Fractals in Chemistry

Fractals in Chemistry is both a valuable working resource for professionals in physical chemistry, chemical physics, and computer modeling and an excellent graduate-level text for courses covering the use of fractals in chemistry.

WALTER G. ROTHSCHILD, PhD, worked for 33 years at the Scientific Research Laboratories of Ford Motor Company in Dearborn, Michigan, where he was engaged in basic and applied research, mainly in gaseous and condensed-phase spectroscopy of structure and dynamics, combustion phenomena, and automotive catalysis. He is a part-time member of the adjunct faculty, Department of Chemical Engineering and Materials Science, Wayne State University, Detroit, Michigan.

Preface

ix

1 Theoretical Outline

1

(11)

1.1 Introduction

1

(1)

1.2 An Example: Fractal Surface Model and Its Fractal Dimension

2

(8)

Notes and References

10

(2)

2 Fractal Surface Aspects of Adsorption and Permeability

12

(34)

2.1 Introduction and Generalities

12

(2)

2.2 Analysis of Fractal Surfaces and Pore Structures

14

(6)

2.3 Fractal Aspects of Physisorption Phenomena

20

(14)

2.3.1 Gas Adsorption by Microporous Solids

20

(4)

2.3.2 Gas Adsorption by Zeolites

24

(2)

2.3.3 Adsorbency of Porous Silica

26

(2)

2.3.4 Generation of Pore Structure: Dehydration of Gibbsite

28

(3)

2.3.5 Adsorptivity of Polymers on Porous Fractals

31

(2)

2.3.6 A Summary

33

(1)

2.4 Fractal Aspects of Chemisorption Phenomena

34

(7)

2.4.1 Fractal Scaling Laws for Chemisorption

35

(1)

2.4.2 Chemisorption of H(2) and CO on Metal Clusters

36

(2)

2.4.3 Metal Dispersion and Adsorbate Uptake: CO Chemisorption on Pt/Gamma-Al(2)O(3)

38

(2)

2.4.4 A Summary

40

(1)

Notes and References

41

(5)

3 Fractality in Aggregation and Growth

46

(30)

3.1 Fractal Aspects of Agglomerate Structures

46

(15)

3.1.1 Application of Gel Formation: Size-Exclusion Chromatography

47

(3)

3.1.2 Application of Diffusion-Limited Aggregation

50

(2)

3.1.2.1 Image Analysis of Silica Aggregation

52

(1)

3.1.2.2 Light Scattering Analysis of Soot Agglomerates and Processed Brown Coal

53

(2)

3.1.3 Mass, Surface, Pore Fractal?

55

(5)

3.1.4 A Summary

60

(1)

3.2 Fractal Aspects of Agglomeration Dynamics

61

(11)

3.2.1 Electrolytic Deposition

62

(1)

3.2.1.1 Silver Aggregation under Damped Electrolyte Convection

62

(3)

3.2.1.2 Formation of Dendrites: Palladium Hydride

65

(3)

3.2.2 Universal Behavior: Growth of Melanin, Colloidal Gold, and Humic Acid Aggregates

68

(3)

3.2.3 A Summary

71

(1)

Notes and References

72

(4)

4 Diffusion and Reactions

76

(25)

4.1 Introduction: The Fracton

76

(2)

4.2 Fractality in Dynamically Disordered Systems

78

(12)

4.2.1 Diffusion-Limited Reaction Systems A + A XXX Products

79

(1)

4.2.2 Diffusion-Limited Reaction Systems A + B XXX Products

80

(3)

4.2.3 Anomalous Diffusion in a Triblock Copolymer During Gelation

83

(2)

4.2.4 Diffusion-Controlled Reactant Density Fluctuation Kinetics: Hydrogen Exchange in Lysozyme-Water

85

(2)

4.2.5 Sintering of Open Sites on Dispersed Platinum

87

(2)

4.2.6 A Summary

89

(1)

4.3 The Reaction Dimension

90

(7)

4.3.1 Particle and Active Site Effects in Catalyzed Reaction Rates

90

(1)

4.3.1.1 Ethylene Epoxidation over Dispersed Silver

91

(1)

4.3.1.2 Oxidative Dehydrogenation of Propane

92

(1)

4.3.1.3 Nitrobenzene Hydrogenation over Platinum Dispersed on Carbon Cloth

93

(1)

4.3.1.4 Effect of Platinum Poisoning by Electrolytic Sulfur Deposition on Maleic Acid Hydrogenation

94

(1)

4.3.1.5 Influence of Pore Volume on Cracking Behavior of Zeolites

95

(1)

4.3.2 Particle Size Effects in Monomer-Polymer Interactions: Vinyl Chloride and Polyvinyl Chloride

96

(1)

4.3.3 A Summary

97

(1)

Notes and References

97

(4)

5 Spectroscopy of Fractal Systems

101

(15)

5.1 Introduction: General Procedures

101

(10)

5.1.1 Connected Structures in Water

102

(3)

5.1.2 Silica Aggregates: Structure and Dynamics

105

(1)

5.1.2.1 Cationic Surfactant-Induced Flocculation of Silica Spheres

105

(2)

5.1.2.2 Fractons in Silica Aerogels

107

(3)

5.1.3 Electron-Transfer Reaction of the Absorbed Anthracene Radical Cation

110

(1)

5.2 A Summary

111

(2)

Notes and References

113

(3)

6 Chemical Degradation

116

(15)

6.1 Introduction: Fractal Aspects in Material Deterioration Processes

116

(12)

6.1.1 Ablation: Ruggedness Changes in Food Particles

116

(3)

6.1.2 Surface Roughening by Dissolution

119

(4)

6.1.3 Fractality of Hydrated Cement Paste

123

(2)

6.1.4 Representing Shrinkage by Loss of Plasticizer: Julia Sets

125

(3)

6.2 A Summary

128

(1)

Notes and References

129

(2)

7 Special Fractal Topics in Chemistry

131

(39)

7.1 Fractal Dimensionality and Universal Properties within Systems

131

(8)

7.1.1 Fractal Dimensions of Coroenes

131

(2)

7.1.2 Graph Invariants and Chain Flexibility: n-Alkanes and Halogenated n-Alkanes

133

(6)

7.2 Fractal Aspects in Biochemical Systems

139

(5)

7.2.1 Protein Surfaces: Fractality and Receptor Sites

139

(3)

7.2.2 Aggregation and Self-Diffusion of Globin Hydrolysate

142

(2)

7.3 Fractal Dynamics in Liquid-Solid and Gas-Solid Flows

144

(3)

7.3.1 Horizontal Water Movement in Soils

144

(1)

7.3.2 Circulating Fluidized Bed Reactors

145

(2)

7.4 Hydrocarbon Sorption in Cross-Linked Polymer Systems

147

(8)

7.4.1 Hydrocarbon Sorption by Vulcanized Natural Rubber

148

(1)

7.4.1.1 Aliphatics n-C(6) to n-C(9)

148

(3)

7.4.1.2 Benzene and Higher Aromatics

151

(2)

7.4.2 Sorption Kinetics of Aromatics in Urethane-Modified Bismaleimide Elastomers

153

(2)

7.5 Wetting and Porosity: The Water-Paper Towel Experiment

155

(1)

7.6 Fractal Parameters of Premixed Turbulent Lean Flames

156

(6)

7.7 Bifractality: Wear between Processed Metal Surfaces

162

(2)

7.8 Photoablation of Polymer Surfaces

164

(1)

7.9 Surface Roughness and Surface Fractality

164

(1)

Notes and References

165

(5)

8 Fractality and Its Measurements

170

(10)

8.1 The Box Counting Method

170

(5)

8.1.1 Dimension of a Branching Molecule: Dendrimer DAB(CN)(64)

171

(4)

8.2 On Determinants Generating Fractality in Chemistry

175

(2)

8.3 Concluding Remarks

177

(1)

Notes and References

178

(2)

Appendix 1: Table of Frequently Used Dimensions

180

(1)

Appendix 2: List of Fundamental Equations

181

(3)

Appendix 3: List of Figures

184

(6)

Glossary 1: Fractals and Structure

190

(7)

Notes and References

197

(2)

Glossary 2: Fractals and Dynamics

199

(6)

Notes and References

205

(2)

Author Index

207

(7)

Subject Index

214

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Fractals in Chemistry

Summary

Author Biography

Table of Contents

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Fractals in Chemistry

Summary

Author Biography

Table of Contents

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