Self-rotation function

Another special case where the signal of the rotation function could be enhanced concerns crystals where the self-rotation fimction can be interpreted without ambiguity in this case, the so-called locked cross-rotation fimction (Tong and Rossmaim, 1997) allows to search for cross rotations which are compatible with the self rotation function. This usually results in a much better signal-to-noise ratio. 

Figure 16.2 A plot of peak signal-to-noise versus maximum vector length for the / = 72 section of a self-rotation function for a picornavirus (approx. 150 A radius), space group P22i2i, a = 354,...

Once diffraction data have been gathered the next stage in the structure analysis is usually focused on seeking a definition of the orientation of the particle and, often, its position in the crystal cell. This information is essential for both phase refinement and the analysis of isomorphous replacement experiments. Because of the inevitable noncrystallographic redundancy (a minimum of 5-fold) and the fixed relationship between the various icosahedral symmetry axes it is often possible to solve the orientation problem by analysis of the diffraction data in the absence of a model, usually by use of a self-rotation function. 

The value of the jump distance in the )0-relaxation of PIB found from the study of the self-motion of protons (2.7 A) is much larger than that obtained from the NSE study on the pair correlation function (0.5-0.9 A). This apparent paradox can also be reconciled by interpreting the motion in the j8-regime as a combined methyl rotation and some translation. Rotational motions aroimd an axis of internal symmetry, do not contribute to the decay of the pair correlation fimction. Therefore, the interpretation of quasi-elastic coherent scattering appears to lead to shorter length scales than those revealed from a measurement of the self-correlation function [195]. A combined motion as proposed above would be consistent with all the experimental observations so far and also with the MD simulation results [198]. 

The desired self-cleaning function led to the development of the intermeshing twin screw. The counter-rotating screw was discarded, because it tended to get blocked by solids and was a poor mixer attention focused instead on the intermeshing, co-rotating extruder. 

The enormous flexibility and variability of the system was possible thanks to the constant development of the process related components, such as the barrels and screw elements and new geometry variants being developed continuously. The initial aim of the design, to maintain the self-wiping function of the screw elements, is sometimes abandoned, in part or in whole, to permit innovative geometries. This enabled the co-rotating, twin-screw extruder to carry out the most diverse processes and handle the most diverse products with this single machine system. 

The orientational van Hove self-correlation function corresponding to the relaxation of the backbone (top panel) and side (lower panel) vectors of glucose (see text for definition) at 220 K show that glucose rotation in the glass proceed by big jumps and does not have a continuous diffusion component. The side rotation, which involves the jump of the smaller glucose bead, the "exocyclic" B6, relaxes faster (ts 3 fjs) than the rotation involving the jumps of the big "backbone" beads B4 and B1 (ts 15 /is). 

The orientational van Hove self-correlation function for the side vector of glucose (see definition in text) develops well-defined secondary peaks corresponding to rotational jumps at the same temperatures that these peaks develop in the translational VHSCF of water (see Figure 3.3 and Figure 3.4). The curves correspond to times (indicated in the figure) for which the side vector has... 

Recently, we have also prepared nanosized polymersomes through self-assembly of star-shaped PEG-b-PLLA block copolymers (eight-arm PEG-b-PLLA) using a film hydration technique [233]. The polymersomes can encapsulate FITC-labeled Dex, as model of a water-soluble macromolecular (bug, into the hydrophilic interior space. The eight-arm PEG-b-PLLA polymersomes showed relatively high stability compared to that of polymersomes of linear PEG-b-PLLA copolymers with the equal volume fraction. Furthermore, we have developed a novel type of polymersome of amphiphilic polyrotaxane (PRX) composed of PLLA-b-PEG-b-PLLA triblock copolymer and a-cyclodextrin (a-CD) [234]. These polymersomes possess unique structures the surface is covered by PRX structures with multiple a-CDs threaded onto the PEG chain. Since the a-CDs are not covalently bound to the PEG chain, they can slide and rotate along the PEG chain, which forms the outer shell of the polymersomes [235,236]. Thus, the polymersomes could be a novel functional biomedical nanomaterial having a dynamic surface. 

Calculation of rotational and vibrational g factors by linear response methods using multiconfigurational self-consistent-field wave functions is described in detail elsewhere [18,27]. 

The coefficient <57 and the coefficients at rotational Wigner functions entering into (j>a) are found by solving self-consistent equations (7.60). According to [Smith, 1990], 57 is equal to 19.65 for CH4 and 48 for CD4. If one neglects the crystalline field potential Vc [Smith, 1985 Huller and Raich, 1979], then the Oh molecules rotate freely, as follows from (7.62). 

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