Cluster network density

Macromolecular entanglements cluster network density v j can be estimated as follows [8] ... 

As it is known [5], in amorphous phase two types of macromolecular entanglements are present traditional macromolecular binary hooking and entanglements, formed by nano clusters, networks density of which is equal to and v, respectively. value is determined within the framework of mbber high-elasticity conception [2] ... 

FIGURE 2.5 The dependences of elasticity modulus E (1) and equilibrium modulus (2) on macromolecular entanglements cluster network density n, for PC [47],... 

The plotted according to the experimental data dependencies of elasticity modulus E on macromolecular entanglements cluster network density (Figs. 2.5 and 2.6) break down into two linear parts, the boundary of which serves loosely packed matrix glass transition temperature which is lower on about 50K of polymer glass transition temperature [50]. Below the value E is defined by the total contribution of both clusters and loosely packed matrix and above - only by clusters contribution. It becomes clear, if to taken into consideration, that above the elasticity modulus value of devitrificated loosely packed matrix has the order of 1 MPa [51], that is, negligible small. It is an extremely interesting the observation, that loosely packed matrix in the value E, determined by the plot E (v, ) extrapolation to = 0, is independent on temperature. Such situation is not occasional and deserves individual consideration. 

Approximate equality of these parameters is observed that assumes association of the yielding with the stability loss by polymers. More precisely, we are dealing with the stability loss by clusters, because parameter V depends upon the cluster network density (the Eq. (1.10)) and value is proportional to V i [32],... 

If to consider the cluster network density v j as and to choose statistical segment length / as the scale, then the Eq. (6.1) is changed as follows... 

FIGURE 6.1 The relationship between maeromolecular entanglements cluster network density v, and parameter for PC(1) and PAr (2) [7],... 

The dependence of impact toughness on macromolecular entanglements cluster network density was considered briefly by the authors of Ref [15]. In Fig. 10.6, the dependence of impact toughness of PASF aged... 

FIGURE 13.3 The dependences of elasticity modulus E on entanglements cluster network density n, in tests with constant strain rate (1), strain discontinuous change (2) and on stress relaxation (3) for PASF [1]. 

The strain energy release critical rate Gj, characterizing polymer local plasticity level (see the Eq. (5.13)), is coupled with material structure. The higher entanglements cluster network density v, is the more intensively shear local deformation mechanism is realized [13], and the larger Gj is. This means, that growth should result to Gj reduction. Actually, for PASF considered samples such correlation was obtained and it can be approximated by the following relationship [1] ... 

FIGURE 13.13 The dependence of stable crack propagation begiiming strain e on entanglements cluster network density n j for PASF film samples [1]. 

FIGURE 14.3 The dependence of entanglements cluster network density on extrusion draw ratio X for polyarylates DV (1) and DF-10 (2) [22]. 

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. 

Figure 1.1 The dependences of the macromolecular entanglements cluster network density on the testing temperature T for (1) PC and (2) PAr [7]...

Figure 1.15 The dependence of the macromolecular entanglement cluster network density on Lyapunov s index Xj for amorphous glassy and semi-crystalline...

Figure 1.27 The temperature dependence of the entanglement cluster network density for polyhydroxyester. The horizontal dashed line indicates the lower boundary (v ) of the stability of the clusters [98]...

In Figure 5.24 the dependence p vf) is adduced, which turns out to be linear. As one can see, an increase in results in p growth, which is accompanied by reduction in d [102]. This corresponds to the common notions in model [98]. As the results of papers [103, 104] have shown, an increase in results in growth of the cluster network density and reduction in the number of segments in one cluster. This means a large number (= vJnJ of small clusters are formed. In Figure 5.25 the... 

Let us show how the value of (i.e., at the molecular and topological levels) influences the suprasegmental level of the structure. Within the frameworks of the cluster model [5,6] the number of densely packed segments in clusters per volume unit is approximately equal to the cluster network density and is connected with v by Equation 2.7, in which the numerical constant accounts for the necessary molecular constants of polymers. 

Figure 5.36 The comparison of experimental values of (1) and those calculated according to Equation 2.7 (2) of the cluster network density on magnitude for...

It should he expected that the indicated structural changes would define the parameters characterising the yielding process of crosslinked polymers. Let us consider this rule on the example of yield strain y. It is natural to suppose that the larger the amount of DS that is subjected to decay in the yielding process the larger the value of e should he. The indicated amount of DS can be determined as the difference of cluster network densities up to (v, ) and after (V /) yielding Av, = which can... 

Figure 6.11 The dependences of cluster network density in the underformed state V, (1, 2) and after yielding V j (3, 4) on the curing agent oligomer ratio value forEP-1 (1, 3)andEP-2(2,4) [47]...

Figure 6.12 The dependence of yield strain on the difference of cluster network densities up to and after yielding Av, for epoxy polymers EP-1 (1) and EP-2 (2)...

It has been shown earlier [78] that an increase in the extended tmns-conformations fraction results in raising of the entanglements cluster network density Hence one may assume that increasing QLj, indicating a rise in gauche-trans transition probability, should also result in increasing In Figure 6.29 the dependence QL ... 

A discrepancy between and at lai e magnitudes is probably due to the approximate character of the fulfilled calculations [76]. Nevertheless, the data of Figures 6.29 and 6.30 assume that cluster model quantitative parameters (cluster network density and cluster size / ) can be used for estimation of such an important characteristic of polymers as the thermal expansion coefficient [77]. 

Figure 6.36 The dependence of the glass transition temperature on the cluster network density for native (1) and aged (2) samples of EP-2 [93]...

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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