Geometrical disorder

The structural picture that was envisaged to represent the temperature-dependent fluctuations of the EFG tensor [15] is based on the X-ray structure of MbOa that exhibits a geometric disorder of Fe02 with two different positions of the terminal O-atom [28]. Within this stmcture, the projection of the 0-0 bond on the heme plane is rotated by about 40° in position 2 compared to 1 (Fig. 9.10). Conventional Mossbauer studies of single crystals of Mb02 have shown that the principal component of the FFG tensor lies in the heme plane and is oriented along the projection of the 0-0 bond onto this plane [29]. If the terminal O-atom is located in position 2, the EFG should be of the same magnitude as in position 1, but its orientation is different. The EFG fluctuates between positions 1 and 2 with a rate that depends on temperature. 

It has been established that geometrical disorder has only a small effect on Brownian motion [S. Havlin, D. Ben Avraham (1987)]. Also, for thermally activated jumps, if the distribution of es and evv in a geometrically regular lattice is chosen to be Gaussian, as characterized by the variances as and crw, it has been ascertained [Y. Limoge, J. L. Bocquet (1990)] that there are two limiting diffusion coefficients ... 

Figure 38. Schematic of an amorphous molecular solid with both energetic and geometrical disorder. Each randomly oriented hopping site (CTM) is represented by a disk with the number of concentric rulings representing the energy of a charge carrier. (Site A is relatively shallow site B is very deep.) Electric field direction is E. See the text for a detailed explanation.

Geometrical disorder, molecular packing, excimer-forming sites... 

There is, at present, no realistic theoretical model of the effect of geometrical disorder. A proper model must take into account the complicated orientation dependence of the matrix element (K) [63g], as well as the distribution of positions and orientations of the CTM. The simple treatment adopted by the Gaussian Disorder Model predicts a dependence of the prefactor mobility (//q) on the geometrical disorder parameter Z, namely //q oc exp(i2 ) [63a], and this relationship has been used often to analyze experimental data. The comparison of TTA and TAPC at low concentrations disagrees with this prediction, and it appears to be untenable a priori anyway [60b, 63e]. A worthy challenge for future work will be to construct a model with enough realism to have predictive value. Recent reports indicate progress in this direction [641,o]. 

As for the WCA system, the fraction of sixfold-ordered particles in DRPs (0.547 0.004) is significantly less than the fraction of six-coordinated particles (/g = 0.7861 0.0018), confirming that the sixfold bond orientational order parameter is a more sensitive indicator of local geometrical disorder than is the coordination number. The average size of ordered clusters in DRPs is (s) = 30.4 0.8, and the normalized average number of ordered clusters is Ac/N = 0.0180 0.0005. These values are comparable to those measured in the dense WCA liquid near freezing (see Figs. 52 and 53). 

It was shown already above that cis-1,4-poly butadiene melts in one step with the expected entropy of fusion. In contrast, cis-l,4-poly(2-methylbutadiene) (natural rubber) has a more complicated fusion and crystallization behavior . The reported entropy of fusion of the common monoclinic (P2ja) crystal polymorph is only 14.4 J/(K mol), less than half of the expected value. The crystal structure has been reported statistically disordered, but only relative to packing of chains that are mirror images of each other along the crystallographic a-axis. Such geometric disorder cannot account for a 50% decrease in entropy of fusion. A full study of the thermod5mamic functions as available for the polybutadienes would be of value. 

The demands related to the prolonged operation of the PHENIX reactor have led us to focus on hypothetical defects which, in the various operating conditions envisioned, might question the principle safety functions, and among these, the control of the reactivity. Therefore the extension of such defects, penetrating the great shells which make up the core support structure, had to be evaluated. In order to facilitate their early detection, the geometric disorders associated with much shorter defects constituted another point of interest in the specification of surveillance methods. 

CNT yams have utilized only a very small fraction (<5%) of the strength of the constituent CNTs, one order of magnitude lower than what is achievable for conventional textile yams. The stmctural mechanics of conventional textile yams is well understood and is the starting point for understanding the relationship between stmcture and properties of CNT yams. The strong van der Waals force, the geometrical disorder of CNTs in the drawn web and the unique CNT fracture mechanisms present new dimensions for yam stmctural mechanics research. 

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