2.5 THE GIBBS ENERGY STATE FUNCTION
44
2.5.1 The direction of spontaneous
change
44
2.5.2 The Gibbs energy and surface
tension
47
2.5.3 Multicomponent systems
and chemical potential
49
2.6 PHYSICAL AND CHEMICAL EQUILIBRIA
50
2.6.1 The equilibrium constant
50
2.6.2 Heterogeneous equilibria
51
2.6.3 The relationship between Gibbs
energy and the equilibrium
constant
52
2.6.4 Temperature dependence of
the equilibrium constant
54
2.6.5 Phase equilibria in bulk materials 55
2.6.6 Phase equilibria in nanoparticles 57
END OF CHAPTER QUESTIONS
60
CITED REFERENCES
61
REFERENCES AND RECOMMENDED READING 61
Chapter 3
Kinetics and Transport
in Nanoscience
63
3.1 RATES OF CHEMICAL REACTIONS
63
3.1.1 The rate of reaction
63
3.1.2 Rate laws and reaction orders
65
3.1.3 A note on reversible reactions
70
3.1.4 Integrated rate laws
71
3.2 THEORETICAL MODELS FOR REACTION
RATES
74
3.2.1 Temperature dependence
of the rate constant
74
3.2.2 Collision theory
75
3.2.3 Catalysis
77
3.3 MODELING SIMPLE MECHANISMS
79
3.4 BIMOLECULAR BINDING KINETICS
81
3.4.1 Kinetics of reversible binding
81
3.4.2 The Scatchard and Hill equations:
Cooperativity of binding
84
3.5 SOLUTION KINETICS AND DIFFUSION
CONTROL
86
3.5.1 Some basic physics of diffusion
of nanomaterials in solution
87
3.5.2 Kinetics of diffusion control
89
END OF CHAPTER QUESTIONS
92
REFERENCES AND RECOMMENDED READING 94
Chapter 4
Quantum Effects at the Nanoscale
95
4.1 QUANTUM CONFINEMENT
IN NANOMATERIALS
96
4.2 BASIC INTRODUCTION TO QUANTUM
MECHANICS
97
4.2.1 Electromagnetic radiation
97
4.2.2 Matter waves and the
uncertainty principle
98
4.2.3 Bound systems and quantization 99
4.2.4 The wavefunction
101
4.2.5 The Schrödinger equation
102
4.3 CONFINEMENT OF ELECTRONS IN BOXES 104
4.3.1 The one-dimensional model
104
4.3.2 The two- and three-dimensional
models and the concept
of degeneracy
113
4.4 NANOSCALE CONFINEMENT ON RINGS
AND SPHERES
118
4.4.1 The particle on a ring model
119
4.4.2 The particle in a sphere model 121
4.5 QUANTIZATION OF VIBRATION
AND ROTATION
122
4.5.1 Quantization of vibrational
motion: The harmonic oscillator 122
4.5.2 Quantization of rotational
motion: The rigid rotator
125
x
Detailed Contents
44
2.5.1 The direction of spontaneous
change
44
2.5.2 The Gibbs energy and surface
tension
47
2.5.3 Multicomponent systems
and chemical potential
49
2.6 PHYSICAL AND CHEMICAL EQUILIBRIA
50
2.6.1 The equilibrium constant
50
2.6.2 Heterogeneous equilibria
51
2.6.3 The relationship between Gibbs
energy and the equilibrium
constant
52
2.6.4 Temperature dependence of
the equilibrium constant
54
2.6.5 Phase equilibria in bulk materials 55
2.6.6 Phase equilibria in nanoparticles 57
END OF CHAPTER QUESTIONS
60
CITED REFERENCES
61
REFERENCES AND RECOMMENDED READING 61
Chapter 3
Kinetics and Transport
in Nanoscience
63
3.1 RATES OF CHEMICAL REACTIONS
63
3.1.1 The rate of reaction
63
3.1.2 Rate laws and reaction orders
65
3.1.3 A note on reversible reactions
70
3.1.4 Integrated rate laws
71
3.2 THEORETICAL MODELS FOR REACTION
RATES
74
3.2.1 Temperature dependence
of the rate constant
74
3.2.2 Collision theory
75
3.2.3 Catalysis
77
3.3 MODELING SIMPLE MECHANISMS
79
3.4 BIMOLECULAR BINDING KINETICS
81
3.4.1 Kinetics of reversible binding
81
3.4.2 The Scatchard and Hill equations:
Cooperativity of binding
84
3.5 SOLUTION KINETICS AND DIFFUSION
CONTROL
86
3.5.1 Some basic physics of diffusion
of nanomaterials in solution
87
3.5.2 Kinetics of diffusion control
89
END OF CHAPTER QUESTIONS
92
REFERENCES AND RECOMMENDED READING 94
Chapter 4
Quantum Effects at the Nanoscale
95
4.1 QUANTUM CONFINEMENT
IN NANOMATERIALS
96
4.2 BASIC INTRODUCTION TO QUANTUM
MECHANICS
97
4.2.1 Electromagnetic radiation
97
4.2.2 Matter waves and the
uncertainty principle
98
4.2.3 Bound systems and quantization 99
4.2.4 The wavefunction
101
4.2.5 The Schrödinger equation
102
4.3 CONFINEMENT OF ELECTRONS IN BOXES 104
4.3.1 The one-dimensional model
104
4.3.2 The two- and three-dimensional
models and the concept
of degeneracy
113
4.4 NANOSCALE CONFINEMENT ON RINGS
AND SPHERES
118
4.4.1 The particle on a ring model
119
4.4.2 The particle in a sphere model 121
4.5 QUANTIZATION OF VIBRATION
AND ROTATION
122
4.5.1 Quantization of vibrational
motion: The harmonic oscillator 122
4.5.2 Quantization of rotational
motion: The rigid rotator
125
x
Detailed Contents