5.19: Chain Branching Explosions
- Page ID
- 547498
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In addition to explosions that occur because heat generated in a reaction increases the rate of the reactions involved, it is also possible to have a radical reaction accelerate because some propagation steps increase the number of radicals. These steps are referred to as chain branching steps. The kinetics are similar to those in nuclear fission bombs where fission of a nucleus is initiated by collision with a neutron. Fissioning nuclei produce more than one neutron. Thus each fission event can trigger multiple new fissions, leading to rapid growth in the rate of fission events.
Hydrogen combustion and explosions
The seemingly simple combustion of hydrogen \(\ce{2H2 + O2 -> 2H2O}\)serves to illustrate how this works. The reaction proceeds by a complex radical chain process. Some examples of the reactions involved are:
Initiation:
\(\ce{H2 + \cdot O2 \cdot -> HO2\cdot + H\cdot}\)
\(\ce{H2 -> 2H\cdot}\)
Propagation:
\(\ce{H\cdot + \cdot O2\cdot -> \cdot O\cdot + HO\cdot}\)
\(\ce{H2 +HO\cdot -> H\cdot + H2O}\)
Branching
\(\ce{H2 + \cdot O\cdot -> H\cdot + HO\cdot}\)
Termination
\(\ce{H\cdot +wall -> 1/2 H2}\)
\(\ce{H\cdot + HO\cdot -> H2O}\)
In the reactions above the fact that the ground state of O2 has two unpaired electrons is acknowledged by indicating that it is a diradical (dots on either side). If all the radicals produced in each branching reaction start reaction chains of their own that include branching reactions the overall reaction rate accelerates leading to an explosion. Whether this occurs depends on the temperature and pressure of the sample. Two behaviors are seen: smooth reaction and explosion as shown in figure \(\PageIndex{1}\).
Figure \(\PageIndex{1}\): Cartoon of explosive behavior dependence on pressure and temperature. Smooth combustion occurs to the left of the curve and explosion to the right. The point 1, 2 and 3 indicate explosion limits 1, 2 and 3 where at the indicated temperature the reaction shifts between smooth combustion and explosive behavior.
- At low pressures radical termination on the walls dominates because a large fraction of the molecules in the sample travel to the walls before encountering each other. Higher temperatures are needed to generate enough radicals to get an explosion.
- If the temperature is low enough termination reactions (with the walls and other molecules) overwhelm the branching and only smooth combustion is observed.
- If the temperature is high enough explosive behavior is observed because radical and energy production is high enough to cause the reaction to accelerate.
- In many cases including the combustion of H2 there is an intermediate temperature region where the reaction cycles between smooth combustion and explosion multiple times as the pressure increases as indicated by the dashed line in figure \(\PageIndex{1}\). The lowest pressure at which explosion is seen is referred to as the first explosion limit, the pressure at which the system reverts to smooth combustion is referred to as the second explosion limit, where it reverts back to explosive behavior is called the third explosion limit as shown in the figure.
- Below the first explosion limit we are in the regime where termination steps (collisions with the walls) dominate.
- Between the first explosion limit and the second explosion limit radicals can react and branch before they encounter the walls or species they can react with in a termination step.
- Between the second and third explosion limits molecular density is high enough that more radicals encounter each other in termination steps or react to form long lived species that can travel to the walls and be quenched (terminated).
- Above the third explosion limit diffusion to the walls becomes slow reducing its contribution to termination and explosive growth of radical chains takes over again.
- At some point the temperature is also high enough that the thermal energy released by the reaction is a significant accelerant of the rates and the explosion is also a thermal explosion.
References
1. This section is based on examples from Atkins, Physical Chemistry, 2nd Ed. (W. H. Freeman and Co. San Francisco, 1982) Section 27.4.