Scattered intensity, calculation

X-ray scattering intensities calculated from these models showed little variation as a function of concentration of EN, indicating that X-ray scattering will not be able to distinguish between PEBB crystalline domains with EN excluded from the domains and the situation where uniform inclusion in the crystalline domains takes place. 

There are two ways to calculate the scattered intensity. One is to first calculate the magnitude of the structure... 

The second method to calculate the scattered intensity or R the Rayleigh ratio) is to square the sum in I... 

In oriented systems (fibres or stretched films), the scattered image often appears as a two-bar or a four-point pattern with the scattering maximum at or near the meridian (fibre axis). The one-dimensional scattered intensity along the meridian must be calculated by the projection method using the following fonnalism... 

In polymer solutions or blends, one of the most important thennodynamic parameters that can be calculated from the (neutron) scattering data is the enthalpic interaction parameter x between the components. Based on the Flory-Huggins theory [4T, 42], the scattering intensity from a polymer in a solution can be expressed as... 

To visualize the effects induced by paramagnetic relaxation, the time-dependent forward-scattering intensity has been calculated by implementing the stochastic relaxation between spin states i ) and j ) into the SYNFOS program package [30]. The transition rates from i) to j ) with , > Ej are described by [53]... 

When low-temperature studies are performed, the maximum resolution is imposed by data collection geometry and fall-off of the scattered intensities below the noise level, rather than by negligible high-resolution structure factor amplitudes. Use of Ag Ka radiation would for example allow measurement of diffracted intensities up to 0.35 A for amino-acid crystals below 30 K [40]. Similarly, model calculations show that noise-free structure factors computed from atomic core electrons would be still non-zero up to O.lA. 

The usual methods for characterization of anisotropic patterns involve the calculations of the scattering patterns and their further analysis [167,168] in the Fourier space. Thus, for an isotropic system, the scattering intensity, S(k) is symmetric, its maxima of the same amplitude are arranged at the circle k = k ... 

Figure 28a shows the result of SAXS on sample BrlOOO. We used Guinier s formula (see eq. 6) for the small angle scattering intensity, I(k), from randomly located voids with radius of gyration, Rg. Although Guinier s equation assumes a random distribution of pores with a homogeneous pore size, it fits our experimental data well. The slope of the solid line in Fig. 28b gives R - 5.5 A and this value has been used for the calculated curve in Fig. 28a. This suggests a relatively narrow pore-size distribution with an equivalent spherical pore diameter of about 14A. Similar results were found for the other heated resin samples, except that the mean pore diameter changed from about 12 A for samples made at 700°C to about 15 A for samples made at 1100°C.

Theoretical work on inhomogeneous molecular distributions is as yet incomplete, but McNulty et al 6) have made some calculations on adsorbed molecules on the surface of particles. Their conclusion was that the angular distributions have structure and that the inelastic scattering intensity in the forward and backward directions is particularly sensitive to particle size. 

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