Mean relaxation time, calculation

I) The H-bond mean lifetime, thb> from mf-18- (2) The probability that an hydrogen bond is randomly intact, pg, from Eq. (S.2). (3) The relaxation time calculated from Eq. (6.1) with conditions (6.2). (4) Measured relaxation time r, from refs. 52 and S3 (+) tg, values foreseen by our model using the parameters in columns 5-7, which list the rotational diffusion parameters utilized for a more accurate calculation of dielectric behavior. (8) The principal relaxation band amplitude Ag. (9) and (10) The characteristic time l/Xj and the amplitude A of the only other significant band, as calculated from Eqs. (6.1) and (6.4), respectively. 

The fluorophore was modeled by two beads that are attached as a short pendant side-chain (tag). Both the absorption and emission dipole moments of the fluorophore are defined by the direction of the tag (parallel), as indicated by the vector in Fig. 19, and the fluorescence anisotropy was calculated from its orientation autocorrelation function. For simplicity, we assumed that the reorientaional motion of the fluorophore is the only source of fluorescence depolarization. We neglected energy transfer and other processes that might occur in real systems. The fluorescence anisotropy decays were interpreted using the mean relaxation time, defined as ... 

TumbuU D (1969) Under what conditions can a glass be formed Contemp Phy 10(5) 473-488 Uhhnann DR (1972) A kinetic treatment of glass formation. J Non-Cryst Sohds 7(4) 337-348 Van den Mooter G, Augustijns P, Kinget R (1999) Stabtiity prediction of amorphous benzodiazepines by calculation of the mean relaxation time constant using the WiUiams-Watts decay function. Eur J Pharm Biopharm 48(l) 43-48... 

In the case when the probe exhibits multiple relaxation times as a result of heterogeneity of the binding sites, Eq. 4 provides the mean relaxation time. Even though some characteristics of the tr distribution can in principle be obtained by fitting the C(f) function by a multiple-exponential decay function, a more reliable way to follow the heterogeneity of the system in terms of solvent relaxation is to plot the full width at half maximum (FWHM) of the emission band, a(t), as a function of time. The o-(t) function can be calculated from the asymmetry parameters of the lognormal function, A(t) and y i), as... 

The three decay constants appearing in the expression for r(t) for an ellipsoid of rotation have been calculated and are own in Table 13. As may be seen, the three relaxation times diverge rapidly Avith increasing axial ratio for a prolate ellipsoid. However, for an oblate ellipsoid the deviations are small even for high axial ratios and experimentally it may prove difficult to resolve more than a single, mean relaxation time for r(t) in this case. Thus, three situatkins exist in which the emission anisotropy may decay exponentially and it is not po le, therefore, to distinguish... 

The polymer is a branched polyethylene melt with = 1.55 x 10 and Mw/M = 11.9, flowing at 170 °C in a 3.3 1 planar contraction. The hnear viscoelastic properties and the nonlinear parameters for a four-mode PTT equation are shown in Table 10.1. Different values of e were used for each mode, but with a constant value of f = 0.08. These parameters provide a reasonable fit to the transient and steady-state shear and extensional data, although the nonlinear parameters for the two longest relaxation times cause small oscillations in startup of simple shear that are not observed experimentally using parameters that ehmi-nate the shear oscillations causes the calculated extensional stresses to be too low, and the contraction flow results are sensitive to the extensional stresses. The mean relaxation time was 1.74 s, the average velocity in the downstream channel was 7.47 mm/s, and the downstream channel half-width (the characteristic length) was 0.775 mm. The Weissenberg number based on downstream channel properties was therefore 16.8. 

From the transient change of the optical rotation the mean relaxation time r is calculated (see Equation (4)) and compared with theoretically predicted values. Such comparison yields valpable information about the models used to interpret the cooperative conformational dynamics of linear polymers. 

In the first concentration domain, c < 6x10 g/cm, it is possible to define a second mean characteristic time, the arithmetic mean relaxation time which is calculated through integration ... 

Experimentally the distribution function p r) is obtained from numerical analysis of g t). Therefore, the mean relaxation time is resolved from each of the distribution modes of p(r), as the first moment of the normalized relaxation spectrum. The diffusion coefficient, which corresponds to each value of , can be calculated using... 

A second approach with respect to anisotropic flavin (photo-)chemistry has been described by Trissl 18°) and Frehland and Trissl61). These authors anchored flavins in artificial lipid bilayers by means of C18-hydrocarbon chains at various positions of the chromophore. From fluorescence polarization analysis and model calculations they conclude, that the rotational relaxation time of the chromophore within the membrane is small compared to the fluorescence lifetime (about 2 ns74)). They further obtain the surprising result that the chromophore is localized within the water/lipid interface, with a tilt angle of about 30° (long axis of the chromophore against the normal of the membrane), irrespective of the position where the hydrocarbon chain is bound to the flavin nucleus. They estimate an upper limit of the microviscosity of the membrane of 1 Poise. 

The relaxation rates calculated from Eq. (15) are smaller than the measured ones at low field, while they are larger at high field. OST is thus obviously unable to match the experimental results. However, water protons actually diffuse around ferrihydrite and akaganeite particles and there is no reason to believe that the contribution to the rate from this diffusion would not be quadratic with the external field. This contribution is not observed, probably because the coefficient of the quadratic dependence with the field is smaller than predicted. This could be explained by an erroneous definition of the correlation length in OST, this length is the particle radius, whilst the right definition should be the mean distance between random defects of the crystal. This correlation time would then be significantly reduced, hence the contribution to the relaxation rate. 

The barrier to methyl rotation in 4-methylpyridine has been measured by means of proton spin lattice relaxation time (74MI20405), and found to be very low, about 0.06 kJ mol-1. This is in line with ab initio calculations using a minimal STO-3G basis set (76JST(32)67), and MINDO/3 MO calculations (79JST(57)209), the second of which also show that the equilibrium position for the methyl group is with one hydrogen atom in the plane of the pyridine ring. 

With the additional assumption of the Poisson distribution for the probability of n jumps in a time t (mean time between jumps r), Equations 8 and 9 can be used in existing lattice diffusion theories to calculate relaxation times (approximately, i.e., within 10%) (16,18). 

Nuclease behaves like a typical globular protein in aqueous solution when examined by classic hydrodynamic methods (40) or by measurements of rotational relaxation times for the dimethylaminonaphth-alene sulfonyl derivative (48)- Its intrinsic viscosity, approximately 0.025 dl/g is also consistent with such a conformation. Measurements of its optical rotatory properties, either by estimation of the Moffitt parameter b , or the mean residue rotation at 233 nin, indicate that approximately 15-18% of the polypeptide backbone is in the -helical conformation (47, 48). A similar value is calculated from circular dichroism measurements (48). These estimations agree very closely with the amount of helix actually observed in the electron density map of nuclease, which is discussed in Chapter 7 by Cotton and Hazen, this volume, and Arnone et al. (49). One can state with some assurance, therefore, that the structure of the average molecule of nuclease in neutral, aqueous solution is at least grossly similar to that in the crystalline state. As will be discussed below, this similarity extends to the unique sensitivity to tryptic digestion of a region of the sequence in the presence of ligands (47, 48), which can easily be seen in the solid state as a rather anomalous protrusion from the body of the molecule (19, 49). 

Kleinberg et al. (2005) and Takayama et al. (2005) show that NMR-log measurement of sediment porosity, combined with density-log measurement of porosity, is the simplest and possibly the most reliable means of obtaining accurate gas hydrate saturations. Because of the short NMR relaxation times of the water molecules in gas hydrate, they are not discriminated by the NMR logging tool, and the in situ gas hydrates would be assumed to be part of the solid matrix. Thus the NMR-calculated porosity in a gas-hydrate-bearing sediment is apparently lower than the actual porosity. With an independent source of accurate in situ porosities, such as the density-log measurements, it is possible to accurately estimate gas hydrates saturations by comparing the apparent NMR-derived porosities with the actual reservoir porosities. Collett and Lee (2005) conclude that at relatively low gas... 

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