Amorphous halo

TEM offers two methods of specimen observation, diffraction mode and image mode. In diffraction mode, an electron diffraction pattern is obtained on the fluorescent screen, originating from the sample area illuminated by the electron beam. The diffraction pattern is entirely equivalent to an X-ray diffraction pattern a single crystal will produce a spot pattern on the screen, a polycrystal will produce a powder or ring pattern (assuming the illuminated area includes a sufficient quantity of crystallites), and a glassy or amorphous material will produce a series of diffuse halos. 

We have found that high molecular weight poly (p-PIN)s readily yields fibers by manual drawing from the melt. X-ray analysis of melt-drawn fibers showed a characteristic amorphous halo with a d spacing at 6.2 A. 

Figure 41.4 shows a typical XRD (X-Ray Diffraction) pattern of TUD-1, along with a TEM image (12). Similar to other mesoporous materials, TUD-1 has a broad peak at low 20. However, it has a broad background peak, commonly called an amorphous halo, and lacks any secondary peaks that are evident for example in the hexagonal MCM-41 and cubic MCM-48 structures. The TEM shows that the pores have no apparent periodicity. In this example the pore diameter is about 5 nm. 

When the diffractogram of the pure amorphous polymer is not available at room temperature, the shape of the halo can be deduced either by peak fitting or estimating the halo pattern from the corresponding shape of the molten material. The uncertainties associated with these methodologies arise from the need to give a... 

Figure 3 Non-linear least-squares curve fitting of the orthorhombic WAXS profile of an ethylene 1-decene random copolymer with 2.7 mol% branches. The two crystalline reflections and the amorphous halo are shown. 

A relative crystallinity or "crystallinity index" has been used as an approximate method [55,56]. The simplest procedure involves determination of the intensity at a single scattering angle (26), in reference to the value for the amorphous halo at the same angular reflection. This method, for example, was useful to follow the variation of crystallinity of an iPP during isothermal melting [57]. 

For semicrystalline isotropic materials a qualitative measure of crystallinity is directly obtained from the respective WAXS curve. Figure 8.2 demonstrates the phenomenon for polyethylene terephthalate) (PET). The curve in bold, solid line shows a WAXS curve with many reflections. The material is a PET with high crystallinity. The thin solid line at the bottom shows a compressed image of the corresponding scattering curve from a completely amorphous sample. Compared to the semicrystalline material it only shows two very broad peaks - the so-called first and second order of the amorphous halo. 

It is obvious that the semicrystalline material contains this amorphous feature as well - underneath the reflections. In the semicrystalline material the halo is shifted... 

A simple phenomenological method can be used to describe changing crystallinity from WAXS data of isotropic materials. It is based on the computation of areas in Fig. 8.2. First we search the border between first-order and second-order amorphous halo. For PET this is at 29 37° (vertical line in the plot). Then we integrate the area between the amorphous halo and the machine background. Let us call the area Iam. Finally we integrate the area between the crystalline reflections and the amorphous halo, call it Icr, and compute a crystallinity index... 

Figure 31 shows the Tsp dependences of log Ks(max) and ED pattern of the monolayer prepared by the process mentioned above. This monolayer preparation corresponds to the case without a quench effect, because the amorphous monolayer was slowly cooled down to the temperature of 283 K. The ED pattern at 283 K exhibited a crystalline triclinic spot which was apparently different from the ED pattern of an amorphous halo, as shown in Figure 30. The magnitude of log Ksf, ) started to decrease apparently at ca. 300 K without any expression of the maximum log K max). Since the ED patterns at 298 and 303 K were a crystalline triclinic spot and an amorphous halo, respectively, Tm of lithium 10,12-heptacosadiynoate monolayer on the water surface was evaluated to be around 300 K. Tm of the monolayer on the water surface is much lower than that of three-dimensional crystal of 10,12-heptacosadiynoic acid (Tm=342 K). This is reasonable, because the monolayer is thermodynamically less stable than its three-dimensional crystal.

The Fourier transform of this quantity, the dynamic structure factor S(q, ffi), is measured directly by experiment. The structural relaxation time, or a-relaxation time, of a liquid is generally defined as the time required for the intermediate coherent scattering function at the momentum transfer of the amorphous halo to decay to about 30% i.e., S( ah,xa) = 0.3. 

Figure 11 MCT P-scaling for the amplitudes of the von Schweidler laws fitting the plateau decay in the incoherent intermediate scattering function for a R value smaller than the position of the amorphous halo, q = 3.0, at the amorphous halo, q = 6.9, and at the first minimum, q = 9.5. Also shown with filled squares is the P time scale. All quantities are taken to the inverse power of their predicted temperature dependence such that linear laws intersecting the abscissa at Tc should result. 

In the discussion on the dynamics in the bead-spring model, we have observed that the position of the amorphous halo marks the relevant local length scale in the melt structure, and it is also central to the MCT treatment of the dynamics. The structural relaxation time in the super-cooled melt is best defined as the time it takes density correlations of this wave number (i.e., the coherent intermediate scattering function) to decay. In simulations one typically uses the time it takes S(q, t) to decay to a value of 0.3 (or 0.1 for larger (/-values). The temperature dependence of this relaxation time scale, which is shown in Figure 20, provides us with a first assessment of the glass transition... 

Figure 20 Temperature dependence of the a-relaxation time scale for PB. The time is defined as the time it takes for the incoherent (circles) or coherent (squares) intermediate scattering function at a momentum transfer given by the position of the amorphous halo (q — 1.4A-1) to decay to a value of 0.3. The full line is a fit using a VF law with the Vogel-Fulcher temperature T0 fixed to a value obtained from the temperature dependence of the dielectric a relaxation in PB. The dashed line is a superposition of two Arrhenius laws (see text).

Figure 21 Coherent intermediate scattering functions at the position of the amorphous halo versus time scaled by the a time, which is the time it takes the scattering function to decay by 70%. The thick gray line shows that the a-process can be fitted with a Kohlrausch-Williams-Watts (KWW) law.

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