Wide angle X ray diffraction

X-rays are the light source that found more extensive application in scattering techniques in the polymer science field. 

A crystal is a regular arrangement of atoms, produced by the periodic repetition of a unit cell, which can also be considered as a family of planes composed of the atoms of the lattice, defined by three integer numbers (the Miller indices, hkl). Incident X-ray waves are assumed to be reflected by these planes, if the Bragg condition is met  

In wide-angle X-ray diffraction (WAXD), diffracted intensities at angles wider than about 2° 26 are detected, allowing to study features of characteristic size of 

Wide angle X-ray diffraction is another technique which has been of vital importance in the understanding of oriented polymers. In this section we shall illustrate the usefulness of the X-ray method for characterising the crystalline orientation in polymers. It is intended that the discussion will be mostly descriptive, and the reader who wishes a review of the principles of measuring the intensity of diffracted X-ray radiation is referred to Refs. 32-34. 

Rather than emphasising the determination of crystal structure we shall 

STRUCTURE AND PROPERTIES OF ORIENTED POLYMERS 2(Stretch axis) 

By virtue of the conveniently sized wavelength diffraction/scattering of X-rays is a long established tool for probing the structure of materials. X-ray diffraction (or WAXS) can be used to measure distances between planes in crystalline strnctnres. For a review of the concepts and methods of WAXS the reader is referred to Cullity s hook [54]. The anthors [13, 49] have found WAXS useful for establishing if any stmctnral order is present in fatty acid coatings on filler surfaces. Gilbert and co-workers [55] have also fonnd the technique useful for analysis of fillers treated with fatty acids and fatty acid salts. 

Stearic acid adsorbed from heptane solution on to magnesium hydroxide (as magnesium stearate) was shown to exhibit structural order [49]. This was manifested as a reflection that became apparent at coverage levels at and beyond monolayer. The d-spacing of the reflection corresponded to the short spacing of magnesium stearate. Isostearic acid and oleic acid adsorbed under the same or similar conditions as the stearic acid showed no evidence of structural order due to the inability of the alkyl/alkenyl chains to pack into an ordered structure [13]. 

WAXS has become the one of the main techniques for analysis of organoclays and polymer layered silicate nanocomposites. These aspects have been thoroughly reviewed by Vaia [56]. 

This chapter has described how the most important property of a particulate filler, with regard to its reactivity, is the acidic or basic character of its surface sites. Furthermore, that the surface of a single filler particle can have sites ranging from strongly acidic to strongly basic. It has been shown that techniques for characterising filler surfaces can be broadly divided into three groups. 

In the first, the reactivity of the filler surface to well defined probe molecules is observed. Of these, FMC is perhaps the more powerful, giving the ability to measure heat of adsorption directly and using the polymers, coupling agents or additives of interest. IGC is more instrumentally developed, but generally requires the use of model probes because of the need for them to be volatile and reversibly adsorbed. 

When a sample is irradiated. X-rays are diffraeted in a way that is characteristic of the compounds present in the sample under analysis. The atomic lattice acts as a three dimensional diffraction grating, causing the X-ray beams to be refracted at specific angles related to interatomic spacings. By measuring the angles and intensities at which diffraction peaks occur, the type and amount of the constituents can be determined. 

X-rays interact with the electron cloud which surrounds the nuclei, whereas neutrons react with the nuclei themselves. Neutron diffraction shows up the positions of hydrogen nuclei more clearly than X-rays. 

If two waves come together in phase, the maxima and minima of both waves are coincident and the waves reinforce, increasing the intensity of the resultant wave, termed constructive interference (coherent scattering). If the waves are out of phase, then the minimum of one wave combines with the maximum of the other and the wave is destroyed, termed destructive interference (incoherent scattering). 

Particle size is not to be confused with crystallite (or grain size) and a crystallite is the smallest diffracting field in a substance, whereas a particle can comprise of many crystallites. 

The crystallite dimension is calculated from the degree of broadening of the (002) reflection using the Scherrer line broadening equation namely  

In polymer-clay nanocomposites, to truly reach the ultimate in property improvements requires full exfoliation. A fully exfoliate composite yields the maximum interfacial interaction between the nanoparticle and polymer matrix. In order to produce optimally exfoliated systems requires that direct methods be available to measure the level of exfoliation. The ideal analytical method should be rapid, nondestructive, applicable to many sample matrices, low cost, and should require minimal sample preparation. The only method that fits these criteria is wide-angle X-ray diffraction (WAXD). This method, however, has some major drawbacks that will be discussed in detail in this chapter. 

The other analytical methods for confirming the level of exfoUation include scanning electron microscopy (SEM), transmission electron microscopy (TEM), and atomic force microscopy (AFM). The utihty and limitations of these three microscopy techniques for measuring exfoliation in nanocomposites will be discussed in detail with specific examples in this chapter. 

There are also a number of indirect methods to measure the level of exfoliation but all of them require a direct method with which to standardize them. As examples, two methods, melt viscosity and tensile modulus, will illustrate the indirect methods. Unfortunately, the overall area has not received a great deal of attention, with limited numbers of publications on the subject [1-3]. 

In X-ray diffraction the wavelength of the X-rays utilized is of the same order of size as the atomic dimensions in the crystalline lattice and will constructively interfere to yield peaks at discrete angles that can be related to the atomic spacing in the lattice by Bragg s law. The Bragg equation is nX = 2d sin 0 

Normally, the experimental variable that is observed is two theta rather than theta due to the geometry of the detector relative to the X-ray source. 

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Figure 1. Wide angle X-ray diffraction pattern from PET films exposed to DMF at various temperatures for 15 min.

Figure 5. Room-temperature, wide-angle X-ray diffraction (WAXD) pictures of stretch-oriented samples of PDHS (left) and PDPS (right).

A Siemens Kratky camera system was utilized for small angle x-ray scattering (SAXS) measurements in conjunction with an M. Braun position sensitive detector from Innovative Technology Inc.. Wide angle x-ray diffraction was obtained utilizing a Philips table-top x-ray generator. 

Figure 7.12 Wide-angle X-ray diffraction spectrum from high density polyethylene...

Figure 7 Plot of the degree of crystallinity (XNMR) by obtained by BC NMR against crystallinity (Xx.ray) obtained by wide angle X-ray diffraction for an unfractionated linear polyethylene sample crystallized in different conditions (data from Ref. [129]).

The crystalline lamellar thickness Dc obtained by StrobPs method is initially 1.4 nm and grows to about 2.0 nm, which is roughly equal to the crystallite size in the chain direction of 2.8 nm estimated from the wide-angle X-ray diffraction (WAXD) [7]. Interestingly, the persistence length /p = 1.45 nm just before crystallization measured by SANS (also see Fig. 11) [9,10] is almost equal to the crystal thickness. 

Wide angle X-ray diffraction, WAXD, studies on the PHAs from octanoic acid (PHA-OCT), nonanoic acid (PHA-NON), and decanoic acid (PHA-DEC) showed that these polymers had the same features as synthetic comb-like polymers [54]. PHA-OCT is the most crystalline (AHm = 8.3 cal/g) and PHA-HEX (the PHA from hexanoic acid) is amorphous, while PHA-HEP (the PHA from hep-tanoic acid) has a very low degree of crystallinity (AHm= 1.3 cal/g). The degrees of crystallinity of PHA-OCT and PHA-NON were determined to be 20 and 30%,... 

Nevertheless, we have often faced the problem that the nanocomposite shows fine and homogeneous distribution of the nanoparticles in the polymer matrix (e.g., poly (L-lactide)) without a clear peak shift of the mean interlayer spacing of the (001) plane, as revealed by wide-angle X-ray diffraction (WAXD) analysis [14], Furthermore we... 

Figure 11.16 shows the wide-angle x-ray diffraction (WAXD) pattern of an oriented PTT and indices of some of the reflections. Although PTT has a 002 reflection, the intensity is weak. It is also not a true meridianal reflection, being offset from the meridian by about 3°. The offset reflections are so close to each other that they overlap and appear as one meridianal reflection [39], and could not... 

Figure 11.16 PTT WAXD pattern and indices of the reflections [45]. From Polym. Bull., Crystal orientation function of poly(trimethylene terephthalate) by wide-angle X-ray diffraction, Chuah, H. H. and Chang, B. T. A., 46, p. 310, Figure 2, Copyright Springer-Verlag (2001). Reproduced by permission of Springer-Verlag GmbH Co. KG...

The 0-values were measured by wide-angle X-ray diffraction. A value of F = 1 indicates that the domains are perfectly aligned along the flow direction, while a value of F = 0 means that the domains are randomly distributed. 

Fig. 4. Wide angle x-ray diffraction profile of imide-aryl ether phenylquinoxaline block copolymers (a) 2c and (b) 2d...

Figure 8.3 Wide angle X-ray diffraction profile of potato starch.

In more recent work, talc-filled polystyrene compounds, with various filler volume fractions, have been processed by compression moulding and through a variety of slit, capillary, rectangular and annular dies [37]. Particle orientation has been characterised using wide angle X-ray diffraction, then expressed in the form of pole figures, and by scanning electron microscopy. It was concluded that... 

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