Perrin formula

For prolate ellipsoid, the rotary diffusion coefficient Dt ( >, = l/6r) is given by the Perrin formula [47]... 

The Perrin formulas are derived on the basis of a hydrodynamic approximation. That is, the rotating system is treated as a particle reorienting in a continuum solvent. This is a good approximation for a macromolecule immersed in a solvent of small molecules, but one would not a priori expect it to apply to the case of molecules such as benzene and mesitylene immersed in solvents composed of molecules of approximately... 

Like so many physical chemists and physicists interested in kinetics, one of Perrin s starting points was Arrhenius s activity formula (1889) for the probability of transformation of a molecule at temperature T, where the probability is... 

In addition, Perrin tended to interest himself in individual atomic events rather than in the molecule as a complex entity. The radiation theory of chemical activation attempted a mathematical representation in simple and general formulas, based on axiomatic principles. Perrin s work in radiation bears more resemblance to his reformulation of thermodynamics in the early 1900s than to his experimental work on x-rays and cathode rays in the 1890s or on colloids and Brownian motion in the early 1900s. What binds all his work together is interest in single events or the individual corpuscle. 106... 

This formula, due to Einstein, was experimentally verified by Jean Perrin 94) by direct microscopic observation of spherical colloidal mastic particles (with radius 6.5-10 cm), which contained. small enclosures of impurities on the surface, thus permitting their rotary motion to be directly followed. 

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. 

The above formulae were experimentally checked by Perrin in 1908. He measured the distances traversed by Brownian particles for equal periods of time with a microscope. Based on his experiments and formulae (483) and (484), Perrin was able to define the Boltzmann constant, k, and calculated the value of Avogadro s number N., both closely approximating their values obtained by other methods. 

The molecular formula sequence is that adopted by Perrin (footnote g) where the formulae are blocked together initially by their carbon number and then by the number of elements. 

When Brownian motion and its attendant randomizing effect is important, an ellipsoid, or colloidal particles of arbitrary shape, will have various orientations. As we have seen, there is a translation coefficient for each orientation. It can be shown that the mean translation coefficient, mean friction coefficient, and mean mobility are given, respectively, by the formulas (Perrin 1936, Happel Brenner 1983)... 

In 1908 and subsequent years, J.B. Perrin (1923) reported consistent values of Avogadro s number based on the Stokes-Einstein equation and experiment. Perrin determined experimentally values of (r ) for different colloidal particle sizes, temperatures, and liquid solutions, and substituted the measured values into the formula... 

Its earliest isolation under the name xanthopicrit by Chevalier and Pelletan (177) from Zanthoxylum caribaeum is of historical interest only. The subsequent isolation under the name of berberine from Berberis vvlgaris (180) and its further examination by Fleitmann (181) served only to facilitate the work of Perrins (167), who not only determined the correct formula, C20H19O6N, but showed that the products from the two sources were identical. 

In the first paper, Perkin gives a short history of the discovery of and earlier work on berberine, taking great pains to confirm the empirical formula of Perrins (167) which was based on the analysis of salts and therefore were actually written as C2oHi704N. The physical properties of the alkaloid and many of its salts were described, as well as a number of color reactions. 

Peierls had already contributed significantly to the debate on the possible explosive effects of fission. The previous May one of Fr6d6ric Joliot s associates in Paris, Francis Perrin, had published a first approximate formula for calculating the critical mass of uranium—the amoimt of uranium necessary to sustain a chain reaction. A lump smaller than a critical mass would be inert a lump of critical size would explode spontaneously upon assembly. 

Similarly the formula of pyridine reveals that it is a weak base, with a pK about 5, and the basic strength of substituted pyridines can quickly be calculated by the procedures of Perrin, Dempsey and Serjeant (1981). Further,... 

Cortisone is sometimes credited with chelating power but, from inspection of the formula, this seems unlikely, and no proof has been produced. The suggestion that indolyl-3-acetic acid exerts plant-growth-regulating effects through chelation has been discounted by showing that it lacks chelating properties (Perrin, 1961). 

The same expression can be derived without the use of the preaveraged Oseen tensor and the Kirkwood approximation [22]. Furthermore, if applied to a rigid sphere and an ellipsoid of rotation (either prolate or oblate), eq 2.26 happens to give the known exact results, the Stokes formula for the former and the Perrin formular for the latter [23]. Thus we may consider that eq 2.33 is exact as long as d/L is much smaller than unity. 

The theoretical Dg value of collagen molecule approximated by a cylinder of radius r and of length 2L may be obtained from a Perrin-like formula, demonstrated by Burgers ... 

Several attempts have been made to experimentally verify the theory of Brownian motion proposed by Einstein. Svedberg s results [18] were close to the expected values, but several researchers remained skeptical. Henri [19] used the recently invented film camera, attached to a microscope, to record the trajectories of latex particles suspended in water, but could not find quantitative agreement with Einstein s formula. The theory was finally verified by Perrin [20] by a series of experiments. In these experiments, the data was obtained using a microscope and a camera, while the displacements and the number of particles were measured manually. 

Berberine was discovered by Chevallier and G. Pelletan and called zanthopicrite, and by J. A. and L. A. Buchner, who called it berberine. Hlasiwetz and H. von Gilm and J. Dyson Perrins foimd the correct formula C2oHx7N04. Harmine was discovered by Fritzsche. Hydrastine was observed by Durand (1851) but first characterised by J. Dyson Perrins. ... 

The distribution formula (124b) has been used in deriving the above formula. The validity of (150) was shown by Perrin who showed that the Boltzmann constant k could be obtained by relating (150) with the Stokes-Einstein equation... 

Perrin et al. [20] reported simultaneous quantitation of 5 -mononucleotides and nucleosides in infant formulas using two 25-cm reversed-phase columns (Nucleosil... 

Perrin, C., L. Meyer, C. Nujahid, and C. J. Blake, 2001. The analysis of 5 -mono-nucleotides in infant formulae by HPLC. Food Chem. 74 245-253. 

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