Amorphous structural parameters

Polymers don t behave like the atoms or compounds that have been described in the previous sections. We saw in Chapter 1 that their crystalline structure is different from that of metals and ceramics, and we know that they can, in many cases, form amorphous structures just as easily as they crystallize. In addition, unlike metals and ceramics, whose thermodynamics can be adequately described in most cases with theories of mixing and compound formation, the thermodynamics of polymers involves solution thermodynamics—that is, the behavior of the polymer molecules in a liquid solvent. These factors contribute to a thermodynamic approach to describing polymer systems that is necessarily different from that for simple mixtures of metals and compounds. Rest assured that free energy will play an important role in these discussions, just as it has in previous sections, but we are now dealing with highly inhomogeneous systems that will require some new parameters. 

A method is described which enables structural parameters of non-crystalline polymers to be determined. It is based on the analysis of wide-angle X-ray scattering and where possible incorporates the additional information obtainable from oriented specimens. Particular emphasis is placed on the analysis of the structure of molten polyethylene. The potential application of the approach to the structure of the amorphous phase in semicrystalline polymers is discussed. 

With a Fourier transformation of (k) in the distance space, one obtains a separation of the contribution of the various coordination shells. This Fourier transform yields the structural parameters Rj, Nj and ah and thus the near range order of the specimen with respect to the absorbing atoms. The EXAFS analysis for the different absorber atoms within the material yields their specific near range order. Thus, one may get the structure seen form several kinds of absorbing atoms. EXAFS does not require highly crystalline materials. It is a suitable method to study disordered, or even amorphous, structures. The a values provide quantitative information about the thermal and structural disorder. 

The fact that both the neat components and their blends are relatively well characterized with respect to their varying structures and morphologies as a result of the applied mechanical and thermal treatments, permits us to follow the gradual variation of microhardness as a function of structural parameters. In this way one can obtain the H values for material components which are not accessible to direct experimental determination. Furthermore, having the extrapolated values for completely amorphous and fully crystalline homopolymers and starting from a knowledge of the number of components (and/or phases) one can make use of the additivity law (eq. (1.5)) to evaluate the mechanical properties of components which cannot be isolated or do not exist as individual materials. A good example of this are the PET microfibrils studied here (Fig. 5.16(b)). 

The potential of Eq. (1) with parameters determined in Refs. [10, 11] was thoroughly tested in computer simulations of silica polymorphs. In Ref. [10], the structural parameters and bulk modulus of cc-quartz, a-cristobalite, coesite, and stishovite obtained from molecular dynamics computer simulations were found to be in good agreement with the experimental data. The a to / structural phase transition of quartz at 850 K ha.s also been successfully reproduced [12]. The vibrational properties computed with the same potential for these four polymorphs of crystalline silica only approximately reproduce the experimental data [9]. Even better results were reported in Ref. [5] where parameters of the two-body potential Eq. (1) were taken from Ref. [11]. It was found that the calculated static structures of silica polymorphs are in excellent agreement with experiments. In particular, with the pressure - volume equation of state for a -quartz, cristobalite, and stishovite, the pressure-induced amorphization transformation in a -quartz and the thermally induced a — j3 transformation in cristobalite are well reproduced by the model. However, the calculated vibrational spectra were only in fair agreement with experiments. 

The disordered nature of the amorphous phase has prevented the direct determination of the structural parameters by the usual structural techniques such as X-ray diffraction. Solid-state NMR can give us those parameters even for amorphous samples. Yannoni and Clark [14] applied nutation NMR spectroscopy, which is specifically designed to measure interatomic distances, to determine the bond lengths in both the cis- and tran -polyacetylenes. They used polyacetylene polymerized from a mixture of 4% doubly C-enriched acetylene and doubly depleted acetylene. In Fig. 7.6, the observed and simulated proton decoupled nutation spectra of the cis sample are shown. The sharp peak in the centre arises from the isolated nuclei in the sample. The remainder of the spectrum is a Pake-doublet arising from the dipolar coupling of adjacent nuclei in the polyacetylene. The best fit to the observed spectrum corresponds to a distribution of bond length with... 

Fig. 14.10. C CP NMR spectra of carbonyl carbon-labeled uniaxially draw (x3 at 45°C) PET film as a function of /3u, the angle between the draw direction and the magnetic field. Solid and dotted lines show observed and calculated spectra, resp>ectively. The fractions of the two components, amorphous (35%) and oriented (65%) were determined computer simulations of the observed NMR lineshapes. The structural parameters ap = 90°, /3p = 18 6° with the distribution of the fiber axis p = 22° were found to be characteristic of the oriented component.

Fig. 14.12. CP NMR spectra of carbonyl carbon-labeled uniaxially draw (x5 at 80°C) PET film after heat treatment at 170°C. 8l is set as 0 and 90°. Full and dotted curves show observed and calculated spectra, respective y. The fractions of the three components, amorphous (30%) and two oriented ones (35 and 35%), was determined by simulation. The structural parameters were ap = 90°, ySp = 20 10° and p = 8° (low oriented component) and ap = 90°, )3f = 11 5° and p = 2° (high oriented component), respectively.

In deuteron NMR studies of the diffusion of benzene within zeolites it was found that the pre-exponential factor for the correlation time was inversely proportional to the number of available sites to which a molecule could jump. The pre-exponential factor is the limiting value of the correlation time as temperature tends to infinity. In previous work, the above findings for zeolites have been generalised to so-called "amorphous structures which exhibit the property of self-similarity. It was assumed that the pre-exponential factor for the correlation time was inversely proportional to the number of adsorption sites contained within a limiting length scale, is a parameter of the model determined... 

Linear aliphatic homopolyamides are partially crystalline materials. Therefore they are characterized by both an unordered amorphous state and an ordered crystalline state. The latter may exhibit polymorphism. The extent to which each state or specific modification is represented depends, for a given chemical structure, considerably on processing conditions and treatment operations. It affects the properties of the shaped polyamide product. Thus the corresponding structure parameters are of importance for optimizing fiber processes as well as for assessing the performance of fiber products in particular applications. 

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