Molecular Fluorescence

and after addition of a given amount of cation at a concentration cM, the absorbance or the fluorescence intensity becomes

Y ¼ a½L& þ b½ML& þ c½M2L& ðB:26Þ

where a, b and c include the molar absorption coe cients (and fluorescence quantum yields) of M, ML and M2L, respectively.

In the presence of an excess of cation so that the complex M2L only is present, Y reaches the limiting value Ylim:

where b21 ¼ K11K21. If the approximation ½M&AcM is valid, K11 and b21 can be determined by a nonlinear least-squares analysis of Y versus cM. Ylim can also be left

as a floating parameter in the analysis, if necessary. It should be noted that there is no explicit expression for Y versus cM if the approximation ½M&AcM is not valid.

Cooperativity

When a ligand can complex more than one cation, the question arises of possible cooperative binding. There are many definitions of cooperativity but they are all consistent with the following criterion (Connors, 1987). A system is

.non-cooperative if the ratio Kðiþ1Þ1=Ki1 is equal to the statistical value calculated when all binding sites are identical and independent. These statistical values are

given in Table 10.B.1.

. positively cooperative if the ratio Kðiþ1Þ1=Ki1 is larger than the statistical value.

348 10 Fluorescent molecular sensors of ions and molecules

Fig. 10.B.2. Job’s plots for a 1:1 complex according to Eq. (B.41). The ratio b=a is chosen to be equal to 2.

Plots of y=y0 ð1 xÞ versus x are drawn in Figure 10.B.2 for b=a ¼ 2 and various values of KsC. The sharpness of the maximum, and therefore the accuracy with which xmax is located, depends on the magnitude of this parameter. Curve fitting with Eq. (B.41) yields Ks.

Molecular Fluorescence: Principles and Applications. Bernard Valeur

> 2001 Wiley-VCH Verlag GmbH

ISBNs: 3-527-29919-X (Hardcover); 3-527-60024-8 (Electronic)

351

11

Advanced techniques in fluorescence spectroscopy

11.1

Time-resolved fluorescence in the femtosecond time range: fluorescence upconversion technique

Chapter 6 described the current techniques employed in time-resolved fluorescence spectrocopy. The time resolution of these techniques ranges from a few picoseconds (streak cameras) to a few hundreds of picoseconds (single-photon timing with flash lamp excitation). The time resolution can be greatly improved by using the fluorescence up-conversion technique.

A schematic diagram illustrating this technique is shown in Figure 11.1. A laser source provides an ultra-short pulse (duration of 50–100 fs) at wavelength l1 corresponding to frequency o1. The second harmonic (frequency o2) is generated in a nonlinear crystal and separated from the fundamental light by a dichroic beam splitter. The probe pulse at frequency o1 passes through an optical delay line, and the excitation pulse at frequency o2 is focused on the sample. The incoherent fluorescence (frequency ofl) emitted by the sample is collected and mixed with the

352 11 Advanced techniques in fluorescence spectroscopy

Fig. 11.1. Principles of fluorescence up-conversion. NLC: nonlinear crystal; DM: dichroic mirror; HW: half-wave plate; PM: photomultiplier.

probe pulse o1 in a nonlinear crystal. This frequency mixing generates light at the sum frequency, osum ¼ o1 þ ofl1), provided that there is a spatial and temporal coincidence of the o1 and ofl beams. The greater the delay time between the probe pulse o1 and the fluorescence beam ofl, the smaller the fluorescence intensity2). The fluorescence intensity versus time is thus obtained by varying the delay time (ajustable thanks to the optical delay line), and by measuring the intensity of the sum frequency light for each delay time.

Currently used nonlinear optical crystals are potassium dihydrogen phosphate (KDP) and barium borate (BBO). Compared to KDP, the advantages of BBO are its transparency in the UV and its larger quantum e ciency of up-conversion by a factor of 4–6. For a given position of the crystal, only a narrow band of the fluorescence spectrum is up-converted. Therefore, if the full fluorescence spectrum is of interest, the crystal must be rotated at a series of angles. An example of experimental set-up is presented in Figure 11.2. The fwhm of the response is 210 fs.

Various ultrafast phenomena occuring in the femtosecond time-scale in the condensed phase have been studied by fluorescence up-conversion (for a review, see Mialocq and Gustavsson, 2001). As already mentioned in Chapter 7 (Box 7.1),

11.2 Advanced fluorescence microscopy 353

fluorescence up-conversion is the method of choice to study solvation dynamics. Moreover, this technique is well suited to the investigation of photoinduced intramolecular processes (e.g. charge transfer, proton transfer) and intermolecular processes (e.g. electron transfer). Applications to the study of light-driven biological processes have also been reported (e.g. photoactive yellow protein, blue fluorescent protein (mutant of the green fluorescent protein)).

11.2

Advanced fluorescence microscopy

Fluorescence microscopy is principally used for the investigation of living cells and tissues by biologists and physiologists, but it is also a powerful tool to study chemical systems such as colloids, liquid crystals, polymer blends, photodegradation of naturally occurring polymers, dyeing of fibers and measurement of the glass transition temperature (Davidson, 1996). This section will focus on the improvements in conventional fluorescence microscopy and to the development of time-resolved fluorescence microscopy.

11.2.1

Improvements in conventional fluorescence microscopy

A conventional fluorescence microscope di ers from a standard microscope by the light source (mercury or xenon lamp), which produces UV–visible light. The excitation wavelength is selected by an interference filter or a monochromator. Observation of the fluorescence is made by eye, photographic film or CCD (charge-