Microrheology / Eric M. Furst, Todd M. Squires.

Format:

Book

Author/Creator:

Furst, Eric M.

Language:

English

Subjects (All):

Rheology.

Physical Description:

xx, 451 pages : illustrations ; 25 cm

Edition:

First edition.

Place of Publication:

Oxford, United Kingdom : Oxford University Press, [2017]

Summary:

This book presents a comprehensive overview of microrheology, emphasizing the underlying theory, practical aspects of its implementation, and current applications to rheological studies in academic and industrial laboratories. The field of microrheology continues to evolve rapidly, and applications are expanding at an accelerating pace. Readers will learn about the key methods and techniques, including important considerations to be made with respect to the materials most amenable to microrheological characterization and pitfalls to avoid in measurements and analysis. Microrheological measurements can be as straightforward as video microscopy recordings of colloidal particle Brownian motion; these simple experiments can yield rich rheological information. This text will cover topics ranging from active microrheology using laser or magnetic tweezers to passive microrheology, such as multiple particle tracking and tracer particle microrheology with diffusing wave spectroscopy. Overall, this text aims to provide an introduction to microrheology for the industrial researcher, academic investigator, or student who wishes either to become informed in this relatively new area of theology, seeks to incorporate these methods into their own research, or simply survey and understand the growing body of micorheology literature. The text consolidates many sources of archival literature into an accessible volume for the rheologist and non-specialist, alike. The material should be suitable for the biologist, chemist, or materials scientist with an interest in microrheology as a characterization method. Indeed, the small sample sizes of many microrheology experiments have made it an important method for studying emerging and scarce materials, like cytoskeletal proteins, pharmaceutical biologics, and novel hydrogelators. Book jacket.

Contents:

1 Introduction 1

1.1 Microrheology 1

1.1.1 Why microrheology? 4

1.2 Soft matter and rheology 6

1.2.1 Linear and nonlinear rheology 11

1.2.2 Linear response measurements 13

1.2.3 Nonlinear-rheology measurements 19

1.3 Colloidal particles 23

1.3.1 Colloidal probe chemistries 25

1.3.2 Probe size uniformity 30

1.3.3 Colloid stability 30

1.3.4 Probe sedimentation, washing, and concentration 38

Exercises 40

2 Particle motion 42

2.1 Introduction 42

2.2 The mechanics of deformable continua 43

2.2.1 The Cauchy Stress Equation: F = Ma for continuum materials 44

2.2.2 Linear-constitutive relations 46

2.2.3 Constitutive relations in the linear response limit 46

2.3 Equations of motion for isotropic continua 51

2.4 Correspondence Principle 53

2.5 Particle motion 56

2.5.1 Mobility and resistance 56

2.5.2 The Stokes resistance and mobility of a translating sphere 57

2.5.3 Stokes resistance of a probe undergoing oscillatory translations 61

2.5.4 Particle inertia 65

2.5.5 Spheres forced within compressible elastic media 66

2.6 Hydrodynamic interactions 67

2.6.1 Method of reflections 68

2.6.2 Hydrodynamic interactions between spheres in incompressible media 69

2.6.3 Hydrodynamic interactions in compressible media 72

2.6.4 Particle-wall hydrodynamic interactions: Confinement effects 73

2.6.5 Higher-order corrections: Faxen's law, and multiple reflections 75

2.7 Elastic networks in viscous liquids: The two-fluid model 77

2.8 Non-isotropic probes 79

Exercises 81

3 Passive microrheology 86

3.1 The Langevin equation 86

3.2 Brownian motion 90

3.2.1 Laplace Transform solutions 91

3.2.2 Fourier Transform solutions 92

3.2.3 Relating VAC to MSD 95

3.3 The Generalized Einstein Relation 98

3.3.1 Fourier Transform 98

3.3.2 Laplace Transform 101

3.4 The Stokes component 103

3.5 The Generalized Stokes-Einstein Relation (GSER) 105

3.6 Passive microrheology examples 107

3.6.1 Limiting behavior of the MSD 109

3.7 GSER for model materials 110

3.7.1 Elastic solid 110

3.7.2 Viscous fluid 112

3.7.3 Kelvin-Voigt model 112

3.7.4 Maxwell fluid 113

3.7.5 Power-law response 114

3.7.6 Rouse and Zimm models 115

3.7.7 Semiflexible polymers 117

3.8 Converting between the time and frequency domains 118

3.8.1 Power-law approximation 119

3.8.2 Constrained regularization 121

3.9 Strengths and limitations of passive microrheology 123

3.10 Validity of the GSER 124

3.10.1 Non-continuum effects 124

3.10.2 Microrheology without probes? 127

3.11 General limits of operation 129

3.11.1 Minimum compliance 129

Exercises 132

4 Multiple particle tracking 135

4.1 Video microscopy 136

4.1.1 Video camera 138

4.1.2 Image file types 139

4.1.3 Imaging basics 139

4.2 Image quality 141

4.2.1 Frame rate and exposure time 141

4.2.2 Detection noise 141

4.2.3 Image signal-to-noise ratio 143

4.2.4 Other image artifacts 146

4.3 Particle tracking samples 146

4.3.1 Sample dimensions 149

4.3.2 Probe concentration 149

4.4 Particle tracking 150

4.4.1 Image filtering 150

4.4.2 Locating the brightest pixels 152

4.4.3 Refining the initial location estimates 153

4.5 Linking trajectories 155

4.5.1 Van Hove correlation function 155

4.5.2 Random walks 157

4.5.3 Application to trajectories 159

4.6 Analysis of particle tracking 161

4.6.1 Mean-squared displacement 162

4.7 Non-Gaussian parameter 165

4.8 Tracking accuracy and error 166

4.8.1 Static error 167

4.8.2 Dynamic error 170

4.8.3 Tracking error and the MSD 170

4.8.4 Convective drift and vibration 172

4.9 Operating regimes of particle tracking 175

4.10 Heterogeneous materials 176

4.10.1 f-test method 178

4.10.2 Global measures of heterogeneity 181

4.11 Two-point microrheology 183

4.11.1 Two-point GSER 183

4.11.2 Data requirements of two-point microrheology 187

4.11.3 Two-point experiments 187

4.11.4 Shell model 189

Exercises 196

5 Light scattering microrheology 198

5.1 Time-correlation functions 199

5.2 Light scattering 202

5.3 Dynamic light scattering 205

5.3.1 Light intensity and the Siegert relation 207

5.3.2 Microrheology with DLS 209

5.3.3 Scattering from the material under test 211

5.3.4 Suppressing multiple scattering 212

5.4 Diffusing wave spectroscopy 213

5.4.1 Multiple scattering 213

5.4.2 Diffusive-light transport 216

5.4.3 Transmission geometry 217

5.4.4 Backscattering geometry 220

5.4.5 Comparison of transmission and backscattering 221

5.4.6 Photon mean-free path 223

5.4.7 Light absorption 225

5.4.8 Mean-squared displacement 226

5.4.9 Operating regime 229

5.5 Light scattering experiment 231

5.5.1 Light scattering samples 232

5.5.2 Laser 235

5.5.3 Detectors 237

5.5.4 Signal-to-noise and measurement error 238

5.5.5 Correlator 240

5.6 High-frequency rheology 243

5.6.1 High-frequency DWS examples 244

5.6.2 Inertia in microrheology 246

5.7 Gels and other nonergodic samples 249

5.7.1 Simple model of nonergodicity 251

5.7.2 Pusey and van Megen's method 252

5.7.3 Ensemble of measurements 252

5.7.4 Optical mixing 253

5.7.5 Multispeckle detection 256

5.7.6 Multispeckle imaging 258

5.8 Broadband microrheology 262

5.9 Other DWS applications 263

5.10 Summary 265

Exercises 266

6 Interferometric tracking 267

6.1 Back-focal-plane interferometry 267

6.1.1 Back-focal-plane experiment 267

6.1.2 Detector sensitivity and limits 269

6.1.3 Linear response 271

6.1.4 Studies using interferometry 273

6.2 Two-point interferometry 276

6.3 Rotational diffusion microrheology 276

Exercise 278

7 Active microrheology 279

7.1 Introduction and overview 279

7.2 Active, linear microrheology 280

7.2.1 Active microrheology of active (non-equilibrium) materials 282

7.3 Active and nonlinear microrheology 284

7.3.1 Measuring nonlinear rheology 285

7.3.2 Nonlinear microrheology; The issues 286

7.3.3 Nonlinear microrheology of continuum materials: Known sources of discrepancy 287

7.3.4 Direct probe-material interactions 295

7.3.5 Nonlinear microrheology: Experiments 298

7.4 Looking ahead 301

8 Magnetic bead microrheology 302

8.1 Magnetism 303

8.1.1 Fields generated by electrical currents 304

8.1.2 Magnetic materials 306

8.2 Magnetic tweezers 308

8.2.1 Magnetic probes 310

8.2.2 Probe interactions 316

8.3 Instrument designs 316

8.3.1 Electromagnet tweezers 316

8.3.2 Tweezers with permanent magnets 319

8.3.3 Force calibration 321

8.4 Linear experiments 324

8.4.1 Creep response 324

8.4.2 Oscillating magnetic tweezers 327

8.4.3 Operating diagram 329

8.5 Nonlinear measurements 331

8.5.1 Yield stress and jamming 331

8.5.2 Shear thinning 333

8.6 Nanorods in steady and rotating fields 335

8.7 Summary 336

Exercises 336

9 Laser tweezer microrheology 338

9.1 Radiation forces and Gaussian beams 339

9.2 A focused Gaussian beam in the diffraction limit 339

9.2.1 Radiant field 340

9.2.2 Irradiance and laser power 341

9.3 Optical trapping 341

9.3.1 Rayleigh regime 341

9.3.2 Ray optic regime 345

9.3.3 Laser tweezer microrheology samples 348

9.4 An optical-trapping instrument 348

9.4.1 Major components 350

9.5 Trapping force calibration 353

9.5.1 Drag in a viscous fluid 354

9.5.2 Oscillating trap in a viscous fluid 356

9.5.3 Thermal motion in a stationary trap 359

9.5.4 In situ calibration in a complex fluid 361

9.5.5 Trap stiffness and index of refraction 365

9.6 Active oscillatory microrheology 366

9.6.1 Fixed reference frame 366

9.6.2 Moving reference frame 368

9.6.3 Active oscillatory examples and limits 371

9.7 Steady drag microrheology 374

9.8 Two-point microrheology with tweezers 376

Exercises 378

10 Microrheology applications 380

10.1 Planning a microrheology experiment 381

10.1.1 Mechanical rheometry 381

10.2 High-throughput microrheology 385

10.3 Gelation 386

10.3.1 Critical gels 388

10.3.2 Time-cure superposition 390

10.3.3 Gelation critical scaling exponents 393

10.3.4 Logarithmic slope 394

10.3.5 Gelation screening 396

10.3.6 Gel degradation 396

10.4 Viscosity measurements 399

10.4.1 Measurement precision and accuracy 399

10.4.2 Measurement limits 402

10.5 Cell Theology 403

10.6 Interfacial microrheology 404

10.7 Perspectives on future work 406.

Notes:

Includes bibliographical references and index.

ISBN:

0199655200

9780199655205

OCLC:

990115841