Effects of L.E.T. and temperature in the radiolysis of cyclohexane. Part 2.—Diffusion kinetic models

Abstract

Two radiation chemical diffusion models are described. In the first, the radical model, the effect of L.E.T. is due to the competing reactions of H· atoms. A Gaussian spherical or cylindrical initial distribution of H· atoms and C₆H^·₁₁ radicals is set up, and the radicals allowed to diffuse and react, the H· atoms being capable of abstracting from C₆H₁₂ to produce more C₆H^·₁₁ or of reaction with each other and with other radicals. The relevant differential equations were discretized over a number n of steps in space into two series of (n+1) simultaneous equations, and progression in time achieved using the Taylor series expansion. A simplification was introduced into the iterative procedure for solving the resulting set of (2n+2) non-linear equations. The cross-reaction term of H· with C₆H^·₁₁ was ignored only for the purpose of achieving the next closest approximation, giving two sets of (n+1) equations, instead of one set of (2n+2), reducing the total computation required for convergence, although the number of iterations was increased. In the second model, the excited molecule model, the relevant competition is between the interaction and decomposition of excited molecules, and H· atoms are considered to yield C₆H^·₁₁ radicals in a very fast (“hot”) reaction. Since the species for which diffusion is important are all C₆ radicals or molecules, a common diffusion constant was assumed, and the Ganguly-Magee “prescribed diffusion” method of solution ⁶ of overlapping Gaussian spherical distributions was used.