Fluorescence Process

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Time Scales

When looking at the electromagnetic spectrum, it is important to consider the absorption by pi conjugated molecules of two or three eV in the visible. The frequency related to a photon that has an energy of 1 eV a few 10¹⁴. This means that three electron volts you get 10¹⁵. This immediately shows the time scale for absorption. Absorption of a photon with a few eV occurs on a time scale on the order of a femptosecond or a rate of 10¹⁵ per second. For absorption of a photon for a core electron, keV (kilo electron volts ) are used. This is the absorption that is found in an x-ray photoelectron spectroscopy. keV correspond to about 10¹⁷ or 10¹⁸ hertz. These values correspond to a timescale of attaseconds. The fastest vibrations in a molecule are the ones that are most energetic. Basically, this refers to the bond length vibrations in the order of a couple thousand wave numbers, .2 eV. These processes occur in a time scale of about 10^-13 seconds, which is a few tenths of a picosecond. A molecule at 0 Kelvin temperature is vibrating on its’ lowest vibrational level. At room temperature, the molecule would be vibrating all over the place and when the photon comes by, it will be absorbed. Given the time scale for the absorption however it is as if that the geometry was frozen in time because the molecular vibrations are much slower than the absorption event. Imagine a situation where you have the molecule in its equilibrium geometry in its ground state. A photon is absorbed and the molecule moves up to the excited state. At this time, the molecule retains the geometry of the ground state. Then after a while it can relax and changes into the optimal geometry of the excited state. Once you have an idea of the energies that are involved, you can figure out the time scales and predict whether the vibrations will be coupling strongly or not.

Light absorption is characterized by k_abs and occurs on a time scale of ~10¹⁵ sec-1 Because the mass of the electron is much less than that of the nuclei, a good approximation is that the nuclei remain fixed on the time-scale of light absorption and then relax to new equilibrium geometries subsequent to the absorption process (Franck-Condon approximation)

Internal conversion is a process by which excess energy is dissipated through heat by internal vibrations. It is characterized k_ic and occurs on a time-scale of ~ >10¹² sec^-1. This is the process by which the nuclei relax to their equilibrium position upon excitation and is a process by which molecules in an electronically excited-state can relax to the ground-state without the emission of a photon.

Fluoresence

Fluorescence is the process by which the molecule that has singlet spin multiplicity in an excited state loses energy (typically back to its ground state) with emission of light it is characterized by k_fl which is typically on the time scale of ~ 10⁶ -10⁹ sec^-1

A molecule that cannot intersystem cross (can not go to the triplet state), then so it will remain in that singlet S1 state and then it will eventually go back to the ground state radiatively or non-radiatively.

Quantum Yield

The rate at which it goes back to the ground state radiatively over all the rates (or processes) that can take place non-raditivaely or radiatively, going to the triplet and so on, gives you the quantum yield ( Ø).

<math>\phi = \frac {photon \, emitted} {photon \, absorbed} = \frac {k_{fl} } {\sum {k}}\,\!</math>

The quantum yield Ø is the probability of getting a photon emitted per photon that has been absorbed. This is the fluorescence quantum yield Ø where the summation in the denominator goes over all processes that lead to a lost of the excited state population. In order to have materials that will be good for displays, it is beneficial for the quantum yield to be as large as possible. In the case of the pi conjugated molecules, most of the time the range will be in nanoseconds. But for fluorescence, the range is in microseconds as well but the systems that will be dealt with go from nanoseconds to 10 nanoseconds (10⁹, to 10⁸ per second). Even with up to 10⁶ per second (microseconds), it can still be fluorescence.

Intersystem Crossing

Molecules can also change their spin multiplicity, thus going from a singlet state to a triplet state this process called intersystem crossing is formally quantum mechanically forbidden and consequently the rate constant is usually rather small k_isc is typically 10^-1 -10⁵ sec^-1 Chemical substitution and certain vibrations can increase this rate dramatically.

Phosphorescence

Phosphorescence is the process by which light is emitted upon relaxation from a state of different spin quantum number��since processes involving change of spin quantum number are quantum mechanically forbidden, the probability of phosphorescence is low and the rate constant for phosphorescence is typically very small, 10^-2 - 10⁴ sec^-1