Geometry - A New Approach to Heterogeneous Catalysis".
    Chem. Indust.. 912-916 , 16 Dec, (issue 24),1991.

    130. D. Farin and D. Avnir
    "Surface Fractality of Dendrimers"
    Angew. Chem., 103, 1409-1410, (1991).
    Angew Chem. Int. Ed. Eng., 30, 1379-1380, (1991).

    139. A. Seri-Levy and D. Avnir
    "Surface Geometry Effects on Adsorption-Desorption Hysteresis, Latent Adsorption and Adsorption Probability Plots"
    Stud. Surf. Sci. Catal., 80, 365-372 (1993) (Fundamentals of Adsorption, IV, M. Suzuki, ed., Kodansha, Japan, 1993).

    140. J. Samuel, M. Ottolenghi and D. Avnir
    "Diffusion Controlled Reactions on Porous Silicas: Mechanisms, Surface Diffusion Coefficients and Effects of Geometry"
    J. Phys. Chem., 96, 6398-6405, (1992).

    144. A. Seri-Levy and D. Avnir
    "The Brunauer-Emmett-Teller equation and the effects of lateral interactions. A simulation study"
    Langmuir, 9, 2523-2529 (1993).

    148. J. Samuel, M. Ottolenghi and D. Avnir
    "Reactions at the Gas Phase - Porous Solid Interface: Mechanisms and Effects of Surface Geometry around Room Temperature"
    Physica A, 191, 153-167, (1992).

    * D. Avnir (Editor)
    "The Fractal Approach to Heterogeneous Chemistry: Surfaces, Colloids, Polymers", Wiley, Chichester, 3rd corrected printing, 1992.

    1993 - 1997

    150. A. Seri-Levy and David Avnir
    "Kinetics of Diffusion Limited Adsorption on Fractal Surfaces"
    J. Phys. Chem., 97, 10380-10384 (1993).

    152. D. Avnir, R. Gutfraind and D. Farin
    "Fractal Analysis of Selected Problems in Heterogeneous Chemistry"
    in: "Fractal and Disordered Systems" Vol. 2, A. Bunde and S. Havlin, eds., Springer, Berlin, 1994, Chap. 8, pp. 229-255.

    153. A. Seri-Levy and D. Avnir
    "Effects of Heterogeneous Surface Geometry on Adsorption"
    Langmuir, 9, 3067-3076 (1993) (+ Front cover).

    168. D. Avnir and M.L. Kagan
    "The Evolution of Chemical Patterns in Reactive Liquids, Driven by Hydrodynamic Instabilities".
    Chaos, 5, 589-601, (1995).

    169. J. Rouquerol, D. Avnir, C. W. Fairbridge, D. H. Everett, J.H. Haynes, N. Pernicone, J. D. Ramsay, K.S.W. Sing and K.K. Unger
    IUPAC "Recommendations for the Characterization of Porous Solids"
    Pure & Appl. Chem, 66, 1739-1758 (1994).

    171. D. Avnir
    "Applications of Fractal Geometry Methods in Heterogeneous Catalysis"
    in "Handbook of Heterogeneous Catalysis" , G. Ertl, H. Knozinger and J. Weitkamp, ed.s, Wiley-VCH, Weinheim, volume 2, chapter 3.1.6., pp. 598 - 614, 1997.

    172. P. W. Schmidt, D. Avnir, H.-B. Neumann, A. Hohr, M. Steiner, J. Lin, D. Levy, V. R. Kaufman, Y. M. Kapoor and J. S. Lin
    Small-Angle X-Ray Scattering Study of Two-Length-Scale Structure in Some Silica Xerogels, Unpublished manuscript, 1995.

    174. D. Lidar (Hamburger), O. Malcai, O. Biham and D. Avnir
    " Randomness and Apparent Fractality"
    in "Fractals and Chaos in Chemical Engineering", M. Giona and G. Biardi, Editors, World Scientific, Singapore, 1997, pp. 103 - 114.

    177. O. Katzenelson, H. Zabrodsky Hel-Or and D. Avnir
    " Chirality of Large Supramolecular Structures"
    Chemistry - A European J. (Angew. Chem. Int Ed. Eng.), 2, 147 - 181 (1996)

    178. O. Katz, J. Samuel, D. Avnir and M. Ottolenghi
    " Diffusion Controlled Reactions of Molecular Oxygen on Porous Silica Glass: Coverage Dependence of Reaction and Diffusion Rates and Evidence of Surface Heterogeneity"
    J. Phys. Chem., 99, 14893 - 14902 (1995).

    182. D. Hamburger, O. Biham and D. Avnir
    " Apparent Fractality Emerging from Models of Random Distributions"
    Phys. Rev. E, 53, 3342 - 3357 (1996)

    185. D. Avnir, O. Katzenelson, S. Keinan, M. Pinsky, Y. Pinto, Y. Salomon and H. Zabrodsky Hel-Or
    "The Measurement of Symmetry and Chirality"
    in " Concepts in Chemistry", D. H. Rouvray , Ed., Research Studies Press, Somerset, 1996, Chapter 9, pp 283 - 324.

    186. D. Avnir, O. Katzenelson and H. Zabrodsky Hel-Or
    "Further Comments on the Chirality of Large Random Objects" Chem. European J. (Angew. Chem. Int. Ed. Eng.), 2, 744-746 (1996)

    188. Chem. European J. (Angew. Chem. Int. Ed. Eng.), 2, 744-746 (1996)
    C. Rottman, G. S. Grader, Y. De Hazan and D. Avnir
    "Sol-Gel Entrapment of ET(30) in Ormosils. Interfacial Polarity - Fractality Correlation"
    Langmuir, 12, 5505-5508 (1996) (+ cover picture)

    190. D. A. Lidar (Hamburger), O. Biham and D. Avnir
    "Limited Range Fractality of Randomly Distributed Rods"
    J. Chem. Phys., 106, 10359 - 10367 (1997)

    191. D. Avnir, O. Biham, D. Lidar (Hamburger) and O. Malcai
    " On the Abundance of Fractals"
    in " Fractal Frontiers", M. M. Novak and T. G. Dewey, Eds, World Scientific, 1997, pp. 199-234.

    195. O. Malcai, D. A. Lidar, O. Biham and D. Avnir
    "Scaling Range and Cutoffs in Empirical Fractals"
    Phys. Rev. E, 56, 2817 - 2828 (1997)

    1998 - 2001

    204. D. Avnir, O. Biham, D. Lidar and O. Malcai
    "Is the Geometry of Nature Fractal?"
    Science, 279 (5347), 39-40 (1998)

    204a. O. Biham, O. Malcai, D. Lidar and D. Avnir
    "Is Nature Fractal?" - response to M. Mandelbrot and P. Pfeifer
    Science, 279 , 785-786 (1998)

    204b. O. Biham, O. Malcai, D. Lidar and D. Avnir
    "Fractality in Nature" - response to A. A. Tsonis
    Science, 279 , 1615-1616, (1998)

    212. O. Biham, O. Malcai, D. Lidar (Hamburger) and D. Avnir
    "Pattern Formation and a Clustering Transition in Power-law Sequential Adsorption"
    Phys. Rev. E., 59, R4713 - R4716 (1999)

    217. D. Avnir "Fractals In Chemistry" by A. Harrison - book review.
    The Chemical Educator, 3(5) 1998.

    220. D. Avnir "Fractals In Chemistry" by Walter G. Rothschild - Book Review
    Angew. Chem. Int. Ed., 38, 2807 - 2808 (1999); Angew. Chem. , 111, 2981 (1999)

    223. O. Katzenelson and D. Avnir
    "Quantitative Chirality/Enantioselectivity Relations in Large Random Supramolecular Structures"
    Chem. Europ. J., 6, 1346 - 1354 (2000).

    248. D. Avnir "In Praise of Imperfection: Some thoughts on future trends in Surface Science"
    in "The History of Colloid and Surface Chemistry in Japan", K. Sakamoto, Chief Editor, 16 17, The Chem. Soc. of Japan, Tokyo, 2001


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