Platelets density profile

The reciprocal space intensity is displayed in Fig. 7. It has the shape of a rod along the Qz axis. Any modulation of the platelet density profile along the z axis yields a form factor ... 

Figure 9 displays schematically the partial scattering function Prs in Eq. 29 for different contrast situations. While the core form factor extends to high Q and has a simple shape, due to the presence of brushes on both sides of the core, the brush form factor displays pronounced oscillating behavior with the first minimum relating to the average distance between the two brushes. Finally, the dashed dotted line (Z) displays the form factor at approximate average contrast zero. At the lower part of Fig. 9 the perpendicular platelet density profile is displayed. 

Here, a is the lattice unit dimension, M is the number of lattice units per clay platelet (so that the product Ma2 = A is the total area of the platelet), a is the grafting density of "surfactants," Xa/3 are the Flory-Huggins parameters between species a and (3, //, is the chemical potential of the zth component, and 0, is the excess amount of the zth component in the system. The density profiles of various species, a(z), and conjugate fields, ua(z), are calculated as described below. Note that we introduce a separate species and component—voids (denoted as subscript v)—to account for density variation within the gallery. 

Figure 5 Density profiles of grafted (solid curves) and free polymer chains (dotted curves) as a function of the spatial coordinate z, calculated using iSAFT (gray curves) and SOFT (black curves) methods, (a) Free polymer bulk volume fraction tpf = 0.75 separation between the platelets H = 50, and (b) free polymer bulk volume fraction (pf = 0.2 separation between the platelets H = 80. Other parameters Ng —101, pg — 0.1, and Nf= 100.

Fig. 2.31 Density profile of hard platelets at a hard wall...

Fig. 2.32 Density profile of hard platelets between two walls for h = AD/5...

Fig. 7 Reciprocal space intensity from a platelet of finite thickness and large but not infinite lateral extension. The intensity is located on a rod along Q, which is modulated by the form factor R(Qz) l of the density profile perpendicular to the surface. The thickness of the rod is indicated by the Gaussian approximation R Q). Its width is inversely proportional to the lateral extension. The sphere represents the locations at which the reciprocal space intensity matches the instrumental acceptance if set to a Q value equal to the radius of the sphere. Each dot on the sphere may be considered as one orientation present in a random ensemble of platelets, i.e., an isotropic solution. The overlap of the sphere and the rod, indicated by C, yields the measured intensity. Due to increase of the sphere surface the intensity combination due to C is as long as C is only a small spot on the sphere, as in this figure...

Density profiles of clay and solvent provide some insight into the distribution of clay and solvent particles that help clarify the effects of temperature and that of the quality of solvent (partide-solvent interaction). Let us define the y-axis (normal to the initial platelet planes) as the longitudinal direction the z- and x-axes constitute... 

The corresponding longitudinal density profile of polymer chains is presented in Figure 2.11. One can immediately note the complementary oscillation in polymer density in the same regions of the lattice, for example, zx planes around y = 20-44. The complementary variation of the polymer density to that of the platelets is rather easy to see by comparing Figures 2.10 and 2.11. For example, the dominant polymer density maxima peaks for Ic = 4 are around y = 24, 30, 36 where the platelet density... 

It was proposed (Johnson et al., 1987a) that this local lattice dilation is stabilized by the direct incorporation of hydrogen atoms through the coordinated formation of Si—H bonds. Results from SIMS (Section III. 1) and Raman spectroscopy (following) are consistent with this view. For example, the 60-min deuterium profile in Fig. 7(b) yields an integrated areal density of D in the near-surface peak of —1.7 x 1014 cm-2. The same deuteration conditions applied to this material produced 5 x 10n platelets per cm2 with an average diameter of 7 nm (Ponce et al., 1987). 

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