Amorphous local ordering clusters

The relative fraction of dynamic local order (clusters) can be estimated within the frameworks of the cluster model of the amorphous state of polymers [11] ... 

Narten et al. also deduced from their data that one fifth of the water molecules are located at this additional distance. In a RDF picture, this corresponds to 4 nearest-neighbours at 2.76 A and 1 second neighbour at 3.3 A. This matches well the atomic surrounding depicted by the cluster corresponding to the structure of ice after the irradiation (cluster 2). The local order before the irradiation is better described by the 4-coordinated tetrahedron found in the normal amorphous low-density ice and in the crystalline ice (cluster 1). Thus we conclude that the structure of the ice film before the irradiation is not that of the high-density phase but that of the normal low-density phase. In addition, since the irradiated ice has a local order similar to what expected in the high-density phase, we also conclude that the photolysis at 20 K has induced the phase transition from the low-density to the high-density amorph. 

This chapter is the introduction to the physics of polycluster amorphous solids. At first the polycluster model was developed as a constructive foundation to describe some properties of metallic glasses. The assumption about the presence of a comparatively perfect local order (LO) (not necessarily of one type) leads naturally to the definition of the locally regular cluster (LRC), after which one must make only one step (not quite ambiguous) to introduce the definition of the polycluster structure. From this definition, there evolves the description of structure defects (Sect. 6.4). 

It is worth mentioning that the influence of the regions of local order, i.e., clusters, on the orientation behaviour of amorphous polymers has been discussed previously [14,15]. 

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],... 

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]. 

For amorphous polymers value is accepted equal to relative total length of polymer segments, included in local order domains (clusters) and estimated as follows [204] ... 

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... 

Proceeding from the said above and analyzing values of polymers limiting strains, one can obtain the information about local order regions type in amorphous and semicrystalline polymers. The fulfilled by the authors of Ref [36] calculations have show that the most probable type of local nanostructures in amorphous polymer matrix is an analog of crystallite with stretched chains, that is, cluster. 

In the model [98] it has been assiuned, that nucleus domain with size u is formed in defect-free part of semicrystalline polymer, that is, in crystallite. Within the frameworks of model [1] and in respect to these polymers amorphous phase structure such region is loosely packed matrix, surrounding a local order region (cluster), whose structure is close enough to defect-free polymer structure, postulated by the Flory felt model [16, 17]. In such treatment the value u can be determined as follows [43] ... 

As it is known [2, 12], within the frameworks of cluster model the elasticity modulus E value is defined by stiffness of amorphous polymers structure both components local order domains (clusters) and loosely packed matrix. In Fig. 13.3, the dependences E(v J are adduced, obtained for tensile tests three types with constant strain rate, with strain discontinuous change and on stress relaxation. As one can see, the dependences E(yJ are approximated by three parallel straight lines, cutting on the axis E loosely packed matrix elasticity modulus E different values. The greatest value E is obtained in tensile tests with constant strain rate, the least one - at strain discontinuous change and in tests on stress relaxation E = 0 [1]. 

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]. 

It should be expected that the formation of the local order domains will affect the general ordering degree of the polymer amorphous state structure. At present, there are some methods allowing characterisation of the polymer structure order (or disorder) degree, and they will be compared below with the parameters characterising the cluster structure of these materials. 

Between order (vj and disorder (Ap/p) indicators the inversely proportional correlation should be observed, confirmed by the data of Figure 1.24, where the values of (Ap/p) were calculated according to Equation 1.38. The correlation (Ap/p) (v /) is one more argument for the benefit of thermofluctuational origin of local domains (clusters) in the polymer amorphous state [89]. 

Strictly speaking, the F value is not an indicator of the local ordering degree for polymer structure, since clusters are formed by segments of different macromolecules, but it can be an indicator of mutual penetration of macromolecular coils. As has been shown in papers [22, 100], the same role can be played by the characteristic ratio C. If this assumption is correct, a definite correlation between F and must be observed. The data of Figure 1.30 show that such a correlation is really observed for nine amorphous and semi-crystalline polymers (the F value is calculated for T= 293 K) [99]. 

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