Cluster model of polymers

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. 

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... 

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). 

Let us note that within the frameworks of the cluster model of polymers amorphous state structure [18] chains deformation in loosely packed matrix only is assumed and since the Eq. (4.42) gives molecular drawing ratio, which is determined in the experiment according to the relationship [81] ... 

Hence, the offered techniques, using the methods of fractal analysis and cluster model of polymers amorphous state structure, allow the theoretical estimation of both deformability and strength of polymers. The side groups influence on these characteristics was considered in detail. It has been shown that the polymer strength is defined by both strength resource and deformability resource. 

Polymer mechanical properties are one from the most important ones, since even for polymers of different special-purpose function a definite level of these properties always requires [20]. Besides, in Ref [48] it has been shown, that in epoxy polymers curing process formation of chemical network with its nodes different density results to final polymer molecular characteristics change, namely, characteristic ratio C, which is a polymer chain statistical flexibility indicator [23]. If such effect actually exists, then it should be reflected in the value of cross-linked epoxy polymers deformation-strength characteristics. Therefore, the authors of Ref [49] offered limiting properties (properties at fracture) prediction techniques, based on a methods of fractal analysis and cluster model of polymers amorphous state structure in reference to series of sulfur-containing epoxy polymers [50]. 

In the Ref [49] the two deformation-strength characteristics prediction was carried out strain up to fracture and fracture stress 0. For the value theoretical estimation two methods can be used. The first from them does not include in the calculation of molecular characteristics and, hence, does not take into account their change, in any case, directly [51], This method is based on the cluster model of polymers amorphous state structure notions [ 14], taking into account the order availability, and the limiting draw ratio value in this case is given as follows [51] ... 

The polymers physical aging represents itself the structure and properties change in time and is the reflection of the indicated materials thermodynamically nonequilibriiun nature [61, 62], As a rule, the physical aging results to polymer materials brittleness enhancement and therefore, the ability of structural characteristics in due course prediction is important for the period of estimation of pol5mier products safe exploitation. For cross-linked polymers the quantitative estimation of structure and properties changes in physical aging process was conducted in Refs. [63, 64] within the frameworks of fracture analysis [65] and cluster model of polymers amorphous state structure [7, 66]. The authors of Ref. [67] use the indicated theoretical models for the description of PC physical aging. Besides, for PC behavior closer definition in the indicated process such theoretical notions were drawn as structure quasiequilibrium state [68] and the thermal cluster model [69], which is one from variants of percolation theory. 

Thus, the structural model for polyethylene and nanocomposites on its basis creep process description is offered, taking into account the indicated polymeric materials structure heterogeneity. This treatment is given within the frameworks of the cluster model of polymers amorphous state structure and shown the good correspondence wit experiment [7]. 

The authors of Ref. [21] supposed, that in orientational drawing process of poly(metyl methacrylate) (PMMA) the following structure changes occur the transition to more equilibrium structure owing to molecular package improvement and internal stresses relaxation. The quantitative structural model absence not allows the authors of Ref [21] to give direct proofs of their suppositions. In Ref [22] such treatment was fulfilled on the example of extruded amorphous polyarylates DV and DF-10 with the cluster model of polymers amorphous state structure using [12, 23],... 

Thus, the Ref [27] results showed, that the obtained by EPR method natural nanocomposites (amorphous glassy polymers) structure characteristics corresponded completely to both the cluster model theoretical calculations and other authors estimations. In other words, EPR data are experimental confirmation of the cluster model of polymers amorphous state structure. 

Hence, the presented above results have shown that elasticity modulus of amorphous glassy polycarbonate, considered as natural nanocomposite, are defined completely by its suprasegmental structure state. This state can be described quantitatively within the frameworks of the cluster model of polymers amorphous state structure and characterized by local order level. Natural nanocomposites reinforcement degree can essentially exceed analogous parameter for artificial nanocomposites [56]. 

However, one should not forget that fractal analysis gives only a common mathematic description of a polymer s structure, i.e., it does not identify those structural units (elements) that any real polymer consists of. The cluster model of polymer amorphous state structure allows one to obtain a physical description of a thermodynamically nonequilibrium polymer s structure with local (short-range) order representations drawing and molecular characteristics usage, which identifies its element quantitatively. Since these models consider polymer structure from different positions, they are a very good complement of one another [7, 29]. 

In the present section notions of the amorphons state structure of a cluster model of polymers [7, 8] were used for the description of a change in nucleation mechanism and melting temperature of an oriented PCP. These notions are developed in the dynamic polymer network concept, since supramolecnlar (more precisely, snprasegmental) structure changes, described by a cluster model, are a logical result of changes on the molecular level, which are due to network tension (see Table 4.1). The cluster model application allows the physical effects predicted within the frameworks of general thermodynamic theory to be concretised and identified and also to be described quantitatively. 

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