Dispersion derivatives

Adsorbed water was observed to have a large effect on the F spin-lattice relaxation time for fluorine-doped aluminas in the dilute and intermediate concentration range of fluorine (0.3-8 wt. % F). An increase in Ti by a factor of 2 to 3 was observed in these samples when adsorbed water was removed from the solid by heating between 200-300°. The effect was completely reversible addition of oxygen-free water back to the solid resulted in recovery of the original (shorter) relaxation time. This effect was observed by the measurement of the in phase and ir/2 out of phase components of the dispersion derivative at resonance dx /6Ho at high rf power, from which effective values of Ti may be calculated 46). Values of Ti were also obtained by saturation of the resonance absorption derivative. 

Fig. 20. Saturation behavior of NMR absorption (x") and dispersion derivative at resonance (axV Ho) for proton resonance of silica-alumina (sample of area 425 meter / gram) dehydrated at 500°. The audio modulation frequency was 40 c.p.s. Arrows on abscissa indicate values of Hi for which saturation of x" and dx / Ho occurs (17S).

PERAPRET WF is a non-ionic dispersion derived from polyvinyl propionate. It has medium viscosity, a solids content of approx. 50%, and a pH of 4-6. 

Fig. 19. Apparent self-diffusion constants Oapp of the triglyceride oil component in a nanocapsule dispersion derived from the plots in Fig. 18. For short diffusion times A, the values for Dapp come close to the self-diffusion coefficient of the hulk oil D = 2.3X10 m /s, top line). For long...

In addition, some ionic vinyl monomers are shown in Figure 4.3. A water-insoluble polymeric dispersant derived from both a hydrophobic constituent unit and a hydrophilic constituent unit can be used. The desirable glass transition temperature is 160-200°C. 

Figure 5.13. (a) Rheological master curves of selected commercially available polymers which approach each other at 300 rad/s and 500 Pa.s, and (b) degree of dispersion derived from LM for composites with 1 vol% MWCNTs (prepared at the same shear level) plotted versus the effective Hamaker constant... 

In fact, the excellent low-loss characteristic of CYTOP-based GI POF (e.g., 10 dB/km) is far beyond the requirement of home networking. However, its real uniqueness is the low material dispersion derived from the low refractive index. In the past, there have been several reports on perdeuterated PMMA (PMMA-dg)... 

In 1930, London [1,2] showed the existence of an additional type of electromagnetic force between atoms having the required characteristics. This is known as the dispersion or London-van der Waals force. It is always attractive and arises from the fluctuating electron clouds in all atoms that appear as oscillating dipoles created by the positive nucleus and negative electrons. The derivation is described in detail in several books [1,3] and we will outline it briefly here. 

In this section we consider electromagnetic dispersion forces between macroscopic objects. There are two approaches to this problem in the first, microscopic model, one assumes pairwise additivity of the dispersion attraction between molecules from Eq. VI-15. This is best for surfaces that are near one another. The macroscopic approach considers the objects as continuous media having a dielectric response to electromagnetic radiation that can be measured through spectroscopic evaluation of the material. In this analysis, the retardation of the electromagnetic response from surfaces that are not in close proximity can be addressed. A more detailed derivation of these expressions is given in references such as the treatise by Russel et al. [3] here we limit ourselves to a brief physical description of the phenomenon. 

Unfortunately none of the various proposed forms of the potential theory satisfy this criterion Equation XVII-78 clearly does not Eq. XVII-79 would, except that / includes the constant A, which contains the dispersion energy Uo, which, in turn, depends on the nature of the adsorbent. Equation XVII-82 fares no better if, according to its derivation, Uo reflects the surface polarity of the adsorbent (note Eq. VI-40). It would seem that after one or at most two layers of coverage, the adsorbate film is effectively insulated from the adsorbent. 

Iditional importance is that the vibrational modes are dependent upon the reciprocal e vector k. As with calculations of the electronic structure of periodic lattices these cal-ions are usually performed by selecting a suitable set of points from within the Brillouin. For periodic solids it is necessary to take this periodicity into account the effect on the id-derivative matrix is that each element x] needs to be multiplied by the phase factor k-r y). A phonon dispersion curve indicates how the phonon frequencies vary over tlie luin zone, an example being shown in Figure 5.37. The phonon density of states is ariation in the number of frequencies as a function of frequency. A purely transverse ition is one where the displacement of the atoms is perpendicular to the direction of on of the wave in a pmely longitudinal vibration tlie atomic displacements are in the ition of the wave motion. Such motions can be observed in simple systems (e.g. those contain just one or two atoms per unit cell) but for general three-dimensional lattices of the vibrations are a mixture of transverse and longitudinal motions, the exceptions... 

The forces which bring about adsorption always include dispersion forces, which are attractive, together with short-range repulsive forces. In addition, there will be electrostatic (coulombic) forces if either the solid or the gas is polar in nature. Dispersion forces derive their name from the close connection between their origin and the cause of optical dispersion. First... 

DMF as solvent [FORMIC ACID AND DERIVATIVES - DITffiTHYLFORMAMIDE] (Vol 11) Polyurethane dispersions... 

The derivatives are hydroxyethyl and hydroxypropyl cellulose. AH four derivatives find numerous appHcations and there are other reactants that can be added to ceUulose, including the mixed addition of reactants lea ding to adducts of commercial significance. In the commercial production of mixed ethers there are economic factors to consider that include the efficiency of adduct additions (ca 40%), waste product disposal, and the method of product recovery and drying on a commercial scale. The products produced by equation 2 require heat and produce NaCl, a corrosive by-product, with each mole of adduct added. These products are produced by a paste process and require corrosion-resistant production units. The oxirane additions (eq. 3) are exothermic, and with the explosive nature of the oxiranes, require a dispersion diluent in their synthesis (see Cellulose ethers). 

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