Molecular Fluorescence

166 6 Principles of steady-state and time-resolved fluorometric techniques

Fig. 6.4. Schematic diagram showing how the four intensity components are measured for determination of the steady-state anisotropy.

The excitation polarization spectrum (which represents the variation of r as a function of the excitation wavelength; see Chapter 5) is obtained by recording the variations of IVVðlEÞ, IVHðlEÞ, IHVðlEÞ, and IHHðlEÞ and by calculating rðlEÞ by means of Eq. (6.8) with GðlEÞ ¼ IVHðlEÞ=IHHðlEÞ. The correction factors for wavelength dependence can be ignored because they cancel out in the ratio.

6.2 Time-resolved fluorometry 167

In some cases, filters are used instead of the emission monochromator. In principle, no G factor is then considered, but in practice, e ects may be due to the sensitivity of the photomultipliers to polarization (in particular, photomultipliers with side-on photocathodes).

6.2

Time-resolved fluorometry

Knowledge of the dynamics of excited states is of major importance in understanding photophysical, photochemical and photobiological processes. Two time-resolved techniques, pulse fluorometry and phase-modulation fluorometry, are commonly used to recover the lifetimes, or more generally the parameters characterizing the d-pulse response of a fluorescent sample (i.e. the response to an infinitely short pulse of light expressed as the Dirac function d).

Pulse fluorometry uses a short exciting pulse of light and gives the d-pulse response of the sample, convoluted by the instrument response. Phase-modulation fluorometry uses modulated light at variable frequency and gives the harmonic response of the sample, which is the Fourier transform of the d-pulse response. The first technique works in the time domain, and the second in the frequency domain. Pulse fluorometry and phase-modulation fluorometry are theoretically equivalent, but the principles of the instruments are di erent. Each technique will now be presented and then compared.

6.2.1

General principles of pulse and phase-modulation fluorometries

The principles of pulse and phase-modulation fluorometries are illustrated in Figures 6.5 and 6.6. The d-pulse response IðtÞ of the fluorescent sample is, in the simplest case, a single exponential whose time constant is the excited-state lifetime, but more often it is a sum of discrete exponentials, or a more complicated function; sometimes the system is characterized by a distribution of decay times. For any excitation function EðtÞ, the response RðtÞ of the sample is the convolution product of this function by the d-pulse response:

Pulse fluorometry The sample is excited by a short pulse of light and the fluorescence response is recorded as a function of time. If the duration of the pulse is long

8)The convolution integral appearing in this equation can be easily understood by considering the excitation function as successive Dirac functions at various times t.

168 6 Principles of steady-state and time-resolved fluorometric techniques

Fig. 6.5. Principles of time-resolved fluorometry.

with respect to the time constants of the fluorescence decay, the fluorescence response is the convolution product given by Eq. (6.9): the fluorescence intensity increases, goes through a maximum and becomes identical to the true d-pulse response iðtÞ as soon as the intensity of the light pulse is negligible (Figure 6.6). In this case, data analysis for the determination of the parameters characterizing the d-pulse response requires a deconvolution of the fluorescence response (see Section 6.2.5).

Phase-modulation fluorometry The sample is excited by a sinusoidally modulated light at high frequency. The fluorescence response, which is the convolution product (Eq. 6.9) of the d-pulse response by the sinusoidal excitation function, is sinusoidally

6.2 Time-resolved fluorometry 169

Fig. 6.6. Principles of pulse fluorometry and multi-frequency phase-modulation fluorometry.

modulated at the same frequency but delayed in phase and partially demodulated with respect to the excitation. The phase shift F and the modulation ratio M (equal to m=m0), i.e. the ratio of the modulation depth m (AC/DC ratio) of the fluorescence and the modulation depth of the excitation m0; see Figure 6.5) characterize the harmonic response of the system. These parameters are measured as a function of the modulation frequency. No deconvolution is necessary because the data are directly analyzed in the frequency domain (Figure 6.6).

6.2 Time-resolved fluorometry 171

If the d-pulse response is not normalized according to Eq. (6.12), then Eqs (6.16) and (6.17) should be replaced by

In practice, the phase shift F and the modulation ratio M are measured as a function of o. Curve fitting of the relevant plots (Figure 6.6) is performed using the theoretical expressions of the sine and cosine Fourier transforms of the d-pulse response and Eqs (6.23) and (6.24). In contrast to pulse fluorometry, no deconvolution is required.

General relations for single exponential and multi-exponential decays For a single exponential decay, the d-pulse response is

172 6 Principles of steady-state and time-resolved fluorometric techniques

For a multi-exponential decay with n components, the d-pulse response is

Xn

Note that the fractional intensity of component i, i.e. the fractional contribution of component i to the total steady-state intensity is

i¼1

Using Eqs (6.18) and (6.19), the sine and cosine Fourier transforms, P and Q , are given by

P

i¼1

These equations are to be used in conjunction with Eqs (6.23) and (6.24) giving F and M.

When the fluorescence decay of a fluorophore is multi-exponential, the natural way of defining an average decay time (or lifetime) is:

i¼1

In this definition, each decay time is weighted by the corresponding fractional intensity. This average is called the intensity-averaged decay time (or lifetime).

Another possibility is to use the amplitudes (pre-exponential factors) as weights:

174 6 Principles of steady-state and time-resolved fluorometric techniques

Fig. 6.7. Schematic diagram of a single-photon timing fluorometer.

depends on the complexity of the d-pulse response of the system; for instance, a high accuracy is necessary for recovering a distribution of decay times.

When deconvolution is required, the time profile of the exciting pulse is recorded under the same conditions by replacing the sample with a scattering solution (Ludox (colloidal silica) or glycogen).

It is important to note that the number of fluorescence pulses must be kept much smaller than the number of exciting pulses (< 0.01–0.05 stops per pulse), so