Anisotropy Decay Laws

The theory for rotatiouai diffusion of anisotropic rotors is complex. This topic is wen unferstood and is described in more detail in Quptre 12. Considreabie contiovet has suirouoded the predicted time-resolved decays for anisotropic molecules. It is now agreed that the anisotropy is expected to decay as a sum of exponentials  

When dealing with n ms dierical mcdecules, it is ns iil to have a definition for the mean corrdationtime. Ibemost commonly used average is the hannonic mean conelatioD time 6, which is given by 

This expression is sometimes used with liP) in piece of re. For a nonsphetical molecule, the initial slope of the anisotropy decay is determined by the hannonic mean correlation time.  

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In the anisotre decay analysis, the value of ro can be considered to be a known CH an unknown value. If the value of ro is known, the anisotropy decay law can be writtoi m... 

Anisotropic rotati onal diffusion has been more Nct sively studied using FD methods. In fact, the earliest reports on the anisotropic rotation of fluorophores concerned experiments performed using fixed-frequency phase-modulation fluorometers. At that time the phase-modulation instruments operated at only one or two fixed hrequendes. Hence, it was not possible to recover the anisotropy decay law. The experiments were performed by measuring the differential polarized phase angles as the temperature was varied. It is relatively simple to predict the maximum value of Ao) for known values of the lifetime and fundamental anisotropy. For an isotropic rotor, the predicted value of Aw is given by... 

With the development of multifrequency phase-modulation technology, Lakowicz and co-workers(171) were able to examine the time dependence of the anisotropy decay of BPTI. They noted that the intensity decay of the fluorescence is best fit by a biexponential decay law and that the anisotropy decay is also complex. At 25 °C and pH 6.5, correlation times of 39 ps and 2.25 ns were recovered from analysis of data obtained over the range 20 MHz to 2 GHz. The longer correlation time is close to that predicted for the overall rotational motion of a molecule of the size of BPTI. They indicated, however, that additional experiments need to be done to resolve whether the 39-ps... 

In these multichromophoric cyclodextrins the fluorophores are randomly oriented. Excitation of one of the naphthoate fluorophores is followed by efficient dipole-dipole excitation energy transfer between the seven fluorophores, with a Forster radius of 14 A. This process is not detectable by fluorescence intensity measurements, as neither the intensity nor the decay law are affected by energy transfer between identical fluorophores (also called homotransfer. The dynamics of energy hopping are on the other hand reflected in the fluorescence anisotropy. To avoid depolarization by rotational motion of the fluorophores, experiments were conducted in a low temperature and optically clear rigid glass (9 1 ethanol-methanol at 110 K). 

The measurements are different in the frequency-domain. In this case we measure the phase shift between the parallel and perpendicular components of the emission, and a frequency-dependent anisotropy, which is analogous to the steady state anisotropy. These two types of data are used to determine the decay law for the anisotropy (equation 15). 

The most direct approach to analyzing the anisotropy data is to fit the measured r(r) values to an assumed anisotropy dec law. The measured values are cakul ued fiom the polarized inteoaty decays. 

Bialik. C. N.,WoIf, B., Rachofsfcy,E. L-, Ross, J. B. A., and Laws, W. R.. 1998, Fluorescence anisotropy decay Finding the correct physical model. Prve. SPIE 3526 60-67. 

Figure 25. (a) Dependence of the absorbance of linearly polarized probe light at 360 nm ( ) and 450 nm ( ), on the angle F between the probe and the UV irradiation lights polarization. This behavior is fitted with a law in cos F with an amplitude that decays in accordance with the cis => trans thermal back reaction. The theoretical fits are indicated by dotted curves. Evolution of (b) the anisotropy, AA" -, and (c) the order parameter S defined in relation 10, for the wavelengths 360 nm ( ) and 450 nm ( ), with the time of UV (360 nm) irradiation. 

As usual in the early stage of investigation different experiments gave inconclusive results on the question of the nature of gap anisotropy. The low temperature specific heat exhibits a Cs(T) r" power law in a rather reduced range between 0.65 K and 1.2 K which points to some kind of nodal state. In Sb-NQR experiments (Kotegawa et al., 2003) the nuclear spin lattice relaxation l/Ti rate was determined. It has an itinerant quasiparticle contribution that contains information on the SC nodal state below Tc and in addition a localised contribution from broadened CEF excitations which decreases exponentially for temperatures T A. There is no unique way to separate these contributions, this problem is similar to the two Knight shift contributions in the case of UPd2Al3 (sect. 4.2) with its isoelectronic 5f localised states. The NQR measurements did not show ai r evidence for a coherence peak below Tc which points to an unconventional SC state, for lower temperatures an exponential decay of r, , in conflict with the existence of gap nodes was reported. However, this result depends critically on the subtraction procedure of the localised contribution. 

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