Nanocluster relative fraction

The theoretical values Q (Q ) as a function of the chain statistical flexibility was performed as follows. Within the frameworks of percolation theoiy it has been shown, that between local order domains (nanoclusters) relative fraction cp j and T the following relationship exists [152] ... 

The main stmcture parameter of cluster model-nanoclusters relative fraction (p, which is polymers structure order parameter in strict physical sense of this tern, can be calculated according to the Eq. (1.11). In its turn, the polymer structure fractal dimension value is determined according to the Eqs. (1.9) and (2.20). 

At amorphous glassy polymers as natural nanocomposites treatment the estimation of filling degree or nanoclusters relative fraction (p j has an important significance. Therefore, the authors of Ref. [27] carried out the comparison of the indicated parameter estimation different methods, one of which is EPR-spectroscopy (the method of spin probes). The indicated method allows to study amorphous polymer structural heterogeneity, using radicals distribution character. As it is known [28], the method, based on the parameter - the ratio of spectrum extreme components total intensity to central component intensity-measurement is the simplest and most suitable method of nitroxyl radicals local concentrations determination. The value of dipole-dipole interaction is directly proportional to spin probes concentration C [29] ... 

In Fig. 15.9, the dependence of on mean distance r between chaotically distributed in amorphous PC radicals-probes is adduced. For PC at T = 77K the values of djd = 0.38 0.40 were obtained. One can make an assumption about volume fractions relation for the ordered domains (nanoclusters) and loosely packed matrix of amorphous PC. The indicated value djd means, that in PC at probes statistical distribution 0.40 of its volume is accessible for radicals and approximately 0.60 of volume remains unoccupied by spin probes, that is, the nanoclusters relative fraction according to the EPR method makes up approximately 0.60 0.62. 

The dependence of elasticity modulus E on nanoclusters relative fraction... 

Hence, the stated above results have demonstrated, that intercomponent adhesion level in natural nanocomposites (polymers) has structural origin and is defined by nanoclusters relative fraction. In two temperature ranges two different reinforcement mechanisms are realized, which are due to large friction between nanoclusters and loosely packed matrix and also perfect (by Kemer) adhesion between them. These mechanisms can be described successfully within the frameworks of fractal analysis. 

As it has been shown above (see the Eqs. (15.7) and (15.15)), the nanocluster relative fraction increasing results to polymers elasticity modulus enhancement similarly to nanofiller contents enhancement in artificial nanocomposites. Therefore, the necessity of quantitative description and subsequent comparison of reinforcement degree for the two indicated above nanocomposites classes appears. The authors of Ref. [58, 59] fulfilled the comparative analysis of reinforcement degree by nanoclusters and by layered silicate (organoclay) for polyarylate and nanocomposite epoxy poly-mer/Na" —montmorillonite [60], accordingly. 

The considered structural changes can be described quantitatively within the fi-ameworks of the cluster model. The nanoclusters relative fraction cp j can be calculated according to the method, stated in Ref [68]. 

FIGU RE 15.31 The dependences of nanoclusters relative fraction cp j on extrusion strain for extruded (1) and annealed (2) REP [62],... 

In the stated above treatment not only nanostructure integral characteristics (macromolecular entanglements cluster network density v, or nanocluster relative fraction cp j), but also separate nanoeluster parameters are important (see Section 15.1). In this case of particulate-filled polymer nanocomposites (artificial nanocomposites) it is well-known, that their elasticity modulus sharply increases at nanofiller particles size decrease [17]. The similar effect was noted above for REP, subjected to different kinds of processing (see Fig. 15.28). Therefore, the authors of Ref. [73] carried out the study of the dependence of elasticity modulus E on nanoclusters size for REP. 

Nanoclusters formation synergetics is directly connected with the studied polymers structure macroscopic characteristics. As it has been noted above, the fractal structure, characterized by the dimension is formed as a result of nanoclusters reformations. In Fig. 15.7 the dependence for the considered polymers is adduced, from which increase at A. growth follows. This means, that the increasing of possible reformations number m, resulting to Aj reduction (Fig. 15.6), defines the growth of segments number in nanoclusters, the latter relative fraction cp j enhancement and, as consequence, d reduction [3-5]. 

For natural nanocomposites (crosslinked epoxy polymers) the failure stress was accepted as being CT, the relative fraction

loosely packed matrix failure stress as (7 , which can be estimated in diagram form as G . For this purpose the value of was calculated according to Relationship 6.15 and then the dependence for the considered epoxy polymers was plotted (Figure 9.12), which turns out to be linear and the value of was determined by extrapolation of this linear dependence to (p, = 0 or tp = 1.0 (where (p, is the loosely packed matrix relative fraction, connected with tp hy Equation 9.10. As follows from the plot of Figure 9.12, G = 50 MPa. 

Figure 9.12 The dependence of the failure stress on the relative fraction of nanoclusters (p, for epoxy polymers EP-1 (1) EP-1-200 (2) EP-2 (3) and EP-2-...

Figure 9.13 The dependence of the stress concentration factor on the relative fraction (p, of nanoclusters for epoxy polymers. The designations are the same as...

The reduction in with growth in supposes that the adaptability of the structure of epoxy polymers decreases with growth in the relative fraction of nanoclusters or increases with a rise in the relative fraction of the loosely packed matrix. In Figure 9.18 the dependence ) is adduced, which has an expected character and... 

As the studies of amorphous linear polymers considered as natural nanocomposites have shown, their elasticity modulus is a linear increasing function of the relative fraction of nanoclusters [48]. Such behaviour of the elasticity modulus of the indicated polymers confirms the treatment of nanoclusters as nanofillers (reinforcing elements). The authors of paper [49] carried out a similar analysis of elasticity modulus behaviour in compression tests for crosslinked epoxy polymers. 

Figure 9.27 The dependences of the thermal expansion linear coefficient a p on the relative fraction (p of nanoclusters. 1 - the adhesion absence on the boundary between components 2 - the mixtures rule 3 - Terner equation 4, 5 - the experimental data for epoxy polymers EP-1 (4) and EP-1-200 (5) [51]...

The calculation of the relative fraction (p, of nanoclusters was carried out with the help of Equation 6.15. In Figure 9.35 the dependence of the thermal cluster order... 

Hence, the results stated above have shown that the order parameter index of a thermal cluster, by which the structure of the considered epoxy polymers is simulated, decreases with growth in the relative fraction of nanoclusters and its variation makes up 0.38-0.76 and this means that the loosely packed matrix and nanoclusters are structural components defining the behaviour of epoxy polymers, and the role of nanoclusters grows as their contents increase. The thermal cluster model allows the glass transition temperature of epoxy polymers as a function of the relative fraction of nanoclusters to be predicted. The order parameter index of the thermal cluster... 

The rarely crosslinked epoxy polymer on the basis of resin UP5-181 has a low glass transition temperatnre T, which can be estimated according to shrinkage measurements data as being equal to 333 K. This means that the testing temperatures T = 293 K and Tg for it are close, which is confirmed by the small AOy valne for the native REP. This supposes (nanostructures) a small relative fraction of the nanoclusters [2, 3] and, since these nanoclusters have arbitrary orientation, an increase in results rapidly in their decay, which causes mechanical devitrification in the loosely packed matrix at > 0.36. The devitrificated loosely packed matrix gives an insignificant... 

The considered structural changes can be described quantitatively within the frameworks of a cluster model. The relative fraction of nanoclusters can be calculated according to the method stated in paper [13]. The dependences quantitative confirmation. The dependence of the density p of REP extruded specimens on adduced in Figure 10.5 is similar to the dependence which... 

In the treatment stated above it is not only the integral characteristics of the nanostructure (macromolecular entanglements cluster network density or relative fraction

particulate-filled polymer nanocomposites (artificial... 

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