Principles of Fluorescence Spectroscopy

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PRINCIPLES OF FLUORESCENCE SPECTROSCOPY 155 P4.6. Data Acquisition Times Using TCSPC With Microsecond Decay Times: Calculate the time needed to acquire the data in Figure 4.45. Assume the lifetime of [Ru(bpy) 3 ] 2+ is 400 ns and that one photon is detected for each excitation pulse. Calculate the data acquisition time to obtain the same data using TCSPC with the same pulse repetition rate and a 1% count rate. P4.7. Data Acquisition Times Using TCSPC With Nanosecond Decay Times: Suppose the lifetime of a fluorophore is 4 ns. Determine the conditions needed for TCSPC. Calcu- late the time required to count 4 x 10 6 photons with 1 photon counted per 100 excitation pulses. Consider dead times of 2 :s and 120 ns. P4.8. Calculation of Fractional Intensities and Pre-Exponential Factors: Suppose two compounds have equal quantum yields but different lifetimes of τ 1 = 1 :s and τ 2 = 1 ns. If a solution contains an equimolar amount of both fluorophores, what is the fractional intensity of each fluorophore?
5 In the preceding chapter we described the theory and instrumentation for measuring fluorescence intensity decays using time-domain measurements. In the present chapter we continue this discussion, but describe frequency-domain fluorometry. In this method the sample is excited with light that is intensity modulated at a high frequency comparable to the reciprocal of the lifetime. When this is done, the emission is intensity modulated at the same frequency. However, the emission does not precisely follow the excitation, but rather shows time delays and amplitude changes that are determined by the intensity decay law of the sample. The time delay is measured as a phase angle shift between the excitation and emission, as was shown in Figure 4.2. The peak-to-peak height of the modulated emission is decreased relative to the modulated excitation, and provides another independent measure of the lifetime. Time-resolved measurements, whether performed in the time domain or in the frequency domain, provides information about intensity decay of the sample. Samples with multiple fluorophores typically display multi-exponential decays. Even samples with a single fluorophore can display complex intensity decays due to conformational heterogeneity, resonance energy transfer, and transient effects in diffusive quenching or fluorophore–solvent interactions, to name just the most common origins. The goal of the timeresolved measurement is to determine the form of the intensity decay law, and to interpret the decay in terms of molecular features of the sample. Intensity decays can be single-exponential, multi-exponential, or non-exponential. Irrespective of the complexity of the decay, one can always define a mean or apparent decay time. For a single exponential decay in the time domain the actual lifetime is given by this the time when the intensity decays to 1/e of its initial value. For a multi-exponential decay, the 1/e time is typically not equal to any of the decay times. In the frequency domain an apparent lifetime (τ φ ) determined from the phase angle (φ ω ) or the appar- Frequency-Domain Lifetime Measurements ent lifetime (τ m ) determined from the modulation (m ω , eqs. 4.5 and 4.6). The apparent lifetimes are characteristic of the sample, but do not provide a complete description of the complex intensity decay. The values of τ φ and τ m need not be equal, and each value represents a different weighted average of the decay times displayed by the sample. In general, the apparent lifetime depends on the method of measurement. The earlier literature on time-resolved fluorescence often describes apparent lifetimes. At present, there are relatively few reports of only the mean decay times. This is because the mean lifetimes represent complex weighted averages of the multi-exponential decay. Quantitative interpretation of mean decay times is usually difficult and the results are often ambiguous. Prior to 1983, frequency-domain fluorometry allowed determination of mean lifetime, but was not able to resolve complex intensity decays. This limitation was the result of phase-modulation fluorometers, which only operated at one, two, or three fixed light modulation frequencies. The resolution of a complex decay requires measurements at a number of modulation frequencies that span the frequency response of the sample. While several variable-frequency instruments were described prior to 1983, these were not generally useful and were limited by systematic errors. The first generally useful variable frequency instrument was described in the mid 1980s. 1–2 These instruments allowed phase and modulation measurements from 1 to 200 MHz. These designs are the basis of currently available instruments. Frequency-domain fluorometry is now in widespread use, 3–9 and instruments are commercially available. Frequency-domain fluorometers are now routinely used to study multi-exponential intensity decays, and non-exponential decays resulting from resonance energy transfer, timedependent solvent relaxation, and collisional quenching. In this chapter we describe the instrumentation for FD measurements and the theory used to interpret the experimental data. We will describe examples that illustrate the 157
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Principles of Fluorescence Spectros
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Joseph R. Lakowicz Center for Fluor
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Preface The first edition of Princi
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x GLOSSARY OF ACRONYMS DNS dansyl o
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xii GLOSSARY OF ACRONYMS TRES time-
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xiv GLOSSARY OF MATHEMATICAL TERMS
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xvi CONTENTS 2.9.4. Conversion betw
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xviii CONTENTS 6. Solvent and Envir
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xx CONTENTS 10.4.4. Alignment of Po
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xxii CONTENTS 14.7.1. Simulations o
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xxiv CONTENTS 19.12. New Approaches
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xxvi CONTENTS 25.3. Optical Propert
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2 INTRODUCTION TO FLUORESCENCE Figu
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6 INTRODUCTION TO FLUORESCENCE inst
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10 INTRODUCTION TO FLUORESCENCE Fig
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12 INTRODUCTION TO FLUORESCENCE ns,
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14 INTRODUCTION TO FLUORESCENCE 1.7
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24 INTRODUCTION TO FLUORESCENCE due
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28 INSTRUMENTATION FOR FLUORESCENCE
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3 Fluorescence probes represent the
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PRINCIPLES OF FLUORESCENCE SPECTROS
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98 TIME-DOMAIN LIFETIME MEASUREMENT
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100 TIME-DOMAIN LIFETIME MEASUREMEN
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102 TIME-DOMAIN LIFETIME MEASUREMEN
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238 DYNAMICS OF SOLVENT AND SPECTRA
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278 QUENCHING OF FLUORESCENCE 8.1.
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280 QUENCHING OF FLUORESCENCE Figur
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282 QUENCHING OF FLUORESCENCE ly ev
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290 QUENCHING OF FLUORESCENCE relat
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298 QUENCHING OF FLUORESCENCE σ ar
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320 QUENCHING OF FLUORESCENCE 47. R
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322 QUENCHING OF FLUORESCENCE 113.
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328 QUENCHING OF FLUORESCENCE P8.3.
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330 QUENCHING OF FLUORESCENCE P8.11
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332 MECHANISMS AND DYNAMICS OF FLUO
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10 Measurements of fluorescence ani
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11 In the preceding chapter we desc
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12 In the preceding two chapters we
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444 ENERGY TRANSFER Figure 13.1. Fl
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446 ENERGY TRANSFER wavelength is e
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448 ENERGY TRANSFER Table 13.1. Cal
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450 ENERGY TRANSFER Figure 13.6. Ab
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452 ENERGY TRANSFER safe for many p
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454 ENERGY TRANSFER Figure 13.12. P
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456 ENERGY TRANSFER Figure 13.16. E
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458 ENERGY TRANSFER Figure 13.21. R
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460 ENERGY TRANSFER Figure 13.24. R
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462 ENERGY TRANSFER tiple acceptors
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464 ENERGY TRANSFER Figure 13.29. A
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466 ENERGY TRANSFER Figure 13.33. F
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468 ENERGY TRANSFER Table 13.3. Rep
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470 ENERGY TRANSFER 55. Clegg RM. 1
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472 ENERGY TRANSFER Tong AK, Jockus
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474 ENERGY TRANSFER Figure 13.39. O
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14 In the previous chapter we descr
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15 In the previous two chapters on
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16 The biochemical applications of
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578 TIME-RESOLVED PROTEIN FLUORESCE
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608 MULTIPHOTON EXCITATION AND MICR
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19 Fluorescence sensing of chemical
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676 NOVEL FLUOROPHORES Figure 20.1.
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678 NOVEL FLUOROPHORES Figure 20.7.
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680 NOVEL FLUOROPHORES Figure 20.12
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698 NOVEL FLUOROPHORES 33. Acherman
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700 NOVEL FLUOROPHORES 103. Demas J
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702 NOVEL FLUOROPHORES 176. Montalt
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21 During the past 20 years there h
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22 Fluorescence microscopy is one o
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758 SINGLE-MOLECULE DETECTION Figur
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766 SINGLE-MOLECULE DETECTION small
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770 SINGLE-MOLECULE DETECTION Table
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786 SINGLE-MOLECULE DETECTION face
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788 SINGLE-MOLECULE DETECTION TCSPC
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790 SINGLE-MOLECULE DETECTION 53. H
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792 SINGLE-MOLECULE DETECTION Ke PC
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794 SINGLE-MOLECULE DETECTION Polar
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24 In the previous chapter we descr
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862 RADIATIVE-DECAY ENGINEERING: SU
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Appendix I Corrected Emission Spect
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Appendix II Fluorescence Lifetime S
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890 APPENDIX III P ADDITIONAL READI
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892 APPENDIX III P ADDITIONAL READI
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894 ANSWERS TO PROBLEMS A1.4. A. Th
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896 ANSWERS TO PROBLEMS Energy tran
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898 ANSWERS TO PROBLEMS Figure 4.65
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900 ANSWERS TO PROBLEMS expected to
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904 ANSWERS TO PROBLEMS where f is
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906 ANSWERS TO PROBLEMS [BSA] Obser
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908 ANSWERS TO PROBLEMS emission. T
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910 ANSWERS TO PROBLEMS dx rA A (
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912 ANSWERS TO PROBLEMS B. A covale
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914 ANSWERS TO PROBLEMS The α i va
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920 ANSWERS TO PROBLEMS CHAPTER 24
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Index A Absorption spectroscopy, 12
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