Short-range diffusion analysis

Short-range diffusion (SRD) analysis is the method used to obtain the distribution of diffusion coefficients of target molecules. In this method, short trajectories with constant time duration are successively extracted from one trajectory, and diffusion coefficients are determined for individual short trajectories, producing a time series of diffusion coefficients. This analysis can be used to detect temporal changes in the mobility of individual molecules (14,15). In this section, we suppose that the images were acquired at 33-ms intervals (i.e., 30 frames per second (fps), = 33 ms). 

A more detailed analysis of the cage effect has been presented by Northrup and Hynes [103]. As before, the diffusion equation was used to describe the relative motion of radicals, but the effect of solvent structures on the radicals when in close proximity to each other was incorporated via the potential of mean force (see Chap. 2, Sect. 6.6 and Chap. 8, Sect. 2.6) and hydrodynamic respulsion (see Chap. 8, Sect. 2.5 and Chap. 9. Sect. 3). The solvent structure is due to short-range liquid structure. Solvent... 

Anderko and Lencka find. Eng. Chem. Res. 37, 2878 (1998)] These authors present an analysis of self-diffusion in multicomponent aqueous electrolyte systems. Their model includes contributions of long-range (Coulombic) and short-range (hard-sphere) interactions. Their mixing rule was based on equations of nonequilibrium thermodynamics. The model accurately predicts self-diffusivities of ions and gases in aqueous solutions from dilute to about 30 mol/kg water. It makes it possible to take single-solute data and extend them to multicomponent mixtures. 

Caspar et al. (1988) described an elegant analysis of the diffuse X-ray scattering from insulin crystals. They found two types of coupled motion one with a characteristic length of about 6 A and amplitude of about 0.4 A, the other with a characteristic length of about 20 A and smaller amplitude. The latter motion represents the jiggle of neighboring molecules of the lattice. The former represents the coupled fluidlike fluctuations within a protein molecule. The short-range motions appear to be similar to those detected by Mossbauer spectroscopy. 

Figure 2.1). An analysis of the Bragg diffraction provides a structural model of the unit cell contents, averaged over time and over all the unit cells in the sample. This information can be complemented by an analysis of the diffuse scattering, which is observed as broad humps of scattering in Q regions between the Bragg peaks (see Figure 2.1), and has its origin in the short-range instantaneous correlations between disordered ions.

Later on, Kimming, Strobl and Stiin [247] performed a detailed analysis of static and dynamic scattering measurements and of infrared and Raman spectra on PTFE oriented samples at different temperatures. In addition, in [247], the influence of different kinds of disorder on the X-ray diffraction intensity distribution was also investigated. The analysis of diffuse scattering on the 7 and 8 layer lines essentially confirmed that an orientational short-range order is retained for sequences in adjacent chains in the intermediate form IV and that the degree of order possibly decreases with increasing the temperature in form I. 

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