This work will be based on fluorescent organic dyes. Therefore, a short introduction into fluorescence will be given in this section, which is based mainly on [70].
The emission of a photon due to the transition of an electronic system from a higher energetic state to a lower energetic state is called luminescence. If the excitation is the result of the absorption of another photon, the luminescence is called photoluminescence. Fluorescence is a special form of photoluminescence. In the case
between the energy of absorption and emission is called the Stokes shift. Phosphorescence is a different type of photoluminescence, characterized by a time delay between absorption and emission.
Fig. 4.6: Energy diagram that illustrates the three processes involved in fluorescence: absorption of a photon, vibrational relaxation, and emission of a photon. The excitation usually starts from the electronic ground state (S0) and the lowest vibrational level (v0=0). The absorption of a photon
excites the molecule to higher electronic and vibrational levels. Vibrational relaxation to the lowest vibrational level of the excited electronic state occurs before emission of a photon and the return of the molecule to the ground state. The vibronic transitions during absorption and emission happen so fast that the nuclear distances of the atoms in the molecule cannot adjust. That is why the transitions are represented as vertical lines. The probability of a transition is determined by the overlap of the vibrational wave function (Franck-Condon principle).
4.1 Introduction to fluorescent concentrators
In organic fluorescent dyes, the fluorescence is caused by the transitions between electronic states of rather complex organic molecules. The energy states of the molecule are determined by its electronic states, the vibrational modes of the molecule, and by its rotational modes. The electronic state determines the distribution of negative charge and the overall molecular geometry. The different electronic states depend on the total electron energy and the symmetry of various electron spin states. Each electronic state is further subdivided into a number of vibrational and rotational energy levels. The difference in energy between two neighboring electronic states usually corresponds to the energy of photons in the ultraviolet and visible spectral range. For comparison, the difference of the vibrational states corresponds to the near-infrared and the difference of the rotational states to the far infrared and the microwave range. In the frame of this work, only the electronic states and the vibrational modes are relevant.
Fluorescence involves three important processes: absorption of a photon, vibrational relaxation, and emission of a photon. They are illustrated in Fig. 4.6.
At room temperature, most molecules are in their ground state (S0) and also at the
lowest vibrational level (v0=0). In consequence, most excitation processes originate
from this level. The excitation by an incoming photon happens in femtoseconds (10-15s), which is the time necessary for a photon to travel the distance of a single
wavelength. For most organic molecules, the ground state is an electronic singlet state, which means that all electrons are spin-paired (have opposite spins). Normally, the excitation of a molecule takes place without a change in electron spin-pairing, so the excited state is also a singlet (S1).
Light in the visible or ultraviolet range usually excites higher vibrational levels of the excited electron level (v1>0). After the absorption of the photon several processes can
occur, but most likely is relaxation to the lowest vibrational energy level of the first excited state (v1=0). This process is called vibrational relaxation. This relaxation takes
picoseconds or less. The excess vibrational energy is dissipated as heat. Because of this relaxation, emission spectra are generally independent of the excitation wavelength, which is known as the Kasha rule. However, there are also materials that show exceptions to this rule.
After a relatively long period of nanoseconds, a photon is emitted and the molecule returns to its ground state. As mentioned before, the excitation started from the ground state to higher vibrational levels of the excited electronic state, and then energy was
vibrational level. It is likely that directly after the emission the molecule is at a higher vibrational level of the electronic ground state and relaxes subsequently to lower vibrational levels. In consequence, the energy of the emitted photon is lower than that of the absorbed photon, which results in the Stokes shift.
During absorption and emission, the electronic energy and the vibrational energy change simultaneously. Those simultaneous changes are called vibronic transitions. The probability of the vibronic transitions, and therefore the shape of the absorption and the emission spectra, is determined by the overlap of the vibrational wave functions of the states involved in the transition: the larger the overlap, the more likely is the transition (see also Fig. 4.6). This rule is also known as the Franck-Condon principle.
Fig. 4.7: Jablonski Energy Diagram showing the different energy states of a molecule and the possible transitions between them. In addition to Fig. 4.6, internal conversion from higher excited singlet states (S2), intersystem
4.1 Introduction to fluorescent concentrators
Several other relaxation pathways compete with the fluorescence emission. They are illustrated in Fig. 4.7. One process is that the excited state energy is dissipated non- radiatively as heat. Alternatively, intersystem crossing can occur, which causes phosphorescence. During intersystem crossing the energy is transferred from the electronic singlet state to a triplet state. Because spin conversion is necessary for this transition, it is relatively unlikely. The transition from the excited triplet state to the singlet ground state by emission of a photon is forbidden by spin selection rules. However, due to several effects it becomes possible, but rate constants remain small. In consequence, the excited triplet state can be long-lived and the emission can occur long after the absorption of a photon.
As discussed extensively e.g. in [47], the non-radiative processes become more likely for a small energy difference between ground state and excited state, while the radiative transitions become less frequent. In consequence, the quantum efficiency of dyes emitting at longer wavelengths and especially in the infrared is lower for principal reasons.
4.1.5.1 Angular anisotropy of fluorescence
When a fluorescent molecule absorbs an incident photon, the excitation arises from an interaction between the oscillating electric field of the incoming radiation and the transition dipole moment created by the electronic state of the molecular orbitals. The molecules preferentially absorb photons that have an electric field vector aligned parallel to the molecule’s absorption transition dipole moment. The fluorescence emission occurs in a plane that is defined by the direction of the emission transition dipole moment. The directions of the transition dipole moments are determined by the molecular structure. Because of changes in the molecular structure due to the excitation, the directions of absorption and emission can differ. Rotation of the molecule further depolarizes the emission in respect to the excitation vector. The molecule’s size and the rigidity of the molecule’s environment therefore determine how strongly the direction of the emission is coupled to the direction of excitation. In the case of fluorescent concentrators, the light impinges from one direction onto the fluorescent concentrator. Therefore the polarization vectors are aligned in one plane. The matrix material of fluorescent concentrators, in which the molecules are embedded, is a rather rigid polymer. In consequence, an angular anisotropy of the emission remains, which is subsequently reduced by reabsorption.