Polymer scattering profiles

The polymer concentration profile has been measured by small-angle neutron scattering from polymers adsorbed onto colloidal particles [70,71] or porous media [72] and from flat surfaces with neutron reflectivity [73] and optical reflectometry [74]. The fraction of segments bound to the solid surface is nicely revealed in NMR studies [75], infrared spectroscopy [76], and electron spin resonance [77]. An example of the concentration profile obtained by inverting neutron scattering measurements appears in Fig. XI-7, showing a typical surface volume fraction of 0.25 and layer thickness of 10-15 nm. The profile decays rapidly and monotonically but does not exhibit power-law scaling [70]. 

There are many different data analysis schemes to estimate the structure and molecular parameters of polymers from the neutron scattering data. Herein, we will present several connnon methods for characterizing the scattering profiles, depending only on the applicable q range. These methods, which were derived based on different assumptions, have... 

Elastic and quasi-elastic (NSE) neutron scattering experiments were performed on dilute solutions of linear poly(isoprene) (PIP) polymers and of PIP stars (f = 4,12,18) [150]. In all cases the protonated polymers were dissolved in d-benzene and measured at T = 323 K, where benzene is a good solvent. Figure 50 shows the results of the static scattering profile in a scaled Kratky representation. In this plot the radii of gyration, obtained from a fit of the... 

The geometric properties of highly denatured states appear to be consistent with those expected for a random-coil polymer. For example, proteins unfolded at high temperatures or in high concentrations of denaturant invariably produce Kratky scattering profiles exhibiting the monotonic increase indicative of an expanded, coil-like conformation (Fig. 1) (Hagihara et al., 1998 see also Doniach et al., 1995). Consistent... 

Further characterization of the mechanical properties and structures of such zeolite-reinforced PDMS elastomers by Wen and Mark [139] also utilized small-angle neutron scattering (SANS) [141, 143, 214—220] and transmission electron microscopy (TEM). The neutron-scattering profiles of the pure and zeolite-filled PDMS networks were identical, which indicated negligible penetration of the polymer into the zeolite pores. The TEM pictures showed that the zeolite with the larger pore size had a somewhat smaller particle size, and this is probably the origin of its superior reinforcing properties [62, 139]. 

Fig. 4.8 Micelle volume fraction () versus polymer concentration at different temperatures for solutions of PEO26PPO39PEO26 in D20 (Mortensen 1993a). 4> was obtained from fits of the hard sphere Percus-Yevick model to neutron scattering profiles (see Fig. 3.9). At high concentration the asymptote = for hard sphere crystallization is reached.

For a system of polymer chains attached to an interface, the polymer concentration may be finite over a small portion of the penetration of EW. In this case varying penetration depth will not yield an accurate estimate of the polymer concentration profile. In addition, the distribution of the polymers on the interface may be inhomogeneous. Measurement of the angular distribution (at a fixed penetration depth) of the scattered light in a plane perpendicular to the interface yields information on the structure factor and hence on the vertical extent of the layer. Measurement of the angular distribution in the plane of the interface yields information on possible aggregation of the polymer chains. 

In reality, most micellar systems made up from polymers are not as perfect as depicted in Fig. 9. Instead, the micelles are expected to be more fuzzy and may more resemble the situation depicted in Fig. 10. In this case, the segmental distribution must be considered [44, 45, 48, 74, 79, 84-86] by calculating the scattering amplitude from a realistic density profile. In addition, the intrinsic polymer scattering must be incorporated by explicitly taking into account long-range excluded volume interactions. 

The investi tion of the X-ray scattering profiles of poly(tetroxocane) prepared by radiation-indiK pcdymeiiration in the solid state si est that two types of crystallites coexist in the polymers obtained above W °C. One is a lamellar type crystallite with a lonptudinal dimension of 100 A and fitaHlar crystals with a crystallite of 250 A. Only fiMllar crystallites, as well as main and sub-crystals, were found in polymers obtained below 80 °C. The lamellar cry aUites were less distorted than the filsillar oi. In the case of pol trioxane), main and subcrystallites are obsraved small amounts of randomly oriented crystals are also noticed. 

The 9%LiSPS ionomer was miscible with PC above 170°C. Samples with different compositions were heated to 210°C, which is well within the one-phase region, and held at that temperature for 40 min. before the scattering was measured in order to allow sufficient time for the polymers to mix. Figure 7 compares the WANS data for a (50/50) 9%LiSPS/PC blend in the two-phase and one-phase regions. A clear and significant change in the scattering profile occurred between two-phase blend and the... 

The micrograph from the same sample (Fig.21a) shows the micron size compact aggregates that give rise to such scattering profile. Nevertheless, when compared with the case of the neat wax solution (Fig.Sd) the wax crystal control ability of the multi-blocks is striking. The polymer seems to operate by a two-fold mechanism on one hand, it templates the wax... 

Fig. 17 X-ray scattering profiles for organically modified montmorillonite clay (Closite 30B) and crosslinked polyester nanocomposites containing 1, 2, 5, and 10wt% clay. Reprinted from (2002) Polymer 43 3699 [158] with permission...

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