Multistep reversible excitation transfer in a multicomponent rigid solution: II. Modeling the dynamics of radiationless transfer as a time-resolved Markov chain
To determine the effect of nonradiative excitation energy transfer on the fluorescence of a rigid multicomponent solution, a new analytical method was developed by treating this transfer as a time-resolved Markov chain (TRMC). In the TRMC approach, we assume that the Markov chain under consideration is governed by bivariate joint probability mass-density functions. One of the random variables is discrete and represents the state number to which the process passes at a given step, while the other random variable is continuous and determines the moment in time at which this transition occurs. In general, the time distributions of this second variable can be arbitrary, continuous or discrete, and not just exponential, as required by the method known as continuous time Markov chains (CTMC). The agreement between the basic expressions of the TRMC method and the analogous expressions of the renewal theory has been demonstrated. The correctness of the TRMC method is confirmed by the fact that the time courses of fluorescence intensities calculated by this method agree with those calculated using ordinary analytical methods. In the section on calculating the quantum yields of individual components, the suitability of a method known as discrete time Markov chains (DTMC) was found. However, we argue that the DTMC method does not refer to time and propose to rename it as time-unspecified Markov chain (TUMC). The results generated by TRMC, when integrated over time, become equivalent to those generated by TUMC. The fluorescence cases of binary and ternary solutions are discussed in detail.