Photothermal Spectroscopy Methods

About the Authors xiii Preface xv Acknowledgments xix 1 Introduction 1 1.1 Photothermal Spectroscopy 1 1.2 Basic Processes in Photothermal Spectroscopy 3 1.3 Photothermal Spectroscopy Methods 5 1.4 Application of Photothermal Spectroscopy 9 1.5 Illustrative History and Classification of Photothermal Spectroscopy Methods 10 1.5.1 Nature of the Photothermal Effect 10 1.5.2 Photoacoustic Spectroscopy 11 1.5.3 Single-Beam Photothermal Lens Spectroscopy 14 1.5.4 Photothermal Z-scan Technique 18 1.5.5 Photothermal Interferometry 20 1.5.6 Two-Beam Photothermal Lens Spectroscopy 25 1.5.7 Photothermal Lens Microscopy 27 1.5.8 Photothermal Deflection, Refraction, and Diffraction 31 1.5.9 Photothermal Mirror 38 1.5.10 Photothermal IR Microspectroscopy 41 1.5.11 Photothermal Radiometry 44 1.5.12 Historic Summary 47 1.6 Some Important Features of Photothermal Spectroscopy 48 References 50 2 Absorption, Energy Transfer, and Excited State Relaxation 57 2.1 Factors Affecting Optical Absorption 57 2.2 Optical Excitation 63 2.2.1 Kinetic Treatment of Optical Transitions 63 2.2.2 Nonradiative Transitions 69 2.3 Excited State Relaxation 72 2.3.1 Rotational and Vibrational Relaxation 73 2.3.2 Electronic States and Transitions 78 2.3.3 Electronic State Relaxation 80 2.4 Relaxation Kinetics 85 2.5 Nonlinear Absorption 88 2.5.1 Multiphoton Absorption 90 2.5.2 Optical Saturation of Two-Level Transitions 91 2.5.3 Optical Bleaching 93 2.5.4 Response Times During Optical Bleaching 95 2.5.5 Optical Bleaching of Organic Dyes 96 2.5.6 Relaxation for Impulse Excitation 98 2.5.7 Multiple Photon Absorption 99 2.6 Absorbed Energy 101 References 104 3 Hydrodynamic Relaxation: Heat Transfer and Acoustics 107 3.1 Local Equilibrium 107 3.2 Thermodynamic and Optical Parameters in Photothermal Spectroscopy 108 3.2.1 Enthalpy and Temperature 108 3.2.2 Energy and Dynamic Change 111 3.3 Conservation Equations 111 3.4 Hydrodynamic Equations 116 3.5 Hydrodynamic Response to Photothermal Excitation 118 3.5.1 Solving the Hydrodynamic Equations 119 3.5.2 Thermal Diffusion Mode 121 3.5.3 Fourier-Laplace Solutions for the Thermal Diffusion Equation 122 3.5.4 Propagating Mode 124 3.5.5 Summary of Hydrodynamic Mode Solutions 125 3.6 Density Response to Impulse Excitation 126 3.6.1 One-Dimensional Case 127 3.6.2 Two-Dimensional Cylindrically Symmetric Example 129 3.6.3 Coupled Solutions 137 3.7 Solutions Including Mass Diffusion 138 3.8 Effect of Hydrodynamic Relaxation on Temperature 143 3.9 Thermodynamic Fluctuation 145 3.10 Noise Equivalent Density Fluctuation 146 3.11 Summary 150 Appendix 3.A Thermodynamic Parameter Calculation 150 Appendix 3.B Propagating Mode Impulse Response for Polar Coordinates in Infinite Media 151 References 153 4 Temperature Change, Thermoelastic Deformation, and Optical Elements in Homogeneous Samples 155 4.1 Temperature Change from Gaussian Excitation Sources 156 4.1.1 Thermal Diffusion Approximation 156 4.1.2 Gaussian Laser Excitation of Optically Thin Samples 157 4.1.3 Short Pulse Laser Excitation 159 4.1.4 Continuous Laser Excitation 160 4.1.4.1 Laser Heating 160 4.1.4.2 On-axis Temperature Change 161 4.1.4.3 Post-excitation Cooling 162 4.1.5 Chopped Laser Excitation 165 4.1.6 On-axis Temperature Change for Periodic Excitation 167 4.1.7 Gaussian Laser Excitation of Absorbing and Opaque Samples 168 4.1.7.1 Short Pulse Laser Excitation 169 4.1.7.2 Continuous Laser Excitation 170 4.1.8 Thermal Gratings 170 4.2 Thermodynamic Parameters 174 4.2.1 Thermodynamic Parameters Affecting Temperature 174 4.2.2 Convection Heat Transfer 178 4.3 Thermoelastic Displacement 180 4.3.1 Continuous Laser Excitation 181 4.3.2 Short Pulse Laser Excitation 182 4.4 Optical Elements 182 4.4.1 Phase Shift and Optical Path Length Difference 184 4.4.2 Phase Shift and Optical Path Length Difference Under Thermoelastic Deformation 185 4.4.3 Deflection Angle 189 4.4.4 Thermal Lens Focal Length 190 4.4.5 Grating Strength 193 4.5 Temperature-dependent Refractive Index Change 194 4.5.1 Density and Temperature Dependence of Refractive Index 195 4.5.2 Population Dependence on Refractive Index 199 4.5.3 Soret Effect 200 4.5.4 Other Factors Affecting Refractive Index 203 4.6 Temperature Change and Thermoelastic Displacement from Top-hat Excitation Sources 204 4.6.1 Temperature Change from Top-hat Excitation Sources 204 4.6.2 Thermoelastic Displacement from Top-hat Excitation Sources 205 4.7 Limitations 206 4.7.1 Excitation Beam Waist Radius Changes 207 4.7.2 Effects of Scattering and Optically Thick Samples 208 4.7.3 Finite Extent Sample Effects 210 4.7.4 Accounting for Finite Cell Radius 211 References 215 5 Photothermal Spectroscopy in Homogeneous Samples 219 5.1 Photothermal Interferometry 219 5.2 Photothermal Deflection 224 5.2.1 Deflection Angle for Pulsed Laser Excitation 224 5.2.1.1 Collinear Probe Geometry 224 5.2.1.2 Crossed-beam Probe Geometry 226 5.2.2 Deflection Angle for Continuous and Chopped Laser Excitation 227 5.2.2.1 Continuous Excitation with Parallel Probe Geometry 227 5.2.2.2 Continuous Excitation with Crossed-probe Geometry 230 5.2.2.3 Chopped Excitation with Parallel Probe 230 5.2.3 Deflection Angle Detection 231 5.2.3.1 Probe Laser Beam Waist Effect 231 5.2.3.2 Straightedge Apparatus 234 5.2.3.3 Position Sensing Detectors 235 5.2.3.4 Other Methods to Detect Deflection Angle 236 5.2.3.5 Differential Deflection Angle 238 5.3 Thermal Lens Focal Length 239 5.3.1 Pulsed Excitation Thermal Lens Focal Length 239 5.3.1.1 Time-dependent Focal Length 239 5.3.1.2 Sample Path Length Limitations 240 5.3.1.3 Crossed-beam Arrangement 242 5.3.2 Continuous and Chopped Excitation Thermal Lens Focal Length 243 5.3.2.1 Continuous Excitation 243 5.3.2.2 Sample Path Length Limitations 243 5.3.2.3 Crossed-beam Geometry 244 5.3.2.4 Chopped Excitation 245 5.3.3 Focal Length for Periodic Excitation 245 5.4 Detecting the Thermal Lens 248 5.4.1 Signal for Symmetric Lens 248 5.4.2 Signal for Different x and y Focal Lengths 250 5.4.3 Lock-in Amplifier or Pulse Height Detected Signal 253 5.4.4 Signal Development with Large Apertures 254 5.4.5 Signal Development Based on Image Analysis and Other Optical Filters 255 5.5 Types of Photothermal Lens Apparatuses 258 5.5.1 Single-laser Apparatus 258 5.5.2 Differential Single-laser Apparatus 260 5.5.3 Two-laser Apparatus 261 5.6 Two-laser Photothermal Lens Spectroscopy 267 5.6.1 Excitation Wavelength Dependence in Two-laser Photothermal Spectroscopy 268 5.7 Differential Two-laser Apparatuses 269 5.8 Diffraction Effects 271 5.8.1 Probe Laser Diffraction Effects for Pulsed Excitation 272 5.8.2 Probe Laser Diffraction Effects for Continuous Excitation 278 5.8.3 Diffraction Effects for Single-laser Photothermal Lens 281 5.8.4 Effect of Diffraction on the Thermal Lens Enhancement Factor 281 References 283 6 Analytical Measurement and Data Processing Considerations 285 6.1 Sensitivity of Photothermal Spectroscopy 286 6.1.1 Photothermal Lens Enhancement Factors 286 6.1.2 Relative Sensitivity of Photothermal Lens and Deflection Spectroscopies 291 6.1.3 Relative Sensitivity of Photothermal Lens and Photothermal Interferometry Spectroscopies 292 6.1.4 Relating Photothermal Signals to Absorbance and Enhancement 295 6.1.5 Intrinsic Enhancement of Two-Laser Methods 295 6.1.6 Enhancement Limitations 297 6.1.7 The Choice of Solvents for Photothermal Lens Measurements 299 6.1.7.1 Aqueous Solutions of Electrolytes 300 6.1.7.2 Aqueous Solutions of Surfactants and Water-Soluble Polymers 302 6.1.7.3 Organo-aqueous Mixtures 303 6.1.7.4 Soret Effect in Mixed Media 305 6.2 Optical Instrumentation for Analysis 306 6.2.1 Dynamic Reserve 306 6.2.2 Differential Measurements 307 6.2.3 Spectroscopic Measurement 310 6.2.4 Fiber Optics 313 6.3 Processing Photothermal Signals 316 6.3.1 Analog Signal Processing 320 6.3.2 Digital Signal Processing 321 6.4 Photothermal Data Processing 326 6.4.1 Excitation Irradiance Curves 327 6.4.2 Calibration 327 6.4.3 Metrological Parameters of Photothermal Lens Spectrometry 329 6.4.3.1 Accuracy of Photothermal Lens Measurements 329 6.4.3.2 Instrumental and Method Detection Limits 329 6.4.3.3 Photothermal Limits of Detection 331 6.4.3.4 Photothermal Error Curves 333 6.5 Considerations for Trace Analysis 336 6.5.1 Unstability of Dilute Solutions 337 6.5.2 Sources of Losses and Contamination 337 6.5.3 Changes in Sensitivity and Selectivity Due to Chemistry at the Trace Level 339 6.5.4 Statistical Features at the Level of Low Concentrations 340 6.6 Tracking Down and Reducing Noise 340 References 342 7 Analytical Applications 347 7.1 Areas of Analytical Application 347 7.2 Applications to Stationary Homogeneous Samples 348 7.2.1 Photothermal Techniques 348 7.2.2 Gas Phase Samples 351 7.2.3 Liquid Samples 361 7.3 Application to Disperse Solutions 364 7.3.1 Nano-sized Particles and Nanocomposite Materials 364 7.3.2 Analysis of Biological Samples 365 7.4 Photothermal Spectroscopy Detection in Chromatography and Flow Analysis 370 7.4.1 Temperature Change in Flowing Samples 371 7.4.2 Deflection Angles and Inverse Focal Lengths in Flowing Samples 373 7.4.2.1 Isotropic and Turbulent Flow 373 7.4.2.2 Laminar Flow 375 7.4.3 Applications in Chromatography 376 7.4.3.1 Gas Chromatography and Flowing Gas Analysis 383 7.4.3.2 Liquid Phase 383 7.4.4 Application to Flow Injection Analysis 385 7.5 Photothermal Spectroscopy Detection in Capillary Electrophoresis 387 7.5.1 Influence of Electrophoretic Flow Rate 389 7.5.2 Effect of the Composition of the Background Electrolyte Solution on the Sensitivity 393 7.5.3 Applications 394 7.6 Photothermal Spectroscopy Detection in Microanalytical and Microfluidic Systems 402 7.7 Determination of Parameters of Reactions 404 7.7.1 Determination of Thermodynamic Parameters and Constants 404 7.7.2 Chemical Reaction Control and Real-time Monitoring 406 7.7.3 Kinetic Parameters of Reactions 406 7.8 Excitation and Relaxation Kinetics 408 7.8.1 Relaxation Kinetics and Quantum Yield Studies 409 7.8.2 Photodynamic Irradiance-dependent Signal Studies 414 7.8.3 Optical Bleaching in Organic Dye Molecules 417 7.8.4 Optical Bleaching Effects in Pulsed Laser Photothermal Spectroscopy 422 References 423 8 Photothermal Spectroscopy of Heterogeneous Samples 435 8.1 Types of Heterogeneity 435 8.2 Apparatuses for Photothermal Deflection 436 8.3 Surface Absorption 437 8.3.1 Thermal Diffusion at Surfaces 437 8.3.2 Temperature Change from Pulsed Excitation 438 8.3.3 Temperature Change from Continuous Excitation 438 8.3.4 Temperature Change from Periodic Excitation 439 8.4 Thermal Diffusion in Volume Absorbing Samples 441 8.4.1 Volume Temperature Change for Pulsed Excitation 441 8.4.2 Periodic Excitation of Volume Absorbers 442 8.5 Temperature Change in Layered Samples 443 8.5.1 Periodic Excitation of Layered Samples 445 8.5.2 Pulsed Excitation of Thick-layered Samples 447 8.6 Surface Point Source 449 8.7 Gaussian Beam Excitation of Surfaces 452 8.8 Gaussian Beam Excitation of Transparent Materials 455 8.9 Excitation of Layered Samples with Gaussian Beams 457 8.10 Deflection Angles with Oscillating Gaussian Excitation 460 8.11 Photothermal Reflection 463 8.12 Experiment Design for Photothermal Deflection 463 8.13 Application to Determination of Solid Material Properties 465 8.13.1 Bulk Properties 466 8.13.1.1 Thermo-optical Properties 468 8.13.1.2 Quantum Yields 469 8.13.2 Solid Surfaces 470 8.14 Applications to Chemical Analysis 471 8.14.1 Application to Surface Determination and Optical Sensing Materials 471 8.14.2 Applications to Gel and Thin-layer Chromatography 472 8.14.3 Other Application to Applied Chemical Analysis 473 8.14.4 Application to Biological Analysis 474 References 476 Index 481

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