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1 | (41) |
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1 | (5) |
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4 | (2) |
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1.2 Soft matter and rheology |
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6 | (17) |
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1.2.1 Linear and nonlinear rheology |
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11 | (2) |
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1.2.2 Linear response measurements |
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13 | (6) |
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1.2.3 Nonlinear-rheology measurements |
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19 | (4) |
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23 | (17) |
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1.3.1 Colloidal probe chemistries |
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25 | (5) |
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1.3.2 Probe size uniformity |
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30 | (1) |
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30 | (8) |
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1.3.4 Probe sedimentation, washing, and concentration |
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38 | (2) |
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40 | (2) |
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42 | (44) |
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42 | (1) |
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2.2 The mechanics of deformable continua |
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43 | (8) |
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2.2.1 The Cauchy Stress Equation: F = Ma. for continuum materials |
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44 | (2) |
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2.2.2 Linear-constitutive relations |
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46 | (1) |
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2.2.3 Constitutive relations in the linear response limit |
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46 | (5) |
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2.3 Equations of motion for isotropic continua |
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51 | (2) |
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2.4 Correspondence Principle |
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53 | (3) |
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56 | (11) |
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2.5.1 Mobility and resistance |
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56 | (1) |
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2.5.2 The Stokes resistance and mobility of a translating sphere |
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57 | (4) |
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2.5.3 Stokes resistance of a probe undergoing oscillatory translations |
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61 | (4) |
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65 | (1) |
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2.5.5 Spheres forced within compressible elastic media |
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66 | (1) |
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2.6 Hydrodynamic interactions |
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67 | (10) |
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2.6.1 Method of reflections |
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68 | (1) |
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2.6.2 Hydrodynamic interactions between spheres in incompressible media |
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69 | (3) |
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2.6.3 Hydrodynamic interactions in compressible media |
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72 | (1) |
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2.6.4 Particle-wall hydrodynamic interactions: Confinement effects |
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73 | (2) |
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2.6.5 Higher-order corrections: Faxen's law, and multiple reflections |
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75 | (2) |
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2.7 Elastic networks in viscous liquids: The two-fluid model |
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77 | (2) |
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79 | (2) |
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81 | (5) |
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86 | (49) |
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3.1 The Langevin equation |
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86 | (4) |
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90 | (8) |
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3.2.1 Laplace Transform solutions |
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91 | (1) |
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3.2.2 Fourier Transform solutions |
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92 | (3) |
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3.2.3 Relating VAC to MSD |
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95 | (3) |
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3.3 The Generalized Einstein Relation |
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98 | (5) |
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98 | (3) |
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101 | (2) |
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103 | (2) |
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3.5 The Generalized Stokes-Einstein Relation (GSER) |
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105 | (2) |
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3.6 Passive microrheology examples |
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107 | (3) |
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3.6.1 Limiting behavior of the MSD |
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109 | (1) |
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3.7 GSER for model materials |
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110 | (8) |
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110 | (2) |
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112 | (1) |
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112 | (1) |
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113 | (1) |
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114 | (1) |
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3.7.6 Rouse and Zimm models |
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115 | (2) |
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3.7.7 Semiflexible polymers |
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117 | (1) |
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3.8 Converting between the time and frequency domains |
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118 | (5) |
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3.8.1 Power-law approximation |
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119 | (2) |
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3.8.2 C onstrained regularization |
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121 | (2) |
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3.9 Strengths and limitations of passive microrheology |
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123 | (1) |
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3.10 Validity of the GSER |
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124 | (5) |
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3.10.1 Non-continuum effects |
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124 | (3) |
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3.10.2 Microrheology without probes? |
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127 | (2) |
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3.11 General limits of operation |
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129 | (3) |
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3.11.1 Minimum compliance |
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129 | (3) |
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132 | (3) |
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4 Multiple particle tracking |
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135 | (63) |
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136 | (5) |
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138 | (1) |
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139 | (1) |
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139 | (2) |
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141 | (5) |
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4.2.1 Frame rate and exposure time |
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141 | (1) |
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141 | (2) |
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4.2.3 Image signal-to-noise ratio |
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143 | (3) |
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4.2.4 Other image artifacts |
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146 | (1) |
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4.3 Particle tracking samples |
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146 | (4) |
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149 | (1) |
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4.3.2 Probe concentration |
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149 | (1) |
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150 | (5) |
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150 | (2) |
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4.4.2 Locating the brightest pixels |
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152 | (1) |
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4.4.3 Refining the initial location estimates |
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153 | (2) |
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155 | (6) |
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4.5.1 Van Hove correlation function |
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155 | (2) |
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157 | (2) |
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4.5.3 Application to trajectories |
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159 | (2) |
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4.6 Analysis of particle tracking |
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161 | (4) |
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4.6.1 Mean-squared displacement |
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162 | (3) |
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4.7 Non-Gaussian parameter |
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165 | (1) |
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4.8 Tracking accuracy and error |
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166 | (9) |
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167 | (3) |
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170 | (1) |
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4.8.3 Tracking error and the MSD |
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170 | (2) |
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4.8.4 Convective drift and vibration |
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172 | (3) |
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4.9 Operating regimes of particle tracking |
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175 | (1) |
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4.10 Heterogeneous materials |
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176 | (7) |
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178 | (3) |
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4.10.2 Global measures of heterogeneity |
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181 | (2) |
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4.11 Two-point microrheology |
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183 | (13) |
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183 | (4) |
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4.11.2 Data requirements of two-point microrheology |
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187 | (1) |
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4.11.3 Two-point experiments |
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187 | (2) |
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189 | (7) |
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196 | (2) |
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5 Light scattering microrheology |
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198 | (69) |
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5.1 Time-correlation functions |
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199 | (3) |
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202 | (3) |
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5.3 Dynamic light scattering |
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205 | (8) |
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5.3.1 Light intensity and the Siegert relation |
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207 | (2) |
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5.3.2 Microrheology with DLS |
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209 | (2) |
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5.3.3 Scattering from the material under test |
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211 | (1) |
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5.3.4 Suppressing multiple scattering |
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212 | (1) |
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5.4 Diffusing wave spectroscopy |
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213 | (18) |
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5.4.1 Multiple scattering |
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213 | (3) |
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5.4.2 Diffusive-light transport |
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216 | (1) |
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5.4.3 Transmission geometry |
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217 | (3) |
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5.4.4 Backscattering geometry |
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220 | (1) |
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5.4.5 Comparison of transmission and backscattering |
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221 | (2) |
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5.4.6 Photon mean-free path |
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223 | (2) |
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225 | (1) |
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5.4.8 Mean-squared displacement |
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226 | (3) |
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229 | (2) |
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5.5 Light scattering experiment |
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231 | (12) |
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5.5.1 Light scattering samples |
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232 | (3) |
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235 | (2) |
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237 | (1) |
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5.5.4 Signal-to-noise and measurement error |
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238 | (2) |
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240 | (3) |
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5.6 High-frequency rheology |
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243 | (6) |
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5.6.1 High-frequency DWS examples |
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244 | (2) |
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5.6.2 Inertia in microrheology |
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246 | (3) |
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5.7 Gels and other nonergodic samples |
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249 | (13) |
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5.7.1 Simple model of nonergodicity |
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251 | (1) |
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5.7.2 Pusey and van Megen's method |
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252 | (1) |
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5.7.3 Ensemble of measurements |
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252 | (1) |
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253 | (3) |
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5.7.5 Multispeckle detection |
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256 | (2) |
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5.7.6 Multispeckle imaging |
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258 | (4) |
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5.8 Broadband microrheology |
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262 | (1) |
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5.9 Other DWS applications |
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263 | (2) |
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265 | (1) |
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266 | (1) |
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6 Interferometric tracking |
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267 | (12) |
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6.1 Back-focal-plane interferometry |
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267 | (9) |
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6.1.1 Back-focal-plane experiment |
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267 | (2) |
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6.1.2 Detector sensitivity and limits |
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269 | (2) |
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271 | (2) |
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6.1.4 Studies using interferometry |
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273 | (3) |
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6.2 Two-point interferometry |
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276 | (1) |
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6.3 Rotational diffusion microrheology |
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276 | (2) |
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278 | (1) |
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279 | (23) |
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7.1 Introduction and overview |
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279 | (1) |
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7.2 Active, linear microrheology |
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280 | (4) |
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7.2.1 Active microrheology of active (non-equilibrium) materials |
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282 | (2) |
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7.3 Active and nonlinear microrheology |
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284 | (17) |
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7.3.1 Measuring nonlinear rheology |
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285 | (1) |
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7.3.2 Nonlinear microrheology: The issues |
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286 | (1) |
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7.3.3 Nonlinear microrheology of continuum materials: Known sources of discrepancy |
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287 | (8) |
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7.3.4 Direct probe-material interactions |
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295 | (3) |
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7.3.5 Nonlinear microrheology: Experiments |
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298 | (3) |
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301 | (1) |
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8 Magnetic bead microrheology |
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302 | (36) |
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303 | (5) |
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8.1.1 Fields generated by electrical currents |
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304 | (2) |
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306 | (2) |
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308 | (8) |
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310 | (6) |
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316 | (1) |
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316 | (8) |
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8.3.1 Electromagnet tweezers |
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316 | (3) |
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8.3.2 Tweezers with permanent magnets |
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319 | (2) |
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321 | (3) |
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324 | (7) |
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324 | (3) |
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8.4.2 Oscillating magnetic tweezers |
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327 | (2) |
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329 | (2) |
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8.5 Nonlinear measurements |
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331 | (4) |
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8.5.1 Yield stress and jamming |
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331 | (2) |
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333 | (2) |
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8.6 Nanorods in steady and rotating fields |
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335 | (1) |
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336 | (1) |
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336 | (2) |
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9 Laser tweezer microrheology |
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338 | (42) |
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9.1 Radiation forces and Gaussian beams |
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339 | (1) |
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9.2 A focused Gaussian beam in the diffraction limit |
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339 | (2) |
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340 | (1) |
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9.2.2 Irradiance and laser power |
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341 | (1) |
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341 | (7) |
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341 | (4) |
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345 | (3) |
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9.3.3 Laser tweezer microrheology samples |
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348 | (1) |
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9.4 An optical-trapping instrument |
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348 | (5) |
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350 | (3) |
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9.5 Trapping force calibration |
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353 | (13) |
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9.5.1 Drag in a viscous fluid |
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354 | (2) |
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9.5.2 Oscillating trap in a viscous fluid |
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356 | (3) |
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9.5.3 Thermal motion in a stationary trap |
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359 | (2) |
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9.5.4 In situ calibration in a complex fluid |
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361 | (4) |
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9.5.5 Trap stiffness and index of refraction |
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365 | (1) |
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9.6 Active oscillatory microrheology |
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366 | (8) |
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9.6.1 Fixed reference frame |
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366 | (2) |
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9.6.2 Moving reference frame |
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368 | (3) |
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9.6.3 Active oscillatory examples and limits |
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371 | (3) |
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9.7 Steady drag microrheology |
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374 | (2) |
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9.8 Two-point microrheology with tweezers |
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376 | (2) |
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378 | (2) |
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10 Microrheology applications |
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380 | (29) |
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10.1 Planning a microrheology experiment |
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381 | (4) |
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10.1.1 Mechanical rheometry |
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381 | (4) |
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10.2 High-throughput microrheology |
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385 | (1) |
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386 | (13) |
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388 | (2) |
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10.3.2 Time-cure superposition |
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390 | (3) |
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10.3.3 Gelation critical scaling exponents |
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393 | (1) |
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394 | (2) |
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10.3.5 Gelation screening |
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396 | (1) |
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396 | (3) |
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10.4 Viscosity measurements |
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399 | (4) |
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10.4.1 Measurement precision and accuracy |
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399 | (3) |
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10.4.2 Measurement limits |
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402 | (1) |
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403 | (1) |
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10.6 Interfacial microrheology |
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404 | (2) |
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10.7 Perspectives on future work |
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406 | (3) |
Appendix A Useful mathematics |
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409 | (12) |
Bibliography |
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421 | (24) |
Index |
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445 | |