Herzfeld

Schwartz R N, Slawsky Z I and Herzfeld K F 1952 Calculation of vibrational relaxation times in gases J. Chem. Phys. 20 1591-9... 

Employing mechanistic equations based on the Rice-Herzfeld postulation yields ... 

Herzfeld, C. M., and Meijer, P. H. E., Group Theory and Crystal Field Theory, in F. Seitz and D. Turnbull, eds., Solid State Physics, Yol. 12, Academic Press, Mew York, 1961. 

Hermitian operators for electric and magnetic field intensities, 561 Herzfeld, C. M., 768 Hessenberg form, 73 Hessenberg method, 75 Heteroperiodic oscillation, 372 Hilbert space abstract, 426... 

From this equation we can calculate the actual crystal radius (for use in normal sodium chloride type crystals) from Ru the univalent crystal radius. A knowledge of the repulsion exponent n is needed, however. This can be derived from the experimental measurement of the compressibility of crystals. Bom11 and Herzfeld,12 give the values in Table III, obtained in this way. 

It is to be expected that the relative values of the univalent crystal radius would be of significance with respect to physical properties involving atomic sizes. That this is true for the viscosity of the rare gases is seen from the radii evaluated by Herzfeld (Ref. 12, p. 436) from viscosity data He, 0.04 (0.93) Ne, 1.18 (1.12) Ar, 1.49 (1.54) Kr, 1.62 (1.69) Xe, 1.77 (1.90). (The values in parentheses are the univalent crystal radii.)... 

E Herzfeld and T. R. Litovitz, Absorption and Dispersion of Ultrasonic Waves, Academic Press, New York, 1959. 

L. Gaiani and D. Herzfeld, Analytical Method for Chimassorb 944LD (KBC/3), Ciba-Geigy Additives, Basel (n.d.). 

In 1919 Christiansen (25), Herzfeld (26), and Polanyi (27) all suggested the same mechanism for this reaction. The key factor leading to their success was recognition that hydrogen atoms and bromine atoms could alternately serve as chain carriers and thus propagate the reaction. By using a steady-state approximation for the concentrations of these species, these individuals were able to derive rate expressions that were consistent with that observed experimentally. 

The basic premises on which Rice-Herzfeld mechanisms are based are as follows. 

A reaction rate expression that is proportional to the square root of the reactant concentration results when the dominant termination step is reaction (4c), that is, the termination reaction occurs between two of the radicals that are involved in the unimolecular propagation step. The generalized Rice-Herzfeld mechanism contained in equations 4.2.41 to 4.2.46 may be employed to derive an overall rate expression for this case. 

In order for the overall rate expression to be 3/2 order in reactant for a first-order initiation process, the chain terminating step must involve a second-order reaction between two of the radicals responsible for the second-order propagation reactions. In terms of our generalized Rice-Herzfeld mechanistic equations, this means that reaction (4a) is the dominant chain breaking process. One may proceed as above to show that the mechanism leads to a 3/2 order rate expression. 

For Rice-Herzfeld mechanisms the mathematical form of the overall rate expression is strongly influenced by the manner in which the chains are broken. It can also be shown that... 

Although the above Rice-Herzfeld mechanisms lead to simple overall rate expressions, do not get the impression that this is always the case. More detailed discussions of these types of reactions may be found in textbooks (31-34) and in the original literature. 

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