Diffusivities reorientation times

Alternatively, in order to take into account the effects of rotational diffusion of a water molecule around the metal-oxygen axis, a rotational correlation time for the metal-H vector was considered as an additional parameter besides the longer overall reorientational time 82). 

As an example of behavior of a typical Gd-complex and Gd-macromolecule we discuss here the NMRD profiles of a derivative of Gd-DTPA with a built-in sulfonamide (SA) and the profile of its adduct with carbonic anhydrase (see Fig. 37) 100). Other systems are described in Chapter 4. The profile of Gd-DTPA-SA contains one dispersion only, centered at about 10 MHz, and can be easily fit as the sum of the relaxation contributions from two inner-sphere water protons and from diffusing water molecules. Both the reorientational time and the field dependent electron relaxation time contribute to the proton correlation time. The fit performed with the SBM theory, without... 

Once the diffusive reorientation contribution has been subtracted from the deconvolved time-domain response, a final Fourier transform yields the intermolecular spectrum (often referred to as the reduced spectral density). 

In [31] kinetics of the surface tension decrease was described using the model accounting for diffusion-controlled adsorption of protein molecule and for conformational changes of adsorbed molecule. The model corresponds to one proposed by Serrien [32] and describes diffusion toward a/w surface and subsequent reorientation and other changes in adsorption layer, which usually one gives a sence of conformational changes the adsorbed protein. The model yields the diffusion relaxation time (t) and (kc) - the rate constant of conformational changes. 

Dielectric measurements of gas adsorption systems can be performed fairly quickly, typically within a few seconds [6.3]. Hence the kinetics of adsorption processes being slow on this time scale can be observed. Indeed these processes are sometimes invisible to purely manometric or even gravimetric measurements. As examples we mention internal diffusion, reorientation or catalytically induced chemical reaction processes of admolecules within a sorbent material. The mass of the adsorbed phase normally is constant during processes of this type, whereas the dipole moment of the admolecules and hence their polarization changes, cp. Sect. 3.2. 

The figure shows that the Lorentzian fits represent the spectra very well at all temperatures, thus justifying the assumption that the rotation about a single axis basically shapes the spectral line. This justifies also the assumption that the motion is essentially a diffusive reorientation of this axis. Under these conditions we can calculate the reorientation time from the linewidth T0 by means of the equation ... 

Figure 2.6 depicts the reorientational time correlation function (RTCF) of ranks, / = 1 and 2 for a representative composition, x, = 1.0 (upper panel) and the product of translational diffusion coefficient and rotational correlation time (D x t ) as a function of Xj (lower panel). RTCF has been calculated by Equation 2.17. The upper panel shows that the RTCF of first rank (/ = 1) decays at a rate slower than that of second rank (Z = 2). This is expected. For other compositions, this trend remains the same. Rotational correlation time constant has been obtained via time integration of RTCF as follows ... 

Gisser and Ediger(41) studied solvent and solute rotation with C and nuclear magnetic resonance. The selectivity of NMR allows separate measurement of reorientation times for multiple components of a mixture. Dilute polystyrene, polyisoprene, and polybutadiene were found to retard the rotational diffusion of the toluene solvent, polystyrene being modestly more effective as a retardant. Solvent Tr depends exponentially on polymer c, at least up to 90 g/1 of polymer. Gisser and Ediger also examined the small-molecule mixture chloronaphthalene ... 

Unfreezable water in the solid-liquid transition of confined water is about two layers thick (Section 4.2). There are two dead water layers in the liquid-vapor transition of water near strongly hydrophilic surfaces (Section 2.2). At mineral surfaces, one to two water layers are highly ordered [441]. Numerous experimental and simulation studies indicate quite different dynamic properties (diffusion coefficient, residence time, reorientational time, etc.) of liquid water within the first 1-2 layers. 

PDS, and 6-PDS using the time-resolved fluorescence depolarization method involving two dissimilar probes, 2,5-dimethyl-l,4-dioxo-3,6-diphenylpyr-rolo[3,4-c]pyrrole (DMDPP) and coumarin 6 (C6). The decay of anisotropy for both probes in all the six micelles has been rationalized on the basis of a two-step model consisting of fast-restricted rotation of the probe and slow lateral diffusion of the probe in the micelle that are coupled to the overall rotation of the micelle. On the basis of the assumption that the fast and slow motions are separable, the experimentally obtained slow and fast reorientation times and Xfajt) are related to the time constants for lateral diffusion (xj, wobbling motion (Xw), and rotation of the micelle as a whole (Xm) by the following relationships ... 

Dynamic information such as reorientational correlation functions and diffusion constants for the ions can readily be obtained. Collective properties such as viscosity can also be calculated in principle, but it is difficult to obtain accurate results in reasonable simulation times. Single-particle properties such as diffusion constants can be determined more easily from simulations. Figure 4.3-4 shows the mean square displacements of cations and anions in dimethylimidazolium chloride at 400 K. The rapid rise at short times is due to rattling of the ions in the cages of neighbors. The amplitude of this motion is about 0.5 A. After a few picoseconds the mean square displacement in all three directions is a linear function of time and the slope of this portion of the curve gives the diffusion constant. These diffusion constants are about a factor of 10 lower than those in normal molecular liquids at room temperature. 

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