Early Origins of "Isothermal" Chaln-Branching Exploslons: Luther's Article on Chemical Waves To the Editor:
The editors and the translators ( I ) and commentators (2) on Luther's early description and analysis of isothermal travelling waves supported by chemical autocatalysis deserve the congratulations and the gratitude of the chemical community. The original paper of 1906 is enlightening. The discussion reported a t the end is entertaining, and Arnold, Showalter, and Tyson (I,2) place us all in their debt. I think i t is worthwhile drawine attention to an almost throwaway remark by Luther ( I ) wiere he focuses attention on the similaritv between autocatalvtic reactions and explosions and writes about the possibiiity of isothermal explosions. This is the idea of branching chains. Luther thus anticipates by more than 20 years the essentials of chainbranching explosion theory invoked by Semenov (3) to explain the oxidation of phosphorus vapor, and hy Semenov (3, 4) and Hinshelwood (5) t o explain the onset of explosion in oxygen-hydrogen mixtures. Textbook treatments of Semenov and Hinshelwood's simnlified annroach often renresent the borderline between auikscent ah;t explosive behavior as requiring the value for'the net-branching factor + = 0 in the equivalent expressions dnldt = 4 nor duldt = +a
Here n denotes the total radical concentration and a their mole-fractional concentration. For the oxygen-hydrogen reaction, the net-hranchina factor reflects the difference hetween iates of hranching>nd termination reactions: H H +0
2
--
+ Oz
+M
H 0 +0 H02 + M
H -loss at wall
rate = kz [HI [02] rate = klM [HI[OZ][MI rate = ks [HI
so that here 4 = k2 - k~ - kdM[MI
Clearly 6 > 0 implies unlimited ex~onentialerowth. Allowance f i r reactan
