The Stokes Shift

For most purposes only the Stokes-shifted Raman spectmm, which results from molecules in the ground electronic and vibrational states being excited, is measured and reported. Anti-Stokes spectra arise from molecules in vibrational excited states returning to the ground state. The relative intensities of the Stokes and anti-Stokes bands are proportional to the relative populations of the ground and excited vibrational states. These proportions are temperature-dependent and foUow a Boltzmann distribution. At room temperature, the anti-Stokes Stokes intensity ratio decreases by a factor of 10 with each 480 cm from the exciting frequency. Because of the weakness of the anti-Stokes spectmm (except at low frequency shift), the most important use of this spectmm is for optical temperature measurement (qv) using the Boltzmann distribution function. 

Also, using dyes as laser media or passive mode-locked compounds requires numerous special parameters, the most important of which ate the band position and bandwidth of absorption and fluorescence, the luminiscence quantum efficiency, the Stokes shift, the possibiHty of photoisomerization, chemical stabiHty, and photostabiHty. AppHcations of PMDs in other technical or scientific areas have additional special requirements. 

Typical absorption and fluorescence spectra are shown in Figure 11.3. Since energy is lost in the activated state (S ) before fluorescence, the emission maximum always occurs at a lower wavenumber than the absorption maximum. The difference, which is termed the Stokes shift, can be calculated approximately from the absorption spectrum using the Pestemer rule [17,18]. This rule states that the Stokes shift is 2.5 times the half-bandwidth at the absorption maximum. 

For the following reasons the Stokes shift of an FBA should not be too large ... 

Fig. 1 Jablonski diagram of energy level for describing processes absorption, fluorescence and phosphorescence in complex molecules where kf and /c arc the radiative and nonradiative rates of fluorescence, respectively, kj and kTnr are the radiative and nonradiative rates of phosphorescence, respectively, k-lsc is the interconversion rate, and kmt is the rate of intermolecular processes Av denotes the Stokes shift of fluorescence...

Evidence for specific solvent-solute interactions can be seen in the Lippert or others solvatochromic plots. One notices that the Stokes shift is generally larger in H-bonding solvents (water, alcohols) than in solvents with less probability to form... 

H-bonds. Such behavior of the Stokes shifts in protic solvents is typical for specific solvent-solute interactions, and has been seen for many solutes phthalimides, FLs, oxazines, and others [1, 2, 4, 50, 51, 72-74]. 

Another important feature of fluorophores is the amount of vibrational energy lost in the excited state. The difference between emission and excitation maxima gives a readout in this respect and is referred to as the Stokes shift. In many sensors, a small Stokes shift is unfavorable for FRET ratio measurements due to overlap of emission spectra. 

A small fraction of the molecules are in vibrationally excited states. Raman scattering from vibrationally excited molecules leaves the molecule in the ground state. The scattered photon appears at higher energy, as shown in Figure lb. This anti-Stokes-shifted Raman spectrum is always weaker than the Stokes-shifted spectrum, but at room temperature it is strong enough to be useful for vibrational frequencies less than about 1500 cm 1. The Stokes and anti-Stokes spectra contain the same frequency information. 

Stokes shift The difference between the absorption maximum and emission maximum of fluorescent dyes or fluorophores. The Stokes shift is... 

Since the same dye molecules can serve as both donors and acceptors and the transfer efficiency depends on the spectral overlap between the emission spectrum of the donor and the absorption spectrum of the acceptor, this efficiency also depends on the Stokes shift [53]. Involvement of these effects depends strongly on the properties of the dye. Fluoresceins and rhodamines exhibit high homo-FRET efficiency and self-quenching pyrene and perylene derivatives, high homo-FRET but little self-quenching and luminescent metal complexes may not exhibit homo-FRET at all because of their very strong Stokes shifts. 

Fig. 1.6. Strategy for the choice of a fluorescent probe. Av, , and t are the Stokes shift, quantum yield and lifetime, respectively (see definitions in Chapter 3).

In general, the differences between the vibrational levels are similar in the ground and excited states, so that the fluorescence spectrum often resembles the first absorption band ( mirror image rule). The gap (expressed in wavenumbers) between the maximum of the first absorption band and the maximum of fluorescence is called the Stokes shift. 

This important parameter can provide information on the excited states. For instance, when the dipole moment of a fluorescent molecule is higher in the excited state than in the ground state, the Stokes shift increases with solvent polarity. The consequences of this in the estimation of polarity using fluorescent polarity probes is discussed in Chapter 7. 

From a practical point of view, the detection of a fluorescent species is of course easier when the Stokes shift is larger. 

Fig. 3.3. Definition of the Stokes shift. Examples of Stokes shift benzoxazinone derivative (BOZ 7) and rhodamine 6G.

Rhodamines (e.g. rhodamine 6G, rhodamine B) were among the first fluorescent dyes to be used as laser dyes. In contrast to coumarins, their absorption and emission spectra are quite narrow and the Stokes shift is small. They emit fluorescence in the range 500-700 nm. 

This expression of the Stokes shift depends only on the absolute magnitude of the charge transfer dipole moment A//g(. — and not on the angle between the... 

A similar sharp red emission exhibit squarylium dyes like the squarylium cyanine dye 64, which emits 650nm [152]. Unfortunately, the Stokes shift is rather small, which leads to high reabsorption. A number of other red emitting dyes have been exploited as well [153-156]. 

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