Molecular Fluorescence

6.2 Time-resolved fluorometry 195

Decomposition in real time is possible by measuring Fl and Ml as a function of wavelength at a single frequency and by calculating Pl and Ql by means of Eqs (6.21) and (6.22)

f1l; f2l and f3l are then solutions of the system of Eqs (6.55) to (6.57).

6.2.10

Comparison between pulse and phase fluorometries

Comparison between the two techniques will be presented from three points of view: theoretical, instrumental and methodological.

(i)Pulse and phase fluorometries are theoretically equivalent: they provide the same kind of information because the harmonic response is the Fourier transform of the d-pulse response.

(ii)From the instrumental point of view, the latest generations of instruments use both pulsed lasers and microchannel plate detectors. Only the electronics are di erent. Because the time resolution is mainly limited by the time response of the detector, this parameter is the same for both techniques. Moreover, the optical module is identical so the total cost of the instruments is similar.

(iii)The methodologies are quite di erent because they are relevant to time domain

and frequency domain. The advantages and drawbacks are as follows:

. Pulse fluorometry permits visualization of the fluorescence decay, whereas

visual inspection of the variations of the phase shift versus frequency does not allow the brain to visualize the inverse Fourier transform!

.Pulse fluorometry using the single-photon timing technique has an outstanding sensitivity: experiments with very low levels of light (e.g. owing to low quantum yields or strong quenching) simply require longer acquisition times (but attention must be paid to the possible drift of the excitation source), whereas in phase fluorometry, the fluorescence intensity must be high enough to get an analog signal whose zero crossing (for phase measurements) and amplitude (for modulation measurements) can be mea-

sured with enough accuracy.

.No deconvolution is necessary in phase fluorometry, while this operation is often necessary in pulse fluorometry and requires great care in recording the

instrument response, especially for very short decay times.

.The well-defined statistics in single-photon counting is an advantage for data analysis. In phase fluorometry, the evaluation of the standard deviation of

phase shift and modulation ratio may not be easy.

.Time-resolved emission anisotropy measurements are more straightforward in pulse fluorometry.

196 6 Principles of steady-state and time-resolved fluorometric techniques

. Time-resolved spectra are more easily recorded in pulse fluorometry.

.Lifetime-based decomposition of spectra into components is simpler in phase fluorometry.

.The time of data collection depends on the complexity of the d-pulse response. For a single exponential decay, phase fluorometry is more rapid. For complex d-pulse responses, the time of data collection is about the same for the two techniques: in pulse fluorometry, a large number of photon events is necessary, and in phase fluorometry, a large number of frequencies has to be selected. It should be emphasized that the short acquisition time for phase shift and modulation ratio measurements at a given frequency is a distinct advantage in several situations, especially for lifetime-imaging spectroscopy.

In conclusion, pulse and phase fluorometries each have their own advantages and drawbacks. They appear to be complementary methods and are by no means competitive.

6.3

Appendix: Elimination of polarization e ects in the measurement of fluorescence intensity and lifetime

When the fluorescence is polarized, the use of polarizers with appropriate orientations allows detection of a signal proportional to the total fluorescence intensity.

The angles y and f will characterize the transmission directions of the polarizers introduced in the excitation and emission beam (Figure 6.16). Let us consider first the relations between the components of the fluorescence intensity Ix; Iy; Iz

Fig. 6.16. Definition of angles y and f characterizing the transmission directions of the polarizers introduced in the excitation and emission beam.

6.3 Appendix: Elimination of polarization effects 197

depending on angle y. According to symmetry considerations explained in Chapter 5, we have:

for vertical excitation ðy ¼ 0 Þ:

Iz ¼ Ik

Ix ¼ Iy ¼ I?

I ¼ Ix þ Iy þ Iz ¼ Ik þ 2I?

for horizontal excitation ðy ¼ 90 Þ:

Ix ¼ Ik

Iy ¼ Iz ¼ I?

I ¼ Ix þ Iy þ Iz ¼ Ik þ 2I?

Now, for a given angle y, excitation can be considered as the superimposition of two beams, one vertically polarized with a weight of cos2 y, and the other horizontally polarized with a weight of sin2 y. Therefore, the intensity components are

Ix ¼ Ik sin2 y þ I? cos2 y

Iz ¼ Ik cos2 y þ I? sin2 y

Iy ¼ I?

I ¼ Ix þ Iy þ Iz ¼ Ik þ 2I?

The total fluorescence intensity is thus again equal to Ik þ 2I?. This equality is therefore valid whatever the value of y.

Regarding the intensity observed in the Ox direction without a polarizer, Ix is not detected and thus Iobs ¼ Iy þ Iz. With a polarizer at an angle f with respect to the vertical, the observed intensity becomes

Iobs ¼ Iy sin2 f þ Iz cos2 f

Taking into account the y-dependent expressions for Iy and Iz, we obtain

Iobs ¼ I? sin2 f þ ðIk cos2 y þ I? sin2 yÞ cos2 f

¼ Ik cos2 y cos2 f þ I?ðsin2 f þ sin2 y cos2 fÞ

Because we want this observed intensity to be proportional to the total intensity, i.e. Ik þ 2I?, the condition to be fulfilled is:

2 cos2 y cos2 f ¼ sin2 f þ sin2 y cos2 f

7.1 What is polarity? 201

tion of chemical equilibria. Such a solvent dependence is also observed for the spectral bands of individual species measured by various spectrometric techniques (UV–visible and infrared spectrophotometries, fluorescence spectroscopy, NMR spectrometry, etc.).

It was mentioned in Chapters 2 and 3 that broadening of the absorption and fluorescence bands results from fluctuations in the structure of the solvation shell around a solute (this e ect, called inhomogeneous broadening, superimposes homogeneous broadening because of the existence of a continuous set of vibrational sublevels). Moreover, shifts in absorption and emission bands can be induced by a change in solvent nature or composition; these shifts, called solvatochromic shifts, are experimental evidence of changes in solvation energy. In other words, when a solute is surrounded by solvent molecules, its ground state and its excited state are more or less stabilized by solute–solvent interactions, depending on the chemical nature of both solute and solvent molecules. Solute–solvent interactions are commonly described in terms of Van der Waals interactions and possible specific interactions like hydrogen bonding. What is the relationship between these interactions and ‘polarity’?

To answer this question, let us first consider a neutral molecule that is usually said to be ‘polar’ if it possesses a dipole moment (the term ‘dipolar’ would be more appropriate)1). In solution, the solute–solvent interactions result not only from the permanent dipole moments of solute or solvent molecules, but also from their polarizabilities. Let us recall that the polarizability a of a spherical molecule is defined by means of the dipole mi ¼ aE induced by an external electric field E in its own direction. Figure 7.1 shows the four major dielectric interactions (dipole– dipole, solute dipole–solvent polarizability, solute polarizability–solvent dipole, polarizability–polarizability). Analytical expressions of the corresponding energy terms can be derived within the simple model of spherical-centered dipoles in isotropically polarizable spheres (Suppan, 1990). These four non-specific dielectric in-

Fig. 7.1. Dielectric solute–solvent interactions resulting from the dipole moments and average polarizabilities (from Suppan, 1990).

202 7 Effect of polarity on fluorescence emission. Polarity probes

teractions should be distinguished from specific interactions such as hydrogen bonding.

To describe solvatochromic shifts, an additional energy term relative to the solute should be considered. This term is related to the transition dipole moment that results from the migration of electric charges during an electronic transition. Note that this transient dipole has nothing to do with the di erence me mg between the permanent dipole moment in the excited state and that in the ground state.

After these preliminary remarks, the term ‘polarity’ appears to be used loosely to express the complex interplay of all types of solute–solvent interactions, i.e. nonspecific dielectric solute–solvent interactions and possible specific interactions such as hydrogen bonding. Therefore, polarity cannot be characterized by a single parameter, although the ‘polarity’ of a solvent (or a microenvironment) is often associated with the static dielectric constant e (macroscopic quantity) or the dipole moment m of the solvent molecules (microscopic quantity). Such an oversimplification is unsatisfactory.

In reality, underlying the concept of polarity, solvation aspects with the relevant solvation energy should be considered. As noticed by Suppan (1990), each term of the solvation energy Esolv is a product of two factors expressing separately the polar characteristics P of the solute and the polar characteristics P of the solvent (Esolv ¼ PP). Suppan has emphasized that P and P are not simple numbers, but matrices describing the properties of the solute molecule (dipole moment, polarizability, transition moment, hydrogen bonding capability) and the solvent molecule (dielectric constant, refractive index, hydrogen bonding capability). This approach is conceptually interesting but it has not so far permitted quantitative evaluation of polarity.

7.2

Empirical scales of solvent polarity based on solvatochromic shifts

Compounds are called solvatochromic when the location of their absorption (and emission) spectra depend on solvent polarity. A bathochromic (red) shift and a hypsochromic (blue) shift with increasing solvent polarity pertain to positive and negative solvatochromism, respectively. Such shifts of appropriate solvatochromic compounds in solvents of various polarity can be used to construct an empirical polarity scale (Reichardt, 1988; Buncel and Rajagopal, 1990).

7.2.1

Single-parameter approach

Kosower in 1958 was the first to use solvatochromism as a probe of solvent polarity. The relevant Z-scale is based on the solvatochromic shift of 4-methoxycarbonyl-1- ethylpyridinium iodide (1). Later, Dimroth and Reichardt suggested using betain dyes, whose negative solvatochromism is exceptionally large. In particular, 2,6-