Molecular Fluorescence

98 4 Effects of intermolecular photophysical processes on fluorescence emission

Fig. 4.8. Fluorescence decays of the monomer and the excimer. (a) Dissociation of the excimer within excited-state lifetime. (b) No dissociation of the excimer.

Under conditions in which the dissociation rate of the excimer is slow with respect to de-excitation, Eq. (4.48) is reduced to

These equations show that the ratio IE=IM is proportional to the rate constant k1 for excimer formation. Assuming that the Stokes–Einstein relation (Eq. 4.12) is valid, k1 is proportional to the ratio T=h, h being the viscosity of the medium. Application to the estimation of the fluidity of a medium will be discussed in Chapter 8.

When the two monomers are linked by a short flexible chain, intramolecular excimers can be formed. This process is still di usion-controlled, but in contrast to the preceding case, it is not translational; it requires a close approach between the two molecules via internal rotations during the excited-state lifetime. Equations (4.44), (4.45), (4.47) to (4.49) are still valid after replacing k1½M& by k1 because intramolecular excimer formation is independent of the total concentration. Estimation of the local fluidity of a medium can be achieved by means of probes capable of forming intramolecular excimers (see Chapter 8).

In some cases, a monomer in the ground state may already be close to another monomer (e.g. in polymers with pendant fluorophores or on solid surfaces with adsorbed or covalently linked fluorophores), so that the displacement and the rotation required to attain the favorable excimer conformation occurs very quickly. These excimers are called ‘excimer-like’ or ‘preformed excimers’, in contrast to the normal case of ‘true excimers’. The rise time corresponding to excimer formation may not be detected with instruments whose time resolution is of a few picoseconds.

A popular method for the determination of micellar aggregation numbers is based on self-quenching of pyrene by excimer formation within micelles (see Box 4.2).

4.5 Photoinduced proton transfer 99

Fig. 4.9. Fluorescence spectra of anthracene (3 10 4

mol L 1) in the presence of diethylaniline at various concentrations in toluene. 1: 0 mol L 1; 2: 5 10 3 mol L 1; 3: 2:5 10 2 mol L 1; 4: 0.10 mol L 1 (from Weller, A. (1967), in Claesson S. (Ed.), Fast Reactions and Primary Processes in Chemical Kinetics, John Wiley & Sons, New York).

4.4.2

Exciplexes

A well-known example of an exciplex is the excited-state complex of anthracene and N,N-diethylaniline resulting from the transfer of an electron from an amine molecule to an excited anthracene molecule. In nonpolar solvents such as hexane, the quenching is accompanied by the appearance of a broad structureless emission band of the exciplex at higher wavelengths than anthracene (Figure 4.9). The kinetic scheme is somewhat similar to that of excimer formation.

When the solvent polarity increases, the exciplex band is red-shifted. The intensity of this band decreases as a result of the competition between de-excitation and dissociation of the exciplex.

It should be noted that de-excitation of exciplexes can lead not only to fluorescence emission but also to ion pairs and subsequently ‘free’ solvated ions. The latter process is favored in polar media. Exciplexes can be considered in some cases to be intermediate species in electron transfer from a donor to an acceptor (see Section 4.3).

4.5

Photoinduced proton transfer

This section will only cover reactions in aqueous solutions. Water molecules acting as either a proton acceptor or a proton donor will thus be in close contact with an acid or a base undergoing excited-state deprotonation or protonation, respectively. Therefore, these processes will not be di usion-controlled (Case A in Section 4.2.1).

The acidic or basic properties of a molecule that absorbs light are not the same in the ground state and in the excited state. The redistribution of the electronic density upon excitation may be one of the possible causes of this observation. The most interesting cases are those where acids and bases are stronger in the excited state

100 4 Effects of intermolecular photophysical processes on fluorescence emission

than in the ground state, because in these cases, excitation may trigger a photoinduced proton transfer. Then, the acidic character of a proton donor group (e.g. OH substituent of an aromatic ring) can be enhanced upon excitation so that the pK of this group in the excited state is much lower than the pK in the ground state (Table 4.4). In the same way, the pK of a proton acceptor group (e.g. heterocyclic nitrogen atom) in the excited state is much higher than in the ground state (pK) (Table 4.4).

The occurrence of excited-state proton transfer during the lifetime of the excited state depends on the relative rates of de-excitation and proton transfer. The general equations will be presented first, but only for the most extensively studied case where the excited-state process is proton ejection (pK < pK); the proton donor is thus an acid, AH , and the proton acceptor is a water molecule. Methods for the determination of pK are then described and finally, the various cases of pH dependence of the absorption and fluorescence spectra are examined.

4.5.1

General equations

Let us consider the possible events following excitation of an acid AH that is stronger in the excited state than in the ground state (pK < pK). In the simplest case, where there is no geminate proton recombination, the processes are presented in Scheme 4.6, where t0 and t00 are the excited-state lifetimes of the acidic (AH ) and basic (A ) forms, respectively, and k1 and k 1 are the rate constants for deprotonation and reprotonation, respectively. k1 is a pseudo-first order rate constant, whereas k 1 is a second-order rate constant. The excited-state equilibrium constant is K ¼ k1=k 1.7)

The question arises as to whether or not the back-reaction can take place during the excited-state lifetime of A . Because this reaction is di usion-controlled (k 1 A5 1010 L mol 1 s 1), its rate is pH-dependent. If pH a2, the back-reaction must be taken into account because at this pH, k 1½H3Oþ& 95 108 s 1. The reciprocal of this value is indeed of the order of the excited-state lifetime of most organic bases.

The time evolution of the fluorescence intensity of the acidic form AH and the basic form A following d-pulse excitation can be obtained from the di erential equations expressing the evolution of the species. These equations are written

7)k1 and k 1 are normalized so that K is dimensionless.

where X ¼ k1 þ 1=t0 and Y ¼ 1=t00 . Therefore, iAH ðtÞ becomes a single exponential and iA ðtÞ is still a di erence of two exponentials with a rise time ð1=XÞ (equal to the decay time of AH ), and a decay time ð1=YÞ (equal to the lifetime of the basic form).

The steady-state intensities reduce to

4.5.2

Determination of the excited-state pK

4.5.2.1 Prediction by means of the Fo¨rster cycle

pK can be theoretically predicted by means of the Fo¨rster cycle (Scheme 4.7) in conjunction with spectroscopic measurements.

According to this cycle, we have

where DH0 and DH0 are the standard molar ionization enthalpies of AH and AH , respectively, hnAH and hnA are the energy di erences (corresponding to the 0–0 transitions) between the excited state and the ground state of AH and A , respectively, and Na is Avogadro’s number. This equation can be rewritten as

Scheme 4.7