Molecular mobility level

Similar linear dependences for SP - OPD with various were obtained in Ref. [7] and they testify to molecular mobility level reduction at decrease and extrapolate to various (nonintegral) values at = 1.0. The comparison of these data with the Eq. (1.5) appreciation shows, that reduction is due to local order level enhancement and the condition = 1.0 is realized at values, differing from 2.0 (as it was supposed earlier in Ref [23]). This is defined by pol5miers sfructure quasiequilibrium state achievement, which can be described as follows [24]. Actually, tendency of thermodynamically nonequilibrium solid body, which is a glassy polymer, to equilibrium state is classified within the fimneworks of cluster model as local order level enhancement or (p j increase [24-26], However, this tendency is balanced by entropic essence straightening and tauting effect of polymeric medium macromolecules, that makes impossible the condition (p j= 1.0 attainment. At fully tauted macromolecular chains = 1.0)

polymer structure achieves its quasiequilibrium state at d various values depending on copolymer type, that is defined by their macromolecules different flexibility, characterized by parameter C. ... 

As it is known [35], the main chain mobility freezing occurs at certain temperature T, that supposes the condition =1.0 achievement. For poly-ethylenes the value 7 = 150 K [35]. At = 408 K polyethylenes turn into rubber-like state [44] and therefore, for them it is excepted = 2.0 [22]. In Table 2.1 the values at the indicated limiting temperatures, obtained according to the four used equations, are adduced. As one can see, the full range of change is obtained for the Eqs. (2.5) and (2.16) only, that confirms the necessity of structural parameters using at molecular mobility level estimation. 

Hence, the adduced above results shown that the main factor, influencing on molecular mobility level in HDPE noncrystalline regions, is these regions structure, characterized by fractal dimension or relative fraction of local order regions (clusters) (p j. Definite influence is exercised by molecular characteristics, especially if to take into account, that between and (p, on the one hand, and S and C, on the other hand, the close intercommunication exists (see, for the example, the Eqs. (1.11) and (1.12)). As consequence, the equations using, taking into account their structural state, will be correct for polymers dimension estimation [38]. 

It is known [13], that molecular mobility intensification results to energy dissipation increase and enhancement of polymer toughness at failure. In chapter two, it has been shown that the molecular mobility level can be characterized by the value of fiactal dimension of chain part between mac-romolecular entanglements nodes DJ < < 2 [14]). Fractional part change (i.e., 1) from 0 up to 1 gives all possible spectrum of molecular... 

From the Eq. (10.28) it follows, that large values d reaching, that is, ductile fracture can be realized either by enhancement or by C reduction. For polymers the value is connected with molecular mobility level, which can be characterized by fractal dimension of the chain part between entanglements [14], In Fig. 10.16 the relation between - 1) and q for the 10 studied in Ref [57] polymers is adduced, from which follows their approximate equality (deviation from the linear dependence for PAr, PSF andPASF is due to the condition 1 in the Eq. (10.1) nonfulfillment [58]. The dependence qj(-D, i - 1) for the 10 different polymers, adduced in Fig. 10.16, is identical to the similar dependence for HD PE samples with various length of notch, tested at different temperatures (Fig. 10.4), that indicates high community degree of the relation between q and... 

As it has been shown in Ref. [70], the value p.j. in the general case is a function molecular mobility level of polymer and p.j. > P, where P is the corresponding critical index of percolation cluster, the fomation oiwhich is controlled by geometrical interactions only [31]. The equality p.. = P is reached only in the case of completely inhibited molecular mobility., that is, in the case of quasiequilibrium state. 

The parameters and characterize polymer chain statistical flexibility and molecular mobility level, respectively [2], The dimension can be determined with the aid of the following equation [2] ... 

The adduced above analysis allows to elucidate the cause of higher values A for nanocomposites PP/CaCOj in comparison with PP/GNC. This cause is higher values for PP/CaCOj D = 33- 3A, for PP/GNC D =. 3- 29, that is, higher molecular mobility level for nanocomposites PP/CaCOj, although Oj, values are somewhat higher for PP/GNC. 

The impact toughness of particulate-filled polymer nanocomposites is defined by a number of factors on various stmctural levels molecular, topological and suprasegmental ones. The indicated levels characteristics are interconnected and changed at nanofiller introduction. The molecular mobility level is the main parameter, defining the considered nanocomposites impact toughness. 

As was shown in Section 4.1, the fractal dimension of a chain part between its fixation points characterises the molecular mobility level of a polymer. In paper [94] the interconnection of molecular mobility and local order was studied in the example of two series of epoxy polymers (native EP-1 and EP-3aged for 3 years in natural conditions). The dependence adduced in Figure 6.37 shows that increasing... 

Thus, the offered treatment assumes not only a change in the nonlinearity coefficient because of nanofiller introduction, but also permits a change in the polymer matrix structure by virtue of variation of the coefficient P, which depends on its molecular mobility level [54]. 

As it is known [6], within the frameworks of fractal analysis the molecular mobility level can be described with the aid of the fractal dimension of the chain part between nanoclusters D p, which changes within the limits of 1... 

In Figure 9.33 the dependence a p(D ) for the considered epoxy polymers is adduced, which has an expected character. The growth in the thermal expansion linear coefficient with an increase in molecular mobility level is observed. In Figure 9.33 a solid straight line shows the similar dependence oc(D p) for amorphous aromatic polyamide (phenylone S-2). As one can see, this straight line corresponds well to the data for the considered epoxy polymers. This means that irrespective of the class of polymers, their thermal expansion coefficient is defined by the molecular mobility level, which in paper [62] is characterised by the dimension... 

It has been shown earlier [67] that index P is a function of the molecular mobility level, characterised by the fractal dimension of a chain part between nanoclusters. At = 1 the indicated part is fully stretched between nanoclusters, its molecular mobility is suppressed and P, = p. At = 2 the molecular mobility is the greatest, which is typical for the rubber-like state of polymers [6]. Calculation of the dimension D, can be carried out with the help of Equation 6.22. 

---