Solid-phase polymers structure

It should be noted, that the considered above correction can be obtained and without fractal analysis application as well, using well-known Flory concept, that follows from the Eq. (1) of Chapter 1. However, obtaining of the anal dical correlation between Flory exponent and structural characteristics of polymers in solid phase is very difficult, if possible at all. At the same time this can be made within the framework of fractal analysis, since both macromolecular coil [25] and solid-phase polymer structure [62] are fractal objects. Hence, the possibility of solid-phase polymers properties quantitative prediction appears in such sequence molecular characteristics (for example, ) structure of macromolecular coil in solution polymer condensed state structure— polymer properties. In Section 2.6, this problem will be considered in detail. These considerations predetermined the choice of fractal analysis in Ref. [59] as a mathematical calculus. 

In Fig. 1.3 amorphous polymers nanostructure cluster model is presented. As one can see, within the limits of the indicated above dimensional periodicity scales Fig. 1.2 and 1.3 correspond each other, that is, the cluster model assumes p reduction as far as possible from the cluster center. Let us note that well-known Flory felt model [20] does not satisfy this criterion, since for it p const. Since, as it was noted above, polymeric mediums structure fractality was confirmed experimentally repeatedly [14-16], then it is obvious, that cluster model reflects real solid-phase polymers structure quite plausibly, whereas felt model is far from reality. It is also obvious, that opposite intercommunication is true - for density p finite values change of the latter within the definite limits means obligatory availability of structure periodicity. 

At solid body deformation the heat flow is formed, which is due to deformation. The thermodynamics first law establishes that the internal eneigy change in sample dU is equal to the sum of woik dW, carried out on a sample, and the heat flow dQ into sample (see the Eq. (4.31)). This relation is valid for any deformation, reversible or irreversible. There are two thermo-d5mamically irreversible cases, for which dQ = -dW, uniaxial deformation of Newtonian liquid and ideal elastoplastic deformation. For solid-phase polymers deformation has an essentially different character the ratio QIW is not equal to one and varies within the limits of 0.35 0.75, depending on testing conditions [37]. In other words, for these materials thermodynamically ideal plasticity is not realized. The cause of such effect is thermodynamically nonequilibrium nature or fractality of solid-phase polymers structure. Within the frameworks of fractal analysis it has been shown that this results to polymers yielding process realization not in the entire sample volume, but in its part only. 

As was shown in paper [52], polymer melt structure in a range of high temperatures, corresponding to could be characterised most precisely by a macromolecular coil dimension which was accepted as being equal to the corresponding dimension d of solid-phase polymer structure [53]. Earlier within the frameworks of fractional derivatives theory the interconnection of and P was shown, which was expressed analytically as follows [51] ... 

The important argument in favor of fractal approach application is the usage of two order parameter values, which are necessary for correct description of polymer mediums structure and properties features. As it is known, solid phase polymers are thermodynamically nonequilibrium mediums, for which Prigogine-Defay criterion is not fulfilled, and therefore, two order parameters are required, as a minimum, for their structure description. In its turn, one order parameter is required for Euclidean object characterization (its Euclidean dimension d). In general case three parameters (dimensions) are necessary for fractal object correct description dimension of Euclidean space d, fractal (Hausdorff) object dimension d and its spectral (fraction)... 

Since according to the indicated above reasons two order parameters are required, as a minimum, for solid-phase polymers elastic constants description, then variable percolation threshold should be introduced in the Eq. (3. 1), that is,p should be replaced on A. Besides, it has been shown earlier, that for polymers structure Vp 1 (see Table 1.1) [10] and therefore, T[=d - 1 can be assumed in the Eq. (3.2) as the first approximation. Then the Eq. (3.1) assumes the following form [6, 7] ... 

Hence, the cluster model of pol5nners amorphous state structure and the model of WS aggregates friction at translational motion in viscous medium [24] combination allows to describe solid-phase polymers behavior on cold flow (forced high-elasticity) plateau not only qualitatively, but also quantitatively. In addition the cluster model explains these polymers behavior features on the indicated part of diagram a - , which are not responded to explanation within the frame woiks of other models [14]. 

Hence, a solid-phase polymers deformation process is realized in fractal space with the dimension, which is equal to structure dimension d. In such space the deformation process can be presented schematically as the devil s staircase [39]. Its horizontal sections correspond to temporal intervals, where deformation is absent. In this case deformation process is described with using of fractal time t, which belongs to the points of Cantor s set [30]. If Euclidean object deformation is considered then time belongs to real numbers set. 

The exploratory solid-state synthetic work of John Corbett has illustrated the diversity, beauty and richness of this chemistry with a large variety of new phases and structures [1-3]. John Corbett was also the pioneer who recognized the potential of these cluster polymers in the development of a versatile solution chemistry [4]. Once the cluster unit has been identified in the solid state, the excision of this motif appears as the most rational method for accessing these cluster complexes in solution [5]. 

A divergent protocol for a solid-phase synthesis of 3-substituted 2,5-biarylfurans was reported. Thus, reaction of furan zincate A with polymer bound aryl bromide or iodide provides resin intermediates 61. Subsequent bromination-Suzuki coupling reaction followed by further transformations gives rise to structurally diverse 2,3,5-trisubstituted furans 68 in good overall yields and chemical purities <00TL5447>. 

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