Small angle scattering 147 plot

Descriptions of the experimental scattering and microscopy conditions have been published elsewhere and are referenced in each section. Throughout this report certain conventions will be used when describing uncertainties in measurements. Plots of small angle scattering data have been calculated from circular averaging of two-dimensional files. The uncertainties are calculated as the estimated standard deviation of the mean. The total combined uncertainty is not specified in each case since comparisons are made with data obtained under... 

A scattering angle of order X/R is needed to observe a feature of size R, where X is the X-ray or neutron wavelength, and hence small angle scattering is needed to observe large features. Fig. 2.13 shows X-ray data for a-Si H and a-Si C H alloys in the form of a Guinier plot (Mahan, Nelson, Crandall and Williamson 1989),... 

Fig. 2. The layout of synchrotron X-ray small angle scattering measiurements. The optical system selects X-rays with a narrow band-width from the continous wavelength distribution of synchrotron radiation. Intensity of the primary>beam at the sample lo is monitored by an ion chamber. ly is the transmitted beam, and, I(s), the scattered intensity is recorded with a position sensitive detector. Scattering patterns of fibres are presented as Log (sl(s)) vs s plots where s = 2 sin 0/X is the scattering vector. 26 is the scattering angle and X is the wavelength.

Fig. 43a. Neutron small angle scattering intensity I(q) plotted vs q for three temperatures T above Tmst (main graph), for a polyethylenepropylene(PEP) — polyethylethylene(PEE) diblock copolymer, with f = 0.55, molecular weight Mw — 57.500, polydispersity index Mw/Mn = 1.05. The microphase separation transition occurs for Tmst = 125°C. For further explanations cl Textb Inverse peak intensity I (q ) dotted vs inverse temperature.The full curve is a one-para meter fit to the theoty of Fredrickson and Helfand [58], while Leibler s [43] prediction for the intensity at the transition is marked as mean field theory . From Bates et al. [317]...

For this case, a plot of log I( ) against - should give a straight line whose slope will be a function of R. Thus for a preparation consisting of particles of approximately the same size (in the range ca. 50-1000 A. diameter) a study of the small angle scattering of. -rays should permit the determination of the particle size. 

Fig. 20. The variation of scattered intensity with angle for an isotropic sphere. The angular variation is plotted in terms of the reduced variable V 4n(K A) sin(0f2). (From Gunier, A. arid Foumet, G. (1955). Small Angle Scattering of X-Rays, Wiley, New York,p.

FIGURE 7 Guinier plots for the small angle scattering spectra. 

Figure C2.17.12. Exciton energy shift witli particle size. The lowest exciton energy is measured by optical absorjDtion for a number of different CdSe nanocrystal samples, and plotted against tire mean nanocrystal radius. The mean particle radii have been detennined using eitlier small-angle x-ray scattering (open circles) or TEM (squares). The solid curve is tire predicted exciton energy from tire Bms fonnula.

FIGURE 17.2 Combined plot of small-angle x-ray and light scattering for a precipitated sihca sample. The silica sample is Dimosil 288, produced by Dimona Sihca Ltd. 

Fig. 53. Small-angle neutron scattering data from the 12-arm polystyrene star PS120A (Mw = 1.49 x 105) where the 11 deuterated arms were matched by the solvent THF. In order to demonstrate the asymptotic Q behavior, the data are plotted in a generalized Kratky representation (Iq01 vs. Q with a = 1.5 and 5/3). The solid line marks the high Q-plateau. (Reprinted with permission from [149]. Copyright 1989 American Chemical Society, Washington)...

Figure 3. Small angle X-ray scattering from an epoxy impregnated PBT film, a) The measured scattering pattern b) data plotted to fit Equation 3. Continued on next page.

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