Dispersion curves between propagation

Figure 2. Dispersion curves between propagation constant and...

Solving this equation for o) and plotting o> versus fc provides a dispersion curve for NaCl as shown in Figure 24.5. Notice that the curve has two branches the upper branch is the phonon dispersion relation for the longitudinal mode and approaches >l at fc = 0 while the lower branch is the dispersion curve for the transverse mode, which approaches wj as fc increases. No frequencies can propagate between < x and o>ij which causes an energy gap in this region. 

Figure 13.2. Dispersion index as a function of monomer conversion for polymerizations with continuous initiation and bimolecular termination (e.g., free radical polymerizations) and no chain transfer, for three reactor types. The initial ratio of propagation and initiation rates is 10. For higher values of this ratio the differences between the curves increase.

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