SANS measurements

Deuterated SPS (d-SPS) was prepared by polymerizing dg-styrene with Cp / methylaluminoxane (MAO) or CpTiCh catalysts in the laboratory, and usual hydrogenous atactic polystyrene (h-APS) was purchased from Aldrich Chemical their characteristics are summarized in Table 17.1. 

The solution of d-SPS and h-APS dissolved in hot xylene was poured into an excess of methanol to precipitate the polymer. Film samples of d-SPS/h-APS blends were made using a compression molding machine at a molding temperature of 300°C. 

The SANS experiments were performed with the SANS instrument at Japan Atomic Energy Research Institute. SANS data obtained from the mixtures were corrected for transmission, scattering from an empty ceU and incoherent scattering, and were calibrated to the absolute intensity using the scattered intensity of water. Since the sample has no orientation, SANS data were circularly averaged. 

The resulting coherent scattering intensity I q) from a mixture is given by the equation developed by deGennes (random-phase approximation) [9] 

TABLE 17.1 Characteristics of Deuterated SPS and Hydrogenous Atactic Polystyrene 

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Figure 2.8 SANS measurement of ligand shell thickness as a function of C02 composition for differently sized DDT-stabilized silver nanoparticles dispersed in n-hexane-t/14 [40].

It is always easy to calculate idealized scattering curves for perfect networks. The experimental systems vary from the ideal to a greater or lesser degree. Accordingly, any estimate of the correctness of a theoretical analysis which is based on an interpretation of experiment must be put forth with caution since defects in the network may play a role in the physical properties being measured. This caveat applies to the SANS measurement of chain dimensions as well as to the more common determinations of stress-strain and swelling behavior. 

Figure 7. SANS measurements of R versus A. of swollen polystyrene networks. Mc is the molecular weight between cross-links. Key A, DVB/LE — 3 , DVB/ LE = 6 O, DVB/LE = 10. Data from Ref. 19.

Figure 8. SANS measurements of R /Fg° and R /Rg° versus A of tetrafunctional polydimethylsiloxane networks. Mw and Mn are weight and number average molecular weights before crosslinking, cp is the polymer fraction in solution before cross-linking. Data from Ref. 20.

Figure 9. SANS measurements of R /Rt° and RL/R ° for stretched radiation cross-linked polystyrene. is determined by measurements in which the neutron is parallel (iso) and perpendicular (aniso) to the stretching direction. Mc is molecular weight between crosslinks. Theoretical curves 2 and 3 are drawn for tetrafunctional networks. Data from Ref. 21.

Figure 10. SANS measurements of Rn/R,° and RL/Re° for stretched trifunctional end-linked polyisoprene. Curves 1 through 4 are theoretical. Data from...

Physical Properties of Alkyl-modified Silica Obtained by SANS Measurements... 

Caselli, M., Maestro, M., and Morea, G. (1988). A simplified model for protein inclusion in reverse micelles. SANS measurements as a control test. Biotech. Prog., 4,... 

Fig. 2.14 Mechanism of transformation of hex phase to BCC phase, proposed by Koppi et al. (1994) on the basis of SANS measurements on asymmetric PEP-PEE diblocks (a) initial state (b) intermediate undulating cylinder phase (c) epitaxially grown BCC spheres. Only one of two possible degenerate BCC orientations is shown in (b) and (c).

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. 

So, c(q = 0) is a finite quantity even when the isothermal compressibility %T tends to diverge in the critical region of any fluid. As will be seen, the former quantity is useful, because of being accessible from direct experiment [12] thanks to recent SANS measurements (see Section V). At variance from g(r), the direct correlation function c(r) in not zero inside the core region (r < a) and its knowledge is crucial in this range of distances, since it is directly related to y T so that... 

As will be seen, a direct comparison with MD calculations, as well as recent SANS measurements [12-14] and available thermodynamic properties [115, 116], attests the efficiency of this approach. The principal motivation for this application is to validate the accuracy of some SCIETs on a concrete problem in investigating the effects of the triple-dipole contribution on structural and thermodynamic properties of Xe and Kr. 

In contrast to the measurements by McDermott et al [58], neutron reflectivity measurements for the Ci2E6/Ci6TAB mixture in 0.1 M NaBr at the air-water interface and SANS measurements of the mixed micelles show close to ideal mixing. Penfold et al. [60] has used neutron reflectivity to investigate this mixture at the solid-solution interface. For the hydrophilic silicon surface, the surface composition of the mixed surfactant bilayer adsorbed at the interface depended strongly upon the solution pH. At pH 2.4, the surface composition... 

Measurement of characteristics of the emulsion droplets in concentrated media is indeed a difficult task. Some indirect methods have been used. The interfacial area and therefore the droplet size were determined by measuring the critical micelle concentration of miniemulsions [43]. Erdem et al. determined droplet sizes of concentrated miniemulsions via soap titration, which could be confirmed by CHDF measurements [44]. Droplet sizes without diluting the system can much better be estimated by small angle neutron scattering (SANS) measurements [23]. 

Fig. 25. Preliminary SANS measurements on post large amplitude oscillatory shear confirm the presence of global alignment of the silicate layers.

Our understanding of miniemulsion stability is limited by the practical difficulties encountered when attempting to measure and characterize a distribution of droplets. In fact, most of the well-known, established techniques used in the literature to characterize distributions of polymer particles in water are quite invasive and generally rely upon sample dilution (as in dynamic and static laser light scattering), and/or shear (as in capillary hydrodynamic fractionation), both of which are very likely to alter or destroy the sensitive equihbrium upon which a miniemulsion is based. Good results have been obtained by indirect techniques that do not need dilution, such as soap titration [125], SANS measurements[126] or turbidity and surface tension measurements [127]. Nevertheless, a substantial amount of experimental evidence has been collected, that has enabled us to estabhsh the effects of different amounts of surfactant and costabihzer, or different costabilizer structures, on stabihty. 

A schematic representation of an experimental device used for SANS measurements is shown in Fig. 4. 

SANS measurements were made at HMI, Berlin, LLB, Saclay and ILL, Grenoble, using the V4, PAXE and D22 spectrometers respectively. 

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