Perrin equation, theory

The Stern—Volmer and Perrin equations, (v) and (vi), both allow a quantitative characterization of the efficiency of non-radiative energy transfers. They are useful for the comparison of various donoi -acceptor systems, although they provide no information concerning the nature of the excited state involved and the mechanism of the energy transfer process. More appropriate theories have been established to describe non-radiative energy transfers that occur when there is close resonance between the initial and final states. 

The departure of the Perrin equation from linearity may be considered more generally. A curvature convex to the T/rj axis may result from the complete kinetic dissociation of rigid units or from increased rotational freedom within the polypeptide chain 26, 32, 65, 66, 68). A curvature concave to the T/rj axis may occur whenever more than one rotational relaxation time is present and may be detected when the two rotational relaxation times differ by more than fivefold 65). The initial slope, for small values of T/tj, depends upon the harmonic mean of the relaxation times involved and is determined practically by the shorter one. Such curvature has been reported in studies with DNS-labeled polyvinylamine and poly-p-amino-styrene 22, 33, 64). By applying a theory which deals with the case of an emitting group which has only one degree of rotational freedom, Gottlieb and Wahl 33) concluded that the rotations activated by temperature in... 

Perrin model and the Johansson and Elvingston model fall above the experimental data. Also shown in this figure is the prediction from the Stokes-Einstein-Smoluchowski expression, whereby the Stokes-Einstein expression is modified with the inclusion of the Ein-stein-Smoluchowski expression for the effect of solute on viscosity. Penke et al. [290] found that the Mackie-Meares equation fit the water diffusion data however, upon consideration of water interactions with the polymer gel, through measurements of longitudinal relaxation, adsorption interactions incorporated within the volume averaging theory also well described the experimental results. The volume averaging theory had the advantage that it could describe the effect of Bis on the relaxation within the same framework as the description of the diffusion coefficient. 

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

A careful experimental test of the theory was carried out by Perrin (1910). Emulsions composed of droplets about 0.4 jum in diameter were observed under an optical microscope and the positions of the particles were noted at regular time intervals. The Stokes-Einstein equation was checked by writing it in the form... 

The Combined Stern-Volmer and Perrin Model A model has been proposed by Morishima et al. [97] which takes account of Manning s theory [98] of polyelectrolytes and introduces a modification into the Stem-Volmer equation to describe sphere-of-action (Perrin) quenching this has been termed combined Stern-Volmer and Perrin Analysis and has been adopted [95,96] in an effort to describe quenching of fluorescence from labeled PMAA by T1+ ions, for example. 

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