K-dispersion

Therefore the dispersion of the LO plasmon-phonon states is formally equivalent to the dispersion of the TO photon-phonon states, with 4irne2/m replacing k2 c2. When the plasmon-phonon frequency to is plotted against fn instead of k, dispersion curves for the LO modes are obtained which are similar to the polariton dispersion curves, the TO phonons showing no dispersion with /n. 

To describe the transport through a molecular system having HOMO and LUMO energy levels, one of the applicable models is the Franz two-band model.75-81 This model provides a non-parabolic energy-momentum E(k) dispersion relationship by considering... 

Dayton, P.K., Dispersion, dispersal and persistence of the annual intertidal algaPostelsiapalmeaformis Ruprecht, Ecology, 54, 433, 1973. 

Figures 1 and 2 show graphically the composition of polyisoprene and polybutadiene, respectively, prepared with a number of initiators. The data C were taken from a review by Foster and Binder (12). The polymerizations were carried out in bulk at tempera-tures ranging from 50° to 100° and using Li, Na or K dispersions in petroleum jelly. Rb and Cs apparently were used as pure solids. Although the results indicated in figures 1 and 2 cannot be compared quantitatively because of differences in temperature and degree of conversion, nevertheless it seemed useful to reduce a very large mass of data to something that could be rapidly scanned. In Fig. 1 the % vinyl indicates the sum of 1,2 and 3,4 addition. As regards the...

The energy bands are no longer described by the -k dispersion relations, but instead by a density-of-states distribution N E), illustrated in Fig. 1.6. Also the electron and hole effective masses must be redefined as they are usually expressed as the ciu-vature of (k). 

Kinra, V. K., "Dispersive Wave Propagation in Random Particulate Composites, Recent Advances in Composites in the U.S. and Japan," ASTM STP 864. 1985, pp. 309-325. 

Prasad R. and Sirkar K.K., Dispersion-free solvent extraction with microporous hollow-fiber modules, 34, 177, 1988. 

Chew, N.Y.K. Chan, H.-K. Dispersion of mannitol powders as aerosols influence of particle size, air flow and inhaler device. Pharm. Res. 1999, 16, 1098-1103. 

If too much organic halide is added to Na or K dispersions a sudden rise in T may occur accompanied by an uncontrolled reaction that may result in explosion if reaction mixture is pushed out of the reaction vessel into the atmosphere . For this reason and because of the fragility of the usual glass apparatus the customary apparatus for alkali-metal reactions should be contained within a second inert atmosphere, such as inside a glove box filled with N,. 

It has an NiAs-type structure (Fig. 15-5), and the isolated methyl groups are presumably in the lattice as the pyramidal CHJ ion.35 Sofiium amd potasstuirralkyl5 can be used for metallation reactions- for example, in eq. 6-2. They can also be prepared from Na or K dispersed on an inert support material, and such solids act as carbanionic catalysts for the cyclization, isomerization or polymerization of alkenes. The so-called alfin catalysts for copolymerization of butadiene with styrene or isoprene to give rubbers consist of sodium alkyl (usually allyl) and alkoxide (usually isopropoxide) and NaCl, which are made simultaneously in hydrocarbons.33... 

If the atomic orbitals s and p do not interact (fi = 0) the solutions become those of two independent valence electron bands. For the p electron chain the dependence of the orbital energy as a function of k (dispersion) is opposite to that of the valence electron band constructed from the s atomic orbitals. For 0 = 0 the solutions of Eq.(2.126) are sketched in Fig.(2.33). 

K... dispersive mixing (kneading, shearing) M... distrlbultive mixing... 

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