Amorphous scattering

Percent Crystallinity. For samples that consist of a mixture of crystalline and amorphous material, it is possible to determine the percent of crystallinity by measuring the integrated intensity of sharp Bragg reflections and the integrated intensity of the very broad regions due to the amorphous scattering. 

A variety of techniques have been used to determine the extent of crystallinity in a polymer, including X-ray diffraction, density, IR, NMR, and heat of fusion [Sperling, 2001 Wunderlich, 1973], X-ray diffraction is the most direct method but requires the somewhat difficult separation of the crystalline and amorphous scattering envelops. The other methods are indirect methods but are easier to use since one need not be an expert in the field as with X-ray diffraction. Heat of fusion is probably the most often used method since reliable thermal analysis instruments are commercially available and easy to use [Bershtein and Egorov, 1994 Wendlandt, 1986], The difficulty in using thermal analysis (differential scanning calorimetry and differential thermal analysis) or any of the indirect methods is the uncertainty in the values of the quantity measured (e.g., the heat of fusion per gram of sample or density) for 0 and 100% crystalline samples since such samples seldom exist. The best technique is to calibrate the method with samples whose crystallinites have been determined by X-ray diffraction. 

Amorphous materials can be oriented by stretching. In some instances, this orientation is also accompanied by crystallization [3]. Isoprene rubber exhibits such behavior. The positions of the maxima in the amorphous scattering pattern provide a measure of the average intermolecular spacing. Bragg s law may be used to calculate the size of the interplanar spacing [3],... 

The relative degree of crystallinity can also be estimated from the WAXS pattern from the ratio of the integrated intensity of the crystal peak to that of the total amorphous and crystalline scattering (Balta-Calleja and Vonk 1989). For PE, the amorphous scattering below the (110) peak (Fig. 5.7) is relatively insensitive to the degree of crystallinity, so the integrated area of the (110) reflection compared to the broad amorphous halo is directly proportional to XPE. However, the absolute degree of crystallinity cannot be determined in this way (Ryan et al. 1995). 

Distribution of amorphous scattering intensity, in particular, angular 20 position, depends on the sizes of cyclic fragment and side substituting agent (Figure 14). 

The germanium films deposited between 190 and 300 °C were characterized for their structural properties by XRD. All films show amorphous scattering pattern with a detection limit of 1 vol % of crystalline component. 

The degree of crystallinity can be determined if the intensities due to the amorphous scattering can be separated, by an appropriate method, from the Bragg diffraction peaks due to crystalline phases. The broadening of diffraction peaks due to crystal imperfections and the consequent overlapping of the diffraction peaks, however, make accurate determination of the degree of crystallinity sometimes difficult. 

By comparison of the dif actograms, an increase of the ratio between the crystalline peak and the amorphous scattering, as well a shift of the crystalline peak to higher Bragg angles, is apparent in the Nafion-silica membrane with respect to Nafion 117. 

An x-ray diffraction pattern of electropolymerized PT published later by Chen and Ni [54] showed, however, only a broad, amorphous maximum between 14° and 28° scattering angle, centred around 21°, corresponding to Q-values centre around 1.4 A . For thiophenes in liquid form (the three liquids thiophene, methylthio-phene and bithiophene (above the melting point) [3,55] and for poly(alkylthiophene)s [56,57] broad, amorphous scattering has been observed in the same Q-range. Interpreted in terms of interplanar distance this gt-value corresponds to rf = 4.4 A. For the monomer and dimer this value is associated with the intermole-... 

Diffraction data for the alkoxy-substituted materials are scarce. For PMEEMT x-ray diffraction patterns were recorded [44] at two temperatures, room temperature and 150°C, showing in both cases three to four rather broad peaks on a diffuse background. The peaks correspond to interplanar distance d= 17.8 A, 7.0 A, 3.8 A and 2.4 A, the latter two being close to two values also found for PATs as the 6-axis parameter and a diffuse feature at 0 = 2.6 A related to the main chain periodicity. It is remarkable that the diffraction pattern survives heating to 150"C, which is above the thermochromic transition for PMEEMT. A recent diffraction study of poly methanol-thiophene) prepared electrochemically showed only broad amorphous scattering around 0= 1.4 A [94],... 

In polymer characterization, it is possible to determine the degree of crystallinity of semicrystalline polymers. The noncrystalline (amorphous) portion simply scatters the X-ray beam to give a continuous background, whereas the crystalline portion gives diffraction lines. A typical schematic diffraction spectrum of a semicrystalline polymer is shown in Fig. 8.46. The ratio of the area of diffraction peaks to scattered radiation is proportional to the ratio of crystalline to noncrystalline material in the polymer. The ultimate quantitative analysis must be confirmed using standard polymers with known percent crystallinity and basing the calculation on the known ratio of crystalline diffraction to amorphous scattering. 

The TEM image of the MN-270-Pt nanocomposite after incorporation of pla-tinic acid is presented in Fig. 3.15. One can see that the material contains nanoparticles with a diameter exceeding 0.7 nm (the estimated resolution of the microscope). The mean particle diameter calculated from a particle size histogram is 1.6nm and standard deviation is 0.6 nm. Evidently, since HPS is a very hydrophobic matrix, Pt species do not dissipate within a polymer matrix but form well defined clusters. light colored areas in the TEM image indicate macropores. The XRD profile of this sample confirms the absence of the Pt-containing crystaUine phase, but suggests the presence of Pt amorphous scatterers. 

Amorphous scatter Smaii-angie Long-range periodicities... 

The intensity of the various reflections and their clear definition above the background amorphous scattering indicate that the [IS] (A )n materials have significant crystallinity. For the [lS] (HS04 )n and [lS] (Cr)n samples, as many as eight re ctions can be identified. The relatively narrow widths of the diffraction peaks (full width at half maximum as narrow as approximately 1 ) indicate relatively long-range structural coherence. 

The method has recently also been used to determine the interchain distance in amorphous polyimides from measurements of the maximum in the amorphous scattering [29,30]. It is clear from figure IV - 42 that amorphous scattering will give rise to a broad band, which implies a d-spacing distribution. However, this approach may be considered critically since it uncertain whether eq. IV - 26 may be used for amorphous scattering to obtain quantitative information about interchain distances. 

Fig. 3. Wide-angle X-ray scattering (WAXS) patterns of iPP, sPP, and aPP. The shaded region illustrates the separation of crystalline and amorphous scattering contributions. Adapted from Ref. 23.

In addition to the discrete reflections from the crystallites, the diffraction pattern of a polymer shows diffuse scattering attributed to amorphous regions. Such polymers are said to be semicrystalline, with the crystalline fraction being controlled by molecular regularity. By comparing the relative amounts of crystalline and amorphous scattering of X-rays the crystallinity has been found to vary from more than 90 per cent for linear polyethylene to about 30 per cent for oriented polyethylene terephthalate. 

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