Perrin s equation

The above considerations can be generalized to complexes of the type M Q ( > 1). The probability that a molecule M is in contact with n quencher molecules can be approximately expressed by the Poisson distribution (Eq. 4.21). Perrin s equation (4.23) is then found again. 

This relationship is called Perrin s equation, because it was established for the first time by Francis Perrin it was written at that time with polarization ratios... 

Perrin s equation will thus be modified by the inclusion of this term to... 

Physically, Perrin s equation is valid for static quenching excited molecules and quenchers don t move in and out the quenching volume within the lifetime of the excited state. 

The changes have been used to provide information about the enviromnent of the fluorescent probe and to follow changes in conformation of the macromolecule. In other work the study of the fluorescence polarization properties of the attached probe under steady state illumination and the application of Perrin s equation enable calcu-latnn of the rotary Brownian motion of the polymer. This technique has been extended by Jablonski and Wahl to the use of time-resolved fluorescence polarization measurements to calculate rotational relaxation times of molecules These experiments are discussed fiilly in the fdlowing section of this review. 

Me R = Br, R = H) by various donors in viscous soJventa are decreased by a factor of <2 in a 0.34 T magnetic field and pressure is reported to accelerate the photoreduction of p-benzoquinone in SOS and CTAB micelles in Aerosol OT reversed micelles, the reaction is retarded.The yield of anthraquinone-2-sulphonate radical anion (AQS) generated by irradiation of AQS in aqueous acetonitrile containing propan-2-oJ has been found to depend on the water concentration and to follow Perrin s equation.Complexation of aryl alkyl ketones with /3-cyclodextrin leads to changes in the ratio of the products of elimination and cyclisation which result from reaction of the... 

Generalizing the hydrod3mamical equations derived by Stokes for spheres, Edwardes (35) calculated the coefficients fj, Ca and for ellipsoids as a function of their axial ratios. The general equations are complicated but for ellipsoids of revolution, which may be characterized by only two values of f, they assume a simpler form, and have been employed by Gans 47) and F. Perrin 92) to evaluate the rotary diffusion constants of molecules which may be treated as ellipsoids of revolution. The formulas of Gans and Perrin are not identical, but the numerical values of 0 calculated from them are nearly so, so that the formulas of either author may be used in practice. In the following discussion we shall employ Perrin s equations. 

Consider first the case of an elongated ellipsoid of revolution a >b). Rotary Brownian movement of the a axis about the b axis is characterized by the relaxation time and the corresponding rotary diffusion constant 0 = 1/2t [see Equation (19a)]. These constants are conveniently expressed by their values relative to those for a sphere of the same volume. Denoting by q the ratio bja, Perrin s equation reads... 

The conditions necessary to observe a quantum chain process (a quantum gain) in solid matrices using the domino mechanism were reported by Ebbesen et al. to find new application of the amplification of the effect of photon in molecular optics [99]. The quantum yield of reaction from A to B (Oq) in solution is described as Eq. (4), where O is the quantum yield of production of the reactive excited state and k, and ki are the rate constants of energy transfer and unimolecu-lar deactivation, respectively. Since the molecular diffusion is slow in the solid matrices, the equation is modified by using Perrin s equation as shown in Eq. 

F. Perrin Theory of fluorescence polarization (sphere). Perrin s equation Indirect determination of lifetimes in solution. Comparison with radiative lifetimes... 

Gans uses the numerical eccentricity [1 — (6 /o )]. His equations, although numerically equivalent to those of Perrin, are less manageable and the latter have therefore been used by most authors. Perrin s equations show that for a prolate ellipsoid b/a < 1) pa increases monotonically with the elongation and for large values of this it is proportional to the cube of the major semiaxis. The relaxation time of the minor axis remains nearly equal to po (slightly smaller in fact) up to 6/a = l/-s/2> increases and... 

As described by the Perrin s equation (13), the molecular rotational correlation time (0) can be obtained by the values of steady-state anisotropy (r) and fluorescence lifetime (r). An inspection of Fig. 4 and Table 2 shows that in buffered solution the steady state anisotropy and fluorescence lifetime of free TPPS are 0.01 and 9.7 ns, respectively. In the presence of high CD concentration, the increase of the steady-state anisotropy and of the fluorescence lifetime indicates that the rotational correlation time 9 is increasing. These findings would suggest the entanglement of TPPS in the CD aggregates. 

As already mentioned in Section 2.2, Perrin s equation allows for an indirect measurement of the rotational correlation time in the case of systems having both a single lifetime and rotational correlation time (assuming unaltered the limiting anisotropy ro). 

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