Preface ...................................................... xiii
Acknowledgments ............................................... xxi
1 Overview of AFM .............................................. 1
1.1 The Essence of the Technique ............................ 1
1.2 Property Sensitive Imaging: Vertical Touching and
Sliding Friction ........................................ 6
1.3 Modifying a Surface with a Tip ......................... 13
1.4 Dynamic (or "AC" or "Tapping") Modes: Delicate
Imaging with Property Sensitivity ...................... 16
1.5 Force Curves Plus Mapping in Liquid .................... 21
1.6 Rate, Temperature, and Humidity-Dependent
Characterization ....................................... 24
1.7 Long-Range Force Imaging Modes ......................... 28
1.8 Pedagogy of Chapters ................................... 30
References .................................................. 31
2 Distance-Dependent Interactions ............................. 33
2.1 General Analogies and Types of Forces .................. 33
2.2 Van der Waals and Electrostatic Forces in a
Tip-Sample System ...................................... 38
2.2.1 Dipole-Dipole Forces ............................ 38
2.2.2 Electrostatic Forces ............................ 41
2.3 Contact Forces and Mechanical Compliance ............... 44
2.4 Dynamic Probing of Distance-Dependent Forces ........... 51
2.4.1 Importance of Force Gradient .................... 51
2.4.2 Damped, Driven Oscillator: Concepts and
Mathematics ..................................... 56
2.4.3 Effect of Tip-Sample Interaction on Oscillator .. 60
2.4.4 Energy Dissipation in Tip-Sample Interaction .... 64
2.5 Other Distance-Dependent Attraction and Repulsion:
Electrostatic and Molecular Forces in Air and Liquids .. 67
2.5.1 Electrostatic Forces in Liquids: Superimposed
on Van der Waals Forces ......................... 67
2.5.2 Molecular-Structure Forces in Liquids ........... 69
2.5.3 Macromolecular Steric Forces in Liquids ......... 72
2.5.4 Derjaguin Approximation: Colloid Probe AFM ...... 76
2.5.5 Macromolecular Extension Forces (Air and
Liquid Media) ................................... 78
2.6 Rate/Time Effects ...................................... 83
2.6.1 Viscoelasticity ................................. 84
2.6.2 Stress-Modified Thermal Activation .............. 85
2.6.3 Relevance to Other Topics of Chapter 2 .......... 86
References .................................................. 88
3 Z-Dependent Force Measurements with AFM ..................... 91
3.1 Revisit Ideal Concept .................................. 91
3.2 Force-Z Measurement Components: Tip/Cantilever/Laser/
Photodetector/Z Scanner ................................ 93
3.2.1 Basic Concepts and Interrelationships ........... 93
3.2.2 Tip-Sample Distance ............................. 96
3.2.3 Finer Quantitative Issues in Force-Distance
Measurements .................................... 99
3.3 Physical Hysteresis ................................... 106
3.4 Optical Artifacts ..................................... 109
3.5 Z Scanner/Sensor Hardware: Nonidealities .............. 113
3.6 Additional Force-Curve Analysis Examples .............. 118
3.6.1 Glassy Polymer, Rigid Cantilever ............... 118
3.6.2 Gels, Soft Cantilever .......................... 123
3.6.3 Molecular-Chain Bridging Adhesion .............. 126
3.6.4 Bias-Dependent Electrostatic Forces in Air ..... 129
3.6.5 Screened Electrostatic Forces in Aqueous
Medium ......................................... 131
3.7 Cantilever Spring Constant Calibration ................ 133
References ................................................. 135
4 Topographic Imaging ........................................ 137
4.1 Idealized Concepts .................................... 138
4.2 The Real World ........................................ 143
4.2.1 The Basics: Block Descriptions of AFM
Hardware ....................................... 143
4.2.2 The Nature of the Collected Data ............... 149
4.2.3 Choosing Setpoinf. Effects on Tip-Sample
Interaction and Thereby on Images .............. 156
4.2.4 Finite Response of Feedback Control System ..... 162
4.2.5 Realities of Piezoscanners: Use of Closed-
Loop Scanning .................................. 167
4.2.6 Shape of Tip and Surface ....................... 180
4.2.7 Other Realities and Operational Difficulties—
Variable Background, Drift, Experimental
Geometry ....................................... 182
References ................................................. 186
5 Probing Material Properties I: Phase Imaging ............... 187
5.1 Phase Measurement as a Diagnostic of Interaction
Regime and Bistability ................................ 189
5.1.1 Phase (and Height, Amplitude) Imaging as
Diagnostics .................................... 189
5.1.2 Comments on Imaging in the Attractive Regime ... 200
5.2 Complications and Caveats Regarding the Phase
Measurement ........................................... 202
5.2.1 The Phase Offset ............................... 202
5.2.2 Drift in Resonance Frequency, Phase Offset,
Quality Factor, and Response Amplitude ......... 207
5.2.3 Change of Phase and Amplitude During Coarse
Approach ....................................... 211
5.2.4 Coupling of Topography and Phase ............... 214
5.2.5 The Phase Electronics and Its Calibration ...... 221
5.2.6 Nonideality in the Resonance Spectrum .......... 230
5.3 Energy Dissipation Interpretation of Phase:
Quantitative Analysis ................................. 234
5.3.1 Variable A/A0 Imaging .......................... 235
5.3.2 Fixed A/A0 Imaging ............................. 240
5.3.3 Variable A/A0 via Z-Dependent Point
Measurements ................................... 243
5.4 Virial Interpretation of Phase ........................ 247
5.5 Caveats and Data Analysis Strategies when
Quantitatively Interpreting Phase Data ................ 248
References ................................................. 255
6 Probing Material Properties II: Adhesive Nanomechanics
and Mapping Distance-Dependent Interactions ................ 258
6.1 General Concepts and Interrelationships ............... 259
6.2 Adhesive Contact Mechanics Models ..................... 261
6.2.1 Overview and Disclaimers ....................... 261
6.2.2 JKR and DMT Models ............................. 263
6.2.3 Ranging Between JKR and DMT: The Transition
Parameter λ .................................... 266
6.2.4 The Maugis-Dugdale Model ....................... 270
6.2.5 Other Formal Relationships Relevant to
Adhesive Contact Mechanics ..................... 273
6.2.6 Summary Comments and Caveats on Adhesive
Contact Mechanics Models ....................... 274
6.3 Capillarity, Details of Meniscus Force ................ 277
6.3.1 Framing the Issues ............................. 278
6.3.2 Basic Elements of Modeling the Meniscus ........ 280
6.3.3 Mathematics of Meniscus Geometry and Force ..... 283
6.3.4 Experimental Examples of Capillarity ........... 287
6.3.5 Capillary Transfer Phenomena: Difficulties
and Opportunities .............................. 293
6.4 Approach-Retract Curve Mapping ........................ 296
6.4.1 Motivation and Background ...................... 296
6.4.2 Traditional Force-Curve Mapping ................ 298
6.4.3 Approach-Retract Curve Mapping in Dynamic AFM .. 306
6.4.4 Approach-Retract Curve Mapping of Liquidy
Domains in Complex Thin Films .................. 313
6.5 High-Speed/Full Site Density Force-Curve Mapping and
Imaging ............................................... 315
6.5.1 Liquidy Domains in Complex Thin Films .......... 317
6.5.2 PBMA/PLMA Blend at Variable Ultimate Load ...... 319
6.5.3 PBMA/Dexamethasone Mixture at Variable
Temperature .................................... 320
6.5.4 Arborescent Styrene-Isobutylene-Styrene Block
Copolymer Plus Drug Rapamycin .................. 322
6.5.5 Comments on "Force Modulation" Mode ............ 323
References ................................................. 324
7 Probing Material Properties III: Lateral Force Methods ..... 330
7.1 Components of Lateral Force Signal .................... 330
7.2 Application of Lateral Force Difference ............... 336
7.3 Calibration of Lateral Force .......................... 343
7.4 Load-Dependent Friction ............................... 346
7.4.1 Motivations .................................... 346
7.4.2 Load Stepping and Ramping Methods .............. 347
7.5 Variable Rate and Environmental Parameters in AFM
Friction and Wear ..................................... 352
7.5.1 Motivations .................................... 352
7.5.2 Interplay of Rate, Temperature, Humidity, and
Tip Chemistry in Friction ...................... 354
7.5.3 Wear Under Variable Rate and Temperature ....... 359
7.5.4 Musings on the Spectroscopic Nature of
Friction and Other Measurements ................ 362
7.6 Transverse Shear Microscopy (TSM) and Anisotropy of
Shear Modulus ......................................... 364
7.7 Shear Modulation Methods .............................. 366
7.7.1 Motivations and Terminology .................... 366
7.7.2 Shear Modulation During ID Lateral Scanning .... 368
7.7.3 Diagnostics of Sliding Under Shear Modulation .. 371
7.7.4 Complementarity of Shear Modulation Methods
to TSM ......................................... 372
7.7.5 Shear Modulation Within Force Curves:
Material Creep ................................. 373
References ................................................. 375
8 Data Post-Processing and Statistical Analysis .............. 379
8.1 PrelirnTnary Data Processing .......................... 379
8.2 ID Roughness Metrics .................................. 383
8.3 2D-Domain Analysis .................................... 385
8.3.1 Slope and Surface Area Analysis ................ 385
8.3.2 2D-Domain Fourier Methods for Spatial
Analysis ....................................... 386
8.3.3 Fourier Methods for Time-Domain Analysis ....... 391
8.3.4 Grain or Particle Size Analysis ................ 394
8.4 "Lineshape" Fitting ................................... 396
References ................................................. 398
9 Advanced Dynamic Force Methods ............................. 400
9.1 Principles of Electronic Methods Utilizing Dynamic
AFM ................................................... 401
9.1.1 Shifted Dynamic Response due to Force
Gradient ....................................... 402
9.1.2 Interleave Methods for Long-Range Force
Probing ........................................ 405
9.1.3 Interleave-Based EFM/KFM on Different Metals
and Silicon .................................... 408
9.1.4 KFM of Organic Semiconductor, Including
Cross-Technique Comparisons .................... 412
9.2 Methods Using Higher Vibrational Modes ................ 414
9.2.1 Mathematics of Beam Mechanics: The Music of
AFM ............................................ 414
9.2.2 Probing Tip-Sample Interactions via
Multifrequency Dynamic AFM ..................... 419
9.2.3 Contact Resonance Methods ...................... 425
9.2.4 Single-Pass Electric Methods ................... 429
References ................................................. 433
Index ......................................................... 451
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