Scattered intensity, measurement

Experimentally, it is these invariants (equation (B 1.3.17), equation (B 1.3.18) and equation (B 1.3.19)) that can be obtained by scattering intensity measurements, though clearly not by measuring the total cross-section only. 

The scattered intensity measured from the isotropic three-dimensional object can be transfonned to the onedimensional mtensity fiinction/j(<3 ) by means of the Lorentz correction [15]... 

Measurements at low angles are subject to considerable error, and for this reason it is often preferred to apply appropriate corrections to scattering intensities measured at larger angles. The observed intensity ie in a direction 0 will be reduced on account of intraparticle interference by a factor cusomarily designated by P(0), which depends on the size and shape of the particle as well as on the angle 0. Thus, by definition... 

Before scattering intensity measurements can be converted to molecular weights, the two corrections previously discussed—the dissymmetry correction for intraparticle interference and the extrapolation to zero concentration—must be introduced, or established to be negligible. The relationships given in the preceding sections unfortunately account rigorously for either only in the absence of the other. The theory of the concentration dependence of the scattered intensity applies to the turbidity corrected for dissymmetry, and the treatment of dissymmetry is strictly valid only at zero concentration (where interference of radiation scattered by different polymer molecules vanishes). 

Direct calibration to absolute intensity is not a usual procedure at synchrotron beamlines. Nevertheless, the technical possibilities for realization are improving. Therefore the basic result for the total scattering intensity measured in normal transmission geometry is presented. At a synchrotron beamline point-focus can be realized in good approximation and the intensity /(s) is measured. Then integration of Eq. (7.19) results in... 

Let us consider a nanostructured thin film built from lamellar particles [84], If the principal axis of layer stacks is oriented normal to the film surface, the scattered intensity measured in symmetrical-reflection geometry (SRSAXS) is... 

In the experimental geometry used in this study, the distribution of scattered intensity measured by the detector is the two dimensional Fourier transform of the cross section of the electron density correlation function with a plane perpendicular to the extrusion direction (11). 

Scattering intensity measured by the pulse height analyzer is related to particle size by calibration with monodisperse latex spheres or nearly mono-disperse NaCl particles. Calibration uncertainties have been studied and discussed (86-91). These studies show that the smallest particles that can be sensed by the ASASP probe are somewhat larger than the 0.12 xm stated by the manufacturer. Similarly, it is reported that detection of particles larger than about 2 xm is unreliable because of attenuation of the laser power. 

In general, the source of light scattering from a polymer (or polyelectrolyte) solution is the existence of spatial and temporal fluctuations in refractive index in this scattering medium. The overall scattering intensity measured in an SLS experiment is proportional to the average of the square of refractive index fluctuations in the scattering volume,... 

The scattered intensity measured far from the sample is calculated by summing the scattering amplitudes, sh for each atom, , in the sample through the following relation ... 

To end this section, we briefly recall some results concerning the scattering intensity measured firom a collection of non-interacting particles like fringed micelles. For a non-spherical compact particle with dimension D in a space of dimension D, the asymptotic behaviour of the form factor is given by [16] ... 

Cyclohexane solutions of a poly(a-methyl styrene) sample prepared by anionic polymerization were examined by light scattering in the temperature range 300 to 320 K(Cowieetal., 1967). Scattered intensity measured at 6 = 90° are listed in the following table as a function of concentration and temperature. 

It can be shown that the weight-average molecular weight can be determined from the ratio of the area of the light-scattering intensity measured at low angle, <10°, and the concentration chromatograms, corrected for their respective calibration constants (29) ... 

The maximum of the scattering intensity measured in experiments first increases with time evolution at h ax, and then shifts to smaller values of A (corresponding to larger sizes of new phases), as illustrated in Fig. 9.7. 

The basic concept of 2D IR spectroscopy based on the correlation analysis of perturbation-induced time-dependent fluctuations of IR intensities could be readily extended to other areas of polymers spectroscopy. The 2D correlation analysis has been successfully applied to the time-dependent variations of small angle X-ray scattering intensity measurement [4], In this study, a small amplitude dynamic strain is applied a sheet of microphase-separated styrene-butadiene-styrene triblock copolymer sample. Intensity variation of scattered X-ray beam due to the strain-induced changes in the interdomain Bragg distances coupled with the reorientation of microdomain structures is analyzed by using the 2D correlation map. Similarly, the formal approach of 2D correlation analysis to time-dependent spectral intensity fluctuations has been extended to UV, Raman [63], and near-IR spectroscopy [64], There seems no intrinsic limitation to the application of this versatile technique in polymer spectroscopy. 

The translational diffusion coefficient D of a polymer coil can be found from the time-dependent correlation function of scattered intensity measured in dynamic light-scattering experiments. Using the Stokes-Einstein equation, the translational diffusion coefficient D can be related to the apparent hydro-dynamic radius (the radius of equivalent hard sphere). In the limit of nondraining for the solvent coil formed by infinitely long chain, the hydrodynamic radius is given by... 

Both modes of relaxation contribute to the scattered intensity measured by SLS, hence to the total Rayleigh ratio Rg. The Rayleigh ratio Re,fast for the faster mode of relaxation has been derived according to equation 3 (see also refs [30] and [31]). 

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