Perrin expression

Coloration efficiency, defined as the magnitude of the absorbance from C at 600 nm, was also found to depend on DA (X = C H5) concentration, and saturation (i.e., nonhnear response) was noted at 25 wt% at a total dose of 1000 Gy. From a plot of coloration intensity versus DA concentration in PS films of constant thickness, an energy transfer distance, R = 14 A, from an aromatic group of PS to a molecule of DA could be calculated using a modified Perrin expression (Equation 3.36). A.,.,and Ap are absorbances extrapolated to infinite concentration and at known concentrations of DA, respectively. N is Avogadro s number and V is the reaction volume, assumed to be 4/3 n where R is the distance at which 50% of the PS transfer their excitation energy to molecules of DA... 

R/Ro)soiv(f/fo)ellip = n + (mib/m2)(P2/Pi)] (f/fo)eiiip-Briefly justify this expansion of the (f/fo oiv factor. Assuming these particles were solvated to the extent of 0.26 g water (g protein)", calculate (f/fo)eiHp-For prolate ellipsoids of revolution (b/a < 1), Perrin has derived the following expression ... 

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. 

Perrin et al. have denoted the fractional coverages of the surface sites as 6, and 4 for =SiH, =Si, and =SiHSiH3, respectively [317], with 0 + 6q 6 = 1. These three fractional coverages can be found by expressing them as rates in terms of creation and destruction. This gives, with the incident SiH3 flux density per surface site [439],... 

Phelan M, Perrine SP, Brauer M, Faller DV. Sickle erythrocytes, after sickling, regulate the expression of the en-dothelin-1 gene and protein in human endothelial cells in culture. J Clin Invest 1995 96 1145-1151. 

Just as above, we can derive expressions for any fluorescence lifetime for any number of pathways. In this chapter we limit our discussion to cases where the excited molecules have relaxed to their lowest excited-state vibrational level by internal conversion (ic) before pursuing any other de-excitation pathway (see the Perrin-Jablonski diagram in Fig. 1.4). This means we do not consider coherent effects whereby the molecule decays, or transfers energy, from a higher excited state, or from a non-Boltzmann distribution of vibrational levels, before coming to steady-state equilibrium in its ground electronic state (see Section 1.2.2). Internal conversion only takes a few picoseconds, or less [82-84, 106]. In the case of incoherent decay, the method of excitation does not play a role in the decay by any of the pathways from the excited state the excitation scheme is only peculiar to the method we choose to measure the fluorescence (Sections 1.7-1.11). 

Perrin s theory was flawed both in his failure to clearly express the radiation hypothesis in quantum terms and in his concrete examples of monomolecular reactions. Thomas Martin Lowry, recently appointed to a new chair of physical chemistry at Cambridge University, argued that Perrin s choices of chemical examples were unfortunate. 

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. 

Here, is the distance between atoms i andj, C(/ is a dispersion coefficient for atoms i andj, which can be calculated directly from tabulated properties of the individual atoms, and /dampF y) is a damping function to avoid unphysical behavior of the dispersion term for small distances. The only empirical parameter in this expression is S, a scaling factor that is applied uniformly to all pairs of atoms. In applications of DFT-D, this scaling factor has been estimated separately for each functional of interest by optimizing its value with respect to collections of molecular complexes in which dispersion interactions are important. There are no fundamental barriers to applying the ideas of DFT-D within plane-wave DFT calculations. In the work by Neumann and Perrin mentioned above, they showed that adding dispersion corrections to forces... 

Jean Perrin derived expressions for the ratio /// for ellipsoids of revolution in terms of the ratio of the equatorial semiaxis to the semiaxis of revolution b/a. The following expressions were obtained ... 

Bauer et al. [237] and Alms et al. [238] have studied a wide range of organic molecules (benzene, mesitylene, methyl iodide, nitrobenzene, etc.) in solution. They have compared the measured long-time rotational relaxation times with both Perrin s ellipsoid rotational times with stick boundary conditions [223] and with those from Hu and Zwanzig s similar calculation based on slip boundary conditions [227]. There is close agreement between experiment and the slip boundary condition model of Hu and Zwanzig. Typical rotational times could be expressed as... 

Stokes-Einstein Relationship. As was pointed out in the last section, diffusion coefficients may be related to the effective radius of a spherical particle through the translational frictional coefficient in the Stokes-Einstein equation. If the molecular density is also known, then a simple calculation will yield the molecular weight. Thus this method is in effect limited to hard body systems. This method has been extended for example by the work of Perrin (63) and Herzog, Illig, and Kudar (64) to include ellipsoids of revolution of semiaxes a, b, b, for prolate shapes and a, a, b for oblate shapes, where the frictional coefficient is expressed as a ratio with the frictional coefficient observed for a sphere of the same volume. 

Since it is possible to measure the rotational diffusion coefficient by optical mixing techniques, and since expressions equivalent to Equations 36 and 37 have also been calculated by Perrin (67) for rotational motion, we may solve the simultaneous equations... 

The Perrin-like expression in equation 27 was used to fit the kinetic decay trace of polymer 7 the fit is illustrated in Figure 5. 

Miclo, L., Perrin, E., Driou, A., Papadopoulos, V., Boujrad, N., Vanderesse, R., Boudier, J. F., Desor, D., Linden, G., and Gaillard, J.-L. 2001. Characterization of a-casozepine, a tryptic peptide from bovine asi-casein with benzodiazepine-like activity. FASEB J. ((Express Article 10.1096/fj.00-0685fje published online June 8, 2001)). 

The validity of this expression was first demonstrated by Perrin (25) by plotting the reciprocal of the polarization as a function of viscosity of... 

Lee CK, Roberts A, Perrin S (1989) Expression of pertussis toxin in Bordefella bron-chiseptica and Bordefella parapertussis carrying recombinant plasmids. In Infect. Immun. 57 1413-1418. 

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 kinetics of hydration and dehydration for quinazoline and 2-methyl-quinazoline were studied in great detail by Bunting and Perrin, and the pH-rate profiles between pH 0.5 and 12.0 were determined. The profiles for quinazoline are illustrated in Fig. 1. The rate of hydration was given by the expression in Eq. (2). 

Before passing on to consider the newer concept of the problem, we may refei to the osmotic pressure of colloidal solutions and emulsions in view of Einstein s use of the term, osmotic pressure, in deducing the expression which was experimentally verified by Perrin (cf Chap I, Vol I)... 

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