Translational diffusivity

The time window available for FRET is dictated by the lifetime of the donor. Is there an optimal lifetime If very short , it is more difficult to measure in FLIM. If it is very long , the levels of fluorescence are low ( /-limited , [1]). In addition, the lifetime is a relevant parameter when one is interested in dynamics, either of binding, conformational change, or diffusion (translational, rotational). These processes influence FRET via the parameters K2 andrDA (Table 12.1). Long lifetimes are useful in luminescence RET (LRET) and can help to reduce background and increase signal-to-noise ratios. 

In sharp contrast to the large number of experimental and computer simulation studies reported in literature, there have been relatively few analytical or model dependent studies on the dynamics of protein hydration layer. A simple phenomenological model, proposed earlier by Nandi and Bagchi [4] explains the observed slow relaxation in the hydration layer in terms of a dynamic equilibrium between the bound and the free states of water molecules within the layer. The slow time scale is the inverse of the rate of bound to free transition. In this model, the transition between the free and bound states occurs by rotation. Recently Mukherjee and Bagchi [14] have numerically solved the space dependent reaction-diffusion model to obtain the probability distribution and the time dependent mean-square displacement (MSD). The model predicts a transition from sub-diffusive to super-diffusive translational behaviour, before it attains a diffusive nature in the long time. However, a microscopic theory of hydration layer dynamics is yet to be fully developed. 

From the preceding it is apparent that the nature of the first excited state has been clarified for CTTS transitions of simple anions, and that both for these and for intramolecular processes following on primary excitation the events are known with some certainty up to the stage of asymmetrization. Also, after the pair of solvated electron and parent species have been established by at least one diffusive translation (so that at least one solvent molecule separates them) all steps following have been elucidated. There remains the question of the detailed nature of the processes in the time interval between 10 u and 10 n to 10-9 sec. after primary absorption. 

Results from irradiations in polyethylene films. Given these analyses, the data from irradiations of (/ )-3b in polyethylene films will now be discussed (Table 13.7). As mentioned above, the ability of the radical pairs from (/ )-3b to diffuse translationally within a cage is related qualitatively to the 2-BN/4-BN ratios whereas the ability of the 1-phenylethyl radical to tumble along the translational course that brings it to combine at either the 2- or 4-position of its 1 -naphthoxy partner is related to or %ee4B. Although a 1-phenylethyl radical center is attracted... 

Fig. 5.4.11 [Cal 11 ] Modulated gradient NMR for probing spectral densities of diffusive translational motion. The pulse sequence (left) consists of a CPMG echo train with interdispersed gradient pulses G(t) which produces the time-dependent wave vector k(t). The spectrum K(co) of k(t) probes the spectral density of diffusive motion at a single frequency (right).

The diffusive translation of molecules has been extensively investigated in a number of molecular crystals. When the diffusing molecules are identical to the molecules of the crystal, one terms this motion self diffiision. Microscopically, it consists of a hopping motion of a molecule from its original lattice site to a neighbouring vacancy (see Chap. 4). For diffusion and self diffusion to take place at all, there must therefore be vacancies present in the lattice. They can either be attached to dislocations or small-angle grain boundaries, or they can be thermally activated. 

The tetrahedral arrangement that characterizes the local ordering of water molecules in the V structure dissipates after about 10 s (at 283 K) because the nearest neighbors of a given molecule are relatively free to change their positions in response to thermal perturbations. This relaxation time is about one order of magnitude smaller than the time scale for diffusive translational and rotational motion of the molecules in liquid water at 283 K, as can be inferred from Table 2.2. The physical meaning of... 

Table 2.2. Correlation time constants for the diffusive translational and rotational motions of a single molecule in liquid water ...

Thus, the task of calculating the diffusion coefficient of a particle is reduced to the task of computing its drag coefficient y. For comphcated particle shapes, one can simulate Stokes flow around the particle, using a finite element simulation, to calculate y. The simplest diffusion translational and rotational diffusion coefficients are those of a spherical particle its one-dimensional translational diffusion coeffi-cient is and its one-dimensional rotational diffusion coefficient is, where n is the dynamical viscosity of the fluid and r is the radius of the sphere. 

The subscripts SD, TD and RD refer to segmental diffusion, translational diffusion and reaction diffusion, with fct sD set to the low conversion values summarized in Table 3.2. The reaction diffusion term kt,RD is proportional to propagation, with proportionality coefficient Crd estimated from experimental data [10] ... 

Diffusion is a process that involves the random motion of particles and the concentration gradient dc/dx in the system. The diffusion coefficient, which is the major concern of this chapter, is a measure of the mass of solute transported in a given period of time under the influence of a known driving force. The driving force is essentially the concentration gradient caused by external forces, such as the gravitational field or centrifugal field. There are two kinds of diffusion translational and rotational. 

Quasielastic neutron scattering (QENS) is a rather indirect method with many limitations. It makes use of the small ( quasielastic ) energy shift that neutrons experience in any scattering by a moving particle, say by the diffusive translations of protons on a molecule. Mathematically, the normalized scattered neutron intensity as a function of kinetic neutron energy E (or frequency (o=2nElh) is related to the time Fourier transform of the dynamic pair-distribution function G(r, i) of the sample material [6, 32]. Hence in Pick s approxima-... 

The very detailed picture of the diffuse translational and rotational molecular motions described above was revealed because of the high energy transfer resolution (typically less than 20 ieV) that is available with the instruments at ILL. However, useful results have also been obtained from medium resolution (-100 peV) quasi-elastic scattering instruments by skilful choice of samples and by fitting different models. It is not generally possible to measure experimentally the EISF for the whole molecule rotational diffusion, because this motion is too slow to give quasi-elastic scattering that is clearly distinct from the elastic peak. 

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