Technologies: Fluorescence

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Definition: Fluorescence is an optical phenomenon where a photon of light absorbed by a material creates a molecular excitation that upon relaxation causes the material to re-emit a photon of light at a longer wavelength. The resulting difference in energy between the absorbed and emitted photons usually ends up as molecular vibrations or heat. Fluorescence is named after the mineral Fluorite (CaF₂) which often exhibits this phenomenon.

Typically, the photon that is absorbed lies in the ultra-violet or visible blue regions of the electromagnetic spectrum, with the emitted photon being in the green to red visible region if an electronic excitation is involved. Vibrational excitations within a single electronic state are confined to the inra-red spectral regions. Ultimately though, it is dependent on the fluorophores absorbance curve and it's Stoke shift

Photophysics

Fluorescence occurs when a fluorophore absorbs a photon of light, undergoes a transition to an excited state and then relaxes back to its ground state releasing a long wavelength photon.

Here hν is a generic term for photon energy where: h is Planck's constant and ν the frequency of light. (The specific frequencies of exciting and emitted light are dependent on the particular system). State S₀ is called the ground state of the fluorophore (fluorescent molecule) and S₁ is its first (electronically) excited state.

A molecule in its excited state, S₁, can relax by various competing pathways. It can undergo non-radiative relaxation in which the excitation energy is dissipated as vibrational energy (heat) to the solvent. Excited organic molecules can also relax via conversion to a triplet state (T₀) which may subsequently relax via phosphorescence or by a secondary non-radiative relaxation step. Relaxation of an S₁ state can also occur through interaction with a second molecule through fluorescence quenching. Molecular oxygen (O₂) is an extremely efficient quencher of fluorescence because of its unusual triplet ground state.

Figure 1: Jablonski diagram illustrating various relaxation pathways

Quantum yield

The fluorescence quantum yield is defined as the ratio of the number of photons emitted to the number of photons absorbed and it gives a measure of the efficiency of the fluorescence process.

The maximum fluorescence quantum yield is equal to 1.0; ie every photon that is absorbed results in a photon emitted (100% efficiency). Although, compounds that possess quantum yields of 0.10 are still considered quite fluorescent. Another way to define the quantum yield of fluorescence, is by the rates of excited state decay

where the numerator of that fraction is the rate of spontaneous emission and the denominator is the sum of all the rates of excited state decay. Other rates of excited state decay are caused by mechanisms other than the emission of photons and are therefore termed "non-radiative rates", which can include: dynamic collisional quenching, near-field dipole-dipole interaction (or resonance energy transfer), internal conversion and intersystem crossing. Thus, if the rate of any pathway changes, this will affect both the excited state lifetime and the fluorescence quantum yield. Fluorescence quantum yield are measured by comparison to a standard with known quantology; ie Fluorescein.

Lifetime

The fluorescence lifetime is defined as the average time the molecule stays in its excited state before relaxing back to its ground state thus emitting a photon. Fluorescence typically follows first-order kinetics

where [S1] is the concentration of excited state molecules at time t, [S1]₀ is the initial concentration and Λ is the decay rate or the inverse of the fluorescence lifetime. This is an instance of exponential decay. Various radiative and non-radiative processes can de-populate the excted state. In such cases the total decay rate is the sum over all rates: Γ_tot = Γ_rad + Γ_nrad. Where Γ_tot is the total decay rate, Γ_rad the radiative decay rate and Γ_nrad the non-radiative decay rate. It is similar to a first-order chemical reaction in which the first-order rate constant is the sum of all of the rates (a parallel kinetic model). If the rate of spontaneous emission, or any of the other rates are fast, then the fluorescence lifetime is correspondingly short. For commonly used fluorescent compounds typical excited state decay times are within the range of 0.5 to 20 nanoseconds. The fluorescence lifetime is an important parameter for practical applications of fluorescence such as fluorescence resonance energy transfer.