Emission anisotropy

Definition and Uses of Standards. In the context of this paper, the term "standard" denotes a well-characterized material for which a physical parameter or concentration of chemical constituent has been determined with a known precision and accuracy. These standards can be used to check or determine (a) instrumental parameters such as wavelength accuracy, detection-system spectral responsivity, and stability (b) the instrument response to specific fluorescent species and (c) the accuracy of measurements made by specific Instruments or measurement procedures (assess whether the analytical measurement process is in statistical control and whether it exhibits bias). Once the luminescence instrumentation has been calibrated, it can be used to measure the luminescence characteristics of chemical systems, including corrected excitation and emission spectra, quantum yields, decay times, emission anisotropies, energy transfer, and, with appropriate standards, the concentrations of chemical constituents in complex S2unples. 

As in the case of most FRET imaging formalisms, Eq. (12.4) applies to the donor at a particular x, y, x coordinate j as a virtual species with an apparent kt(j) it applies for arbitrary absolute and relative local concentrations of donor and acceptor but only if population distributions are properly considered (see other chapters). For example, assuming a population of donors, a fraction a of which are in a unique DA environment (e.g., as a bound complex) and the rest free, one can generate an expression for a in terms of known parameters and experimental signals (varying from point to point), kt/kf, Qd, and Qa- Related expressions can be formulated in terms of donor and acceptor emission anisotropies and lifetimes, and for conditions of nonlinearity such as ground state depletion of the donor and/or acceptor [1] (see Section 12.3). 

Fisz, J. J. (2007). Another look at magic-angle-detected fluorescence and emission anisotropy decays in fluorescence microscopy. J. Phys. Chem. A 111, 12867-70. 

Fluorescence anisotropy is generally used to provide information about the dipolar orientational dynamics occurring after excitation of a system. This technique has successfully been used to probe ultrafast dynamics of energy transfer in organic conjugated dendrimers. The detected emission intensities Tar and Ter for parallel and perpendicularly polarized excitation respectively, were used to construct an observable emission anisotropy R(t) in accordance with the equation [121] ... 

Ultrafast emission measurements are possible with the dendrimer metal nanocomposites. The gold and silver internal dendrimer nanocomposites showed a fast emission decay of approximately 0.5 ps, which was followed by a slower decay process. The fast decay emission is attributed to decay processes of the gold (or silver) metal nanoparticles. Ultrafast emission anisotropy measure-... 

The chromophore environment can affect the spectral position of the absorption and emission bands, the absorption and emission intensity (eM, r), and the fluorescence lifetime as well as the emission anisotropy, e.g., in the case of rigid matrices or hydrogen bonding. Changes in temperature typically result only in small spectral shifts, yet in considerable changes in the fluorescence quantum yield and lifetime. This sensitivity can be favorably exploited for the design of fluorescent sensors and probes [24, 51], though it can unfortunately also hamper quantification from simple measurements of fluorescence intensity [116], The latter can be, e.g., circumvented by ratiometric measurements [24, 115],... 

Characterization of the polarization state of fluorescence (polarization ratio, emission anisotropy)... 

In the expression of the polarization ratio, the denominator represents the fluorescence intensity in the direction of observation, whereas in the formula giving the emission anisotropy, the denominator represents the total fluorescence intensity. In a few situations (e.g. the study of radiative transfer) the polarization ratio is to be preferred, but in most cases, the use of emission anisotropy leads to simpler relations (see below). 

When the incident light is horizontally polarized, the horizontal Ox axis is an axis of symmetry for the fluorescence intensity Iy = Iz. The fluorescence observed in the direction of this axis (i.e. at 90° in a horizontal plane) should thus be unpolarized (Figure 5.3). This configuration is of practical interest in checking the possible residual polarization due to imperfect optical tuning. When a monochromator is used for observation, the polarization observed is due to the dependence of its transmission efficiency on the polarization of light. Then, measurement of the polarization with a horizontally polarized incident beam permits correction to get the true emission anisotropy (see Section 6.1.6). 

The components ly and Ih, vertically and horizontally polarized respectively, are such that Jz = Jy = Ix, Iy = IH (Figure 5.3). The total fluorescence intensity is then 2fy + Ih- The polarization ratio and the emission anisotropy are given by... 

It is easy to show that rn = r/2. Therefore, the emission anisotropy observed upon excitation by natural light is half that upon excitation by vertically polarized light. In view of the difficulty of producing perfectly natural light (i.e. totally unpolarized), vertically polarized light is always used in practice. Consequently, only excitation by polarized light will be considered in the rest of this chapter. 

Following an infinitely short pulse of light, the total fluorescence intensity at time t is I(t) = J (t) + 2 I (t), and the instantaneous emission anisotropy at that time is... 

After recording J (t) and I (t), the emission anisotropy can be calculated by means... 

The important consequence of this is that the total emission anisotropy is the weighted sum of the individual anisotropies4 ... 

This equation shows that, at time t, each anisotropy term is weighted by a factor that depends on the relative contribution to the total fluorescence intensity at that time. This is surprising at first sight, but simply results from the definition used for the emission anisotropy, which is based on the practical measurement of the overall ly and I components. A noticeable consequence is that the emission anisotropy of a mixture may not decay monotonously, depending of the values of r, and Ti for each species. Thus, r(t) should be viewed as an apparent or a technical anisotropy because it does not reflect the overall orientation relaxation after photoselection, as in the case of a single population of fluorophores. 

Relation between emission anisotropy and angular distribution of the emission transition moments... 

Let us consider a population of N molecules randomly oriented and excited at time 0 by an infinitely short pulse of light polarized along Oz. At time t, the emission transition moments ME of the excited molecules have a certain angular distribution. The orientation of these transition moments is characterized by 0E, the angle with respect to the Oz axis, and by (azimuth), the angle with respect to the Oz axis (Figure 5.5). The final expression of emission anisotropy should be independent of

[Pg.134]

Finally, because y = cos dE, the relation between the emission anisotropy and the angular distribution of the emission transition moments can be written as... 

The difference between the theoretical value of the emission anisotropy in the absence of motions (fundamental anisotropy) and the experimental value (limiting anisotropy) deserves particular attention. The limiting anisotropy can be determined either by steady-state measurements in a rigid medium (in order to avoid the effects of Brownian motion), or time-resolved measurements by taking the value of the emission anisotropy at time zero, because the instantaneous anisotropy can be written in the following form ... 

It should first be noted that the measurement of emission anisotropy is difficult, and instrumental artefacts such as large cone angles of the incident and/or observation beams, imperfect or misaligned polarizers, re-absorption of fluorescence, optical rotation, birefringence, etc., might be partly responsible for the difference between the fundamental and limiting anisotropies. 

Fast librational motions of the fluorophore within the solvation shell should also be consideredd). The estimated characteristic time for perylene in paraffin is about 1 ps, which is not detectable by time-resolved anisotropy decay measurement. An apparent value of the emission anisotropy is thus measured, which is smaller than in the absence of libration. Such an explanation is consistent with the fact that fluorescein bound to a large molecule (e.g. polyacrylamide or monoglucoronide) exhibits a larger limiting anisotropy than free fluorescein in aqueous glycerolic solutions. However, the absorption and fluorescence spectra are different for free and bound fluorescein the question then arises as to whether r0 could be an intrinsic property of the fluorophore. 

Quantitative information can be obtained only if the time-scale of rotational motions is of the order of the excited-state lifetime r. In fact, if the motions are slow with respect to r(r ro) or rapid (r 0), no information on motions can be obtained from emission anisotropy measurements because these motions occur out of the experimental time window. 

A distinction should be made between free rotation and hindered rotation. In the case of free rotation, after a (5-pulse excitation the emission anisotropy decays from ro to 0 because the rotational motions of the molecules lead to a random orientation at long times. In the case of hindered rotations, the molecules cannot become randomly oriented at long times, and the emission anisotropy does not decay to zero but to a steady value, r (Figure 5.10). These two cases of free and hindered rotations will now be discussed. 

The emission anisotropy r0(A) at a wavelength of excitation X results from the addition of contributions from the JLa and b excited states with fractional contributions fa(X) and fh(X), respectively. According to the additivity law of emission anisotropies, ro(X) is given by... 

The fractional contributions of the 1La and Lb excited states to the emission anisotropies are given by... 

Using the same method that led to Eq. (5.27), it is easy to establish the rule of multiplication of depolarization factors when several processes inducing successive rotations of the transition moments (each being characterized by cos2 C,) are independent random relative azimuths, the emission anisotropy is the product of the depolarization factors (3 cos2 c, — l)/2 ... 

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