Invariant point confirmation

Invariant Point Confirmation. The weight percentages of the prepared complexes, arbitrarily chosen within the three-phase, solid-liquid-liquid region, are tabulated in Table III. Tabulated in the same table are the weight percentages of the denser liquid layers and those of the less dense layers. 

From the recorded data it was possible to determine the solubility curves for each system, the liquid-liquid tie-lines, the solid-solid tie-lines, and to confirm the invariant point found in one of the solubility curves. 

This kinetic pathway confirms that a co-crystallization started in domain 3, converges to the invariant point A as predicted by the thermodynamics but could cross over several domains for kinetic reasons. 

Neither interpretation is correct. Assumption (1) leads to the prediction that vapp should be strongly dependent on the specific surface area (S) of carbon black, for vf = SS, where d is the number of adsorption points per unit surface of black — a quantity expected to be essentially constant for all blacks of similar surface chemistry. The experimental evidence is that vapp is not strongly surface area dependent. Assumption (2) leads to the prediction that cross-link yields in vulcanization are almost invariably increased by the presence of highly reinforcing carbon blacks. Chemical evidence indicates that this is not so. There are demonstrated instances in which vapp exceeds vr by significant amounts (typically 50% or more) without confirmation by chemical means (129). 

The photocurrents of both octacyano- and octamethoxyphthalocyaninato-zinc show a similar dependency on the incident light intensity and invariance of the y-values on the wavelength of the incoming light. These results point to ohmic photocurrents and the presence of exponentially distributed traps. The ohmic character of the photocurrent for the two zinc complexes is further confirmed by their current-voltage characteristics. The photoconductivities of... 

Fig. 5 Superimposition of point-by-point, 8.47 T l Pt NMR spectra of a 2.5 nm, carbon-supported Pt electrocatalyst without and with different chemisorbed ligand Ru, CO, O, H, CN-, and S. The spectra were normaiized by equalizing the ampiitude at 1.131 C kHz-1 (indicated by the arrow). The invariance of signais beyond 1.131 G kHz i provides experimental confirmation of the Friedel-Heine invariance theorem. The surface peaks range over 11 000 ppm. (Reproduced with permission from Ref [10], Copyright by 2000 American Chemical Society.)...

As discussed in the previous chapter concerning the structure of smectite clays, it was pointed out that these clays are turbostatic and have WAX patterns that only exhibit 001 or hkO reflections with no hkl reflections. The hkO reflections are invariant and can be used to confirm the presence of the clay in a composite at any level of exfoliation. The 001 reflections are a result of the basal spacing between the clay plates as stacks in tactoids. These peaks are highly variable and are dependent upon a number of variables, including level of exfoliation, intercalate type, and level of order. Figure 3.1 illustrates these two types of reflection for montmorillonite intercalated with dodecylpyrrolidone surface treatment where the peak at approximately 20° two theta is of the hkO type and the peaks at 2.58, 5.26, and 7.84 are of the 001 type. The three peaks are related, being the 001, 002, and 003 reflections. 

Anisotropic Fluctuation Approach The above formula of scattered intensity under HV and W modes are based on a model. The method requires a presumption of the stmcture from a given supramolecular aggregate composed of unit scatterers. The scattered intensity can also be derived from the fluctuation point of view using a statistical method as demonstrated by Stein et al. [114]. The authors derived the intensity formula based on anisotropic fluctuations, which also confirmed that the Deybe-Beche equation is a special case when no optical anisotropy is present in the scatterers [115]. The invariants ot orientation fluctuation and density fluctuation can be obtained as ... 

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