Structure of amorphous polymers

Measurements of molecular weight and its distributions are generally performed in dilute solution by a variety of techniques. These are discussed, e.g., by Billmeyer (1984) and Sperling (2001). 

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The structure of amorphous polymers has often been compared with that of a mass of cooked spaghetti i.e. without correlation between the end-to-end vectors of segment sequences. A number of experimental data, however, point to the existence of more ordering, than implied by this picture, perhaps even in the equilibrium state. 

Weber and Helfand were among the first to propose an MD-based approach to the study of the structure of amorphous polymers. In particular, they modeled polyethylene at 425 °C by employing a box of edge length 18.2 A. The box contained 200 carbons. 

T Hatakeyama, H Hatakeyama. Effect of chemical structure of amorphous polymers on heat capacity difference at glass transition temperature. Thermochimica Acta 267 249-257, 1995. 

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. 

This article describes the present state of knowledge regarding the structure of amorphous polymers as obtained from scattering techniques and the corresponding dynamic properties from a structural point of view. A detailed knowledge of the structure is very important because the thermal, mechanical, viscoelastic, optical, and even electrical properties are strongly governed by the structure and its temporal fluctuations. 

An amorphous polymer does not exhibit a crystalline X-ray diffraction pattern, and it does not have a flrst-order melting transition. If the structure of crystalline polymers is taken to be regular or ordered, then by difference, the structure of amorphous polymers contains greater or lesser amounts of disorder. 

In the previous chapter the structure of amorphous polymers was examined. In this chapter the study of crystalline polymers is undertaken. The crystalline state is defined as one that diffracts X-rays and exhibits the first-order transition known as melting. 

This network model was developed for PS with its relatively large entanglement distance d of about 10 nm and average mesh diameter D (Z) = d Vi = 1.4d) of about 14 nm. However, it can also be used for other amorphous polymers with smaller entanglement molecular weights and distances. These density fluctuations in a domain-like form are the weakest supramolecular structures in amorphous polymers. Therefore, the typical amorphous polymers, often used as models of an amorphous material, are also not really structureless. In the literature, there are some other results relating to the structures of amorphous polymers, ranging... 

Multidimensional s-NMR spectroscopy has yielded ample molecular-scale information on re-orientational and translational dynamics in semicrystalline and amorphous polymers, on their chemical and phase structure, and on orientational order. The dynamics and structure of amorphous polymers studied by multidimensional solid-state exchange NMR spectroscopy has been reviewed [762]. 

From the study of disordered chain conformations, while threedimensional order of some feature of the structure is maintained, we went into the consideration of model building of the "structure" of amorphous polymers. 

We have so far been concerned principally with the structure of crystalline polymers which can readily be studied by using standard X-ray and electron diffraction methods. However, there is an important category of polymers which have not yet been considered which can be completely non-crystalline. They are generally termed amorphous and include the well-known polymer glasses and rubbers. Although the properties of these materials have been studied at length, very little is known about their structure. This is because there is no well-defined order in the structure of amorphous polymers and so they cannot be analysed very easily using standard diffraction techniques. 

It is obvious that the structure of amorphous polymers (or the amorphous phase of semi-crystalline polymers) gives grounds to assume the availability in them of a definite chaos degree. It is also quite obvious that the chaos degree of an amorphous phase structure represents an important parameter determining structural characteristics and, consequently, a polymer s properties. That is why the question about interconnection of these parameters arises. The second important problem is the physical nature of chaos in polymers is it random (and unpredictable) or deterministic chaos ... 

Let us note that the study of the degree of disorder of the structure of amorphous polymers is not only of theoretical significance. In Figure 1.21 the dependence of the yield stress of the three studied polymers on the reciprocal value 8 is presented. As one can see this dependence has the simplest shape it is linear and passes through the coordinates origin. That is why it is quite suitable for prediction of the mechanical properties of polymers. Similar dependences were obtained for the yield strain and the elasticity modulus E [75]. 

Let us note one more important aspect. The treatment of the structure of amorphous polymers adduced above belongs to elastomers [56]. Transference of these notions on amorphous glassy polymers assumes the description of densely packed domains freezing , i.e., a sharp increase in their life time. In addition, fractal forms of macromolecules (statistical macromolecular coils), formed in non-equilibrium physical-chemical processes, are preserved ( frozen ) in polymers. This assumes that in a glassy state the mobility of chain parts between their fixation points will be the main factor defining molecular mobility [57]. 

Wide angle X-ray diffractometry is a perspective method of the study of the structure of amorphous polymers on a molecular level [1,2]. However, the obvious discrepancy between its large possibilities and information received according to the experimental data requires further development of this method. 

In paper [126] it was shown that universality of the critical indices of the percolation system was connected directly to its fractal dimension. The self-similarity of the percolation system supposes the availability of the number of subsets having order n (n = 1, 2, 4,. ..), which in the case of the structure of amorphous polymers are identified as follows [125]. The first subset (n = 1) is a percolation cluster frame or, as was shown above, a polymer cluster network. The cluster network is immersed into the second loosely packed matrix. The third (n = 4) topological structure is defined for crosslinked polymers as a chemical bonds network. In such a treatment the critical indices P, V and t are given as follows (in three-dimensional Euclidean space) [126] ... 

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