Clusters relative fraction

The structure correct quantitative model is necessary for analytic intercommunication between polymers structure and properties obtaining. As it has been noted above, the cluster model of polymers amorphous state structure will be used with this purpose [106, 107], The notion of local (short-order) order forms the basis of this model and loeal order domains (clusters) relative fraction is connected with glass transition temperature according to the following percolation relationship [107] ... 

Then nano clusters relative fraction (p, can be calculated by using the following equation [8] ... 

There are two main physical reasons, which define intercommunication of fractal essence and local order for solid-phase pol miers the thermodynamical nonequilibrium and dimensional periodicity of their structure. In Ref. [9], the simple relationship was obtained between thermod5mamical nonequilibrium characteristic - Gibbs function change at self-assembly (cluster structure formation of pol miers AG - and clusters relative fraction (p jin the form ... 

FIGURE 1.1 The dependence of clusters relative fraction j, on absolute value of specific Gibbs function of nonequilibrium phase transition AG" for amorphous glassy polymers -polycarbonate (1) and polyarylate (2) [3],... 

The Gibbs specific function notion for nonequilibrium phase transition overcooled liquid —> solid body is connected closely to local order notion (and, hence, fractality notion, see chapter one), since within the ffamewoiks of the cluster model the indicated transition is equivalent to cluster formation start. In Fig. 1.1, the dependence of clusters relative fraction (p, on the... 

Let us consider in the present chapter conclusion the treatment of dependences of yield stress on strain rate and crystalline phase structure for semicrystalline polymers [77]. As it known [91], the clusters relative fraction is an order parameter of polymers structure in strict physical significance of this term and since the local order was postulated as having thermofluctuation origin, then cp, should be a function of testing temporal scale in virtue of... 

Having determined value t as duration of linear part of diagram load -time P -1) in impact tests and accepting is equal to clusters relative fraction in quasistatic tensile tests [92], the values (p, (r) can be estimated. In Fig. 4.22, the dependences on strain rate for HOPE and polypropylene (PP) are shovm, which demonstrate increase at strain rate growth, that is, tests temporal scale decrease. 

Then clusters relative fraction rp is estimated from the obvious relationship [102] ... 

FIGURE 5.1 The relation between loeal plasticity zone length h and clusters relative fraction in double logarithmic coordinates, corresponding to the Eq. (5.4) for HOPE (1) and PS (2) [10]. 

Let us consider stmctural aspect of x change, which is due to Z introduction. As it is known [32], for the composition HOPE + 0.05Z clusters relative fraction (p j extreme increasing is observed, that results to stmcture fractal dimension dj. decreasing according to the Eq. (1.12). In its turn, the dimensions and are connected with each other by the relationship [29] ... 

Let s consider structural aspect of t50 change due to introduction Z. As it is known [3, 15], for compositions HDPE+Z is observed the extreme rise of relative fraction of local order regions (clusters) cpci, that results to decrease of fractal dimension of structure df according to the equation [15] ... 

A more precise method of the dependence E T) calculation exists. As it is known through Ref [107], by virtue of clusters thermofluctuational origin their relative fraction is the reducing function of temperature (the Eq. (96)). This allows calculation (Rvalue according to the Eq. (97) and subsequent estimation according to the Eq. (100). Then the Eq. (158) can be used directly for the dependence E T) evaluation at the obvious... 

Then the relative fraction of local order regions (clusters) cp< / have been estimated with the aid of the equation [7] ... 

FIGURE 8.2 The dependence of statistical segments number per one nano cluster on interfacial regions relative fraction for nano composites LLDPE/MMT. Horizontal shaded line indicates the minimum value n =2. 

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]. 

As it IS known [13], the value increases at molecular mobility intensification and the latter is associated with chains mobility in polymer structure loosely packed regions [71]. Within the fi ameworks of model [7] loosely packed matrix, surrounding clusters is such region. Its relative fraction cpj can be determined according to the Eq. (2.4). In Fig. 10.20, the dependence Ap((p,j ) is shown, which has the expected character. In conformity with the data of Ref. [13] linear growth at increase is observed and the condition Ap = 0 is realized not at (Pj = 0, what was to be expected, but at cpj 0.352. This value (p, according to the Eq. (2.4) corresponds to cp j 0.648,... 

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