Mechanical Behaviour of Metal-Organic Framework Materials

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Half Title
Inorganic Materials Series No. 12
Mechanical Behaviour of Metal–Organic Framework Materials
Copyright
Preface
Contents
1. Fundamentals of MOF Mechanics & Structure–Mechanical Property Relationships
	1.1 An Overview of Metal–Organic Framework Materials
	1.2 MOF Mechanics
	1.3 Central Concepts in the Study of Mechanical Properties of Solids
	1.4 Nanoindentation of MOF Materials
		1.4.1 General Principles of Nanoindentation
		1.4.2 Nanoindentation of ZIFs
		1.4.3 Nanoindentation of Perovskite MOFs
		1.4.4 Young’s Modulus vs. Hardness (E–H) Materials Property Chart
	1.5 Elastic Anisotropy of MOF Single Crystals
		1.5.1 ZIF-8: Experimental and Theoretical Determination of Elastic Constants
		1.5.2 ZIF-8: Impact of Structural Defects on Elasticity
		1.5.3 HKUST-1: Elastic Anisotropy From Density Functional Theory (DFT)
	1.6 Mechanical Properties of Monoliths, Glasses, Nanocrystals and Thin Films
		1.6.1 MOF Monoliths: HKUST-1
		1.6.2 Amorphous Phases: ZIFs
		1.6.3 Nanocrystals: ZIF-8
		1.6.4 Thin Films: HKUST-1
	1.7 Framework Lattice Dynamics Dictating MOF Mechanics
		1.7.1 Terahertz Modes
		1.7.2 THz Dynamics of ZIFs
		1.7.3 THz Dynamics of HKUST-1
		1.7.4 THz Dynamics of DUT and MIL Structures
	1.8 Beyond Elasticity: Inelastic Mechanical Behaviour and Structural Failure
		1.8.1 Hardness, Yield Strength, and Plasticity
		1.8.2 Nanosheets of 2-D MOFs: Pop-ins and Shear-induced Failures
		1.8.3 Interfacial Strengths of MOF Polycrystalline Films and Coatings
		1.8.4 Fracture Toughness, Bond Breakage and Cracking
	1.9 Time-dependent Mechanical Behaviour
	1.10 Summary and Outlook
	List of Abbreviations
	References
2. Anomalous Mechanical Behaviour Arising From Framework Flexibility
	2.1 Introduction
	2.2 Anisotropic Elasticity
		2.2.1 Elasticity Theory
			2.2.1.1 Tensor Transformations and Euler Angles
			2.2.1.2 Averaging Schemes
			2.2.1.3 One-direction Properties: Young’s Modulus and Linear Compressibility
			2.2.1.4 Two-direction Properties: Shear Modulus and Poisson’s Ratio
		2.2.2 Complete Elastic Tensors of MOFs
		2.2.3 Anisotropy Measures
		2.2.4 Thermo-elasticity
	2.3 Anomalous Mechanical Behaviour
		2.3.1 Negative Linear Compressibility (NLC)
			2.3.1.1 Definitions, Properties and Mechanisms of NLC
			2.3.1.2 NLC in MOFs
		2.3.2 Negative Thermal Expansion (NTE)
			2.3.2.1 Definitions, Properties and Mechanisms for NTE
			2.3.2.2 NTE in MOFs
		2.3.3 Negative Poisson’s Ratio (NPR)
			2.3.3.1 Definitions, Properties and Mechanisms for NPR
			2.3.3.2 NPR in MOFs
	2.4 Framework Flexibility of MOFs
		2.4.1 Which Kind of ‘Flexibility’ Is Relevant for MOFs Material Flexibility vs. Framework Flexibility
		2.4.2 Estimates for Material Flexibility
		2.4.3 Mathematical Methods for Framework Flexibility
			2.4.3.1 Group Theoretical Approaches
			2.4.3.2 Rigidity Theory
		2.4.4 Atomistic Methods for Framework Flexibility
			2.4.4.1 Rigid Unit Modes
			2.4.4.2 Template-based Geometric Simulation
			2.4.4.3 Molecular Truss Models
		2.4.5 Macro-mechanical Models
	2.5 Conclusions and Outlook
	Acknowledgements
	References
3. Computational Modelling of MOF Mechanics: From Elastic Behaviour to Phase Transformations
	3.1 Introduction
	3.2 From a Continuum to an Atomic Description of Stress and Strain
		3.2.1 The Atomic Definition of Deformation Gradient and Strain
		3.2.2 The Atomic Definition of Stress
	3.3 Ingredients Necessary to Atomically Model MOF Mechanics
		3.3.1 Generating an Accurate Structural Model of the Material
		3.3.2 Approximating the Interactions in a Material: the Level of Theory
		3.3.3 Exploring the Potential Energy Surface for a System under Stress Control
	3.4 The Equilibrium Mechanical Behaviour of MOFs: the Elastic Regime
		3.4.1 Extracting Elastic Constants Through Explicit Deformations
			3.4.1.1 General Methodology
			3.4.1.2 The IRMOF Family
			3.4.1.3 Zeolitic Imidazolate Frameworks (ZIFs) and Associated Materials
			3.4.1.4 The UiO-66 Series
			3.4.1.5 HKUST-1
			3.4.1.6 Wine-Rack Type MOFs: MIL-47 and MIL-53-type Materials
			3.4.1.7 Other Systematic Observations in MOF Mechanics
		3.4.2 Extracting Elastic Constants Through Fluctuation Formulae to Predict Temperature Effects
			3.4.2.1 General Methodology
			3.4.2.2 Application to MOFs
		3.4.3 Predicting Flexibility from Equilibrium Elastic Properties
		3.4.4 Determining the Stability Range of MOFs: Elasticity Under Pressure
			3.4.4.1 Determining Elastic Stability through the Born Stability Criteria
			3.4.4.2 Determining Dynamic Stability through the Vibrational Spectrum
	3.5 The Response of Flexible MOFs to Large Pressures: the Inelastic Regime
		3.5.1 Directly Modelling Phase Transformations in Flexible MOFs and Its Limitations
		3.5.2 Modelling Flexible MOFs at 0 K: Energy Equations of State
		3.5.3 Modelling Flexible MOFs at Finite Temperature: Free Energy Equations of State
			3.5.3.1 General Methodology
			3.5.3.2 Application to MOFs
	3.6 The Response of ‘Rigid’ MOFs to Large Pressures: the Inelastic Regime
		3.6.1 Nucleation and Propagation of Mechanical Instability in the IRMOF Series
		3.6.2 Failure Modes in ZIFs and their Melting Behaviour
		3.6.3 The Impact of Defects on the Amorphisation of the UiO-66 Series
		3.6.4 Other Computational Studies on the Plastic Deformation of MOFs
	3.7 Conclusions and Outlook
	Acknowledgements
	References
4. High-pressure Mechanical Behaviour Under Hydrostatic Compression
	4.1 Introduction
	4.2 High-pressure Experimental Techniques
		4.2.1 Hydrostatic Pressure Generation
			4.2.1.1 DACs
				4.2.1.1.1
Diamond Anvils.The operational pressure range of the DAC is principally determined by the size and geometry of the diamond anvil...
				4.2.1.1.2
Gasket Material.The generated pressure also depends upon the gasket material. The relationship between pressure and the gasket p...
				4.2.1.1.3
Pressure-transmitting Medium.The pressure-transmitting medium must be suitably inert and maintain hydrostatic conditions in the ...
				4.2.1.1.4
Pressure Determination.The pressure inside the sample chamber is measured using an internal standard with pressure-dependent pro...
			4.2.1.2 Capillary Pressure Cells
		4.2.2 High-pressure X-ray Diffraction
			4.2.2.1 Merrill–Bassett DAC
		4.2.3 High-pressure Neutron Diffraction
		4.2.4 High-pressure Spectroscopy
	4.3 Equations of State (EoS)
	4.4 Zeolitic Imidazolate Frameworks (ZIFs)
		4.4.1 ZIF-8
			4.4.1.1 Guest Adsorption and Gate Opening in ZIF-8
		4.4.2 Other ZIFs
	4.5 UiO Frameworks
	4.6 MIL Frameworks
		4.6.1 Breathing
		4.6.2 Negative Linear Compressibility (NLC)
	4.7 Sc2bdc3
		4.7.1 Guest Intrusion at High Pressure
	4.8 Pillared–Layered MOFs
		4.8.1 Guest-mediated Flexibility
	4.9 Zinc Alkyl Gate Frameworks
	4.10 DUT Frameworks
	4.11 Inflexible MOFs
	4.12 Natural Product MOFs
	4.13 Piezoresponsive Functional MOFs
	4.14 Pressure-stimulated Post-synthetic Modification
	4.15 Concluding Remarks
	References
5. Mechanical Energy Absorption of Metal–Organic Frameworks
	5.1 Introduction: Energy Absorption
		5.1.1 Concept of Mechanical Energy Absorption
		5.1.2 Energy Absorption Materials
	5.2 Nanofluidic Energy Absorption
		5.2.1 Concept of Nanofluidic Energy Absorption
		5.2.2 The Emergence of the Field
		5.2.3 Water Intrusion of Microporous Zeolites
		5.2.4 Water Intrusion of Mesoporous and Macroporous Silica
	5.3 Liquid Intrusion of MOFs
		5.3.1 Intrusion of Water
		5.3.2 Intrusion of Electrolyte Solutions
		5.3.3 Intrusion of Alcohol Solutions
		5.3.4 Effect of Crystal Size and Other Design Considerations
		5.3.5 Materials Stability Under Liquid Intrusion
		5.3.6 Thermal Effects of Liquid Intrusion
	5.4 Dynamic Liquid Intrusion
		5.4.1 High-rate Water Intrusion of ZIFs
		5.4.2 Dynamic Liquid Intrusion of Other Nanoporous Solids
	5.5 Structural Transition of Flexible MOFs for Energy Absorption
		5.5.1 MOF Structural Transition for Energy Absorption
		5.5.2 Materials Design for Structural Transition
		5.5.3 Thermal Effects of Structural Transition
	5.6 Plastic Deformation of MOFs for Energy Absorption
	5.7 Conclusions and Outlook
	References
Subject Index