Frank-Kamenetski

MS Shchepinov, KU Mir, JK Elder, MD Frank-Kamenetski, EM Southern. Nucleic Acids Res. 27 3035-3041, 1999. 

There are many theories that enable the prediction of when a thermal runaway will occur and how it will proceed (Semenov, 1928 Frank-Kamenetski, 1969 Thomas, 1961). 

D. A. Frank-Kamenetsky, Diffusion and Heat Transfer, in Chemical Kinetics (Translated from Russian), Princeton, Princeton University Press, 1955. 

Trubetskoy, V. S., Frank-Kamenetsky, M. D., Whiteman, K. R., Wolf, G. L., and Torchihn, V. R Stable polymeric micelles Lymphangiographic contrast media for gamma scintigraphy and magnetic resonance imaging. Acad. Radiol. 1996, 3, 232-238. 

Dunkle s Syllabus (1957-1958), pp 137-38 (Frank-Kamenetsky formulation for instantaneous heating), 138 (Arrhenius equation) ... 

Addnl information on Frank-Kamenetsky formulation) 13e (Description of spontaneous initiation listed in Ref 4, p 154) 7) T.B. 

Frank-Kamenetsky, D. A., "Diffusion and Heat Transfer in Chemical Kinetics. Plenum, New York, 1969. 

Frank-Kamenetski, D.A. (1955) Diffusion and Heat Exchange in Chemical Kinetics, Princeton University Press, Princeton, USA. 

Remark 17. In this definition (i) is a convention that involves no loss of generality and (iii) is a condition that implies that all the reactions in the mechanism are needed. The species s7a have been called Bodenstein-products by Frank-Kamenetsky [77]. 

Thus the ratio of the forward and back rate constants. (K2IK ) is not the equilibrium constant for the overall reaction, but K, the exponent being the reciprocal of the stoicheiometric number of the limiting reaction. This significance and its exploitation have been examined by Horiuti [10. Frank-Kamenetsky [11] has developed some safe conditions for the applicability of certain forms of the hypothetical method, in the form of rather strong inequalities on the partial derivatives of the kinetic expressions. 

Frank-Kamenetsky has called these Bodenstein-products (cf. P. Rem. 17) and it will be convenient to retain this usage and extend it to the t elements and it reactions. 

The ignition criteria for stagnation-point flow Semenov-Frank-Kamenetski or van t Hoff (with X, Song and L.D. Schmidt). Combust. Sci. Tech. 75, 311-331 (1991). 

A new small-scale test has been developed which needs only a few g of thermally unstable material, which may be contained in an open cell version of the apparatus if aerobic processes are involved, otherwise in a closed cell apparatus, both with full temperature control and monitoring systems. Such materials may be divided into 2 types, depending on the behaviour of a sample after introduction into adiabatic storage at elevated temperature. The first type, which after attaining the adiabatic temperature shows a steady further increase in temperature in line with Frank-Kamenetski s thermal explosion theory, exhibit thermal combustion (TC) behaviour. In the second type, after adiabatic temperature has been reached, the sample shows a sudden rapid rate of rise, exhibiting autocatalytic (AC) behaviour as chain branching... 

A more elaborated approach is that of Frank-Kamenetski who relaxed the assumption of homogeneous solid temperature allowing conduction within the solid. A similar eigenvalue analysis will lead again to a critical ignition temperature (Tc) and the ambient temperature required for ignition to occur (T0). Nevertheless, the ambient temperature, given that conduction of heat from the core to ambient is allowed, becomes a function of the volume of the solid, and hence, for each 7 0 a critical volume, Vc is obtained. 

The results have been used to test the theory of thermal explosions in several ways. The agreement is excellent for example, Frank— Kamenetski s theory predicts that the maximum temperature rise in a system which just fails to explode should be I.6IRTIIE (where Tq is the initial temperature, and E the activation energy of the reaction). At 204 °C, this corresponds to 20.5 °C, while the measured values was 20 °C. 

The first estimate of kinetic parameters for the thermal decomposition of nitric oxide were made by Zeldovich and Frank-Kamenetsky . From a study of nitric oxide formation in H2-O2-N2 flames these workers proposed a value of 82+10 kcal. mole for the activation energy of decomposition. Vetter studied the reaction over the temperature range 1200-1900 K. He found a small rate increase on addition of oxygen and postulated a chain process involving the reactions... 

It is interesting to note that both thermal and non-thermal plasmas nsnally have the highest temperature (Te in one case, and To in the other) on the order of magnitnde of 1 e ( which is about 10% of the total eneigy required for ionization (about 10 eV). It reflects the general rule found by Zeldovich and Frank-Kamenetsky for atoms and small molecules in chemical kinetics the temperature required for a chemical process is typically about 10% of the total required energy, which is the Arrhenius activation eneigy. A funny fact is that a similar rule (10%) can usually be apphed to determine a down payment to buy a house or a new car. Thus, the plasma temperatures can be somewhat identified as the down payment for the ionization process. 

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