Autocorrelation fluorescence

Figure 8.3 Interferometric autocorrelation traces of the fluorescence intensities of perylene (a) and anthracene (b) microcrystals irradiated by two NIR Cr F laser pulses centered at 1.26 Xm with the same intensity.

Fluorescence intensity detected with a confocal microscope for the small area of diluted solution temporally fluctuates in sync with (i) motions of solute molecules going in/out of the confocal volume, (ii) intersystem crossing in the solute, and (hi) quenching by molecular interactions. The degree of fluctuation is also dependent on the number of dye molecules in the confocal area (concentration) with an increase in the concentration of the dye, the degree of fluctuation decreases. The autocorrelation function (ACF) of the time profile of the fluorescence fluctuation provides quantitative information on the dynamics of molecules. This method of measurement is well known as fluorescence correlation spectroscopy (FCS) [8, 9]. 

The autocorrelation function, G(x), of the temporal fluctuation of the fluorescence intensity at the confocal volume is analytically represented by the following equation [8, 9] ... 

Pigure 8.8a and b, respectively, show fluorescence autocorrelation curves of R6G in ethylene glycol and R123 in water at 294.4 K. The solid lines in these traces are curves analyzed by the nonlinear least square method with Eq. (8.1). Residuals plotted on top of the traces clearly indicate that the experimental results were well reproduced by the... 

Figure 8.8 Typical fluorescence autocorrelation curves of R6G in ethylene glycol (a) and R123 in water (b) without the NIR laser light with calculated curves (solid line) based on Eq. (8.1) and residuals. Fluorescence autocorrelation curves of R6G in ethylene glycol (c) and R123 in water (d) under irradiation of the NIR laser at several powers up to 240 mW. The inset of Figure 8.8d shows a magnified view of a partofthe figure enclosed by a rectangle.

As mentioned in the introductory part of this section, quantum dots exhibit quite complex non-radiative relaxation dynamics. The non-radiative decay is not reproduced by a single exponential function, in contrast to triplet states of fluorescent organic molecules that exhibit monophasic exponential decay. In order to quantitatively analyze fluorescence correlation signals of quantum dots including such complex non-radiative decay, we adopted a fluorescence autocorrelation function including the decay component of a stretched exponential as represented by Eq. (8.11). 

Figure 8.12 Typical fluorescence autocorrelation curve (gray closed circles) of the CdTe quantum dots with 4.6 nm diameter in water with a calculated curve (solid line) based on Eq. (8.1) (a) and based on Eq. (8.3) (b). Residuals are also indicated at the top of each trace.

The NIR femtosecond laser microscope realized higher order multi photon excitation for aromatic compounds interferometric autocorrelation detection of the fluorescence from the microcrystals of the aromatic molecules confirmed that their excited states were produced not via stepwise multiphoton absorption but by simultaneous absorption of several photons. The microscope enabled us to obtain three-dimensional multiphoton fluorescence images with higher spatial resolution than that limited by the diffraction theory for one-photon excitation. 

The characterization of the laser pulse widths can be done with commercial autocorrelators or by a variety of other methods that can be found in the ultrafast laser literature. " For example, we have found it convenient to find time zero delay between the pump and probe laser beams in picosecond TR experiments by using fluorescence depletion of trans-stilbene. In this method, the time zero was ascertained by varying the optical delay between the pump and probe beams to a position where the depletion of the stilbene fluorescence was halfway to the maximum fluorescence depletion by the probe laser. The accuracy of the time zero measurement was estimated to be +0.5ps for 1.5ps laser pulses. A typical cross correlation time between the pump and probe pulses can also be measured by the fluorescence depletion method. 

Fig. 3. Variation of autocorrelation function with changes in the equilibrium constant in the fast reaction limit. A and B have different diffusion coefficients but the same optical (fluorescence) properties. This figure illustrates how, for the simple isomerization process, A B, a change in the diffusion coefficient is sufficient to indicate the progress of the reaction. This example is calculated for a two-dimensional (planar) system in the fast reaction limit (kf + k ) 4Dj /w2. Therefore, only a single diffusion process is...

Fig. 11.10. Schematic illustration of fluorescence correlation spectroscopy. The autocorrelation function characterises the fluctuations of the fluorescence intensity its decay time expresses the average duration of a...

For a single fluorescent species undergoing Brownian motion with a translational diffusion coefficient Dt (see Chapter 8, Section 8.1), the autocorrelation function, in the case of Gaussian intensity distribution in the x, y plane and infinite dimension in the z-direction, is given by... 

Triplet state kinetics can also be studied by FCS (Widengren et al., 1995). In fact, with dyes such as fluoresceins and rhodamines, additional fluctuations in fluorescence are observed when increasing excitation intensities as the molecules enter and leave their triplet states. The time-dependent part of the autocorrelation function is given by... 

When the excitation light is polarized and/or if the emitted fluorescence is detected through a polarizer, rotational motion of a fluorophore causes fluctuations in fluorescence intensity. We will consider only the case where the fluorescence decay, the rotational motion and the translational diffusion are well separated in time. In other words, the relevant parameters are such that tc rp, where is the lifetime of the singlet excited state, zc is the rotational correlation time (defined as l/6Dr where Dr is the rotational diffusion coefficient see Chapter 5, Section 5.6.1), and td is the diffusion time defined above. Then, the normalized autocorrelation function can be written as (Rigler et al., 1993)... 

J. Manz The theoretical method of Prof. Field (See Field et al., Intramolecular Dynamics in the Frequency Domain, this volume.) evaluates the fluorescence dispersion spectra of HCCH in terms of the Fourier transform of the autocorrelation function,... 

Figure 12. UV (protein) fluorescence decay of the red-light adapted mixture P, + Pfr (124kDa) at 275 K Aelc = 295 nm, = 330 nm. Inset calculated lifetimes t(t,P)i -4 and relative amplitudes Rftrp)1 -4 °f the decay components calculated by single-decay analysis. Top weighted residuals plot and autocorrelation function of the residuals. The fluorescence decay of pure Pr exhibited a comparable tetraexponential behaviour (Holzwarth et al. [108]).

We have seen that the limitations of the time characteristics of electronic devices requires the use of optical delays between the pump and probe pulses in ps flash photolysis. There are also indirect ways of using optical properties to measure the kinetics of laser pulses and of fluorescence, known as autocorrelation and up-conversion . These rely on the non-linear properties of certain materials or chemical systems, i.e. they are based on fast biphotonic processes. 

There are many variations on these basic systems of autocorrelation and up-conversion. In the former the SHG crystal can be replaced by a solution of molecules which can be excited only by light of frequency 2v anthracene for example cannot be excited directly by a laser light of 532 nm, but will fluoresce when excited by two photons. 

Three of the experiments are completely new, and all make use of optical measurements. One involves a temperature study of the birefringence in a liquid crystal to determine the evolution of nematic order as one approaches the transition to an isotropic phase. The second uses dynamic laser light scattering from an aqueous dispersion of polystyrene spheres to determine the autocorrelation function that characterizes the size of these particles. The third is a study of the absorption and fluorescence spectra of CdSe nanocrystals (quantum dots) and involves modeling of these in terms of simple quantum mechanical concepts. 

The fluorescence fluctuations measured by FCS can be analyzed in several ways. The most common technique, autocorrelation analysis, provides information about characteristic diffusion time of fluorescent molecules through the observation volume. It also reports on the average number of molecules present in the observation volume, and thus the concentration of fluorescent moleculesn (14, 49, 56, 57). Other types of FCS analysis can be used to analyze molecular brightness and the oligomeric state of the fluorescent molecule. Finally, cross-correlation FCS monitors fluctuations jointly from molecules labeled with two or more different fluorophores. This technique provides a powerful approach to assay for intermolecular interactions, because molecules that are bound either directly or indirectly to one another should diffuse as a single unit (8, 59). 

The arrival times of fluorescence photons contain information about correlations in fluorescence signals. Eluorescence correlation spectroscopy (FCS) (26) exploits these correlations to measure the magnitude and time scales of fluctuations in fluorescence. These fluctuations contain information about the dynamic time scales of the system and the concentration of fluorescing molecules. Correlations may span time ranges from nanoseconds to milliseconds, which extends the dynamic time window for fluorescence measurements far beyond what is achievable in fluorescence lifetime measurements. The autocorrelation function is calculated as ... 

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