Neutron scattering blends

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... 

Briber RM, Bauer BJ (1991) Macromolecules 24 1899. By small-angle neutron scattering from blends of cross-linked and liner polystyrene they found that the intensity increased as the cross-link density was increased. This finding apparently contradicts our theoretical expression (4.11) below. See Sect. 4-4 for a comment on this point... 

Whitmore and Noolandi (1985b) developed the self-consistent field theory to examine micellization in AB diblocks in a blend of AB diblock and A homopolymer solvent . The model was applied specifically to the case of PS-PB diblocks in PB homopolymer for comparison with the results of small-angle neutron scattering (SANS) experiment by Selb et al. (1983). This model is discussed in more detail in Section 3.4.2. 

Since its introduction in the early 1970s, the small angle neutron scattering (SANS) method has had a substantial impact on polymer research. When used with partially deuterated polymers, SANS permits a close monitoring of macro-molecular conformations in polymer solutions, melts, and blend mixtures. This advantage has made it a unique tool for the understanding of the morphology of polymer materials and of the relationship between their structures and physical properties. 

The presence of SEBS at the interface was confirmed by small angle neutron scattering (SANS) experiments run on blends where the dispersed component, either sPS or HDPE, had been alternatively deuterated [34]. 

Rg is the polymer radius of gyration, Xs is the value of the x parameter (see Section 2.3.1) at the spinodal point, and D is the mutual diffusion coefficient of the two polymer components. Bates and Wiltzius (1989) have confirmed the predictions of Eqs. (9-4) and (9-5) for early-time SD of binary blends of perdeuterated and protonated 1,4-polybutadiene. Neutron-scattering studies of SD on a similar system by Jiimai et al. (1993a, 1993b) also confirm the Cahn theory at early times, but the spinodal growth rates deviate somewhat from Eq. (9-5). 

For the pair styrene/isoprene, various other dependences of x or temperature have been reported in the literature, which give values of x that at 100°C differ by almost a factor of two, from 0.06 to around 0.14 (see Fig. 13-3) (Lin et al. 1994 Han et al. 1995). These estimates of x ot obtained by direct calorimetric measurements (the energetic effects are too minute to measure), but by fitting the predictions of thermodynamic theories (such as that of Leibler or Fredrickson and Helfand see below) to x-ray or neutron scattering data for diblock copolymers or blends. The values of / thereby obtained are only as accurate as the theories to which the data are fitted. 

In summary, IGC is an experimentally attractive method for obtaining polymer-polymer interaction parameters in polymer blends at temperatures above Tm for a crystalline blend, and above Tg for an amorphous blend. This technique yields interaction parameters that are generally consistent with data obtained with other techniques such as vapor sorption, melting point depression, neutron scattering, and small-angle X-ray scattering (40). Advances in IGC of polymer blends will require increased experimental precision in order to improve the consistency of the data, as well as refinements of thermodynamic models to allow better interpretation of interactions in ternary solutions. 

Polymer conformations are studied by various scattering experiments (light, small-angle X-ray and neutron scattering). These techniques are based on the contrast between the polymer and the surrounding media (solvent in the case of polymer solutions and other polymers in the case of polymer melts or blends). The contrast in light scattering arises from differences in refractive index between polymer and solvent, and the scattered intensity is proportional to the square of the refractive index increment dn/dc [see Eq. (1.86)]. 

This means that the Flory interaction parameter y can be determined from the low wavevector limit of the scattering function of a single-phase blend of A chains (with monomers) and B chains (with monomers), where o is the volume fraction of A chains. In practice, the concentration fluctuations in the blend provide sufficient scattering contrast for neutron scattering, as long as one of the components is at least partially labelled with deuterium. 

The Flory interaction parameter in miscible polymer blends is measured using small-angle neutron scattering, usually involving deuterium label-... 

Interfacial agents, such as block copolymers, are known to reduce the Interfaclal tension and hence are expected to Increase the degree of dispersion in blends. The measurement of Interfacial tension for polymer systems is not easy. Most measurements have been made by the pendant drop technique. Measurements of Interfacial thickness are also difficult. They have been made using electron microscopy and, mostly in the case of block copolymers, by x-ray and neutron scattering. Recent results using neutron reflection suggest that this will be a useful technique in the future. 

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