Local order, degree

For the studied polymers all data in coordinates < T-T) lie down on one straight line [111]. Hence, as /SH the local ordering degree in polymers is defined by closeness of T to and this allows one to suppose the possibility of correlation of A77 and or (p, . Let us note, that similar by... 

In Figure 1.15 the dependence of the density of the macromolecular entanglements clnster network on is shown. As might be expected, chaos intensification X increase) reduces the value, i.e., the local ordering degree in the polymer amorphous state structure [68]. More precise interpretation of the polymer structure chaotic character within the frameworks of multifractal formalism will be given below. 

Finishing this section, let us consider from the position of thermodynamics the interconnection between polymer structure disorder degree and local ordering degree. One of the possible characteristics of disorder can be the fluctuation free volume value [72], which is connected with entropy change AS as follows [73] ... 

Strictly speaking, the F value is not an indicator of the local ordering degree for polymer structure, since clusters are formed by segments of different macromolecules, but it can be an indicator of mutual penetration of macromolecular coils. As has been shown in papers [22, 100], the same role can be played by the characteristic ratio C. If this assumption is correct, a definite correlation between F and must be observed. The data of Figure 1.30 show that such a correlation is really observed for nine amorphous and semi-crystalline polymers (the F value is calculated for T= 293 K) [99]. 

Typical results for a semiconducting liquid are illustrated in figure Al.3.29 where the experunental pair correlation and structure factors for silicon are presented. The radial distribution function shows a sharp first peak followed by oscillations. The structure in the radial distribution fiinction reflects some local ordering. The nature and degree of this order depends on the chemical nature of the liquid state. For example, semiconductor liquids are especially interesting in this sense as they are believed to retain covalent bonding characteristics even in the melt. 

Let us fix attention on a particular H20 molecule A in the interior of water (if we wish to identify this molecule we can suppose that it contains a nucleus of the oxygen isotope 01S) and let us consider the water molecules which happen to be nearest neighbors of this molecule at the moment. These molecules have been in contact with A for different lengths of time. Since all the molecules in the liquid wander about, there was a time when none of these molecules was in contact with A. Further, if we could now begin to watch these molecules, we should find that, after the lapse of different periods of time, they become separated from A and each is replaced by another molecule. Similar remarks can be made about the molecules which come into contact with any chosen molecule. We can now raise the question—-What is the rate of turnover of this process The rate depends on the degree of local order and disorder, which in turn depends on the strength and character of the forces between adjacent molecules. 

We also examined the fold statistics in this Ciooo system. The distribution of the inter-stem vectors connecting stems linked by the loops, and their radial distribution function again indicated that about 60-70% of the folds are short loops connecting the nearest or the second and third nearest stems, though the crystallization did not complete. The presence of local order in the under cooled melt in the present Ciooo system is also examined through the same local order P(r) parameter, the degree of bond orientation as a function of position r, but again we did not detect any appreciable order in the undercooled melt. 

Diffuse interfaces of certain types can move by means of self-diffusion. One example is the motion of diffuse antiphase boundaries which separate two ordered regions arranged on different sublattices (see Fig. 18.7). Self-diffusion in ordered alloys allows the different types of atoms in the system to jump from one sublattice to the other in order to change the degree of local order as the interface advances. This mechanism is presented in Chapter 18. 

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