Macromolecules fractal characteristics

Strictly speaking, there is no fundamental difference between the molecular structure above and below the T in both cases, the structure is formed by long-chain macromolecules. They differ in the fact that the thermodynamically unstable state of the polymer existing below Tgis replaced by a quasi-equilibrimn state above Tg. Within the framework of fractal analysis, this means that the polymer structure ceases to be a fractal at T>Tg and becomes a Euclidean body (or, at least, a fairly close approximation). As noted by Flory [43], the ability to withstand severe deformations and restore entirely the initial characteristics when... 

As noted above, a change in the density of chemical crosslinking vf) in epoxy polymers results in an extremal variation of the characteristic ratio (C ) with the minimum K 1.0 [118]. If the section of a macromolecule between chemical crosslinks is modelled by a freely jointed chain, the use of known and values results in a typical fractal dependence [122] ... 

FIGURE 14 The dependence of interaction parameter e on macromolecular coil fractal dimension Dj. A hnear macromolecule characteristic states according to the classification [10] are indicated by points. 

Hence, the performed above analysis has shown that different solvents using in low-temperature nonequilibriiun polycondensation process can result not only in symthesized polymer quantitative characteristics change, but also in reaction mechanism and polymer chain structure change. This effect is comparable with the observed one at the same polymer receiving by methods of equilibrium and nonequilibrium polycondensation. Let us note, that the fractal analysis and irreversible aggregation models allow in principle to predict symthesized polymer properties as a function of a solvent, used in synthesis process. The stated above results confirm Al-exandrowicz s conclusion [134] about the fact that kinetics of branched polymers formation effects on their topological structures distribution and macromolecules mean shape. 

Hence, the perfonned within the framewoik of fractal approach analysis of behavior of polystirene, modified by Dendron s, in diluted solutions gave the same conclusions, as the analysis within the fiamewoik of classical approaches. The main distinction of the indicated approaches is the fact, that the structural model, allowing to describe quantitatively macromolecules structural state and conformation, was placed in the fractal approach base. Other characteristics (gyration radius, Kuhn segment length and so on) are the function of the indicated structural state of a macromolecule. The fractal analysis methods, used for the description of linear flexible-chain polymers behavior, can be applied successfiilly also in case of polymers with more complex macromolecular architecture. 

Equation 2.7 gives two forms of analytical relation between d and fractal dimension depends not only on the order parameter value (p, but also on the polymer s molecular characteristics (C and 5), where is the characteristic ratio, which is an indicator of polymer chain statistical flexibility [42], S is a macromolecule cross-sectional area. This is the reflection of the above-mentioned rule, that for description of a polymer s condensed state structure, as a minimum two order parameters are required [12, 25]. 

Figure 8 (a) Time evolution of the SANS profiles during enzymatic polymerization to cellulose. SANS from the enzyme solution was also included as a reference, (b) Time change in surface characteristics (the surface fractal dimension, Ds, and front factor. A), and monomer conversion. Cm. From Tanaka, H. Koizumi, S. Hashimoto, T. etal. Macromolecules 2007, 40,6304-6315. ... 

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