Amorphous polymers cluster model

The concept of amylopectin forming double helices easily integrates into the currently-accepted cluster model, with the short linear chains of the branches being intertwined into double helices, while the branch points are located in the more amorphous regions between the clusters of double helices. Understanding that parts of amylopectin molecules are capable of forming double helices explains the apparent anomaly that a branched polymer is the source of structural order within granules. 

The cluster model of the structure of amorphous polymers (Figure 11.4) provides a quantitative description of supermolecular (supersegmental) structures in this type of polymer. 

Figure 11.4 Cluster model of the structure of an amorphous polymer.

In the present review, an attempt will be made to consider some of the structural aspects of interfacial adhesion using modern physical models the cluster model of the amorphous structure of polymers [10], fractal analysis [11, 12] and the model of irreversible aggregation [13]. 

The cluster model assumes availability in the amorphous polymers structure of local order domains (clusters), consisting of several densely packed collinear segments of different macromolecules (amorphous analog of crystallite with stretched chains). These clusters are connected between themselves by tie chains, forming by virtue of this physical entanglements network, and are surrounded by loosely packed matrix, in which all fluctuation free volume is concentrated [107],... 

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] ... 

Polymers mechanical properties are some from the most important, since even for polynners of different special purpose functions this properties certain level is required [199], However, polymiers structure complexity and due to this such structure quantitative model absence make it difficult to predict polymiers mechanical properties on the whole diagram stress-strain (o-e) length—fi-om elasticity section up to failure. Nevertheless, the development in the last years of fractal analysis methods in respect to polymeric materials [200] and the cluster model of polymers amorphous state structure [106, 107], operating by the local order notion, allows one to solve this problem with precision, sufficient for practical applications [201]. 

The strain at fracture of film samples can be calculated within the framework of a cluster model of polymers amorphous state structure [205] ... 

Hence, the results stated above demonstrated that the cluster model of polymers amorphous state stmcture and fractal analysis allowed quantitative prediction of mechanical properties for pol5miers film samples, prepared from different solvents. Let us note, that the properties prediction over the entire length of the diagram a- was performed within the framework of one approach and with precision, sufficient for practical applications. This approach is based on strict physical substantiation of the analytical intercommunication between structures of a macromolecular coil in solution and pol5miers condensed state [201]. 

Kozlov, G. V. Novikov, V. U. The cluster model of polymers amorphous state. Achievements ofPhysical Sciences, 2001,171(7), 717-764. 

One of the first studies of PNC physical aging was published by Lee andLichtenhan [1998] for epoxy containing w = 0 to 9wt% of polyhedral oligomeric silsesquiox-ane (POSS). The presence of POSS increased Tg and the relaxation time thus, the nanoflller slowed down the molecular dynamics. For amorphous polymers at Tpstructural cluster model. The cluster volume fraction depends on temperature ... 

Lately it was offered to consider polymers amorphous state stmcture as a natural nanocomposite [6]. Within the frameworks of cluster model of polymers amorphous state stmcture it is supposed, that the indicated structure consists of local order domains (clusters), immersed in loosely packed matrix, in which the entire polymer free volume is concentrated [7, 8]. In its turn, clusters consist of several coUinear densely packed statistical segments of different macromolecules, that is, they are an amorphous analog of crystallites with stretched chains. It has been shown [9] that clusters are nanoworld objects (tme nanoparticles-nano clirsters) and in case of polymers representation as natural nanocomposites they play nanofiller role and loosely packed matrix-nanocomposite matrix role. It is significant that the nanoclusters dimensional effect is identical to the indicated effect for particulate filler in polymer nano composites sizes decrease of both nano clusters [10] and disperse particles [11] resrdts to sharp enhancement of nanocomposite reinforcement degree... 

In Fig. 1.3 amorphous polymers nanostructure cluster model is presented. As one can see, within the limits of the indicated above dimensional periodicity scales Fig. 1.2 and 1.3 correspond each other, that is, the cluster model assumes p reduction as far as possible from the cluster center. Let us note that well-known Flory felt model [20] does not satisfy this criterion, since for it p const. Since, as it was noted above, polymeric mediums structure fractality was confirmed experimentally repeatedly [14-16], then it is obvious, that cluster model reflects real solid-phase polymers structure quite plausibly, whereas felt model is far from reality. It is also obvious, that opposite intercommunication is true - for density p finite values change of the latter within the definite limits means obligatory availability of structure periodicity. 

For the observed distinetions explanation it is necessary to point out, that the Eqs. (2.8) and (2.12) take into consideration only molecular characteristic, namely, maeromolecule flexibility, characterized by the value C. Although the Eq. (2.12) takes into account additionally topological factor (traditional macromolecular binary hooking network density v ), but this factor is also a function of [40, 42], The Eqs. (2.16) and (2.5) take into account, besides C, the structural organization of HDPE noncrystalline regions within the frameworks of cluster model of polymers amorphous state structure [5] or fractal analysis with the aid of the value [22], Hence, HDPE noncrystalline regions structure appreciation changes sharply the dependence DJJ). 

Hence, the cluster model of polymers amorphous state structure allows to identify structural relaxation mechanisms in them. In the case of glassy loosely packed matrix relaxation process is realized by conformational reorganizations in this structural component (mechanism I) and in the case of its devitrification - clusters mutual motions (mechanism II). 

Kozlov, G. V, Beloshenko, V. A., Shogenov, V. N. (1999). An Amorphous Polymers Structural Relaxation Description within the Framewoiks of Cluster model Fiziko-Khi-micheskaya Mechanika Materialov, 35(5), 105-108. 

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