The Master Equation ME Approach

The master equation approach considers the state of a spur at a given time to be composed of N. particles of species i. While N is a random variable with given upper and lower limits, transitions between states are mediated by binary reaction rates, which may be obtained from bimolecular diffusion theory (Clifford et al, 1987a,b Green et al., 1989a,b, 1991 Pimblott et al., 1991). For a 1-radi-cal spur initially with Ng radicals, the probability PN that it will contain N radicals at time t satisfies the master equation (Clifford et al., 1982a) 

Equation (7.24) can be compared with the corresponding prescribed-diffusion equation, namely d(N)/dt = (l/2)pi(t)(N)((N) - 1) (Clifford et al., 1982a). These two equations would be equivalent if (N2) = (N)2—that is, the variance of N would be zero. This implies that all spurs would have exactly the same number of radicals at a given time. Since stochasticity denies this, a considerable difference is expected between the results of these two methods however, this difference tends to decrease with the spur size Ng (Clifford et al, 1982a Pimblott and Green, 1995). 

Chapter 7 Spur Theory of Radiation Chemical Yields 

The master equation methodology can be readily generalized to multiradical spurs, but it is not easy to include the reactions of reactive products (Green et al, 1989 Pimblott and Green, 1995). This approach is therefore limited to spur reactions where the reaction scheme is relatively simple. 

---