SANS structure factors

Figure 6.30 displays the relaxation rate T(Q)=Deff(Q)Q. The fine corresponds to the Einstein-Stokes diffusion of a sphere with 69 A radius (from SANS a radius of 60 A was obtained). The dip at Q=0.035 A and the enhancement at lower Q for the high concentrations with low salt corresponds to a modulation that follows the inverse of the (paracrystalhne) structure factor. Unlike the case... 

The extension of SCIETs to the many-body interactions is presented in Section V. Rare gases, whose constituents interact through three-body forces, are a test case to examine the validity of the SCIETs in describing real systems. Again, the problem of the thermodynamic consistency is covered in this section, since recent SANS measurements provide the structure factor S(q) at very low-q and allow us to deduce the strength of the three-body interactions. A direct comparison of the theoretical results against sharp experiments is feasible. The conclusions are given in Section VI. 

The first two terms correspond to the combinatorial entropy terms of Eq. (1) and form the non-interacting part of the structure factor which is just a weighted average of the single-chain structure factors SA(q) and SB(q) of both blend components. SA(q) and SB(q) are characterized by the radius of gyration RgA= aA(NA/6)1/2 and RgB=aB(NB/6)1/2, where aA and aB are the statistical segment lengths of polymer A and polymer B, respectively. The last term of Eq. (4) yields the SANS determined interaction parameter %SANS ... 

In this subsection, the theoretical background for SANS and neutron spin-echo measurements carried out with o/w- and w/o-droplet microemulsions will be presented. According to Milner, Safran and others, shape fluctuations in droplet microemulsions can be described in terms of spherical harmonics [42-44]. This offers the possibility to calculate a dynamic structure factor S(q,w) or its Fourier transform, i.e. the intermediate scattering function I(q,t) for the problem, which can be used to analyse dynamical measurements by neutron spin-echo spectroscopy [45]. For the scattering from thin shells I(q,t) was calculated [43]... 

San Jose, J. J., Farinas, M. R., and Rosales, J. (1991). Spatial patterns of trees and structuring factors in a Trachypogon savanna of the Orinoco Llanos. Biotwpica 23,114-123. 

A systematic SANS study of the PS-PA block copolymer has been achieved. The PS-PA co-polymers were obtained through thermal annealing of the diblock precursor PS-PPVS (polyphenylsulfoxide), a detailed description of the synthesis and preparation of the PA sequence free from defect can be found in references [54-55], To get a perfectly dispersed micelle structure in solution, the PA must be short and so the study was devoted to the diblock PS64-PA1 [56-58], The contrast factor of the PS unit is about 95 x 10 cm , while the contrast of the PA chain is negligible. As given in Section 1.2.2 the structure factor of a particle varies as a function of its geometrical shape. For instance, a... 

Fig. 10.1. SANS spectra of the 4>o = 0.24 solution after cooling from 120.0°C to various temperatures. The symbols are experimental data and the curves through symbols are the best model fitting. The low temperature (85.0"C, 90.0 C and 95.0°C) spectra show both the characteristic form and structure factors of stacked lamellae...

The SANS scattering function, which is analogous to the structure factor (O Eq. (29.21)), can be written as follows ... 

Figure 21 SANS data from microgels in diluted (a) and crystalline state (b) and structure factor with Bragg peaks. Reproduced with permission from Hellweg, T. Dewhurst, C. D. Bruckner, E. etal. Colloid Polym. Sci. 2000, 278, 972. ...

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