Lec1 Light: Generation Prof. Gabriel Popescu Light Emission, Detection, and Statistics Fluorescence • Luminescence • Comprised of fluorescence and phosphorescence • The phenomenon that a given substance emits light • Light in the visible spectrum is due to electronic transitions • Vibrationally excited states can give rise to lower energy photons, i.e. infrared radiation • Rotational modes produce even lower energy radiation, in the microwave region. • Application • Fluorescence-based measurements • Microscopy, flow cytometry, medical diagnosis, DNA sequencing, and many other areas. • Biophysics and biomedicine • Fluorescence microscopy, image at cellular and molecular scale, even single molecule scale. • Fluorescent probes, specifically bind to molecules of interest, revealing localization information and activity (i.e., function). • Challenge in microscopy: Merge information from the molecular and cellular scales. Prof. Gabriel Popescu Light Emission, Detection, and Statistics Jablonski Diagram • Fluorescence • The radiative transition between two electronic states of the same spin multiplicity. • Spin multiplicity: Ms=2s+1, with s the spin of the state. • The spin s • s is the sum of the spins from all the electrons on that electronic state. • s=0, two paired (antiparallel spins) electrons on the electronic sate. • s=1/2, a single, unpaired electron in the state. • s=1, two electrons of parallel spins. • Electronic states • Singlets (Ms=2s+1=1, s=0) • Doublets (Ms=2, s=1/2) • Triplets (Ms=3, s=1) • The singlet-singlet transition is the most common in fluorescence. Prof. Gabriel Popescu Light Emission, Detection, and Statistics Jablonski Diagram • Jablonski diagram a S • The energy levels of a molecule. 2 Internal Conversion • 푆0, 푆1, 푆2 denote the ground, first, and second electronic state. S1 Intersystem Crossing • A typical scenario: T Absorption 1 • Absorb a photon of energy hvA , 푆0→푆2, at the Fluorescence 1fs=10-15 s scale hv hv A hvA hvF P -12 • Internal conversion:푆2→ 푆1, within 1ps=10 s 2 Phosphorescence or less. S0 1 0 • Emit a photon of energy hvF , 푆2→ 푆1, in an b Figure 5.1. a) Jablonski diagram depicting a average time of 10-9—10-8 s. three level system: 푆0, 푆1, 푆2 are singlet • Assume: The internal conversion is complete electronic states, each containing vibrational prior to emission. levels. Absorption takes place at frequencies A .T1 denotes a triplet state, from which phosphorescence takes place. b) Music score illustrating the similarity with the Jablonski diagram. Prof. Gabriel Popescu Light Emission, Detection, and Statistics Jablonski Diagram • Born-Oppenheimer approximation • A molecule’s wave function can be factorized into an electronic and nuclear (vibrational and rotational) components. total= e N • Phosphorescence • Intersystem crossing: The conversion from the S1 state to the first triplet state T1 • Phosphorescence: Triplet emission (emission from T1 ), which is generally shifted to lower energy (longer wavelengths) • Phosphorescence has lower rate constants than fluorescence. • Phosphorescence with decay times of seconds or even minutes. • Molecules of heavy atoms tend to be phosphorescent. Prof. Gabriel Popescu Light Emission, Detection, and Statistics Emission Spectra • Symmetry property between the power Wavelength ( ) a ) 1 350 370 390 410 450 490 530 570 spectrum of absorption (or excitation) 1.0 32 and emission (or radiative decay) — 1 mirror symmetry 24 • Excitation: Absorption, S0 → S1 (higher 0.5 vibrational levels)→ nonradiative decay, S 16 1 Emission (lowest vibrational level). Absorption 8 • Emission: Radiatively decays, S1 → S0 (high vibrational level) → thermal equilibration, S0 0 0 (ground vibrational state). coefficient Extincion 28,800 26,800 24,800 22,800 20,800 18,800 1 (normalized) intensity Fluorescence • The peaks in both absorption and emission Wavenumber ( ) correspond to vibrational levels, which results Figure 5.2. a) Mirror-image rule (perylene in benzene). in perfect symmetry. Prof. Gabriel Popescu Light Emission, Detection, and Statistics Emission Spectra • Note: The local maxima are due to b ) the individual vibration levels. 1 Wavenumber ( ) 280 320 360 400 440 480 520 600 • The emission spectrum remains 1 10 1.0 constant irrespective of the excitation 8 6 wavelength (exceptions exist). 0.5 4 Absorption Emission • Exception to the mirror rule 2 • Absorption spectrum: The first peak is 0 0 35,500 31,500 27,500 23,500 19,500 15,500, due to S0 — S2, the larger wavenumber 1 peak is from S0 — S1. Wavenumber ( ) Extincion coefficient coefficient Extincion • Emission: Occurs predominantly from S1, (normalized) intensity Fluorescence the second peak is absent. Figure 5.2. b) Exception to the mirror rule (quinine sulfate in H2SO4). Adapted from Lakowicz, J. R. (2013). Principles of fluorescence spectroscopy, Springer Science & Business Media. Prof. Gabriel Popescu Light Emission, Detection, and Statistics Rate Equations • The population of each level is determined by the S2 Relaxation(10−12 s ) rate of absorption, nonradiative decay, S spontaneous emission, and stimulated emission. 1 • Stimulated emission h h • The radiative transition from an excited state to the ground A A state triggered (stimulated) by the excitation field. • By stimulated emission, one excitation photon results in two identical emitted photons (development of lasers). S0 Figure 5.3. Jablonski diagram for a three-level system. • Rate equations for levels S0 and S1 -3 N0,1 —concentrations, m dN1 -1 = B N − B N − A N − N B01 — absorption rate, s dt 01 0 10 1 10 1 nr 1 B10 — stimulated emission rate dN0 dN1 (B01 = B10 for nondegenerate levels) = −B01N0 + B10 N1 + A10 N1 + nr N1 = − dt dt A10 — spontaneous emission rate γnr —rate of nonradiative decay Assume: NN 01 + =const, or d（N0 + N1）/ dt = 0 Prof. Gabriel Popescu Light Emission, Detection, and Statistics Rate Equations • Note: The energy lost from nonradiative decay, γnr , eventually converts into heat. • For thermal equilibrium • N1 << N0, the stimulated emission term can be neglected (B10 N1 ≈0) • Note: The rate of decay is much higher than that of absorption, A01 + γnr >> B10. • For active medium • N1 > N0, when there is population inversion. • The solutions for the populations of the two levels A10 + nr NN0 = N0 + N1 = N BA01++ 10 nr B B01 N0 − A10 N1 − nr N1 = 0 01 NN1 = BA01++ 10 nr Prof. Gabriel Popescu Light Emission, Detection, and Statistics Quantum Yield • The fluorescence quantum yield • The ratio of the number of photons emitted to that of photons absorbed N A A Q = 1 10 = 10 N0 B01 A10 + nr • For thermal equilibrium NNBA1//() 0=+ 01 10 nr • The quantum yield can approach unity if the nonradiative decay, γnr , is much smaller than the rate of radiative decay, A10. • Note: Even for 100% quantum yield, the energy conversion is always less than unity because the wavelength of the fluorescent light is longer (the frequency is higher, i.e. hωA>hωF ). Prof. Gabriel Popescu Light Emission, Detection, and Statistics Fluorescence Lifetime • The lifetime of the excited state • The average time the molecule spends in the excited state before returning to the ground state. • For a simplified Jablonski diagram, the lifetime is the inverse of the decay rate. 1 = A10 + nr • Natural lifetime τ0 • The lifetime of a fluorophore in the absence of nonradiative processes, γnr →0. • Depends on the absorption spectrum, extinction coefficient, and emission spectrum of the fluorophore. • Natural lifetime τ0 and measured lifetime τ (τ > τ0, nonradiative processes) 1 A = = 10 = Q = 0 A 0 0 0 10 A10 + nr Q Prof. Gabriel Popescu Light Emission, Detection, and Statistics Quenching • Fluorescence quenching • The nonradiative decay to the ground state. • Collisional quenching • Due to the contact between the fluorophore and quencher, in thermal diffusion. • Quenchers include: halogens, oxygen, amines, etc. • Other quenching • Static quenching: The fluorophore can form a nonfluorescent complex with the quencher • The attenuation of the incident light by the fluorophore itself or other absorbing species. • Photon absorption takes place at femtosecond scale, 10-15 s, while emission occurs over a larger period of time. Prof. Gabriel Popescu Light Emission, Detection, and Statistics Quenching • During its lifetime, a fluorophore can interact with quenchers from within a radius of 7 nm. 2 The diffusion coefficient of oxygen in water D = 2.5 10 − 5 m ,the lifetime of a fluorophore t =10ns s The root mean squared distance that the oxygen molecule can travel during this time =x2 2. Dt The significant distance = x 2 7 nm , the thickness of a cell membrane bilayer is 4-5 nm . • It is possible for a molecule to absorb light outside the cell and fluoresce from the inside (and vice versa), one lifetime later. Prof. Gabriel Popescu Light Emission, Detection, and Statistics Black Body Radiation Prof. Gabriel Popescu Light Emission, Detection, and Statistics Black Body Radiation • Black body n = ... • An idealized model of a physical object that absorbs all incident electromagnetic radiation, and an ideal emitter of thermal radiation. • Spectral distribution of radiation by bodies at thermal equilibrium led into the development of quantum n =11 mechanics. • Thermal radiation • Reverse process to absorption: Internal energy → Thermal radiation. • Cavity mode: The spatial frequency content of n = 0 the electromagnetic field within the cavity, which satisfies the condition of vanishing electric field at the wall. Figure 6.1. Cavity modes: the sinusoids represent the