Deforming real and ideal chains

Parameters A,- are the multiplication factors of a linear deformation of the Flory ball along the corresponding axis s of multiplication factor of the volumetric deformation. For a polymeric chain into the ideal solution the all = 1 and X = 1. Under any deformations of the F/ory ball its conformational volume is decreased, that is why in the real solution X, < 1. 

At the transfer of the polymeric chain from the ideal into the real solution its conformational volume is deformed with the transformation of the spherical Flory ball into the conformational ellipsoid elongated or flattened along the axis connecting the begin and the end of a chain 26, that leads to decrease of the conformational volume and accordingly to the Eq. (8) to decrease of X. at any deformations of the Flory ball X became less than the one. That this why the effects related with the notions hardness of the polymeric chain and the thermodynamic quality of the solvent can be quantitatively estimated via the multiplicity of the volumetric deformation X <. The indicated effects are visualized in the adsorption layer weaker than in the solution firstly, because the conformational volume in the adsorption layer equal to //2, is less, than in solution. This increases the elastic properties of the conformational volume of polymeric chain and thereafter increases the deformation woik. Moreover, the concentrated adsorption layer corresponding to the quasi-plateau on the adsorption isotherm is more near to the ideal than the diluted real solution. That is why under other equal conditions X > X. This means, that the adsorption of polymer from the real solution is more than ftom the ideal one. 

The real stmcture of brownmillerite phases is more difficult to resolve because the apex-linked chains of tetrahedra are not regular (Figure 2.8a) but display a cormgation compared to the ideal motif. There are two possibilities for this chain deformation, either right (R) or left (L) handed (Figure 2.8b and c). The organisation of these chains has repercussions for the space group and unit cell axes of the brownmillerite phase ... 

Figure 4.49 gives an overall idealized view of tensile deformation. In real situations, major variations can be observed, depending on the molecular weight, the structural regularity of the chain, and the values of the other independent structural parameters. As an example. Fig. 4.50 illustrates the force-length curves for various molecular weight fractions of rapidly crystallized linear polyethylene [250]. All of these samples display ductile behavior and the yield for each is well defined. 

Let us consider two limiting cases of the adduced in Fig. 4.15 dependence at = 0 and 1.0, both at d = 3. In the first case (d = 2) the value dU = 0 or, as it follows from dU definition (the Eq. (4.31)), dW = dQ and polymer possesses an ideal elastic-plastic deformation. Within the frameworks of the fractal analysis d =2 means, that (p, = 1.0, that is, amorphous glassy polymer structure represents itself one gigantic cluster. However, as it has been shown above, the condition d =2 achievement for polymers is impossible in virtue of entropic tightness of chains, joining clusters, and therefore, d > 2 for real amorphous glassy polymers. This explains the experimental observation for the indicated polymers dU 0 or dW dQ [57], At Vg, =... 

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