The scattering experiment

The angle between O Y and Oyff) equals 0. Scattering is studied in the plane which is orthogonal to OX. 

When the polarization is a parameter in the experiment, it is convenient to choose polarization axes in the reference system of the laboratory. For the incident radiation, these axes OX and O Y are orthogonal to the direction OZ. For the scattered radiation, the polarization axes which are orthogonal to r, are defined with respect to the scattering plane (OZ, r). These axes are Ox(f), perpendicular to the scattering plane. 

Actually, it will be necessary to specify other characteristics of the radiation, such as the divergence of the incident flux with respect to the axis OZ, the distribution of the wave number k0 and the random noise. The values of these parameters are imposed on the experimentalist by requirements related to the experimental process and by technological constraints 

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There are two generic types of external fields that are of general interest. In one of these, which relates to the scattering experiments, the external fields are to be taken as periodic perturbations... 

The pair-correlation function for the segmental dynamics of a chain is observed if some protonated chains are dissolved in a deuterated matrix. The scattering experiment then observes the result of the interfering partial waves originating from the different monomers of the same chain. The lower part of Fig. 4 displays results of the pair-correlation function on a PDMS melt (Mw = 1.5 x 105, Mw/Mw = 1.1) containing 12% protonated polymers of the same molecular weight. Again, the data are plotted versus the Rouse variable. 

The results of the scattering experiments are shown in Table 2.1. They leave little room for doubt as to the essential correctness of Flory s deduction about chain dimensions in undiluted polymers. 

For polystyrene fractions in diethyl phthalate solution (30000average value of 1.6 x 10 18 ( 50%). In dilute solution e/36M is 1.27 x 10 18 for polystyrene (21). No systematic variations with concentration, molecular weight or temperature were apparent, the scatter of the data being mainly attributable to the experimental difficulties of the diffusion measurements. The value of Drj/cRT for an undiluted tagged fraction of polyfn-butyl acrylate) m pure polymer was found to be 2.8 x 10 18. The value of dilute solution data for other acrylate polymers (34). Thus, transport behavior, like the scattering experiments, supports random coil configuration in concentrated systems, with perhaps some small expansion beyond 6-dimensions. 

In concluding this section, we draw attention to the amplitudes 0 derived from the scattering experiments. As shown later, 0 enters into theoretical expressions for the crossover temperature. Large 0 favor a small Ising regime. In simple nonelectrolyte mixtures, 0 is of the order of the molecular... 

Crossed molecular beams have been used to study nearly as wide a range of alkali metal atom reactions as has been examined by diffusion flames. An excellent review has been provided by Herschbach2. The multi-step mechanism displayed for chemiluminescence studies does not apply to the scattering experiments. Only the initial bimolecular reaction is important at the low pressures used. 

The data in this work were obtained by quenching either uniaxially stretched samples for which the low thickness of the specimens allows rapid cooling, or samples deformed in simple shear where higher thickness of the specimens was required in order to perform the scattering experiments along the three principal shear directions. For both types of flow, special devices were developed to control the flow kinematics in the molten state as well as the quenching process which freezes the molecular orientation. These devices are briefly described in the next paragraphs. 

At present time the X-ray range is of most interest for polymer research. One sees that in the conventional sources a gap appears in the region of long X-ray wave length. Here synchrotron radiation is the only source available. This is of importance for the scattering experiments in the anomalous dispersion region which are discussed in the paper by Stuhrmann (this book). At wave length of about 0.1 nm,... 

The scattering experiments were carried out at the Microfocus Beamline (ED 13) in the European Synchrotron Radiation Facility (ESRF) in Grenoble, France. The most remarkable characteristics of this beamline are ... 

The coefficient k normalizes V d). Eqs. (2,3) and finally Eq. (5) presume the existence of an isotropic two-phase system, in which cylindrical pores are arranged. Interferences between two cylinders are not allowed. The latter is not fulfilled in the scattering experiment. A step of separation performed in real space, operating with the CLD of the pores and the CLD of the walls, will separate the interference between pore and wall. 

According to Equation (24) AQj (il) is related to I(s) by a three dimensional Fourier transformation. Since the phase of the scattered waves is lost in passing from A(5) over to I( ) only the self convolution of Q,(jl) and not Qe(X) itself as in Equation (20) is obtained from the scattering experiment. Therefore, additional information is needed for a unique structural description. 

The structural information from the scattering experiment is contained in the structure function Ft( d) which is defined as follows for both X-ray and neutron... 

Our only direct information about the structure of water comes from X-ray diffraction and neutron-scattering studies. The scattering experiments yield information in the form of a radial distribution function, specifying essentially the average number of neighboring water molecules as a function of the distance from any one given molecule. Unfortunately, however, there is no direct way this information can reveal the structure. Instead, specific models have to be proposed and predictions made as to the likely position of neighbors based on the model these predictions are then compared to the actually observed radial distribution function. 

The regime for which q > tr, where the length scale of the scattering experiment can resolve below the fractal scaling regime and see the individual monomers. In this regime S(q) q, which is known as Porod s law. This feature is not included in Equation 14.35 but may be included by multiplying Equation 14.35 by the form factor, i.e., the normalized differential cross section, for the monomer. 

The importance of q is that its inverse, represents the length scale of the scattering experiment. This follows from the second term in Equation 14.B4, which cannot be written as... 

The scattering experiments considered in this work are exclusively incoherent in nature ( 2.1) and neutrons are scattered by individual... 

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